Hydrology and forests approaches to modelling...• The direct runoff hydrograph that results from 1 cm excess rainfall, occurring uniformly over the basin at a uniform rate during

PESFOR-W Training School - Porto, Portugal – 23.-26. October 2018.

Hydrology and forests – approaches to modelling

Dr. Potočki Kristina, CE

University of Zagreb

Faculty of Civil Engineering

Water Research Department


Contents

1. Introduction to hydrological modeling

2. Classification of mathematical hydrological models

3. Processes in a Hydrologic Simulation Model

4. Model building approach

5. Overview of some models


1. Introduction to hydrological modeling


Models in general

• What is a model? What is the purpose of a model?

• Types of Models• Physical

• Analog• Special case of physical models• Ohm’s law analogous to Darcy’s law

• Mathematical• Equations to represent hydrologic process


Classification of mathematical hydrological models

DETERMINISTIC STOCHASTIC

Probabilistic Time SeriesPhisically Based

Conceptual Empirical

Distributed Lumped

Grid Based Subwatershed No Distribution

Semi-distributed



1. Degree of knowledge about system

• deterministic• Outcomes are obtained through known

relationships among states and events.

• One outcome for defined inputs

• stochastic• Evaluates historical time series, based on

probability

• Multiple possible outputs/outcomes

• Uncertainty analysis



2. Process representation• Empirical: Based on highly simplified relationships

• data-driven, including statistical models• e.g. Flow-stage relationship

• Conceptual: Based on mathematically convenient components that capture essential processes• abstractions of physical processes• e.g. Linear reservoir model

• Physically Based• Derived from equations representing actual physics of process• e.g. St. Venant equations for overland flow, kinematic wave


Statistically and data driven based modelling

Classical statistical models• Regression based models

• Time series models

Data-driven models (based on AI) • Genetic algorithms (GAs)

• Artificial neural networks (ANN)

• Fuzzy logic (FL)

com

plexity

• Stand/alone models

• Assistance in watershed modeling• processing data

• developing relationships between hydrologic processes

• filling voids in measured data

• combining these processes at a much larger, watershed-scale

• requires additional expertise and data resources



3. Spatial representation • Lumped: Watershed is a single spatial unit

• Semi-distributed: Watershed is divided into a number of spatial units, areas that are considered to be "homogeneous" according to some specified criteria

• Distributed: Watershed is represented by a grid/cells

Lumped

Distributed



3. Spatial representation

Lumped

Distributed


Temporal scale of hydrological models

• The computational time step of a model must be matched to its spatial scale and process descriptions.

• Time steps - from minutes to a year.

• Typical hydrologic simulation models - time step of one day or less.


Hydrologic Models - Goals

• Understand and Predict the Movement of Water

• Example: hydrograph modeling - simulate shape of hydrograph for measured or designed water input

time

Pre

cip

itati

on

time

flo

w

Hydrologic

Model

Hyetograph Hydrograph

V – surface runoff volume[m3]

Qmax– max discharge [m3/s]


Processes in a Hydrologic Simulation Model

• Each process in the watershed system represents a flux and storage of mass and/or energy. These processes have mathematical representations of one kind or another in a hydrologic simulation model.

Precipitation Runoff

Evapotranspiration Snow

Interception Glaciers

Infiltration Groundwater

Percolation

• The water balance

• system of fluxes and storages for each spatial and temporal unit


Processes in a Hydrologic Simulation Model

LumpedMODEL

P

SW1

SW2

SW3

SW4

SW5

Semi Distributed MODEL

Distributed MODEL

Formalization of Hydrologic process in each spatial unit

e.g. Stanford Watershed Model

e.g. HEC-HMS, HSPF e.g. SHE

Complexity and Data Requirement 𝝏∅

𝝏𝒕= 𝜵. ∅𝑼 + 𝜵. 𝜞𝜵∅ + 𝑸𝒔𝒔


Hydrologic Models – Approach examples

• Physically Based, distributed

• Mass transfer, momentum, and energy - simulated using partial differential equations

• Solved by various numerical methods

• E.g. SHE model

• Major physical processes in each cell/grid

• Evapotranspiration – Penman-Monteith

• Overland flow - St. Venant equations

• Unsaturated zone flow – Richards equations

• Saturated zone flow –Boussinesq equation


Hydrologic Models – Approach examples

• A transfer function - represents the lumped processes operating in a watershed

time

Pre

cip

itati

on

time

flo

w

Mathematical transfer function

input output

• Empirical and conceptual, lumped

• Transforms numerical inputs through simplified parameters that “lump” processes to numerical outputs

• Model is calibrated to obtain proper parameters

• Predictions - at outlet only

• E.g. Unit hydrograph, SCS CN method

outlet


History od watershed models1850 Rational model

1932 ShermanUnit Hydrograph

1941 GumbelExtreme Flow Analysis

Lumped conceptual modeling

Physical based Distributed modeling

Macroscale Distributed modeling

CHM

Watershed models

1800

1900

19501960

19701980

1990

1794 Chezy formula

1856 Darcy Law

1871 Saint-Venant

1802 Dalton equation

1891 Manning Formula

1911 Green & Ampt

1931 Richards

1933 Horton

Theory (physics)

MHM

Aplications

Urban Design

Hydrological Design

Hydrological Design

Design,Forecasting

Research + Management

Impact + Management

History ofWatershedModels


Watershed based modeling

• models primarily focused on individual processes

• multiple processes at relatively small-or field-scale without full incorporation of a watershed area

watershed modeling approach

Integrated Hydrologic Models – integrated processes


Watershed based modeling

VS

COUPLED models - e.g. surface-groundwater interactions


Excess Precipitation

Model

WS FlowTransformation

“Routing”UHG Methods

Stream and/or Reservoir “Routing”

EXCESS PRECIPITATION

Precipitation


RUNOFF HYDROGRAPH

RUNOFF HYDROGRAPH

DOWNSTREAM HYDROGRAPH

Necessary for a single catchment

Necessary for a whole basin

1. After all „losses” –Excess precipitation

2. Flow generation• Within sub-basin/cells• excess water

concentration /routing/ transformation

• Time-area method or unit hydrograph (UGH) method

3. Flow routing between cells using river flow routing method

1

2

3

Hydrological modeling – Components


Transfer function approach

• Transfer functions

1. Estimate “losses”.• P minus losses = effective

precipitation (Peff)

• Determines the volume of streamflow response

2. Distribute Peff in time• Gives shape to the

hydrograph

• Loss function examples:• SCS CN, rational method


Model


Precipitation




RUNOFF HYDROGRAPH


STEP 1: Excess precipitation modeling


Model


Precipitation

P

Losses

Peff = Qef

General concept

Time

P Flo

w

Base Flow

Event Flow(Weff)

Time

Recall that Qef = Peff


• Loss methods

• Conceptual method • SCS CN

• Physically-based infiltration equations• Green-ampt, Richards equation, Darcy…

• Kinematic approximations of infiltration and storage

P

Uniform: Peff(t) = P(t) - constant

Exponential: Peff(t) = P0e-ct

c is unique to each site



• SCS CN

Uniform: Peff(t) = P(t) - constant


SCS - “Soil Conservation Service” (NRCS –“National Resources Conservation Service”)

P

Time


• SCS CN


SCS - “Soil Conservation Service” (NRCS –“National Resources Conservation Service”)


• Transfer function

• After determining excess volume in STEP 1

• Temporal distribution estimation in STEP 2 - shape of hydrograph

1. Methods based on flow translation time (time of concertation, lag time,…)

2. Unit hydrograph approach

3. Time-area approach (isochrones)




RUNOFF HYDROGRAPH

STEP 2: Event flow (overland and subsurface)

P

Flo

w

Base Flow

Event Flow(Weff)

TimeVolume of effective Precipitation or Event Flow



Methods based on flow translation time (time of concertation, lag time,…)

• Time of concertation (Tc) - Time required for runoff to travel from the hydraulically most distant point on a watershed to another point of interest within the watershed

• Tc= Sheet flow (30-100m) + Shallow concentrated flow +Open channel flow

• Tc =f (Area, Slope, Surface roughness, Channel shape, Flow patterns)

• Empirically derived, based on watershed properties




RUNOFF HYDROGRAPH


Time

w

Flo

w

Time

Tb=2.67Tr

On top of base flow

Tw = duration of effective P

Tc= time concentration



• Unit hydrograph method




RUNOFF HYDROGRAPH


Watershed

Excess rainfallPm

Direct RunoffQn

u(l)

l0

Instantaneous unit hydrograph

1 in/h or cm/h instantaneousexcess rainfall

Input Pm

OutputQn

System

𝑄𝑛 =

𝑚=1

𝑛≤𝑀

𝑃𝑚𝑈𝑛−𝑚+1


• UHG method• The direct runoff hydrograph

that results from 1 cm excess rainfall, occurring uniformly over the basin at a uniform rate during a specified duration of time




RUNOFF HYDROGRAPH



• The event hydrograph that would result from 1 unit (cm, in,…) of effective precipitation (Weff=1)• A watershed has a “characteristic” response

• This characteristic response is the model

• Many methods to construct the shape

Qef

t

1

1



• Transfer function approach

• Time-area method


Concentration time per surface element

Direct runoff hydrograph


STEP 2: Baseflow component

• What is contribution of the delayed interflow and groundwater runoff to the total runoff?

Flo

w

Time

Baseflow

Direct runoff from overland and subsurface slow


Baseflow models

1. Constant monthly

2. Exponential recession model


Baseflow

recession constant

Starting runoff

Recessionlines


3. Non-linear reservoir model• Eg. Soil Moisture Accounting

(SMA)

4. Physical model -groundwater flow in aquifer



STEP 3: River routing method

• Flow Routing is a procedure to determine the time and magnitude of flow at a point on a watercourse from known or assumed hydrographs at one or more points upstream.


RUNOFF HYDROGRAPH


QTranslation

Attenuation

Time


STEP 3: River routing method

Methods – Hydrological methods (lumped or distributed models)

• Linear reservoir method

• Muskingum method

Network response function –Hydraulics methods (distributed models)

• St Venant equations

• Diffusion wave

• Kinematic method


RUNOFF HYDROGRAPH



Model building approach


Model Building Approach

• The main steps of model building may be explained as follows (James, 1996):

1. Formulation of objectives

2. Review of theoretical background

3. Formulation of the model.

4. Creation of a model structure Formulation of equations

5. Formulation of methods of solution

6. Selection of a computer code / model

7. Calibration of the model

8. Validation of the model

9. Statistical assessment of paired observations and simulations

10. Sensitivity analysis.

(http://echo2.epfl.ch/VICAIRE/mod_2/chapt_9/main.htm)


Procedure of Model evaluation

MODEL SELECTIONChoice of working hypotheses

MODEL CALIBRATIONEstimation of model parameters

MODEL TESTINGIs the model suitable?

MODEL APPLICATION

NO

YES

Model calibration and verification


Model calibration and verification

• Calibration: minimizing differences between observation and model output by tuning model parameters

• Validation: test model performance on data not used during calibration

• Regionalization: obtaining parameter value at ungauged sites from catchment physical data

• Sensitivity analysis: test how the model are dependent on model parameters

• Assimilation: Adjust input and output data in proportion to their estimation errors by minimizing the total uncertainty with the constrain that they satisfy the basic model equations.


Overview of some (process-based) models


Models Overview

WATERSHED MODELS Overview (Edsel et al. 2011)

• Suited Applications – urban, agriculture

• Main Components - water balance components

• Overland Flow: Methods

• Subsurface Flow: Methods / Availability

• Chemical Simulation: Methods / Availability

• Spatial Scale: Distributed (D) / Semidistributed (SD)

• Temporal Scale: Continues (C) / Event based (E)

• Availability: Public (Pu) / Private (Pr)


ModelSuited

Applications

Main

Components

Runoff on

OverlandSubsurface Flow

Chemical

Simulation

Spatial

Scale

Temporal

ScaleAvailability

ANSWERS

Suited for agriculture watersheds;

designed for ungaged

watershed

Runoff, infiltration, subsurface

drainage,

soil erosion,

interception & overland

sediment transport

Manning &

continuity

Equations

No component No component

D

Square grids,

1-D Simulations

E Pu

ANSWERS-

2000

Suited for medium size

agriculture watersheds; designed for

ungaged watershed, useful in

evaluating the effectiveness of

BMPs;

capable of simulating transformation

and interactions between four

nitrogen pools

Runoff; infiltration, water /

river routing, drainage,

river routing, chemical /

nutrient transport

Manning

equation

Darcy’s

equation

N,P, sediment

transport

D

Grid/cellsC Pu

AGNPS Suited for agriculture watershedsRunoff, infiltration & soil

erosion / sediment transport

CN, TR-55

for peak flowNo component No component

D

Homogeneous

land areas

E Pu

AnnAGNPS

Suited for agriculture watersheds;

widely used for evaluating a wide

variety of conservation practices and

other BMPs

Hydrology, sediment, nutrients

and pesticide transport,

DEM used to generate grid and

stream network

CN, TR-55

for peak flow

Darcy’s

equation

N, P, pesticides,

organic carbon &

nutrients

D

Homogeneous

land areas, reaches,

& impoundments

C- daily

or

sub-daily

steps

Pu

WATERSHED MODELS Overview(Edsel et al. 2011)


ModelSuited

Applications

Main

Components

Runoff on


Chemical

Simulation

Spatial

Scale

Temporal

ScaleAvailability

GSSHA/CAS

C2D

Suited for both agriculture

or urban watersheds; diverse

modeling capabilities in a variety of

climates and watersheds with

complex spatial datasets

Spatially varying rainfall; rainfall

excess and 2-D flow routing; soil

moisture, channel routing,

upland erosion, & sediment

transport

2-D diffusive wave

equationsNo component No component

D

2-D square over-land

grids; 1-D channels

E; C Pr

HEC-1/HEC-

HMS

Suited for urban watersheds; widely

used for modeling floods and impacts

on land use changes

recipitation, losses, baseflow,

runoff transformation & routing

CN, kinematic

wave

equations

No component No component

SD

Dendritic network or

grid)

E Pu

HSPF

Suited for both agriculture or urban

watersheds; diverse water quality

and sediment transport at any point

on the watershed

Runoff /water quality

constituents, simulation of

pervious/impervious areas,

stream channels & mixed

reservoirs

Empirical

outflow

Interflow

outflow,

percolation;

groundwater

outflow

Soil / watertemp.,

DO, CO2, N, NH3,

organic N/P, N/P,

pesticides

SD

Pervious / impervious

land areas, stream

channels, & mixed

reservoirs; 1-D

simulations

C Pu

KINEROS2

Suited for urban environments and

studying impacts of single sever or

design storm even; Also can be

applied to agriculture watersheds

Distributed rainfall inputs,

rainfall excess, overland flow,

channel routing, sediment

transport, interception,

infiltration, surface runoff &

erosion

Kinematic

wave equationsNo component No component

D

Cascade of planes &

channels; 1-D

simulations

E Pu



ModelSuited

Applications

Main

Components

Runoff on


Chemical

Simulation

Spatial

Scale

Temporal

ScaleAvailability

MIKE SHE

Wide range of spatial and temporal

scales; modular design facilitates

integration of other models;

advanced

capabilities for water quality,

parameter estimation and water

budget analysis

Interception, over-

land/channel flow,

unsaturated/saturated zone,

snowmelt; aquifer/rivers

exchange, advection/dispersion

of solutes, geochemical

processes, plant growth, soil

erosion & irrigation

2-D diffusive wave

equations

3-D

groundwater flow

Dissolved

conservative

solutes in surface,

soil, & ground

waters

D

2-D rectangular /

square overland

grids; 1-D channels;

1-D unsaturated / 3-D

saturated flow

E; C;

variable

steps

Pr

SWAT

Best suited for agriculture

watersheds; excellent for calculating

TMDLs and simulating a wide variety

of conservation practices and other

BMPs; successfully applied across

watersheds in several countries

Hydrology, weather,

sedimentation, soil temperature

and properties, crop growth,

nutrients, pesticides

agricultural management and

channel & reservoir routing

CN for

runoff; SCS TR-55

for peak flow

Lateral subsurface

flow / ground flow

N, P,

pesticides,

C

SD

Sub-basins based on

climate, HRU, ponds,

groundwater, & main

channel

C; daily

stepsPu

PRMS/MMS

Suited for agriculture watershed;

modular design facilitates integration

of other

models (e.g., climate models)

Hydrology and surface runoff,

channel flow, channel reservoir

flow, soil erosion, overland &

sediment transport

Kinematic

wave equationsNo component No component

D

Flow planes, channel

segments, & channel

reservoirs; 1-D

simulations

E Pu



ModelSuited

Applications

Main

Components

Runoff on


Chemical

Simulation

Spatial

Scale

Temporal

ScaleAvailability

WEPP

Best suited for agriculture watershed

and analyzing hydrologic and soil

erosion on small watersheds

Weather generation, frozen

soils, snow accumulation and

melt, irrigation, infiltration,

overland flow hydraulics, water

balance, plant growth, erosion,

deposition & residue

decomposition

Kinematic wave

equations

Green-Ampt

equationNo component

D

Channel segments &

impoundments

C Pu



Non-point source pollution - physically based models

Watershed-scale models - provide assistance in predicting non-point source pollution (Borah and Bera, 2003) :

• Agricultural Non-Point Source Pollution Model (AGNPS)

• Areal Non-Point Source Watershed Environment Simulation (ANSWERS)

• Kinematic Runoff and Erosion Model (KINEROS)

• Hydrological Simulation Program-FORTRAN (HSPF)

• MIKE SHE

• Soil and Water Assessment Tool (SWAT)


Scale and Water Quality VariablesSource: Mazdak Arabi – Nutrient modeling overview

Less C

om

plex M

ore

Co

mp

lex

USGSRegression

SARROW

GWLF

QUAL2E

SWMM

WASP

SWAT

AnnAGNPS

HSPF

Emp

irical/StatisticalP

hysically-B

ased/D

etermin

istic

MODEL Time Step Spatial Scale Water Quality

USGS Regression Annual Large basins Nutrients

SPARROW Annual Large basins Sediment, Nutrient, Pesticides

GWLF Monthly HUC12, 8 Sediment, Nutrient

QUAL2E Steady-St. Water body TN, TP, NH3, DO, chlorophyll a, pathogens

WASP Hourly Water body TN, TP, NH3, DO, chlorophyll a,TSS, Toxics

SWMM Sub-Daily Small basins Sediment, Nutrient, Pesticide, Metals, BOD

SWAT Daily M-L basins Sediment, Nutrient, Pesticide, Metals, BOD

HSPF Sub-Daily M-L basins Sediment, Nutrient, Pesticide, Metals, BOD


Land and Water Features Supported Source: Mazdak Arabi – Nutrient modeling overview

MODEL Urban Ag / Rural Forest River Lake Reservoir Coastal / Estuary

USGS Regression + + +

SPARROW ++ ++ ++ ++ ++ ++

GWLF ++ ++ ++ +

QUAL2E +++

WASP +++ +++ +++ +++

SWMM +++ + + + + ++

SWAT + +++ +++ +++ + +

HSPF ++ +++ +++ +++ ++ ++


Land and Water Features Supported Source: Mazdak Arabi – Nutrient modeling overview

MODEL Urban Ag / Rural Forest River Lake Reservoir Coastal / Estuary

USGS Regression + + +

SPARROW ++ ++ ++ ++ ++ ++

GWLF ++ ++ ++ +

QUAL2E +++

WASP +++ +++ +++ +++

SWMM +++ + + + + ++

SWAT + +++ +++ +++ + +

HSPF ++ +++ +++ +++ ++ ++


Sediment & erosion - physically based models

• The present study reviews 50 physically based soil erosion and sediment yield models with respect to these factors including shortcomings and strengths. The literature generally suggests the use of models like:

• SWAT, WEPP, AGNPS, ANSWERS and SHETRAN for soil erosion and sediment studies.

(Pandey, A., Himanshu, S. K., Mishra, S. K., & Singh, V. P. (2016). Physically based soil erosion and sediment yield models revisited. Catena, 147, 595-620.)


Forest – hydrological models

• Amatya, D., Williams, T., Bren, L., & de Jong, C. (Eds.). (2016). Forest Hydrology: Processes, Management and Assessment. CABI.


Forest – hydrological models

Model Hydrologic approachSimulation outputs:

HydrologyTime steps Spatial Scales

Level of

Complexity

Appropriate regions of

application

iTree-Hydro Six main routines for rainfall runoff

processes: interception,

impervious surface, soils,

evaporation and transpiration,

routing, and pollution. Uses time-

area delay function or

one/parameter diffusion-based

exponential function for

constructing downstream

hydrograph

Daily hydrograph Daily Multi-scale

catchments and

plots (i.e. city or

parcel)

Medium Multiple – can be applied to

watersheds with different

rainfall-runoff mechanisms;

recent cold region module

development (version 2; Yang

et al. 2011)

PnET (all) Lumped-parameterized one-

dimensional water balance model

for canopy to soil

ET, out flow Daily to

monthly

Plot to regional Low All forest ecosystem both

upland and lowland

CENTURY Simplified water balance

incorporating evapotranspiration,

soil water content, saturated flow

Carbon, nitrogen,

phosphorus, sulfur flows

within each model

component

Monthly Plot Low Temperate and tropical forests




Level of

ComplexityAppropriate regions of application

ForHyM One-dimensional process-

based water balance model

that also embodies some

general empirical

relationships for multiple

model layers (forest canopy,

snowpack, forest floor, soil,

and subsoil)

Hydrograph outflow, ET,

soil moisture, snow

accumulation,

infiltration

Daily,

Weekly

Watershed Medium Typically applied for northern forested watersheds

with one or multiple biomes

TOPMODEL Semi-distributed rainfall-

runoff model; Variable source

area dynamics but models

both saturated excess and

infiltration excess overland

flows, assumes water table

follows topography

Various water balance

component including

streamflow, overland

flow (saturated and

infiltration excess),

subsurface flow, and

return follow

Daily Multi-scale

catchments

Medium Multiple – typically best in systems with moderate to

steep topography and shallow soils

VELMA Spatially-distributed

ecohydrological model;

simulated daily infiltration,

evapotranspiration, and

surface/subsurface runoff

through four soil layers


component including

streamflow, overland

flow (saturated and

infiltration excess) and

subsurface flows

through four user-

defined soil

Daily Multi-scale

catchments

Medium Multiple – developed in small forested catchments of

Pacific NW of US but applied/tested elsewhere




Level of

Complexity

Appropriate regions of

application

APEX Curve Number method (Five

options) and Green&Ampt

Infiltration (Four options),

Subsurface drainage, and five

options of PET for ET estimate

Precipitation, snowfall,

interception, Surface runoff,

subsurface flow, snowmelt,

irrigation, total water yield,

PET, ET

Daily,

monthly or

annual

Field/Small

catchment; grid-

based

Medium Upland agricultural and

forested fields or watersheds

PRMS Semi-distributed processed-based

rainfall-runoff model for multiple

spatial and temporal scales


component including

evaporation, transpiration,

runoff, infiltration and

considers the interaction

with the forest/plant canopy,

snowpack, dynamics, and soil

hydrological

Daily to

centuries

Multi-scale

catchments

Medium Multiple

DHVMS Saturation-excess infiltration,

Darcy’s law for unsaturated and

kinematic for saturated subsurface

Surface runoff, snow and

snowmelt, soil moisture and

evapotranspiration,

streamflow

Sub-daily to

annual

Catchments Medium Mountainous watersheds in

Pacific Northwest of USA

BROOK90 One-dimensional water balance

with canopy and multi-layer soil

profile

Soil water content, overland

flow, bypass flow from soil

layers, groundwater flow

Daily Plot Low Applied worldwide though

designed for forests within US

northeast

VIC Grid-cell based water balance with

canopy, and three-layer soil profile

Component water balance

and streamflow with

accompanying routing model

Daily to

monthly

Regional, global Medium Any as intended to accompany

large-scale general circulation

models

INCA Semi-distributed water balance

with canopy, soil, and riparian

components

Streamflow, nitrate and

ammonium loadings

Daily Catchment Medium No limitations but extensively

applied in Europe


Models Overview - SWAT

Soil and Water Assessment Tool (SWAT)

• physically based semi-distributed model with daily and monthly calculations of hydrological balance parameters in the watershed (Arnold et al., 1998; Neitsch et al., 2011).

• designed to predict the impact of management on water, sediment, and agricultural chemical yields in ungauged watersheds

Spatial and temporal scale

• Spatial: Flexible

• Time scale: Continuous (Events – NO)

• Computational Time step: Daily


Water balance equation:

𝑺𝑾𝒕 = 𝑺𝑾𝟎 +

𝒊=𝟏

𝒏

(𝑹𝒅𝒂𝒚 − 𝑸𝒔𝒖𝒓𝒇 − 𝑬𝒂 − 𝒘𝒔𝒆𝒆𝒑 − 𝑸𝒈𝒘)

𝑺𝑾𝒕 - Final soil water content (mm)𝑺𝑾𝟎 - Initial soil water content (mm)t - Time in days𝑹𝒅𝒂𝒚 - Amount of precipitation on day I (mm)

𝑸𝒔𝒖𝒓𝒇- Amount of surface runoff on day i (mm)

𝑬𝒂 - Amount of evapotranspiration on day i (mm)𝒘𝒔𝒆𝒆𝒑- Amount of percolation on day i (mm)

𝑸𝒈𝒘 - Amount of return flow on day i (mm)




Governing equations in modeled hydrological processes

• Runoff volume: Modified SCS-Curve Number or G&A infiltration method

• Peak runoff rate: Modified rational formula or the SCS TR-55 method

• Lateral sub-surface flow & percolation: Kinematic storage routine (Sloan et al., 1983)

• Potential evapotranspiration: (I) Hargreaves (II) Priestley-Taylor and (III) Penman-Monteith equations

• Snow melt: degree-day based method

• Sediment yield: Modified Universal Soil Loss Equation (MUSLE)

• Water routing: Variable storage coefficient method or Muskingum routing method & Manning’s equation to define flow


Input data required to run the model

• DEM, land use/land cover, soils,

• daily precipitation

• max. and min. temperature

• solar radiation, relative humidity, wind speed

• daily discharge

• sediment, nutrient delivery,

• fertilizer and pesticides application data

• point source of pollution and management practices

• Output data – related to hydrological services

Source: Carvalho – Santos, C. et al, 2016



Models Overview - Farmscoper

• Next session!

• Farm based model


References

• Amatya, D., Williams, T., Bren, L., & de Jong, C. (Eds.). (2016). Forest Hydrology: Processes, Management and Assessment. CABI.

• Daniel, E. B., Camp, J. V., LeBoeuf, E. J., Penrod, J. R., Dobbins, J. P., & Abkowitz, M. D. (2011). Watershed modeling and its applications: A state-of-the-art review. The Open Hydrology Journal, 5(1).

• Pandey, A., Himanshu, S. K., Mishra, S. K., & Singh, V. P. (2016). Physically based soil erosion and sediment yield models revisited. Catena, 147, 595-620.

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• Chong-yu Xu. Hydrological modeling – lecture notes ftp://www.w-program.nu/Modelling%20course/L7_Introduction%20to%20distributed%20modeling.pdf (accessed: 15. Oct 2018)


Thank you!

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Hydrology and forests approaches to modelling...• The direct runoff hydrograph that results from 1 cm excess rainfall, occurring uniformly over the basin at a uniform rate during