Ecological Modelling 139 (2001) 177– 199
www.elsevier.com/locate/ecolmodel
A dynamic model of salinization on irrigated lands
Ali Kerem Saysel a,*, Yaman Barlas b,1
a
b
Institute of En6ironmental Sciences, Bogazici Uni6ersity, 80815, Bebek, Istanbul, Turkey
Industrial Engineering Department, Bogazici Uni6ersity, 80815, Bebek, Istanbul, Turkey
Received 23 September 1999; received in revised form 13 December 2000; accepted 9 January 2001
Abstract
A dynamic simulation model of salt accumulation on irrigated lands is presented. The original version of the model
is part of a large-scale socio-economic model of irrigation-based regional development. The model introduced in this
paper is a systemic one in the sense that it integrates four major sub-processes of rootzone salinization: irrigation,
drainage, groundwater discharge and groundwater intrusion. It provides a comprehensive and general description of
the long-term process of salt accumulation in lowlands under continuous irrigation practice, where irrigated lands are
annually increased. Analysis of the model and simulation results reveal, under what conditions the salinity reaches
alarming levels and with what strategies it can be controlled. For instance, in situations where the mixing of drainage
water into irrigation water supplies is high, rootzone salinity quickly reaches alarming levels. More importantly, in
this setting, the typical strategy of increasing the drainage in order to control the salinity level yields unprecedented
exponentially growing salinity levels, a catastrophic result for the agriculture. The model structure can represent the
basin wide salinization process on different geographical settings in agricultural development. In general, the model
provides an experimental simulation platform, which can be used by the policy makers in the long term strategic
management of large scale irrigation development projects. The model can also be of interest to the students and
learners in teaching and research, in the related fields of environmental sciences. © 2001 Elsevier Science B.V. All
rights reserved.
Keywords: Salinization; Irrigation; Simulation modeling; System dynamics method
1. Introduction
Salinization is the process that leads to an
excessive increase in the salinity of the soil due to
* Corresponding author. Present address: Department of
Information Science, 5020, University of Bergen, Bergen, Norway. Tel.: +47-555-84108; fax: + 47-555-84107.
E-mail addresses: [email protected] (A.K. Saysel),
[email protected] (Y. Barlas).
1
Tel.: + 90-212-2631540 ext. 2073; fax: + 90-212-2651800
agricultural practices, such that plant growth is
inhibited. Most salinization processes result from
poor agricultural practices associated with irrigation. The processes of salt accumulation in irrigated lands are largely determined by the salinity
of the irrigation water and the groundwater level
in the area (Johnson and Lewis, 1995, pp. 78).
Salinization due to poor irrigation practices is one
of the major processes in land degradation, resulting in reduced productivity. According to global
0304-3800/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 3 0 4 - 3 8 0 0 ( 0 1 ) 0 0 2 4 2 - 3
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A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
estimates, about 953 million ha of land are salt-effected and about 10 million ha irrigated land are
abandoned every year because of salinization
(Sczabolcs, 1987).
As irrigation water is evaporated or transpired,
the salt ions are largely left behind to accumulate
in the soil. Gradually, the soil solution becomes
highly concentrated to inhibit plant growth unless
surplus water is added to flush the salts. However,
if this surplus water is not removed from the
irrigated lands before it reaches the groundwater,
it may result in a rising water table. Irrigation
systems are particularly vulnerable when groundwater rises to within 1.5– 2.5 m of the surface and
can evaporate through capillary action of soil
particles or can be transpired by plants, causing
salts to accumulate (O’hara, 1997). Therefore,
‘drainage canals’ that capture and divert the incremental salt flushing waters from the irrigated soils
prior to reaching the water table are as critical in
managing a sustainable irrigation scheme as the
irrigation canals that deliver the water to the fields
(Johnson and Lewis, 1995, pp. 79).
In this paper, a dynamic simulation model of
salt accumulation in soil root zone is introduced.
The original model is an integral part of a largescale regional model, developed for long-term
comprehensive environmental analysis of ‘Southeastern Anatolian Project (GAP)’ in semiarid
South-eastern Turkey (Saysel, 1999). (The structure and policy conclusions of this integrated
model are summarized in Saysel et al. (2001)).
The original version of the model represents the
effects of salinization and water availability on
regional crop yields, which alters the dynamics of
agricultural production and land use through decreasing income levels for certain crop selections.
The salinization model introduced in this paper
provides a general structure representing the longterm process of basin wide salt accumulation in
lowlands under continuous irrigation practice,
where irrigated lands are annually increased. This
is a typical situation in irrigation based regional
development projects, (see Kishk 1986; O’hara
1997 for two specific examples: Nile valley and
Turkmenistan). The model may serve as an experimental simulation platform for studying the different aspects of the salinization problem, with an
integrated, systemic perspective, where the subproblems of irrigation, drainage, groundwater discharge and groundwater intrusion interact
simultaneously.
2. Model description
The dynamic salinization model represents the
quantity of irrigation water applied on arable
lands with respect to crop irrigation requirements
and water availability constraints. The model
traces the portion of the water evapotranspired,
which leaves salt in soil root zone, and the portion
infiltrated through root zone, which flushes the
salt and recharges the groundwater. The dynamics
of watertable and groundwater intrusion to the
root zone are also represented. As a result of the
interactions between these processes, the dynamics of rootzone salinity is obtained. Since the
purpose of the model is to understand the longterm process of salinization and evaluate the alternative macro-level policies, it works on annual
basis; i.e. the micro-level or ‘noisy’ fluctuations in
salt concentrations within the year or problems
related with irrigation throughout the season are
ignored in this ‘big picture’. The basic model
assumption is a homogenous environment where
the average values of annual precipitation, irrigation, runoff and water table level apply. On the
other hand, by integrating the groundwater dynamics, intrusion, discharge and basin wide salinization of irrigation water supplies into the
problem of rootzone salinization, a comprehensive, systemic model of salinization is provided.
Such a salinization model could be useful to
policy makers of regional development projects in
understanding the multiple mechanisms behind
salinization and designing proper strategies.
(Kishk, 1986 estimates that from 1/3rd to 1/2 of
all irrigated land in the Nile basin in Egypt has
experienced salinization problems after the construction of Aswan High Dam. Some areas in
Upper Egypt have experienced water table rises of
almost 2 m. O’hara, 1997 reports wide scale salinization of cotton production lands in
Turkmenistan).
A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
The model is based on the principles of ‘system
dynamics’ methodology (Forrester, 1968; HPS,
1996; Sterman, 2000). This is a modeling and
simulation methodology specifically designed for
long-term, chronic, dynamic management problems, such as high levels of inflation or unemployment, declining market shares of a firm, rising
pollution levels in a city, declining productivity in
an organization, declining population of an endangered species, and in our case, rising salinity
levels. The methodology focuses on understanding
how the physical processes, information flows and
managerial policies interact so as to create the
dynamics of the variables of interest. The totality
of the relationships between these components are
called the ‘structure’ of the system. Thus, it is said
that the ‘structure’ of the system, operating over
time, generates its ‘dynamic behavior patterns’
(such as exponential growth or decline, S-shaped
growth, collapse or fluctuations). The ‘structure’
of the model refers to the totality of the equations
that make up the model. It is therefore, most
crucial in system dynamics method that the model
structure provide a valid description of the real
processes (Forrester and Senge, 1980; Barlas,
1996; Sterman, 2000). The typical purpose of a
system dynamics study is to understand how and
why the dynamics of concern are generated and
search for ‘policies’ to improve the situation. Policies refer to the long-term, macro-level decision
rules used by upper management. (Such as deciding on the interest rates of the central bank,
choosing new products or markets for a growth
company, deciding on anti-pollution laws and regulations and determining a set of irrigation policies so as to prevent salinization in the long-term).
The model is constructed by the building blocks
(variables) categorized as stocks, flows and converters (Fig. 1). Stock variables (symbolized by
rectangles) are the state variables and they represent the major accumulations in the system. Flow
variables (symbolized by valves) are the rate of
change in stock variables and they represent those
activities, which fill in or drain the stocks. Converters (represented by circles) are intermediate
variables used for miscellaneous calculations. Finally, the connectors (represented by simple arrows) are the information links representing the
179
cause and effects within the model structure
(HPS, 1996).
For example, in the stock-flow structure of the
model in Fig. 1, rootzone salinity (salinity – rootzone) is modeled as a stock variable (an accumulation) and the processes increasing and
decreasing this quantity due to evapotranspiration
(rootzone – salinity – increase) and due to flushing
of salts by infiltration (rootzone – salinity – decrease) are modeled as flow variables. Porosity of
soil at root zone (porosity – rootzone), root zone
depth (rootzone – depth) and infiltration water
salinity (salinity – infiltration) are the converters
used in the calculation of rootzone salinity
decrease.
2.1. Model 6ariables
In this section, beginning with the stock variables, important variables and their units are
defined.
rootzone – salinity: salt concentration at soil
root zone (mg/l).
watertable – le6el: average watertable depth
(mm).
Flow variables associated with these stock variables are:
rootzone – salinity – increase: increase in rootzone salinity due to evapotranspiration (mg/l
per year).
rootzone – salinity – decrease: decrease in root
zone salinity due to flushing of salts by infiltration (mg/l per year).
watertable – increase: increase in watertable due
to percolation (mm/year)
watertable – decrease – discharge: decrease in watertable due to groundwater discharge into surface water supplies (mm/year).
watertable – decrease – intrusion: decrease in watertable level due to intrusion to the soil root
zone (mm/year).
Major converters are presented below in alphabetical order:
adsorbtion – fraction: fraction of ions annually
adsorbed on soil particles and not flushed by
infiltrating water (dimensionless).
A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
Fig. 1. The stock-flow structure of the dynamic salinization model.
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basin – recharge: basin recharge is the portion of
annual precipitation which is retained by interception, depression storage and soil moisture
(mm). It is the portion that it does not contribute to streamflow or groundwater recharge
(Linsley et al., 1992, pp. 43).
basin – yield – freshwater: freshwater basin yield
is a constant representing maximum quantity of
water supplied from surface water supplies in
an irrigation scheme (m3/year).
critical – discharge – le6el: the critical level of watertable, above which a certain fraction of
groundwater is discharged (mm).
critical – watertable – le6el: a threshold value for
watertable level where groundwater intrusion
begins (mm).
crop – consumpti6e – use: the theoretical water requirement of the crop for optimum growth
(mm/year).
crop – irr – requirement: crop irrigation requirement calculated as the difference of crop consumptive use and effective precipitation in mm
(Linsley et al., 1992, pp. 472).
drainage – efficiency: a fraction representing the
portion of infiltration drained out prior to percolation (dimensionless).
effecti6e – precip: the portion of annual precipitation available for plant consumption (mm/
year).
e6apotranspirating – water: water that will evapotranspire through root zone calculated as the
summation of irrigation water stored at root
zone, effective precipitation and annual quantity of groundwater intrusion (mm/year).
groundwater – intruding – root – zone:
annual
quantity of groundwater intrusion (mm/year).
infiltration: total infiltration (mm/year).
irr – infiltration: portion of excess irrigation water infiltrated through soil root zone, which
flushes salts (mm/year).
irr – runoff – infiltration: excess of the applied irrigation water, which is not stored at soil root
zone (mm/year).
irr – water – applied: the minimum of delivered
irrigation water and farm delivery requirement
(mm/year).
irr – water – deli6ered: water delivered to the
farmlands for irrigation (mm/year).
181
irr – water – stored – rootzone: the portion of irrigation water available for crop consumption
(mm/year).
irrigation – efficiency: the portion of water
stored at root to the water delivered to the
farmland for irrigation (dimensionless) (Linsley
et al., 1992, pp. 475).
percolation: portion of infiltration which is not
drained out and which recharges groundwater
(mm/year).
precip – infilt – runoff: portion of annual precipitation, which is surplus and recharges
streamflow or groundwater (mm/year).
precip – infiltration: portion of precip – infilt –
runoff infiltrated through soil root zone (mm/
year).
precipitation: long term average of annual precipitation represented by Gaussian distribution
(mm/year). This variable is ‘exponentially
smoothed’ in order to prevent unrealistic magnitudes in generated precipitation (see list of
equations in the Appendix A).
salinity – effect – on – yield: effect of rootzone
salinity on farm yield (dimensionless)
salinity – e6apotranspirating – water: salt concentration of water that will evapotranspire
through root zone (mg/l).
salinity – freshwater: salt concentration of freshwater set as a model constant (mg/l).
salinity – groundwater: salt concentration of
groundwater (mg/l).
salinity – infiltration: salt concentration of
infiltration water (mg/l).
salinity – irr – water: salt concentration of irrigation water (mg/l).
salinity – precipitation: salt concentration of precipitation (mg/l).
water – deli6ery – requirement: water required to
be delivered to the farmlands in order to supply
sufficient water for optimum plant growth
(mm/year).
2.2. The causal loop diagram
In system dynamics modeling, causal loop diagrams represent the major feedback mechanisms,
which reinforce (positive feedback loop represented by ‘+ ’) or counteract (negative feedback
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A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
loop represented by ‘ −’) a given change in a
system variable. A feedback loop is a succession
of cause and effects such that a change in a given
variable travels around the loop and comes back
to affect the same variable. If an initial increase in
a variable in a feedback loop eventually results in
an increasing effect on the same variable, then,
the feedback loop is identified as a ‘reinforcing or
positive’ feedback loop. If an initial increase in a
variable eventually results in a decreasing effect
on the same variable, then the feedback loop is
identified as a negative, counteracting or balancing’ loop (HPS, 1996; Sterman, 2000). The positive feedback loops potentially stimulate unstable
exponential growth or collapse patterns in system
behavior. For instance, in the salinization model,
rootzone salinity is reinforced by three positive
feedback loops representing the processes activated by drainage discharge, groundwater discharge and groundwater intrusion into the soil
Fig. 2. Causal loop diagram for dynamic salinization model.
A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
rootzone (see Fig. 2 and description in the next
paragraph). On the other hand, the negative feedback loops potentially stabilize the systems and
stimulate asymptotically stable growth and decay
patterns. The watertable level is controlled by two
negative feedback loops representing groundwater
discharge and groundwater intrusion. (See Fig. 2
and description in the next paragraph). Causal
connections constituting the feedback loops are
identified by bold arrows and for each connection
the increasing or decreasing effect is denoted by
‘ +’ or ‘ −’signs, respectively. For instance, an
increase in groundwater salinity increases the
salinity of the evapotranspiring water. An increase
in groundwater discharge decreases the water
table level. The polarity of a feedback loop is
obtained by the algebraic product of individual
signs around the loop and is represented by bold
( + ) and ( −) signs.
The first negative feedback loop in Fig. 2 represents groundwater discharge: as the watertable
rises by percolation above some critical discharge
level, the groundwater discharges. The larger the
discrepancy between the water table and the critical level, the larger the groundwater discharge,
which in turn lowers the water table level, completing the negative or balancing loop. (The algebraic product of these three connections yields a
negative feedback loop). Similarly, the second
negative feedback loop represents groundwater
intrusion. As the watertable level rises, it exceeds
the critical watertable depth and groundwater intrusion increases. But increased groundwater intrusion results in lowered watertable level. These
processes constitute two negative feedbacks,
which control the groundwater level, discharge
and intrusion.
Positive feedback loops identify those processes
reinforcing rootzone salinization. In the first positive feedback loop, as the rootzone salinity rises,
salinity of infiltration, hence the salinity of
drainage water, then the salinity of irrigation water increases through drainage discharge into
freshwater supplies. As the salinity of irrigation
water elevates, so does the salinity of evapotranspiring water and this in turn, further increases
the rootzone salinity.
183
In the second positive feedback loop, as rootzone salinity increases, salinity of infiltration,
hence groundwater salinity increases through percolation. As groundwater salinity increases, the
salinity of irrigation water increases through
groundwater discharge into irrigation water supplies. Then, increased salinity of irrigation water
creates increased rootzone salinity as the salinity
of evapotranspiring water increases. This completes the second positive feedback loop. In the
model, there exists a third positive feedback loop
representing the increase in rootzone salinity
through groundwater intrusion into the root zone.
An increase in rootzone salinity results in increased infiltration salinity and groundwater salinity through percolation. This, in turn, results in
increased salinity of evapotranspiring water
through groundwater intrusion. Hence, rootzone
salinity increases.
The analysis of the causal loop diagram reveals
that the three positive feedback loops acting on
the rootzone salinity through drainage discharge,
groundwater discharge and groundwater intrusion, respectively, may be critical in salinization
control. On the other hand, we observe that the
groundwater discharge and intrusion in the second and third positive feedback loops are stabilized by the first and second negative feedback
loops (due to self-stabilized watertable level).
Therefore, the first positive feedback representing
drainage into freshwater supplies may be more
critical in salinization control in certain settings.
Drainage may act as a control parameter in this
feedback process. Further analysis of this system
by simulation experiments is needed, as illustrated
in the validation and analysis sections of the
paper.
2.3. Important formulations
In this section, selected formulations related to
important model assumptions are presented. (All
model equations, initial values for stock variables
and model constants are given in the Appendix
A).
All calculations in the model obey the law of
conservation of mass and for each calculation,
dimensional consistency is observed. The stock
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A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
and flow equations for a given stock variable
represent the conservation of mass for that stock
variable. As earlier mentioned, rootzone salinity is
modeled as a stock variable which represents the
accumulating ions in soil root zone in mg/l. The
rate of change in rootzone salinity is modeled by
two flow variables, one representing the increase
through evapotranspiration, and the other representing the decrease through flushing, both in mg/l
per year. Hence the mathematical expression is the
following stock (or ‘integral’) equation:
rootzone – salinity(t + dt) =rootzone
– salinity(t)
+ (rootzone – salinity – increase
– rootzone – salinity – decrease) × dt
(mg/l)
The rate of increase in rootzone salinity is the
amount of salts released by annual evapotranspiration. (In this calculation, salt removal by crops is
ignored, because, this quantity is too small to make
a significant contribution to salt removal (Schwab
et al., 1993, pp. 390)).
rootzone – salinity – increase= evapotranspiring
– water/rootzone – depth/porosity
– rootzone× salinity – evapotranspiring
– water (mg/l)
where evapotranspiring water is in mm/year, rootzone – depth in mm, salinity in mg/l and porosity –
rootzone dimensionless.
The decrease in rootzone salinity is the annual
amount of salts flushed by infiltration:
rootzone – salinity – decrase= infiltration/rootzone
– depth/porosity – rootzone × salinity
– infiltration (mg/l)
where infiltration is in mm/year and the salinity of
infiltration water is formulated as a function of
rootzone salinity and fraction of ions adsorbed on
soil particles:
salinity – infiltration=salinity – rootzone × (1 − adsorbtion – fraction) (mg/l)
The principles of conservation of mass and
dimensional consistency are also observed in the
calculations related to watertable level. Watertable
level is modeled as a stock variable, representing the
accumulation of groundwater in mm. The rate of
change in watertable level is represented by three
flow variables, watertable – increase, watertable –
decrease – discharge and watertable – decrease – intrusion, representing the processes of groundwater
recharge, groundwater discharge and groundwater
intrusion, respectively. The mathematical expression for watertable level is:
watertable – level(t + dt)= watertable
– level(t)
+ (watertable – increase− watertable
– decrease – discharge− watertable
– decrease – intrusion)× dt (mm)
The flow variable watertable – increase represents
the rate of increase in watertable level due to
groundwater recharge by percolation:
watertable – increase= percolation/porosity
– below – root – zone (mm/year)
The flow variable watertable – decrease – discharge represents the rate of decrease in watertable
level due to groundwater discharge. According to
its formulation, a certain fraction of groundwater
above critical discharge level is annually discharged
into freshwater supplies.
watertable – decrease – discharge= -discharge
– level – discrepancy× groundw – disch
– fraction (mm/year)
where,
discharge – level – discrepancy= critical – discharge
– level-watertable – level (mm)
Finally, groundwater intrusion into soil rootzone
is represented by the flow variable watertable – decrease – intrusion in mm/year. When the watertable
level exceeds the critical watertable level, groundwater intrusion begins due to capillary forces
acting by soil particles on water (Foth, 1990,
pp.79). For the numeric representation of this
process, an exponential function intruding –
groundwater – fraction is used (Fig. 3). When the
critical watertable level is exceeded, exponentially
increasing fractions of groundwater above the
critical level intrudes the root zone. The critical
level is set as − 2500 mm and the root zone is set
A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
185
The above equation states that the salinity –
groundwater gradually approaches the salinity –
infiltration, with an average delay time of 6 years.
Salinity of irrigation water is a function of
freshwater salinity, drainage water salinity (infiltration salinity) and groundwater salinity. For the
calculation of irrigation water salinity, relative
weights of drainage, groundwater discharge and
basin yield of freshwater and their respective salt
concentrations are used. For example:
drainage – volume =irrigated
– lands(hectare)× drainage(mm/year)
×10 (m3/year)
Fig. 3. Watertable level discrepancy (mm) versus intruding
groundwater fraction (dimensionless).
as − 500 mm. If watertable level exceeds the root
zone, then not just a fraction, but all of this
exceeding quantity intrudes. Based on this, groundwater intrusion is formulated as follows:
critical – watertable – level= -2500
(mm)
watertable – level – discrepency = watertable
– level-critical – watertable – level
(mm)
Then, groundwater intrusion to the root zone is
calculated as:
groundwater – intruding – rootzone = watertable
– level – discrepency × intruding
– groundwater – fraction × porosity
– below – rootzone (mm/year)
Thus, the rate of change in watertable level is:
watertable – decrease – intrusion = groundwater
– intruding – root – zone/porosity – below
– root – zone (mm/year)
Since groundwater is recharged through percolating water, the groundwater salinity is formulated
as a time-delayed function of infiltration salinity.
For this delay formulation, salt concentration at
root zone is exponentially smoothed with 6 years
delay according to the following equation:
salinity – groundwater(t + dt) = salinity
– groundwater(t) + dt
× (salinity – infiltration(t)-salinity
– groundwater(t))/6 (mg/l)
where 10 (m3/ha.mm) is the factor to convert
drainage in ha.mm into m3.
drainage – ratio= drainage – volume/basin – yield
– freshwater (dimensionless)
Salinity of irrigation water is then calculated
according to the following equation:
salinity – irr – water= salinity
– groundwater× groundwater – discharge
– ratio+ salinity – rootzone× drainage
– ratio+ salinity – freshwater×freshwater
– ratio (mg/l)
groundwater – discharge – ratio= groundwater
– discharge – volume/basin – yield
(dimensionless)
– freshwater
freshwater – ratio= freshwater – volume/basin
– yield – freshwater (dimensionless)
Salinity of evapotranspiring water is calculated
similarly according to the relative weights of precipitation, irrigation water and groundwater in annual
evapotranspiration and their respective salinities.
Effects of rootzone salinity and water scarcity on
crop yields are model outputs, which are useful in
the integrated environmental analysis of the regional development project, GAP. For example,
based on the crop salt tolerance data available in
Foth (1990), pp. 90, the effect of rootzone salinity
on cereals and cotton yield (yield potential) is
formulated in Fig. 4. In these calculations,
whenever necessary, for unit conversions from
electrical conductivity to mass concentration, the
conversion factor 1 ds/m = 670 mg/l is used
(Schwab et al., 1993, pp. 380).
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A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
When the model is run with parameters set at
their ‘base’ values (‘base’ or ‘reference’ condition),
it generates the dynamic behavior patterns illustrated in Fig. 10. We observe that under irrigation,
salinity levels of rootzone, groundwater and irrigation water, all rise exponentially first and then
asymptotically reach their equilibrium levels. Similar behavior patterns are observed for watertable,
groundwater intrusion, discharge, and drainage
variables. These dynamics are caused by the interaction of the positive and negative loops described
in the earlier section. The validity of the model and
its behavior will be further discussed below, in
Section 3 and Section 4.
3. Validation and analysis of the model
Since system dynamics models seek to explain
how and why the problematic dynamics are created, it is crucial that their structure be a valid
representation of the real processes that play significant roles in creating the dynamics of concern. This
is crucial, because the purpose of a system dynamics
study is to evaluate policy alternatives in order to
improve the behavior. This purpose is quite different than that of a statistical/correlational ‘forecasting’ model. In the context of forecasting, the main
(often the only) criterion of model validity is the
match between the model output and real data,
since the purpose of the model is to provide
Fig. 4. Rootzone salinity (mg/l) versus the yield potential
(dimensionless).
accurate forecast. In the context of system dynamics model, on the other hand, the main criterion of
model validity becomes ‘structure’ validity, the
validity of the set of relations used in the model,
as compared with the real processes. Otherwise, the
entire study becomes a useless exercise. The validity
of the ‘behavior’ is also important, but it is different
in two ways: first, behavior validity is meaningful
only after the structure validity is established (‘right
behavior for the right reasons’ principle). Second,
a point-by-point match between the model behavior and the real behavior is not as important as it
is in forecasting modeling. What is more important
in system dynamics method is that the model
produce the major ‘dynamic patterns’ of concern
(such as exponential growth, collapse, asymptotic
growth, S-shaped growth, damping or expanding
oscillations, etc). Thus, the purpose of such a
salinization model would not be to predict what the
salinity levels would be each month for the next 30
years. The purpose would be to reveal under what
conditions and policies the salinity would continue
to rise, if and when it would reach destructive levels,
if and how it can be controlled, if and how the
salinization can be stopped or even reversed. (See
Forrester and Senge, 1980; Barlas, 1996; Sterman,
2000 for extensive discussion of system dynamics
model validity).
For detection of structural flaws in system dynamics models, certain procedures and tests are
used. These structure validity tests are grouped as
‘direct structure tests’ and ‘indirect structure tests’.
Direct structure tests involve comparative evaluation of each model equation against its counterpart
in the real system (or in the relevant literature).
Direct structure testing is important, but its disadvantage is that it is a very qualitative, subjective
process that involves comparing the forms of
equations against ‘real relationships’. It is therefore, very hard to communicate to others in a
quantitative and structured way (Barlas, 1996).
Indirect structure testing on the other hand, is a
more quantitative and structured way of testing the
validity of the model structure. The two most
powerful and practical indirect structure tests are
extreme-condition and behavior sensitivity tests.
Extreme-condition tests involve assigning extreme
values to selected model parameters and
A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
comparing the model generated behavior to the
‘anticipated’ behavior of the real system under the
same extreme condition. The test exploits the fact
that we, human beings, are weak in anticipating
the dynamics of a complex dynamic system in
arbitrary operating conditions, but are much better in anticipating the behavior of the system in
extreme conditions. (We do not know how the
inventories would behave in normal conditions,
but we know they would gradually approach zero,
if the raw material supply is set to zero. We do
not know how the population of a country would
evolve in the next 20 years, but we know that it
would grow exponentially, if we set the death rate
to zero). If the model has any hidden structural
flaws or inconsistencies, they would be revealed
by such tests. (Barlas, 1996). Behavior sensitivity
test consists of determining those parameters to
which the model is highly sensitive and asking if
these sensitivities would make sense in the real
system. If we discover certain parameters to which
the model behavior is surprisingly sensitive, it
may indicate a flaw in the model equations. Alternatively, all model equations may be valid, in
which case this may lead to the discovery of an
unknown, non-intuitive property of the system
under study.
In this section, the application of some indirect
structure tests to the salinization model will be
illustrated. The ‘behavior validation’ of the model
with respect to real data is also important and
desirable, but there exists no long-term salinization data compatible with the time horizon of the
model. Nor is it possible to collect such long term
field data within the scope of this research. Therefore, this section will illustrate only the structural
validation tests. Later in Section 4, the plausibility
of the behavior of the model will also be
discussed.
Fig. 5 illustrates the ‘extreme’ behavior of the
system when irrigation is abandoned. In the first
graph (a), the behavior of the variables rootzone
salinity (1), groundwater salinity (2) and irrigation
water salinity (3); and in the second graph (b) the
behavior of the watertable level (1), groundwater
intrusion (2) and groundwater discharge (3) are
demonstrated. According to this ‘extreme condition’ run, salinity values are in equilibrium
187
throughout the 32 years simulation horizon. Watertable level is also in equilibrium, since the
watertable level is below critical watertable depth,
there is no groundwater intrusion and groundwater discharge stays at equilibrium (which is just
enough to compensate for the groundwater
recharge due to percolation). This extreme condition test states that, if the system is not disturbed
by irrigation practice, it stays at equilibrium,
which demonstrates that the model formulations
have no logical errors or inconsistencies.
In Fig. 6, the behavior of watertable level,
groundwater intrusion and groundwater discharge
under ‘excessive irrigation’ is illustrated. In this
run, irrigation water is set to an unrealistically
high value of 6000 mm/year and the robustness of
the model is tested. It is observed that watertable
level reaches a new equilibrium at − 250 mm
(above the − 500 mm rootzone) and groundwater
intrusion and discharge values are very high, at
900 and 300 mm/year, respectively. (Compare Fig.
6 and Fig. 10). In this run, the model demonstrates waterlogging under excessive (extreme) irrigation, which is consistent with the irrigation
literature and practice. (For instance, Hansen et
al., 1979).
In Figs. 7–9, ‘behavior sensitivity’ tests are
illustrated. In Fig. 7, sensitivity of rootzone salinity to the freshwater salinity is demonstrated. The
runs from 1 to 3 correspond to the input freshwater salinity values of 400, 600 and 800 mg/l,
respectively. It is observed that rootzone salinity
is quite sensitive to freshwater salinity. This sensitivity shows that the model portrays a logically
meaningful relation between freshwater salinity
and rootzone salinity.
In Fig. 8, sensitivity of rootzone salinity to
consumptive water use of crops is demonstrated.
In these runs from 1 to 3, crop consumptive-use
values of 600, 900 and 1200 mm/year are used,
respectively. As water application rates increase,
rootzone salinity increases, which is consistent
with the irrigation literature and practice. (For
instance, Hansen et al., 1979).
Finally in Fig. 9, sensitivity of root zone salinity
to ‘drainage efficiency’ is demonstrated. In these
runs from 1 to 4, drainage efficiency parameter is
set to 0.1, 0.3, 0.5 and 0.8 (dimensionless), respec-
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A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
Fig. 5. System behaviour when irrigation is abandoned.
tively. As drainage efficiency increases, i.e. as
larger portion of infiltration is drained out,
rootzone salinity decreases. These runs show
that the model entails valid relationships between the drainage and salinization processes.
The indirect structure tests demonstrated in
this section reveal that the model structure
yields meaningful behavior under extreme
parameter values and model behavior exhibits
meaningful sensitivity to the parameters: freshwater salinity, crop consumptive-use and
drainage efficiency. These are consistent with the
empirical and theoretical evidence, offered in
textbooks such as (Foth, 1990; Schwab et al.,
1993; Johnson and Lewis, 1995). In the next
section, the model reference behavior and the
effects of some selected modifications on the behavior are analyzed.
A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
4. Analysis of results
In the base run, it is assumed that, the irrigated land in the basin is constant at 2000 ha,
irrigation water applied is 1500 mm/year and
the basin yield of freshwater is 3.5 billion m3/
year. The drainage efficiency, i.e. the fraction of
infiltration drained before reaching to the
189
groundwater is 0.1. Other parameters and initial
values are kept constant in the experiments and
their values are provided in the Appendix A. In
Fig. 10, the behavior obtained in the base run is
illustrated.
Since groundwater acts as a self-stabilizing
mechanism controlled by two negative feedback
loops (see Fig. 2.), watertable level, groundwater
Fig. 6. System behavior under excessive (6000 mm/year) irrigation.
Fig. 7. Sensitivity of rootzone salinity (mg/l) to freshwater salinity (mg/l).
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A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
Fig. 8. Sensitivity of rootzone salinity (mg/l) to crop consumptive-use (mm/year).
Fig. 9. Sensitivity of rootzone salinity (mg/l) to drainage efficiency (dimensionless).
intrusion and discharge are eventually stabilized.
This controls the potentially self-reinforcing salinization mechanisms through groundwater discharge and intrusion (second and third positive
feedback loops in Fig. 2, respectively). For the
selected crop, at the end of the simulation, the
annual percentage of yield loss due to salinization
is 6%.
In the second experiment, irrigated lands are
annually increased, until they finally reach 160 000
ha. As the irrigated lands are increased, drainage
into freshwater increases too. But, increased
drainage also activates the first positive feedback
loop in Fig. 2. The result of this experiment is
illustrated in Fig. 11: it is observed that the salinity values for the rootzone, groundwater and irrigation water are higher and annual percentage of
yield loss reaches 10%.
A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
If this yield loss reaching 10% is not tolerable,
the salinization problem can perhaps be managed
by increased drainage efficiency. For example, in
the runs in Fig. 12, drainage efficiency is increased
to 0.5 and a yield loss percentage of 6% is
achieved at the end of the simulation. It can be
191
observed that, by increased drainage, higher
drainage volume but lower watertable level and
therefore, lower groundwater intrusion is
achieved.
Up to this point, salinization patterns showed
asymptotic behavior in all the runs. The causal
Fig. 10. The base run of the model.
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A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
Fig. 11. Model behavior when irrigated lands are annually increased.
loop analysis of the model indicates that this
asymptotic growth is by the virtue of groundwater
dynamics being controlled by the two negative
feedback loops described earlier. But, under certain settings where basin yield of freshwater is
low, i.e. the ratio of drainage water mixing is
high, the drainage discharge into freshwater supplies can create severe salinization problem.
Drainage efficiency is the only control parameter
in the salinization process, but it acts to increase
A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
the gain of loop ( +1) while decreasing the gains
of ( +2) and (+3). Under certain conditions, if
the gain of the first positive feedback loop in Fig.
2 is high enough to dominate the behavior of the
193
system, the salinity values may grow exponentially
for a long time. For example, in the runs in Fig.
13, when the basin yield for freshwater supply is
dropped to 1.5 billion m3/year, the salinity values
Fig. 12. Management of salinization problem by drainage.
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A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
Fig. 13. Model behavior when the basin freshwater supply is low (i.e. the drainage mixing ratio is high).
exhibit exponential growth for the entire time
horizon. In this run, the yield loss reaches up to
30%.
Under these settings, what is more important is
that, as the drainage control is increased, the
rootzone salinity is not rehabilitated, but on the
contrary, it becomes worse. In Fig. 14, under
increased drainage, model behavior and corre-
A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
sponding yield loss percentage at the end of the
simulation horizon are illustrated.
Model analysis reveals that, starting with favorable initial salinity values for rootzone, ground-
195
water and irrigation water (600, 300 and 400 mg/l,
respectively) high salinity values (4000, 2000, 600
mg/l, respectively, when irrigated lands are annually increased) are reached and this may result in
Fig. 14. Effect of drainage when the ratio of drainage mixing is high.
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A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
about 10% yield loss even in salt tolerant crops
such as cotton. This is due those self-reinforcing
mechanisms illustrated by Fig. 2. But, if the
drainage mixing in irrigation water is high, irrigated fields may even face exponentially increasing severe salinization problems in the long run
which may cause about 30% yield loss in salt
tolerant crops. Under these settings, increased
drainage cannot be a management option on its
own and it’s mixing into irrigation water supplies
must be strictly avoided.
5. Conclusion
The dynamic salinization model provides a
generic and comprehensive description of the
long-term process of salt accumulation in lowlands under continuous irrigation practice, where
irrigated lands are annually increased. By integrating the groundwater dynamics, intrusion, discharge and the salinization of irrigation water
supplies into the problem of rootzone salinization,
a comprehensive, systemic model of salinization is
obtained. Model analysis reveals three self-reinforcing, hence, critical processes of rootzone salinity related to drainage, groundwater discharge
and groundwater intrusion. The groundwater discharge and intrusion mechanisms are in effect
self-stabilizing, since these two processes lower the
watertable, which in turn means reduced discharge and intrusion. But the drainage mechanism
may play a critical role: if the fresh water supply
is low, (i.e. the ratio of drainage water in the
irrigation water supplies is high), rootzone salinity
quickly reaches alarming levels. More importantly, in this setting, the typical strategy of increasing the drainage in order to control the
salinity level yields unprecedented exponentially
growing salinity levels, a catastrophic result for
the agriculture. More generally, the model provides an experimental simulation laboratory
where many other scenarios and questions about
long-term salinization on irrigated lands can be
analyzed. The model can potentially be used by
the policy makers in the long term strategic management of large scale irrigation development
projects. The model can also be of interest to the
students and learners, in teaching and research in
environmental sciences and environmental
management.
Acknowledgements
This research is financially supported by the
Bogazici University Research Fund, project number: 97Y0003.
Appendix A. Model equations
salinity – rootzone(t)= salinity
– rootzone(t − dt)
+ (rootzone – salinity – increase-rootzone
– salinity – decrease)× dt INIT salinity
– rootzone= 600 {mg/l}
Inflows:
rootzone – salinity – increase= evapotranspirating
– water/rootzone – depth/porosity
– rootzone × salinity
– evapotranspirating – water {mg/l/year}
Outflows:
rootzone – salinity – decrease
= infiltration/rootzone – depth/porosity
– rootzone× salinity
– infiltration {mg/l/year}
watertable – level(t)= watertable – level(t − dt)
+ (watertable – increase− watertable
– decrease – intrusion-watertable
– decrease – discharge) × dt
INIT watertable – level= −2800 {mm}
Inflows:
watertable – increase= percolation/porosity
– below – root – zone {mm/year}
Outflows:
watertable – decrease – intrusion= groundwater
– intruding – root – zone/porosity – below
– root – zone {mm/year}
A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
watertable – decrease – discharge = − discharge
– level – discrepancy × groundw – disch
– fraction {mm/year}
adsorbtion – fraction= 0.5 {dimensionless}
basin – recharge=precipitation × basin – recharge
– percentage {mm/year}
basin – recharge – percentage
= 0.45 {dimensionless}
basin – yield – freshwater =3.5E9{m3/year}
critical – discharge – level = −4500{mm}
critical – watertable – level= − 2500{mm}
crop – consumptive – use = 1200{mm/year}
crop – irr – requirement =crop – consumptive
– use-effective – precip{mm/year}
– freshwater-drainage
– volume-groundwater – discharge
3
– volume{m /year}
groundwater – discharge= watertable – decrease
– discharge× porosity – below – root
– zone{mm/year}
groundwater – discharge – ratio=groundwater
– discharge – volume/basin – yield
– freshwater{dimensionless}
groundwater – discharge – volume =irrigated
– lands× groundwater
3
– discharge× 10{m /year}
groundwater – intruding – root – zone= watertable
– level – discrepency× intruding
– groundwater – fraction× porosity
– below – root – zone {mm/year}
groundw – disch – fraction= 0.18 {dimensionless}
discharge – level – discrepancy =critical – discharge
– level-watertable – level{mm}
infiltration =irr – infiltration +precip
– infiltration {mm}
drainage=infiltration × drainage
– efficiency{mm/year}
intruding – groundw – ratio= groundwater
– intruding – root
– zone/evapotranspirating
– water {unitless}
drainage – efficiency = 0.8{dimensionless}
drainage – ratio=drainage – volume/basin – yield
– freshwater{dimensionless}
drainage – volume
=(irrigated – lands ×drainage)
×10{m3/year}
effective – precip =precipitation × effective – precip
– percentage{mm/year}
effective – precip – percentage
= 0.35{dimensionless}
evapotranspirating – water = effective
– precip +groundwater
– intruding – root – zone + irr
– water – stored – root
– zone{mm/year}
freshwater – ratio= freshwater – volume/basin
– yield – freshwater{dimensionless}
freshwater – volume =basin – yield
197
irrigated – lands
= SMTH1(160000,7,20000)+2000 {ha}
irrigation – efficiency = 0.6 {dimensionless}
irr – infiltration = irr – runoff – infilt × irr
– infiltration – percent {mm/year}
irr – infiltration – percent= 0.5 {unitless}
irr – runoff – infilt =irr – water – applied-irr – water
– stored – root – zone {mm/year}
irr – water – applied
=MIN(water – delivery – requirement, irr
– water – delivered) {mm/year}
irr – water – delivered= 1500 {mm/year}
irr – water – ratio= irr – water – stored – root
– zone/evapotranspirating – water {unitless}
irr – water – stored – root – zone=irr – water
– applied×irrigation – efficiency {mm/year}
A.K. Saysel, Y. Barlas / Ecological Modelling 139 (2001) 177–199
198
porosity – below – root – zone
=0.4 {dimensionless}
water – delivery – requirement= crop – irr
– requirement/irrigation
– efficiency {mm/year}
porosity – rootzone= 0.4 {dimensionless}
water – scarcity= evapotranspirating – water/crop
– consumptive – use
percolation =infiltration-drainage {mm/year}
precipitation
= SMTH1(NORMAL(500, 120), 4, 500)
{mm/year}
precipitation – ratio= effective
– precip/evapotranspirating
– water {dimensionless}
precip – infiltration = precip – infilt
– runoff ×precip – infiltration
– percentage {mm/year}
precip – infiltration – percentage
= 0.5 {dimensionless}
precip – infilt – runoff = precipitation-basin
– recharge {mm/year}
rootzone – depth = 500 {mm}
salinity – evapotranspirating – water = salinity
– groundwater × intruding – groundw
– ratio+salinity – irrigation – water × irr
– water – ratio+salinity
– precipiation× precipitation – ratio {mg/l}
intruding – groundwater – fraction
= GRAPH(watertable – level
– discrepency {1/year})
(0.00, 0.00), (200, 0.055), (400, 0.12), (600, 0.18),
(800, 0.25), (1000, 0.335), (1200, 0.425),
(1400, 0.54), (1600, 0.665), (1800, 0.815),
(2000, 1.00)
water – scarcity – effect – on – yield
= GRAPH(water – scarcity{dimensionless})
(0.00, 0.005), (0.1, 0.015), (0.2, 0.025),
(0.3, 0.055), (0.4, 0.115), (0.5, 0.235), (0.6, 0.485),
(0.7, 0.755), (0.8, 0.905), (0.9, 0.97), (1, 1.00)
yield – potential= GRAPH(salinity
– rootzone{dimensionless})
(0.00, 0.996), (1200, 0.975), (2400, 0.948),
(3600, 0.888), (4800, 0.818), (6000, 0.688),
(7200, 0.541), (8400, 0.437), (9600, 0.359),
(10800, 0.321), (12000, 0.307)
salinity – freshwater=400 {mg/l}
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