APPROVED: Miguel F. Acevedo, Major Professor Wilfredo Franco, Committee Member Paul Hudak, Committee Member and Chair of

the Department of Geography Sandra L. Terrell, Dean of the Robert B.

Toulouse School of Graduate Studies

SOIL CHARACTERISTICS ESTIMATION AND ITS APPLICATION

IN WATER BALANCE DYNAMICS

Liping Chen, B.S.

Thesis Prepared for the Degree of

MASTER OF SCIENCE

UNIVERSITY OF NORTH TEXAS

December 2008

Chen, Liping. Soil Characteristics Estimation and Its Application in Water

Balance Dynamics. Master of Science (Applied Geography), December 2008, 92 pp.,

11 tables, 43 illustrations, references, 59 titles.

This thesis is a contribution to the work of the Texas Environmental Observatory

(TEO), which provides environmental information from the Greenbelt Corridor (GBC) of

the Elm Fork of the Trinity River. The motivation of this research is to analyze the short-

term water dynamic of soil in response to the substantial rainfall events that occurred in

North Texas in 2007. Data collected during that year by a TEO soil and weather station

located at the GBC includes precipitation, and soil moisture levels at various depths. In

addition to these field measurements there is soil texture data obtained from lab

experiments. By comparing existing water dynamic models, water balance equations

were selected for the study as they reflect the water movement of the soil without

complicated interrelation between parameters. Estimations of water flow between soil

layers, infiltration rate, runoff, evapotranspiration, water potential, hydraulic conductivity,

and field capacity are all obtained by direct and indirect methods. The response of the

soil at field scale to rainfall event is interpreted in form of flow and change of soil

moisture at each layer. Additionally, the analysis demonstrates that the accuracy of soil

characteristic measurement is the main factor that effect physical description.

Suggestions for model improvement are proposed. With the implementation of similar

measurements over a watershed area, this study would help the understanding of

basin-scale rainfall-runoff modeling.

ii

Copyright 2008

by

Liping Chen

iii

TABLE OF CONTENTS

Page

INTRODUCTION............................................................................................................. 1 Soil and Flooding.................................................................................................. 2 Soil and Irrigation.................................................................................................. 3 Rainfall-Runoff Modeling ...................................................................................... 3 Soil Water Flow and Hydrology ............................................................................ 4

PROBLEM STATEMENT ................................................................................................ 7 OBJECTIVES.................................................................................................................. 9 METHODS AND APPROACHES.................................................................................. 10

History of Rainfall-Runoff Modeling .................................................................... 10 Flow in Saturated and Unsaturated Soil ............................................................. 12 Soil Water Dynamics by Layer............................................................................ 17 Water Cycle Part I -Entry of Water into Soil-Infiltration ....................................... 21

Infiltration Rate and Capacity Equation.................................................... 21 Effective Rainfall and Runoff Models ....................................................... 26

Water Cycle Part II-Redistribution of Soil Moisture Following Infiltration ............ 30 Water Balance Dynamics ................................................................................... 30

Potential Evapotranspiration (PET).......................................................... 30 DATA SOURCES.......................................................................................................... 34

Techniques Overview ......................................................................................... 34 Study Area and Automated Station .................................................................... 35 Soil Moisture Sensor and Its Calibration............................................................. 39

RESULTS...................................................................................................................... 43

Soil Texture ........................................................................................................ 43 Porosity .............................................................................................................. 45 Hydraulic Conductivity ........................................................................................ 46 Potential ............................................................................................................. 49 Flow 53 Infiltration Capacity and Infiltration Rate ............................................................. 53

iv

Soil Moisture Variations Without Rainfall ............................................................ 60 Soil Moisture Responses to Rainfall Event ......................................................... 62 Data Analysis and Model Improvement .............................................................. 70

Assumptions ............................................................................................ 70 PET Estimation Results ........................................................................... 72 Example of Calculations of Runoff ........................................................... 73

CONCLUSION .............................................................................................................. 85 REFERENCES LIST ..................................................................................................... 88

1

INTRODUCTION

Plants provide food, fiber and foundation of our existence, and soil nutrients and

water are the two most important elements for plant life. The soil acts as a home to

organisms, a waste decomposer, a filter of water and waste, a source of materials for

construction, and medicine. Seventy five percent of the earth is covered by water and

the remaining 25% is covered by land. This land is made up of 50% desert, polar, or

mountainous regions (NASA 2008). If you remove the portion being severely limited by

terrain, fertility, or excessive rainfall, the remaining 10% is what we depend on for

producing food and living. Soil properties provide the right combination of chemicals to

plants so that they will grow properly. In Egypt, the whole agriculture industry depends

on the soil. When the floods receded, they left thick rich mud in which plant life could

flourish. The soil along the Nile River is referred to “black gold” (Collins 2002). Analysis

of soil information helps reveal the history of rainfall patterns and land formations. For

example, the formation of red colored soil is due to intense weathering by rain and heat

(Steila and Pond 1989). Also, soil is also an important player in climate change. Well-

nourished soil can help in carbon sequestration and remove carbon dioxide from the air

(EPA 2008). A Russian geologist Vasily Dokuchaev, first identified the distinctiveness

and complexity of soil, and since then soil has been separated from geology and

became an independent science (Krasilnikov 1958).

2

Soil and Flooding

Usually, flooding is caused by dam failure, reduced watershed drainage, or

excessive precipitation. In winter, a watershed with saturated soils, frozen ground,

leafless coniferous species, or poor drainage to stream channels can have a great

probability to turn a common thunderstorm into flood. Though Texas is exposed to heat

and dryness during the summer, the area is prone to extremely heavy rains and

flooding. Half the world record rainfall rates belong to Texas; this state leads the nation

in flood-related deaths and property damage (Floodsafety 2008). In 2001, 40 people

died and there was 5 billion dollars in disaster damages due to flooding (Floodsafety

2008). Floods also have a great impact on soil and vegetation. The fine particles near

the surface, which contain most of the nutrients needed to sustain plant life, can be

washed away. The non-riparian plants are inclined to being drown in water. Meanwhile,

soils with fine texture and structure help mitigate flooding because of high porosity and

infiltration rates that absorb water from intense precipitation. The soil acts as water

storage media before the water returns to the atmosphere through evaporation.

Excluding 45% mineral matters and 5% organic residue, the rest of the soil volume is

pore space (USDA 2008). It has the ability to absorb and store water keeps plants

growing through a drought. Soil texture and structure might be affected by flooding.

Satellite mapping of soil moisture could help predict flooding; by using the soil’s natural

microwave emissions, sensors could detect the sign of flooding in an area as patches of

oversaturated soil (NASA 2001).

3

Soil and Irrigation

Irrigation is implemented in crop production to maintain the soil moisture level

above the wilting point by supplying water resources in the absence of rain. The amount

of water that the growing plants can use depends on soil moisture tension. Saturated

soil has a soil moisture tension that requires little energy for a plant to pull water away

from the soil. At field capacity, it is relatively easy for a plant to remove water from the

soil. The wilting point is reached when the maximum energy exerted by a plant is equal

to the tension with which the soil holds the water (Scherer et al. 1996). Good irrigation

scheduling starts with measures of rain and soil moisture at the early stage of plant

growth. These measures will help determine when the irrigation should be triggered so

that the correct amount of water would be applied (Muñoz-Carpena and Dukes 2008).

Rainfall-Runoff Modeling

Hydrological information is essential in the design, operation, and management

of flood-control works, irrigation systems, water-supply projects, storm-runoff drainage,

erosion controls, and highway culverts (Chang 2006). It is not a surprise that hydrology

employs vanguard technology to explore the causes and effects of water-related events

to benefit society and the environment. One of the practical objectives is to find the laws

that govern forest-water-climate-soil-topography interactions, in order to predict and

reduce the risks resulting from hydrological damage. There are many societal concerns

over interrelations between water and the environment, as well as the impacts of human

activities on the occurrence, circulation, and distribution of water. Careful planning for

4

human activities, conduct farming, urban development, and deforestation during dry

season can mitigate the impact of flood occurrence (Chang 2006).

The study focusing on modeling the responses of a watershed to rainfall events

is called ‘rainfall-runoff modeling’ (Beven 2001). This discipline involves frequency

analysis of hydrologic events, depth-area-duration analysis, hydrograph analysis,

stream flow routing, stream flow simulation, estimation of soil erosion and stream

sedimentation due to detachment and transport by runoff and rainfall, and flood risk

analysis (Chang 2006). Rainfall-runoff modeling is valuable in practical hydrological

applications, such as water resource assessment; evaluate the positive effects of forest

on runoff generation, estimate flood potentiality caused by human activities by using

watershed resources; predict discharges in real time during flood periods and flood

frequencies of different flood peak magnitudes (Chang 2006).

Soil Water Flow and Hydrology

Soil moisture is one of the components constituting the hydrological cycle. The

procedure of continuous water transferring is indicated in Figure 1, which is a diagram

describing the processes involved during a storm. Atmospheric water precipitates over

land; it is initially stored as interception by plants and vegetation. As precipitation

continues, water will enter the soil as infiltration or flow over the surface. Infiltration rate

is limited by rainfall intensity and infiltration capacity. Infiltrated water might rapidly pass

through the subsurface layer to join the adjacent stream, or percolate slowly through the

soil profile and become groundwater. If the water input rate exceeds the infiltration rate,

5

runoff is generated. Surface flow or runoff will feed streams within the watershed.

Runoff includes subsurface and snowmelt flows, amounts that are harder to estimate.

On vegetated surface, rainfall rarely exceeds the infiltration capacity unless the

antecedent soil moisture is saturated. However, the soil surface does not need to be

saturated for overland flow to occur. At the end of the cycle, the water is returned

through evaporation from soil. Obviously, soil is involved in large part of the water

movement around the earth.

Figure 1 Processes of water cycle involved during storms.

6

Balance of rates is used to explain the water movement in Figure 1. Effective

precipitation reaching the ground equals to precipitation minus interception, and is

composed of through-fall plus stem-flow rates. Infiltration rate is effective precipitation

reaching the ground minus runoff. Finally, the rate of change in soil water content is

infiltration rate minus evapotranspiration (ET) and percolation to deeper layers

(Acevedo 2004). Several stages in the process might occur simultaneously or

interdependently. The earlier stage is the moment when the occurrence of flooding is

most likely to happen. During the first stage, the infiltration rate often determines the

amount of runoff or the hazard of erosion during rainstorms. Especially when the

antecedent soil water content is high, stream channels slow down the drainage of the

runoff. Once the infiltration ceases, ET will deplete water. Thereafter is the post-

infiltration stage. In the absence of groundwater, redistribution of soil moisture follows

infiltration. In the presence of high water table, the post-infiltration is called internal

drainage.

7

PROBLEM STATEMENT

Studying water dynamics in the soil is of great practical importance. It helps

evaluate soil wetting or drying rate for irrigation management, predicting runoff flow for

flood risk estimation and management. However, this is a complicated problem with

interaction of numerous variables and parameters. Infiltration related processes are

illustrated in Figure 2. As water seeps in, the pore spaces are filled with water. Then

water moves through the soil by gravity and capillary forces. Water movement continues

downward until a balance is reached between the capillary forces and the force of

gravity. Water is pulled around soil particles and through small pore spaces in any

direction by capillary forces (Scherer et al. 1996). Moreover, as the textural attributes of

soil with respect to depth are not uniform, it is unlikely that the laboratory test could

replicate the flow process in the field.

This thesis concerns itself with measuring and modeling the water dynamics in a

soil column illustrated by Figure 2 as applied to a relatively small area, 2 m×2 m of

horizontal cross section and 2 m in depth. The problem to solve in this thesis is how to

use soil characteristics for each layer measured in the laboratory, together with in-situ

measurements of soil water content and rainfall to implement a model of water

dynamics.

8

Figure 2 Soil moisture profile. Soil properties are assumed to be homogeneous within a

layer.

9

OBJECTIVES

The main objectives of this thesis are:

1. Measure soil properties in order to establish soil characteristics

determining soil water dynamics with respect to soil depth.

2. Analyze the interrelation among the soil characteristics and variables. For

example, unsaturated flow processes entail changes in the state and content of water,

and the changes involve relations among the wetness suction and conductivity.

3. Discuss existing models include their limitations to the dynamics by layer

illustrated in Figure 2.

4. Collect high-frequency in-situ data including rainfall and soil moisture at

various depths.

5. Infer the variables from the data record: Based on theoretical models and

high-frequency data, complete the estimation of runoff, evaporation, and infiltration rate.

6. Describe flow as a function of soil moisture. Infiltration as function of

rainfall and infiltration capacity.

7. Analyze the incompleteness of current research and propose the further

work

Though the approach described here is applied to a small area (2 m×2 m× 2 m)

where the rainfall gauge and soil moisture sensors are located, the methodology could

have broader application in: plant transpiration, agriculture irrigation, flood risk

management or even large-scale watershed responses to precipitation events in forest

if measurements can be replicated over many areas of the watershed.

METHODS AND APPROACHES

History of Rainfall-Runoff Modeling

Research in rainfall-runoff modeling has a long history; the starting point traces

back to 150 years ago. Thomas James Mulvaney, in 1851, proposed a rational model to

estimate peak flow discharge Qp

RQp CA= Equation 1

The input variables are the watershed area, A, the average rainfall intensity, R ,

and a runoff coefficient C (Dooge 1957). This model describes how the discharges are

expected to increase with area and rainfall intensity. This equation assumes that rainfall

continues at a uniform intensity with duration equal to the time of concentration. It is still

difficult to predict the effective values for an extreme storm using this model because it

does not account for the nonlinearity of the runoff production process.

Since then, wide ranges of analysis have been carried out for predicting peak

discharges under different rainfall and antecedent soil moisture conditions. Moreover,

many computer models have been developed to estimate watershed response to

rainfall events: physical or systematic, lumped catchment-scale, distributed,

deterministic, or stochastic models (Chang 2006).

Singh and Frevert (2006) carefully select several popular watershed models as a

comprehensive overview of various types of models. Examples included are the

Stanford Watershed Model (SWM) developed in the 1950s (Crawford and Linsley

10

1966), which was the first systematic hydrologic model to simulate the whole phase of

the hydrologic cycle of a watershed. And the Precipitation / Runoff Modeling System

(PRMS) (Leavesley et al. 1983, Leavesley and Stannard 1995) is established based on

SWM.

Many models are based on a generic structure consisting of a collection of

mathematical functions describing the fluxes between the storages. Beven (2001) also

reviews some successful models. The Explicit Soil Moisture Accounting (ESMA) model

by O’Connell (1991) was derived from the ‘generic’ model structure. Except for the

World Meteorological Organization (WMO) reports (WMO, 1975, 1986, 1992), no

comprehensive effort has been made to compare most major watershed hydrological

models. (Singh and Frevert 2006).

Hydrological modeling can be categorized as based on ‘induction’ or ‘deduction’.

’Induction’ relies more on the extrapolation of the temporal and spatial data; the neural

network is a typical technique being applied in this category (Beven 2001). However, it

requires long-term and high frequency measurements. The measurements from devices

only reflect the conditions of the area around the device. ‘Deduction’ focuses on the

first-principles of hydrological processes and less on empirical relations (Beven 2001).

‘Deduction’ is carried out as a ‘black box’ separated from input and output data. We

need to control one of the parameters and analyze the responses of the others. Both

induction and deduction are types of models requiring data; even though the deduction

type employs data once the equations are established by first principles. Shortage of

11

long-term and reliable data and incomplete knowledge are some of the major difficulties

of all types of modeling.

Flow in Saturated and Unsaturated Soil

Most of the processes involving soil-water flow in the field, and in the rooting

zone of most plant habitats, occur while the soil is in an unsaturated condition.

Unsaturated flow processes are complicated and difficult to model, since they involve

changes in suction, conductivity and wetness. The most important difference between

saturated and unsaturated flow is in the hydraulic conductivity. Saturated soil has the

highest conductivity. A commonly used model for both saturated and unsaturated

subsurface flows is based on Darcy’s law (Darcy 1856), which assumes that the

discharge per unit area (or Darcian velocity) can be represented as the product of a

gradient of hydraulic potential and a scaling constant called the hydraulic conductivity.

Thus

Vx Kx

!"= #

" Equation 2

Where Vx [LT-1] is the Darcian velocity in the x direction, K [LT-1] is the hydraulic

conductivity, and φ [L] is the total potential (Φ=Ψ+z) where Ψ [L] is capillary potential

and z[L] is elevation above some datum). In the case of unsaturated flow, the hydraulic

conductivity will change in a nonlinear way with moisture content so that

( )Vx Kx

!"

#= $

# Equation 3

12

Where θ[m3/m3] is volumetric moisture content.

An important equation is the three-dimensional mass balance equation

( , , , )T

Vx Vx VxE x y z t

t x y z

!" ! ! !!

# # # #= $ $ $ $

# # # # Equation 4

Where ρ is the density of water [ML-3] (often assumed constant) and ET(x, y, z, t)

[T-1] is a rate of ET loss expressed as a volume of water per unit volume of soil that may

vary with position and time. This is the nonlinear partial differential equation now known

as the Richards equation (after Richards 1931). Combining Darcy’s law with this

equation we get

!"#

!t= $

!

!x["K(#)

!%

!x]$

!

!y["K(#)

!%

!y]$

!

!z["K(#)

!%

!z]$ "E

T(x, y, z,t) Equation 5

It is difficult to obtain analytical solutions to the nonlinear differential equations in

rainfall-runoff modeling practical applications.

In the following we will focus on the flow along the vertical dimension only and

look more simplified models. Going back to Darcy’s law, we can describe the flow along

the vertical dimension describing changes of an alternative state variable defined as

“hydraulic head” (h) with depth

( )h

q K Pdz

!= " Equation 6

z=depth [m] is the independent variable, P(t,z) is soil water potential, h [m] is the

alternative state variable, ( , ) ( , )h t z P t z z= ! ! , dependent on both potential and depth,

13

K(P) is hydraulic conductivity[m/sec] it is a function of soil water potential ( , )P t z , q is

flow density [m3/sec m2] or [m/s], this is water flow rate per unit of cross sectional area

(and equivalent to Darcian velocity). If we substitute h=-P-z, we will obtain

( )( ) ( )

P z P zq K P K P

dz z z

! " " ! !# $= " = +% &! !' (

Equation 7

which can also be written as

( ) 1 ( ) ( )P P

q K P K P K Pz z

! !" #= + = +$ %! !& '

Equation 8

We can build a simplified lumped ordinary differential equation (ODE) model for

soil moisture using the continuity equation

( )0

Sw P q

t z

! !+ =

! ! Equation 9

Where Sw(P) is soil moisture content dependent on potential P, known as the

retention curve. This last equation states that the rate of change of Sw with respect to

time should be accounted for changes of q with depth. It should be noted that

( , )P t z and ( , )Sw t z are inversely related. Using the chain rule and defining capacity C(P)

as the derivative of Sw(P) with respect to P, we get

( ) ( )Sw Sw P P

C Pt P t t

! ! ! != =

! ! ! ! Equation 10

( )C P =capacity [1/m] =change of water content per unit change of potential.

14

Brooks and Corey (1964) specified single-valued function forms for hydraulic

conductivity K, soil retention Sw, and capacity C. Let’s see,

1

( ) ( )ba

Sw PP

=

Equation 11

Where a=bubbling suction, b=pore-size distribution index. This equation allows

us to calculate water content after calculating P. ( )C P , defined as the slope of the water

retention curve, is given by

1( 1)

21( ) ( ) ( / )b

dSw aC P a P

dP b P

!

= = !

Equation 12

At any particular value of P, the value of Sw is given by

Sw =W !Wr

Wc !Wr Equation 13

Where W is water content as wetness, Wr= residual soil moisture, Wc=total

porosity, W≤Wc, W≥Wr. The saturated conductivity is

Ks =0.86

(b +1)(2b +1)

!

"#

$

%&

Wc 'Wr

a

!

"#$

%&

2

Equation 14

Non-saturated conductivity depends on wetness and can be written using Sw

K(P) = KsSw(2b+3) Equation 15

15

Table 1 lists the parameters of different soil types (Chang 2006) (the shadowed

rows indicate the types of soil texture in my study). Figure 3 is an example of calculated

curve for silty clay using Brooks-Corey functions as given in equation 16.

Table 1 Parameter values for various types of soil.

Soil type Wc volumetric total porosity

Wr volumetric residual

saturation

a(cm) bubbling pressure

b pore-size distribution

index Clay 0.475 0.090 37.30 11.40

Silty clay 0.479 0.056 34.19 10.40 Sandy clay 0.430 0.109 29.17 10.40

Silty clay loam 0.471 0.040 32.56 7.75 Clay loam 0.464 0.075 25.89 8.52

Sandy clay loam

0.398 0.068 28.08 7.12

Loam 0.463 0.027 11.15 5.39 Silty loam 0.501 0.015 20.76 5.30

Sandy loam 0.453 0.041 14.66 4.90 Loamy sand 0.437 0.035 8.69 4.38

Sand 0.437 0.020 7.26 4.05

16

Figure 3 Water content vs. non-saturated conductivity; silty clay.

Van Genuchten (1980) specifies a similar form of relationship for moisture

content, capillary potential and hydraulic conductivity.

Soil Water Dynamics by Layer

For each layer i of thickness idz write the discrete approximation of the continuity

equation.

1( )

i iq qdPiC Pi

dt dzi

!!

= ! Equation 16

17

where 1iq!

is the flow density in layer i from layer i-1 above and iq is the flow

density out from layer i to layer i+1 below, also for each pair of layers i-1 and i, we can

write Darcy’s law as

1

1( )

i i

i

h hq K Pi

dzi

!

!

!= ! Equation 17

Using ( , ) ( , )h t z P t z z= ! ! to substitute

1 1

1( )

i i i i

i

P z P zq K Pi

dzi

! !

!

! ! + += !

Equation 18

The difference in depth between the two layers1i iz z

!! is thickness idz so

1

1( ) ( )

i i

i

P Pq K Pi K Pi

dzi

!

!

!= ! +

Equation 19

If we use equation 20 to substitute qi!1 in 1( )

i iq qdPiC Pi

dt dzi

!!

= !

Equation 16, we can obtain

1 1

1 1

1

( ) ( ) ( ) ( )

( )

i i i i

i i

i

P P P PK Pi K Pi K P K P

dzi dzdPi

dt C Pi dzi

! !

+ +

+

! !! + + !

= Equation 20

If we include actual ET (AET) demand at each layer, infiltration rate 0Q , and

percolation rate Qn , 1( )

i iq qdPiC Pi

dt dzi

!!

= ! Equation 16 can be rewritten as

18

dP1

dt=!(0 ! q1)

C(P1)dz+ !Q0 + AET1

Equation 21

1 ( 1 2)2

( 2)

dP q qAET

dt C P dz

! != + Equation 22

1( 0)

( )

nqdPnQn AETn

dt C Pn dz

!! !

= + +

Equation 23

Use Darcy’s law to substitute each flow density qi , then equation 21 is rewritten

as

1 2(0 ( 2 ) )

10 1

( 1)

P PK P

dzdPQ AET

dt C P dz

!! !

= + ! + Equation 24

2 31 2

3 3( ( 2) ( 2) ( ) ( ) )

22

( 1)

P PP PK P K P K P K P

dz dzdPAET

dt C P dz

!!! ! + + !

= + Equation 25

1

1

( ( ) ( ) )

( )

n n

n

P PK Pn K Pn

dPn dz Qn AETndt C P dz

!

!

!! ! +

= + + Equation 26

PETAETi Fwi

n= Equation 27

Swi WpFwi

Fc Wp

!=

!Equation 28

Wp =effective saturation at wilting point (~1,500KPa) and Fc =effective saturation

at field capacity. AET is calculated from PET and soil moisture. PET is estimated by

19

Penman, or by the Priestley-Taylor method (see chapter Potential Evapotranspiration

(PET)).

20

Water Cycle Part I -Entry of Water into Soil-Infiltration

Infiltration Rate and Capacity Equation

Horton (1933, 1940) first suggested the theory of infiltration. Infiltration capacity

rapidly declines during the early part of a storm and then tends towards an

approximately constant value for the remainder of the event. Previously penetrated

water fills the available storage spaces and reduces the capillary forces drawing water

into the pores.

Infiltration rate is the rate at which a particular soil is able to absorb rainfall or

irrigation. The rate decreases as the soil becomes saturated. If the precipitation rate

exceeds the infiltration rate, runoff will usually occur and the value inversely related to

the saturated hydraulic conductivity of the soil near the surface. Generally, the soil

infiltration rate depends on: initial water content, hydraulic conductivity, time elapsed

from the initial rain, and soil surface conditions. After infiltration ceases, the surface

storage is depleted by evaporation or infiltration rate becomes steady and the water is

redistributed. As illustrated in Figure 4, Horton described this type of curve by an

empirical function in exponential decay form

kt

cocm effff!

!+= )( Equation 29

Where fo is an initial infiltration capacity, [mm h-1], fc is a final infiltration

capacity [mm h-1] and k is an empirical coefficient [h-1]. The values of fo , and k depend

21

on soil type as well as the antecedent state of the soil. The final infiltration

capacity fc will be close to the hydraulic conductivity of the soil at field saturation.

Figure 4 Decline of infiltration capacity with time since the start of rainfall. In this

example, fo=80mm/h, fc=50mm/h, and k=1.

The integral of Equation 29 yields the total infiltration F (mm) in Figure 5

)()(1

0

+!"#

$%&

'!!

+== ( ktco

c

t

ek

ffftfmdtF

Equation 30

22

Figure 5 Cumulative infiltration (mm/h).

As the second part of F decreases rapidly, t(fc) is the dominant of F. So the total

infiltration is linearly increasing. The coefficient k can be calculated by

k = [ln( fo! f

c) ! ln( f

m! f

c)] / t Equation 31

Soil physical theory suggests that infiltration can be described by the Richards

equation, and the nonlinear form of Darcy’s law for partially saturated flow. There are no

general analytical solutions to the Richards equations but a number of different

solutions are available for infiltration at the soil surface based on different simplifying

assumptions. Eagleson (1970) has shown that Horton equation is an approximate

23

solution of the Richards equation under certain simplifying assumptions. There are other

hydrological models derived from Horton’s theory.

Green and Ampt (1911) assumed that the infiltrating wetting front in

Figure 6 forms a sharp jump from constant initial moisture content ahead of the

front to saturation at the front. This allows a simple form of Darcy’s law to be used to

represent the infiltration such that infiltration rate f is calculated as

f = q = !Ks

dh

dz= !K

s

h2! h

1

z2! z

1

= !Ks

("f+ z

f) ! (H + 0)

zf! 0

= Ks"

f+ z

f! H

zf

Equation 32

Figure 6 Soil moisture profile in the Green-Ampt infiltration model.

H = the depth of ponding [cm], Ks = saturated hydraulic conductivity (cm/s), q =

flux at the surface (cm/h) and it is negative, ψf = suction at wetting front (negative

pressure head), θi = initial moisture content (dimensionless) and θs = saturated

moisture content (dimensionless).

The original Green and Ampt infiltration equation assumes constant soil

characteristics with depth. Variation of Green-Ampt infiltration equation parameters with

soil

water

z (negative direction)

! s! i!

wetting front f!! =

H=! 0

1+= Hh

ff zh +=!2

fzz =

0=z

24

soil texture can be found in Rawls and Brakensiek (1989). Figure 7 is a comparison of

Green-Ampt method and Horton with other methods to estimate infiltration capacity

such as Smith-Parlange (1978) and Philip (1957).

Figure 7. Comparison of Infiltration rate calculated by Horton, Green-Ampt, Smith-

Parlange, and Philip.

25

Effective Rainfall and Runoff Models

Considering basin wide processes, Sherman (1932) assumes that the routing

procedure is linear, and so uses a discrete transfer function to transform effective

rainfall in runoff to reach the basin outlet. Figure 8 to Figure 10 represent different

descriptions for effective rainfall. Runoff is a nonlinear process, and it does not merely

come from infiltration excess, whereas many models simply estimate the runoff without

considering environmental factors such as surface retention, and snowpack.

Figure 8 Example showing rainfall intensity is higher than the infiltration capacity of the

soil, taking account of the time to ponding. Infiltration capacity

26

fm

= fc+ ( f

o! f

c)e

!k (t! t0 ) f0=130 mm/h, fc=50 mm/h, empirical coefficient k=1, and t0=6h.

(Beven 2001).

Figure 9 Example showing rainfall intensity higher than some constant ‘loss rate’ (the Φ-

index) suppose Index value=130 mm/h (Beven 2001).

27

Figure 10 Example showing effective rainfall is a constant proportion of the rainfall

intensity at each time step. Proportion is assumed to be 0.3. (Beven 2001).

Following the work of Robert Horton, early applications of the unit hydrograph

technique assumed that all storm runoff was generated by an infiltration excess

mechanism. The Soil Conservation Service’s (USDA SCS 1979, McCuen 1982) curve

number approach is one of the most commonly used methods for estimating storm

runoff volume. The approach estimates direct runoff Q from storm rainfall P and

watershed storage S by:

2( ) /( )a aQ P I P I S= ! ! + Equation 33

28

Where Ia is the initial abstraction in inches and S is the maximum potential

difference between P and Q. Both Ia and S are affected by factors such as vegetation,

infiltration, depression storage, and antecedent moisture conditions. Empirical evidence

shows that Ia=0.2S; so 2( ) /( )a aQ P I P I S= ! ! + Equation 33 becomes

2( 0.2 ) /( 0.8 )Q P S P S= ! + Equation 34

The parameter S is defined by

(1000 / ) 10S CN= ! Equation 35

Where CN is an arbitrary parameter called the runoff curve number, which

ranges from 0 to 100. CN describes the land use, soil-infiltration rate, and soil moisture

conditions prior to the storm event. Other models like Manning’s Equation are used for

estimation of flows require measurements of channel depth, cross-sectional area, and

water surface slope.

29

Water Cycle Part II-Redistribution of Soil Moisture Following Infiltration

In the absence of ground water, water movement is dominated by gravity; the

movement of water from upper moister to the drier lower zones is called redistribution.

However, the redistribution process is in fact continuous; equilibrium is approached after

a very long period. Type of clay, evapotranspiration, soil texture, organic matter content,

depth of wetting and antecedent moisture are the factors that affect the redistribution.

Water Balance Dynamics

In spite of the complexity of soil-water flow with various rates and directions,

water balance itemizes all gains and losses of water to the system. The outline of the

approach is described as follows (Huang et al.,1996). We balance all rates

dW (t)

dt= P(t) ! E(t) ! R(t) ! G(t) Equation 36

W(t) the soil water content at time t, P(t) precipitation, E(t) evapotranspiration,

R(t) runoff, G(t) the net groundwater loss (through deep percolation). The stream flow

divergence R(t) consists of a surface runoff component S(t)and a subsurface runoff

component B(t) .

Potential Evapotranspiration (PET)

We can apply the Penman (Penman 1948), the Penman-Monteith method

(Monteith 1965) or the Priestley-Taylor model (Priestley and Taylor 1972) to calculate

PET. The Penman model requires solar radiation, air temperature, wind speed and

30

relative humidity. Total evaporation is composed of Er energy term (solar radiation) and

Ea aerodynamic (driven by wind speed and relative humidity)

E = Er + Ea Equation 37

Er is the contribution from radiation

Er =Rn

L(T )WR(T )

Equation 38

is weight factor for radiation, and is latent heat of vaporization

WR(T ) =! (T )

! (T ) + " Equation 39

( ) 2.5 0.0022L T T= ! " (J/Kg) Equation 40

Rn is net radiation, it equals to the incoming radiation Q (daily in MJm-1) minus

the reflected energy Q×α due to the albedo. Here the soil heat flux and outgoing long

wave are ignored.

Rn = Q(1!" ) Equation 41

! is surface albedo, which typically is 0.23 for vegetation

Ea is another part from aerodynamics and is

Ea(T , RH ,u) = f (u)(es! e)WA(T ) Equation 42

Compared with WR(T), WA(T) is the weight factor for aerodynamics,

31

WA(T ) = 1!WR(T ) ="

# (T ) + " Equation 43

f(u) is a factor of wind speed at z=10m

f (u) = 2.7 +1.63u Equation 44

es is vapor pressure at saturation in mbar as a function of T, in KPa

6791( ) 0.1 exp[54.88 5.03 ln( 273) ]

273se T T

T= ! " ! + "

+ Equation 45

vapor pressure e is a fraction RH of es

e(T ,P, RH ) = es(T ,P)RH Equation 46

RH is relative humidity in %. Also ! (T ) is the slope of saturation vapor pressure

curve (kPa/° C), and ! =psycrometer constant (kPa/ ° C)

! (T ) =6791

T + 273" 5.03

#

$%&

'(es

(T + 273)

#

$%

&

'(

Equation 47

3 7 26.6 10 6.6 10 3 [101 0.0115 5.44 10 ]P H H! " "

= # = # " # " # + # Equation 48

P is barometric pressure (1000mBar), H is the elevation.

The Priestley-Taylor estimation is a simplified form of Penman,

30.6 ( ) ( )E ho Q WR T= ! Equation 49

ho(Q) =2!

365Q(1"# )

Equation 50

32

E(t) can also be estimated by the Hamon (1963) method (Beven 2001).

Other factors like soil erodibility factor and various soil properties and biological

characteristics in turn affect soil infiltration and percolation, water-holding capacity, and

surface runoff, will not be considered. From the above equations, we can get monthly

value of ET. However, the calculation of ET is required to break down to quarter-hourly

time-steps. ASCE (American Society of Civil Engineering) standardized reference ET

Equation (ASCE 2005), is presented in hourly or quarter-hourly

ETsz

=

0.408!(Rn" G) + #

Cn

T + 273u

2(e

s" e

a)

! + # (1+ Cdu

2)

Equation 51

The parameters include the air temperature, air pressure, relative humidity, wind

direction, wind speed. (See ASCE for details of calculations as reference)

33

DATA SOURCES

Techniques Overview

The success of a hydrological model critically depends on the data. Modern

techniques such as rainfall radar can detect spatial rainfall variations, improvements in

transducers and robust electronic data-loggers have led to more reliable and more

continuous measurements of discharges, water tables and soil moisture (Beven 2001).

Besides, the hydrologic data sources are available from inventory of unpublished

hydrological data USGS, hydrological bulletin, daily and hourly by US weather bureau.

Geographic information systems (GIS) and remote sensing as cutting-edge techniques

are supplements for the previous methods.

With those techniques, it is possible to establish an experimental watershed.

There are several selections of experimental watershed: paired- single and replicated-

watershed, upstream-downstream approach and experimental plots. Four hundred

major experimental watersheds located at 51 different sites throughout the U.S. are

engaged in studying the interactions between water and forests. Experimental

watershed studies are costly, time consuming, weather dependent and difficult to

replicate (Chang 2006). In the case of paired-watershed, despite the high reliability of

paired-watershed approach, it is excessively time-consuming, hard to locate ideal

paired-watershed, and cost consuming to maintain the control watershed. Based on

those field experiments, simulation software is created for scientists to research in

34

providing watershed responses during single or long-term rainfall-runoff event, if

provided necessary weather condition.

Study Area and Automated Station

The study area for this thesis is located in a bottomland forest of the Greenbelt

Corridor (GBC) of the Lake Ray Roberts State Park. It is located in a flood plain, which

runs north and south along the Elm Fork of the Trinity River in North Central Texas. One

of the reasons for this site selection is that forest has the least runoff generation due to

high vegetation coverage and soil absorption.

At the site, the TEO project (TEO 2008) operates a soil-water and weather

automated station, which is within an open area being exposed to abundant sunshine,

to make sure enough solar power is available. Table 2 gives the coordinates and Figure

11 is the map showing the location of the soil-water/weather station at the GBC.

Table 2. Coordinate information of the soil-water/weather station at the GBC.

Latitude Degree Decimal

Longitude Elevation Coordinate system

33.25925 -97.040972 520 ft. WGS 84(NAD 83)

The soil-water/weather station is collecting precipitation and soil water content

every fifteen minutes. Figure 12 is the overview of the system. This whole system is

composed of three modules: real-time data collection, immediate transferring terminal

and memory space for intermediate storage before the data is retrieved. A wireless

transferring component part is under development. As we have discussed in the

35

previous sections of this thesis, soil moisture, evaporation and precipitation are the

variables needed to perform a water balance calculation. We have available

meteorological sensors including: wind direction, wind speed, relative humidity, rainfall,

temperature and six soil moisture sensors installed at different depths. All the probes

continuously collect data every fifteen minutes.

All those sensors are connected to the Datalogger processing the Analog to

Digital conversion and providing EEPROM. Normally, the physical memory size is

limited to 62,280 units’ storage space. Each variable occupies one unit. One variable

occupies 24 hours ×60 minutes÷15 minutes/time-1 =95 units per day. The size of the

total memory is 62,280 records, if converted to length of time for taking 20 variables =

62,280 ÷95÷20=30+ days. Without extra memory supported, the data must be backed

up once a month to avoid being overwritten. A cell phone modem is recently

implemented for wireless data transmission during real-time monitoring. As an

alternative resolution for limited data space, the data can be transferred immediately to

the server at the UNT campus. Also, emergency signals such as when the battery is low

and data loss could be included. Upon necessary processing, the information of soil

moisture condition could be accessible to the public immediately. In the future, wireless

sensors network will be installed in other areas of the watershed. So that observation on

responses for basin-scale area can also be obtained.

36

37

Figure 11 Map of Greenbelt Corridor.

Figure 12 Data collection system.

38

Soil Moisture Sensor and Its Calibration

The selection of soil moisture probe is based on the requirement of data

resolution and accuracy. Besides dielectric constant soil moisture probes, TDR (time

domain reflectometry) and FDR (frequency domain reflectometry) are two types of

sensors, both of which measure the difference in capacity of a non-conductor to

transmit high-frequency electromagnetic waves or pulses. The pulse’s width is

proportional to soil moisture content. Other methods are neutron probe, gypsum-porous

blocks/electrical resistance, gypsum-porous blocks/electrical resistance, calcium

carbide gas pressure meter, and tensiometers (Pritchard 2008).

At the GBC station there are Decagon EC-5 TDR sensors installed at several

depths. The EC-5 provides direct and accurate readouts of volumetric soil moisture

percentage with typical accuracy in all soil types without calibration of ±3%. With

calibration, it can be lowered to 1-2%. The manufacturer has set default calibration for

mineral soil, which is

VWC = mV !11.9 !10"4" 0.401 Equation 52

mV is the output from sensor in mille-volts, the output of the sensor VWC is in

percentage value.

Though the TDR technology has the advantage that there is no necessity for

calibration, the results from large rainfall event are generally around 100%. Normally,

VWC is around 60% at soil saturation. Additionally, sensor is sensitive to soil texture,

vegetation coverage. So calibration is necessary to acquire greater accuracy. As

39

described in the application note provided by Decagon (Colin, 2002), the methods

followed the standard procedure for calibrating capacitance probes outlined by Starr

and Palineanu ( 2002). Soil samples were weighed and dried to determine gravimetric

water content. For this purpose, I added water to wet the soil to a uniform condition,

recorded the output of sensor, weighed certain amount of soil in a jar, recorded its

volume, and dried it for 24 hours in a convention oven. Table 3 shows the results of

calculation gravimetric water content. Volumetric water content (θ)

! = w"

b

"w

Equation 53

was determined from the gravimetric water content(w)

w =m

w

mm

Equation 54

where m is mass and the subscripts w and m refer to water and minerals. The

bulk density !b is

!b

=m

m

VtEquation 55

Vt is the total volume of the sample. The density of water, !w

is 1Mg/m3

Derived from the above equations, θ (Soil water content) =mass of water/volume

of sample, so that θ is linear with respect to the readout of sensor. Note that the mass of

water is soil initial weight minus dry soil weight.

Table 4 Sensor calibration record.

40

Sample Output of sensor(mV)

Vt-volume

Soil initial weight(g)

Dry soil weight(g)

Jar weight

Mw-mass of water(g)

Soil weight

θ Theta

1 220.099 N/A 0.000

2 438 57 285 271 193 14 0.246

3 471 57 277 264 193 13 0.228

4 508.73 57 302 284 193 18 0.316

5 574 57 338 311 193 27 0.474

6 503.528 35 59 52 13 7 39 0.200

7 518.639 35 70 59 13 11 46 0.314

8 541.688 35 71 59 13 12 46 0.343

9 550.25 35 74 61 13 13 48 0.371

10 566.063 35 75 62 13 13 49 0.371

11 580 35 73 59 13 14 46 0.400

12 610.883 35 79 62 13 17 49 0.486

13 616 80 358 316 194 42 0.525

14 625 80 366 324 194 42 0.525

41

Figure 13 Linear regression results of calibration.

The calibration curve I obtained in Figure 13 was generated by using simple

linear regression. The calibration equation is Y=0.0013x-0.3456, with R2 0.881

42

RESULTS

Soil Texture

Soil texture and structure are the factors that affect drainage, stability and

aeration, retention of the soil. One way to determine the texture and structure is

manually test its hardness, stickiness, and plasticity. The standard method is to sieve,

separate, dry and weigh the proportion of clay, silt, sand particles that compose the soil

and use equations of Saxton et al. (1986), or US soil textural triangle (USDA 1951) to

calculate its composition. Table 5 lists the soil texture of each layer and the locations of

sensors being installed.

Table 5 Soil texture analysis results for each layer.

Sensor ID

Depths of

sensor (cm)

Soil texture by feeling Structure Soil

Profile(cm) %of clay % of silt % of

sand

N/A Silty clay loam 0-10 30.00 50.72 19.28

1 12.7 Silty clay blocky, fine strong 10-22

2 38.1 Sandy loam Medium weak 22-44

N/A Sandy loam 44-57 3 63.5 Loamy sand massive 57-78

N/A Silty loam 78-88

4 91.44 Clay loam Blocky medium weak,

88-115

5*/6 116.8/167.6 Silty clay

Water table occurred at

depth around 140 cm

115-170 40 48.72 11.28

43

Note: the results of sensor No. 5 and 6 are not included in the analysis

Combined with the information in Table 6, initial analysis of soil texture would

help compare the hydraulic properties of each layer. The first layer’s texture is silty clay,

which has the highest field capacity, saturation and wilting point, lowest saturated

conductivity among these four layers. That means its pores have high capillary force to

hold the water. Compared to the first, the second layer loses water more easily, due to

its loose structure. Then, the third layer is loamy sand, which has high saturation

conductivity, allowing the layer below to get wet in a short time. Finally, the fourth layer,

whose texture is clay loam, has finer structure and larger retention than the other three

layers, and its field capacity and saturation are comparatively higher than third and

second layers.

Table 6. Estimated water characteristic values for texture classes (Saxton and Rawls

2006).

Texture class*

Sand % Clay % Wilting point 1500kPa

Saturation 0kPa%v

Field cap 33kPa%v

Saturated conductivity mmh-1

Matric density gcm-3

SiC 10 35 27 52 41 3.7 1.26 SaL 65 10 8 45 18 50.3 1.46 LSa 80 5 5 46 12 96.7 1.43 CL 30 35 22 48 36 4.3 1.39

*Note: Sa, sand; L, loam; Si, Silt; C, clay

Pressure conversion: 1mbar=1Hpa, 1000mbar=1bar=100KPa

44

Porosity

Porosity describes the fraction of void space in the porous medium such as rock

or sediment. It is defined by ratio

T

v

V

V=!

Equation 56

Where vV is the volume of void-space and TV is the total or bulk volume of

material. Porosity is indirectly related to hydraulic conductivity; for two similar sandy

soils, the one with a higher porosity will typically have a higher hydraulic conductivity,

but there are many complications to this relationship. Clay, which typically has very low

hydraulic conductivity as well as high porosities, can hold a large volume of water per

volume of bulk material, but they do not release water very quickly. One commonly used

relationship between porosity and depth is given by the Athy (1930) equation

kzez!

=0

)( "" Equation 57

Where 0

! is the surface porosity, k is the compaction coefficient [ !1m ] and z is

depth [m]

Alternatively, porosity can be calculated from bulk density !bulk and particle

density !particle (Brady & Weil, 1996)

particle

bulk

!

!" #= 1

Equation 58

45

Normal particle density is assumed to be the same as quartz’ approximately 2.65

[g/ cm3]. With the value of porosity, volumetric soil water content can be calculated as

porosity!soil moisture as wetness. Table 7 shows that the first layer has the highest

porosity, which explains why the first layer has highest field and saturation capacity

among those four layers

Table 7 Bulk density and porosity of soil sample (Provided by Wilfredo Franco).

Texture class Depth in cm Depth in inch Bulk density g/cm3 Porosity SiC 12.7 5 1.15 0.564906 SaL 25.4 10 1.49 0.437736 LSa 48.3 19 1.38 0.479245 CL 28.6 27 1.43 0.460377

Hydraulic Conductivity

Hydraulic conductivity (K) defines the rate of movement of water through a

porous medium such as a soil or aquifer. It is the constant of proportionality in Darcy’s

Law. Hydraulic conductivity cannot be directly measured but inferred from field,

laboratory or modeled data. Different approaches include: seepage meter, infiltrometer,

pump test, and grain size test.

Using empirical equations is a good method to estimate K, where no

measurement is accessible. The water retention curve Sw of each layer can be

calculated from Sw =W !Wr

Wc !Wr Equation 13, W=soil moisture in

wetness×porosity, water potential P(t, z) was calculated through 1

( ) ( )ba

Sw PP

=

46

Equation 11, then Ks =

0.86

(b +1)(2b +1)

!

"#

$

%&

Wc 'Wr

a

!

"#$

%&

2

Equation 14 derives

non-saturated conductivity through K(P) = KsSw(2b+3) Equation 15. The results

are illustrated in Figure 15 and Figure 15

Figure 14 Kp1 and Kp2.

47

Figure 15. Hydraulic conductivity (cm/s) Kp3 and Kp4 vs. soil moisture

The saturated hydraulic conductivity Ks of each layer is

Table 8 Saturated hydraulic conductivity.

Layer Ks

1 0.0002517286

2 0.0012433594

3 0.0033387088 4 0.0003945638

48

The first layer (silty clay) has the lowest hydraulic conductivity K, while the

second layer (sandy loam) has the highest K. Under normal conditions, the high

capability of absorbing water makes first layer absorbs most of the precipitation. The

combination of high conductivity and its loose structure explains why the second layer is

not easily saturated. Only during the continuous rainfall event happened on April 24,

May 29, and June 16, the water content of the second layer exceeded 60%. The third

layer’s (loamy sand) high conductivity results in rapid wetting of the fourth layer.

Potential

Water potential is the potential energy of water per unit mass of water in the

system. It is the potential energy measured in reference condition, namely, compared to

pure water. It quantifies the tendency of water moving from higher potential area to

lower potential area. And it must be defined as a ‘difference’ in potential energy since

absolute potential energy cannot be measured. Hydraulic potential is the sum of the

matric, pressure, and gravitational potential components. Water potential is the sum of

matric, osmotic, and pressure potential components. The total water potential of a

sample is the sum of four component potentials: gravitational, matrix, osmotic, and

pressure. Soil binds water mainly through matric potential, and therefore matrix potential

is the dominant factor of total potential.

Decagon’s WP4 and WP4-T dew point potentiometer measures water potential

by determining the relative humidity of the air above the sample in a closed chamber, in

less than 5 minutes, range from 0 to -300 MPa with a resolution of 0.1 MPa.

49

Potential P(t, z) and water retention curveSw(P) are inversely related.

50

Figure 16 Soil moisture vs. water potential (Mpa).

From Figure 16, we can get similar analysis as in Figure 15 for hydraulic

movement pattern. First layer’s high potential restrains the water flowing into deeper

layer. In short term, if rainfall does not last for a long time (less than one day), rain

penetrate into the soil immediately and runoff is unlikely to occur. However, despite the

fact that the second layer has high hydraulic conductivity, the flow goes through first

layer is restricted due to its high potential. Once the rainfall lasts longer, the excessive

precipitation and the blocky soil of first layer facilitate the formation of runoff.

51

Flow

From ( ) 1 ( ) ( )P P

q K P K P K Pz z

! !" #= + = +$ %! !& '

Equation 8, flows could be

derived from potential and hydraulic conductivity. Figure 17 includes the estimation of

downward flow of each layer. The result again indicates the rapid flow from third layer to

the fourth one.

52

Figure 17 Soil moisture vs. flux (m/s).

Infiltration Capacity and Infiltration Rate

To determine the water state as a function of time and depth in soil system,

infiltration could not be ignored. It is a measure of the rate at which water soaks into the

ground as a function of time. kt

cocm effff!

!+= )( Equation 29. There are two

methods of measuring infiltration capacity:

a. rainfall hyetograph and runoff hydrograph

b. infiltrometer, there are various types of infiltrometer: flooding type infiltrometer

and rainfall simulators, tube infiltrometer or double ring infiltrometer (Reddi 2005).

Figure 22 include the graphs of infiltration capacity test obtained by the detailed

procedure of testing.

53

Figure 18 infiltration capacity test and NLS curve 1a &2a.

54

Figure 19 Infiltration capacity test and NLS curve 3a &11.

55

Figure 20 Infiltration capacity test and NLS curve 13 & 31.

56

Figure 21 Infiltration capacity test and NLS curve 32& 21a.

57

Figure 22 infiltration capacity test and NLS curve 21b.

In Figure 22, each test runs longer than 30 minutes but less than 45 minutes.

Each site is near the weather station to make sure it matches the soil condition around

the soil sensors. Tests 11 and 13 are the first trial without refilling water immediately

after water was depleted. Tests 1a, 2a, 3a, 31, 32 are performed by infiltrometer, and

they located at about 12.70cm from the site. Tests 31, 32 are measured by infiltrometer,

1a, 2a, 3a are measured in a bare hole. Tests 21a, 21b, are at a position around 38.10

cm from the site.

To solve the power k in kt

cocm effff!

!+= )( Equation 29 , I use nonlinear

regression generating the power ( k ) of exponential-decay. Table 9 lists the results from

estimation. For example, the curve for K13 is fm = 0.05 + (4.2 ! 0.05)e!1.1926t

Table 9 Value of k, f0, and fc for each curve

Test Coefficient k Initial infiltration f0 Final infiltration Note

58

(cm/min) fc (cm/min) 1a 1.760 11.723 0.270 2a 1.76 18.863 0.204 3a 1.530 4.482 0.167 11 0.089 0.574 0.002 First time test 13 1.193 4.200 0.050 First time test 31 0.46 17.143 1.250 The third time test 32 0.392 7.500 0.321 The third time test

21a 0.658 0.181 0.004 38.10 cm 21b 1.076 3.594 0.030 38.10 cm

1a-3a 3.30018~3.80 11.723 0.2~0.3 Final result

To remove the measurement errors in experiment, I combined the curves of

those samples with similar condition, and got fm = 0.2 + (4.2 ! 0.2)e!1.53t cm/min fc is close

to the saturated hydraulic conductivity. In previous estimation, Ks of first layer equals

0.0002517286 m/s, which was near to 1.5cm/min. Measurement error from infiltrometer

will affect accuracies of fc and fo , but they should not affect the decay coefficient k .

The actual infiltration rate is determined by both rainfall and infiltration capacity

R < Icapcity

, Irate

(t) = Ra inf all(t)

R > Icapacity

, Irate

(t) = Icapacity

(t)Equation 59

59

Soil Moisture Variations Without Rainfall

Figure 23 and

Figure 24 come from Campbell Scientific soil moisture sensors (type CS615) that

were located at two different soil layers from the EC-5 decagon sensors. Under normal

condition without rainfall, the change of the soil moisture was caused by evaporation.

Figure 23 shows that on March 20th in 2007, during nighttime, the curve hit the peak

when less evaporation occurred. The lowest point during a day occurred between 14:00

and 15:00, when the sunshine is the most intensive. After that, the curve sloped up

quickly and reached a higher point at the end of day. Comparatively, records from a

sensor at a deeper position in

Figure 24 show that ET had less impact on it. The soil water content did not show

obvious variations but minor changes in the early morning and at noon.

60

Figure 23 Daily soil moisture near surface with no rainfall. (last two digits of numbers in

time series represent minutes, the first two digits denote hour).

61

Figure 24. Soil moisture at deeper position (last two digits of numbers in time series

represent minutes, the first two digits denote hour).

Soil Moisture Responses to Rainfall Event

Figure 25 through Figure 30 show the values of rainfall (in cm) as well as soil

moisture at 15 minutes time interval in several periods of interest in 2007. Generally, the

hydrological conditions in North Texas in 2007 were dry. However, the rainfall events in

June and July 2007 broke the historical rainfall record. A tropical rain belt brought the

repeated flood in June, which also caused 11 deaths.

Figure 25 Records from February 2 to March 2. Soil moisture/ Rainfall (cm).

62

Figure 26 Records from February 23 to March 23.

Some rainfall events scattered in February and March (Figure 25 and Figure 26),

but they did not generate notable changes of soil moisture except the one on March 13

resulting in immediate response of each layer. The peak rainfall for this event was

above 0.15, which was above all values of the period shown.

63

Figure 27 Records from Mar 19 to April 29.

Figure 27 shown above and Table 10 shown below, illustrate that short storms

did not result in runoff. According to the records on April 12 (Table 10), at 18:30, the

rainfall intensity jump- started at 0.3048 cm in 15 minutes; soil moisture of the first layer

immediately increased to 39%, which was normally 30%. Meanwhile, the soil water

contents at the second and third layers showed no change. Due to the high soil

retention, the first layer restricted water from sinking to deeper layers. After 15 minutes,

soil water content of the first layer drastically increased to 61%, which was the

saturation value. The third and fourth layers attained 49% and 53%, respectively.

64

Figure 28 Records from April 11th to May 10.

The rainfall ceased between 18:30 and 18:45, and the water content sloped

down promptly. It can be inferred that runoff did not occur and the infiltration capacity of

first layer exceeded the rainfall intensity. Otherwise, soil moisture of each layer would

remain saturated for a period.

Table 10 Soil moisture changes due to intensive rainfall.

Year Day Time Rain(in.) SM1 SM1% SM2 SM2% SM3 SM3% SM4 SM4%

2007 4/12 1815 0 493.6 0.29608 452.9 0.24317 522.3 0.33339 558.9 0.38097

65

2007 4/12 1830 0.3048 567.6 0.39228 452.9 0.24317 522.2 0.33326 559.6 0.38188

2007 4/12 1845 1.4478 737 0.6125 600.3 0.43479 646.3 0.49459 676.3 0.53359

2007 4/12 1900 0 535.6 0.35068 510.9 0.31857 571.6 0.39748 650.3 0.49979

2007 4/12 1915 0 529.6 0.34288 499 0.3031 550.3 0.36979 611.7 0.44961

The next event happened on April 24. The station site at the GBC received 2.03

cm of rain in a matter of hours. The first layer turned to its saturated status, which had

over than 60% soil water content. All the layers display similar tendencies. The runoff

stood at high level until the third day after the rain stopped. And then the water content

of each layer plunged from the peak on April 27. Before that, the water content of each

layer was mostly maintained at the same level. Due to the third layer’s (loamy sand)

high-saturated conductivity, the fourth layer accepted the high flow and responded

immediately.

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Figure 29 Records from May 2 to May 31.

Most of the rainfall events in May were not intensive as April 24’s. It is noticeable

that the heavy rainfall on May 25 had marginal effect on second layer. However, on May

29, another smaller precipitation pushed second layer’s soil moisture to 60% and stood

at high level for the next two days. It can be concluded that runoff occurred despite that

none of the layer was saturated. The first layer (blocky, strong structure) has high field

capacity (highest porosity) and low conductivity. So that runoff formed before it reached

its saturation. With the additional rain supply on May 29, the second layer was

ascending significantly. And the second layer’s reaction was the least stable at the initial

stage of precipitation.

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Figure 30 Records from May 23 to June 22.

During the first quarter of June, the hydrological condition is similar to the

observed in May. The fourth layer reacted contrarily to the second layer. Its curve was

stable and dropped down the most slowly among those four layers. Since both second

and third layers have high saturation conductivity, their trends are fluctuated responding

to each rainfall event. At the end of the June, the consistent massive rainfall in Figure

31 not only generated the renounces of soil water content to highs, but also brought

flooding of Trinity River. Within two months since then, the whole area of the GBC was

drowned in flooding.

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Figure 31 Records from June 15 to July 13.

69

Data Analysis and Model Improvement

In this section, I use the data collected to inform the models

Assumptions

Figure 32 Water balance: Any increment of moisture content of certain layers at Δt =

tk+1-tk time is determined by calculating water input and output of the layer.

Figure 32 is a schematic of the model process, with eleven variables: four soil

moisture contents, rainfall, runoff, four flows, and ET. Assume that the responses of

limited area are obtained during a short time after a rainstorm, so that groundwater

change can be ignored, G=0. Additionally, the subsurface flow is hard to separate from

surface flow Ron , subsurface from other plots can be omitted as Ron needs

comparatively long time to generate. So that Ron =0, Δ R=- Roff , then the water

balance equations can be simplified as

Layer 1

Layer 2

Layer 4

Layer 3

Flow1

Flow2

Flow3

Flow4/Groundwater

Rainfall

Runoff

Evapotranspiration

70

dW1(t)

dt= P(t) ! E(t) ! R(t) ! P1(t)

Equation 60

dW 2(t)

dt= P1(t) ! P2(t)

Equation 61

dW 3(t)

dt= P2(t) ! P3(t) Equation 62

dW 4(t)

dt= P3(t) ! G(t) Equation 63

P1(t) : flow from first to second layer

P2(t) : flow from second to third layer

P3(t) : flow from third to fourth layer

Add them up,

dW1(t) + dW 2(t) + dW 3(t) + dW 4(t)

dt= P(t) ! E(t) ! R(t)

Equation 64

R(t) = P(t) !dW1(t) + dW 2(t) + dW 3(t) + dW 4(t)

dt! E(t) Equation 65

P1(t) = P(t) ! E(t) !dW1(t)

dt! P(t) +

dW1(t) + dW 2(t) + dW 3(t) + dW 4(t)

dt+ E(t)

Equation 66

P1(t) =dW 2(t) + dW 3(t) + dW 4(t)

dt Equation 67

Substitute P1(t) by equation 58 we obtain

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P2(t) =dW 4(t) + dW 3(t)

dt Equation 68

P3(t) =dW 4(t)

dt Equation 69

For those situation deep percolation could not be ignored

Rainfall(t)=Infiltration(t)+Runoff(t)+Evaportranspiration(t)

Equation 70

dw1(t)

dt= Infiltration(t) ! flow1(t)Equation 71

dw2(t)

dt= flow1(t) ! flow2(t) Equation 72

dw3(t)

dt= flow2(t) ! flow3(t)

Equation 73

dw4(t)

dt= flow3(t) ! Groundwater(t)Equation 74

PET Estimation Results

For easy reference we repeat here

ETsz

=

0.408!(Rn" G) + #

Cn

T + 273u

2(e

s" e

a)

! + # (1+ Cdu

2)

Equation 51

Which is the equation based on the Penman-Monteith method provided by ASCE

to estimate ET. (See ASCE for calculation details). Figure 33 is the result of PET at 15

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minutes interval derived from the data source in July, 2007. The time index is an integer

denoting the position of the observation point in the time series. The impact of ET on

runoff and infiltration are small enough to be omitted.

Figure 33 ET and Rainfall (mm/15mins) in July. The time index is an integer denoting

the position of the observation point in the time series.

Example of Calculations of Runoff

I apply the infiltration rate, rainfall as input to the equations discussed above to

get the output flow and runoff. The first scenario is the least complicated case as the

precipitation penetrated through the soil immediately. This rainfall event took place on

Mar 13, (see Figure 34 ) which last for less than an hour. Before Mar 13, some

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scattered events had marginal effects on the soil moisture level. As it does not generate

runoff but obvious soil moisture change, Equation 70 can be simplified

as Ra inf all(t) = inf iltration(t) .

From the previous experiment, the exponential decay curve decreases to fc

within the first two minutes. It could be assumed that the infiltration capacity is

approximate to the final infiltration fc .

Figure 34 Records from February23 to March 23.

Table 11 the data on March 13.

1727 Time Rain(cm) SM1 SM2 SM3 SM4 1728 1445 0 0.29491 0.229 0.32611 0.3694 1729 1500 0 0.29491 0.229 0.32702 0.3694 1730 1515 0.4826 0.39722 0.30102 0.32702 0.37122 1731 1530 0.1016 0.35393 0.30804 0.35055 0.37044

74

1732 1545 0.0254 0.34197 0.28906 0.34197 0.37057 1733 1600 0 0.33599 0.27788 0.33859 0.36979

Figure 35 Rainfall and infiltration rate starting on March 13 (corresponding to time index

1728-1750). The infiltration rate is illustrated as red curve. The time index is an integer

denoting the position of the observation point in the time series.

Since infiltration capacity is larger than rainfall, the infiltration rate equals to the

precipitation.

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Figure 36 Soil Moisture values on March 13 (corresponding to time index 1728-1750)

The time index is an integer denoting the position of the observation point in the time

series.

By observing the flow of each layer on March 13 in Figure 37, time index 1728-

1750, we find the exceptional point with negative value. Which means the total change

of the soil moisture content exceeds the precipitation. As in Figure 38, there is one point

the total water content change jumping higher the infiltration rate.

76

Figure 37 Flow of each layer (The time index is an integer denoting the position of the

observation point in the time series).

77

Figure 38 Comparison of total change of the soil water content with infiltration rate. Red

curve represents the Infiltration rate. The time index is an integer denoting the position

of the observation point in the time series.

The second scenario on April 24, generates runoff. Recall the records of April in

Figure 39

78

Figure 39 Record of April.

79

Figure 40 Rainfall (black points) and Infiltration rate (red lines) The time index is an

integer denoting the position of the observation point in the time series.

In Figure 40, during the rainfall event starting from time index 1200, partial rainfall

was not drained promptly. With the antecedent saturated condition, the overflow from

precipitation would become runoff.

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Figure 41 Soil moisture from April 24 (time index from 1200 to 1700) The time index is

an integer denoting the position of the observation point in the time series.

Figure 41 is soil’s water content diagram corresponding to rainfall event on April

24. In Table 12, all the soil moisture did not change until half an hour later after the

rainfall started. And there was another 15 minutes delay for fourth layer, which brought

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it up to 52% from 39%. At 14:15, all of them arrived at the saturation level. Before the

next peak at 18:45, the water content of each layer was swinging back and forth.

Table 12 Data for April 24.

1201 Date Time R(cm) SM1 SM2 SM3 SM4 1202 4.24 1330 0.01 0.30375 0.25006 0.33846 0.38786 1203 4.24 1345 0.05 0.30284 0.25006 0.33924 0.38786 1204 4.24 1400 0.32 0.40346 0.37746 0.48315 0.39046 1205 4.24 1415 0.59 0.6229 0.6164 0.49355 0.52566 1206 4.24 1430 0.11 0.36706 0.36615 0.49797 0.53268 1207 4.24 1445 0.01 0.35484 0.32884 0.39657 0.48926 1208 4.24 1500 0.01 0.34886 0.31857 0.37668 0.44948 1209 4.24 1515 0.1 0.34717 0.31168 0.36797 0.43739 1210 4.24 1530 0.05 0.35237 0.30726 0.36459 0.42959 1211 4.24 1545 0.34 0.40268 0.39059 0.45728 0.4877 1212 4.24 1600 0.32 0.39917 0.38357 0.45819 0.48848 1213 4.24 1615 0.72 0.3993 0.3837 0.46001 0.48861 1214 4.24 1630 0.44 0.39761 0.3837 0.46001 0.48952 1215 4.24 1645 0.48 0.3967 0.3837 0.46092 0.49043 1216 4.24 1700 0.13 0.3967 0.38292 0.46183 0.49043 1217 4.24 1715 0.15 0.39761 0.3837 0.46183 0.49043 1218 4.24 1730 0.33 0.39761 0.38461 0.46261 0.49134 1219 4.24 1745 0.75 0.39332 0.3811 0.46352 0.49303 1220 4.24 1800 0.14 0.39852 0.38721 0.46443 0.49303 1221 4.24 1815 0.27 0.39761 0.42803 0.46521 0.49303 1222 4.24 1830 0.85 0.40021 0.6112 0.46794 0.49394 1223 4.24 1845 0.33 0.5956 0.6138 0.46703 0.49472

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Figure 42 Flow of each layer (corresponding to time index 1200-1700) The time index is

an integer denoting the position of the observation point in the time series.

Similar to scenario one, I estimated the flow using the input parameters. In Figure

42, the first spot is at time index 1200, where the soil moisture of all layers increases

drastically. The curve of the flow is swinging back and forth. There are some negative

values, which are generated due to the same reason in the first scenario. (Figure 43).

During the period when the soil moisture stand high, there is no flow which means that

there is no water exchange. All the water is stabilized in the pores of the soil. The

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second spot is located near time index 1380, the curve of first layer plummeted. At that

time, the rainfall had ceased. The third spot being concerned is approximate to time

index 1450; second layer’s curve sloped down. There are minor peaks in layer 2

through layer 4. And between the second spot and third spot, layer 1’s soil moisture

value dropped down to lowest level, there is no water supply from upper layer to the

below ones.

Figure 43 Infiltration rate vs. Summary of SM of all layers. The red curve represents

infiltration rate . The time index is an integer denoting the position of the observation

point in the time series.

84

CONCLUSION

This research intends to study the field-scale response of soil moisture to rainfall

events, which is interpreted in the form of models of soil water dynamics. The results

could be applied in flood forecasting and irrigation scheduling. I started by studying

existing hydrological models. Besides Horton and Darcy’s and other hydrologists’

invaluable pioneer work in this area, advanced computer technology allows for the

implementation of watershed models to simulate runoff and stream flow. Shortage of

long-term reliable data and incomplete knowledge are some of the major difficulties of

all types of hydrological modeling. The water balance approach was selected for this

thesis based on its feasibility of implementation.

Data being used in this study comes from an automated station collecting soil

moisture data within a small area (about 2 m × 2 m × 2 m). Starting from February 2007,

the data set contains several historical rainfall records especially the one in July 2007.

Before installing the sensors, soil texture properties were preliminarily measured, so

that the position of each sensor could be determined to represent the texture conditions

of each layer identifiable in the soil column.

Analysis of soil’s potential and hydraulic conductivity explains the first layer’s high

porosity and field capacity. These properties determine that first layer absorbs effective

precipitation very rapidly. However, once saturated, runoff would occur since the high

potential as well as low hydraulic conductivity of the first layer restrained the downward

flow. Despite that the second layer’s high hydraulic conductivity facilitates the flow of

water; the excessive amount of water could not penetrate the first layer. Due to the

85

same reason, during several storms, the runoff was generated quickly and its level

stood high until several days after the rain ceased.

Due to the difficulties of measurement of hydraulic conductivity and

evapotranspiration, these quantities were estimated by simulation as an alternative.

Besides modeling, an infiltration capacity test was conducted in the field. From which I

inferred the infiltration rate. By applying those parameters to the water balance

equation, I estimated the downward flow of each layer as well as runoff. In the first

scenario, the flow’s tendency is closely related to the soil moisture pattern. In the

second scenario, the flow stops when the soil moisture stays at saturated value.

The possible explanation for this surprising result is that the sensor is sensitive to

soil texture. I calibrated the sensor using only the top layer texture and implemented the

same calibration to all layers. This problem can be verified in the laboratory in future

work related to this project. Another possible explanation is that water movement in soil

is heterogeneous even within the same layer. The sensor could only reflect the water

condition around it. Therefore, the real water content can be underestimated by

assuming that the soil water content is the same within one layer, and calculate the

water stored in that layer by the measured moisture and multiplying by porosity and

thickness.

The results of the water balance also help underline the importance of using

detailed soil characteristics in models of water dynamics. A complete, systematic

analysis of soil properties and calibration of probes are necessary. Also, rather than

86

model simulation, measuring soil properties such as water potential, saturated hydraulic

conductivity could improve the model accuracies.

87

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