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This is to certify that the

thesis entitled

An Interactive Hydrologic Model for Semi-arid Watersheds

presented by

Abdelaziz Aslouni

has been accepted towards fulfillment
of the requirements for

M.S. Agricultural Technology

degree in

 

 

and Systems Management

M

Major professor

Dr. John B. Gerrish, P.E.

Date ‘22) 5&0? 7??
(J

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1/98 cJCIRC/DateDm.p65-p.14

AN INTERACTIVE MODEL FOR
SEMI ARID WATERSHEDS

By

Abdelaziz Aslouni

AN ABSTRACT OF A THESIS

submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
in

Agricultural Technology and Systems Management

Department of Agricultural Enginnering

1997

ABSTRACT
AN INTERACTIVE MODEL FOR
SEMI ARID WATERSHEDS
By

Abdelaziz Aslouni

Semi-Arid Watershed Model (SAWM) was developed using an
object-oriented interactive software. In the model, rainfall is
partitioned to four components of the hydrologic cycle, namely, a
river, the atmosphere, a shallow aquifer, and a deep aquifer.

SAWM estimates water yield, evapotranspiration, soil loss, and
aquifer recharge - both flows and accumulations. Theoretical step-
function storms of 30 days’ duration and six uniform intensities
(5 through 50 mm/day) were used to calibrate SAMW against a
secondary reference model, previously validated.

When realistic rainfall and weather were applied, SAWM
overestimated the annual ET by 6%, water yield by 38%, and
sediment yield by 120%. Discrepancies are related to SAWM’s
oversimplification of the soil and shallow aquifer. Interactively
improving and tuning SAWM can be readily done for a particular

watershed using real data.

ACKNOWLEDGMENTS

I thank God for His guidance.

I would like to thank my major professor Dr. John B. Gerrish for his
encouragement, expertise, and friendship throughout my graduate
studies. His dedication to the profession and extreme generosity is an
inspiration to all who have had the chance to work with him.

I thank also Dr. Echart Dersh for his council and expertise on my
research committee and credit him for inspiring my interest in
watershed management issues. I also extend my recognition and
sympathy to Dr. Fred Nurnberger for his help and positive role as a
member of my research committee.

In addition. I would like to express my thanks to USAID and the
Moroccan government for financial support.

Thanks can not express enough the support and patience my parents
and the rest of my family have given over the years to make this

research work possible.

iii

 

TABLE OF CONTENTS

LIST OF TABLES ........................................................ v
LIST OF FIGURES ....................................................... vi
CHAPTERI INTRODUCTION ..................................... 1
CHAPTER 2 LITERATURE REVIEW ........................... 3
CHAPTER 3 METHODS .............................................. 29
CHAPTER 4 RESULTS AND DISCUSSION .................. 49
CHAPTER 5 CONCLUSIONS ....................................... 75
CHAPTER 6 RECOMMENDATIONS ............................ 76
APPENDIX A SAWM ALGORITHM ............................. 77
APPENDIX B USDA SOIL DATA ................................. 80
APPENDIX C SWRRB COMPUTER PRINTOUT ............ 82
REFERENCES ............................................................. 109

LIST OF TABLES

Table 1- Tuned parameters, their values and sensitivities .................. 48

Table 2- Summary of the outputs from the tuning simulations ........... 50

Figure 1. Subsurface hydrologic zones .......................................... 23
Figure 2. Aquifer types ................................................................ 24
Figure 3. Conceptual model of SAWM using STELLA II ................ 32
Figure 4. The pulse-rainstorm of 900mm and the response of other
components .................................................................................. 47
Figure 5. Comparison of water yields from the two models ............. 51
Figure 6. Comparison of evapotranspiration from the two models....52
Figure 7. Comparison of soil losses from the two models ................ 53
Figure 8. One year rainfall input to SAWM ................................... 55
Figure 9. One year rainfall input to SWRRB ................................... 56
Figure 10. Runoff estimated by SAWM .......................................... 57
Figure 11. Runoff estimated by SWRRB ......................................... 58
Figure 12. Cumulative water yield estimated by SAWM ................... 60
Figure 13. Daily water yield estimated bt SWRRB ........................... 61
Figure 14. Total ET estimated by SAWM ........................................ 62
Figure 15. Evapotranspiration estimated by SWRRB ........................ 63.
Figure 16. Return flow estimated by SAWM .................................... 64
Figure 17. Return flow estimated bt SWRRB ................................... 65

LIST OF FIGURES

vi

Figure 18.
Figure 19.
Figure 20.
Figure 21.
Figure 22.

Figure 23.
values ......

Recharge of the deep aquifer estimated by SAWM ............. 66

Sediment yield estimated by SAWM ................................. 67
Sediment yield estimated by SWRRB ................................ 68
Comparison of water budgets for the two models ............... 70
Comparison of soil loss estimated by the two models ......... 71

Main outputs from simulating real conditions and their

....................................................................................... 73

vii

Chapter 1

INTRODUCTION

Water is a limiting factor for biosystems in arid and semi-arid
regions. Human conditions in many areas are becoming degraded due to
overpopulation and the continual abuse of water resources.
Agricultural, industrial and urban areas are encroaching on lands that
once were rangelands or deserts. Surface water and groundwater are
unable to keep up with the continual growth in needs. Water quality is
declining because of the contamination of aquifers by waste water. The
conventional approach that takes water resources for granted is no
longer acceptable. It is urgent to address water management problems
in a holistic manner, understanding how all components of the
hydrological cycle interact.

Computerized modeling techniques are rapidly becoming an
integral tool in water management and planning due to the availability
of appropriate technology and the cost effectiveness of computerized
simulations compared to field experimentation. Hydrological modeling
( at the scale of a watershed ) allows one to better understand each
system component and to make predictions according to the response of

the system to inquiries. Methods at the scale of a single watershed

 

 

command the attention of local authorities and citizens who are
immediately affected by water management policy.

This study is intended to evaluate the impact of management
scenarios on both surface and groundwater resources within a watershed
by quantifying the major components of the hydrologic balance
including surface runoff, return flow, impoundment storage, plant
uptake, consumptive use, and depletion of groundwater by pumping
wells. Scenarios are limited to arid and semi-arid regions in developing
countries where the technology is at a low level and data are scarce.
Typically, rivers are ungaged and potential users are novices with
computers.

This study has three main objectives. The first objective is to
make a continuous lumped-parameter descriptive model of the
hydrological cycle at the scale of a rural watershed using an object-
oriented software (STELLA II, High Performances Systems, Inc. 1990-
1994). The second objective is to keep this model simple, user-friendly,
educational and adaptable to developing countries’ conditions. The
third objective is to link surface water and groundwater by considering
flow interconnections in the water budget in order to predict the effects
of management decisions. The fourth objective is to validate this
lumped-parameter model against a secondary reference - i.e., a validated

distributed model such as WMS, SWRRB, SWAT or MODFLOW.

Chapter 2

LITERATURE REVIEW

Prior to the development of modeling and simulation techniques,
classical hydrological methods relied mostly on observed values, pencil
and paper. Despite the simplification of procedures. the task was
tedious and time-consuming. People who used models tended to be
highly trained in relevant areas and possessed an appreciation for
problem-solving in general. Use of complex models as management
tools has grown as the power of computers has increased and
particularly as microcomputers have become powerful, inexpensive and
easier to use.

Computer simulation in hydrology started to be common since the
development of the Stanford Watershed Model (Crawford and Linsley,
1966). In the 1960’s the challenge was to make a program that would
simulate many continuous years of streamflow, that would be fast
enough, and that would be physically based to allow the hydrologist to
extrapolate beyond the range of the validating data.

In recent years, mathematical modeling of water resources has
become possible due to the computer technology and the substantial

level of funding in this relatively new area. The modeling is driven by

the public’s concern for environmental quality and by the increasing
severity of water resource management problems worldwide.

In early 1980’s, the Office of Technology Assessment (OTA) of the
US Congress found that mathematical modeling of water resources was
very useful to managers and decision makers (Friedman et al., 1980).
One recognizes, however, that many organizational, financial and
institutional barriers are to be surpassed before development of
modeling can occur. Institutional constraints include lack of
information about available models, lack of training in model use and
interpretation, lack of communication between modelers and decision
makers, and lack of general support services. Development and use of
complex models, require highly qualified personnel as well as adequate
budgetary support for computer facilities, collecting and processing
data. According to OTA, most federal agencies have no comprehensive
strategy for developing and using models due to the newness and
technical complexity of such work.

The role of models in managing water resources expanded after
many regions had noticed decreased availability of water from major
aquifers (e.g Ogallalla), and increased public concern for the quality of
its drinking water, lakes and rivers. Models that merely determine
water yields at the watershed outlet are inadequate ( Friedman, ibid).

Models should be perceived as a part of the water quality planning

process; they should be comprehensive with the biological and
chemical facets in a comprehensive manner.

The watershed models are of different types, depending on the
purpose for which they were developed. The most evident division is
between water quantity models and water quality models. Water
quantity models are concerned with the physical allocation and the
prediction of stormwater runoff, expected demands, and water supply
shortfalls ( Biswas, 1975). Water quality models focus on physical
attributes, biological processes, and chemical substances ( Ott, 1976).
Simulation models are the most common type of model in water
resource planning. They are usually descriptive in explaining the causal
connection between policy and model parameters. However, despite
their flexibility and ability to compress or expand the time scale,
models may lead the planner to non-feasible solutions because they use
trial and error to assess the response of selected outputs to the input
variables.

A simulation may be either time-sequenced or event-sequenced
(Goodman, 1983). The time-sequenced form uses a fixed time interval
to examine the watershed at regular time intervals. The event-
sequenced simulations model events only as they happen, by simply
recording the time they occurred. The time-sequenced type is more
appropriate for watershed simulations because of the structure of water

resource data.

The watershed models can be classified also according to other
criteria such as process description, scale, and technique of solution
(Singh, 1995). The processes are dependent on the watershed
characteristics, the resulting models can be described as lumped or
distributed, deterministic or stochastic or mixed. Lumped-parameter
models are expressed only by differential equations, without considering
the spatial variability of processes, the boundary conditions or the
watershed geometry. The lumped-parameter approach considers the
whole catchment as a single entity and maps the input rainfall excess to
an output hydrograph. Typical of this type of model is the Universal
Soil Loss Equation ( USLE, Wishmeier and Smith, 1978). On the other
hand, distributed models consider spatial variability, boundary
conditions and watershed characteristics. Distributed models divide the
catchment into a number of smaller areas (which could be square
elements or subcatchments), which are assumed to be internally uniform
with respect to the hydrologic parameters. Hydrology is simulated
within each of these small areas and the output routed to the outlet.
Examples of distributed models include AGNPS (Agricultural Non-
Point Source Pollution, Young et al., 1987), and SWRRB (A Basin
Scale Simulation Model for Soil and Water Resources Management,
Williams et al., 1985). Considerable time and effort are required to
collect data, run the models and interpret results. Integration with GIS

(Geographic Informatin System) can eliminate many of the data-entry

problems. Several models have been integrated with GIS including
AGNPS, GRASS GIS ( Srinivasan and Engel,l994), and SPUR and
ERDAS (Sasowsky and Gardner, 1991).

The description of the process can be either deterministic,
probabilistic (stochastic) or mixed ( Singh, 1988). Deterministic
models treat the relationships among the elements of the system to
provide results as the mean of different parameters values based on
physical laws and empirical information. Stochastic models rely on
assumptions about the system, including uncertainty in both inputs and
relationships. Stochastic models require large amounts of data to
determine the probability distribution and to validate the model. Mixed
models have some components stochastic and some deterministic.

The time-scale classification is critical in watershed modeling and
can be defined as a combination of two time-intervals (Diskin and
Simon, 1979). One interval is used for input and internal computations.
The other interval is used for the output and calibration of the model.

The spatial scale can be used to classify models into small-
watershed (100km2 or less), medium-sized watershed ( 100 to 1000km2)
and large watershed ( More than 1000km2). However , this
classification may not be meaningful, depending on the heterogeneity
of the soils and the land. use characteristics.

The technique used for modeling is driven by the need to solve a

particular problem . Data availability determines both the model size

and the accuracy needed. Some simple models rely only on locally
available data; others may rely on remote sensing and GIS capabilities
to satisfy their needs in data. The cost of the first type of models is
cheap because data are at hand, but the second type is costly at present
due to technological and expertise overheads.

The previous generation of models( e.g. SWRRB, AGNPS, etc..)
needed much hydrological and meteorological records for their
calibration. They used curve fitting to calibrate their parameters, but
were always error-prone because they did not include critical data, such
as topography, soil type and changes in vegetation. Physically-based
models can overcome these anomalies if their parameters are physically
significant ( Abott et al., 1986). However, even with the improvement
of computer software, simulation models are always subject to errors,
because they are involved in either exploring the implications of making
certain assumptions about the nature of the real world system, or
predicting the behavior of the real world system under a set of
naturally-occurring circumstances ( Beven, 1989). Both assumptions
and predictions are essential in model building, but their impact on
results may vary from acceptable to completely surprising outcomes.

The experience with many complex models showed that the
results depend more on the understanding of the hydrologic processes
rather than the sophistication of methods used. A lumped-parameter

model based on a good hydrological knowledge of the system may

provide better outputs in ungaged areas than a mathematically and
technologically sophisticated approach. Beven (1989) pointed out
that increased model complexity does not necessarily mean better
accuracy. This is confirmed by Wilcox et al.(1990) in their
comparison of two very different hydrology models designed to
predict runoff from ungaged rural catchments. They found that the
improved and complex Green and Ampt model is not noticeably more
accurate than the simple Soil Conservation Service curve number
method. On some catchments, the simple model was more accurate
than the complex one. The SCS method is found in many actual
models because it is simple, trustworthy, and widely recognized.
Sorooshian and Michaud (1994) compared the accuracy of
simulations of rainfall-runoff forecasting of a complex distributed
model ( KINEROS) developed by Woolhiser et al.(1990) and a simple
distributed model based on the SCS method. Sorooshian and
Michaud conclude that for a semi-arid watershed the two models are
similar in accuracy.

Today, four federal agencies are widely recognized for their
leadership and activity in water resources modeling: The US. Army
Corps of Engineers, US. Department of Agriculture, US.
Environmental Protection Agency, and US. Geological Survey. All

are developing and using their own models.

10

Army Corps of Engineers’ Hydrologic Engineering Center (HEC):
HEC provides assistance in applying mathematical models to
hydrological planning, design and operation problems. This includes
developing and maintaining many computer models. teaching of
techniques and model use in formal training courses. and assisting
Corps of Engineers officers in applying models and techniques
(Fledman, 1981).

The HEC’s areas of technical expertise are in hydrologic
engineering, related computer applications and analytical techniques
used in water resources planning. The areas include: Precipitation-
runoff processes, water resources systems, frequency and risk analysis,
fluvial hydraulics, urban hydrology, water resources planning, real-time
water control, hydropower, and water supply. The main HEC goal in
software development is to provide efficient tools to a diverse group of
managers and planners. The codes are written in FORTRAN77 for this
purpose.

The rainfall-runoff model called HEC-1( Hydrologic
Engineering Center, Army Corps of Engineers, 1990) is very widely
used. It is a distributed parameter, physically based, single event
model. The model components are simple mathematical relationships
derived from the kinematic wave approach (Hjelmfelt, 1986) to
represent meteorologic, hydrologic and hydraulic processes.

Hydrographs and flood waves can be described as either dynamic or

ll

kinematic. Kinematic waves are determined by the weight of the
fluid flowing in response to gravity. Dynamic waves are determined
by mass, inertial forces, and pressure. The kinematic procedure uses
both momentum and continuity principles with solution by finite
differences. The fundamental laws that govern and describe fluid

flow are described by the momentum and continuity equations (Chow,

1959)
dy/dx + v/g dv/dx +1/g dv/dt = So - Sf (2.1)
dA/dt + dQ/dx = q (2.2)
where:

y = depth (ft);
v = velocity (ft/s);
x = longitudinal distance (ft);
t=time in sec);
g = gravitational acceleration (ft/sec2);
So = ground slope (ft/ft);
Sf = friction slope (ft/ft);
Q = flow rate (cfs);
A = flow area (ft2);
and q = discharge per unit length (cfs/ft).

Equations 1 and 2 have been approximated respectively by
Manning’s equation and the Continuity equation:

V=(1.486/n) RA2/3 SoA1/2 (2.3)

Q = VA (2.4)

where:

A = average area (ft2);

R = hydraulic radius (ft);

V = velocity(ft/sec);

n = Manning’s coefficient;

So = ground slope (ft/ft);

and Q = flow rate (ft3/sec).

Volume and time distribution of runoff are controlled through
three parameters: Manning’s surface roughness coefficient, initial
moisture loss, and constant rate of infiltration during overland flow.
HEC-1 was mainly designed for flood event studies because flood
protection was the Corps’ major responsibility. It is not limited to
any watershed or river basin size and has been used on complex sub-
basins provided that they are in a converging treelike form. Even
though HEC-1 is a distributed-parameter model, it assumes that
precipitation and infiltration are uniform. within the sub-basin (unit
area). This lumped-parameter characteristic is common to many
other models, but can be solved in HEC-1 by making the simulation
building blocks small enough to capture the desired variability.

HEC-1 has benefitted from the support of the US. Army Corps
of Engineers to evolve from a small rainfall-runoff program to an
integrated software package including, Data Storage System to pass
data from one analysis program to another, and Geographic

Information System technology to capture the spatial process of

watersheds. However, because HEC-1 was mainly designed for flood

13

event studies, it does not recover precipitation losses, such as
infiltration, interception, and detention storage.

The U. S. Army Engineer Experiment Station and Brigham
Young University have developed a computer program that combines
surface water and groundwater. The surface water module is a two
dimensional, depth-averaged, free surface, finite element program
and is a part of the TABS-MD numerical modeling system (Thomas
and Mc Anally, 1991). The groundwater module consists of a flow
and transport model (3DFEMFT) model ( Yeh, 1991) and a 3-D finite
element mesh graphical user interface (GeoSolid) to view the results.

The US. Department of Agriculture had its Agricultural
Research Service worked for eleven years on a special model: SPUR-
91 (Simulation of Production and Utilization of Rangelands Carlson
and Thurow, 1992). SPUR-91 is physically based. integrating
climate, hydrology, plant, animal and economics in a complex
system. The hydrology and plant submodels are influenced by the
climate submodel, while they interact with the animal module, the
economic part depends on the animal and plant models. The most
critical outputs of SPUR-91 are water yield and plant production.

SPUR uses the curve number method to simulate overland flow
and to determine how much water will infiltrate. It is a complete
hydrology model in that the major components of rangeland water

budgets are simulated: overland flow, subsurface flow. soil water,

l4

and evapotranspiration. The curve number method, as a runoff
prediction tool, is widely used as a part of models because it is
simple, does not require calibration, and the Curve Number can be
easily obtained from land use and soils maps. A major limitation of
the curve number method however is that rainfall intensity and
duration are not considered, only total volume.

SPUR is one of several models which simulate the surface and
root zone. These models include spatially detailed, single-event
models such as ANSWERS (Beasley et al., 1980) and AGNPS (Young
et al., 1987), and continuous time models such as HSPF (Johansen et
al., 1984) and SWRRB (Arnold et al., 1990). Weather data is
generated stochastically by CLIGEN (Nicks and Lane, 1989) which
was originally developed to simulate weather for SPUR. The weather
elements generated on daily time step are: precipitation amount,
maximum intensity, duration, temperature maximum, temperature
minimum, dew point, solar radiation, wind speed and wind direction.

The hydrology submodel in SPUR is based on daily water
balance, and is similar to SWRRB (Williams et al., 1985) with some
adaptations for rangeland conditions:

The water budget equation is:

SW=Swo+P-Q-ET-PL-QR (2.5)

where:

SW = Current soil water content;

Swo = Initial (current day - 1) soil water contenet;

P = Precipitation;

Q = Surface runoff;

ET = Evapotranspiration;

PL = Percolation loss below the root zone to groundwater
storage;

and QR = Return flow.

Runoff is estimated using the Soil Conservation curve number
method (USDA, Soil Conservation Service, 1985). Daily curve
number is computed based on soil water storage (Williams and
LaSeur, 1976). Water storage is modified because plants can extract
moisture at soil water tensions down to -5.0 MPa under rangeland
conditions instead of -1.5MPa under cropping conditions (Carlson
and Thurow, 1992). The rest of the hydrology submodel and
subroutines are similar to those of SWRRB. Unlike SWRRB,
however, the interaction between vegetation, soil and climatic
variables is well-developed and detailed in SPUR to accommodate a
diversity of rangelands and to better simulate the hydrologic process.
SPUR is a complicated but powerful tool for assessing various
management practices because it combines hydrology, climate,
ecology and economy.

A model called Simulation for Water Resources in Rural Basins
(SWRRB) was designed to predict the effect of management decisions
on water and sediment with reasonable accuracy for ungaged rural

basins (William et al., 1985). SWRRB is chosen as a secondary

reference model against which my lumped-parameter Semi-Arid

16

Watershed Model (SAWM, hereinafter) is to be validated. The
reasons why SWRRB is chosen are: (a) adaptable for semi-arid
watersheds which are ungaged; (b) simple enough to cope with
developing countries’ technology and computer literacy; (c) and cost
effectiveness because it is free of charge for educational and
governmental uses.

SWRRB operates on daily time step for up to 100 years. The
major processes of the model are surface runoff, percolation, return
flow, evapotranspiration, transmission losses, pond and reservoir
storage, sedimentation, and crop growth.

The hydrology model is based on the water balance equation.

SW = SWo+ 2 (Ri - Qi - Eti - Pi - Qri) (mm) (2.6)

where: SW is the soil water content minus the 15-bar non-
removable water content; t is time in days; R is daily amount of
precipitation; Q is runoff; ET is evapotranspiration; P is percolation,
and Or is return flow.

The model requires daily rainfall, maximum and minimum
temperatures, and solar radiation as input. In addition, it is capable
of working on different soil classes and divides the soil profiles into
as many as ten layers. Surface runoff is estimated using a
modification of the SCS curve number method ( US. Department of

Agriculture (USDA) Soil and Conservation Service, 1972). It uses a

procedure similar to its predecessor, the CREAMS model (Knisel,
1980; Williams and Nicks, 1982). The runoff is predicted separately
for each sub-area and routed to obtain the total runoff for the basin.
The SCS curve number equation for predicting surface runoff
is:
Q = (P - 0.2 S)2 / (P + 0.8 S) P > 0.2 S (2.7)
where:
Q is daily runoff (mm);
P is daily rainfall (mm);
and S is a storage index related to curve number by:
= 25400 / (CN - 254) (2.8)
The curve number CN is dimensionless and varies non linearly

from condition 1 (dry) at wilting point to condition 3 (wet) at field

capacity, and approaches 100 at saturation

Peak runoff rate is based on the Rational Method
Qp = p r A /360 (2.9)
where:
Qp is peak runoff rate in m’/ s;
p is runoff coefficient equal to ratio of runoff volume to
percolation;
r is rainfall intensity in mm/h;
and A is drainage area in ha.
The percolation component of SWRRB uses a storage routing

technique to predict flow through each soil layer in the root zone.

Upward flow and downward flow are allowed from the layer where

18

field capacity is exceeded to the less saturated layer. However, due
to gravity forces and low rate of recharge, downward flows are more
likely to occur than upward flows.

Lateral subsurface flow is simulated when the storage in any
layer is more than field capacity after percolation. It is calculated
simultaneously with percolation. The flow is dictated by the
hydraulic conductivity of the media as well as by the topography and
geology of the subsoil. According to Sloan and Moore (1984),
subsurface flow is likely to be significant in watersheds with soils
having high hydraulic conductivities and an impermeable layer at
shallow depths that can support a perched water table.

The evapotranspiration component of SWRRB is critical for
semi-arid watersheds. It is based on the concepts of Richie’s model
(Richie, 1972). Potential evaporation is computed using the equation
( Priestley and Taylor, 1972):

E0 = 1.28 (ho) (A) (2.10)

where:
E0 is the potential evaporation rate in mm/d ;
ho is the net solar radiation in ly ;
and A is a psychrometric constant.
ho=RA(1-AB)/58.3 (2.11)
where:

RA is the daily solar radiation in ly
and AB the albedo.

19

Soil and plant evaporation are computed separately. Potential
soil evaporation is estimated by the equation ( Richardson and Richie,
1973)

Eso = E0 exp (-0.4 LAI) (2.12)

where:

Eso is the potential evapotation rate at the soil surface in
mm/d;
and LAI is the leaf area index defined as the area of
plant leaves relative to the surface soil area.

LAI is difficult to measure on semi-arid rangelands because
plants grow randomly. However, Weltz (1987) reported “LAI maximum
is equal to 3 for shrub clusters and equal to 2 for herbaceous vegetation
on a range site near Alice, Texas.”

Transmission losses are included in SWRRB water budget,
primarily in semi-arid watersheds where alluvial channels abstract a big
part of the streamflow ( Lane, 1982). The portion of the flood wave
that is lost from the system can be estimated in SWRRB by the method
suggested by the SCS Hydrology Handbook ( USDA, 1983) based on the
channel’s width, length, depth, and flow duration.

Ponds and reservoirs are also simulated to manage excess water

whenever this may happen. Required inputs are capacity and surface

area.

20

The main weather variables in SWRRB are precipitation, air
temperature and solar radiation. Precipitation and temperature data if
not available, can be generated using the first-order Markov chain
method developed by Nicks (1974). The method uses probability to
estimate daily rain given the previous day was either dry or wet. Daily
maximum and minimum air temperature and solar radiation are
generated from a normal distribution corrected for wet-dry probability
state. The probabilites of wet or dry day following a dry or wet day are
associated with a random number (0-1). If the random number is less
than or equal to the wet-dry probability, precipitation occurs on that
day.

Sediment yield is estimated for each sub-basin with the Modified
Universal Soil Loss Equation (MUSLE) (Williams and Berndt, 1977).
The equation requires varied data about the watershed, such as surface
runoff, peak flow, soil erodibility factor, crop management factor, slope
and length of basin. Complimentary data can be provided from the SCS
Soil-5 database and by Wischmeier and Smith (1978).

For estimated nutrients, such as nitrogen and phosphorous,
SWRRB uses a modification of the method used in the EPIC model
(Williams et al., ibid, 1984).

Transport of pesticides by runoff or percolation is also part of the
model, which comes from its predecessor GLEAMS (Leonard et al.,

1987). The model’s scope is extended to the EPIC crop model

21

(Williams et al ibid, 1987) to follow the growth of crops and simulate
their needs in water and monitor their content in biomass and pesticides.
Even the effect of land management on ponds and lakes is predicted in
SWRRB.

Despite its lack of accuracy in water partitioning to the different
components of the system watershed and the weakness of its
groundwater component, SWRRB uses a broad analysis approach to
predict the effect of management decisions on water and sediment
yields.

The study of the hydrologic cycle would not be complete without
understanding and incorporating the exchanges of water between ground
and surface supplies. Many streams and lakes are fed primarily by
groundwaters. Excess stormwater is also used to recharge groundwater
and compensate depletion caused by increasing needs.

Groundwater is the water below the land surface that saturates the
pore spaces in the subsurface media. It begins as infiltration from
precipitation on the ground, and from streams, lakes and reservoirs.
Water flows downward through the zone of aeration by gravity. This
percolation leaves a film of water on the soil grains known as soil
moisture. The amount of water in the profile depends on climatic, soil
conditions, and depth of the aeration zone.

Groundwater dynamics are dictated by Darcy’s law which

provides the underlying theory for groundwater flow and is relevant to

22

such concerns as groundwater drawdown, rate of flow from a well, and
speed of movement through an aquifer. The basic principle defining the
flow of groundwater is:

v=K*h/s (2.13)

where:

v is the velocity of the flow (L/T);

K is the saturated hydraulic conductivity (UT);

3 is the distance through which the head h is dissipated (L).

The subsurface is divided into two regions, the unsaturated zone
and the saturated zone (Figure 1,). The unsaturated zone is the upper
portion that contains air and water in the pores. It contains the root
zone where plants can obtain water and nutrients. It is also separated
from the saturated zone by the water table where the pressure is equal to
the atmospheric pressure. The saturated zone is the subsurface zone
where all voids and pores are filled with groundwater. The flow of
water is so slow that is noticeable only on a long term.

The saturated zone can contain two types of aquifers, confined
and/or unconfined (Figure 2). The unconfined zone is immediately
beneath the unsaturated zone and topped by the water table. The
confined aquifer is below the unconfined zone where pressure is higher
due to the weight of overlying layers. Aquifers are permeable geologic

strata that hold and convey groundwater. Most are large enough to be

considered as huge storage reservoirs.

Infiltration

3UOZ

+0

003

a:
c
o
N
'0
o
'5
h
3
u
«I
in
s:
D

23

Water table

 

Saturated zone

Figure 1. Subsurface hydrologic zones.

24

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$.on ucm 9.0.20
9.9.25 ommxmmd

 

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25

Watersheds are complex and dynamic natural systems that display
variable behavior temporally and spatially. When a watershed is
pertutbed by a storm, its outputs fluctuate for a time before returning to
equilibrium (Kort and Kassel, 1993).

Most models that simulate real watershed behavior are hard to
understand because they consist of many lines of computer code, which
only experienced users can customize. STELLA 11 (High Performance
Systems 1990, 1992) is an object oriented software that uses a dynamic
approach to view a system as a collection of individual elements
connected in a way so that feedbacks are allowed to operate as observed
in reality. STELLA II uses four types of building blocks that may be
interconnected to imitate the process modeled. These are stocks,
pipelines, converters, and connectors. Stocks are rectangular in shape
and act like reservoirs by accumulating flows. Pipelines convey the
flow from the source to the stock or from the stock to the sick (end).

Pipelines have controllers which contain equations , logical
statements, and numerical relationships that regulate the flow.
Converters (circles) are used to convert inputs into outputs. Connectors
(arrows) depict the causal linkages among the objects in the model.
Sources and sinks are infinite in size and will provide amount of input

or accept any amount of output.

26

STELLA II simplifies model-building via a three-step method:
mapping (in which equations that state the logic of simulation are
automatically generated); modeling (where the software automatically
creates equations); and simulation (where graphs, tables and animation
can be viewed).

The tool enables testing of different scenarios and viewpoints in a
simple and interactive way; the user can experiment with
interconnections and feedback, unburdened by codes and book keeping.
The user needs to concentrate on the real-world problem, for example, a
place like Morocco where water problems are urgent. The modeling of
the hydrologic cycle in a Moroccan watershed seems an ideal
application for using STELLA II.

Morocco is a typical semi-arid area where ungaged watersheds are
numerous and remote enough to be monitored for data collection.
Moroccan geography and climate are similar to those of California.
Both have high mountains, bordering oceans to the west, and desert in
the south. Their climate is Mediterranean, with seasonal precipitation
occurring in the coldest months of the year (October through March)
and a hot, dry season for the rest of the year.

Morocco is located in northwest Africa. A 3.500 kilometer
coastline on the Mediterranean Sea and Atlantic Ocean bounds the

country on the north and west. Algeria is to the east and Mauritania to

27

the south. The country’s area is about 750,000 square kilometers,
almost 45 percent of which is in the Sahara region (GATT, 1990).

Four mountain ranges divide the country into three agroecological
zones: the fertile agricultural plain in the northwest with 400-1000mm
of rain per year; mountains and plateaus in the east with 200-400mm of
rain per year; and, deserts in the south with less than 200mm.)

A climatic zoning based on the moisture index has been
established (UNESCO, 1979) as

= P / PET (2.14)
where:
P is the average annual precipitation, according to Penman’s
formula;
and PET is the potential evapotranspiration.
Four classes were considered:

a / Hyper-arid zones such as deserts with I<0.03

b / Arid zones with 0.2> I>0.03

c / Semi-arid zones including steppes, prairies, with 0.20<I<0.50.

d / Sub-humid zones 0.50<I<0.75

Semi-arid areas have usually one completely dry season, lasting 3
to 4 months. The annual precipitation varies between 200 and 800mm.
Storms occur briefly and intensively, causing floods and soil erosion,
and cover only small areas aroud the epicenter. Precipitation varies

considerably from year to year. In addition, the distribution of rains

during the agricultural cycle varies such that the aggregate production

28

levels fluctuate significantly. For example, rainfall in Morocco, in
three out of ten years falls by 80-99 percent of the average (Ait kadi,
1989)

Evapotranspiration is high and poorly estimated in the water
balance budget. Morocco receives an average annual amount of
precipitation of 150 billion cubic meters( Ambrogi, 1985). However,
only 20 percent of water is captured, and the remaining 80 percent
returns to the atmosphere as evapotranspiration (Ambri, 1986). Aquifer
recharge is low because precipitation is low and unevenly distributed on
the time scale, so that the soil is seldom saturated.

Moroccan soils are shallow and poor in organic matter. Only 15
percent of the lands have potential agricultural value, with appropriate
soils and satisfactory rainfall (GATT, 1990). Due to recurrence of
drought, many rural families combine livestock and crop production.
They cultivate rangelands which are inappropriate for agriculture due to
the steepness'and low level of fertility. Therefore, those lands are
experiencing permanent soil erosion under the effect of human and
animal activities. Modeling ungaged watersheds which are under such
conditions would be a useful tool for planners and managers, to better
understand interconnections between the components of the hydrologic
cycle, and anticipate the consequences of management interventions on

the water budget and the ecology of the watershed .

Chapter 3

METHODS

The model suggested in this study is designed to simulate the main
components of the hydrologic cycle at the scale of a semi-arid watershed,
including the interconnections between surface water and groundwater.
The lumped-parameter model is built using STELLA II. STELLA II
views the system (watershed) as a collection of individual elements
connected in a dynamic network such that realistic feedback mechanisms
are allowed to Operate. Since the model permits evaluation of the impact
of interconnections between groundwater and surface water within the
watershed, it can be used to predict the effect of management decisions.
The lumped-parameter SAWM is to be validated against the surface,
groundwater and sediment submodels of the distributed model, SWRRB.

SAWM is a representation of the mass balance of water within a
particular control volume dictated by the watershed’s hydrologic and
climatic conditions. It represents the law of conservation of mass.
Thus, the rate of change of storage of water within an element is “equal”
to the difference between its rates of inflow and outflow across the
control surface. The water balance is coupled to a simplification of
Darcy’s momentum law for groundwater flow. Darcy’s law defines how

quickly water can move between different parts of a porous medium.

29

30

The water that is discharged from an aquifer can be approximated with
Darcy’s law:
Q=k*A*dh/dx (3.1)

The discharge from an aquifer, thus, is dependent on the cross-
sectional area through which the flow occurs (A), the hydraulic
conductivity of the material constituting the aquifer (k), and the hydrulic
gradient (dh/dx). The value of k is dependent on the properties of the
porous medium.

The hydrologic processes represented in the model are shown in the
conceptual model(Figure 3). Four submodels or building blocks can be
placed in the screen to form the dynamic process being modeled. Figure
3 shows the STELLA II screen on which a simplified hydrological cycle
displays its most important components within a watershed.
Components are either interconnected between them in the soil or related
to other atmospheric components of the cycle.

The four submodels - soil water, river, shallow aquifer and deep

aquifer - are detailed below.

1. SOIL WATER:
The model considers soil water as the moisture contained within
the soil column from the surface to the lower limit of the root zone.
Unlike SWRRB (that divides the soil into ten layers), this model

considers the soil as a single block 2 meters deep at a single uniform

31

moisture. The water content in the profile is the difference between the
input ( precipitation, irrigation, shallow aquifer return) and the outputs
(runoff, lateral flow, evapotranspiration, percolation). To keep the model
simple and interactive with the user, the following assumptions are made:
(i) the root zone is considered homogeneous; (ii) the water content is
uniform in each layer; (iii) the flow is two-dimensional; (iv) water flow
from the soil is partitioned according to the priority given to each
outflow in the cycle; (v) the hydraulic conductivity used in determining
the flow between layers is estimated by an arbitrary coefficient acting as
a resistance to the flow; (vi) only removable moisture is computed as

part of the water budget. Thus initial soil moisture can be zero.

32

 

 

 

HW—M EVAS]. f; l}

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

S
VER WATER YIELD
rtnoff v
a c
l}
strearrflow
sou. LCBS
latera fl
percolation EB
erosion
seepage
retu'n flow runoff
deep percolation

 

 

 

 

Figure 3. Conceptual model of SAWM using STELLA II.

The excess water from the soil which should flow from the soil to
become either surface and/or groundwater recharge is influenced by the
time step of the simulation. After a dry period, if it rains heavily for one
day, the soil can be quickly saturated due to the intensity and the brevity
of the storm - as semi-arid areas are characterized - ; the water surplus
can be transformed to runoff and/or percolation. However. if the same
rain volume is averaged over an entire month, it may be just enough to

return to the atmosphere by evaporation and/or transpiration. Therefore,

33

computation on a daily basis will always yield more water surplus than
computation on a monthly basis.

The water balance equation is:

SW=Z(R-Q-ET-P-QR) (3.2)
where:

SW is the increase in soil water content over the duration;

R is the amount of precipitation;

Q is the surface runoff;

ET is the evapotranspiration from the soil profile;

P is the percolation from the soil ;

and QR is the return flow (lateral subsurface flow).
a / Inputs:

Precipitation: Unlike SWRRB , SAWM does not generate
rainfall data using the Markov chain method when data are not available.
Instead, SAWM can take either daily or monthly rainfall data up to the
duration of simulation. The lack of a weather generator in this model is

compensated by the ability to simulate multiple rain storms and rapidly

analyze the effects.

Irrigation: The Irrigation feature of the model is not used in this
study. Eventually it can imitate the real conditions in semi-arid
rangelands. When productivity of the shallow aquifer or deep aquifer is

sufficient (through the process of recharge), the water table can be

34

exploited efficiently by allocating excessive water to irrigation or human

and livestock consumption.

Upward flow: Upward flow from the shallow aquifer is set to a rate
determined by the volume of water in the shallow aquifer. The 0.01
factor works in combination with percolation and resistance of the soil to
limit the moisture coming from the saturated shallow aquifer. It is
added separately from the percolation component to simulate the portion
of moisture that leaves the shallow aquifer to the soil profile when the
soil is very dry (SOIL<7) and the shallow aquifer is sufficiently saturated
(SHALLOW AQUIFER>15) to yield some of its water under the effect of

soil sorptivity and capillarity forces.

35

The equation is:
upward flow =IF((SOIL<7)AND(SHALLOW_AQUIFER>l5))

THEN((SHALLOW_AQUIFER-l5)*0.01)ELSE(O) (3.3)

Equations 3.3-3.18 can be seen in SAWM’s algorithm joined in

Appendix A.

b / Outputs:
The model outputs, in order of priority, are: plant transpiration,

surface runoff, percolation, lateral flow, and soil evaporation.

Runoff: Surface runoff is an important component of the water
budget. It has priority 2 and is computed from the SCS curve number.
Q = k*SOIL*(l-S/1000) k=0.12 (3.4)
and S=254*(100/CN-1) (3.5)
where:
S is a retention parameter;
k is a coefficient to adjust the shape of the runoff curve;
and CN is the average curve number of the watershed.
CN depends mostly on the soil cover and the soil hydrologic group

(USDA, 1972; see Appendix B) which provides CN for different groups

of soils and type of soil cover.

36

The coefficient k is adjusted during the model tuning process to
provide the best volume of runoff that approximates the one simulated by

SWRRB. SAWM was not tuned for peak runoff; but this can be done in

the future.

Lateral flow: Lateral subsurface flow in the soil profile (0-2m)
occurs not only after the soil is saturated, but also occurs depending on
the topography of the site and the difference in pressure between the soil
water and the river. The model simplifies the estimate of the lateral flow
to a fraction of the excessive moisture of the soil beyond 25mm using
IF/THEN reasoning and giving it priority 3.

Lateral flow =IF(SOIL >25) THEN (1.2*(SOIL' - 25)/40) ELSE (0)

(3.6)

where 25 is the water content of the soil, above which, the excess
moisture can freely leave the soil profile as a lateral flow. The
coefficients 1.2 and 40 have been adjusted to give a realistic
accumulation of the lateral flow over time. They also act as a resistance
to the flow to compensate for the Darcy’s hydraulic gradient between the

soil and the river.

Percolation: Percolation in this model is the downward flow
which occurs when field capacity of the soil is exceeded. The excessive

moisture flow downward under the combined effect of gravity and suction

37

(negative pressure) from the unsaturated lower zone. Temperatures
below 0° Celsius that may prevent flows from occurring are rare under
Mediterranean semi-arid conditions. Therefore the model does not
consider temperature in the subsurface water flow.
The Percolation equation is:
percolation = IF(SOIL>15) THEN(SOIL-15)*0.05 ELSE(0)
(3.7)
where 15 is set as the limit of saturation of the soil, above which the
excessive soil moisture can be lost to the shallow aquifer. The
coefficient 0.05 is used to adjust the accumulated amount of percolated

water (estimated by the area under the percolation curve).

Evapotranspiration: The evapotranspiration component considers
only the potential evapotranspiration but not the actual
evapotranspiration . The model computes evaporation from soil and
plants separately. Potential soil water evaporation is estimated as a
function of potential ET and leaf area index (LAI is the area of plant
leaves relative to the soil surface area).

PT is computed from the equation of Priestley and Taylor (1972).

PT = 0.5*(1.28*delta*HO)/(delta+0.68) (3.8)

where:

PT is the plant transpiration rate in mm/d;
H0 is the net solar radiation in 1y;

38

and delta is a psychrometric constant.

The value of H0 is calculated with the equation
H0 = (0.77/58.3)*Solar (3.9)
where Solar is the daily solar radiation in ly and delta is determined

using the equation:

delta = 5304*EXP(21.255-(5304/T))/(T)2 (3.10)
where:
T = 273 + °C

and °C is the soil temperature in degrees Celsius.
PT VOLUME stock is used as a fictitious reservoir to compute the
accumulated water lost from the soil by evapotranspiration to the

atmosphere.

Soil evaporation: The evaporation from the soil is ranked 5 in
priority; however, it is part of the evapotranspiration submodel, even
though computed separately. It is a function of the plantl transpiration
PT and the leaf area index LAI. Potential soil evaporation is estimated
by the equation (Richie and Richardson, 1973):

solev = PT*EXP(-0.4*LAI) (3.11)
where:

solev is the potential evaporation at the soil surface;

and LAI is the area of plant leaves relative to the surface soil

area, estimated by Weltz (ibid, 1987) as 3 for shrub and
clusters.

39

2. RIVER:
The river body is considered in the model as a reservoir
regulated by three inflows and three ouflows. The inflows are surface
runoff, subsurface lateral flow, and return flow from the shallow aquifer.

The outflows are evaporation and streamflow.

a / Inputs:

Runoff: The amount of surface runoff estimated by the SCS curve
number method as the main output from the previous model component,
namely SOIL, is supposed to flow laterally to the river without any
losses en route to simplify the model. See equations 4 and 5 discussed

previously.

Lateral flow: The lateral flow is an outflow from the unsaturated
zone of the soil profile. It is estimated as a fraction of the runoff. Its
coefficients are adjusted in the tuning process . Equation 6 describe the
flow without considering the time delay between surface runoff and

subsurface flow.

Return flow: The return flow is the part of the shallow aquifer’s

saturated water that does not move vertically (upward to the soil profile

40

or downward to the deep aquifer), but horizontally from the shallow
aquifer to the river. This flow may come partially or completely due to
the excess recharge of the shallow aquifer by water percolating from the
root zone.
The equation estimates the lateral flow as a small fraction of the
shallow aquifer.
return flow = IF(SHALLOW_AQUIFER>20)
THEN(0.01*(SHALLOW_ AQUIFER -20)ELSE(0).
(3.12)
where 0.01 is set to describe the amount of the return flow as well as
the delay vis-a-vis to surface runoff and lateral flow. The value of 20 is
the minimum moisture in the
shallow aquifer. Only the excess amount beyond 20' mm can return to

the river.

b / Outputs:

Streamflow: The streamflow describes the main output and the only
concrete outflow from the system. It is generally more important than
the other outputs from the river combined, namely river evaporation and
seepage. The streamflow is simulated on a daily basis as a fraction of the

total volume of the water in the river.

41

The equation is:
stream flow = 0.0018*days*RIVER (3.13)
where: 0.0018 is a coefficient of adjustment of volume and “days”

causes a realistic delay of the flow over time.

Evaporation: The evaporation from the river is simplified to a
fraction of the water in the river that evaporates daily as a fraction of the
volume of water in the river.

Temperatures below 0° Celsius that may prevent flows from occurring
are so rare under semi-arid conditions that is why the model does not
consider temperature in the subsurface water flow.

Evaporation equation is:

evaporation = 0.002*RIVER (3.14)
where: 0.003 was adjusted to estimate the average fraction of river

water that can be lost by evaporation.

Seepage: Seepage is the flow of water from the river to the
shallow aquifer. It occurs to compensate for decrease in pressure of the
saturated zone in areas along the river channel where the shallow aquifer
may become unsaturated. The model estimates the seepage as a simple

fraction of the river. The equation of the seepage is :

42

seepage = 0.006*RIVER (3.15)
where: the coefficient 0.006 is tuned estimate the loss from the river

to the shallow aquifer in some areas.

3. SHALLOW AQUIFER:

In semi-arid developing countries, the shallow aquifer and the deep
aquifer are the most difficult submodels to verify due to the lack of
appropriate technologies to monitor water table dynamics and their
interconnections with hydrogeologic aquifers. This model simulates
primarily the shallow aquifer as a part of the system watershed, but
approximates the amount of water lost from the shallow aquifer to the
deep aquifer (deep percolation ) as part of the total water budget.

The shallow aquifer is considered as reservoir with two inputs
(percolation and seepage), and four outputs (return flow, deep

percolation, revap and upward flow).

a / Inputs:

Percolation: Percolation is the fraction of water from the rain event
which cannot be retained by the soil because it exceeds the field capacity
and migrates downward to the shallow aquifer either by gravity or
capillary action in the media below.

The equation describing percolation was seen before in (equation

3.7) as output from the SOIL.

43

b/ Outputs:

Return flow: The return flow is the opposite of seepage. It occurs
in areas where the shallow aquifer is saturated and the water table level
is higher than the river level. The return flow is approximated as a
fraction of the shallow aquifer. Equation (3.11), which was used as input

to the river, regulates the return flow as output from the shallow aquifer.

Deep percolation: The deep percolation is particular in this model.
It is simulated at the same time as input to the shallow aquifer as well as
output from it (biflow). However, water is more likely to flow
downward through cracks and breaks in confining layers. than upward
from confined aquifer to unconfined aquifer. Except for artesian
aquifers). Unlike the percolation that is simulated only during the rain
event, the deep percolation is estimated as a fraction of the shallow
aquifer that is continuously leaking to the deep aquifer and
proportionally to the volume of water in the shallow aquifer storage. The
equation below describes this flow lost to the deep aquifer as :
deep percolation = 0.0006*SHALLOW AQUIFER (3.16)
where the coefficient 0.0006 is chosen to compute the amount of

percolated water in the leakage process.

44

Revap: The revap is added to estimate the proportion of moisture
that may evaporate directly from the shallow aquifer to the atmosphere
through the soil’s existing cracks and fissures under hot arid conditions.
This happens frequently during dry seasons in semi-arid areas located in
the range of latitudes between 28 and 35 such as Morocco, South
California, and North Texas. That is why the amount of revap is
approximated as a function of the amount of water in the shallow aquifer
as well as the number of days. The amount of water lost by evaporation
and revap are counted in the water budget whenever they are not small
enough to be negligible. The equation describing this loss is:

revap = 0.0016*SHALLOW AQUIFER (3.17)
where 0.0016 is used to approximate the amount of water lost by

revap from the shallow aquifer.

Upward flow: The upward flow simulates the flow from the
shallow aquifer to the soil when the soil is dry. The equation stating this
process is the same as equation (3.3) simulating the upward flow as an

input to the soil.

4. DEEP AQUIFER:
Deep aquifer: The dynamic behavior of the deep aquifer is

generally not known. SAWM simulates the deep aquifer as a huge

CG

reservoir connected to the shallow aquifer by a “biflow which allows

 

45

the movement of water in two directions. Only the increases from its
initial level are simulated to evaluate its productivity . It has been put in
the model for use in the future when it can guide management decisions
such as irrigation or recharge.

The deep percolation from the shallow aquifer is both input and
output for the deep aquifer. Equation (3.16) states the relationship
(mentioned above) prioritizing shallow aquifer losses according to the
recharge from the deep aquifer.

The stocks (reservoirs) are linked to the end of all output flows to
allow the user to monitor the amount of water allocated by the model to

each component of the hydrologic cycle.

5.SEDIMENT YIELD:

Unlike SWRRB which uses the Modified Universal Soil Loss
Equation (MUSLE by Williams and Berndt, 1977) to compute the
sediment for each subbasin, SAWM simplifies the method from a six-
parameter formula to a single equation requiring only the values of
runoff above a certain threshold where the flow becomes enough to
transport soil.

The equation is:

erosion = IF (runoff<5)THEN (0) ELSE(0.12*(runoff - 5))2)

(3.18)

46

where 5 is the maximum runoff that causes no erosion and 0.12 and
the exponent are set to represent the parabolic shape of the soil erosion
as a function of runoff.

The technique chosen to validate SAWM against SWRRB is to
generate six artificial rainstorms of 30 days duration (30 days is required
by SWRRB) and constant intensities of 50, 40, 30, 20, 10, and 5min per
day. These step-function storms (pulses) are simulated on both SAWM
and SWRRB while keeping sensitive parameters on both models constant
and similar. The Figure 4 shows this theoretical rainstorm pulse and the

simulated response of percolation, lsoil transpiration, streamflow and

seepage.

47

1: precip 2: percolation 3: ET 4: streamflow

 

32.00

 

(mm) f\

16.00 '

 

 

 

 

 

 

 

 

 

 

 

0.00
0.00 91.25 182.50 273.75 365.00

days

Figure 4. The pulse-rainstorm of 900mm and the response of other
components.

The other graphs from SAWM are compared to those of SWRRB and
tuned, one at a time, so that they match reasonably. The tuning process
is tedious and time- consuming because areas under the graphs are
computed by hand, approximating the area as a sum of multiple
trapezoids:

Area=((H+h)/2)*w (3.19)

where H and h are the heights and w is the width of each trapezoid.

The list of tuned parameters and their values are listed in Table l.

48

Table 1. Tuned parameters, their values and their sensitivities.

omponent t 11
N0.
ow m er
threshold
m er
m p er
threshold
perco on m p er
threshold

return ow m p er
threshold

m er

er

n1
n1 er
n1 er
n1 er
in p er
threshold

nent

 

To cover a wide range of rainfall amounts. the rainstorms tested for
the tuning process are respectively 1500, 1200, 900, 600, 300, and 150
mm. These amounts include the range of annual semi-arid rainfall. The
main output curves from SAWM and SWRRB at are compared to guide
the tuning process are Water Yield, ET, and Sediment Yield. Water Yield
and evapotranspiration are in mm in both models, while the soil loss

estimate is in kg/ha.

 

Chapter 4

RESULTS AND DISCUSSION

The graphs that compare the water yield, total evapotranspiration
and sediment yield from the two models and for the six rainfall
simulations appear in Table 2.

This table also displays the input rain for each model. Results
from the tuning process are plotted in Figures 4, 5, and6 to better
compare the response of each model to each rainstorm event.

The simulated water yields from SAWM shown in Figure 5 track
the water yield from SWRRB fairly for the six storms simulated. The
general shape of Figure 5 is not linear, this is probably because the
system is completely dry before the 30-day rainfall event begins. The
early rain goes into the soil. For small storms (less than 300mm , i.e. 30
days at 10mm per day), no runoff is produced. Thus, no yield.

Figure 6 reveals that the evapotranSpiration simulated by SWRRB
stays constant above the 300mm storm, while it keeps increasing in
SAWM. Figure 6 shows an inherent difference in the two models. The
constant ET which SWRRB shows for all large storms is unrealistic and
fails to account for prolongation of moist soil conditions following large

rainfall events. I tend to trust SAWM model on this difference.

49

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54

The sediment yield in Figure 7 is registered only above the 300mm
storm on both models. The tuned soil loss quantities from the two
models are similar for rainstorms of 600mm and more. SAWM
consistently yielded more sediment than SWRRB, although differences
were small . The small sediment yield from a 300mm event signals
problems if many such events occur every few weeks.

Once the sensitive parameters of SAWM were tuned against their
counterparts in SWRRB, a realistic simulation was performed for a
theoretical watershed. This watershed features many climatic and
hydrologic similarities with Moroccan arid regions. The watershed is
538 km2 in area, located at 31° 37’ latitude similar to Morocco. The
weather data file used to simulate realistic conditions is taken from a
watershed located in Waco, Texas (one of the many locations where
SWRRB was validated). The rest of the input data reflects Moroccan
conditions, such as soil data, slopes, land use, and may be seen in the
SWRRB computer printouts added as Appendix C.

The graphs showing the results of this simulation from the two
models are matched and presented here as Figures 8 - 24 and discussed.

Figure 8 displays the one-year input rainfall applied to the two
models. The distribution of the runoff generated from these rainfall data
is well represented in SAWM as shown in Figure 10, but generates no
runoff in SWRRB except for the main storm that occurs around day 300

(between of October and November). This means that SAWM is more

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sensitive to low intensity rains than SWRRB. The water yield is
conveniently accumulated from the river stream flow as shown in Figure
12, making it easy to read the yearly amount of water transported by the
river. However, in SWRRB, this amount is estimated by computing the
area under the curve in Figure 13. This estimation is subject to errors
due to the irregularity of the curve’s shape. The evapotranspiration is
also better estimated in SAWM (Figure 14) than in SWRRB (Figure 15)
because it can be read directly in SAWM by summing its four
components of ET. The unstable curve generated by SWRRB shown in
Figure 15 makes it very hard to estimate evapotranspiration, let alone its
four components.

The return flow simulated in SAWM (which contributes to the
river’s water yield, Figure 16) tracks fairly its couterpart in SWRRB
(Figure 17), but with less intensity.

SAWM goes below the shallow aquifer and simulates the recharge of
the deep aquifer. Figure 18 provides a valuable updated water budget of
the deep aquifer by simulating the amount of recharge (or withdrawals to

satisfy human and animal needs).

Soil erosion:
The sediment yield resulting from the erosion process is more
sensitive to runoff in SAWM (Figure 19) than in SWRRB (Figure 20).

However, the threshold set for a minimum runoff to cause soil erosion

60

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69

and the constancy of the curve number CN during the whole year causes
the discrepancy between the sediment yields simulated by each model.
Similar discrepancies, however, are frequent when USLE is used to
estimate soil loss from watersheds where precipitation is infrequent and
low in intensity. Figures 10 and 11 explain some of the discrepancy in
sediment yield.

Despite the simplifications in SAWM, the main hydrologic outputs
(water yield and evapotranspiration, (Figure 21) show that the
evapotranspiration submodel in SAWM is accurate enough to make
predictions similar to those of SWRRB. However, the water yield
output from SAWM is 38% less than the water yield from SWRRB, even
though precipitation is the same for both.

Comparison of precipitation, ET, and water Yield for both models
during the tuning process (Table 1), as well as for the realistic
situation simulation( Figure 21), shows that SWRRB always is better.
This fact explains the difference between the two water yields as well as
sediment yields (Figure 22), since soil erosion is function of runoff in
SAWM. The weakness in water yield estimation and the time delay can
be corrected by introducing gradually more stocks (reservoirs) in the
conceptual model to better imitate the soil component of SWRRB (which
does a better job of storing excessive moisture and simulates better the

slow motion of water through the soil.

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72

The technique of the tuning process worked well. It was a pleasant
surprise that the realistic weather scenario for SAWM emulated SWRRB
on the first attempt; no tuning had to be done for the stochastic input
rainfall.

Unlike SWRRB which was designed by a multidisciplinary team to
be used by professionals, SAWM is simple enough to be used by people
with no Mathematics or hydrology background. The user can
communicate interactively with the model from conception to execution.
The process can be explained to other people interested in the problem
modeled. Even when soil and weather data are available as input files in
SWRRB, the remaining of inputs require at least 20 minutes to enter.
The output file is printed on tens of pages of numbers, hardly
comprehensible to the common user. The graphical outputs, however, are
only ten in numbers but their areas are difficult to translate to numbers
without accumulating errors. On the other hand, outputs from SAWM are
clear as graphsn The single screen summary of outputs (Figure 23) is
clear to users who are interested only in the results.

Considering these advantage of convenience, the results provided
by SAWM are encouraging. Because SAWM is interactive, fast, and
user- friendly, the user is encouraged to try multiple scenarios before
deciding on the appropriate one.

As public domain software, SWRRB is free-of-charge for students

and governmental agencies. However, it was corrupted when I

73

 

 

APPROXIMATE REPARTITION OF RAINFALL
OVER THE WATERSHED
(mm)

 

TOTAL RAIN 1,008.2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TOTAL EVAPOTRANSPIRATION WATER YIELD
| WATER YIELD [ 419 i j
ET VOLUME [ 430.5
[ DEEP AQUIFER 5.0 ]
EVAP VOL [ 3.7 I R'VER 0 1 1
| SOIL 0,1 ]
EVASOL [ 110.7 I ISHALLOWAQUIF. .. 26.9 ]
SOIL LOSS IN (T/Ha)
REVAP VOL I 13-3 I SOIL LOSS 2.33 J

 

 

 

 

 

 

 

 

Figure 23. Main outputs from simulating real conditions and their values.

 

 

 

 

74

downloaded it from the EPA web and caused me considerable time and
inconvenience. SWRRB also lacks flexibility because it does not accept
storm durations of less than 30.

A positive thing about SWRRB is its large view of the watershed’s
hydrology. Soils, land use, and water bodies (reservoirs and ponds) are
detailed and considered as important components of the model to make
predictions of the impact of management decisions on the watershed.
These features are so important that they should be considered for a
future version SAWM. so that it can be used as a convenient tool in
watershed management and planning.

SAWM was reasonable in that it handled large storms as well as
SWRRB. This means that it might be applicable in humid or sub-humid
conditions. The evidence is scant, however, since entirely differnt soils

would be involved, as well as cropping practices.

Chapter 5

CONCLUSIONS

SAWM describes fairly well the hydrologic cycle within a semi-
arid watershed. It has also a flexible and interactive approach in
describing the interconnections between surface water and groundwater.
It permits simulating different scenarios and allowing immediate
analysis and interpretation. SAWM is therefore useful in predicting the
effect of management decisions on water balance and sedimentation of
watersheds. The simulation of the deep aquifer is encouraging because
allows consideration of both surface and groundwater in management
decisions. The validation of SAWM against SWRRB is satisfactory,
given the simplicity of the equations stating the relationships between

different components and given the convenience in running simulations.

75

Chapter 6

RECOMMENDATIONS

Modeling the hydrologic cycle using STELLA II has proven to be
and interesting exercise that needs to be considered in the curriculum of
both Civil Engineering and Agriculture Engineering to stimulate
curiosity and interest of undergraduate students.

Graduate students interested in soil and water issues can improve
SAWM by better simulating the soil component as multiple stocks
(reservoirs) interconnected in a fashion so that they can mimic the soil in
retaining moisture and delaying its motion.

The improved SAWM can be validated against a better secondary
reference model than SWRRM; such as SWAT (improved SWRRB with
GIS capabilities). This will allow SAWM to be extended and consider
the interconnections between the ecological, economical and social as a

an integrated and useful tool of planning and management of watersheds.

76

APPENDIX A

 

APPENDIX A - SAWM ALGORITHM

E] DEEP_AQUIFER(t) = DEEP_AQUIFER(1 - dt) + (deep _percolation - Irrigation) ' dt
INIT DEEP_AQUIFER = o

lNFLOWS:
3 deep _percolation = SHALLOW_AQU|FER’0.00060
OUTFLOWS:
3 Irrigation = 0 '
I: ET_VOLUME(t) = ET_VOLUME(t - dt) + (PT) " dt
INIT ET_VOLUME = 0
INFLOWS:
3 PT = 0.5‘(1.28'delta'H0)/(delta+0.68)
I: EVAP_VOL(t) = EVAP_VOL(t - dt) + (evaporation) " dt
INIT EVAP_VOL = 0
INFLOWS:
3 evaporation = 0.002'RIVER
D EVASOL(t) = EVASOL(t - dt) + (solev) " dt
INIT EVASOL = 0
lNFLOWS:
3 solev = PT'EXP(-0.4'LAI)
D REVAP_VOL(t) = REVAP_VOL(t - dt) + (revap) " dt
INIT REVAP_VOL = 0
INFLOWS:
3 revap = 0.0016'SHALLOW_AQUIFER
D RIVER(t) = RIVER(t - dt) + (lateral_flow + runoff + retum_flow - evaporation - seepage - streamflow) '
dt
INIT RIVER = 0
INFLOWS:
3 iateral_flow = IF(SOIL>25)THEN(1.2'(SOlL-25)/40)ELSE(0)
3 runoff = O.12'SOIL'(1-S/1000)
3 retum_flow = lF(SHALLOW_AQUIFER>20)THEN( 0.01'(SHALLOW_AQUIFER-20) )ELSE
OUTFLOWS: '
3 evaporation = 0.002'RIVER
3 seepage = 0.006'RIVER
3 streamflow = 0.0018'days‘RlVER
[:1 SHALLOW_AQUIFER(t) = SHALLOW_AQUIFER(t - dt) + (percolation + seepage - upward_flow -
revap - deep _percolation - return_flow) ' dt
INIT SHALLOW_AQUIFER = 0
NF LOWS:
3 percolation = lF(SOlL>15)THEN(SOlL-15)‘.05
‘ELSE(0) + PT‘0+runoff'0
3 seepage = 0.006'RIVER
OUTFLOWS:
3 upward_flow =
lF((SOIL<7)AND(SHALLOW_AQUIFER>15))THEN((SHALLOW_AQUlFER-15)'.01)ELSE(0)
3 revap = 0.0016'SHALLOW_AQUIFER
3 deep _percolation == SHALLOW_AQUIFER'0.00060

77

78

Q C = GRAPH(month)
(0.00, 0.00), (1.08, 9.00), (2.17, 12.5), (3.25, 13.2), (4.33, 19.2), (5.42, 28.0), (6.50, 27.0), (7.58, 29.0),
(8.67, 29.0), (9.75, 25.0), (10.8, 21.0), (11.9, 14.0), (13.0, 10.0)

Q Sol. = GRAPH(month)
(0.00, 0.00), (1.00, 250), (2.00, 320), (3.00, 427), (4.00, 488), (5.00, 562), (6.00, 651), (7.00, 613),
(8.00, 593), (9.00, 503), (10.0, 403), (11.0, 306), (12.0, 245)

79

3 retum__flow = IF(SHALLOW_AQUIFER>20)THEN( 0.01*(SHALLOW_AQUIFER-ZO) )ELSE
[:1 SOIL(t) = SOIL(t - dt) + (precip + upward_flow + Irrigation - PT - percolation .- runoff - lateral_flow -
solev) * dt
INIT SOIL = 1
INFLOWS:
3 precip = GRAPH(days)
(0.00, 0.00), (1.00, 0.00), (2.01, 0.00), (3.01, 0.00), (4.01, 0.67), (5.01, 1.13), (6.02, 0.00),
(7.02, 0.00), (8.02, 0.00), (9.02, 0.00), (10.0, 23.1), (11.0, 0.00), (12.0, 0.00), (13.0, 0.00),
(14.0, 0.00), (15.0, 0.00), (16.0, 5.90), (17.0, 0.00), (18.0, 0.00), (19.1, 0.00), (20.1, 0.00),
(21.1, 0.00), (22.1, 13.4), (23.1, 1.76), (24.1, 0.01), (25.1, 4.31), (26.1, 0.00), (27.1, 0.00),
(28.1, 9.65), (29.1, 0.00), (30.1, 0.00), (31.1, 0.00), (32.1, 0.00), (33.1, 0.00), (34.1, 0.00),
(35.1, 0.00), (36.1, 0.00), (37.1, 0.00), (38.1, 0.00), (39.1, 0.00), (40.1, 0.01), (41.1, 0.00),
(42.1, 0.00), (43.1, 0.00), (44.1, 0.00), (45.1, 0.00), (46.1, 0.00), (47.1, 0.00), (48.1, 0.00),
(49.,1 0.,00) (501,000), (51.1, 00,0) (52.,1 66.4)

3 upward _flow -
' IF((SOIL<7)AND(SHAI.LOW_ AQUIFER>15))THEN((SHALLOW_ AQUIFER-15)‘. 01)ELSE(0)
3 Irrigation: 0
OUTFLOWS:
PT: 0. 5*(1.28'delta'HO)l(delta+0. 68)
percolation= IF(SOIL>1 5)THEN(SOIL-1 5)‘. 05
ELSE(0) + PT."0+runoff"0 _
3 runoff= 0. 12"SOIL'(1-S/1000)
3 lateral_flow= IF(SOIL>25)THEN(1.2'(SO|L-25)/40)ELSE(0)
3 solev = PT’EXP(-0.4"LAI)
1:] SOIL_LOSS(t) = SOIL_LOSS(t - dt) + (erosion) " dt
INIT SOIL_LOSS = 0 -
. INFLOWS:
3 erosion = IF(runoff<5)THEN(0)ELSE((0.12*(runoff-5))"2)
D TOTAL_RAIN(t) : TOTAL_RAIN(t - dt) + (ACCUMULATOR) ‘ dt
INIT TOTAL_RAIN = 0
INFLOWS:
3 ACCUMULATOR= precip
I: WATER _YI=ELD(t) WATER __YIELD(t- dt) + (streamflow)* dt
INIT WATER_YIELD= 0
INFLOWS: .
3 streamflow = 0.0018*days*RIVER
CN = 70 .
days = COUNTER(1,366)
delta = 5304*EXP(21:255-5304/(C+273))I(C+273)"2
H0 = (0.77/58.3)*Solar
LAI = 3
month = lNT(COUNTER(1,366)/30)
S =~254*((100/CN)-1)

0191

0000000

APPENDIX B

APPENDIX B - USDA SOIL DATA

80

 

 

 

Cover
Land use Treatment or practice Hydrologic WW9—
condition A B C D
Fallow Straight row ---. T7 86 91 94
Row crops Straight row Poor 7‘2 81 88 91
" Good 67 78 85 89
Contoured Poor 70 79 84 88
" Good 65 65 82 86
Contoured and terraced Poor 66 74 80 82
" Good 62 71 78 81
Small grain Straight row Poor 65 76 84 88
" Good 63 75 as 87
Contoured Poor 63 74 82 85
" Good 61 73 . 81 84
Contoured and terraced Poor 61 72 79 82
" - Good 59 70 78 81
Close-seeded Straight row Poor 66 77 85 89
legumes” or " Good 58 72 81 85
rotation meadow Contoured Poor 64 75 83 85
" Good 55 69 78' 83
Contoured and terraced Poor 63 73 80 83
" Good 51 67 76 80
Pasture or range Poor 68 79 86 89
Fair 49 69 79' 84'
Good 39 61 74 80
Contoured Poor 47 67 81 88
" Fair 25 59 75 83-
" Good 6 35 70 79
Meadow Good 30 58 71 78
Woods Poor 45 66 77 83
Fair 36 60 73 79
Good 25 55 70 77
Farmsteads ---- 59 74 82 86
Roads min)” 72 82 37 89
(hard surface)” 74 84 9o 92

 

y Close-drilled or broadcast.

2’ Including right-of-way.

Taken from USDA (1972).

8l

Runoff curve numbers for hydrolog'c soil-cover complexes in Puerto Rico.
(Antecedent moisture condition 11, and l. = 0.2 S).

 

 

H l I . 1
Cover and condition A B C D
Fallow 77 86 91 93
Grass (bunch grass or poor stand of sod) 51 70 80 84
Cofl'ee (no ground cover, no terraces) 48 68 79 83
Coffee (with ground cover and terraces) 22 52 68 75
Minor crops (garden or truck crops) 45 66 77 83
TrOpical kudzu 19 50 67 74
Sugarcane (trash burned; straight-row) 43 65 77 82
Sugarcane (trash mulch; straight-row) 45 66 T7 83
Sugarcane (in holes; on contour) - 24 53 69 76

- Sugarcane (in furrows; on contour) 32 58 ‘ 72 79

 

Runoff curve numbers for hydrologic soil-cover complexes of a typical watershed in
Contra Costa County, California. (Antecedent moisture condition 11, and L = 02 S).

 

 

Cover Condition A B C D
Scrub (native brush) --- 25-30 41-46 57-63 66
Grass-oak (native oaks with understory Good 29-33 43-48 59-65 67
of forbs and annual grasses)
Irrigated pasture Good 32-37 46-51 62-68 70
Orchard (winter period with understory Good 37-41 50-55 64-69 71 '
of cover crop)
Range (annual grass) Fair 46-49 57-60 68-72- 74
Small grain (contoured) Good 61-64 69-71 76-80 81
Truck crops (straight-row) Good 67-69 74-76 80-83 84
Urban areas:
Low density (15 to 18 percent 69-71 75-78 82-84 86
impervious surfaces)
Medium density (21 to 27 percent 71-73 77-80 84-86 88
impervious surfaces)
High density (50 to 75 percent 73-75 79-82 86-88 90

impervious surfaces)

 

APPENDIX C

 

82

APPENDIX C - SWRRB COMPUTER PRINTOUT

 

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