A System Dynamics Model-Based Exploratory A nalysis of Salt
Water Intrusion in C oastal A quifers
Jan .H. Kwakkel and Jill .S. Slinger
Delft University of Technology
Faculty of Technology, Policy and Management
Jaffalaan 5
2628 BX Delft, The Netherlands
+31(0)15 27 88487
-H.Kwakkel@ tudelft.nl
.S.Slinger@ tudelft.nl
Abstract: Coastal communities dependent upon groundwater resources for drinking water
and irrigation are vulnerable to salinization of the groundwater reserve. The increasing
uncertainty associated with changing climatic conditions, population and economic
development, and technological advances poses significant challenges for freshwater
management. The research reported in this paper offers an approach for investigating and
addressing the challenges to freshwater management using innovative exploratory
modeling techniques. We present a generic system dynamics model of a low lying coastal
region that depends on its groundwater resources. This systems model covers population,
agriculture, industry, and the groundwater reserve. The system model in turn is coupled to a
powerful scenario generator, which is capable of producing a comprehensive range of
plausible future scenarios. Each scenario describes a unique future pathway of the evolution
of population, the economy, agricultural and water purification technologies. We explore
the behavior of the systems model across a wide range of scenarios and analyze the
implications of these scenarios for freshwater management in the coastal region. In
particular, the results are summarized in a decision tree that provides insights into the
expected outcomes given the various uncertainties, thus supporting the development of
effective policies for managing the coastal aquifer.
Key words: salt intrusion, coastal aquifer, salinization, freshwater management, system
dynamics, exploratory modeling and analysis, deep uncertainty, policy analysis
1 Introduction
Many coastal regions in the world are subject to seawater intrusion in aquifers resulting in
severe deterioration of the quality of the groundwater resources (Narayan et al. 2003).
Indeed, saltwater intrusion as a result of groundwater over-exploitation is a major concem
in many aquifers throughout Europe (EEA 1999), America (Barlow 2003; NRC 2011),
Australia (Narayan et al. 2003) and the developing world (Sales 2008). In its fourth
assessment report the IPCC includes the following major projected impacts as examples of
the possible effects of climate change due to changes in extreme weather and climate
events: decreased freshwater availability due to saltwater intrusion, salinization of irrigation
water, water shortages for settlements, industry and societies, potential for population
migration, land degradation, lower yields/crop damage and failure, amongst others (IPCC
2007). Each of these potential impacts may affect coastal communities with low per capita
income who are dependent upon groundwater resources for drinking water and agricultural
purposes (Sales 2008; NRC 2011), making them particularly vulnerable.
Despite our current understanding that these communities are vulnerable to becoming
climate refugees, few analytical tools for studying the interrelationships between the factors
influencing human migration, and the land and water use practices of the coastal
communities dependent upon aquifers are available. The analysis of such socio-ecological
systems is further complicated by the omnipresence of a wide variety of uncertainties,
related to future climate change, other external forces such as technological developments,
and uncertainty about the internal functioning of the system
In this paper, we seek to address this gap first by developing a simple yet generic system
dynamics model of a coastal community dependent upon its groundwater resources. This
model covers population, land use including agriculture, and the groundwater reserve. The
Coastal Community Aquifer model captures the key dynamics of the subsystems and their
interactions. The systems model, in turn, is coupled to a powerful scenario generator, which
is capable of producing a comprehensive range of plausible future scenarios (Lempert,
Popper, and Bankes 2003), thus allowing to explore the behavior of the model across a
wide range of plausible future developments.
We explore the behavior of the systems model across the wide range of scenarios and
analyze the implications of the scenarios for population growth and land use policy for
freshwater management in the coastal region. We conclude that irrespective of the
scenarios, the modeled system is likely to deteriorate, both in terms of the population that
can be sustained by the region and in terms of the amount of salt in the aquifer.
After first addressing the need for an exploratory modeling approach to studying the
vulnerability of coastal communities who are dependent on groundwater resources, and
describing the fit between system dynamics and exploratory modeling techniques (section
2), we move on to describing the Coastal Community Aquifer model (section 3). The
results of applying exploratory modeling techniques to the analysis of the potential range of
system dynamics model outcomes are described in section 4. First the base case results are
described, next the range of uncertainties that are tested are detailed and the manner in
which this is undertaken is described in the experimental set-up. Finally the results are
depicted and further research is delineated.
2 A New Approach to Studying the Resilience of Agricultural
Communities in Semi-Arid Coastal Areas: Exploratory Modeling and
Analysis
Most models are intended to be predictive and use consolidative modeling techniques, in
which known facts are consolidated into a single ’best estimate’ model. The consolidated
model is subsequently used to predict system behavior (Hodges 1991; Hodges and Dewar
1992). In such uses, the model is assumed to be an accurate representation of that portion of
the real world being analyzed. However, the consolidative approach is valid only when
there is sufficient knowledge at the appropriate level and of adequate quality — that is, only
when we are able to validate the model in a strict empirical sense. We can validate models
only if the situation is observable and measurable, the underlying structure is constant over
time, and the phenomenon permits the collection of sufficient data (Hodges and Dewar
1992). Unfortunately, for many systems, such as the socio-ecological coastal communities
system, these conditions are not met. This may be due to a variety of factors, but is
fundamentally a matter of not knowing enough to make predictions (Cambell et al. 1985;
Hodges and Dewar 1992). Many scientists have realized this. Some claim “the forecast is
always wrong” (Ascher 1978); others say such predictive models are “bad” (Hodges 1991;
Hodges and Dewar 1992), “wrong” (Sterman 2002), or “useless” (Pilkey and Pilkey-Jarvis
2007). Decision making about systems for which our ability to predict is severely limited is
sometimes termed decision making under deep uncertainty. Decision making under deep
uncertainty is typically encountered in situation in which decisionmakers do not know or
cannot agree on a system model, the prior probabilities for the uncertain parameters of the
system model, and/or how to value the outcomes Deep uncertainty bears a strong family
resemblance to the wider literatures on wicked problems (Churchman 1967) and messy
problems (Ackoff 1974). It can be argued that decision making under deep uncertainty is a
subclass of wicked problems or messy problems. Analytically, deep uncertainty can be
defined as being able to enumerate multiple alternatives for how something is or will be
without being able or willing to rank order the alternatives in terms of how likely or
plausible they are judged to be (Kwakkel, Walker, and Marchau 2010).
The potential for using a consolidative modeling approach is limited for decisionmaking
under deep uncertainty. However, there is still a wealth of information, knowledge, and
data available that can be used to inform decisionmaking. Exploratory Modeling and
Analysis (EMA) is a research methodology that uses computational experiments to analyze
complex and uncertain systems (Bankes 1993; Agusdinata 2008). EMA specifies multiple
models that are consistent with the available information and the implications of these
models are explored. A single model run drawn from this set of models is not a prediction.
Rather, it represents a computational experiment that reveals how the world would behave
if the assumptions any particular model makes about the various uncertainties were correct.
By conducting many such computational experiments, one can explore the implications of
the various assumptions. EMA aims at offering support for exploring this set of models
across the range of plausible parameter values and drawing valid inferences from this
exploration (Bankes 1993; Agusdinata 2008). From analyzing the results of this series of
experiments, analysts can draw valid inferences that can be used for decisionmaking,
without falling into the pitfall of trying to predict that which is unpredictable.
The basic steps in EMA are: (1) conceptualize the policy problem, (2) specify the
uncertainties relevant for policy analysis, (3) develop a fast and simple model of the system
of interest, (4) design and perform computational experiments, (5) explore and display the
outcomes of the computational experiments to reveal useful patterns of system behavior,
(6) make policy recommendations (A gusdinata 2008). EMA is a new, innovative research
approach to supporting policymaking under deep uncertainty and has been applied to
various climate change related cases (Lempert, Popper, and Bankes 2003; Agusdinata
2008).
EMA takes a particular stance on how models can be usefully applied to inform
decisionmaking despite their limited predictive power. This stance is independent of the
type of modeling paradigm that is being used. EMA researchers have utilized agent based
models, spreadsheet models, operation research models, and domain specific modeling
approaches. Recently, there has been an upsurge in combining EMA with exploratory
System Dynamics models. EMA and System Dynamics are perfect partners (Pruyt 2010,
2010; Pruyt and Hamarat 2010). System dynamics is traditionally used for modeling and
simulating dynamically complex issues, analyzing the resulting non-linear behaviors over
time, and developing and testing structural policies. Many dynamically complex problems
are characterized by deep uncertainty, since in case of dynamic complex issues the cause
effect relations are subtle (Senge 1990). The omnipresence of uncertainty has been
recognized by many system dynamicists and is the underlying motivation for interpreting
the quantitative results of system dynamics models qualitatively (e.g. in term of modes of
behaviors or behavioral trajectories)(Meadows and Robinson 1985; Pruyt 2007). This
qualitative interpretation of model results is compatible with the interpretation of model
results in EMA.
3 A Model of Salinization in a Semi-Arid Coastal Agricultural
Community
3.1 Conceptual description of the model
At present, various integrated System Dynamic water cycle models exist at both global and
regional scales. These models have been used to define global or regional limits to the use
of blue water. On a global scale, AQUA (Hoekstra 1998), WorldWater (Simonovic 2002)
and ANEMI (Davies 2007; Davies and Simonovic 2011) are prime examples. On a regional
scale, a several System Dynamic models are available. Most of these are prepared to
analyze socio-economic development in relation to water resources at a basin level. Aqua
(Hoekstra 1998) can be used for the regional level, but case specific models exist as well.
Saysel and Barlas (2001; 2000) present a model for the South-eastern Anatolian Project in
semiarid South-easten Turkey. Simonovic and Rajasekaram (2004) present a System
Dynamics model of water resources and water use for Canada, which borrows various
constructions from the W orldWater model.
The coastal aquifer is conceptualized as a single hydro stratigraphic unit of sand/gravel,
bounded at the base by impermeable bedrock of negligible gradient. According to Narayan
et al.(2003), the assumption of uniformity of the aquifer is defensible even for coastal
aquifers with laterally discontinuous strata that exhibit vertical connections between sandy
units. In common with Kooi and Groen (2000), the aquifer is conceptualized as unconfined
at the upper boundary representing the unconsolidated nature of the sediments of many
alluvial coasts.
A cross-sectional vertical slice through the aquifer is depicted in Figure 1 (adapted from
Barlow 2003), with the groundwater source entering from the left and the hydrostatic
pressure of the seawater present on the right. When the aquifer is fully charged with
freshwater it extends 100m in length and contains a volume of 1,8 x 10° m3,
Land surface
Figure 1: Cross-section through a uniform sand aquifer indicating the fresh groundwater resource on
the left, the sea water on the right and the halocline forming the interface or transition zone between
the two water bodies (from Barlow 2003).
In contrast to many groundwater models (Barlow 2003; Kooi and Groen 2000; Narayan et
al. 2003), we include the population and land-use dynamics of the coastal community as
well as water management practices in our model. In short, we treat the coastal community
and its aquifer as a social-ecological system and build a finite difference equation model
according to the system dynamics modeling method (Meadows 1985). This means that we
are able to cross disciplinary boundaries and investigate the effects of climate change and
land and water-use rules on the interlocking social and resource-based sub-systems.
Outcomes of interest to this investigation are the time evolution of the water and food
shortages, as these are indicative of the potential migratory response of climate refugees.
wee meee
. Se of salt
> *
area io for *
agriculture
\ On) ier salt intrusion
area used for
oe: + cs
+
—_———S
Oe rae water availability
[, OF CG}
water demand.
‘water use
Figure 2: High level conceptual diagram of the main feedbacks
Figure 2 shows the main feedbacks in the model. The population in the area is constrained
by both the availability of land and the availability of water. If the population grows, the
land area available for agriculture declines, in turn resulting in a decline of food production.
The decline of food production results in a negative food balance, resulting in a decline in
population. If the population grows, the water demand will increase. The increasing water
demand lead via water balance to an increase in use. The increasing use negatively affects
the available water, which, via the water balance leads to a decline in the population. Water
availability and land availability both affect the amount of land that is being irrigated. The
more land is irrigated, the higher the food production. Irrigation of land leads to an increase
of salt in the aquifer. Salt is also increased due to salt intrusion. Salt intrusion increases if
water availability decreases. The buildup of salt in the aquifer in turn negatively affects
food production. The current version of the model does not the buildup of salt in the top
soil, but does not yet translate it to desertification and the resulting loss of land for
agriculture.
The model as presented is a generic model. Parameter values related to water demand from
agriculture and population are in line with values used in World Water and Anemi (Davies
and Simonovic 2011; Simonovic 2002). The buildup of salt in the top soil is inspired by
Saysel and Barlas (2001; 2000).
3.2 Detailed model specification
The coastal community aquifer model (CCA) comprises four sub-sections, namely: a
population section, an aquifer (quantity and quality) section, a land-use section and a water
use section. In the population section, the birth, death and emigration rates are modeled as
dependent on the number of people making up the coastal community. This is described in
the following equations.
d
Get = X11 — X12 — X13
where x, is the population, x,,is the birth rate, x, is the death rate, and x,3is the
emigration rate. The birth rate in turn depends on the population, the normal birth rate (bn)
and a non-linear function indicating the trend in the average birth rate over time. The
people living along the coast are modeled as migrating in response to shortages in food and
water in accordance with observed and predicted responses to environmental stresses
(IPCC 2007; Sales 2008; NRC 2011). Those that stay may be forced to drink water of a
quality lower than the standards prescribed for drinking water by the World Health
Organisation (EEA 1999). The death rate is formulated as depending on the product of the
death normal (dn) and a non-linear function (df(x3)) indicating the influence of the
chloride content of the water on the death rate. The emigration rate depends on the
emigration normal (emn) and the independent effects of water and food shortages on
emigration (emf, (shortware-)) and emf, (shortyooq)).
X41 = x,.bn. bf (t)
X42 = —xX1.dn. df (x3)
X43 = —x,.emn. emf; (shortwarer).eMf2(shortyooa)
Although the people of the agriculturally-dependent coastal community are primarily
employed in the agricultural sector, a small percentage is employed in the industrial sector
(%ind).
The Aquifer
The volume of freshwater in the aquifer (x2) is influenced by is the replenishment by
rainwater x,,, the replenishment by a remote riverine source (x,2), the irrigation retumn
flow (x3) and by the extraction of freshwater by the coastal community (x2,). Whereas the
replenishment by rainfall is dependent on the land area (area) and a time dependent
rainfall function (rainf(t)), a certain proportion (irn) of the water used in irrigation (irr)
filters down into the aquifer (Barlow 2003; Narayan et al. 2003). The extraction of
freshwater occurs in response to the demand for domestic water (demand gomestic) Water
for industry (demandinduseria:) and water for agriculture (demandagricuiture)-
Unfortunately, the total demand cannot always be met. The degree to which the demand is
met is determined by formal water management agreements. In the model, these
agreements are specified in terms of the length of the aquifer (1), which is directly related to
the volume of freshwater present in the aquifer.
a = X21 + X22 + X23 — X24
X21 = area.rainf (t)
X22 = riverf (t)
X22 = irr.irn
X24 = (demandgomestic + demand industria + demand agricuiture)-extrf (l(X2))
The amount of salt diffusing across the seawater-freshwater halocline that bounds the
seaward extent of the aquifer per unit time (x3,) is directly proportional to the cross-
sectional area at the interface (area,,.;,). However, the diffusion rate per unit area varies
according to the length of the aquifer. When the aquifer extends to its full length, the
diffusion rate per unit area is about 0,7 of the nominal diffusion constant (difn). When the
aquifer reduces to below 40% of its length, the diffusion rate per unit area increase to 1,6
times the diffusion constant. As the aquifer empties this rate even approaches 1,75 times the
diffusion constant. This non-linear behavior is captured in the diffusion function
(dif (l(x,))) which reflects the enhanced diffusion of salt owing to the increased
hydrostatic pressure from the seawater associated with reduced freshwater. The diffusion
process is responsible for the salinization of the freshwater aquifer (Barlow 2003; Narayan
et al. 2003), an effect additional to the landward intrusion of seawater that accompanies the
reduction in the volume of freshwater (Kooi and Groen 2000). A further source of salt to
the aquifer is provided by the seepage of salt from agricultural return flow (x32)(Narayan et
al. 2003). This is represented as a third order exponential material delay (Kirkwood 1998)
with a delay time of 6 years. Finally, salt is removed from the aquifer when water is
pumped out. The salt present in the aquifer is assumed to be distributed uniformly, so that
the salt removed by extraction (x33) is given by the product of the extraction rate of
freshwater (x24) and the average concentration of salt in the aquifer (“2 if xg)
da
ap Xa = X31 + X32 — X33
X31 = ATCAcross. difn. dif (U(x2))
X32 = DELAY (x2,6 yr)
= x2
X33 = X24- |x
Land Use
The available land area is utilized for the functions of infrastructure, nature areas, housing,
industry and agriculture. The percentage of land area allocated to infrastructure and nature
is assumed constant. However, as the community grows, the area occupied by housing and
industry will grow at the expense of agricultural land. This housing and industrial area
growth rates (x,,and x42, respectively) are modeled by comparing the demand of people
for housing and industrial area with the existing housing and industrial areas. The required
housing area is determined by first determining the number of houses required and then
multiplying this by the average area per house (areapoyse). The number of houses required
is the quotient of the population and the average number of people per household (pph).
The required industrial area is determined by first calculating the number of people
working in industry and then multiplying by the area required per worker (aredyorzer)- If
the required areas are less than the existing area of houses and industry, no changes are
made. If the required housing area exceeds that allocated to houses, then the difference
between the required area and the actual area is eliminated over a period of years (adj). In
effect, if this period is 5 years this means that one fifth of the housing area shortage is
supplied annually. A similar approach is adopted for industrial land with a percentage of
the industrial land shortage being supplied on an annual basis.
d
XxX, =X, x
ae 41 — X42
d
Xs =X.
ae 41
d
=X =X,
qa* 42
x i ap ©
Xa = C “Lop WeInouse _ x5)/adj if “/pph: & ethouse
> xs and 0 otherwise
Xa2 = (%1.%ind. aredworker — X6)/adj if x1. %ind. aredworker
> x, and 0 otherwise
The land not in use for housing and industry is available to agriculture. The agricultural
land use can be divided into irrigated lands (x7) and rain-fed or non-irrigated lands
(xg)(Saysel, Barlas, and Y enigun 2000). The rate at which the conversion to agricultural
land occurs differs for irrigated (x7) and non-irrigated land (xg,), with a higher percentage
generally going to irrigated land (ad;,) than to non-irrigated land (adg,). As the demand
for housing and industrial land increases (in response to increasing population) and exceeds
the stock of available land, the land available to agriculture declines and agricultural land
has to be converted to urban area. The rates at which the irrigated and non-irrigated land
become available for urban usage (x72 and xg2, respectively) depend on the land area
required for urban development and the fraction of agricultural land irrigated or not
irrigated.
Another land conversion mechanism is also at work. The irrigated land can only be
sustained when there is sufficient water to irrigate (Saysel and Barlas 2001; Saysel, Barlas,
and Y enigun 2000). The product of the minimum water demand of irrigated land (irrwd)
and the land area under irrigation (x,) provides an indication of the maximum sustainable
irrigated land area at that time (x7ma,). When the maximum sustainable irrigated land area
is smaller than the area under irrigation, irrigated land is converted into rain-fed agriculture
over a certain adjustment time (ad). The rate at which this conversion occurs is called the
irrigation to rain fed rate (x73).
a X7 = X71 — X72 — X73
aXe = Xg1 — Xe2 + X73
X71 = (x4 — (x5 + X6))-ad7, if x, > (xs + x6) and 0 otherwise
X70 = (x4 — (x5 + x6) Me, +x) if x, < (x5 + x6) and 0 otherwise
Xq3 = @,— Mines) if X7max < X7 and 0 otherwise
73
Xamax = X7.irrwd
Xe1 = (x4 — (x5 + X6))-adg; if x, > (xs + x6) and 0 otherwise
Xeo = (%4 — (x5 + x6). 8c, +x) if x, < (x5 + x6) and 0 otherwise
Water and Food Shortages
The food requirement of the coastal community is simply modeled as the product of the
population and an annual food requirement per person (fpp). This requirement is then
compared with the total yield from agriculture, which comprises the yield from the irrigated
lands and the yield from the non-irrigated lands. The yield of the irrigated lands is
detrimentally affected by the chloride content of the groundwater according to the relation
given in Saysel & Barlas (2001). This effect is captured in the function syf (x3).
shortyooa = X1-fpp — yieldrora: if x1. fpp > yieldrorq, and 0 otherwise
yieldroa = X7.yieldiry. SYf (X3) — Xg. Yieldnon—irr
The supply of water to the different demand sectors occurs on the basis of proportional
demand. When water is plentiful everyone’s water demands are met, but when water is
short the allocation is made depending on the fraction of the total demand required by the
different sectors.
supplydomestic = X24- demand gomestic/dEMANA to tar
supplYinaustriat = X24. demand inaustriar/deMandgotat
supplYagricutture = X24-demandgagricuiture/demand ora
where demand jozq,is the sum of the domestic, industrial and agricultural water demands.
The domestic water shortage is then given by the difference between the domestic water
demand and the domestic water supply.
shortwarer = demandgomestic — SUPPlYaomestic if demand aomestic >
suppl¥qomestic and 0 otherwise
This completes the description of the coastal community aquifer model. The model is
implemented in the Vensim software. The stock and flow diagrams are presented in the
appendix.
4 Results
In section 3, the policy problem (ema step 1) and a model of the system of interest (ema
step 3) have already been introduced. In this section, the uncertainties and the experimental
setup will be discussed shortly and the results analyzed.
4.1 Uncertainties
Table 1 presents an overview of the uncertainties that are explored in the EMA study of the
Coastal Community Aquifer model. In total, 13 uncertainties are explored across the
specified range. A number of the uncertainties are represented as multiplier factors that will
10
be used to alter the base value of the corresponding functions. For example, the birth rate is
described by a non-linear function representing the time-dependent variation of births per
1000 people, by multiplying this with a multiplier factor ranged between 0.8 and 1.2, up to
twenty percent more or less births per 1000 people can be simulated.
Table 1: The uncertainties and their ranges
Model variable description range
Births bf (t) Multiplier factor on the non-linear birth function representing 0.8-1.2
the time-dependent variation in the number of births per 1000
people per year
Deaths df (x3) Multiplier factor on the non-linear death function describing the | 0.8-1.2
effect of increased salinization of the ground water on the
number of deaths per 1000 people per year
Migration in response to Multiplier factor on the nonlinear effects of water shortage on 0.5-1.5
water shortage the emigration of people from the region
emf, (shortwater)
Migration in response to Multiplier factor on the nonlinear effects of food shortage on the | 0.5-1.5
food shortage emigration of people from the region
emf,(shortooa)
Slope of diffusion lookup | The diffusion of salt from the sea into the aquifer. This is 0.5-5
function described by a sigmoidal function and varies according to the
dif (U(x2)) volume of freshwater in the aquifer. The sigmoid contains a
parameter beta that affects the slope of the sigmoid
adj Multiplier factor alters the adjustment time for land use change | Change by
from agriculture to urban land. The time it takes for irrigated factor of 0.8 -
agricultural land to be converted into non-agricultural land 1.2
Salt effect on agricultural | Multiplier factor on a non-linear relation between salt 0.8-1.2
yield concentration and the agricultural yield
Adaptation time in Adaptation time of agricultural area in response to water 1-10 years
response to water shortage
Adaptation time of non- The time it takes for non - agricultural land to be converted into | 0.01-0.5 year
agricultural land into irrigated agricultural land
irrigated land
Adaptation time of non- The time it takes for non - agricultural land to be converted into | 0.01-0.5 year
agricultural land into non- | non-irrigated agricultural land
irrigated land
Adaptation times of non- | The time it takes for non-irrigated agricultural land to be 0.5-2 year
irrigated agricultural area | converted into non -agricultural land
in response to other land
usages
Evaporation constant The fraction of rainfall that evaporates 0.4-0.8
Water usage by crops The amount of water crops extract from the top soil. 0.95 - 1.25
m/year
Technological Multiplier factor on the reduction in water usage of irrigated 0.005,0.02
developments in irrigation
agriculture owing to technological innovation
4.2 Experimental setup
The model is implemented in Vensim. Through the Vensim DLL, the model is executed
from Python using the ‘EMA workbench’. Python is an open source high level
programming language. Extensive open source libraries for scientific computing, jointly
11
known as Scipy (http://www.scipy.org/), are readily available. The EMA workbench offers
functionality similar to that available in most System Dynamics software packages. We use
it, because of its convenience in easily specifying the parameters and their ranges, its ease
of storing results and the support it offers for subsequent analysis of the results using
various machine learning algorithms. Using the EMA workbench, a Latin Hypercube
sample (Iman, Helton, and Cambell 1981) across the specified uncertainties is generated
consisting of a total of 10 000 cases. Given our stated interest in understanding system
behavior, a uniform distribution is assumed for all uncertainties. By assuming a uniform
distribution, an effective sampling of the space of possible parameterizations of the model
takes place. The assumed uniform distribution should not be interpreted as a statement
about prior beliefs. For the population, groundwater volume, amount of salt in the aquifer,
the agricultural yield, water shortage, and food balance, the time series data are extracted
and stored, together with the values for the uncertainties.
4.3 Analysis of Results
Figure 3 shows the results for a subset of all the runs. In total, 100 randomly selected runs
are visualized here, combined with a Gaussian kernel density estimate of the terminal
values. As can be seen, the model typically shows an overshoot and decline dynamic. The
population grows up to the point that the salt concentrations in the aquifer becomes passes a
threshold after which the agricultural yield declines sharply. This declining yield results in
food shortages and the associated exodus of people from the region because of this. It
appears that only a few runs deviate from this dynamic, namely those runs that have a
slower increase of the population. This is also suggested by the Gaussian kernel density
estimate of the end state, which show a clear double hump.
12
v wr 7 @ To 00a Too0s
31 popul
To a 3s
Figure 3: Results for a subset of all the runs
The next step is to develop insight into which ranges of values for the various uncertainties
result in which outcomes. That is, insight into the mapping of inputs to outputs is needed.
One technique that can be employed for this is the Patient Rule Induction Method (PRIM)
(Friedman and Fisher 1999; Chong and Jun 2008). PRIM can be used for data analytic
questions where the analyst tries to find combinations of values for input variables that
result in similar characteristic values for the outcome variables. Specifically, one seeks a set
of subspaces of the input variable space within which the values of output variables are
considerably different from the average value over the entire domain. PRIM describes these
subspaces in the form of ‘boxes’ of the input variable space. PRIM induces boxes by
iteratively peeling of small parts of an initial box that covers all the data. For each iteration,
all possible new boxes are generated and the one that has the highest increase on the
objective function is selected. The iteration stops when the amount of data inside the box
falls below a particular user specified threshold. Next, PRIM iteratively adds a small
amount of data back to the box by extending it again. This pasting continuous as long as the
objective function keeps increasing. This results in a very concise representation, for
typically only a limited set of dimensions of the input variable space is restricted. That is, a
subspace is characterized by upper and/or lower limits on only a few of the input
dimensions.
13
We used PRIM to identify the subspace of the full uncertainty space that produces a
terminal value for the population higher than 2.2 million (an estimate of where the split
between the two humps in the kemel density is located). In total 3264 cases meet this
criterion. PRIM finds 4, partially overlapping subspaces that have a concentration of cases
higher then 0.8. These subspaces are spanned by a relatively low value for the births
multiplier, coupled to a high value for the water shortage multiplier and food shortage
multiplier. This implies that high values for the end state of the population occur if the net
growth of the population is relatively low.
5 Concluding Remarks
In this paper, we introduce a simple generic model of the interdependency of a coastal
community, its water resource, its water use, and land use practice. The aim of this model
was to provide insight in the vulnerability of coastal communities to climate change. This
model has been combined with a scenario generator, exploring the behavior of the model
over a wide range. This exploration reveals that in fact these coastal communities are very
vulnerable. Under almost all conditions, the system collapses, resulting in a large number of
emigrants. This suggests that the modeled adaptation mechanisms of the system are not
able to avoid a collapse. Using PRIM, a mapping of inputs to outputs is made. This
provides a first step towards designing effective management strategies.
Research into effective management strategies for prolonging the life time of the aquifer is
currently underway. In addition, research on further development of the Coastal
Community Aquifer model is ongoing. For instance, the inclusion of a salt dispersion
mechanism in the model is under study. Moreover, in the current implementation, the
population has no impact on how much land is actually producing food, thus, if the
population is near zero, there is still a huge production in agriculture. Making the arable
land dependent on the population will address this. Related, the model does contain a
buildup of salt in the top soil, but this in tum can be translated into a loss of agricultural
land due to desertification. This mechanism is currently not present in the model. Another
line of research is to complement the existing scenario generators with various climate
change scenarios. For example, how will the system evolve if there is an extensive wet
period followed by an extensive drought? Finally, so far we have only explored the ranges
of behaviors that are possible using a Latin Hypercube sampling approach. A more directed
search, utilizing Active Non-linear testing (Miller 1998) can be utilized to find worst case
scenarios under the specified ranges of the various uncertain parameters.
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16
APPENDIX 1
) emigration fraction
exported lookup
food shortage
multiplier climate emigration
refugees watershortage lookup
water shortage
multipli water shortage per
Mer person
emigration”
<Time>
deat lier
p> population
ents deaths
Ze New oS
birth lookup ia Jookup
births domestic water <Time>
multiplier demand
; influence of salt on
deaths
say erect <salt concentration
i alt concentratio1
water demand per multiplier ring
person
Figure 4: Population
17
waler,
Se
ground waler>
porosiy top soi
supply de to ran
bf. Sk
water use asl ction —
vial » ang, | mporad> pale
ee ae ee rere a
‘ | a demand
| verona wth
evaporaton | | verfow quer
constant wateruse by cops upsteam water component
cetacton postion of sd poms
exch sono er
‘ ae ‘ot with of "ohms
cae / seer sme
deft extractable
assumption here is thatthe water erotn
that goes into the rootmne is only bola fr water
the water that falls on agricultural extraction
land
emps
Figure 5: Groundwater reserve
<pervolation> normal diffusion
constant
<avererage width
aquiver>
diffusion of salt into the
aquifer from sea
crt ~~ diffusion lookup
a Py aa
inflow of salt SOL salt inflow from salt outflow
agriculture
seepage 7
igation <extraction>
<inigation> eek actio
salt concentration
<flushing to sea>
<ground water
volume> salt concentration
inmgl
tranlsation factor
m’3 to liter
Figure 6: Salt
18
perc
unemployed
increase percentage mp
‘unemployed
actually working
total working”
<population» "population
industrial demand
a
working in industry Gama per
percentage working employee
population
percentage working
in industry
Figure 7; Labor
housing
smoothing time
‘max agriculture
housing areal wag. fee ‘area fame
house construction erable business
i, building time ———— construction
difference démand
saan total demand
<population> | a
“Sg demand housing
wetness deinand buitess
people per louse area per house
area per worker
Figure 8: Land use for population and businesses
19
“apa”
adaptation time from
non imigted agriculture
‘area non |.
increase non inigated pn - r
ee aie ae
ae <ciferen
change caused by laptation time <area auriule> area>
‘water
area imigated} =
increase inated =. inigeted
|
adaptation time from
technological
developments in
max area with ‘rigaton
water
Figure 9: Land use agriculture
20
