Chapter 4 The model: SHIA Landslidebdigital.unal.edu.co/11473/7/71765068.2013_ 2.pdf · observation of tropical mountain terrains supported by hydrology and geotechnical theory for

Chapter 4

The model: SHIA_Landslide

4.1 Introduction

The simulation of shallow landslides triggered by rainfall requires an integral approach

that includes both hydrological and geological components. The SHIA_Landslide model

integrates mechanical and hydrological properties of the soil with the hydrologic model

SHIA, which simulates water flow and storage as a hydrological response unit,

simulating rain events, spikes in pore-pressure, loss of shear strength, and providing

an early-warning tool that can be applied to areas with similar conditions.

Numerous studies have demonstrated that landslides triggered by rainfall have causal

factors in common, such as rainfall intensity and duration, antecedent soil moisture,

hillslope gradient and morphology. The present study integrates a hydrological model

with soils, and establishes testing criteria for areas vulnerable to exceeding threshold

levels of pore pressure and hazard of landslide.

To obtain consistent and coherent results for modeling landslides triggered by rainfall,

the conceptual model components and assumptions must be carefully weighed. This

chapter initially describes the conceptual model and assumptions considered in order

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to propose a computational program with the intent to forecast the potential occurrence

of shallow landslide triggered by rainfall in tropical and mountainous terrains. The

document offers details of hydrological and geotechnical modules, as well as describes

the model program proposed and how it works.

There is a need to combine hydrological with geological models to simulate shallow

landslides in tropical mountain areas. The literature has examples of models for other

areas that consider the infiltration, pressure head variation, and infinite slope criteria to

predict a resulting slope stability factor. However, no model has yet incorporated these

geotechnical factors into a complete hydrologic conceptual model, one that simulates

the storage and movement of rainwater through soil profile, providing multiple

components that can be calibrated along with measurements of perched water

pressure head, such as surface discharge and water table fluctuation.

Another important consideration is the spatial scale of available models that can range

from the regional scale that considers large basins to smaller areas of few square

meters for the analysis of single hillslopes or individual landslides. The quality and

quantity of hydrologic, hydraulic and geotechnical available data as well as details of

the model can change considerably, and as a consequence, the consistency and

coherency of applications to the model can also vary widely.

The aim of the model presented in this research is to explore and clarify the dynamics

of the physical and mechanical processes leading to the development of shallow

landslides triggered by rainfall in tropical and mountainous terrains, pointing out the

factors and parameters that play the main roles in this occurrence. As a consequence

of the latter, it also aims at forecasting landslide occurrence and producing maps

regarding the relative potential of shallow landsliding.

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4.2 Conceptual model for landslides triggered by rainfall in tropical and

mountainous terrains

Usually, models consider different conceptual approaches and assumptions. For the

model proposed in this work, it is necessary to define assumptions related to the

spatial-temporal variability of hydraulic and mechanical parameters of the soil, to the

water content of the soil and to sub-horizontal flow formation that the authors consider

to result in a coherent model. Most assumptions made in the model are based on field

observation of tropical mountain terrains supported by hydrology and geotechnical

theory for tropical residual soils.

4.3 Tropical weathering profile

Tropical mountainous residual soils result from weathering processes important to

understanding rainfall infiltration and subsurface flow in tropical environments.

Hillslopes are covered with deep residual soils characterized by a wide range of

physical and mechanical properties, depending on their parental bedrock and degree of

weathering.

The susceptibility of rocks to chemical action is a function of mineralogical composition

and texture as well as of the presence of fractures; however, the dominant control of

the weathering mode are rainfall, mean temperature, and their variability for very short

time periods (Curtis, 1976; Ollier, 1988; Anon, 1995). All these variables present high

values for tropical and complex terrains, explaining the presence of deep residual soils

over these areas.

Weathering processes propagate downward, causing rock material to become more

porous and deformable, leading to reduced shear strength, and its permeability may

change depending upon the nature of the rock, the presence and type of weathering

products and the stage of weathering (Anon, 1995). The weathering processes that

form tropical residual soils include physical disintegration, chemical decomposition and


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biological intervention, which produce a succession of distinct horizons parallel to the

slope surface called soil weathering profile (Fookes, 1997).

Several classifications for soil weathering profile have been adopted based on multiple

purposes (Little, 1969; Deere & Patton, 1971; Anon, 1995). All these classifications

converge on identifying four general horizons: (a) a mobile horizon, (b) rock completely

weathered, (c) rock partially weathered, and (d) fresh rock.

In tropical regions chemical weathering of primary minerals is a dominant process and

produces extensive lateritizacion and formation of deep weathering profile (Fookes,

1997; Aristizábal et al., 2005). Intensive tropical weathering is reflected in the formation

of iron and aluminum sesquioxides. Iron and aluminum oxides and hydrated oxides

released by tropical subsurface weathering are not completely dissolved and

consequently they tend to remain insitu, forming laterites (Shellmann, 1981; Blight,

1997).

For this model, based on studies proposed by Little (1969) and Anon (1995), the

tropical residual soil profile is divided into three basic units of particular qualities to

which can be assigned engineering characteristics (Figure 4.1).

Residual soil, in which all material has been converted to soil and mass structure and

material fabric decomposed with significant change in volume increasing permeability

and hydraulic conductivity. This unit includes laterites or organic soil over the surface,

when they consist of just few centimeters of depth. Permeability and hydraulic

conductivity are higher at shallow depths. This upper soil horizon is influenced by

vegetation root zone, animal disturbance and chemical processes, generating

macropores structures such as natural soil pipes or open relict joints. Colluvium or

transported soils are not specifically considered with in this typical profile because of

they are common on footslopes where slopes tend to be stable. However, when

colluvial soils represent an important thick layer, they should be considered as a

different horizon, as well as laterites or organic horizons.

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Saprolite, in which mass properties are still “soil-like”, it corresponds to highly to

completely weathered material, in which original structure and fabric are preserve

because of pseudomorphic replacement of clay minerals and the lack of subsequent

disturbance or transportation. The saprolite formation is an isovolumetric process, but

up to half of the rock mas is lost by leaching of silica, bases and iron (Fookes, 1997).

Although porosity increases regarding to parental rock, hydraulic conductivity is less

than in the disturbed upper soil layer, where channels that conduct water more rapidly

has been formed;

And finally, slightly weathered to fresh rock, where rock-like characteristics begin to

dominate and permeability is very low.

a) Figure 4.1 Typical weathering profile of tropical environments and complex terrains

Each of these basic units or layers present different and complex hydrological and

geotechnical properties; on the other hand, the variability of soil properties does not

concern only the weathering vertical profile. One of the most complex elements for

tropical environments corresponds to the wide ranging changes of the hydrological and

mechanical properties of the soil along hillslopes.


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Wide ranging changes also occur in soil depth, which is an important factor controlling

shallow landsliding. Topographic control over soil properties is particularly strong in

tropical environments, reflecting the importance of lateral movement of water and soil

material down-slope, as well as down-profile (Fookes, 1995). Topographic indeces are

used extensively in recent physically-based models of shallow landslides induced by

rainfall (Montgomery & Dietrich, 1994).

It is important to define the catena soil pattern to represent the lateral variability of soils

along hillslopes. Milne (1935) used the term catena to describe the succession of soils

down a slope and repeated in a pattern across the landscape. These profile differences

are attributable either to downslope movement of fine soil particles and material in

solution or to site differences related to slope angle and depth of water table (Fookes,

1995).

Multiple sequences of soil properties and profiles have been proposed by several

authors. Ollier (1976) describes multiple catenas in different climates. Considering

previous studies, which have described the typical weathering profile in tropical humid

and complex terrains (Aristizábal et al, 2011b), a simple catena soil pattern has been

selected for this model and is shown in Figure 4.2. It is characterized by deep profiles

above and below hillslopes retaining shallow weathering profile, and soil eroded from

the top of the slope tending to accumulate near the bottom.

The soil thickness on a hillslope, which coincides with failure depth, is a critical

parameter in performing a slope-instability analysis (Segoni et al., 2012; Ho et al.,

2011). Relatively thin soils are more prone to saturated overland flows compared to

thicker soils that hold greater water storage potential. In this study, we believe it is

reasonable to assume that under the catena soil pattern, soil thickness can be linked to

slope angle on a basic wide scale.

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Figure 4.2 Catena and hillslope hydrological processes. Soil thickness distribution varies according to the slope inclination.

Slope-derived soil thickness patterns are widely used because they can be applied

over large areas without extensive field information available. In the catena soil pattern

proposed here, soil thickness values are inversely proportional to slope gradient,

according to a linear law derived from several calibration measures. In the same

direction to the catenas, this soil thickness pattern relies on the assumption that on

steeper slopes, erosive processes are more intense, thus soils are shallower and

erosion is weaker on flat surfaces so that deposition prevails and thicker soils are

usually found (Segoni et al., 2012; Salciarini et al., 2006).

Much more complex methods that make use of multivariate statistical analyses or

employ process-based models exist for soil thickness patterns, although they require a

huge effort to be correctly applied and calibrated (Segoni et al., 2012). Therefore, it is

necessary to keep in mind that a particular region can have its own particular catena

pattern, and hence they should be defined based on field and laboratory tests. Any

catenas and soil thickness pattern could be integrated into the model proposed

according to the information available of the area selected. For this initial approach, a

simple catenas and slope-derived soil thickness pattern has been selected.


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4.4 Subhorizontal flow formation

Shallow landsliding in tropical environments is related to the formation of a subsurface

flow parallel to the slope. Subsurface flow, also known as interflow, lateral flow or soil

water flow, is a saturated water flow phenomenon parallel to the slope inclination. The

phenomenon of shallow landslides occurs for a brief moment in time in what is

ordinarily an unsaturated zone. According to the literature, there are two recognized

mechanisms for rainfall infiltration and subsurface flow formation: (i) by the rising of a

perched water table from the potential failure surface or (ii) by the development of an

advancing wetting front from the slope surface.

According to the soil profile formation, hillslopes for tropical environments are

heterogeneous, then hydraulic conductivity and permeability varies with depth,

controlling rainfall infiltration, subsurface flow formation and location of shear surface.

This permeability and hydraulic conductivity, contrasting with underlying horizon forces,

start a perched water table, and then positive pore water pressure caused by

subsurface flow will occur near the ground surface. For tropical conditions, in most

cases, the contrasting permeability is located in the weathering profile changes from

residual soils to saprolite.

According to the literature and based on laboratory and field tests carried out by

multiple investigations, the contrast of physical-mechanical properties, in which

perched water table is formed, also corresponds to the failure surface. This assumption

is imposed to the model.

4.5 Hydraulic conductivity

Soil hydraulic conductivity plays an important role in landsliding, especially in areas

with thick weathered profiles like most of the tropical hillslopes. Differential weathering

usually generates hydraulic discontinuities inside the weathered mantle, allowing rapid

infiltration and interflow along soil cracks and roots (Fernandez et al., 2004)

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Residual soils may exhibit a wide range of hydraulic conductivities depending on the

clay minerals as a result of chemical weathering and of the presence of relict structures

and discontinuities. Residual soils are susceptible to the formation of natural soil pipes

due to relict joints and biological effects; they develop a secondary porosity system,

substantially increase the permeability of soils and act as preferential flow paths for

subsurface flows. These secondary pores allow the rapid increase in saturation and

water pore pressure builds-up to take place.

Another important element is the variation of hydraulic conductivity according to

unsaturated conditions. Capillarity provides an isotropic confining pressure that

decreases the hydraulic conductivity when the soil is unsaturated, but before and

during a storm, the soil is likely or nearly saturated, so conductivity is higher (Anderson

& Sitar, 1995).

Considering that failure occurs after some period of rainfall when most water has

infiltrated through preferential flows paths, it becomes quite difficult to quantify the

influence of preferential flows on slope stability and using saturated hydraulic

conductivity is a reasonable approach.

4.6 Soil capacity for storing water

The model needs to have the information of the amount of water contained in the soil

and how much water it can absorb. Soil water storage capacity depends of the open

spaces or pores found within the soil. Although it is affected by soil structure and

organic matter content, soil water storage capacity is determined primarily by soil

texture. It means porosity determines the total amount of water that a soil will hold, and

it varies from one soil to another.

When water falls on the land surface through precipitation, some of it runs off the land

into ponds and streams, and some infiltrates into the ground. Water infiltrated first goes

through an unsaturated zone in the soil, and some of the voids among soil particles are


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filled with water. While the pull of gravity tends to draw water downward, soils in the

unsaturated zone are able to hold some water within the smaller voids because surface

tension acts as a film around soil particles. This water is called hygroscopic water. If

gravity exerts a force sufficient to exceed surface tensions, the excess of water will flow

downward. This water is called gravitational or free water.

Water availability is illustrated in Figure 4.3 according to soil water content. Free or

gravitational water drains quickly from the soil after rainfall because of gravitational

forces (saturation point to field capacity). Available water is retained in the soil after the

excess has drained (field capacity to wilting point).

Saturation (Ws) occurs when all interconnected voids in the soil are completely filled

with water. Field capacity (Wfc) means water content of the soil, in which all free water

has been drained from the soil through gravity. It is the maximum value of water

content that can be maintained without water draining rapidly. Field capacity is reached

when soil water tension is approximately 30 kPa in clay or loam soils, or 10 kPa in

sandy soils (Richards & Weaver, 1944; Saxton & Rawls, 2006). Excess water over the

field capacity usually drains, according to the soil permeability, within one or several

days back to the field capacity.

Permanent wilting point (��) occurs when the volumetric water content is too low

for the plant to remove water from the soil and it will wilt and die. Some authors

consider the permanent wilting point when the water content of the soil is at -1.5 MPa

water potential (Veihmeyer & Hendrickson, 1928; Saxton & Rawls, 2006). It is

important to differentiate that in this case soil is not dry, as water is still present, in the

soil, but plants are unable to access it. Hygroscopic water is held tightly on soil

particles below permanent wilting point and cannot be extracted by plant roots.

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Figure 4.3 Water content into the soil and water available. root depth (Zr), Soil thickness (Zs), permanent wilting point (Wpwp), field capacity (Wfc), Saturation (Ws)

The difference between field capacity and wilting point is named plant available water

storage. And the difference between saturation and field capacity is called drainable

porosity.

4.7 Water content in the soil

In regards to the water content in the soil, shallow landslide modeling considers the soil

condition under saturated or partially saturated conditions.

During the last years, matrix suction and hydraulic conductivity as a function on

saturation degree has been incorporated for modeling partially saturated soils, in which

shallow landslides are caused by the corresponding suction reduction and the resulting

slope movement is in the form of a relatively rigid slab (Collins & Znidarcic, 2004).

To achieve a predominantly unsaturated soil condition, previous long periods without

rainfall are necessary, and the unsaturated condition is preserved just at the beginning

of the rainfall event. During the initial rainfall period, unsaturated condition controls soil

mechanics and shallow landslides occur by suction reduction, and after a short period


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of rainfall, when rainfall intensity is higher than soil permeability, saturated conditions

appear and control shallow landslide occurrence.

To simulate these mechanisms of water storage and movement under unsaturated

condition during the first stage of the rainfall event, the model is simplified including a

static storage tank, which corresponds to capillary water in order to receive the initial

rainfall, and just when this tank is full, infiltration occurs under saturation condition of

the upper soil layer.

On the other hand, for tropical climate conditions, rainfall is a common phenomenon,

resulting in a soil profile at or near field capacity; and consequently shallow landslides

occur mostly under saturated or near saturated conditions, during wet periods or after

intense rainfall because of positive pore pressures. The result of such shallow

landslides are in the form of a liquefied soil mass such as soils slips or mud/debris

flows, in which the displaced material of shallow landslides changes suddenly into a

flow.

In conclusion, the model proposed simulates the initial unsaturated condition during a

rainfall event including a static storage tank, but considering shallow landslides

triggered by rainfall in tropical environments occur mostly as mud or debris flows under

saturated conditions, the model is focused on simulating the increasing of positive pore

pressure. It means that shallow landslides in the form of a relatively rigid slab, which

occur at the beginning of rainfall events under unsaturated conditions by negative pore

pressure reduction, are no included into the modeling.

4.8 Rainfall

Relating to rainfall conditions, antecedent rainfall could play an important role

concerning the starting time of landslide occurrence and during a storm, rainfall

intensity and duration are fundamental factors. In this sense, the model integrates both

the initial conditions and rainfall variation during the storm.

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4.9 Vegetation

The effect of vegetation over slope stability may broadly be classified as either

hydrological or mechanical, with positive and negative effects on slope stability.

Mechanical effects such as root reinforcement increase the structural properties of the

soil as well as its stability, while at the same time surcharge and wind loading transmit

forces to the soil, reducing stability. Regarding hydrological effects, evapotranspiration

positively affects slope stability, but at the same time, roots increase secondary

hydraulic conductivity and infiltration.

Considering this complex influence on both sides of the slope stability equation,

vegetation is not directly considered into the model. However, the influence of

vegetation on cohesion could be indirectly included by increasing the values of theses

parameters. To evaluate hillslopes with similar geology and residual soil, but different

soil cover, this procedure could improve coherency and the final results of the model.

4.10 Spatial and temporal scale

Another important element for the model is the spatial scale. Catchment inputs change

in space, and traditional lumped models cannot reproduce any spatial variability

(Frances et al., 2007). In contrast to traditional lumped models, grid cell distributive

models represent better the organization and randomness associated with spatial

heterogeneity.

Detailed models include a very complex, analytical physical process, which increase

running time and the need of a considerable number of soils and hydraulic parameters.

On the other hand, for extend areas, the models have to oversimplify the natural

process involved in landslide occurrence, loosing fundamental elements on this kind of

processes.

Increasing this complexity, tropical soils are not just characterized by changes in

function of space; they also change in function of time. To consider all soil variations


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under tropical conditions, it is necessary to propose a model that has to be supported

by a robust hydrological component that considers the spatial and temporal scale of the

processes. As a consequence, the model proposed should consider this important

factor as to implement distributed modeling that could consider this variation in space

and time, dividing the catchment into uniform grid cells.

The model proposed focuses on a basin scale, in which the following most important

processes are considered: antecedent rainfall and pattern, water infiltration, slope

configuration, subsurface flow formation, and hydrological and soils properties.

4.11 Hydrological module

The hydrological module to be implemented for the development of the model is based

on the Open and Distributed Hydrological Simulation (in Spanish Simulación

HIdrológica Abierta–SHIA-), methodology developed by Vélez (2001). It is formed by

some fundamental components: a water balance that simulates the dominant

hydrological processes in the catchment, and a routing component that simulates the

flow of water through the river network. Initially, the overland, the subsurface and the

base flows are defined by a 3D mesh of connected tanks which drain toward the

corresponding tank in the downstream cell, following the surface flow directions until it

reaches the channel network.

This hydrological module, due to its open source, was adjusted to the needs and

specific conditions for landslides triggered by rainfall in tropical environments. A more

detailed description of the SHIA can be found in Vélez (2001), Vélez et al. (2004) and

Frances et al. (2007).

In regards to the computational program, catchment is divided into regular horizontally

layered grid cells to control the infiltration and percolation processes. According to the

tropical weathering profile assumed, each grid cell is formed by three layers with three

different saturated hydraulic conductivities: (�) residual soil, (��) saprolite, and (��)

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rock, in which the residual soil is more permeable than the underlying saprolite soil and

the impermeable rock.

Spatial interpolation of rainfall data is based on a Delaunay Triangulation method

proposed by Velásquez et al. (2011), using the incremental algorithm developed by

Watson, in which the rainfall stations are used as the vertices of the triangles that

represent a three dimensional plane of the rainfall.

The centre of each grid cell forms the computational point. The hydrology module

simulates flow over and through the discrete catchment by moving water between

adjacent cells and soil layers in the horizontal and vertical direction, respectively

(Figure 4.4).

Figure 4.4 Hydrological conceptual model. Static storage (T1),surface storage (T2), Gravitational storage (T3), aquifer (T4), channel (T5), rainfall (R1), excedence (R2), Infiltration (R3), Percolation (R4), groundwater outflow (R5), overland flow (E2), subsurface flow (E3), base flow (E4), stream flow (E5), inflow to the tanks (D1:5), and evapotranspiration (EVP).

Each grid cell corresponds to a system of five interconnected tanks that communicates

with the respective tanks in the downstream cell, which represents water flow and


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storage as a hydrological response unit, including the following hydrological processes:

interception, detention, infiltration, evapotranspiration, overland runoff, percolation,

subsurface flow, and return base flow in the channels of the drainage system.

Initially, the model determines the portion of the rainfall that is intercepted on the

vegetation of the basin and as capillary water entering into the ground. Then, the

portion of rainfall estimated infiltrates by means of gravitation and is left as overland

runoff. The model considers the gravitational water storage of the soil divided into two

parts: the first is the residual soil with higher permeability, and the second one

corresponds to saprolite with lower permeability and slower response.

The first four tanks represent the runoff production processes of the basin, while the

last tank represents the transfer process runoff thereof, as follow:

The first tank (T1) is called static storage and represents interception and water

detention in puddles and the capillarity water storage in the upper part of the soil.

Capillarity storage is the water retained by capillary forces in the soil rooting zone,

which is a function of field capacity and effective root depth (Figure 4.3).

This tank models the water that passes through the catchment without participation in

the process of horizontal transfer or runoff. According to the saturation assumptions

discussed before, rainfall (R1) is stored first in the static storage, until maximum

capacity is reached. The amount of water that gets into the static storage during a time

step is the minimum value (Min) and depends on the maximum capacity of T1 (�� ),

type of soil and moisture content, in the following way:

�� = �� 1 − � ��∗�� !" , �� − �∗$ (Eq. 1)

Where S*1 is the volume of water in T1 at the end of the previous time step. When the

volume of water in T1 increases, the content of water that could get into T1 decreases.

The maximum volume of water that could get into T1 occurs when the tank is empty; it

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means the soil is completely dry. The excedence of water that continues to the next

tanks increases when T1 is almost full or wet.

The �� is equal to the sum of plant available water storage in the soil (Fig. 4.3). This

value could increase according to the ability of the surface coverage for storing water.

�� = (�&' −�)*)),- (Eq. 2)

The excedence of water of the static storage that goes to Tank 2 is:

�! = �� −�� (Eq. 3)

The volume of water in T1 updates at for each time step considering the maximum

capacity, �� , in the following way:

� = ��(�∗ +�� −�!, �� ) (Eq. 4)

The only outflow from this storage is evapotranspiration (/�). It has been included in

the model as a function of available water (�� ), and potential evapotranspiration:

/� = �� /0� ∗ � �� 1.3 , �$ (Eq. 5)

In which Evp is the potential evapotranspiration defined by a parameter according to

the local area.

The second tank (T2) is called surface storage and represents water on the hillslope

surface flowing over the slope that has not infiltrated. After ponding the static storage

tank (T1), the infiltration capacity can be approximated by the upper soil saturated

hydraulic conductivity (Figure 4.5). Then the amount of water that continues and

infiltrate into the soil is:

�4 = ��(�!, �5) (Eq. 6)

In which Ks is the saturated permeability of the upper layer, and 4675)is the available

water volume of T3 (Fig. 4.3). It means infiltration is control by the saturated


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permeability and the capacity of the residual soil to receive more water. It is important

to note that this saturated permeability should consider macropore structures.

Figure 4.5 Hydrological module proposed, modified from Vélez (2001)

The volume of water that goes to surface storage during a time interval is:

�! = �! −�4 (Eq. 7)

The volume of water in T2 is updated for each time step in the following way:

! = !∗ +�! + ,4 (Eq. 8)

In which S*2 is the volume of water in T2 at the end of the previous time step, and ,4 is

the excedence of water from the Tank 3 when is full.

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The overland flow at each cell can be represented in different ways: as constant

velocity with a linear reservoir or a no linear approach using different proposal from

several authors.

For a constant velocity, overland runoff will be given by a linear reservoir equation:

/! = 8! =�1 − 6�9:6;<6� ! (Eq. 9)

In which the water level of the tank 2 is represented by S2 and the discharge coefficient

of the linear reservoir (8) is function of cell size (dx), temporal discretization (dt) and

hillslope surface velocity (v2).

For a no linear approach, most authors recommend a uniform flow such as Manning

equation, in which the slope of the energy line is similar to the slope angle of the terrain

(Vélez, 2001). In this way, the equation for overland runoff velocity is a function of

transversal flow section (A), slope angle (=) and manning coefficient (n):

>! = ?@(: A⁄ )C�D� :⁄E (Eq. 10)

In which ξ and e1 are parameters associated to surface type. For flows over natural

terrains, Parsons et al. (1994) recommend values of 0.038 and 0.315, respectively.

The transversal section area (A) changes according to velocity and outflows.

G = �:6�<96; (Eq. 11)

Then, using an assumed value for the initial velocity (vinitial), the area is calculated and

the velocity is obtained (vcal). This process is repeated three times for each interval of

time, searching for a convergent velocity value (vmean).

0�H I = !9J�K<9LMLNL�K4 (Eq. 12)

Finally, the outflows of this tank to the downstream cell according to the overland flow

velocity is:


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/! = G0�H I 6;6� (Eq. 13)

The volume of water in T2 updates considering the outflows during this time interval:

! = ! −/! (Eq. 14)

The third tank (T3) represents the gravitational water storage in the residual soil

between field capacity and saturation (Figure 4.5). It models water column due to

subsurface flow parallel to the slope surface through the soil layer and into the

drainage system. This tank corresponds to the residual soil, where the conductivity is

considered by the model as saturated and vertically constant. One small portion of the

water can percolate or flow towards the saprolite, according to the saprolite

permeability (Kp), to feed the subsurface flow.

According to Figure 4.3, the maximum capacity of T3 is drainable porosity:

4� � = (�5 −�&O),5 (Eq. 15)

The volume of water that percolates to the saprolite is:

�P = ��Q�4, �)R (Eq. 16)

The volume of water that goes into T3 during a time interval is:

�4 = �4 −�P (Eq. 17)


4 = min{4∗ +�4; 4� �} (Eq. 18)

In which S*3 is the volume of water in T3 at the end of the previous time step. If the

capacity of the tank 3 is full, then it is produced an excedence, which goes to the

overland runoff, according to the next expression:

,4 = max{0;4 +�4 −4� �} (Eq. 19)

In order to estimate the subsurface flow (E3), a linear reservoir or a no linear approach

could be similarly assumed. In the case of linear reservoir, equation 9 is applied, in

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which constant velocity is given by the horizontal hydraulic conductivity of the upper

part of the soil, this being mainly defined by its macropore structure (Frances et al.,

2007).

For a no linear approach, subsurface flow velocity is estimated according to Kubota &

Sivapalan (1995) as a lateral subsurface flow in mountains terrains covered by forests:

>4 = \] ^_ED(`<�)(�A��)a (4)b (Eq. 20)

In which Ks is the saturated hydraulic conductivity, = is the slope angle, and b is a

parameter that depends of the soil type. Kubota & Sivapalan (1995) used b = 2 for a

mountain basin covered by forests, which represents a no homogeneous hydraulic

conductivity along the weathering profile. S3 is a volume and should be provided in

terms of the transversal section area (A) of the flow in the following way:

4 = Gcd (Eq. 21)

The transversal section area, the mean velocity and the volume of water that flow out

from T3 to the downstream cell according to the subsurface flow velocity are estimated

similar to tank 2, using the equations 11,12 and 13.

Finally, the volume of water in T3 is updated considering the flow out during this time

interval:

4 = 4 −/4 (Eq. 22)

The fourth tank (T4) corresponds to the aquifer, where vertical flow represents the

system groundwater outflow and horizontal flow is the base flow. This tank models flow

and storage in the aquifer. The model takes into account that the portion of water

entering into the aquifer is not incorporated into the base flow of the basin, although in

most basins this amount is very small and could be excluded from the model. The

volume of groundwater outflow is:

�e = ��Q�P, �))R (Eq. 23)


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82

In which Kpp is the groundwater outflow, which could be understood as water losses.

The volume of water that goes into T3 during a time interval is:

�P = �P −�e (Eq. 24)


P = P∗ +�P (Eq. 25)

The outflow from this storage to the downstream cell is estimated by using the linear

equation 9 in terms of water level with a discharge coefficient that can be related to the

aquifer saturated hydraulic conductivity. In addition, the volume of water in T4 is

updated taking into account outflows during this time interval:

P = P −/P (Eq. 26)

Finally, the last tank (T5) represents the stream flow channel at the cell, in which each

cell is connected to the downstream cell according to the drainage network, and

models the flow of water in the drainage basin. Only the ephemeral and perennial

channel grid cells are contained in T5; slope grid cells do not have T5. Propagation of

channel flow to the outlets of overland, subsurface flow and base flow are collected by

the river channel network represented by T5 (Figure 4.4).

Similar to the previous tanks, the stream flow velocity can be estimated by means of a

linear reservoir or a no linear approach. For a constant velocity, a linear reservoir could

be similarly assumed using equation 9, in which constant velocity is provided for the

modeler according to field observation and expert judgment.

For a no linear approach, the routing along the channel network is carried out a non-

stationary velocity using the Geomorphological Kinematic Wave (GKW) proposed by

Vélez (2001). The GKW is a simplification of the Saint Venant equations, in which

inertial and pressure terms are neglected. Assuming prismatic canals with constant

section along the reach, the discrete continuity equation can be expressed in terms of

the two unknowns, water velocity (>;) and the cross section (G;) as:

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83

G;∆d +>;G;∆g = h; + ;i� (Eq. 27)

In which S represents the volume of water in the channel reach and h; is the total input

flows from connected hillslopes (overland flow, subsurface and/or base flow) and/or

upstream flow from river channels. The GKW simplification assumes that the energy

line slope is equal to the slope of the river bed (β). Then, flow velocity and flow cross

section can be directly related by the Manning’ s equation. Water velocity, according to

Manning´s equation, is expressed in terms of the flow section top width (wt), which is a

function of the section (G;).

0P = �I �@NjN

! 4⁄ =�⁄! (Eq. 28)

Velocity is controlled by the channel hydraulic characteristics (geometry and slope) at

each reach and time step. The slope for each cell can be easily computed from a DEM.

However, unfortunately, in practice it is not economically feasible to measure the

channel geometry for all cells. The GKW uses the Leopold & Maddock (1953)

correlation, which relates the cross section geometry and velocity to the river discharge

(Qt) using potential equations:

kb =l�mn (Eq. 29)

�b =o�kbp� (Eq. 30)

�; =o!k;p: (Eq. 31)

In which Qb is bank full discharge along the river network, m is drainage area, and the

coefficients and the exponents k1, c1, cn, q, 8�, 8! are constant at the regional scale.

In order to estimate the roughness the GKW proposes a general equation in terms of

the slope (=), the accumulated area (m) and the height of the water (r):

� = oIo6srst=st (Eq. 32)


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84

In which the coefficient oI and o6, and the exponents u and v are constant regional

parameters.

In this way, the velocity of the water in the channel is a function of the geometry of the

channel and the geomorphology of terrains (Frances et al., 2012):

>P = w @�:Axyz (�x{:)D(�:xyz)'M'|y�'�}�({�x{:)~�({�x{:) (: A⁄ xyz)�

��{:Q: A� xyzR (Eq. 33)

This equation is simplified in the following way:

>P =�!G*�m*:=*A (Eq. 34)

In which:

�! = oIo6s �o�(! 4⁄ ist)l�(! 4⁄ ist)(p�ip:) i* (Eq. 35)

� = ��<p:Q! 4� istR (Eq. 36)

�� = �(2 ⁄ 3 − uv)(1 − 8!) (Eq. 37)

�! = −�qQ2 3� − uvR(8� − 8!) (Eq. 38)

�4 = �Q1 2� − uvR (Eq. 39)

The result is that the GKW needs nine independent exponents and coefficients, which

can be obtained with a geomorphologic regional study for hydrological homogeneous

zones. However, empirical studies have been carried out by multiple authors proposing

different values according to local conditions (e.g. Vélez, 2001; Frances et al., 2007;

Frances et al., 2012).

Similar to the previous tanks, velocity is developed with a similar algorithm, because it

is a function of the storage water in the tank, using equations 11, 12, and 13.

Table 4.1 shows the constant regional parameter range values proposed by Vélez

(2001) and Frances et al., (2007).

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Table 4.1 Geomorphological Kinematic Wave parameter ranges proposed for the model

Propagation

parameter

Range

K1 0.5 -0.75

q 0.65 - 0.8

�� 0.5 – 5.75

�� 0.34 - 0.55

�� 0.05 – 0.2

�� 0.5–50.0

� 0.5 – 2.75

�� 0.025 – 0.07

� 0.125 – 0.18

Vertical and horizontal transfer of water. The vertical connections between tanks

describe the rainfall, evapotranspiration, infiltration and percolation processes.

Simultaneously, the model considers the horizontal transfer of water between adjacent

cells by using a sub-model to infer the direction of flow between them based on the

topology of the basin. The horizontal connections describe the overland flow, interflow

and base flow.

Tank interconnection depends of grid cell type. There are three types of grid cell: (i)

slopes, (ii) rill or ephemeral channels, and (iii) perennial channels (Figure 4.6).

The grid cell type is assigned for the model according to the accumulated area or cells

(threshold area). These thresholds are defined considering field work observation and

local studies. There are two thresholds that should be defined and input to the models

like parameters. The minimum accumulated area to form a rill or ephemeral channel,

between overland runoff and subsurface flow, and the minimum area to form a

perennial channel, between subsurface flow and base flow. The threshold for base flow

is estimated based on the starting point of permanent flow in the channel network.

According to these threshold area values, the model defines the type of grid cell to the

whole catchment.


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86

Figure 4.6 Interconnection tanks of the hydrological module

For slope grid cells, the horizontal flow of water between tanks becomes the same

level, the water tank E2 passes to the tank E2 cell downstream, and similarly for the

other tanks in which it is possible to transfer. Only T1 does not transfer water to the

similar tanks because the only outflow from this tank is evapotranspiration. For

ephemeral channel grid cells, the horizontal flow of water occurs just between tanks

T4, the outflows from T2 and T3 goes out to the tank 5. And finally, for the perennial

channel grid cells, the flow occurs just from T5 to T5.

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Figure 4.7 Schematic division of the basin into grid cells and flows

A slope grid cell may drain to any kind of grid cell, and rill grid cell can drain to a rill or

perennial channel grid cell, and a channel grid cell can only drain just to a similar grid

cell.

The model shows that when a landslide occurs in a slope grid cell, it changes into a rill

grid cell, considering that the geoform printed by the landslide produces a rill where

overland runoff and subsurface flow is concentrated along the new rills form by the

landslide occurrence.

Finally, the model carries out a mass balance between rainfall input, infiltration, and

runoff over the entire grid by allowing excess water to flow to downslope cells, and the

balance is performed to update the cumulative volume in each of the tanks.

4.12 Geotechnical module

The geotechnical module propose here is based on the idea that the weathering soil

profile increases soil density with depth with a corresponding decrease in hydraulic

conductivity and, when the rainfall rate exceeds the percolation rate between the

residual soil and saprolite, a perched water table, which correspond to the susbsurface

flow, starts to be formed.


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88

The implicit assumption is that soil is in saturated conditions and that the subsurface

flow in this saturated zone is roughly parallel to the slope; according to this fact, the

stability conditions associated to the positive pore water pressure is constrained by the

height of the perched water table.

On hillslopes mantled by tropical soils, the potential failure surface is typically located

at or near the level of contact between the relatively permeable residual soil and

underling relatively impermeable saprolite. If the residual soil has limited thickness

compared with the length of the slope, an infinite slope stability hypothesis can be

assumed in the analysis.

The term infinite slope represents a uniform slope of an extent large enough that a

typical element can be considered representative of the slope as a whole, and

irregularities at the toe and the crest of the slide can be ignored, where soil properties

and pore-water pressures at any given distance below the ground surface are assumed

constant (Graham, 1984).

The one-dimensional infinite-slope stability analysis is the most common approach in

order to model the slope failure within a distributed catchment scale framework. It is

based on a simplified landslide geometry that assumes a planar slip surface on an

infinitely extended planar slope, both laterally and distally. The analysis assumes that

slip surface is parallel to the ground surface and coincident with the impermeable

substrate.

The soil is subject to two major opposing influences: the downslope component of soil

weight, which acts to shear the soil along a potential failure plane parallel to the

hillslope; and the resistance of the soil to shearing. The relationship between the two

influences is expressed as a factor of safety. The factor of safety for an infinite soil

slope can be expressed as:

FS =��^_^�_E��^��_�_E��^ (Eq. 40)

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89

The side forces for any vertical slice are equal and opposite, and the stress conditions

are the same at any point of the failure surface. It is also assumed that the rigid

perfectly plastic rheological model holds for the soil, that is, there is null strain until

failure and shear strength are constant after the failure independently on strain.

Typically, the higher the pore water pressure, the lower the frictional resistance and the

shear strength; increased soil water content also increases the bulk weight of the soil

(Figure 4.8).

Figure 4.8 Geotechnical conceptual model proposed. � is the soil bulk density, �w is the water density, Zw is the saturated soil thickness above the slip surface, Z is the soil thickness measured vertically, = is the gradient of the hillslope, QL & QR resultant forces on the sides of the slice.

Equilibrium of the soil longitudinal section by a vertical resolution of forces, the vertical

force across the base of the slice must equal the weight (W). This can be resolved into

its normal and tangential components P and T respectively.

� = ��, (Eq. 41)

� = ��,��= (Eq. 42)

� = ��,��= (Eq. 43)

The length of the slide surface is ��o8, and the average normal and shear stresses

produced by P and T are:


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90

�I = �,��!= (Eq. 44)

= �,��=��= (Eq. 45)

The shear strength of the soil along the potential failure plane is given by the Mohr-

Coulomb failure criterion, and the downslope shear stress ( ) must not exceed the

shear strength ( &) of the clay.

& = o +�I�¡�¢ (Eq. 46)

The safety factor in the slope can be defined in terms of effective stresses by £¤£ , that is:

FS = O¥<(¦§O¨5:Di©) �ªE«

¦§ ^_ED ��^D (Eq. 47)

When a slope is subjected to pore pressure increase due to infiltration or rising perched

water table, total stresses and shear stresses remain essentially constant, but effective

stresses, and more specifically mean effective stress, decrease. The effective stress

principle states that the total stresses applied to soils are supported by the sum of

effective interparticle stresses and neutral pore water pressure (Graham, 1984).

According to Graham (1984) in natural hillslopes with steady subsurface flow parallel to

the slope, and the perched water level at distance ,* above the slide surface, the pore

water pressure is ¬ = �*,*��!=, and therefore:

FS = O¥<(§i®§®)O¨5:D¯ I«

§�7IDO¨5D (Eq. 48)

Then, limit equilibrium condition for the slope occurs when:

o′ + (�, − �*,*)��!=�¡�¢ = �,��=��= (Eq. 49)

This equation solved for ,* provides the critical value of landslide-triggering saturated

depth:

,*'-7; = ® , �1 −¯ ID¯ I« + O¥

®O¨5:D¯ I« (Eq. 50)

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91

To evaluate the slope stability for each grid cell in every time step, it is necessary to get

the perched water table height and compare with the critical value of landslide-

triggering saturated depth (,*'-7;). The hydrological component of the model provides

the water content in gravitational storage; this value has to be transformed taking into

consideration the water content of the soil. In this way, according to Figure 4.3, the

perched water table height is:

,* = �AQ*]i*¤JR (Eq. 51)

However, to increase the computational efficiency of the model, the minimum and

maximum residual soil thickness computed beforehand, to define the unconditional

stable grid cells and the unconditional unstable grid cells (Figure 4.9), since these two

states are independent of the water content.

Figure 4.9 Landslide susceptibility as a function of slope angle and soil thickness. Β0 is the maximum angle where the slope is always stable, ¢ is the friction angle, Zsmin is the immunity soil depth, and Zsmax is the maximum stable soil thickness (modified from D’Odorico & Fagherazzi, 2003).

Equation 49, solved for ,* = ,, provides the immunity depth:

,�7I = O¥®O¨5:D¯ I«<O¨5:D(¯ IDi¯ I«) (Eq. 52)

Because saturated depth is necessarily smaller than residual soil thickness (,* ≤ ,), when , < ,�7I the deposit is always stable, independently of rainfall (Iida, 1999).


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92

And for a certain value of soil thickness, ,� �, the saturated depth necessary to trigger

a landslide is zero and the soil is always unstable, regardless of rainfall occurrence

(Iida, 1999). For soil thickness higher than ,� � the soil is then always unstable. ,� �

is determined by setting ,* = 0 in Equation 49:

,� � = O¥O¨5:D(¯ IDi¯ I«) (Eq. 53)

Additionally, it is necessary to find the maximum value of the slope angle (=1), where

the slope is always stable because a saturated depth larger than the soil thickness

would be needed to trigger a landslide. =1 is found when c’ = 0 and ,* = , in Equation

49. When = < =1 the slope is always stable.

=1 = tani� ´tan¢ (1 − ® )µ (Eq. 54)

Figure 4.10 shows the entire geotechnical module of SHIA_Landslide.

Figure 4.10 Geotechnical module of SHIA_Landslide

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93

4.13 Correction factors

In general, the parameter value that reproduces the average of the process in an area,

called effective parameter value, is not the mean value of the parameter within the

area, and considering scale effects, the models can be calibrated, but will not be

properly validated in a different scenario. According to this problem, Frances et al.

(2012) propose that the effective parameters for the model at each cell should be split

in two components: a hydrological or geotechnical characteristic and a correction

factor, common for all cells and taking into account all modeling errors including the

temporal and spatial scale effects.

With the split-parameter structure proposed by Frances et al. (2007), the correction

factors take into account the time and space scale effects and also the model and input

errors, leaving the hydrological characteristics free of these problems while maintaining

the physical meaning of the parameters.

The infiltration model and the flow channel routing model proposed herein include a

few correction factors which apply globally to the different soil property maps instead of

each cell value of the calibration maps, thus reducing drastically the number of factors

to be calibrated. This strategy allows a fast and agile modification in different

hydrological and geotechnical processes.

For the factor of safety, a correction parameter is included, which allows defining the

minimum value that is accepted as stable. According to the geotechnical criteria, this is

1, although sometimes it is valid to consider as unstable values higher than 1.

Table 4.2 shows the minimum and maximum values for each correction parameter

recommended by Vélez (2001) and Frances et al. (2007).

Table 4.2 Model split parameter structure and correction range values proposed by Vélez (2001) and Frances et al., 2009)

CELL PARAMETER CORRECTION DECOMPOSITION Cx MIN Cx MAX

Maximum static storage (¶�·¸¹) �� ∗ = �� 0.1 1.5

Evapotranspiration (EVP) �! />�∗ = �!/>� 0.5 2.0


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94

Infiltration capacity (º») �4 �5∗ = �4�5 0.0 1.0

Percolation capacity (º¼) �P �)∗ = �P�) 0.0 2.0

Groundwater outflow capacity (º¼¼) �e �))∗ = �e�)) 0.0 10

Surface runoff velocity (½�) �3 >!∗ = �3>! 0.1 2.0

Subsurface velocity (½¾) �¿ >4∗ = �¿>4 1.0 1000

Base flow velocity (½À) �Á >P∗ = �Á>P 1.0 1000

Channel velocity (½Â) �Ã >e∗ = �Ã>e 0.5 1.5

Cohesion (�´) ��1 o´∗ = ��1o´ - -

Friction angle (Å) �� ¢∗ = ��¢ - -

Soil thickness (Æ») ��! ,5∗ = ��!,5 - -

Gravitational storage (¶¾·¸¹) ��4 4� �∗ = ��44� � 0.1 1.5

Factor of Safety (FS) ��P FS∗ = ��PFS - -

4.14 Model evaluation

To perform the evaluation, it is necessary to input observed stream flow data in order to

compare with simulated data. SHIA_Landslide prediction uncertainty and performance

for the hydrological component is measured using the Root Mean Square Error

(RMSE), and Nash-Sutcliffe efficiency coefficient (NS). RMSE and NS are provided for

the model after each simulation.

The RMSE measures the average magnitude of the error, its range is from 0 to infinity,

with 0 being a perfect score. The RMSE of a model prediction with respect to the

estimated variable (ÉÊË»)is defined as the square root of the mean squared error.

��/ =Ì∑ (ÎÏa]iÎ]L�):ÐNÑ� ¯ (Eq. 55)

In which Qobs is the observed, Qsim is the modeled discharge at time t. T is the time

horizon and Qobs is the mean of the observed discharge.

The Nash-Sutcliffe model efficiency coefficient (E) is commonly used to assess the

predictive power of hydrological discharge models. Nash-Sutcliffe efficiencies can

range from -∞ to 1. An efficiency of 1 corresponds to a perfect match between model

and observations. An efficiency of 0 indicates that the model predictions are as

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95

accurate as the mean of the observed data, whereas an efficiency less than zero (-

∞<NS< 0) occurs when the observed mean is a better predictor than the model.

Ò = 1 −∑ (ÎÏa]iÎ]L�):ÐNÑ�∑ QÎÏa]iÎÏa]R:ÐNÑ� (Eq. 56)

Additionally, for RMSE and NS, SHIA_Landslide calculates the water balance in terms

of percentage, making a balance by using the total rainfall over the catchment, the

outflows along the different grid cells and finally considering the storage water that is

conserved into the tanks at the end of the simulation.

Rainfall is estimated considering the rain for each grid cell (x) during all the time (t)

modeling:

�¡��Ó¡ÔÔ = ∑ ∑ �¡��Ó¡ÔÔ(d, g)�;Õ�I�Õ� (Eq. 57)

For the lowest point of the catchment, where it is closed, the outflows providing from

the overland (E2), subsurface (E3), groundwater (E4), and stream (E5) are considered

for each time interval

Ö×gÓÔ�� = ∑ ∑ /; I}(g)e; I}Õ!�;Õ� (Eq. 58)

For the static storage the outflow, which corresponds to EVP, it is considered for all the

grid cells during all the time intervals, in the following way:

/>� =∑ ∑ />�(d, g)�;Õ�I�Õ� (Eq. 59)

The water that is conserved into the tanks at the end of the simulation is estimated in

the following way:

g�Ø¡Ù� = ∑ ∑ ; I}(d)e; I}Õ�I�Õ� (Eq. 60)

At last, water balance is obtained.

�¡g�Ø�¡Ô¡�o�(%) = Û©;&Ü¨*5<ÝÞß<�;¨- àHiá 7I& ÜÜÛ©;&Ü¨*5<ÝÞß (Eq. 61)


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96

4.15 The coupled hydrologic – geotechnical model: SHIA_Landslide

SHIA_Landslide is a model program for computing positive pore pressure changes,

and attendant changes in the factor of safety, due to rainfall infiltrations using a

hydrological module coupled with an infinite stability slope geotechnical module.

The model is composed by a hydrological module, to analyze rainfall infiltration in

saturated condition, and by a geotechnical module which, starting from limited

equilibrium methods, evaluates slope stability. The model requires an input rainfall,

which causes a rise of perched water table, and consequently a rise in pore pressures

leading to instability conditions.

The model focuses its attention on topographic control of hydrological process, on the

process that control subsurface flow at the hillslope scale and on the effect of water

infiltration on soil strength and slope stability.

Infiltration (R3), gravitational storage (S3) and subsurface flow (E3) are the most

important processes to be concerned with the model. The water stored in the tank 3

(S3) from the hydrological module corresponds to the height of the perched water table

to input in the geotechnical module.

Figure 4.11 presents the flow diagram showing the steps used by the model in

hydrological and slope stability calculation.

4.16 Programming language

In regards to the language program, there are different languages to carry out this kind

of model. However, due to the fact that this model corresponds to a detailed and

distributed hydrological module combined with a geotechnical approach for the

catchment scale, it was necessary to use a robust language and compiler. For this

reason FORTRAN was selected as the programming language.

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97

Figure 4.11 SHIA_Landslide model

4.17 Subroutines

The main program is integrated by 5 subroutines: Input data, Basin, Rainfall, Matrix,

and Model, which contains the hydrological and geotechnical components. Figure 4.12

shows the program structure of SHIA_Landslide model.

The initial subroutines prepare the information needed to run the hydrological and

geotechnical modules properly. The subroutine SHIA_Landslide calls all the

subroutines one by one, and Module declares all the variables.

The Basin subroutine determines the position of the grid cells according to the flow

direction map. The algorithm for defining flow direction is known as D8 (8 flow

directions), which assigns flow from each grid cell to only one of its eight possible

neighbors, either adjacent or diagonally, in the direction with the steepest downward


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98

slope. In the model, each grid cell can receive flow from multiple neighbors, but can

discharge to only one neighbor grid cell.

The Basin subroutine uses algorithms, starting from the lowest grid cell in the

catchment towards upstream, establishing the number and position of the grid cells that

drain to each grid cell, and forming a vector from bottom to top.

The Matrix subroutine forms a multiparameter matrix of the catchment to all the input

parameters for each grid cell. All these previous subroutines have the purpose to

prepare the needed information for the final subroutine: the Model. This subroutine

runs the hydrological and the geotechnical components of the models.

The subroutine Model initially prepares a susceptibility matrix that classifies the grid

cells into: unconditional stable, unconditional unstable and potential unstable grid cells.

In this subroutine, the critical height of the perched water table is also calculated (Eq.

50) and included into the multiparameter matrix. This step allows the subroutine Model,

during each time step, to only test the stability of the potentially unstable grid cells.

In the hydrological component, subsurface flow is calculated according to the local

drain direction imposed by the topographical relief, depending on GKW. Changes in

height of the perched water table directly relates to a change in pore pressures, which

are estimated for the stability module.

In the geotechnical component, for each time step, the program evaluates the stability

of the potential unstable grid cells, comparing the perched water table height (Zw) with

the critical water table height previously estimated. For the grid cells that do not show

failure, the model estimates the Factor of Safety.

4.18 Input and output data

SHIA_Landslide derives its slope stability evaluation from inputs of topographic slope

and specific catchment area from parameters quantifying geotechnical and hydrological

properties.

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99

The digital elevation model (DEM) constitutes a preliminary point of the modeling since

direction drainage system, accumulated drainage area and slope angle of the

catchment are derived from it. Each parameters used is delineated on a numerical grid

over the study catchment.

Figure 4.12 Flow chart of SHIA_Landslide program

The program operates on a gridded elevation model of a map area and accepts the

input parameters from a series of ASCII text files. Rainfall, hydraulic properties, and


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100

slope stability input parameters are allowed to vary over the grid are thus making it

possible to analyze complex rainfall events over complex terrains.

The program allows the following input parameters to vary from cell to cell throughout

the basin in Input Data Subroutine: cohesion (o´), evapotranspiration (/>�), soil

thickness (,5), slope inclination (=), friction angle (∅), maximum static storage (�� ),

maximum gravitational storage (�� ), saturated hydraulic conductivity of the soil (�5), saturated hydraulic conductivity of the saprolite (�))), saturated unit weight of soil (ã5), flow direction, and flow accumulation area. Rainfall data to simulate input are in txt file.

The rainfall data should include rain gauges number and location, time and rainfall

information. Figures 4.13 and 4.14 show the formats for the ASCII maps and rainfall file

to input into the model.

Figure 4.13 Format for the ASCCI files to introduce the parameters into SHIA_Landslide.

Figure 4.14 Format for the rainfall data to be introduced into SHIA_Landslide. Each ID number corresponds to a rain gauge station.

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101

The initial conditions, the calibration factors, the control point, and the thresholds areas

are input into the model using an application programming interface designed. The

control point correspond to the grid cell, which the model shows the simulated

hydrograph and perched water table variation.

Concerning the output data, the model simulates landslide activity in the form of maps

where the factor of safety for conditional unstable grid cells is calculated for areas with

perched water table lower than the critical value. The user could observe the change in

the factor of security as the storm progresses and until the slope failure takes place.

The location of the sites where landslides are triggered is therefore represented in

raster maps in terms of potential unstable cells. The program saves output to a series

of ASCII text files that can be imported to GIS software for display or further analysis.

The model outputs four useful products during the simulation process. From the

hydrological module outputs the hydrograph and perched water table variation for any

point of the catchment. The geotechnical module outputs are two matrices, the

susceptibility map before the target area is exposed to rainfall, and the landslide hazard

map with the spatial distribution of landslides triggered by rainfall.

The first output map provided for the model is the susceptibility map, which highlights

the regional distribution of potentially unstable slopes. The susceptibility map is useful

to establish the pixels where the model needs to check the slope stability according to

the perched water table increasing and loss of shear strength.

On each time interval of the simulation, pore water pressures are calculated for each

cell in the catchment. The pore water pressures are then used in the stability analysis

incorporated directly into the Mohr-Coulomb equation for soil shear strength. By

calculating both the effective shear stress along the failure surface and the soil shear

strength, it is possible to determine the factor of safety. For each time interval of the


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102

simulation, it is possible to obtain the factor of safety for the slope, with any temporal

variations arising from the dynamic hydrological responses.

Although the model works by comparing critical perched water table for each time

interval and calculating the factor of safety, the final forecasting map is presented as a

binary landslide map, which can easily be understood in an early warning system.

However, for detailed analysis, the model program could be adjusted to provide maps

showing the factor of safety distribution along the catchment.

Besides a spatial prediction, the dynamic section of the model also provides a temporal

prediction by means of the observation of landslide occurrence at a fixed time interval.

Hence, the temporal scale of the model is defined by the duration of the simulated

event, which consequently involves time increments.

4.19 Graphical user interface (GUI)

SHIA_Landslide is accessible through a graphical user interface (GUI) written in

FORTRAN that allows user to interact with the model. The GUI is an executable file,

located in a folder of the user choice, and does not require to install any program or to

have a FORTRAN compiler. Figure 4.15 shows the GUI designed for SHIA_Landslide.

Figure 4.15 Graphical user interface main window designed for SHIA_Landslide.

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The SHIA_Landslide user interface main window contains all the tools that allow the

user to run the model. The top part of the main windows contains three scroll down

menu whose functions are clearly identified by their label. The first one, called

SHIA_Landslide, correspond to the GUI main window, the second menu, called

Results, correspond to the figures provided by the model, and the last one to Exit.

From the SHIA_Landslide panel all hydrological and geotechnical parameters,

calibration factors and initial conditions are entered to the model. This window can be

divided into 7 main groups of panels that from left to right are: Maps, Even Data,

Threshold Area, Initial conditions, control points, Correction factors and Output

directory.

The Maps area allows the user to enter geotechnical and hydrological distributed

parameter maps as ASCII files using the format shown in Figure 4.13. They could be

located in any folder; however it is recommended to avoid long directory addresses and

save the folder with the maps in the local disk C. Long direction could produce an error

in the program due to FORTRAN does not permit these long directions. The

Thresholds, Initial conditions, and Correction factors area are entered by the user as

numbers.

The lowest point of the catchment and the control point for hydrological calibration

should be provided by the user, as well. The control point usually corresponds to a

point where a gauge station is located, and observed data are available. The stream

flow and perched water table simulated by SHIA_Landslide correspond to the control

point input by the user. When a control point correspond to a hillslope grid cell it is

useful to evaluate the perched water table changes during the rainstorm; and when the

control point correspond to an ephemeral or perennial grid cell it is useful to evaluate

the stream flow. If the user wants to evaluate the perched water table or stream flow in

a different point of the catchment, should run again the model for this point; however, it

is important to keep in mind that the susceptibility and hazard maps, which correspond


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to the entire catchment, are preserved without any changes. These maps only change

if the rainfall event, parameters, initial conditions or correction factors are changed.

The rainstorm that user wants to simulate inputs by using the file format of the Figure

4.14. If the user provides the observed stream flow in the control point position, it is

necessary to check the Qobserved box, and input the file as a vector in txt format. In

this case, the figure stream flow in the result menu shows both stream flow, simulated

and observed, with the RMSE and NS efficiency.

Finally, it is possible to name the folder in which output data will be saved. The folder is

located in local disk C by default. If the user does not provide a name, the program will

call the folder as SHIA_L and the simulation date.

While SHIA_Landslide is running provides the percentage of simulation and time

interval, and when the simulation finishes, it shows to the user the water balance and

the time taken for the simulation. The RMSE and NS efficiency only is shown when the

user enters to the model the observed stream flow data (Figure 4.16).

Figure 4.16 Result window provides for SHIA_Landslide

SHIA_Landslide’s output is displayed in the Results submenu. It provides 4 figures: the

simulated and observed stream flow, the perched water table, and the susceptibility

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and hazard maps (Figure 4.17). All these graphs are plotted using the limited graphical

tools of FORTRAN. However, the files are saved in the output library, and the user can

import and display or work with them in any other program such as Excel, Matlab or

ArcGIS.

Additionally to the figures provided for the model, SHIA_Landslide also save in the

output folder a file which contains the multiparameter matrix. Each row of the

multiparameter matrix shows the position for each grid cell of the catchment and the

hydrological and geotechnical parameters, and the critical Zw, Z min, Zmax and

stability conditions. This file permits to the user to check the final results and go further

in the analysis of the catchment.

A. Simulated and observed stream flow


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106

B. Simulated perched water table

C. Susceptibility map

D. Hazard map

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Figure 4.17 SHIA_Landslide product: A) Simulated and observed stream flow, B) simulated perched water table, C) susceptibility map, D) hazard map.

Chapter 5

CALIBRATION AND IMPLEMENTATION OF THE

MODEL: La Arenosa case

5.1 Introduction

A tropical and complex terrain catchment was selected for the implementation of the

model. However, the framework and applications developed herein may be calibrated

and applied to other landslide-prone areas with different settings; it is necessary to

adjust hydrological and geotechnical assumptions or conditions such as the weathering

profile, catena, soil thickness, and saturated conditions.

La Arenosa catchment is typical of the Colombian Andean Mountains according to the

description in Chapter 1, where a massive event of landslides was triggered by rainfall

on 21 September 1990. This event allows comparing and evaluating the performance

of the model proposed.

In order to evaluate the performance and results of the model, both conditions of

SHIA_Landslide, namely the linear reservoir equation and the nonlinear approach were

Chapter 5: Calibration and implementation of the model: La Arenosa case

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110

implemented. Hydrological and geotechnical parameters are the same for both models,

and only correction factors were adjusted independently.

5.2 Digital Terrain Model (DTM)

A digital elevation dataset with sub-meter resolution was obtained from aerial

photographs provided by the Instituto Geográfico Agustin Codazzi (IGAC). Figure 5.1

shows the watershed boundaries and stream network extracted from the dataset using

a DEM.

Figure 5.1 Digital Elevation Model of La Arenosa catchment.

Spatial discretization of the model was obtained splitting the study area into a number

of squared grid elements, with a raster size of 10 m according to the DTM. The

corresponding DEM grid file presents a matrix composed by 436 columns and 456

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rows. From the total matrix a number of 98.646 grid cells comprise the La Arenosa

catchment. Morphometric parameters such as slope angle, flow direction and flow

accumulation are calculated using the DEM and ArcGIS 10.1 hydrologic tools.

5.2.1 Digital Elevation Model (DEM)

To obtain morphometric parameters, it was necessary to adjust the grid elements

surrounded by higher terrain that do not drain (potholes). They are eliminating using

different free GIS tools available, which raises the elevation of each pit grid cell within

the DEM to the elevation of the lowest pour point of the perimeter of the cell.

Figure 5.1 shows the adjusted DEM of La Arenosa catchment. Altitudes range from

1,094 to 1,971 m above mean sea level. The upper catchment and highest elevation

are located to the S – SE of the catchment, and lowest elevation are located to the N –

NW, draining from south to north.

5.2.2 Slope map

Landslides are defined as gravitational processes, so slope gradient has a great

influence on susceptibility of a slope concerning landsliding. The slope map of La

Arenosa catchment is showed in Figure 5.2.

The steepest slopes are in yellow-orange-red colors and the gentlest slopes are in blue

color. Slope angles are showed in degrees. However, for SHIA_Landslide angle

measurement should be input in radians. Slopes degrees range from 0° to 62°. Very

steep terrains to the upper portion of the catchment and areas in the central and lower

portion are dominantly flat. Gently sloping terrains are found to the east forming a NE-

NS trending.

5.2.3 Flow direction map

The flow direction map determines the natural drainage direction for every pixel

according to the DEM. Figure 5.3 shows the flow direction map for the La Arenosa

catchment. Most slopes drain to the northern, northeastern and northwestern.


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Figure 5.2 Slope map of La Arenosa catchment.

Figure 5.3 Direction flow map of La Arenosa Catchment.

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5.2.4 Flow accumulation map

Based on the output flow direction map, the flow accumulation map corresponds to the

drainage area for each grid cell. SHIA_Landslide use the maximum fall direction out of

each grid cell, then the number of contributing cells times the area of each grid cell

determines the drainage area to a cell. Maximum drainage area corresponds to the

lowest point, where the hydrologic system is closed. Figure 5.4 shows the flow

accumulation map.

Figure 5.4 Flow accumulation map of La Arenosa catchment.

5.3 Soil properties

Soil properties are strongly related to the parental material, permitting to assume that

hydrological and geotechnical soil parameters are uniform within parental geological

units. The catchment presents a quite homogeneous geology, characterized by sandy


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soils with high permeability. The geology of the catchment is defined by two main soil

types that were identified by the Instituto Geografico Agustin Codazzi (IGAC, 2007a)

and shown in Figure 5.5.

For each geological unit, a detailed stratigraphic profile was constructed to support the

definition of geotechnical and hydrological input parameters according to the official soil

map (IGAC, 2007a): Stratigraphic detailed profiles are showed in the Table 5.1 and 5.2.

Figure 5.5 Soil map of La Arenosa catchment elaborated by IGAC (2007a).

Yarumal soils (YAe1 - YAf2). The soils are derived from igneous rocks and granites

quarzodiorites of the Antioquia Batholit. It presents medium and fine textured, well-

drained, deep and in some cases limited by gravel or stones in the profile.

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This soil association is formed by: Hapludands (35%), Humic Dystrudepts (25%), typic

Dystrudepts (25%) and Hidric Hapludands, and Typic Kandiudults Dystrudepts Oxicic

each with 5%.

Yarumal soils association covers 924.37 ha, corresponding to 93.32% of the catchment

area. The subcategories present in the study area are: YAe1 (Yarumal association,

slightly steep phase, slightly eroded) and YAf2 (Yarumal association, moderately steep

phase, moderately eroded).

Table 5.1. Depth and particle size of the soil profiles present in Yarumal association.

SOIL PORCENTAJE DEPTH PARTICLE SIZE (%)

(cm) Sand Silt Clay Texture TypicHapludands 35% 0 25 56 28 16 FA

25 50 60 24 16 FA 50 65 44 24 32 Far 65 130 42 24 34 Far

HumicDystrudepts 25% 0 10 63 12 25 FarA 10 20 56 32 12 FA 20 35 45 39 16 F 35 50 40 38 22 F 50 110 49 28 23 FarA

TypicDystrudepts 25% 0 33 55 22 22 FarA 33 60 57 24 18 FA 60 75 52 22 26 FarA 75 140 37 22 40 Ar

HidricFulvudands 5% 0 26 70 26 4 FA 26 42 78 19 2 AF 42 90 83 15 2 AF 90 120 85 13 2 AF

OxicicDystrudepts 5% 0 15 50 17 33 FarA 15 50 46 11 43 ArA 50 120 44 9 47 Ar 120 150 47 10 43 ArA

TypicKandiudults 5% 0 20 35 36 28 Ar 20 32 31 24 44 Ar 32 106 31 30 38 F Ar 106 140 37 24 38 F Ar

Poblanco soils (POc1). This soil association covers 66.14 ha of the catchment,

corresponding to 6.68% of the total area. The soils of this association have been

developed from heterometric deposits mixed with colluvium and alluvial materials. Soils

are deep to moderately deep limited by the presence of fragments of rock and gravel,

gravel and stones in the profile. They are well drained, fine-textured to moderately

thick, with very low to low pedogenetic evolution, with particular structure in the upper

horizons.


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This soil association is formed by: HumicDystrudepts with 35%, Oxic Dystrudepts with

20%, Fluventic Dystrudepts with 20% and inclusions Hapludox Inceptic soils, Typic

Hapludolls, Typic Eutrudepts, Typic Udorthents and Andic Dystrudepts with 5 % each.

Land cover. Land cover is an important parameter considered for most models to

parameterization. It was used for the definition of root depth, which corresponds to a

fundamental data for the static water storage capacity. Figure 5.6 shows the land cover

map of La Arenosa catchment elaborated by IGAC (2007b). According to this

information La Arenosa is mainly occupied by crops, which correspond to subsistence

farming, these occupy 73.3% of the total area of the basin, followed by covered

stubble, with 15.6%, then the pastures are 7.6% and 3.2% natural forests, and areas

without vegetation, classified as bare soil, occupying 0.16% of the total study area.

Table 5.3 has the root depth for each land cover according to IGAC (2007b).

Table 5.2 Particle size of the soil profiles present in Poblanco association.

Soil Percentage Depth Particle size (%)

(cm) Sand (S) Silt (M) Clay (C) Texture HumicDystrudepts

35%

0 20 40 38 32 F 20 70 36 32 32 F Ar

OxicDystrudepts

20%

0 20 47 24 28 FArA 20 40 43 20 37 F Ar 40 75 42 20 38 F Ar 75 140 48 24 28 FArA

FluventicDystrudepts

20%

0 20 19 30 51 Ar 20 70 11 28 61 Ar 70 150 12 35 53 Ar

IncepticHapludox

5%

0 25 51 18 30 FArA 25 45 52 16 32 FArA 45 80 43 14 42 Ar 80 120 42 20 38 FArA

TypicHapludolls

5%

0 20 49 25 25 FArA 20 40 62 19 19 FA

TypicEutrudepts

5%

0 30 30 38 32 F Ar 30 55 24 30 46 Ar 55 75 18 30 52 Ar

TypicUdorthents

5%

0 20 23 39 38 F Ar 20 120 35 44 21 F 120 150 10 44 46 ArL

AndicDystrudepts 5% 0 44 41 26 33 F Ar 44 70 41 20 39 F Ar 70 104 17 28 54 Ar

Soil description, field tests and laboratory analyses on soil samples of La Arenosa

catchment have been performed by Mejía & Velásquez (1991) and INTEGRAL (1990)

after the landslide event. Using this information with soil typology correlation and field

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work corroboration based on the soils and land cover maps, those soil parameters

were extended to the whole catchment. Finally, the parameter values were compared

with literature data to estimate a range of liable values to calibrate the model. Table 5.4

shows the soil parameters obtained for the implementation of the model.

Table 5.3 Land cover for La Arenosa catchment by IGAC (2007b).

LAND COVER HA % ROOT DEPTH (cm)

Natural forest 32,24 3,26 150

Crops 726,35 73,33 80

Pastures 75,83 7,66 60

Stubbles 154,45 15,59 100

Baresoil 1,62 0,16 0

Figure 5.6 Land cover map of La Arenosa Catchment elaborated by IGAC (2007b).


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118

5.3.1 Geotechnical parameters

Cohesion (c). According to the studies elaborated by Mejía & Velásquez (1991),

cohesion for the soils of La Arenosa ranges from 5 kPa to 12.5 kPa, in accordance with

values reported in literature for silty sands originated from weathering profiles of

granitic rocks. For soils derived from alluvial deposits, composed of sands and

boulders, the cohesion was assumed as 1kPa.

Soil friction angle (ä). Soil friction angle for the residual soils in La Arenosa

catchment range from 15.95° to 23.63° according to the laboratory tests carried out by

Mejía & Velásquez (1991). For the alluvial deposits, there are no geotechnical

laboratory tests; however, they have very gently slopes considered not critical for the

stability model component, then higher values were assumed due to the high content of

boulders and gravels.

Unit weight of saturated soil (å). According to the laboratory test carried out by Mejía

& Velásquez (1991), unit weight of saturated soil ranges from 18 kN/m3 to 18.8 kN/m3,

and dry unit weight ranges from 14.3 to 14.9 kN/m3. For the model, saturated values

are used.

Soil thickness (Z). A distributed soil thickness map from slope gradient was built.

According to the Catena assumed, there is a link between the thickness of the soil and

the slope angle. For the site evaluated in field work, values of the soil depth were

compared with the slope inclination and all data were plotted and interpolated.

Soil thicknesses range from 1 m to 2.7 m, in which thin soil was found on the narrow

ridges, and thick soils and colluviums accumulated at the bottom of the valleys (Fig.

5.7).

5.3.2 Hydrological parameters

The hydrological parameters were obtained using the Hydraulic Properties Calculator

of the SPAW model developed by Agricultural Research Service (ARS) of the United

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119

States Department of Agricultural (USDA), according to the soils properties and texture

described of the map soils provided by IGAC (2007a).

Because for each soil association, the study area have more than one soil profile with

different size particles; weighted averages of each profile were carried out as the

percentage that each profile represents in each one of these units.

Figure 5.7 Soil thickness map of La Arenosa Catchment.

Maximum static storage (S1max). The maximum static storage is the weighted

averages of the maximum static storage of each soil horizon. Maximum static storage

corresponds to the difference between permanent wilting point and field capacity, along

with root depths (Table 5.3).


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Root depth was obtained from the Land Cover map (IGAC, 2007b) and permanent

wilting point and field capacity using the SPAW software. Figure 5.8 shows the

distribution of the maximum static storage for La Arenosa catchment. Values range

from 0 to 136 mm.

Maximum gravitational storage (S3max). A similar procedure to the maximum static

storage was carried out for gravitational water storage. The maximum gravitational

water storage corresponds to the difference between saturation and field capacity,

along the soil thickness (Fig. 5.9).

Saturated hydraulic conductivity (Ks). It describes the water movement through

saturated media. The initial value for the saturated conductivity was obtained using

SPAWL software and weighted average, according to the size particle of each soil

horizon. The secondary conductivity is considered into the correction factors.

Figure 5.8 Maximum static storage for La Arenosa catchment.

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Saturated hydraulic conductivity of subsoil (Kp). There is not reported data in the

catchment for the saturated hydraulic conductivity of the subsoil, for this reason, the

permeability of saprolite derived from granitic rocks proposed in the literature was

used.

Figure 5.9 Maximum gravitational storage for La Arenosa catchment.

Table 5.4 Soil parameters of La Arenosa catchment.

SOIL PARAMETER ALLUVIAL

SOIL

RESIDUAL

SOIL (YAE1)

RESIDUAL

SOIL (YAF2)

Cohesion (kPa) 1 5 5

Soil friction angle (°) 34 24 24

Unit weight of saturated soil (kN/m3) 20 18 18

Saturated hydraulic conductivity (cm/h) 0.479 1.96 1.96

Sat. hyd. conductivity of subsoil (cm/h) 0.0799 0.0799 0.0799


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122

Evapotranspiration (EVP). Evapotranspiration time series can be either estimated or

measured for input into the model. For the study area, real evapotranspiration data was

not obtained; and, therefore, it was estimated using the equation of CENICAFE

(Jaramillo, 1989) for potential evapotranspiration:

/>� = 4.658(i1.11!ê¯ë) (mm/day)

In which DTM is the elevation in meters. Figure 5.10 shows the potential

evapotranspiration.

Figure 5.10 Potential evapotranspiration map for La Arenosa catchment.

5.4 Historical rainfall and stream flow data

A time series is used to define the rain input values. The rainfall amount is reported

hourly from the interpolation between the Calderas rain gauge located in a close

proximity to the upper part of the catchment, and the La Arenosa rain gauge located in

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the lower part of the catchment. Figure 5.11 shows the location of rain gauges station

and stream level station for La Arenosa catchment.

Figure 5.11 shows the time series of rainfall for the Calderas and La Arenosa rain gauges.

Hourly precipitation from 2007 to 2012 was used to calibrate and validate the

hydrological component of the model (Figures 5.12 and 5.13).

Figure 5.12 Hourly rainfall of Calderas rain gauge between august 2007 and December 2012


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124

Figure 5.13 Hourly rainfall in La Arenosa catchment for the period August 2007 - December 2012

The landslide scar inventory concerning the September 1990 rainstorm event

elaborated by Mejía & Velásquez (1991) was used for the calibration of the

geotechnical model. For this period, the hourly rainfall information from July 01, 1990 to

September 30, 1990 was used. These data were provided by ISAGEN (Hydropower

Energy Company), which operates the rain gauge stations in the catchment.

Naturalized flows for the same precipitation time period were estimated. La Arenosa

stream received the discharge provided by Calderas Hydropower Energy Plant of

ISAGEN, water that is provided by the Calderas river. The flow discharge from the

energy plant is just 40 meters upstream the only stream flow gauging of the catchment.

This gauging station on La Arenosa channel includes an automatic water-level sensor;

however, there is not a rating curve. There are just a few given measurements of

discharge at few river levels. Using this information and considering the discharge

coming from the Calderas hydropower plant according to the energy generation rating

curve, an effort was made to obtain the naturalized stream flow series. Nevertheless, it

was not possible because of the given measurements and problems observed in the

rating curve of the Hydropower Plant.

Using rainfall data available, the hydrological lumped model TETIS, which has the

same conception of SHIA model, was implemented for La Arenosa catchment. The

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parameters of the hydrological model were estimated using regional information from

Calderas catchment, which is a neighboring river with similar characteristics. The

model was calibrated using a long term balance and the flow-duration curve using the

software HIDROSIG implemented by CORNARE for the catchment´s region of. Figure

5.14 shows the naturalized flow discharge obtained for La Arenosa. The long term

balance was calculated in the following way, where P and E are the mean precipitation

and evapotranspiration along the catchment.

( ) ( )[ ]∫ −=Área

dAyxEyxPeDisch ,,arg

Figure 5.14 Hourly stream flow time series simulated of La Arenosa stream station between august 2007 and December 2012

5.5 Geomorphological and correction parameters of the model

5.5.1 Geomorphologic Kinematic Wave (GKW) parameters.

Table 5.5 shows the parameters proposed by Frances et al., (2007) for a non-

stationary stream flow velocity using the Geomorphological Kinematic Wave (GCW)

and adopted for the SHIA_Landslide model in La Arenosa catchment.

5.5.2 Correction parameters

Despite of the reasonable good quality of the available set of parameter values, the

high variability of the natural processes determines the unfeasibility of obtaining an

exact parameterization in a deterministic way.


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126

Soil and hydrological parameters were adjusted using the correction factors to find the

effective parameters in order to reproduce the hourly naturalized stream flows. It is

important to highlight that the correction parameters being specific for the target area,

due to parameter values are conditioned for the hydrological simulated event, for the

observed data being simulated, for the errors of the data used, and for the temporal

and spatial scales. All these conditions vary with each catchment.

Table 5.5 Geomorphological Kinematic Wave parameters for SHIA-Landslide

Propagation

parameter

Range Adopted

k1 0.5 -0.75 0.6

q 0.65 - 0.8 0.75

�� 0.5 – 5.75 3.26

�� 0.34 - 0.55 0.5

�� 0.05 – 0.2 0.2

�� 0.5–50.0 20

� 0. 5 – 2.75 1.26

�� 0.025 – 0.07 0.047

� 0.125 – 0.18 0.1667

Table 5.6 summarizes the correction parameters for the linear and nonlinear approach

used to model the hillslopes pore water pressure and to perform the stability analyses

during the rainfall event of September 21, 1990.There is general agreement among the

nonlinear and linear parameter sets. Only for the subsurface flow nonlinear model

requires higher values.

5.5.3 Initial conditions

The initial conditions correspond to the thresholds of accumulated drainage area,

outflow velocities, the initial water content for each tank, and the grid cell position of

control point.

The minimum accumulated drainage area to form a rill or ephemeral channel, and the

minimum area to form a perennial channel was selected according to field work and

DEM analysis.

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For both version of the model, it is necessary to initiate it with starting values of

velocities for each level of the flows: overland runoff, subsurface flow and stream flow.

For the nonlinear version these values are only considered during the first time interval

for the first iteration; after that, the velocities are calculated in the iteration process

using the last value obtained for each grid cell. On the other hand, for the linear

version, velocity is conserved constant during the modeling.

Table 5.6 Correction parameters used for the model

Parameter Correction Min Max Nonlinear Linear

S1max C1 0.1 1.5 0.1 0.1

EVP C2 0.5 2.0 2 2

Ks C3 0.0 1.0 4 4

Kp C4 0.0 2.0 0.5 0.5

Kpp C5 0.0 10 0 0

v2 C6 0.1 2.0 0.025 0.025

v3 C7 1.0 1000 450 1.2

v4 C8 1.0 1000 50 50

v5 C9 0.5 1.5 1 1

C C10 - - 1.45 1.45

ä C11 - - 1.15 1.15

Zs C12 - - 0.8 0.8

S3max C13 0.1 1.5 1.0 1

FS C14 - - 1 1

For the initial water content in the hydrological tanks a considerable warming period of

2 months previous to the target period was used for all the simulations, with reasonable

values for the initial water content for each tank. Table 5.7 shows drainage thresholds

areas and initial water content of the tanks.

5.6 Calibration procedure

Hydrological calibration was carried out in the traditional performance identifying how

well the model can reproduce observed data. SHIA_Landslide calibration was carried

out by a manual procedure, adjusting the model parameter values until the output of

the model closely matches the observed data. The adjustment of the parameter values

was made by a trial and error process. The calibration process carried out determines


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the “best fit”, although different results could be obtained by different modelers. The

adjusting process by hand was selected because it allows to perform a sensibility

analysis of the model and fully checking and understanding of the model structure.

Table 5.7 initial condition

PARAMETER VALUE

Ephemeral channel 1000 m2

Perennial channel 1.000.000 m2

Overland runoff 0.1 m/s

Subsurface flow 0.0002 m/s

Groundwater flow 0.000005 m/s

Stream flow 1 m/s

Static storage 100 mm

Surface storage 0 mm

Sub surface storage 50 mm

Groundwater storage 100 mm

Stream channel 0.4 m3

Hydrological and geotechnical calibration were conducted for different periods, since

there was no coincidence of good quality data of rainfall (hourly temporal resolution)

and landslide inventory maps for simultaneous periods (Table 5.8). For the period 2007

to 2012, there is an hourly rainfall database for two rain gauges in the catchment;

however, there is not landslide inventory database. On the other hand, for the period of

September, 1990, when a landside inventory database is available, hourly rainfall

information is just available for a very short time period. The antecedent rainfall

information for 1990 is available in a daily temporal resolution; to distribute daily rainfall

information to hourly resolution, the rainfall diurnal cycle obtained for the La Arenosa

and Calderas rain gauge stations was used.

Table 5.8 Calibration and validation periods selected. Maximum rainfall intensity (MRI).

Periods Initial date Final date Test MRI

Period1

01/03/2011,

00:00 h

31/05/2011

24:00 h

Hydrological

calibration

60 mm/h

Period2 01/06/1990,

00:00 h

30/09/1990,

24:00 h

Geotechnical

calibration

90 mm/h

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Period 3 01/09/2012,

00:00 h

30/11/2012,

24:00 h

Hydro. &

Geotech

Validation 1

35 mm/h

Period 4 01/09/2007,

00:00 h

30/11/2007,

24:00 h

Hydro. &

Geotech

Validation 2

70 mm/h

The Mar-May/2013 period was used for the calibration of the hydrological component,

and posterior the Jul-Sep/1990 period was used to calibrate the geotechnical

component. The Sep-Nov/2012 and Sep-Nov/2007 periods were used to validate both

components of the model.

It is important to consider the following aspects about the calibration and validation

periods: (i) For the period of the September 21, 1990 rainstorm, there is not observed

streamflow for La Arenosa. It means that it is not possible to compare the simulated

streamflow; (ii) For the September 21, 1990 rainstorm there was only one rainfall

gauge station: La Arenosa. And the temporal resolution of this station was daily. Only

for a small period of time during the September 21 was it possible to get hourly

information. For this reason, it was necessary to distribute the daily rainfall into an

hourly resolution using the annual diurnal cycle of La Arenosa and Calderas rainfall

station for the period between 2007 and 2012. This limitation impacts the results,

because the model is simulating a similar rainfall value obtained from one rain gauge

station for the entire catchment, and secondly the adjusting of the temporal resolution

eliminate the rainfall peaks that could occurred in the previous days of the rainstorm;

(iii) Finally, the maps used for the construction of the geotechnical and hydrological

parameters (land use, land covers) do not correspond to 1990, when the event

occurred. This information is posterior to the landslide occurrence, and possible

changes that occurred after this date obviously affect the results obtained for the

model.


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5.6.1 Hydrological calibration.

Model calibration for the hydrological component was conducted for the period from

March to May of 2011. Figures 5.15 and 5.16 show the rainfall data for these periods.

The calibration results for La Arenosa discharge for nonlinear and linear vertion are

shown in Figure 5.17 and 5.18, respectively. They illustrate the simulated discharge

provided for linear and nonlinear SHIA_Landslide compared to the stream flow of La

Arenosa for the calibration period. Overall, the simulated hourly flows resulting from the

nonlinear and linear SHIA_Landslide agreed very well with La Arenosa stream flow.

Both model approaches predicted flow peaks and slightly under-predicted low flows.

Figure 5.15 Rainfall time series of Calderas rain gauge for the period March and May 2007

Figure 5.16 Rainfall time series of La Arenosa rain gauge for the period March and May 2007.

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Figure 5.17 Results using nonlinear SHIA_Landslide of simulated hourly discharges at the calibration flow gauge station La Arenosa during the calibration period compared with the discharges obtained for La Arenosa stream.

Comparison of predicted and discharge data of La Arenosa suggest that the nonlinear

model gives good prediction of the landslide hydrology. Most of the peaks are

simulated for the model with a good time precision. For the highest peaks the model

slightly overestimates the stream flow.

The root mean square error (RMSE = 0.292) and the Nash – Sutcliffe coefficient

(NS=0.852) show good correlation between simulated and La Arenosa stream flows.

The water balance shows a low negative difference (WB= -1.59 %).

Figure 5.18 Results using linear SHIA_Landslide of simulated hourly discharges at the calibration flow gauge station La Arenosa during the calibration period compared with the discharges obtained for La Arenosa stream.

For the linear version, the simulation is acceptable with values of RMSE (0.347) and

NS (0.791), slightly less than for the nonlinear version. Moreover, the water balance


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shows similar negative values (WB = -1.61%). Although the linear model simulates

adequately the event, it simulates recession curves substantially lower when compared

to La Arenosa stream flows.

Figures 5.19 and 5.20 show the simulated perched water table level using nonlinear

and linear model for the calibration period evaluated in a slope grid cell with an

accumulated drainage area of 800 m2, it means 8 slope grid cells flow through this grid

cell. During all the simulated period, perched water table conserve a level around 0.2

m, and the maximum value was 0.6 - 0.7 meters, correlated to a rainfall peak in the last

week of April.

For the linear model, the values in general decrease, the two remarkable peaks are

lower, and the valleys get values of zero for short time periods. Evaluating the slope of

the peaks, it can be seen that the linear version obtains a faster positive pore pressure

response of the soils, increasing and reducing the peaks quicker than the nonlinear

version.

Figure 5.19 Nonlinear simulated perched water table level for an slope grid cell (accumulated area = 800 m2) of La Arenosa for the period between March and May 2007.

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Figure 5.20 Linear Simulated perched water table level for an slope grid cell (accumulated area = 800 m2) of La Arenosa for the period between March and May 2007.

5.6.2 Geotechnical calibration.

The geotechnical component of the model was calibrated by overlying the digital scar

landslide inventory map of the September 1990 event to the map obtain from the

simulations. We assume that the scar identifies where the landslide starts. The

calibration of soil properties against a map of scars obtained from aerial photograph

interpretation allows calibration of effective values for soil parameters in basin scales

models (Guimaraes et al., 2003).

Figure 5.21 shows the rainfall time series for the period analyzed. A period of three

months was selected to assure that the initial conditions previous to the event are

reach previously to the target time.

Figure 5.22 and 5.23 show the simulated discharge for the September 1990 rainstorm

for the nonlinear and linear vertion of the model. According to SHIA_Landslide, the

channel discharge flow at the point of La Arenosa station was 55 m3/s for the nonlinear

version, and a flow discharge of about 35 m3/s for the linear version. It means more

than 30 times the base flow of La Arenosa. It is important to note that this discharge

only considered the water flow; according to the description provided by Hermelin et al.

(1992), the event was characterized by a huge volume of sediments, estimated by the

authors in 1.5 Mm3. Considering this volume, the total water and sediments discharge

increased considerably.


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Figure 5.21 Rainfall from La Arenosa rain gauge for the period July to September 1990.

Figure 5.22 Stream flow simulated for nonlinear SHIA_Landslide for the period July to September 1990. Observe discharge is not available to compare with simulated data.

Figure 5.23 Stream flow simulated for linear SHIA_Landslide for the period July to September 1990. Observe discharge is not available to compare with simulated data.

Figure 5.24 shows the nonlinear simulated perched water table level for the September

1990 event evaluated in the same slope grid cell used for the hydrological calibration,

which has an accumulated drainage area of 900 m2. Perched water tables reached a

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peak of 1.3 m during the most intense period of the rainstorm. The peak obtained for

the linear version (Figure 5.25) is higher than the peak reach for the nonlinear version

(Figure 5.24). For the nonlinear version, there is a minimum level that is conserved for

the perched water table close to 0.1m, even for periods with very low rainfall,

Figure 5.24 Perched water table level simulated for nonlinear SHIA_Landslide for the period July to September 1990 for a slope grid cell (800 m2).

Figure 5.25 Perched water table level simulated for linear SHIA_Landslide for the period July to September 1990 for a slope grid cell (800 m2).

Figure 5.26 shows the matrix 1, which corresponds to the susceptibility map for La

Arenosa catchment. Yellow areas are the potential unstable areas for landslides

triggered by rainfall, which correspond to 52% of the total area. 92% of the scars of the

September 1990 event are located into these areas, the rest 8% corresponds to an

induce error in the hazard map (Table 5.9), due to there is no way to predict this small

percentage of landslides in the next step of the model, due to the fact these areas has

been identified as unconditionally stable by the model.


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Figures 5.27 and 5.28 shows the matrix 2 provided for the nonlinear and linear version

of SHIA_Landslide respectively, which correspond to the final product, providing the

areas with landslide occurrence triggered by rainfall.

The areas prone to rainfall-induced landslides change considerably depending on the

model used. For the nonlinear version (Fig. 5.27) 23,456 grid cells that fail during the

rainstorm were identified, which amount to 24% of the total catchment area. For the

linear version (Fig. 5.28) the model identified 34,268, which correspond to 35% of the

total catchment area (Table 5.10). Comparing with the nonlinear version, it means an

overestimation of 11%.

Figure 5.26 Susceptibility map obtain for SHIA_Landslide.

Table 5.9 Susceptibility grid cells classification by SHIA_Landslide

Susceptibility map Grid cells Percentage (%)

Unconditionally stable 45,852 46.7%

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137

Unconditionally unstable 1,618 1.6%

Potentially unstable 51,176 51.87%

Total 98,646 100%

5.6 Validation

Considering that validation provides a direct measure of the degree of uncertainty that

may be expected when the model is applied to conditions outside of the calibration

series, several verification tests were applied to evaluate the performance of the model.

Two representative validation tests are presented. In the first test, data from September

2012 to November 2012 were used and in the second test data from September 2007

to November 2007 were used.

Figure 5.27 Areas with landslide occurrence triggered by the September 1990 rainstorm simulated by nonlinear SHIA_Landslide.


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Table 5.10 Hazard map: landslides triggered by rainfall for linear and nonlinear SHIA_Landslide for the period July to September 1990. Partial percentage is estimated according to the total number of potentially unstable grid cells (51,176), and total percentage is estimated according to the total number of grid cells (98,646).

Nonlinear Linear

Unstable 23,456 34,268

Partial percentage 46% 67%

Total percentage 24% 35%

Figure 5.28 Areas with landslide occurrence triggered by the September 1990 rainstorm simulated by linear SHIA_Landslide.

Figures from 5.29 to 5.36 show rainfall times series, the discharge simulated compared

to the La Arenosa discharge, and the landslide occurrence triggered by rainfall map for

each of these periods. Landslide susceptibility map does not have any change due to it

only depends of the geotechnical parameters, such as slope, cohesion, friction angle,

soil unit weight, which are assumed that does not change during the simulated

rainstorm.

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Overall, the simulated hourly flows agreed well with La Arenosa stream flows for both

nonlinear and linear SHIA_Landslide. Despite occasional discrepancies for peak flows,

most peaks are predicted correctly.

For the nonlinear version, the RMSE is 0.297 and NS efficiency 0.724. The water

balance decrease compare to calibration value (-0.568). For the linear version, values

decrease conserving good correlation values, RMSE is 0.322 and NS is 0.677. The

water balance was -0.62%.

Figure 5.29 Rainfall time series for La Arenosa rain gauges.

Figure 5.30 Rainfall time series for Calderas rain gauges.


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Figure 5.31 Simulated discharge from nonlinear SHIA_Landslide compared to La Arenosa discharge.

Figure 5.32 Simulated discharge from linear SHIA_Landslide compared to La Arenosa discharge for the period September to November 2012.

For the perched water table simulated for SHIA_Landslide, results are consistent with

the validation (Fig. 5.33 and 5.34). The small peaks show lower values for the

nonlinear version, but the highest peak has similar maximum values for both versions.

Similar to the calibration procedure, the nonlinear version conserve higher minimum

values than the linear version.

Landslide areas identified as unstable due to the simulated rainstorms were also used

to validate the geotechnical component of the model. During the validation periods

there were no reported landslides, so the hazard map should have reported no

landslides or unstable grid cells. The cells identified for the model as unstable after the

simulated rainstorms should be understood as an error of the model.

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Figure 5.33 Nonlinear Simulated perched water table level slope grid cell (Accumulated area = 800 m2)

Figure 5.34 Linear Simulated perched water table level slope grid cell (Accumulated area = 800 m2)

The results obtained for the hazard map show a considerable increase of the grid cells

that fail due to the simulated rainstorm. The Figures 5.35 and 5.36 show the maps

obtained for the nonlinear and linear version, respectively. The grid cells identified as

unstable for the nonlinear model after the rainstorm is 1,091, and this number for the

linear model increase to 3,272 (Table 5.11). However, for both cases, values are very

low compared to the 98,646 grid cells that the catchment has. It means only an error

for the model of 1.1% for the nonlinear version and 3.3% for the linear version.

Table 5.11 Simulated unstable grid cells for linear and nonlinear SHIA_Landslide Landslide for the period September to November 2012. Total percentage corresponds to the number of potentially unstable grid cells (51,176)

Nonlinear Linear

Unstable 1,091 3,272

Percentage 2.13% 6.39%


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A second validation period was used for the period between September and November

2007. Figures 5.37 and 5.38 show La Arenosa and Calderas rainfall data used. Figures

5.39 and 5.40 show La Arenosa simulated stream flow for the nonlinear and linear

version of SHIA_Landslide. Result indicates an acceptable correlation; however, there

is a tendency to maintain lower flow levels during all the period. The simulated flows

from the nonlinear SHIA_Landslide agreed better with La Arenosa stream flows in the

middle and high flow range.

Figure 5.35 Areas reported for nonlinear SHIA_Landslide with landslide occurrence triggered by rainfall for the period September to November 2012.

The nonlinear SHIA_Landslide shows better performance than the linear version. The

RMSE for the nonlinear version is 0.451, NS is 0.506, and water balance is -0.458%.

For the linear version, the RMSE is 0.438, NS is 0.506, and water balance is -0.618%.

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Figure 5.36 Areas reported for linear SHIA_Landslide with landslide occurrence triggered by rainfall for the period September to November 2012.

Figure 5.37 Rainfall time series for La Arenosa rain gauges Landslide for the period from September to November 2007.


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Figure 5.38 Rainfall time series for Calderas rain gauge for the period from September to November 2007.

Figure 5.41 and 5.42 show the perched water table results. The perched water table

simulated for the nonlinear and linear version of SHIA_Landslide are coherent with the

results obtained for the calibration and previous validation period. The nonlinear model

shows values slightly higher for periods with low rainfall, this characteristic is probably

associated to nonlinear model flow velocities is function on tank water height, it means

when water height decreases the velocity decreases as well.

Figure 5.39 Simulated discharge according to nonlinear SHIA_Landslide compared to La Arenosa Discharge for the period from September to November 2007.

Figure 5.43 and 5.44 shows the hazard maps for the nonlinear and the linear version of

SHIA_Landslide. Unstable grid cells increase from 691 in the nonlinear version to

1,618 in the linear version (Table 5.12).

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Figure 5.40 Simulated discharge according to linear SHIA_Landslide compared to La Arenosa Discharge Landslide for the period from September to November 2007.

Figure 5.41 Simulated perched water table level using nonlinear SHIA_Landslide for the period from September to November 2007.

Figure 5.42 Simulated perched water table level using linear SHIA_Landslide for the period from September to November 2007.

Table 5.12 Simulated unstable grid cells for linear and nonlinear SHIA_Landslide Landslide for the period from September to November 2007. Total percentage corresponds to the number of potentially unstable grid cells (51,176)

Nonlinear Linear

Unstable 691 1,618

Percentage 1.35% 3.16%


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Figure 5.43 Areas simulated by nonlinear SHIA_Landslide with landslide occurrence triggered by rainfall for the period from September to November 2007.

Figure 5.44 Areas simulated by linear SHIA_Landslide with landslide occurrence triggered by rainfall for the period from September to November 2007.

Chapter 6

RESULTS & DISCUSSION

6.1 Comparing linear and nonlinear model

A comparative analysis between linear and nonlinear SHIA_Landslide for all four

calibration and validation tests was performed with the intent to examined which model

would provide better predictions. The results from the four tests are summarized in

Table 6.1.

In terms of the hydrological component, the nonlinear model was the best model, with

the highest NS efficiency and lowest RMSE values.

Concerning the geotechnical component, both approaches identified the same number

of observed scar grid cells; however, the linear model simulated 45% more incorrectly

unstable grid cells. The difference resides on the total number of unstable grid cells

identified. The nonlinear SHIA_Landslide identified a number of 23,456 grid cells as

unstable, 46% of potentially unstable cells, and the linear SHIA_Landslide identified a

total number of 34,268 grid cells as unstable, 67% of potentially unstable cells. That

means an increase of 21.13% of potentially grid cells identified as unstable.

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Furthermore, considering that both approaches identified similarly the actual scars grid

cells, it means this additional percentage corresponds to erroneous grid cells identified

as unstable, or cells that actually did not fail.

Table 6.1 Comparison between nonlinear and linear SHIA_Landslide. Maximum rainfall intensity (MRI).

Test RMSE NS

efficiency

Water

balance

Unstable grid

cells induce by

rainfall

Calibration 1 (Mar-May 2011)

(MRI = 60 mm/h)

Nonlinear 0.292 0.852 -1.59 2899

Linear 0.347 0.791 -1.61 3948

Calibration 2 (Jul-Sep 1990)

(MRI = 90 mm/h)

Nonlinear - - - 23.456

Linear - - - 34.268

Validation 1 (Sep-Mon 2012)

(MRI = 35 mm/h)

Nonlinear 0.297 0.724 -0.568 1091

Linear 0.322 0.677 -0.620 3272

Validation 2 (Sep-Nov 2007)

(MRI = 70 mm/h)

Nonlinear 0.451 0.506 -0.458 691

Linear 0.438 0.506 -0.618 1618

One of the disadvantages of nonlinear model is that the parameter-fit process is

iterative, consuming valuable time for an early warning system. To estimate the

velocities of the overland runoff, subsurface flow, and stream flow, the nonlinear

process must start with a set or user-supplied starting values. SHIA_Landslide then

tries to find the correct velocities by adjusting the values provided using velocities

equations that are function of the transversal flow section. All this process takes

additional time.

For the La Arenosa catchment, composed by 98,646 grid cells with a simulation period

of three months, which means a number around 2,200 hours, the nonlinear model

takes 5 minutes, whereas the linear model takes about 1 minute for the same

conditions. The nonlinear model obviously requires more time to execute, due to the

area-velocity iterative process to arrive at the velocity fitting parameter. The linear

model is approximately 5 times faster than the nonlinear model. Although time is a

valuable factor for early warning system, the time used for the nonlinear model is

reasonable for an early warning system. The results suggest that non-linearity

increases the predictions of the model, conserving appropriate time running.

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Considering a much better performance of the nonlinear model, the analysis of the

result and discussion in the next sections are based on the result of the nonlinear

model.

6.2 Spatial performance of the model

The model proposed in this study matches the rainfall and landslide occurrence in the

1990 event in the La Arenosa catchment. Model evaluation was carried out through the

analysis of predicted landslides with respect to the distribution of triggered landslides

on the September 21, 1990 event in the La Arenosa catchment.

Before analyzing and evaluating model performance, it is important to highlight that

although Mejía & Velásquez (1991) reported 699 landslides in the La Arenosa

catchment, only 350 landslides are mentioned in the landslide inventory maps

presented by Mejía & Velásquez (1991) and INTEGRAL (1990). To evaluate the model

performance, only the scars of landslide inventory maps elaborated by Mejía &

Velásquez (1991) and INTEGRAL (1990) were rasterized. Although the inventory maps

consisted of landslides polygons including the depletion and accumulation zone, most

of the area actually corresponded to displaced material over areas which did not fail.

However, considering only the landslide scars will surely increase the error of the

model associated to areas classified correctly by the model as unstable that

erroneously appears as stable in the landslide scar maps.

The model performance is related to the capacity of predicting a relatively small

number of unstable pixels. The 350 landslide scars corresponds to 2,194 pixels, just

2.2% of the study area. Although INTEGRAL (1990) estimated that a 16% of the entire

catchment was impacted by landslides during the September 21, 1990 rainstorm, there

is only spatial certainty of just this 2.2%.

An ideal model performance simultaneously maximizes the agreement between known

and predicted landslide locations and minimizes the area outside the known landslides


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predicted to be unstable. Spatial performance was evaluated for the susceptibility map

and hazard map independently in the following way:

6.2.1 Susceptibility map

The first product of the model corresponds to a susceptibility map, where

unconditionally unstable and unconditionally stable areas are identified previously to

the rainfall event. The stability condition of these areas is a function of cohesion, friction

angle, weight unit of the soil, and failure surface depth, and is independent of rainfall.

This elimination of grid cell for unconditionally unstable and unconditionally stable

areas is not considered for the analysis during the rainfall event.

Unconditionally unstable areas correspond to 1.64% in La Arenosa catchment. Most of

them are located in the lower part of the catchment on the channel bank formed by

alluvial sediments. These unstable areas are originated by the fluvial erosion of the

stream over their banks, and it is not a direct consequence of rainfall occurrence.

Another important source is “orphan cells”, unstable cells that are surrounded by stable

cells. They correspond to specific cells where the DTM shows steep slopes by the

presence of natural or man-made cut slopes.

Unconditionally stable areas make up 46.48% of the total catchment. These areas are

located in the lower part of the basin formed by alluvial sediments with gently slopes.

They are also found along the valleys bottom and crests, characterized by flat surfaces.

These areas are stable under rainfall events due to very low slope angles, where the

shear stress does not exceed the shear strength of the soil material.

Potentially unstable areas correspond to 51.8% of the total area of the catchment. They

correspond to areas which could be affected by landslide occurrence under rainstorm

and that will be checked during the rainfall event modeling. This previous step of the

model allows saving running time, which is essential in an early warning system,

focusing the next step of the model only on potentially unstable areas

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151

These potentially unstable areas are located in the upper and middle part of the slopes,

moderately to extremely steep. Comparing the susceptibility map with the landslide

scars inventory, 92% of the scar pixels are located into these potential unstable areas.

Only 8% of scar cells are erroneously identified by the model as unconditionally stable.

These areas were checked in the DTM and most of them corresponded to boundaries

around potentially unstable areas, where, during the digitalization process, landslide

scars, were extended and included one or, at most, two unconditionally stable

neighboring pixels. Three reason could explain this problem (i) a digitalization problem

during the landslide inventory mapping; (ii) these landslide areas are originated by the

erosion processes of displaced material from neighboring unstable areas or by

propagation of the failure surface, not considered for the model; or (ii) particular

conditions which are nor represented by the DTM, probably human intervention, which

is not considered in the model.

6.2.2 Hazard map

The second and most important product of the model corresponds to the matrix 2,

landslide occurrence by rainfall. It is the result of the stability conditions of the slopes

under perched water table and pore water pressure changes generated by rainfall.

These stability conditions are checked every time interval for all potential pixels

identified in the susceptibility map.

The model replicates with very good reliability the activity process observed during field

surveys carried out by Mejía & Velásquez (1991). For the La Arenosa catchment,

51,176 pixels are potentially unstable under rainfall conditions. It corresponds to 55.3%

of the total watershed. From this area, 77% scar pixels were correctly predicted by the

model as unstable areas, and 1.2% scar pixels were classified as unconditionally

unstable areas. 21.8% of scar pixels were erroneously classified by the model as

stable. This value includes 8% of pixels erroneously classified as stable from the


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susceptibility map, so in any case it was not possible to identify these cells as unstable

during the rainstorm.

6.3 Temporal performance of the model

A correct estimation of the timing of failure is constrained by the capability of the

hydrological components to simulate pore-pressure response to hydrological forcing

(Carrara et al., 2008).

In order to evaluate the temporal performance of the model, landslide occurrence was

checked hourly during the rainstorm to compare it with the time reported for landslides.

Rain started at 20:00, and 208 mm fell in the next three hours. Landslides were

reported during the night of September 21, and according to Mejía & Velásquez (1991),

most landslides occurred during the second hour of the rainstorm, but there is not any

detailed temporal record.

At 19:00 local time, 2.57 % of unstable grid cells identified for the model have already

failed. In the next hour, at 20:00, 29.4% failed, reaching a total percentage of 31.9% of

unstable grid cells. At 21:00, 40.3% failed, with a total percentage of 72.3%, and finally

at 22:00, the last 27.7% of unstable grid cells failed, reaching 100%.

Considering only the pixels correctly classified by the nonlinear model as unstable

during the rainstorm event, the occurrence of the landslides during the rainfall peak

was: (i) at 19:00 the model showed that 2.4% of the total scars pixels correctly

classified has already failed, (ii) at 20:00, after the first hour of the rainstorm peak,

there was an increase of 44.9% of landslides, reaching a total of 47.3%, (iii) at 21:00,

after the second hour, failure rate increase to 88.3%, which means 41% of pixels

correctly classified fail during this hour; and (iv), at the end of the rainfall peak, at

22:00, it gets the 100 % of the scar pixels correctly classified as unstable. Figure 6.1

shows the temporal evolution of landslide.

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153

Using an hourly temporal scale, the model results reproduced coherently the time of

the occurrence, in which most landslides were reported during the first and second

hour of the rainstorm. The saturation processes and the pore pressure rose, leaning to

instability conditions match with the intensity of the rainfall.

6.4 ROC analysis and comparison

To assess the accuracy of the model’s performance, several previous studies have

focused on the rate of successfully predicted landslide, while ignoring the component of

stable areas erroneously classified as unstable, false positives. To reach a balanced

analysis, a quantitative performance evaluation of SHIA_Landslide was accomplished

through GIS-based, map overlay operations, and by calculating Receiver Operating

Characteristic (ROC) values.

ROC analyses have been extensively used in recent years for comparative evaluation

of landslide models. A receiver operating characteristics (ROC) analysis is a technique

for visualizing, organizing and selecting classifiers based on their performance; it has

been applied for extended for use in signal detection theory to depict the tradeoff

between hit rates and false alarm rates classifiers, and many other fields such as

medical diagnostic testing, data mining, and evaluating and comparing algorithms

(Fawcett, 2006).

19:00 �2,4% (2,4%)

20:00 �44,87% (47,27%)


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154

21:00 �41,04% (88,31%)

22:00 �11,69% (100%)

Figure 6.1 Temporal analysis of model performance for the September 21, 1990 rainstorm. Considering only cells correctly classified as unstable for the nonlinear model.

ROC analysis for assessment of performance of landslide models is based on the fact

that each grid cell could be mapped using actual classes, called positive and negative

class labels, according to landslide inventory databases, and predicted classes, called

true and false class labels, produce by a model. There are four possible outcomes

(Figure 6.2). If the grid cell is positive and it is classified as positive, it is counted as a

true positive(the unstable area correctly classified as unstable); if it is classified as

negative, it is counted as a false negative (the unstable area erroneously classified as

stable). If the grid cell is negative and it is classified as negative, it is counted as a true

negative (the stable area correctly classified as stable); and if it is classified as positive,

it is counted as a false positive (the stable area erroneously classified as unstable).

Figure 6.2 ROC analysis matrix.

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155

The model correctly predicted 77% of observed unstable areas and 76% of observed

stables areas (Table 6.2). In contrast, the model erroneously predicted93% of unstable

grid cells provided for the model when actually landslide did not occur over them, and

0.52% of stable grid cells provided for the model where landslide indeed occurred

(Figure 6.3).

Table 6.2 ROC analysis for La Arenosa rainstorm event.

Figure 6.3 ROC analysis map for La Arenosa rainstorm event.

Classifier SHIA_LANDSLIDE

Pixel Area (m2) Total percentage (%) Partial percentage (%)

Unstable areas

TP 1.689 168.900 1.71% 76.98%

FN 505 50.500 0.51% 23.02%

Stable areas

TN 73.067 7.306.700 74.06% 75.68%

FP 23.385 2.338.500 23.70% 24.22%


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A great advantage of ROC analysis is that several metrics have been defined for

evaluating models performance. During the performance evaluation sensitivity,

specificity, false alarm, and precision of the simulations were calculated and used for a

quantitative comparison.

The true positive rate, also called hit rate, sensitivity, or positive accuracy, is defined

as the ratio between true positives and the total actual positives; the true negative rate,

also called specificity or negative accuracy, is the ratio between true negatives and

the total actual negatives; the false positive rate, also called false alarm rate or

negative error, is defined as the ratio between false positive and the total actual

negatives; finally the positive predictive value, also called precision, is the ratio

between true positives and the total predicted positives.

Hit rate (%)

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ï¡Ô��g�0�Ø¡g�(Ó�) = ìß¯í<ìß = IHà ;79H57I'¨--H';Üî'Ü 557&7H6

;¨; Ü ';© ÜIHà ;79H5(í) = 5; bÜHà-76'HÜÜ57I'¨--H';Üî'Ü 557&7H65; bÜHà-76'HÜÜ5

Precision (%)

��g�0��Ø�c�og�0�0¡Ô×�(��) = ¯ß¯ß<ìß = )¨57;79H5'¨--H';Üî'Ü 557&7H6

;¨; Ü)-H67;H6)¨57;79H5 =©I5; bÜHà-76'HÜÜ5'¨--H';Üî'Ü 557&7H6

©I5; bÜHà-76'HÜÜ5¨&;ðH�¨6HÜ

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Table 6.3 Statistical indexes measuring the performance of SHIA_Landslide shown in Figure 6.3.

Index Value Range

Hit rate 76.98 [0,100]

False alarm rate 24.24 [0,100]

Specificity 75.75 [0,100]

Precision 0.067 -

The approach develops by Montgomery & Dietrich (1994), called SHALSTAB model,

has been widely applied in engineering practice for shallow landslide susceptibility

assessment. SHALSTAB, similarly to SHIA_Landslide, simulates the fluctuation of a

perched water table lying above a slope-parallel impermeable layer controlled by

rainfall. However SHALSTAB is based on the coupling of a steady-state hydrological

model and an infinite-slope-limit-equilibrium slope stability analysis.

Martinez (2012) applied the SHALSTAB model to the rainstorm event of La Arenosa

(Figure 6.4). Table 6.4 shows the performance evaluation for both models in the

rainstorm of La Arenosa. Clearly, model performance will increase as the hit rate

increases quicker than the false alarm rate.

Table 6.4 Comparison of SHALSTAB and SHIA_Landslide for La Arenosa rainstorm event.

SHIA_Landslide shows a considerable higher hit radio without a considerable increase

in false alarm rate, specificity and accuracy. Precision and likelihood ratio show better

performance of SHIA_Landslide for La Arenosa rainstorm of September 21, 1990.

SHIA_Landslide was also compared to a physically based model in the literature.

Rosso et al. (2006) improves the capability of the SHALSTAB model of reproducing

hydrologic control by coupling the conservation of mass soil water with the Darcy´s Law

used to describe seepage flow in the Mettman Ridge catchment in the Oregon Coastal

Range. This modification of SHALSTAB tries to incorporate the combined effect of

Model Hit rate False alarm rate Specificity Precision

SHIA_LANDSLIDE 77 22 76 0.06

SHALSTAB 29 21 79 0.05


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storm duration and intensity in the triggering mechanism of shallow landslides. Results

of the simple and modified SHASLTAB implemented by Rosso et al. (2006) are shown

in Table 6.5 and compared to SHIA_Landslide results. SHIA_Landslide has a much

better prediction hit rate than SHALSTAB, without a considerable increasing on false

alarm rate, and compared to the SHALSTAB modified, SHIA_Landslide improves the

prediction hit rate conserving the same false alarm rate. For all the cases, there is a

high number of grid cells that are incorrectly classified as unstable, although

SHIA_Landslide has the lower value 93% of total simulated unstable grid cells

compared to 96% and 95%.

Figure 6.4 SHALSTAB model applied for the September 21, 1990 rainstorm by Martinez (2012).

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Table 6.5 Comparison of SHIA_Landslide and SHALSTAB performance.

Model Hit rate

(%)

Unstable Simulated

error (%)

Specificity

(%)

False alarm

rate (%)

SHIA_Landslide 77 93 76 22

SHALSTAB 56 95 84 16

SHALSTAB_mod 71 96 78 22

SHIA_Landslide was also compared with a transient vertical model groundwater flow

model. The Transient Rainfall Infiltration ad Grid-based Regional Slope-stability

analysis (TRIGRS) was considered, which was implemented for Godt et al. (2008) in

the north of Seattle. Similarly to the previous results, SHIA_Landslide presented a

much better hit rate prediction, without a considerable increase of the false alarm rate

(Table 6.6).

Table 6.6 Comparison of SHIA_Landslide and TRIGRS performance.

Model Hit rate False alarm rate Specificity Precision

SHIA_Landslide 77 22 75 0.06

TRIGRS 42 16 80 0.23

6.5 Sensitivity analysis

Good sensitivity to the thickness of the soil was found, since a lower depth of the

contact between residual soil and saprolite directly induced a higher occurrence of

landslides. At the same time, these outcomes confirm the reliability of the hydrological

module, once faster saturation and consequently instability conditions are expected

with a decrease of soil thickness. However, for the susceptibility map, unconditionally

unstable areas increase when soil thickness increase.

With regards to geotechnical properties, the modification of the angle of internal friction

or cohesion demonstrates that the parameter values are in inverse relation to the

number of unstable cells, as expected by the stability module, which applies the infinite

slope model. The factor of safety is most sensitive to changes in the soil cohesion, soil

thickness, and slope angle; moderately sensitive to changes in internal friction angle;

and insensitive to changes in soil unit weight.


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6.5.1 Antecedent rainfall

It has been recognized in the literature that antecedent rainfall can be a predisposing

factor in the activation of soil slips. Antecedent rainfall role in landslide triggered by

rainfall has been an interesting debate. The influence of antecedent rainfall is difficult to

quantify as it depends on several factors, including the heterogeneity of soils and the

regional climate.

To assess the effect of antecedent rainfall, the temporal evolution of the perched water

table was studied. For this purpose, it was used the rainfall time series for September

1990, modifying the antecedent rainfall to the maximum rainstorm peak, which

occurred between 20:00 to 22:00 local time.

The increase of the antecedent rainfall in the previous days prior to the September 21,

1990 rainstorm did not perform any significant change in the perched water table peak.

Moreover, the increase of antecedent rainfall in the previous 24 hours of the maximum

peak does not represent any change in the perched water table. These results are

coherent with the findings of different authors for residual soils with high hydraulic

conductivities, characteristic of sandy residual soil from granite rocks.

These results imply that the high-permeability soils require only short rainfall durations

before failure occurs and antecedent moisture conditions do not always play a

significant role, in accordance to the observations carried out by Rahardjo et al. (2008),

Brand (1985), and Corominas & Moya (1999).

Similarly, the influence of the rainstorm pattern was studied. Four representative

rainstorm patterns, including uniform, advanced, central and delayed rainstorms were

used for a time period of 1,000 hours and a maximum rainfall intensity of 50 mm/h. The

uniform pattern conserves equal rainfall intensity (50 mm/h) during the entire

simulation. The advanced pattern stars with maximum rainfall intensity and decreases

progressively up to a rainfall intensity of 0 mm/h. The delayed pattern is opposite to the

advanced pattern, in which rainfall intensity stars with 0 mm/h, increasing progressively

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up to 50 mm/h. Finally, the central pattern starts with a rainfall intensity of 0 mm/h,

reaching maximum rainfall intensity in the middle of the period of simulation and

decreasing progressively until it reach a rainfall intensity of 0 mm/h once again.

The four rainfall patterns yielded the same number of unstable grid cells induced by

rainfall. There is not difference for the La Arenosa catchment if the rainfall peak is at

the beginning of the rainstorm, in the middle or at the end. The difference is on the time

of occurrence; due to the fact that most landslides occur during the peak of the

rainstorm.

6.5.2 Hydraulic conductivity changes

For the sensitivity analysis of the model to saturated hydraulic conductivity, it was used

the same calibration period, from March to May 2011.

If hydraulic conductivity is reduced by two orders of magnitude, perched water table

peaks are eliminated, showing a constant increase and reaching a maximum peak

around 0.75 m. The perched water table conserves high levels even after the rainfall

events, indicating a lower capacity to release positive pore pressure (Figure 6.5 and

6.7).

Figure 6.5 Perched water table simulated for nonlinear SHIA_Landslide for a slope grid cell with a accumulated drainage area of 800 m2 and a hydraulic conductivity of 0,01Ks

If hydraulic conductivity is reduced by one order of magnitude, at the beginning there is

a constant increase of perched water table, with small peaks that response to short

rainfall events; when it gets a peak close to 0.75 m, there is an abrupt decrease in the


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perched water table depth, and the behavior changes completely, with small peaks and

valleys according to rainstorm occurrence (Figure 6.6). On the other hand, maximum

peaks are reduced.

Figure 6.6 Perched water table simulated for nonlinear SHIA_Landslide for a slope grid cell with a accumulated drainage area of 800 m2 and a hydraulic conductivity of 0,1Ks

Figure 6.7 Perched water table simulated for nonlinear SHIA_Landslide for a slope grid cell with a accumulated drainage area of 800 m2 and a hydraulic conductivity of Ks

Figures 6.8 and 6.9 show the perched water table increasing the hydraulic conductivity

in one and two orders of magnitude, respectively. The mean level and peaks are

reduced considerably.

6.5.3 Rainfall thresholds

As part of the sensitivity analysis, it is possible to establish rainfall thresholds to predict

the occurrence of abundant landslides. Rainfall thresholds for this case are defined as

the minimum amount of rainfall necessary to trigger an important number of landslides.

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For a rainstorm event with repeated peaks of 20mm/h, 13.12% of potentially unstable

areas fail (Figure 6.10), and for a rainfall peak of 40 mm/h, 31.82% of potentially

unstable areas fail. And for a rainfall peak of 80 mm/h, 47.92 % of potentially unstable

grid cells fail.

Figure 6.8 Perched water table simulated for nonlinear SHIA_Landslide for a slope grid cell with a accumulated drainage area of 800 m2 and a hydraulic conductivity of 10Ks

Figure 6.9 Perched water table simulated for nonlinear SHIA_Landslide for a slope grid cell with a accumulated drainage area of 800 m2 and a hydraulic conductivity of 100Ks.

Figure 6.11 shows the percentage of unstable grid cell that fail due to rainfall, with the

maximum percentage obtained tending around 51%. For high rainfall peaks (>100

mm/h) there is not a significant increase of landsliding. It shows an asymptotic

relationship between rainfall peaks and landslide occurrence, and tendency to increase

linearly for small rainfall peaks, decreasing until it reaches an asymptotic value of

approximately 50 %. This value means a maximum percentage of landslide

occurrences due to rainfall. It could be explained as a limitation of the model imposed


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by calibration processes carried out as a result of unstable grid cells identified for the

model in the geotechnical calibration processes during the September 1990 rainstorm

was 45.8%, a very close percentage to the maximum value in Figure 6.11. The

calibration process could induce the model to consider the landslide occurrence as a

maximum. In the other hand, it is also possible that the 50% indicates a natural

threshold for the La Arenosa catchment, associated with its hydrological and

geotechnical conditions, although much more work needs to be done, which includes

implementing the model to the catchment with different hydrological and geotechnical

parameters.

20 mm �13,12%

40 mm �31,82%

80mm �47,92%

Figure 6.10 Landslide triggered by rainfall according to the maximum rainfall peaks. Percentage is related to the potentially unstable grid cells.

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6.5.4 Saturated conditions

In order to simplify the analysis an important number of models often assumed that the

perched water table rises to coincide with the slope surface and that the slope is

completely saturated. It could be considered as the worst case. For La Arenosa

September 21, 1990, rainstorm saturated condition were not completely reached. The

unstable condition is not a function only of an increasing perched water table, since

cohesion, friction angle, and slope also play an important role. Thresholds relating to

increasing perched water table are different along the catchment

Figure 6.11 Percentage of potentially unstable grid cells according to the maximum rainfall peak for La Arenosa catchment

A sensitivity analysis was carried out for the La Arenosa catchment to determine

landslide occurrence according to an increasing perched water table. For Zw = Zs, in

which the entire soil thickness is completely saturated, the entire number of potentially

unstable grid cells fail. For Zw = 0.5Zs, most potentially unstable grid cells maintain

safe conditions, and just 13.6% of grid cells fail. When the perched water table gets

close to saturated conditions, the number of unstable cells increase considerably, when

Zw=0.8Zs, 65.6% of grid cells fail (Figure 6.12).

Figure 6.13 shows the percentage of unstable grid cells as a function of the perched

water table increase. For the La Arenosa catchment, when perched water table

increase more than 40% of soil thickness, potentially unstable grid cells start to show

failure.


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Figure 6.12 Landslide occurrences according to saturation percentage for La Arenosa catchment.

6.6 An early warning system

The analysis of the temporal recurrence of natural disasters have shown that damages

arising from such events occur more often than resilience capacity of society, so new

approaches focus on the development and implementation of early warning systems

and land use planning to minimize the loss of human lives and infrastructure (IEWP,

2005; Guzzetti et al., 2005). Local officials and decision makers regarding the

evacuation of people are interested both in determining the time when landslides occur,

and in its probable location, when and where. Early warning systems are currently

considered one of the most practical and effective measures for disaster prevention

(UN/ISDR, 2010).

Zw=0.5Zs �13.63%

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Zw=0.8Zs �65.61%

Zw=Zs�100%

Figure 6.13 Landslide occurrences according to perched water table increasing.

The modeling of shallow landslide triggered by rainfall for implementation in early

warning systems is of great interest within the scientific community. These shallow

landslides are largely rapid, which is the reason why failure detection using ground-

movement tools is of limited use. And considering that most landslides are caused by

rain storms, warnings of landslide occurrence to the community can be provided based

on rainfall detection, and forecasts, and landslide modeling. Early warning systems

have been largely empirical in nature because the current understanding of the failure

mechanism and the conditions leading to failure are not sufficient to develop physically

based systems.

Early warning systems for landslides in real time and based on physical models must

constantly calibrate and verify pore pressure and landslide occurrence (Terlien, 1998).

Due to the complex processes that are part of the triggering of landslides, there is a

considerable probability of false alarms, not all storms that exceed critical thresholds

trigger landslides, so that these alerts are very useful for handlers and emergency and

disaster, although they are not in all the cases useful to the community in general

(Arattano & Marcho, 2008).

Sidle & Ochiai (2006) considered early warning systems for landslides as a factor of

saving lives and protecting properties in areas highly developed and densely


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populated. They highlight the advances that are being obtained for the real-time

forecasting based on radar systems. It has been suggested that in areas such as

mountainous catchments, where rain gauges are sparsely distributed, radar can be

better capture the spatial variation of rainfall fields than gauged data (Chiang & Chang,

2009).

Currently, an early warning system has been implemented into the Aburrá Valley,

which is called SIATA (www.siata.gov.co). SIATA consists of a dense public and

private rainfall and stream flow gauges stations, and a C-band dual polarization radar.

The system provides weather forecasting, and currently they are developing models to

provide warnings.

SHIA_Landslide performance has demonstrated high capacity of prediction and low

false alarm rate, so it may be used to include in SIATA. The elaboration of a detailed

shallow landslide early warning system based on SHIA_Landslide is out of the scope of

this work. However, a general proposal that could be integrated to SIATA is presented.

It is initially, suggested as a prototype for validation in the Aburrá Valley, that, with

additional programming effort, could be implemented in near-real-time to generate

web-based map products.

SHIA_Landslide products could be integrated into a GIS-based system with the

capacity to publish the factor of security to a Web GIS platform, based on near real-

time monitoring. The model combined with regional empirical rainfall triggering

landslides thresholds can be incorporated in a common server with the local and

regional risk management offices for emergency planning purposes. The essence of

Web GIS platform is not to automatically show the landslide occurrence area, but

rather use a judgment process by which information is collected to help experts judging

the location of the potential landslide occurrence areas.

Quantitative precipitation forecasts obtained by the radar make it possible to increase

lead time considerably. The radar is able to detect approaching heavy rain cells, and its

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169

data is used to extrapolate rain amounts that are likely to fall within the next hour or two

(NOAA, 2005). This now casting capability combined with a physically based model

provide precious forecast lead time along specific areas for warnings that cannot be

obtained with a rain gauge network and empirical thresholds.

A great advantage of SHIA_Landslide is that the hydrological component of the model

could be integrated as a flooding warning as well, and in the future could be developed

under the same hydrological component a module for flash floods and debris flow using

a distributed sediment runoff module including landslide sediment volume.

For this case of warning systems, it is necessary to implement different kinds of alert

levels according to time occurrence and certainty of the information. Each of these

levels should be associated with the coordination with emergency managers, the

media, and other end users.

We proposed to define three alert levels for landslide occurrence: forecasting,

monitoring and warning. (i) Forecasting is based on the susceptibility map provide by

SHIA_Landslide and detailed studies of landslide susceptibility. These maps show the

areas were potentially landslide could occur by rainfall, as well as actions to be taken

continuously in the direction of urbanization control and mitigation interventions. (ii) The

next level is Monitoring, and is activated during the rainy season in which landslides

triggered by rainfall are common. (iii) The final level is Warning, which is activated

when defined rainfall thresholds are exceeded or when an extreme rainstorm event is

forecasted by the meteorological model or radar-based now casting. During this level,

SHIA_Landslide should be run with forecasted rainfall to identify areas where landslide

could occur.

Figure 6.14 shows the draft of the prototype for an early warning system in the Aburrá

Valley.


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170

Figure 6.14 Early warning system for the Aburrá Valley based in modules.

A critical part of SHIA-Landslide is to be able to parameterize the hydrology and

geotechnical model components for the Aburrá Valley. Consistent databases are

needed concerning rainfall and, stream flow discharges, which are available for SIATA,

and landslide inventories, where much more work needs to be done. Moreover, the

monitoring and analysis of perched water table or water content in the soil could be

included in the SHIA_Landslide as calibration parameters.

At last, it is important to identify the three sources of uncertainties in the use of

landslide warning systems. According to Schmidt et al. (2008), uncertainties are related

to (i) uncertainty in the weather forecast, in which rain will never be exactly distributed

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171

in space and time as predicted due to the inaccuracies in the weather models,

parameters, and initial conditions; (ii) uncertainties regarding the soil hydrology model

component; and (iii) uncertainties in the geotechnical model, model structure and initial

conditions, due to inaccuracies in the hydrological and to geotechnical parameters

respectively, especially for tropical residual soils.

When fully operational, the system will help to issue warnings for the possible

occurrence of rainfall-induced shallow landslides. A measure of the success of the

system will be the reduced number of fatalities and injured people caused by rainfall.

6.7 Final remarks

SHIA_Landslide was developed to simulate the failure of shallow landslides and

changes in the factor of safety. It is based on hydrological and geotechnical response

of soil stability affected by rainfall. Rain water infiltration and pore water pressure

increase in the slope and shear stresses along a potential failure surface increase

because of the reduction of normal effective stresses. When rainfall occurs, the factor

of safety of the slope varies as a function of positive pore pressure in terms of perched

water table level and time.

SHIA_Landslide provides hydrological and geotechnical outputs. Hydrological products

are: (i) hydrograph and (ii) perched water table variation. However, several other

products could be obtained from the hydrological model such as overland runoff,

subsurface flow, groundwater level, and groundwater flow. Hydrological outputs allow

an initial calibration and water balance according to the rainfall event evolution. The

geotechnical products are: (i) landslide susceptibility map, and (ii) landslide hazard

map with landslide indices by rainfall over the entire catchment.

Models available in the literature have been developed for basin scale or hillslope

scale, and according to this consideration rainfall is incorporated. Basin scale models,

in general, consider steady state conditions, and do not permit to incorporate rainfall


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events, and evaluate the response of a basin to rainstorms. On the other hand,

hillslope models consider transient conditions to evaluate hillslope response to vertical

infiltration, but they do not consider subsurface flow and it is not possible to obtain the

response of the entire basin to a rainfall event. Both kinds of model cannot take

advantage of rainfall spatial distribution, which thanks to new developments such as

radar has been improved.

SHIA_Landslide uses rainfall events and incorporates into the model all the available

characteristics, such as duration, intensity, antecedent conditions, and spatial

resolution. SHIA_Landslide is a distributed model which allow including not only

hydrological variation, but also morphological and geotechnical parameter variation in

the vertical and horizontal directions of the slopes.

The approach, based on a subsurface flow model by linking topography and rainfall

variability, provides a way to capture both topographic and climatic forcing on shallow

landsliding. SHIA_Landslide can be distinguished by:

a) it is at a basin scale;

b) includes a hydrologically complete water process that permits perched water

table calibration;

c) considers vertical infiltration and horizontal flow in saturated conditions;

d) it works for rainfall events or long term rainfall conditions;

e) it works for different temporal and spatial resolution;

f) the geotechnical module produces landslide susceptibility maps, showing the

previous condition before rainfall, and landslide hazard map with landslide

occurrence triggered by rainfall.

All these conditions of SHIA_Landslide make the model as an interesting tool to be

implemented in early warning system, combined with real-time rainfall monitoring and

dissemination of alerts and communication. It can also be applied to land-use

management and emergency planning, as it can be used for evaluating the landslide

susceptibility or landslide hazard under mean rainfall conditions for a specific region,

before urban development can be carried out.

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173

In order to research scopes, SHIA_Landslide can be a useful framework for

investigations of how a catchment system would likely respond in the short and long

term to a rainfall perturbation from its current state. This SHIA_Landslide advantage

permits to evaluate responses of tropical residual soil slopes under rainfall conditions.

The knowledge of the processes, which govern slope stability conditions and evolution,

could help in arranging proper tools for hazard analysis and risk management.

Most of physically based models that show high levels of prediction also overestimate

landslide occurrence. SHIA_Landslide was quantitative compared to SHALSTAB.

SHIA_Landslide shows a much better performance in terms of unstable grid cells

correctly classified (hit rate), conserving similar values for false alarm rate, precision

and specificity. Nevertheless, SHIA_Landslide results also show that more cells are

predicted to be unstable than are observed.

Clearly, the lack of a complete landslide database for the entire catchment may be (at

least partially) responsible for hazard overestimation when simulated and actual scars

are compared. However, local effects are not included in the infinite slope model which,

coupled with the uncertainty in some of the model parameters, may generate

significant uncertainty in the model results.

It is important to keep in mind that the spatial and temporal distribution of landslides is

a result of the interaction of many and complex hydrological and geotechnical

parameters. A reliable, accurate landslide forecasting map depends on the proper

determination of the role of these parameters. The inclusion or omission of some of

these parameters may change significantly the capability of landslide forecasting.

SHIA_Landslide considers eleven landslide-controlling parameters, namely flow

accumulation, flow direction, soil thickness, slope angle, cohesion, saturated unit soil

weight, soil friction, saturated soil hydraulic conductivity, rock hydraulic conductivity,

maximum static water storage, and maximum gravitational water storage.


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The landslide overestimation could be due to the elimination of other affecting factors

on landslide occurrence such as vegetation, detailed geological setting, artificial or

man-made structures. In this study, the effects of vegetation in the geotechnical

component were neglected. The estimate of the stability is therefore conservative,

since slopes considered as unstable may be stable in reality if significant amounts of

root cohesion add to shear strength.

The model has some limitations imposed by simplifying assumptions, approximations

and other shortcomings in the underlying theories. There are still major uncertainties

that should be considered for a completely full modeling of these processes, such as

lateral and vertical variability of hydrological and geotechnical parameters of the soil,

unsaturated conditions, secondary permeability and subsurface flow complexity, and

soil thickness. All these important aspects were simplified; however SHIA_Landslide

results prove that the most important parameters in tropical environment and complex

terrains have been considered for the model.

SHIA_Landslide model considers the simplest case for weathering tropical profile and

catena, and it is focused on fundamental processes involved on landslide occurrence:

rainfall, perched water table and positive pore pressure. The increase of pore pressure

is not only controlled by the amount of rain but also by the amount of water stored in

the soil according to drainage area. SHIA_Landslide assumes, although, site specific

properties control the size and the moment when shallow landslides are triggered, the

main controlling factor defining their location is topography which control subsurface

flow and perched water table level.

The success of SHIA_Landslide for La Arenosa catchment suggests that the primary

factor controlling shallow landsliding triggered by rainfall is surface topography,

because the only other factors accounted for in the model, that is, soil properties are

very homogeneous throughout the hillslopes of the La Arenosa catchment. Thus, it can

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175

be concluded that the water convergence in hollows is an important factor in governing

water supply at landslide sources areas.

Although the comparisons of the results with the real landslide inventory has shown a

good fitting, the research is still in progress and new efforts are still required for

improving both data quality and model reliability. Further investigations may concern

with testing results in areas with different hydrological and geotechnical conditions

different from the ones where SHIA_Landslide was applied, and evaluate its influence

on SHIA_Landslide.

The resolution and accuracy of the model predictions cannot be better than the

resolution and accuracy of available data. Although the model allows the incorporation

of the spatial variability of soil properties, it is necessary to consider that the spatial

distribution of landslides is a result of the interaction of many parameters. Shallow

landslide initiation depends on spatially distributed variables, morphometric and

physical-mechanical properties of the soil. Hydrological influences on hillslopes are

affected by the highly variable rainstorm behavior and tropical residual soils have some

unique characteristics related to their composition and the environment under which

they develop. Most classical concepts related to soil properties and soil behavior have

been developed for temperate zone soils, and there have been difficulties to accurately

model procedures and conditions to which residual soils are subjected.

Every landslide, therefore, is the result of a unique combination of different parameters,

which is the underlying reason for why time-space predictions of landslides require

focusing efforts on critical instability elements. Nonetheless, the difficulties regarding

prediction and control of some of the attributes of slope failures cannot be

overstresses.

Detailed field-based observational data, including possible results of in situ monitoring,

is essential to improve the reliability and prediction of the models, and is influenced by

human activities on slope, particularly timber exploitation and other engineering works.


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Because of the high variability and complex process associated to landslide

occurrence, a stochastic approach could be a useful application, which can explicitly

account for the uncertainty of the models (Frattini et al., 2009). In general, model

predictions should be presented as ranges or probability distributions rather than as

single values (Uhlenbrook et al., 1999).

Another important point is that SHIA_Landslide only considers the initial collapse of the

soil for those shallow landslides triggered by rainfall in saturated conditions due to

water pore pressure and the reduction of effective stresses. The model is not

applicable to deep-seated landsides, in which slip surface geometry may differ from a

planar surface and flow field variations may cause pore pressure increases that a

simple slope-parallel flow model is unable to compute (Iverson, 2000).

Further research concerns the interactions between the initial collapse, and the

resulting debris flow and fluvial sediments transport will provide coupled models for

automated mapping of spatial pattern of failure potential and downstream hazard.

There is a great potential for new research to develop and implement physical and

statistical models for early warning systems in our country. Surely, it will allow reducing

annual losses associated with such phenomena, as they have done in a large number

of countries. The current practices of using statistical thresholds to identify landslide

producing storms can be made more useful if they are coupled with mechanistic

models that are spatially explicit in identifying areas of high hazard (Casadei et al.,

2003).

Chapter 7

CONCLUSIONS

Shallow landslides triggered by rainfall are common landscape forming processes in

tropical mountain environments with the potential to become deadly in populated areas.

SHIA_Landslide offers a new approach that combines hydrological and geotechnical

components, and predicts 77% of landslides at La Arenosa – and providing an early

warning system with potential to be used in basins like the Aburrá Valley.

SHIA_Landslide’s prediction rate is an improvement over most literature values

reported in other parts of the world, with an 8.4% improvement over the rate obtained

using the SHALSTAB modified model of the Mettman Ridge catchment in the Oregon

Coastal Range, and a 38% improvement over the rate reported using the SHALSTAB

model by Rosso et al (2006) in the same catchment. However, the most notable

improvement concerning prediction rate was in comparison to an earlier SHALSTAB

simulation of the same La Arenosa catchment by Martinez (2012), with a 165%

improvement in predicting shallow rain-triggered landslides.

Chapter 7: Conclusions

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However, the SHIA_Landslide model has done little to improve the rates of false

alarms, with a 22% false alarm rate similar to that reported by SHALSTAB and

TRIGRS (Rosso et al., 2006; Godt et al., 2008; Martinez, 2012). This lack of precision

diminishes the efficiency of possible remedial and response efforts.

The reduction in false alarms rate can serve to focus and improve the remediation and

rescue response. Regardless of that, there is still a considerable overestimation for

unstable areas and potential to improve false alarm. Landslide inventory database

used for the calibration identified as little as the 2.2% of the total catchment as unstable

grid cells, and SHIA_Landslide predicts an order of magnitude more instability. Some

of this overestimation can be explained by only a partial inventory, as suggested by

INTEGRAL (1990), due to a lack of topographic information, estimating that a 16% of

the entire catchment was affected by landslides during the September, 1990 event. It

could mean a good match between the simulated total area and the area affected;

considering as well that the landslide comparison was establish by just matching

landslide scars.

Tropical environments such as the Colombian Andes are characterized by deep

weathering profiles and intense long rainfall periods. Most of the landslides that occur

over these regions are induced by rainfall. In Colombia, however, few compulsory

events have been characterized in detail, including landslide databases. For La

Arenosa rainstorm event in September 21, 1990, Mejía & Velásquez (1991) and

INTEGRAL (1990) carried out a detailed evaluation and a partial landslide inventory,

which allow implementing a model for landslide induced by rainfall.

SHIA_Landslide is a FORTRAN program for computing positive pore pressure changes

as well as resulting changes in the factor of safety due to rainfall infiltration, using a

physical and conceptual based, distributed hydrological and geotechnical coupled

model to provide an assessment of slope-failure condition.

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The demonstration of the model´s applicability shows that the developed model can be

assess landslides triggered by the increase of positive water pressure in saturated soil

due to a rise in the perched water table. The ability of the model to represent actual

conditions has been demonstrated through a process of model calibration and

validation using the September 21, 1990 event in the La Arenosa catchment.

The results of this study indicate that SHIA_Landslide is useful and suitable for tropical

and complex terrains in the basin scale adopted in this study. The spatial distribution

and temporal occurrence of the simulated landslides was compared to the real

occurrence related to the event. A good consistency was obtained and the model

provided valuable results, indicating that the most influential factors involved on

landslide occurrence in La Arenosa were also significant in the simulation.

The model should also be applicable in similar regions. For application elsewhere, the

hydrological and geotechnical parameters should also be modified using data specific

to the region of interest.

SHIA_Landslide could be implemented using linear and nonlinear flow velocities for the

different tanks levels. Comparisons between nonlinear and linear model indicate that,

although a linear approach of the model takes much less time to run, a nonlinear

SHIA_Landslide shows much better performance, decreasing false alarm rate.

SHIA_Landslide constitute an innovative approach to modeling shallow landslide

triggering by rainfall at the basin scale. Some of the advantages of the hydrological

model SHIA_Landslide are:

a) the capacity to capture the surface topography and its effects concerning the

overland flow and the concentration cells of subsurface flow;

b) it uses DTM to establish the relationships among cells, geomorphologic

parameters, slope angle, direction, etc., needed for the model;

c) rainfall dataset can be incorporated with the spatial and temporal resolution

preferred and available;

Chapter 7: Conclusions

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180

d) continuous simulation for long periods of rainfall data (years) or event

simulations for specific storms;

e) it consider the effect of horizontal and vertical flow

A detailed sensitivity analysis of SHIA_Landslide was carried out. The model has a

good sensitivity to the thickness of the soil, since a lower depth of the contact between

residual soil and saprolite directly induce a higher occurrence of landslides.

Nevertheless, for the susceptibility map, unconditionally unstable areas increase when

soil thickness increase. With regards to geotechnical properties, a modification of the

angle of internal friction or cohesion demonstrates that the parameter values are in

inverse relation to the number of unstable cells. The factor of safety is most sensitive to

changes in the soil cohesion, soil thickness, and slope angle; moderately sensitive to

changes in internal friction angle; and little sensitive to changes in soil unit weight.

Results about antecedent rainfall, saturated hydraulic conductivity and saturated

conditions implied that high-permeability soils require only short rainfall durations

before failure occurs, and antecedent moisture conditions do not always play a

significant role, in agreement with the observation carried out by Rahardjo et al. (2008),

Brand (1992) and Corominas & Moya (1999).

Different approaches related to the use of the SHIA_Landslide model are proposed: (i)

a first one regards the use of the model for real-time forecasting in order to predict

future landslide hazard conditions; and (ii) a second approach is to determine landslide

susceptibility evaluation and land-zoning for land-use planning as an aid to a

sustainable development in mountainous terrains; and finally (iii) the model may be

used for research purposes to understand landslide occurrence under rainfall condition

in tropical and mountainous conditions.

Early warning systems are currently considered one of the most practical and effective

measures for disaster prevention. SHIA_Landslide performance has demonstrated a

high capacity of prediction with a low false alarm rate, so it could be included in SIATA

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such as prototype for validation into the Aburrá Valley. It could be operated in near-

real-time to generate web-based map products. The model, combined with regional

empirical rainfall triggered landslides thresholds can be incorporated in a common

server with the local and regional risk management offices for emergency planning

purposes.

Results suggests that further research should focus on the geotechnical character of

the geologic materials, hydrology, hydraulic conductivity, geotechnical features of

materials, rainfall characteristics, and microtopografic conditions. It should be kept in

mind that the reliability and accuracy of data during collection and storage are crucial

factors to assess landslide susceptibility and hazard correctly.

Much more work need to be done, as well (i) to assess the performance of the model

under different hydrological and geotechnical parameter sets, (ii) to assess model

limitations associated with simplified approaches for the water content of the soil and

vertical and horizontal soils variations incorporating into the hydrological and

geotechnical components of unsaturated soils conditions and more complex

weathering profiles and catena, and finally (ii) to include more appropriate the effects of

roots, vegetation cover, and the role of human interventions and other engineering

works.

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APPENDIX A: SHIA_LANDSLIDE PROGRAM !**************************************************************************** ! ! PROGRAM: SHIA_LANDSLIDE ! ! PURPOSE: This program models landslide occurrence triggered by rainfall. ! It is composed by a distributed hydrological model which simulate the ! hydrological cycle, and a geotechnical model which simulate hillslope stability ! ! The model has 8 subroutines, the initial 4 subroutines, prepares the information ! for the 07_Model subroutine. ! ! By Edier Aristizàbal, Jaime Ignacio Vèlez, Hernàn Martinez (2013). SHIA_LANDSLIDE: ! Physically and conceptual based model for shallow landslide prediction triggered ! by rainfall in tropical and complex terrains. PhD Thesis. Universidad Nacional de ! Colombia. ! !**************************************************************************** Subroutine SHIA_LANDSLIDE Use DFLIB Use DFLOGM use modgeneral Implicit none Real time_begin, time_end Integer :: I4 Call CPU_TIME ( time_begin ) Call CLEARSCREEN($GCLEARSCREEN) I4=SETBKCOLOR(15) I4=SETTEXTCOLOR(0) ! Error archivo If ( file1 == " ".or.file2 == " ".or.file3== " ".or.file4 == " ".or.file5 == " ".or.file6== " " & & .or.file7 == " ".or.file8 == " ".or.file9== " ".or.file10== " ".or.file11 == " " & & .or.file12== " ".or.file13== " ") then Err = 121 end if If ( inicon1 == " ".or.inicon2 == " ".or.inicon3== " ".or.inicon4 == " ".or.inicon5 == " ".or.inicon6== " " & & .or.inicon7 == " ".or.inicon8 == " ".or.inicon9== " ".or.inicon10== " ".or.inicon11 == " ") then Err = 122 end if If ( calib1 == " ".or.calib2 == " ".or.calib3== " ".or.calib4 == " ".or.calib5 == " ".or.calib6== " " & & .or.calib7 == " ".or.calib8 == " ".or.calib9== " ".or.calib10== " ".or.calib11 == " " & & .or.calib12== " ".or.calib13== " ".or.calib14== " ") then Err = 123 end if If ( xlpoint == " ".or.ylpoint == " ".or.xcpoint== " ".or.ycpoint == " ") then Err = 124 end if If (Err.NE.0) then; goto 110; End if write(1,*) " P R O G R A M S H I A L A N D S L I D E" write(1,*) Call Input_Data() write(1,*) ' Reading the maps and parameters .... Ready!' If (Err.NE.0) then; goto 110; End if Call Basin() write(1,*) ' Creating a table of the basin drainage .... Ready!' Call Rainfall() write(1,*) ' Creating precipitation triangles and pixel maps .... Ready!' Call Matrix() write(1,*) ' Creating matrix with parameters for the model .... Ready!' write(1,*) ' Running the model SHIA_Landslide..........................!' Call Model() Call CPU_TIME ( time_end ) write(1,*) ' Time of simulation' , time_end - time_begin, 'seconds'


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110 Return end Module Modules Implicit none !---------------------------------------------------------------------------------------------------------! Integer:: i,j,row2,col2,nrows,ncols,no_data1 Integer:: Trows,Tcols,cantptos,npt,nReg Integer, allocatable :: Dire(:,:),PtosCont(:,:),MatLevel(:,:) Integer, allocatable :: Level(:),Trif(:,:) Integer, dimension(:,:), allocatable :: res,MatEst,matest1,matest2 Double precision,Parameter :: GammaW = 10.0 Double precision,Parameter :: fc = 0.0028 !Factor to convert cm/hour to mm/sec Double precision :: xll,yll,dx,dy, dt,Num,Den,Hillslope,Channel Double Precision :: iV2,iV3,iV4,iV5,si1,si2,si3,si4,si5 Double precision :: R1,R2,R3,R4,R5,R6,R7,R8,R9,R10,R11,R12,R13,FS Double precision :: alfa1,alfa2,fhi,c1,cn,cd,teta,es,ey,ez,w1,w2,w3,k2,k1,epsi,e1,manning Double precision :: entradas,salidas,diferencia,acumulado Double precision :: Diff1,Diff2,SE,RMSE,Nash,NS,mean Double precision,dimension(:),allocatable :: EVP,Ks,kp,slope,qreal,Friction,Cohesion Double precision,dimension(:),allocatable :: Zmin,Zwcrit,Zmax,Zw,Zs,GammaS,Bo,Est Double precision,dimension(:),allocatable :: s1,s2,s3,s4,s5,S1max Double precision,dimension(:),allocatable :: v2,v3,kpp,v4,v5,acum,Stream_flow,Subsur_level Double precision, allocatable ::S3max(:),matiS3(:,:) Double precision, allocatable :: az(:,:),bz(:,:),cz(:,:),dz(:,:),coef(:) Double precision, allocatable :: MatSlope(:,:),areaA(:,:),Matks(:,:),Matkp(:,:),MatEVP(:,:) Double precision, allocatable :: MatFriction(:,:),MatGammaS(:,:),MatS1max(:,:),MatS3max(:,:) Double precision, allocatable :: MatZs(:,:),MatCohesion(:,:) Double precision, allocatable :: resultado(:,:),resultado2(:,:),precip(:,:),Pevento(:,:) Character cols*5,rows*5,xllcenter*9,yllcenter*9,cellx*8,nodata*12, Nfilas*6,ntri*4 Character*100 :: Archivo CHARACTER*200 :: Mensaje End Module ! ================================================================================= ! Subroutine for reading integer maps Subroutine Reading_Maps_Int(Na,filename,Matrix,Err) Use Modules Implicit none ! Declaration of variables Integer,intent(in) :: Na ! File number Character*100,intent(in):: filename ! File name Integer,dimension(ncols,nrows),intent(out) :: Matrix integer,intent(out)::Err !All maps must have the same input format Open(Na, file = filename, Status ='Old') read(Na,*); read(Na,*); read(Na,*) ; read(Na,*); read(Na,*); read(Na,*) !dimension attributes read(Na,*,Err=100)((matrix(i,j),i=1,ncols), j=1,nrows) close(Na) goto 101 100 Err = 1 101 Return End Subroutine !------------------------------------------------------------------------------------------------------------! ! Subroutine for reading real maps Subroutine Reading_Maps_Real(Na,filename,Matrix,Err)

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Use Modules Implicit none ! Declaration of variables Integer,intent(in) :: Na ! File number Character*100,intent(in):: filename ! FIle name Double precision,dimension(ncols,nrows),intent(out) :: Matrix Integer,intent(out) :: Err !All maps must have the same input format Open(Na, file = filename, Status ='Old') read(Na,*); read(Na,*); read(Na,*) ; read(Na,*); read(Na,*); read(Na,*) !dimension attributes read(Na,*,Err=100)((matrix(i,j),i=1,ncols), j=1,nrows) close(Na) goto 101 100 Err = 1 101 Return End Subroutine Subroutine Input_data() Use Modules Use Modgeneral implicit none !Subroutine to read maps: slopes, acumulated area, model parameters, initial !conditions, control points, pixels map,parameters for calibration, and !parameters for the Geomorphological Kinematic Wave . ! !=========================================================================== !Files ASC !To read maps in format .asc it is necessary to keep the same format !cols, ncols, rows, nrows, xllcenter, xll, yllcenter, yll, cellc, dx, ! nodata, no_data1. These values have to be the same for all the maps !Map of drainage direction inside the folder Input Maps Archivo = file1 ! 'Input Maps\flowdir.asc' Open(10, file = Archivo, status = 'old') Read(10,*) cols, ncols Read(10,*) rows, nrows Read(10,*) xllcenter, xll Read(10,*) yllcenter, yll Read(10,*) cellx,dx Read(10,*) nodata,no_data1 Close(10) !Reading the drainage direction map inside the folder Input Maps Archivo = file1 ! 'Input Maps\flowdir.asc' Allocate(Dire(ncols,nrows)) Call Reading_maps_int(20,Archivo,Dire,Err) if (Err.Ne.0) then go to 100 End if !Reading the slope map inside the folder Input Maps in degrees Archivo = file2 !! 'Input Maps\slope_rad.asc' ![º] Allocate(MatSlope(ncols,nrows)) Call Reading_maps_real(30,Archivo,MatSlope,Err) if (Err.Ne.0) then go to 101 End if !Reading the acumulated area map inside the folder Input Maps Archivo = file3 !'Input Maps\flowacum_m2.asc' ![m^2] allocate(AreaA(ncols,nrows)) Call Reading_maps_Real(40,Archivo,AreaA,Err) if (Err.Ne.0) then go to 102 End if !Reading the saturated ks.asc' Archivo = file4 !'Input Maps\ks.asc' ![cm/h] Allocate(Matks(ncols,nrows)) Call Reading_maps_Real(50,Archivo,Matks,Err) if (Err.Ne.0) then


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go to 103 End if !Reading the saturated permeability of saprolite map inside the folder Input Maps Archivo = file5 !'Input Maps\kp.asc' ![cm/h] Allocate(Matkp(ncols,nrows)) Call Reading_maps_Real(60,Archivo,Matkp,Err) if (Err.Ne.0) then go to 104 End if !Reading the friction angle map inside the folder Input Maps Archivo = file10 !'Input Maps\friction_rad.asc' ![rad] Allocate(MatFriction(ncols,nrows)) Call Reading_maps_Real(70,Archivo,MatFriction,Err) if (Err.Ne.0) then go to 105 End if !Reading the saturated soil weigth map inside the folder Input Maps [kN/m2] Archivo = file9 !'Input Maps\gammas.asc' !![kN/m^3] Allocate(matGammaS(ncols,nrows)) Call Reading_maps_Real(80,Archivo,matGammaS,Err) if (Err.Ne.0) then go to 106 End if !Reading the failure surface depth map inside the folder Input Maps Archivo = file8 !'Input Maps\zs.asc' ![m] Allocate(MatZs(ncols,nrows)) Call Reading_maps_Real(90,Archivo,MatZs,Err) if (Err.Ne.0) then go to 107 End if !Reading the cohesion map inside the folder Input Maps[kN/m2]" Archivo = file11 !'Input Maps\cohesion.asc' !![kN/m^2] Allocate(MatCohesion(ncols,nrows)) Call Reading_maps_Real(100,Archivo,matCohesion,Err) if (Err.Ne.0) then go to 108 End if !Reading the maximum capacity of the static storage map inside the folder Input Maps [% in dry weight] Archivo = file6 !'Input Maps\S1max.asc' Allocate(MatS1max(ncols,nrows)) Call Reading_maps_Real(110,Archivo,MatS1max,err) if (Err.Ne.0) then go to 109 End if !Reading the maximum S3 capacity map inside the folder Input Maps [% in dry weight] Archivo = file7 !'Input Maps\s3max.asc' Allocate(MatS3max(ncols,nrows)) Call Reading_maps_Real(120,Archivo,MatS3max,Err) if (Err.Ne.0) then go to 110 End if !Reading the potential evapotranspiration inside the folder Input Maps Archivo = file12 !'Input Maps\EVP.asc' ![mm] Allocate(MatEVP(ncols,nrows)) Call Reading_maps_Real(150,Archivo,MatEVP,Err) if (Err.Ne.0) then go to 111 End if !------------------------------------------------------------------------------- !Files TXT !Reading the parameters of the model inside the folder Input Data folder !and creating control point and pixel type maps hillslope = inicon(1) channel = inicon(2) iv2 = inicon(3)

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iv3 = inicon(4) iv4 = inicon(5) iv5 = inicon(6) si1 = inicon(7) si2 = inicon(8) si3 = inicon(9) si4 = inicon(10) si5 = inicon(11) col2 = int(point(1)) Row2 = int(point(2)) allocate(PtosCont(2,1)) PtosCont(1,1) = int(point(3)) PtosCont(2,1) = int(point(4)) !Creating pixel type map allocate(MatLevel(ncols,nrows)) do i=1,ncols do j=1,nrows if (areaA(i,j) /= no_data1) then if (areaA(i,j) < Hillslope) then MatLevel(i,j)=1 elseif (areaA(i,j) >= Hillslope .and. areaA(i,j) < Channel) then MatLevel(i,j)=2 elseif (areaA(i,j) >= Channel) then MatLevel(i,j)=3 endif else MatLevel(i,j)=no_data1 endif enddo enddo ! -------------------------------------------------------------------------------- !Reading the calibration parameters and FS inside the folder Datos_cuenca R1 = CALIB(1) R2 = CALIB(2) R3 = CALIB(3) R4 = CALIB(4) R5 = CALIB(5) R13 =CALIB(6) R6 = CALIB(7) R7 = CALIB(8) R8 = CALIB(9) R9 = CALIB(10) R10= CALIB(11) R11= CALIB(12) R12= CALIB(13) FS = CALIB(14) !Reading the parameters of Geomorphological Kinematic Wave inside the folder Datos_cuenca es =0.16670d0 teta=1.260d0 ! alfa1: Wb & Qb [rango: 0.34 a 0.55] alfa1 = 0.50d0 ! alfa2: Wt & Qt [rango: 0.05 a 0.2] alfa2= 0.20d0 ! k1: Qb & Acum [rango: 0.5 a 0.75] k1= 0.60d0 ! Fhi: Qb & Acum [rango: 0.65 a 0.8] fhi = 0.750d0 !c1: Calibration coefficient [rango: 0.5 a 5.75] c1= 3.260d0 !cd: cd= 20.0d0 !cn: cn= 0.0470d0 !-----------------------------------------------------------------------! !Parameters for the overland flow velocity and subsurface flow velocity !E: Coeficiente de la ecuacion del rad hidraulico epsi=0.0380d0


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!e1: exponente de la ecuacion del radio hidraulico e1=0.3150d0 !mn: manning manning= 0.50d0 !Reading the raingauges and the precipitation event inside the folder Datos_cuenca archivo = file13 open(50,file=archivo,status='old') read(50,*); read(50,*); read(50,*); read(50,*); !Reading dt read(50,*) dt Read(50,*); read(50,*); !Reading the total number of precipitation data read(50,*) nreg read(50,*); read(50,*) !Reading the number of raingauges read(50,*) npt read(50,*); read(50,*); read(50,*) !Dimension attributes allocate (precip(npt,nReg)) allocate (Pevento(2,npt)) !Reading the array of raingauges location read(50,*)((Pevento(i,j),i=1,2), j=1,npt) read(50,*) read(50,*) read(50,*) read(50,*) read(50,*) !Reading the precipitation data [mm] read(50,*) ((precip(i,j),i=1,npt),j=1,nreg) close(50) !Reading the observed data (Qreal) data inside the folder Output data IF (INCQ==.TRUE.) Then archivo = file14 open(60, file = archivo, Status ='Old') Allocate (Qreal(nreg)) Do i=1,nreg Read (60,*,Err=114) Qreal(i) End do close(60) End if Err = 0 Go to 150 100 mensaje="100 Internal error found in"//file1 Call errores(mensaje) goto 150 101 mensaje="101 Internal error found in"//file2 Call errores(mensaje) goto 150 102 mensaje='102 Internal error found in'//file3 Call errores(mensaje) goto 150 103 mensaje='103 Internal error found in'//file4 Call errores(mensaje) goto 150 104 mensaje='104 Internal error found in'//file5 Call errores(mensaje) goto 150 105 mensaje='105 Internal error found in'//file10 Call errores(mensaje) goto 150 106 mensaje='106 Internal error found in'//file9 Call errores(mensaje) goto 150 107 mensaje='107 Internal error found in'//file8 Call errores(mensaje) goto 150 108 mensaje='108 Internal error found in'//file11 Call errores(mensaje) goto 150 109 mensaje='109 Internal error found in'//file6

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Call errores(mensaje) goto 150 110 mensaje='111 Internal error found in'//file7 Call errores(mensaje) goto 150 111 mensaje='112 Internal error found in'//file12 Call errores(mensaje) goto 150 114 mensaje='112 Internal error found in'//file14 Call errores(mensaje) 150 Return End Subroutine ! ****************************************************** ! * Subrutina que muestra el tipo de error encontrado ! * en una ventana y lo alamcena en el fichero errores ! ****************************************************** Subroutine errores(mensaje) Use DFLIB Use DFLOGM Implicit none Character mensaje*200,hora*10,dia*8,artem*128,dirtra*128 Integer :: i4 Call date_and_time(dia,hora) i4=SETTEXTCOLOR(12) !red Write(1,*)'Fecha:'//dia(7:8)//'/'//dia(5:6)//'/'//dia(1:4)//' Hora:'//hora(1:2)//':'//hora(3:4)//':'//hora(5:10) Write(1,*)mensaje Return End subroutine Subroutine Basin() use modules implicit none !=============================================================================== !Declaration of variables integer tipo, prueba, sum integer, allocatable :: vfinal(:,:) integer cont,area,lugar,drenaid,z,cont2,tam1 integer tenia real long !----------------------------------------------------------------------------------------------------! !Creating the basin drainage array: vfinal(1,:)=ID consecutivo, vfinal(2,:)=Contador de res (cont2), !vfinal(3,:)=column (col), vfinal(4,:)=row (row), vfinal(5,:)=Puntos de control area=ncols*nrows allocate (vfinal(5,area)) vfinal =0.0 vfinal(1,area)=1; vfinal(2,area)=0; vfinal(3,area)=col2; vfinal(4,area)=row2; vfinal(5,area)=1; tenia = 1 cont2 = 1 sum=1 ! Calling subroutine position to find the cells draining from down to up do while (col2 > 0) call posicion(row2,col2,DIRe,ncols,nrows,cont) do i=1,cont vfinal(1,area-tenia+1-i)=tenia+i vfinal(2,area-tenia+1-i)=cont2 vfinal(3,area-tenia+1-i)=res(1,i) vfinal(4,area-tenia+1-i)=res(2,i)


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vfinal(5,area-tenia+1-i)=0.0 end do !updating "tenia" to define the dimension of the final vecor tenia=tenia+cont !updating the row and column taking the next one col2=vfinal(3,area - cont2) row2=vfinal(4,area - cont2) cont2=cont2 + 1 deallocate (res) end do !Creating the array called resultado using the previous vfinal, and adding three new columns allocate(resultado(7,cont2-1)) resultado =0.0 do i=2,cont2 do j=1,5 resultado(j,cont2-i+1)=vfinal(j,area-i+2) end do !Calculating the effective longitude of each vector Lugar = Dire(vfinal(3,area - i + 2),vfinal(4,area - i + 2)) prueba=mod(Lugar,2) if (prueba==0) then long=dx else long=sqrt(2*dx**2) end if resultado(6,cont2-i+1)=long end do deallocate(vfinal) !Including the control points to the basin drainage array do i=1,cont2-1 if (int(resultado(3,i)) == PtosCont(1,1) .and. int(resultado(4,i))==PtosCont(2,1)) then resultado(5,i)=2 go to 10 End if end do !Writing the array called result such as tabla !Table for the model 10 cont2=cont2-1; tam1=7 !number of rows and columns of the matrix or table Trows = cont2 Tcols = tam1 end subroutine ! ------------------------------------------------------------------------- Subroutine posicion(rowe,cole,Dire,ncols,nrows,cont) use Modules,only:res implicit none !Definición de variables integer ncols,nrows integer rowe,cole,Dire(ncols,nrows) integer, intent(out) :: cont integer kf,kc,c,f,z integer, allocatable :: aux1(:,:) integer, allocatable :: aux2(:,:) allocate (aux1(2,1)) cont=0 do kf=1,3

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do kc=1,3 c=cole + kc - 2 f=rowe + kf - 2 if (((c <= ncols) .and. (c>0)) .and. ((f <= nrows) .and. (f>0))) then if (Dire(c,f)== 3*kf - kc+1) then cont=cont+1 allocate (aux2(2,cont)) aux2(1,cont)=c aux2(2,cont)=f if (cont>1) then do z=1,cont-1 aux2(1,z)=aux1(1,z) aux2(2,z)=aux1(2,z) end do end if deallocate (aux1) allocate (aux1(2,cont)) aux1=aux2 deallocate (aux2) end if end if end do end do allocate (res(2,cont)) res=aux1 !-----------------------------------------------------------------------------------------------! End subroutine Subroutine Rainfall() !This subroutine was developed by Velásquez G., N., 2011. Simulaciòn !de sedimentos a partir de un modelo conceptual y distribuido no lineal !MSc Thesis. Universidad Nacional de Colombia. 131 p. use modules implicit none ! ================================================================================= ! Part 1 Tesselacion !-----------------------------------------------------------------------------------------------! !Declaration of variables integer k,z,a,b,c,g,flag,flag1,flag2,cont1,cont2,cont3,tam2,prueba,n real Ymin(2),Ymax(2),Ymin1,Ymax1,Xmed(2),Xmed1,Ptri(2,3),mL,mR,xL,xR,m1,a1,m2,a2,ar,al real Ax,Ay,Bx,By,Cx,Cy, radio, dist,xmin1,xmin2,xmax1,xmax2,ymin2,ymax2,x,y,ccx,ccy real, allocatable ::Pt(:,:) integer, allocatable :: conex(:,:),conex2(:,:),Tri(:,:) real*8 punto(2,1),oriP,Ori1,Ori2,Ori3 real, allocatable :: mapapert(:,:) integer, allocatable :: perte(:) real, allocatable :: tabla(:,:) !------------------------------------------------------------------------------------------------! !Se crea el triangulo que abarca los demás puntos !Busca el Ymin y el Ymax Ymax=maxval(Pevento,DIM=2) Ymax1=Ymax(2) Ymin=minval(Pevento,DIM=2) Ymin1=Ymin(2) if (Ymin1==0) then Ymin1=-1 end if !Valor medio en el eje de las X Xmed=sum(Pevento,DIM=2) Xmed1=Xmed(1)/npt; !--------------------------------------------------------------------------------------------------! !Comienza a iterar buscando el triangulo que contenga todos los puntos !Designa los puntos originales del triangulo imaginario Ptri(1,1)=Xmed1 Ptri(2,1)=Ymax1+0.5*Ymax1 Ptri(1,2)=Xmed1+abs(2*Xmed1)


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Ptri(2,2)=Ymin1-abs(0.5*Ymin1) Ptri(1,3)=Xmed1-abs(2*Xmed1) Ptri(2,3)=Ymin1-abs(0.5*Ymin1) !Comienza a iterar el triangulo imaginario flag1=0 do while (flag1==0) flag2=0 !Define la pendiente de ambos lados del triangulo mR=(Ptri(2,1)-Ptri(2,2))/(Ptri(1,1)-Ptri(1,2)) aR=Ptri(2,1)-mR*Ptri(1,1) mL=(Ptri(2,1)-Ptri(2,3))/(Ptri(1,1)-Ptri(1,3)) aL=Ptri(2,1)-mL*Ptri(1,1) !Busca si los puntos se encuentran dentro del triangulo do i=1,npt xR=(Pevento(2,i)-aR)/mR xL=(Pevento(2,i)-aL)/mL if (Pevento(1,i) > xR .or. Pevento(1,i) < xL) then flag2=flag2+1 end if end do !Si alguno de los puntos queda por fuera, crece el tamaño del triangulo if (flag2/=0) then Ptri(1,2)=Ptri(1,2) + abs(2*Xmed1) Ptri(1,3)=Ptri(1,3) - abs(2*Xmed1) flag=0; else flag1=1 end if end do !---------------------------------------------------------------------------------------------------------------------! !Comienza a introducir puntos dentro del triangulo !Crea un vector de tamaño n+3 y le asigna todo lo existente allocate (Pt(2,npt+3)) allocate (conex(npt+3,npt+3)) allocate (Tri(3,npt*npt*2)) do i=1,npt*npt do j=1,3 Tri(j,i)=-9999 end do end do do i=1,npt Pt(1,i)=Pevento(1,i) Pt(2,i)=Pevento(2,i) end do do i=1,3 Pt(1,npt+i)=Ptri(1,i) Pt(2,npt+i)=Ptri(2,i) end do !Comienza la agregación de puntos cont1=1 cont2=1 Tri(1,1)=npt+3 Tri(2,1)=npt+2 Tri(3,1)=npt+1 do a=1,npt !Limpia los conexiones en cada iteración do i=1,npt+3 do j=1,npt+3 conex(i,j)=0 end do end do !Observa en que triangulos cae el pt introducido !tam1=size(tri,DIM=2) do b=1,cont2 if (Tri(1,b)/=-9999) then !Obtiene Ax, Ay, Bx, By, etc... Ax=Pt(1,Tri(1,b)) Ay=Pt(2,Tri(1,b)) Bx=Pt(1,Tri(2,b)) By=Pt(2,Tri(2,b)) Cx=Pt(1,Tri(3,b))

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Cy=Pt(2,Tri(3,b)); !Calcula el centro en X CCx=(By*Ax**2 - Cy*Ax**2 - By**2*Ay + Cy**2*Ay + Bx**2*Cy + Ay**2*By + Cx**2*Ay & & - Cy**2*By - Cx**2*By - Bx**2*Ay + By**2*Cy - Ay**2*Cy)/(2*(Ay*Cx+By*Ax-By*Cx-Ay*Bx-Cy*Ax+Cy*Bx)); !Calcula el centro en Y CCy=(Ax**2*Cx+ Ay**2*Cx + Bx**2*Ax - Bx**2*Cx + By**2*Ax - By**2*Cx - Ax**2*Bx - & & Ay**2*Bx - Cx**2*Ax + Cx**2*Bx - Cy**2*Ax + Cy**2*Bx)/(2*(Ay*Cx+By*Ax-By*Cx-Ay*Bx-Cy*Ax+Cy*Bx)); !Calcula el radio del circulo radio=sqrt((CCx-Pt(1,Tri(1,b)))**2+(CCy-Pt(2,Tri(1,b)))**2); !Observa si el punto queda dentro de la circunferencia dist=sqrt((CCx-Pt(1,a))**2+(CCy-Pt(2,a))**2) if (dist<radio) then !Crea las conexiones pertenecientes al poligono de incerción conex(Tri(1,b),Tri(2,b))=conex(Tri(1,b),Tri(2,b))+1 conex(Tri(2,b),Tri(1,b))=conex(Tri(2,b),Tri(1,b))+1 conex(Tri(1,b),Tri(3,b))=conex(Tri(1,b),Tri(3,b))+1 conex(Tri(3,b),Tri(1,b))=conex(Tri(3,b),Tri(1,b))+1 conex(Tri(3,b),Tri(2,b))=conex(Tri(3,b),Tri(2,b))+1 conex(Tri(2,b),Tri(3,b))=conex(Tri(2,b),Tri(3,b))+1 !Destruye el triangulo si este cumple la regla do c=1,3; Tri(c,b)=-9999; end do end if end if end do !Selecciona los puntos donde existe conexión do c=1,size(conex,2) if (sum(conex(c,:))/=0) then conex(c,a)=1; end if end do !Obtiene los triangulos nuevos do i=1,npt+3-1 if (conex(i,a)==1) then do j=i+1,npt+3 if (conex(j,a)==1) then if (conex(j,i)==1) then cont2=cont2+1; !Tri: matriz que indica que nodos pertenecen a que triangulo Tri(1,cont2)=a;Tri(2,cont2)=i;Tri(3,cont2)=j; end if end if end do end if end do end do !---------------------------------------------------------------------------------------------------------------------! !Borra los triangulos imaginarios do i=1,cont2 if (Tri(1,i)>npt .or. Tri(2,i)>npt .or. Tri(3,i)>npt) then do j=1,3; Tri(j,i)=-9999; end do end if end do !---------------------------------------------------------------------------------------------------------------------! !Completa triangulos incompletos !Limpia los conexiones en cada iteración allocate (conex2(npt,npt)) do i=1,npt; do j=1,npt; conex2(i,j)=0; end do; end do !Indica las conexiones dadas por los triangulos do i=1,cont2 if (Tri(1,i)/=-9999) then conex2(Tri(1,i),Tri(2,i))=1;conex2(Tri(2,i),Tri(1,i))=1; conex2(Tri(1,i),Tri(3,i))=1;conex2(Tri(3,i),Tri(1,i))=1; conex2(Tri(2,i),Tri(3,i))=1;conex2(Tri(3,i),Tri(2,i))=1; end if end do


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!Observa que conexiones faltan do i=1,npt do j=i+1,npt if (conex2(j,i)/=1) then if (Pevento(2,i)/=Pevento(2,j)) then if (Pevento(1,i)/=Pevento(1,j)) then !Calcula la pendiente e intercepto m1=(Pevento(2,i)-Pevento(2,j))/(Pevento(1,i)-Pevento(1,j)) a1=Pevento(2,i)-m1*Pevento(1,i) prueba=0 !Compara la linea con las demas a ver si se cruza do z=1,cont2 if (Tri(1,z)/=-9999) then a=2 do k=1,2 do g=a,3 !calcula pendiente e intercepto m2=(Pevento(2,Tri(k,z))-Pevento(2,Tri(g,z)))/(Pevento(1,Tri(k,z))-Pevento(1,Tri(g,z))) a2=Pevento(2,Tri(k,z))-m2*Pevento(1,Tri(k,z)) !Calcula el intercepto x=(a1-a2)/(m2-m1); y=(a1*m2-a2*m1)/(m2-m1) !Encuentra maximos y minimos xmin1=min(Pevento(1,i), Pevento(1,j)); xmin2=min(Pevento(1,Tri(k,z)), Pevento(1,Tri(g,z))) xmax1=max(Pevento(1,i), Pevento(1,j)); xmax2=max(Pevento(1,Tri(k,z)), Pevento(1,Tri(g,z))) ymin1=min(Pevento(2,i), Pevento(2,j)); ymin2=min(Pevento(2,Tri(k,z)), Pevento(2,Tri(g,z))) ymax1=max(Pevento(2,i), Pevento(2,j)); ymax2=max(Pevento(2,Tri(k,z)), Pevento(2,Tri(g,z))) !Observa si el intercepto se encuentra entre ambas linea if (x>xmin1 .and. x<xmax1 .and. y>ymin1 .and. y<ymax1 .and. x>xmin2 .and. x<xmax2 .and. y>ymin2 .and. y<ymax2) then prueba=prueba+1; end if end do a=a+1; end do end if end do !Si no cruza ninguna linea se genera la nueva linea if (prueba==0) then conex2(i,j)=1; conex2(j,i)=1; end if end if end if end if end do end do !---------------------------------------------------------------------------------------------------------------------! !Selecciona finalmente los triangulos !Vacia el vector do i=1,npt*npt; do j=1,3; Tri(j,i)=-9999; end do; end do !Encuentra los triangulos cont3=0 do z=1,npt do i=1,npt if (conex2(i,z)==1) then do j=i+1,npt if (conex2(j,z)==1) then if (conex2(j,i)==1) then !Tri: matriz que indica que nodos pertenecen a que !triangulo. cont3=cont3+1; Tri(1,cont3)=z Tri(2,cont3)=i Tri(3,cont3)=j; end if end if end do conex2(z,i)=2;

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end if end do conex2(npt,z)=2; end do !Deja el vector listo pa ser impreso allocate (Trif(3,cont3)) Trif=0.0 do i=1,cont3 do j=1,3; Trif(j,i)=Tri(j,i); end do end do ! ================================================================================= ! Part 2: Asignacion !--------------------------------------------------------------------------------------------------------------------! !Lectura de variables !Comienza a buscar el triangulo de pertenencia de cada uno de los puntos de la cuenca n = Trows allocate(perte(n)) do i=1,n !Inicializa una bandera que revisa si el punto se encuentra dentro de algún triangulo flag=0 !Obtiene el punto a evaluar punto(1,1)=xll+Resultado(3,i)*dx-0.5*dx punto(2,1)=yll+(nrows-resultado(4,i))*dx+0.5*dx !Comienza a buscar el triangulo de pertenencia do j=1,cont3 !Calcula la orientación del triangulo oriP=(Pevento(1,Trif(1,j))-Pevento(1,Trif(3,j)))*(Pevento(2,Trif(2,j))-Pevento(2,Trif(3,j)))-(Pevento(2,Trif(1,j))-Pevento(2,Trif(3,j)))*(Pevento(1,Trif(2,j))-Pevento(1,Trif(3,j))) !Calcula la orientación de los triangulos resultantes de unir P con los vertices del Tri Ppal. !Ori1: A1A2P ori1=(Pevento(1,Trif(1,j))-punto(1,1))*(Pevento(2,Trif(2,j))-punto(2,1))-(Pevento(2,Trif(1,j))-punto(2,1))*(Pevento(1,Trif(2,j))-punto(1,1)) !Ori2: A2A3P ori2=(punto(1,1)-Pevento(1,Trif(3,j)))*(Pevento(2,Trif(2,j))-Pevento(2,Trif(3,j)))-(punto(2,1)-Pevento(2,Trif(3,j)))*(Pevento(1,Trif(2,j))-Pevento(1,Trif(3,j))) !Ori3: A3A1P ori3=(Pevento(1,Trif(1,j))-Pevento(1,Trif(3,j)))*(punto(2,1)-Pevento(2,Trif(3,j)))-(Pevento(2,Trif(1,j))-Pevento(2,Trif(3,j)))*(punto(1,1)-Pevento(1,Trif(3,j))) !Si las cuatro orientaciones son o positivas o negativas el punto se encuentra dentro if ((oriP>0 .and. ori1>0 .and. ori2>0 .and. ori3>0) .or. (oriP<0 .and. ori1<0 .and. ori2<0 .and. ori3<0)) then perte(i)=j resultado(7,i)=j flag=1; end if end do if (flag==0) then perte(i)=no_data1 resultado(7,i)=0 end if end do ! ================================================================================= End subroutine Subroutine Matrix() use modules implicit none ! ================================================================================= !Introducing the parameters to the matrix allocate(Level(Trows+1)) allocate(Evp(Trows),S1max(Trows),S3max(Trows),Ks(Trows),Kp(Trows)) allocate(Slope(Trows),Cohesion(Trows),Friction(Trows),acum(Trows))


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allocate(GammaS(Trows),Zs(Trows)) Do i = 1,Trows !Forming a vector of the grid cell level accroding to the hillslope and channel thresholds Level(i)=MatLevel(resultado(3,i),resultado(4,i)) ![no units] !Forming vectors with the hydrological parameters S1max(i)=MatS1max(resultado(3,i), resultado(4,i)) ![%] if (S1max(i)==0.0) then S1max(i)=1.0 endif S3max(i)=MatS3max(resultado(3,i), resultado(4,i)) ![%] if (S3max(i)==0.0) then S3max(i)=1.0 end if EVP(i) =MatEVP(resultado(3,i),resultado(4,i)) ![mm] Ks(i) =MatKs(resultado(3,i),resultado(4,i)) ![cm/h] Kp(i) =MatKp(resultado(3,i),resultado(4,i)) ![cm/h] !Forming vectors with the geotechnical parameters Friction(i) =MatFriction(resultado(3,i), resultado(4,i)) ![Rad] Cohesion(i) =MatCohesion(resultado(3,i), resultado(4,i)) ![kN/m^2] GammaS(i) =MatGammaS(resultado(3,i), resultado(4,i)) ![kN/m^3] Zs(i) =MatZs(resultado(3,i), resultado(4,i)) ![m] !Forming vectors with the DEM variables Slope(i) =MatSlope(resultado(3,i), resultado(4,i)) ![Rad] Acum(i) =AreaA(resultado(3,i),resultado(4,i)) if (Acum(i)==0.0) then Acum(i)=(dx**2.0) ![m^2] endif end do End subroutine Subroutine Model() use modules use modgeneral,only: INCQ,file15 Use DFLIB Use DFPORT use dflogm Implicit none !================================================================================= !Declaration of variables Integer :: z,cont,drenaid,selecti,i4,op,ii,jj Double precision :: a3,b3,c3,coef1,conver,E,E2,E3,E4,E5,Z3,Ac,area1 Double precision :: R(5) Double precision,allocatable :: Vn(:) logical sim2,folder character*100 path Type (rccoord) curpos Allocate(s1(Trows),s2(Trows),s3(Trows),s4(Trows),s5(Trows)) Allocate(Vn(Trows),Zw(Trows)) Allocate(az(2,Trows),bz(2,Trows),cz(2,Trows),dz(2,Trows),coef(Trows)); Allocate(Bo(Trows), Est(Trows)) Allocate(Stream_flow(nReg),Subsur_level(nReg)) Allocate(v2(Trows),v3(Trows),v4(Trows),v5(Trows),kpp(Trows)) Allocate(Zmin(Trows),Zwcrit(Trows),Zmax(Trows)) Allocate(MatEst(ncols,nrows),MatEst1(ncols,nrows),MatEst2(ncols,nrows)) !--------------------------------------------------------------------------------------------------------------------! Archivo = 'C:\'//TRIM(ADJUSTL(file15))//"\Qsim.asc" open(70,file=archivo,status='unknown') archivo = 'C:\'//TRIM(ADJUSTL(file15))//"\subsurface_level.asc" open(80,file=archivo,status='unknown') 102 az=1; bz=1; cz=1; dz=1; coef=1;

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!Starting water balance [mm] entradas=0.0 ; salidas=0.0 ; R=0.0 Stream_flow=0.0 !For calculating RMSE & NS SE=0.0 ; Nash=0.0 mean=sum(Qreal)/nreg !Calculating GKW coefficients and the exponents ey=2.0/3.0-(es*teta) ez=1.0/(1.0+ey*alfa2) k2=(cn*(cd)**es*(c1**ey)*(k1**(ey*(alfa1-alfa2))))**-ez w1=ey*ez*(1-alfa2) w2=-ez*ey*fhi*(alfa1-alfa2) w3=ez*(ey-1.0/6.0) !To convert mm a m^3 conver=(dx**2)/1000.0 ![m2]*[m/mm]=[m3/mm] MatEst = no_data1 Est = 0.0 Zwcrit = 0.0 Zmin = 0.0 Zmax = 0.0 Bo =0.0 !Iteration to get values for the table do i=1,Trows !----------------------------------------------------------------! !Initial conditions of the tanks for each pixel S1(i)=si1 ![mm] S2(i)=si2 ![mm] S3(i)=si3 ![mm] S4(i)=si4 ![mm] S5(i)=si5 ![mm] !----------------------------------------------------------------! !Water balance entradas=entradas+S1(i)+S2(i)+S3(i)+S4(i)+S5(i)/conver !----------------------------------------------------------------! !Getting values for the rainfall iteration if (resultado(7,i) == 0) then !Just to be sure there is one trinagle for each pixel resultado(7,i) = 1 endif az(1,i)=Pevento(1,Trif(1,resultado(7,i))) az(2,i)=Pevento(2,Trif(1,resultado(7,i))) bz(1,i)=Pevento(1,Trif(2,resultado(7,i))) bz(2,i)=Pevento(2,Trif(2,resultado(7,i))) cz(1,i)=Pevento(1,Trif(3,resultado(7,i))) cz(2,i)=Pevento(2,Trif(3,resultado(7,i))) dz(1,i)=xll+resultado(3,i)*dx-0.5*dx dz(2,i)=yll+(nrows-resultado(4,i))*dx+0.5*dx coef(i)=(bz(1,i)-az(1,i))*(cz(2,i)-az(2,i))-(cz(1,i)-az(1,i))*(bz(2,i)-az(2,i)) !----------------------------------------------------------------! !Calibration process S1max(i) =S1max(i)*R1 ![mm] EVP(i) =evp(i)*R2 ![mm] Ks(i) =Ks(i)*R3*dt*fc ![mm] Kp(i) =Kp(i)*R4*dt*fc ![mm] Kpp(i) =Kp(i)*R5*dt*fc ![mm] v2(i) =iv2*R6 ![m/sec] v3(i) =iv3*R7 ![m/sec] v4(i) =iv4*R8 ![m/sec]


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v5(i) =iv5*R9 ![m/sec] Cohesion(i) =Cohesion(i)*R10 ![KPa] Friction(i) =Friction(i)*R11 ![Rad] Zs(i) =Zs(i)*R12 ![m] S3max(i) =S3max(i)*R13 !To be sure S1(j) <= S1max(j) if (S1(i) > S1max(i)) then S1max(i) = S1(i) End if !========================================================================================= !FIRST STABILITY ANALYSIS ! Calculating the immunity or critical depth Zmin(i) = Cohesion(i)/((GammaW*(COS(Slope(i)))**2*TAN(Friction(i)))+(GammaS(i)*(COS(Slope(i)))**2*(TAN(Slope(i))-TAN(Friction(i))))) ! Calculating the minimum value of landslide-triggering saturated depth Zwcrit(i) = (GammaS(i)/GammaW)*Zs(i)*(1.0-(TAN(Slope(i))/TAN(Friction(i))))+(Cohesion(i)/(GammaW*(COS(Slope(i)))**2*TAN(Friction(i)))) !Calculating soil thickness for unstable conditions Zmax (i) = Cohesion(i)/((GammaS(i)*(COS(Slope(i)))**2)*(TAN(Slope(i))-TAN(Friction(i)))) !Calculating slope angle for unconditional stable conditions Bo(i) = ATAN(-TAN(friction(i)*(GammaW-GammaS(i))/GammaS(i))) !-----------------------------------------------------------------! ! Forming the initial matrix of stability If (Level(j)==3) then MatEst(resultado(3,i),resultado(4,i)) = 0 !Unconditionally stable else if (slope(i) < Bo(i)) then MatEst(resultado(3,i),resultado(4,i)) = 0 !Unconditionally stable else if ( Zs(i) < Zmin(i)) then MatEst(resultado(3,i),resultado(4,i)) = 0 !Unconditionally stable else if (Zs(i) > Zmax(i)) then MatEst(resultado(3,i),resultado(4,i)) = 1 !Unconditionally unstable else MatEst(resultado(3,i),resultado(4,i)) = 2 !Conditional stability end if end do ! Printing the stability matrix Archivo = 'C:\'//TRIM(ADJUSTL(file15))//"\MatEst1.asc" open(90,file=archivo,status='unknown') write(90,'("ncols",1x,I4)') ncols write(90,'("nrows",1x,I4)') nrows write(90,'("xllcorner",1x,F15.7)') xll write(90,'("yllcorner",1x,F15.7)') yll write(90,'("cellsize",1x,F5.2)') dx write(90,*) 'nodata_value',no_data1 Do jj = 1, nrows write(90,'(<ncols>(1x,I5))') (MatEst(ii,jj),ii=1,ncols) End Do close(90) !*********************************************************************************************************************************! !To iterate for each time interval do i=1,nReg cont=0.0

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!================================================================================================================================! !To iterate along each grid pixel in the time interval do j=1,Trows !--------------------------------------------------------------------------------------------------------! !Getting the value where the pixel drainage drenaid=resultado(1,j)-resultado(2,j) + j !--------------------------------------------------------------------------------------------------------! !Getting R1 for the pixel according to the triangle where it belongs !Getting the determinant values a3=precip(Trif(1,resultado(7,j)),i) b3=precip(Trif(2,resultado(7,j)),i) c3=precip(Trif(3,resultado(7,j)),i) !Gettting the coefficient to obtain the rainfall coef1=(cz(1,j)-az(1,j))*(dz(2,j)-az(2,j))*(b3-a3)+(bz(2,j)-az(2,j))*(c3-a3)*(dz(1,j)-az(1,j))-(b3-a3)*(cz(2,j)-az(2,j))*(dz(1,j)-az(1,j))-(dz(2,j)-az(2,j))*(c3-a3)*(bz(1,j)-az(1,j)) !Rainfall for the pixel (j) R(1)=a3-coef1/coef(j) ![mm] !Water balance updating entradas=entradas+R(1) ![mm] !--------------------------------------------------------------------------------------------------------! !First Tank T1 (Static storage) !Excedence that permit to continue water accoding to the water content in the soil R(2)=R(1) - min(R(1)*(1-(S1(j)/S1max(j))**2),S1max(j)-S1(j)) ![mm] !T1 level S1(j)=min(S1(j)+R(1)-R(2),S1max(j)) ![mm] !Calculating real evapotranspiration !E=min(Evr(i)*R2,S1(j)) ![mm] !If there is no real evapotranspiration data, it is used the potential evapotranspiration E=min(Evp(j)*(S1(j)/S1max(j))**0.6,S1(j)) ![mm] !T1 level updating S1(j)=S1(j)-E ![mm] !Water balance salidas=salidas+E ![mm] !--------------------------------------------------------------------------------------------------------! !Infiltration R(3)=min(R(2),Ks(j)) ![mm] !--------------------------------------------------------------------------------------------------------! !Third Tank T3 (Gravitational water storage) !Percolation R(4)=min(R(3),Kp(j)) ![mm] !T3 water level S3(j)=min(S3(j)+R(3)-R(4),S3max(j)) ![mm] !T3 excedence Z3=max(0.0,S3(j)+R(3)-R(4)-S3max(j)) !Subsurface outflow using the equation of Kubota & Sivapalan (1995) for mountain basins covered by forests and b=2 do z=1,3 Area1=S3(j)*conver/(dx+v3(j)*dt) ![m^2] vn(j)= R7*((Ks(j)/(dt*1000.0))*sin(Slope(j))*(Area1*dx)**2)/(3*((S3max(j)/1000.0)*(dx**2))**2) v3(j)=(2.0*vn(j)+v3(j))/3.0 end do E3=Area1*v3(j)*dt/conver ![mm] !Subsurface outflow usin linear reservoir equation !E3=(1-resultado(6,j)/(v3(j)*dt+resultado(6,j)))*S3(j) ![mm], resultado(6,j) =ddx(j) !T3 level updating S3(j)=S3(j) - E3 ![mm] !Water balance if (j==Trows) then Salidas = Salidas + E3 endif !--------------------------------------------------------------------------------------------------------!


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!Second Tank T2 (Surface storage) !T2 water level S2(j)=S2(j)+R(2)-R(3)+Z3 ![mm] !Overland flow velocity do z=1,3 Area1=S2(j)*conver/(dx+v2(j)*dt) ![m^2] !Using an equation function of transversal section area ofthe flow over natural surfaces vn(j)=R6*(epsi*Area1**(0.667*e1)*(ATAN(Slope(j))**0.5))/manning v2(j)=(2.0*vn(j)+v2(j))/3.0 enddo !Flow out E2=Area1*v2(j)*dt/conver ![mm] ! E2=(1-resultado(6,j)/(v2(j)*dt+resultado(6,j)))*S2(j) ![mm], resultado(6,j) =ddx(j) !T2 level updating S2(j)=S2(j)-E2 ![mm] !Water balance if (j==Trows) then Salidas = Salidas + E2 endif !--------------------------------------------------------------------------------------------------------! !Four Tank T4 (Aquifer) !Groundwater outflow R(5)=min(R(4),Kpp(j)) ![mm] !T4 water level S4(j)=S4(j)+R(4)-R(5) ![mm] !Flow out using a linear equation E4=(1-resultado(6,j)/(v4(j)*dt+resultado(6,j)))*S4(j) ![mm], resultado(6,j) =ddx(j) !T4 level updating S4(j)=S4(j)-E4 ![mm] !Water balance if (j==Trows) then Salidas = Salidas + E4 endif !--------------------------------------------------------------------------------------------------------! !Water distribution according to the type of pixel select case(Level(j)) case(1) S2(drenaid)=S2(drenaid)+E2 ![mm] S3(drenaid)=S3(drenaid)+E3 ![mm] S4(drenaid)=S4(drenaid)+E4 ![mm] case(2) S5(j)=S5(j)+(E2+E3)*conver ![m3] S4(drenaid)=S4(drenaid)+E4 ![mm] case(3) S5(j)=S5(j)+(E2+E3+E4)*conver ![m3] end select !--------------------------------------------------------------------------------------------------------! !Fith Tank T5 (Channel) !If there is water in T5 then it is flow downslope if (S5(j)>0) then do z=1,3 Area1=S5(j)/(dx+(v5(j)*dt)) ![m2] vn(j)=R9*K2*(Area1**w1)*(acum(j)**w2)*(ATAN(Slope(j))**w3) v5(j)=(2.0*vn(j)+v5(j))/3.0 enddo E5=Area1*v5(j)*dt ![m3] S5(j)=S5(j)-E5 ![m3] !Pass the water to the apropiate grid cell if (resultado(2,j)/=0) then if (level(drenaid)==1) then S2(drenaid)=S2(drenaid)+E5 else S5(drenaid)=S5(drenaid)+E5 ![m3] end if end if !Water balance if (j==Trows) then salidas=salidas+E5/conver endif

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end if !----------------------------------------------------------------------------------------------! !Control points if (resultado(5,j)==2) then !cont = cont+1 Stream_flow(i)=E5/dt ![m3/s] Subsur_level(i)=S3(j)*Zs(j)/S3max(j) ![mm] End if !----------------------------------------------------------------------------------------------! !calculating perched water table Zw(j) = (S3(j)*Zs(j))/S3max(j) !==============================================================================================! ! SECOND STABILITY ANALYSES !Susceptibility: !Matest = 1, high susceptibility !MatEst = 0, no susceptibility !MatEst = 0, low susceptibility !MatEst = 2, Potential unstable if ( MatEst(resultado(3,j),resultado(4,j)) > 1) then !For potential unstable pixels if ((Zw(j))>=(Zwcrit(j))) then MatEst(resultado(3,j),resultado(4,j)) = -1 !Failure Level(j)=2 else Num=Cohesion(j)+(GammaS(j)*Zs(j)-Zw(j)*GammaW)*(COS(Slope(j)))**2*TAN(Friction(j)) Den=GammaS(j)*Zs(j)*SIN(Slope(j))*COS(Slope(j)) if ((Num/Den)<=FS) then MatEst(resultado(3,j),resultado(4,j)) = -1 Level(j)=2 end if end if end if if (i==nreg) then if (MatEst(resultado(3,j),resultado(4,j)) > FS .or. (MatEst(resultado(3,j),resultado(4,j)) == 1)) then MatEst(resultado(3,j),resultado(4,j)) = 0 end if end if !Hazard: !MatEst = 0, no hazard !MatEst = -1, landslide end do !j=Trows !------------------------------------------------------------------------------------------------------ !Water balance sim2 = .True. If (sim2) Then Call SETTEXTPOSITION(INT2(2),INT2(5),curpos) i4=SETTEXTCOLOR(9) write(1,*) write(1,*) write(1,*) write(1,*) write(1,*) write(1,*) write(1,*) CALL OUTTEXT(' % Simulation : ') write(1,'(2x,F5.1)') i*100.0/Nreg CALL OUTTEXT(' Time Interval:') write(1,'(2x,I6)') i Endif


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!Printing flow discharge in control points write(70,'(F16.6)') Stream_flow(i) write(80,'(F16.6)') Subsur_level(i) if (INCQ == .true.) Then !calculating Root Mean Square Error (RMSE) Diff1 = (stream_flow(i)-Qreal(i))**2 SE = SE + Diff1 !calculating Nash-Sutcliffe coefficient Diff2=(Qreal(i)-mean)**2 Nash=Nash+Diff2 End if end do !i=nreg Close(70) Close(80) if (INCQ == .true.) Then !RMSE & Nash-Sutcliffe coefficient RMSE = sqrt(SE/nreg) NS = 1.0-(SE/Nash) end if !----------------------------------------------------------------------------------------! !Printing Stability matrix archivo = 'C:\'//TRIM(ADJUSTL(file15))//"\MatEst2.asc" open(100,file=archivo,status='unknown') write(100,'("ncols",1x,I4)') ncols write(100,'("nrows",1x,I4)') nrows write(100,'("xllcorner",1x,F15.7)') xll write(100,'("yllcorner",1x,F15.7)') yll write(100,'("cellsize",1x,F5.2)') dx write(100,*) 'nodata_value',no_data1 Do jj = 1, nrows write(100,'(<ncols>(1x,I5))') (MatEst(ii,jj),ii=1,ncols) End Do close(100) !************************************************************************************************! !Printing water balance and multiparameter matrix archivo = 'C:\'//TRIM(ADJUSTL(file15))//"\Matrix.dat" open(200,file=archivo,status='unknown') write(200,'("RMSE=",F5.3)')RMSE write(200,'("Nash-Sutcliffe=",F5.3)')NS write(200,600) 'Rdrain','Cdrain','Row','Col','CP','Tri','Level','S1max','S3max','Ks','Kp','Slope','Bo','Friction','Cohesion','GammaS','Zs','Zmin','Zmax','Zwcrit','Est','acum' do i=1,Trows acumulado = acumulado + S1(i)+S2(i)+S3(i)+S4(i)+S5(i)/conver !forming a vector with stability values Est(i) = MatEst(resultado(3,i),resultado(4,i)) write(200,500) resultado(1,i),resultado(2,i), resultado(3,i), resultado(4,i),resultado(5,i),resultado(7,i),Level(i),S1max(i),S3max(i),Ks(i),Kp(i),slope(i),Bo(i),Friction(i),Cohesion(i),GammaS(i),Zs(i),Zmin(i),Zmax(i),Zwcrit(i),Est(i),acum(i) end do 500 format(2(1x,F7.0),2(1x,F5.0),2(1x,F3.0),1x,I1,2(1x,F7.2),2(1x,E9.2),3(1x,F4.2),2(1x,F5.2),4(1x,F6.2),1x,F4.0,1x,F10.0) 600 format(2(1x,A7),2(1x,A5),2(1x,A3),1x,A1,2(1x,A7),2(1x,A9),3(1x,A4),2(1x,A5),4(1x,A6),1x,A4,1x,A10) write(1,'(" Outflows =",F15.3," mm ")') salidas write(1,'(" Rainfall =",F15.3," mm ")') entradas write(1,'(" Storage =",F15.3," mm ")') acumulado diferencia=((salidas+acumulado-entradas)/salidas)*100 write(1,'(" Water balance (%) =",F15.5)') diferencia if (INCQ == .true.) then write(1,'(" RMSE =",F15.3)') RMSE write(1,'(" Nash-Sutcliffe =",F15.3)') NS end if !-----------------------------------------------------------------------------------------------------!

SHIA_Landslide

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End Subroutine Subroutine DEALLOCAT Use MODULES Implicit none deallocate(Dire,matslope,areaa,matks,matkp,matfriction,matgammas) deallocate(matzs,matcohesion,mats1max,mats3max,matevp,ptoscont,matlevel) deallocate(precip,pevento) If (Allocated(qreal)) Deallocate (qreal) deallocate(Resultado,trif) deallocate(level) deallocate(evp,s1max,s3max,ks,kp) deallocate(slope,cohesion,friction,acum) deallocate(gammas,zs) deallocate(s1,s2,s3,s4,s5) deallocate(zw) deallocate(az,bz,cz,dz,coef); deallocate(bo, est) deallocate(stream_flow,subsur_level) deallocate(v2,v3,v4,v5,kpp) deallocate(zmin,zwcrit,zmax) deallocate(matest,matest1,matest2) End subroutine


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Documents

Chapter 4 The model: SHIA Landslidebdigital.unal.edu.co/11473/7/71765068.2013_ 2.pdf · observation of tropical mountain terrains supported by hydrology and geotechnical theory for