wr- systems planning & mmt - 03_chapter03

8/2/2019 WR- Systems Planning & Mmt - 03_chapter03

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3. Modelling Methods for Evaluating Alternatives

1. Introduction 59

1.1. Model Components 60

2. Plan Formulation and Selection 61

2.1. Plan Formulation 61

2.2. Plan Selection 63

3. Modelling Methods: Simulation or Optimization 64

3.1. A Simple Planning Example 65

3.2. Simulation Modelling Approach 66

3.3. Optimization Modelling Approach 66

3.4. Simulation Versus Optimization 67

3.5. Types of Models 69

3.5.1. Types of Simulation Models 69

3.5.2. Types of Optimization Models 70

4. Model Development 71

5. Managing Modelling Projects 72

5.1. Create a Model Journal 72

5.2. Initiate the Modelling Project 72

5.3. Selecting the Model 73

5.4. Analysing the Model 74

5.5. Using the Model 74

5.6. Interpreting Model Results 75

5.7. Reporting Model Results 75

6. Issues of Scale 756.1. Process Scale 75

6.2. Information Scale 76

6.3. Model Scale 76

6.4. Sampling Scale 76

6.5. Selecting the Right Scales 76

7. Conclusions 77

8. References 77

WATER RESOURCES SYSTEMS PLANNING AND MANAGEMENT ISBN 92-3-103998-9 UNESCO 2005


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1. Introduction

Water resources system planners must identify andevaluate alternative water resources system designs or

management plans on the basis of their economic, eco-logical, environmental, and social or political impacts.One important criterion for plan identification and evalu-ation is the economic benefit or cost a plan would entailwere it to be implemented. Other criteria can include theextent to which any plan meets environmental, ecologicaland social targets. Once planning or management per-formance measures (objectives) and various general alter-natives for achieving desired levels of these performancemeasures have been identified, models can be developedand used to help identify specific alternative plans thatbest meet those objectives.

Some system performance objectives may be inconflict, and in such cases models can help identify theefficient tradeoffs among these conflicting measures ofsystem performance. These tradeoffs indicate what com-binations of performance measure values can be obtainedfrom various system design and operating policy variablevalues. If the objectives are the right ones (that is, they are

Modelling Methodsfor Evaluating Alternatives

Water resources systems are characterized by multiple interdependent

components that together produce multiple economic, environmental, ecological

and social impacts. Planners and managers working to improve the performance

of these complex systems must identify and evaluate alternative designs and

operating policies, comparing their predicted performance with the desired goals

or objectives. These alternatives are defined by the values of numerous design,

target and operating policy variables. Constrained optimization together with

simulation modelling is the primary way we have of estimating the values of the

decision variables that will best achieve specified performance objectives. Thischapter introduces these optimization and simulation methods and describes what

is involved in developing and applying them in engineering projects.

3

what the stakeholders really care about), such quantive tradeoff information should be of value during debate over what decisions to make.

Regional water resources development plans desig

to achieve various objectives typically involve investmin land and infrastructure. Achieving the desired enomic, environmental, ecological and social objecvalues over time and space may require investmentstorage facilities, including surface or groundwreservoirs and storage tanks, pipes, canals, wells, pumtreatment plants, levees and hydroelectric generafacilities, or in fact the removal of some of them.

Many capital investments can result in irreverseconomic and ecological impacts. Once the forest ovalley is cleared and replaced by a lake behind a damis almost impossible to restore the site to its origcondition. In parts of the world where river basincoastal restoration activities require the removal of eneering structures, water resources engineers are learn

just how difficult and expensive that effort can be.The use of planning models is not going to elimin

the possibility of making mistakes. These models chowever, better inform. They can provide estimates of



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Modelling Methods for Evaluating Alternatives

reservoirs storage capacity. Both the storage volume overtime and the reservoir capacity might be unknown. Ifthe capacity is known or assumed, then it is among theknown model parameters.

Model parameter values, while assumed to be known,can often be uncertain. The relationships betweenvarious decision variables and assumed known modelparameters (i.e., the model itself) may be uncertain. Inthese cases the models can be solved for a variety ofassumed conditions and parameter values. This providesan estimate of just how important uncertain parameter

values or uncertain model structures are with respect tothe output of the model. This is called sensitivity analysis.Sensitivity analyses will be discussed in Chapter 9 inmuch more detail.

Solving a model means finding values of its unknowndecision variables. The values of these decision variablescan define a plan or policy. They can also define the costsand benefits or other measures of system performance

associated with that particular management planpolicy.

While the components of optimization and simulamodels include system performance indicators, moparameters and constraints, the process of model deopment and use includes people. The drawing shown

Figure 3.1 illustrates some interested stakeholders bstudying their river basin, in this case perhaps with use of a physical model. Whether a mathematical moor physical model is being used, one important consiation is that if the modelling exercise is to be of any vait must provide the information desired and in a form the interested stakeholders can understand.

2. Plan Formulation and Selectio

Plan formulation can be thought of as assigning particvalues to each of the relevant decision variables. Pselection is the process of evaluating alternative plans selecting the one that best satisfies a particular objecor set of objectives. The processes of plan formulation selection involve modelling and communication amall interested stakeholders, as the picture in Figure suggests.

The planning and management issues being discusby the stakeholders in the basin pictured in Figure

could well include surface and groundwater water allotions, reservoir operation, water quality management infrastructure capacity expansion.

2.1. Plan Formulation

Model building for defining alternative plans or poliinvolves a number of steps. The first is to clearly spethe issue or problem or decision(s) to be made. Whatthe fundamental objectives and possible alternativSuch alternatives might require defining allocation

water to various water users, the level of wastewater trment, the capacities and operating rules of multipurpreservoirs and hydropower plants, and the extent reliability of floodplain protection from levees. Eachthese decisions may affect system performance criteriobjectives. Often these objectives include economic mures of performance, such as costs and benefits. They malso include environmental and social measures

Figure 3.1. These stakeholders have an interest in how their

watershed or river basin is managed. Here they are using a

physical model to help them visualize and address planning

and management issues. Mathematical models often replace

physical models, especially for planning and management

studies. (Reprinted with permission from Engineering

News-Record, copyright The McGraw-Hill Companies, Inc.,

September 20, 1993. All rights reserved.).



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expressed in monetary units. (More detail on performancecriteria is contained in Chapter 10.)

To illustrate this plan formulation process, considerthe problem of designing a tank to hold a specific amountof water. The criterion to be used to compare differentfeasible designs is cost. The goal in this example is to find

the least-cost shape and dimensions of a tank that willhold a specified volume, say V, of water.

The model of this problem must somehow relatethe unknown design variable values to the cost of thetank. Assume, for example, a rectangular tank shape. Thedesign variables are the length, L, width, W, and height,H, of the tank. These are the unknown decision variables.The objective is to find the combination ofL, W, and Hvalues that minimizes the total cost of providing a tankcapacity of at least Vunits of water. This volume Vwill beone of the model parameters. Its value is assumed knowneven though in fact it may be unknown and dependent inpart on the cost.

The cost of the tank will be the sum of the costs ofthe base, the sides and the top. These costs will dependon the area of the base, sides and top. The costs perunit area may vary depending on the values ofL, WandH; however, even if those cost values depend on thevalues of those decision variables, given any specificvalues for L, W and H, one can define an averagecost-per-unit area. Here we will assume these average

costs per unit area are known. They can be adjusted ifthey turn out to be incorrect for the derived values ofL,Wand H.

These average unit costs of the base, sides and top willprobably differ. They can be denoted as Cbase, Cside andCtop respectively. These unit costs together with the tanksvolume, V, are the parameters of the model. IfL, W, andH are measured in metres, then the areas will beexpressed in units of square metres and the volume willbe expressed in units of cubic metres. The average unitcosts will be expressed in monetary units per square

metre.The final step of model building is to specify all the

relations among the objective (cost), function and deci-sion variables and parameters, including all the condi-tions that must be satisfied. It is often wise to first statethese relationships in words. The result is a word model.Once that is written, mathematical notation can bedefined and used to construct a mathematical model.

62 Water Resources Systems Planning and Management

The word model for this tank design problem is tominimize total cost where:

Total cost equals the sum of the costs of the base, thesides and the top.

Cost of the sides is the cost-per-unit area of the sidestimes the total side area.

Cost of the base is the cost-per-unit area of the basetimes the total base area.

Cost of the top is the cost-per-unit area of the toptimes the total top area.

The volume of the tank must at least equal some spec-ified volume capacity.

The volume of the tank is the product of the length,width and height of the tank.

Using the notation already defined, and combining someof the above conditions, a mathematical model can be

written as:Minimize Cost (3.1)

Subject to:

Cost (Cbase Ctop)(LW) 2(Cside) (LHWH) (3.2)

LWH V (3.3)

Equation 3.3 permits the tanks volume to be larger thanthat required. While this is allowed, it will cost more if thetanks capacity is larger than V, and hence the least-costsolution of this model will surely show that LWH will

equal V. In practice, however, there may be practical,legal and/or safety reasons why the decisions with respectto L, Wand H may result in a capacity that exceeds therequired volume, V.

This model can be solved a number of ways, whichwill be discussed later in this and the next chapters. Theleast-cost solution is

W L [2Cside V/(Cbase Ctop)]1/3 (3.4)

and H V/[2Cside V/(Cbase Ctop)]2/3 (3.5)

or H V1/3

[(Cbase Ctop)/2Cside]2/3

(3.6)The modelling exercise should not end here. If there isany doubt about the value of any of the parameters, a sen-sitivity analyses should be performed on those uncertainparameters or assumptions. In general these assumptionscould include the values of the cost parameters (e.g., thecosts-per-unit area) as well as the relationships expressedin the model (that is, the model itself). How much does



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the total cost change with respect to a change in any of thecost parameters or with the required volume V? Howmuch does any decision-variable change with respectto changes in those parameter values? What is the percentchange in a decision-variable value given a unit percentchange in some parameter value (what economists call

elasticity)?If indeed the decision-variable values do not change

significantly with respect to a change in the value of anuncertain parameter value, there is no need to devotemore effort to reducing that uncertainty. Any time andmoney available for further study should be directedtoward those parameters or assumptions that substan-tially influence the models decision-variable values.

This capability of models to help identify what data areimportant and what data are not can guide monitoringand data collection efforts. This is a beneficial attribute ofmodelling often overlooked.

Continuing with the tank example, after determining,or estimating, all the values of the model parameters andthen solving the model to obtain the cost-effective valuesofL, Wand H, we now have a design. It is just one of anumber of designs that could be proposed. Anotherdesign might be for a cylindrical tank having a radius andheight as decision-variables. For the same volume Vandunit area costs, we would find that the total cost is less,simply because the areas of the base, side and top are less.

We could go one step further and consider the possibilityof a truncated cone, having different bottom and topradii. In this case both radii and the height would be thedecision-variables. But whatever the final outcome of ourmodelling efforts, there might be other considerations orcriteria that are not expressed or included in the modelthat might be important to those responsible for plan(tank design) selection.

2.2. Plan Selection

Assume P alternative plans (e.g., tank designs) havebeen defined, each designated by the index p. For eachplan, there exist np decision variables xj

p indexed withthe letter j. Together these variables and their values,expressed by the vector Xp, define the specifics of thepth plan. The index j distinguishes one decision-variablefrom another, and the index p distinguishes one planfrom another. The task at hand, in this case, may be to

find the particular plan p, defined by the known vaof each decision-variable in the vector Xp, that maximthe present value of net benefits, B(Xp), derived fthe plan.

Assume for now that an overall performance objeccan be expressed mathematically as:

maximize B(Xp) (

The values of each decision-variable in the vector Xp

meet this objective must be feasible; in other words, tmust meet all the physical, legal, social and institutioconstraints.

Xp feasible for all plansp. (

There are various approaches to finding the best planbest set of decision-variable values. By trial and error, could identify alternative plans p, evaluate the net be

fits derived from each plan, and select the particular pwhose net benefits are a maximum. This process coinclude a systematic simulation of a range of posssolutions in a search for the best. When there is a lanumber of feasible alternatives that is, many decisvariables and many possible values for each of them may no longer be practical to identify and simulatefeasible combinations of decision-variable values, or ea small percentage of them. It would simply take too loIn this case it is often convenient to use an optimizaprocedure.

Equations 3.7 and 3.8 represent a discrete optimtion problem. There are a finite set of discrete alternatiThe set could be large, but it is finite. The tank probexample is a continuous optimization problem havat least mathematically, an infinite number of feassolutions. In this case optimization involves findfeasible values of each decision-variable xj in the sedecision variables X that maximize (or minimize) soperformance measure, B(X). Again, feasible values those that satisfy all the model constraints. A continuconstrained optimization problem can be written as:

maximize B(X) (

X feasible (3

While maximization of Equation 3.7 requires a comparof B(Xp) for every discrete plan p, the maximizationEquation 3.9, subject to the feasibility conditions requin Equation 3.10, by complete enumeration is impossiIf there exists a feasible solution in other words, at l



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one that satisfies all the constraints mathematically thereare likely to be an infinite number of possible feasiblesolutions or plans represented by various values of thedecision-variables in the vector X.

Finding by trial and error the values of the vector Xthat maximizes the objective Equation 3.9 and at the same

time meet all the constraints is often difficult. Some typeof optimization procedure, or algorithm, is useful in suchcases. Mathematical optimization methods are designedto make this search for the best solution (or better solu-tions) more efficient. Optimization methods are used toidentify those values of the decision-variables that satisfyspecified objectives and constraints without requiringcomplete enumeration.

While optimization models might help identify thedecision-variable values that will produce the best plandirectly, they are based on all the assumptions incorpo-rated in the model. Often these assumptions are limiting.In these cases the solutions resulting from optimizationmodels should be analysed in more detail, perhapsthrough simulation methods, to improve the values of thedecision-variables and to provide more accurate estimatesof the impacts associated with those decision-variablevalues. In these situations, optimization models are usedfor screening out the clearly inferior solutions, not forfinding the very best one. Just how screening is performedusing optimization models will be discussed in the next

chapter.The values that the decision-variables may assume are

rarely unrestricted. Usually various functional relation-ships among these variables must be satisfied. This is whatis expressed in constraint Equations 3.8 and 3.10. Forexample, the tank had to contain a given amount of water.In a water-allocation problem, any water allocated to andcompletely consumed by one user cannot simultaneouslyor subsequently be allocated to another user. Storagereservoirs cannot store more water than their maximumcapacity. Technological restrictions may limit the capaci-

ties and sizes of pipes, generators and pumps to thosecommercially available. Water quality concentrationsshould not exceed those specified by water qualitystandards or regulations. There may be limited fundsavailable to spend on water resources developmentprojects. These are a few examples of physical, legal andfinancial conditions or constraints that may restrict theranges of variable values in the solution of a model.


Equations or inequalities can generally express anyphysical, economic, legal or social restrictions on thevalues of the decision-variables. Constraints can alsosimply define relationships among decision-variables.For example, Equation 3.2 above defines a new decision-variable called Cost as a function of other decision-

variables and model parameters.In general, constraints describe in mathematical terms

the system being analysed. They define the system com-ponents and their inter-relationships, and the permissibleranges of values of the decision-variables, either directlyor indirectly.

Typically, there exist many more decision-variablesthan constraints, and hence, if any feasible solution exists,there may be many such solutions that satisfy all the con-straints. The existence of many feasible alternative plans isa characteristic of most water resources systems planningproblems. Indeed it is a characteristic of most engineeringdesign and operation problems. The particular feasiblesolution or plan that satisfies the objective function thatis, that maximizes or minimizes it is called optimal. It isthe optimal solution of the mathematical model, but itmay not necessarily be considered optimal by any decision-maker. What is optimal with respect to some model maynot be optimal with respect to those involved in a plan-ning or decision-making process. To repeat what waswritten in Chapter 2, models are used to provide infor-

mation (useful information, one hopes), to the decision-making process. Model solutions are not replacements forindividuals involved in the decision-making process.

3. Modelling Methods: Simulationor Optimization

The modelling approach discussed in the previous sectionfocused on the use of optimization methods to identifythe preferred design of a tank. Similar methods can be

used to identify preferred design-variable values and oper-ating policies for multiple reservoir systems, for example.Once these preferred designs and operating policies havebeen identified, unless there is reason to believe that aparticular alternative is really the best and needs no fur-ther analysis, each of these preferred alternatives can befurther evaluated with the aid of more detailed and robustsimulation models. Simulation models address what if



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questions: What will likely happen over time and at oneor more specific places if a particular design and/oroperating policy is implemented?

Simulation models are not limited by many of theassumptions incorporated into optimization models. Forexample, the inputs to simulation models can include a

much longer time series of hydrological, economic andenvironmental data such as rainfall or streamflows,water supply demands, pollutant loadings and so onthan would likely be included in an optimization model.The resulting outputs can better identify the variationsof multiple system performance indicator values:that is, the multiple hydrological, ecological, economicand environmental impacts that might be observed overtime, given any particular system design and operatingpolicy.

Simulating multiple sets of values defining the designsand operating policies of a water resources system cantake a long time. Consider, for example, only 30 decision-variables whose best values are to be determined. Even ifonly two values are assumed for each of the 30 variables,the number of combinations that could be simulatedamounts to 230 or in excess of 109. Simulating and com-paring even 1% of these billion at a minute per simulationamounts to over twenty years, continuously and withoutsleeping. Most simulation models of water resourcessystems contain many more variables and are much more

complex than this simple 30-binary-variable example. Inreality there could be an infinite combination of feasiblevalues for each of the decision-variables.

Simulation works when there are only a relatively fewalternatives to be evaluated, not when there are a largenumber of them. The trial and error process of simulationcan be time consuming. An important role of optimiza-tion methods is to reduce the number of alternativesfor simulation analyses. However, if only one methodof analysis is to be used to evaluate a complex waterresources system, simulation together with human judge-

ment concerning which alternatives to simulate is often,and rightly so, the method of choice.

Simulation can be based on either discrete events ordiscrete time periods. Most simulation models of waterresources systems are designed to simulate a sequence ofdiscrete time periods. In each discrete time period, thesimulation model converts all the initial conditions andinputs to outputs. The duration of each period depends in

part on the particular system being simulated and questions being addressed.

3.1. A Simple Planning Example

Consider the case of a potential reservoir releasing wto downstream users. A reservoir and its operating pocan increase the benefits each user receives over timeproviding increased flows during periods of otherwlow flows relative to the user demands. Of intereswhether or not the increased benefits the water uobtain from an increased flow and more reliadownstream flow conditions will offset the costs of reservoir. This water resources system is illustratedFigure 3.2.

Before this system can be simulated, one has to de

the active storage capacity of the reservoir and how mwater is to be released depending on the storage voluand time period; in other words, one has to define reservoir operating policy. In addition, one must define the allocation policy: how much water to alloto each user and to the river downstream of the ugiven any particular reservoir release.

For this simple illustration assume these operating allocation policies are as shown in Figure 3.3. Alsosimplicity assume they apply to each discrete time per

The reservoir operating policy, shown as a red lin

Figure 3.3, attempts to meet a release target. If insufficwater is available, all the water will be released in the tperiod. If the inflow exceeds the target flow and the revoir is at capacity, a spill will occur. This operating pois sometimes called the standard operating policy. not usually followed in practice. Most operatorsindeed specified by most reservoir operating policies, reduce releases in times of drought in an attempt to s

riverQtX1t

user1

user 2

user 3

X2t X3t

reservoir

Figure 3.2. Reservoir-water allocation system to be simula



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some water in the reservoir for future releases in caseof an extended period of low inflows. This is called ahedging policy. Any reservoir release policy, including ahedging policy, can be defined within the blue portion ofthe release policy plot shown in Figure 3.3. The dashdotline in Figure 3.3 is one such hedging function.

Once defined, any reservoir operating policy can besimulated.

3.2. Simulation Modelling Approach

The simulation process for the three-user system shownin Figure 3.2 proceeds from one time period to the next.The reservoir inflow, obtained from a database, is addedto the existing storage volume, and a release is determinedfrom the release policy. Once the release is known, thefinal storage volume is computed and this becomes the


initial volume for the next simulation time period. Thereservoir release is then allocated to the three downstreamusers and to the river downstream of those users asdefined by the allocation policy. The resulting benefitscan be calculated and stored in an output database.

Additional data pertaining to storage volumes, releases

and the allocations themselves can also be stored in theoutput database, as desired. The process continues for theduration of the simulation run. Then the output data canbe summarized for later comparison with other simula-tion results based on other reservoir capacities and oper-ation policies and other allocation policies. Figure 3.4illustrates this simulation process.

It would not be too difficult to write a computer programto carry out this simulation. In fact, it can be done on aspreadsheet. However easy that might be for anyone familiarwith computer programming or spreadsheets, one cannotexpect it to be easy for many practicing water resourcesplanners and managers who are not doing this type of workon a regular basis. Yet they might wish to perform a simula-tion of their particular system, and to do it in a way thatfacilitates changes in many of its assumptions.

Computer programs capable of simulating a wide vari-ety of water resources systems are becoming increasinglyavailable. Simulation programs together with their inter-faces that facilitate the input and editing of data and thedisplay of output data are typically called decision support

systems. Their input data define the components of thewater resources system and their configuration. Inputsinclude hydrological data and design and operating policydata. These generic simulation programs are now becom-ing capable of simulating surface and groundwater waterflows, storage volumes and qualities under a variety ofsystem infrastructure designs and operating policies.

3.3. Optimization Modelling Approach

The simple reservoir-release and water-allocation plan-

ning example of Section 3.1 can also be described as anoptimization model. The objective remains that of maxi-mizing the total benefits that the three users obtain fromthe water that is allocated to them. Denoting each usersbenefit as Bit (i 1, 2, 3) for each ofTtime periods t, thisobjective, expressed symbolically is to:

maximize total benefits (3.11){ }B B Bt t tt

T

1 2 3+ +

initial storage and inflowE020108x

re

lease

release target

storage capacity

00

spill=

releaseonareas

oftargetrelease

zone of feasible release

hedgin

g

reservoir release flow

E020108y

all

oca

tio

n 10

8

6

4

2

00 2 4 6 8 10 12 14 16 18 20

user

river

useruser

3

Q

12

Figure 3.3. Policy defining the reservoir release to be made

as a function of the current storage volume and current inflow

and the reservoir release allocation policy for the river flow

downstream of the reservoir. The blue zone in the reservoir

release policy indicates the zone of feasible releases. It is

physically impossible to make releases represented by points

outside that blue zone.



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The benefit, Bit, for each user i in each time period tdepends on the amount of water, Xit, allocated to it.These benefit functions, Bit Bit(Xit), need to beknown and expressed in a form suitable for solutionusing the particular optimization solution algorithmselected. The unknown variables include the allocations,Xit, and associated reservoir releases Rt for all periodst 1, 2, 3,. .. , T. Assuming there is no significant incre-mental runoff between the upstream reservoir and thesites where water is diverted from the river, the amountsallocated to all users, the sum of all Xit in each period t,cannot exceed the amount of water released from thereservoir, Rt, in the period. This is one of the optimiza-tion model constraints:

Rt X1t X2t X3t (3.12)

The remaining necessary constraints apply to the reser-voir. A mass balance of water storage is needed, along

with constraints limiting initial storage volumes, St, to thecapacity, K, of the reservoir. Assuming a known time-series record of reservoir inflows, It, in each of the timeperiods being considered, the mass-balance or continuityequations for storage changes in each period t can bewritten:

St It Rt St1 for t 1, 2, . . . , T;

Ift T, then T1 1. (3.13)

The capacity constraints simply limit the unknown instorage volume, St, to be no greater than the resercapacity, K.

St K for t 1, 2, . . . , T. (3

A one-year analysis period with T12 time periods of month each in combination with three allocation vables,Xit, a storage variable St, and a release Rt, variabl

each period t, includes a total of sixty unknown decisvariables. The job of the optimization solution procedis to find the values of these sixty variables that will satthe objective, Equation 3.11, that is to say, maximize tbenefits, and at the same time satisfy all of the thirtyconstraint equations and inequalities as well.

In this example the reservoir inflows, It, its storage capity, K, and each users benefit functions, Bit, are assumknown. In some cases such information is not known. were other purposes, such as hydropower, flood conwater quality or recreation considered in this examplemention only a few possible extensions. Such conditand extensions will be considered in later chapters.

3.4. Simulation Versus Optimization

Unlike simulation models, the solutions of optimizamodels are based on objective functions of unknodecision-variables that are to be maximized or minimi

E02

0108

z

stopend

data

storage

compute (t),

i(t), i(t) and (t)

R

X B Q

file

t

S S

= 0

( ) = o1start

yesno

read (t)

S

S

(t+ ) =

(t) +

1

(t) (t)R

t t= +1

(t)

S(t)

R(t)

i(t)X

Q(t)

Bi(t)

- inflow

- initial storage volume

- reservoir release

- allocation to user i

- allocation to stream

- benefit for user i

- time periodt

Figure 3.4. Flow diagram of t

reservoir-allocation system

simulation process. Thesimulation terminates after

some predefined number of

simulation time steps.



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The constraints of an optimization model containdecision-variables that are unknown and parameterswhose values are assumed known. Constraints areexpressed as equations and inequalities. The tank model(Equations 3.1, 3.2 and 3.3) is an example of an opti-mization model. So is the reservoir water-allocationmodel, Equations 3.11 to 3.14. The solution of an opti-mization model, if one exists, contains the values of allof the unknown decision-variables. It is mathematicallyoptimal in that the values of the decision-variables satisfyall the constraints and maximize or minimize an objectivefunction. This optimal solution is of course based on the

assumed values of the model parameters, the chosenobjective function and the structure of the model itself.

The procedure (or algorithm) most appropriate forsolving any particular optimization model depends inpart on the particular mathematical structure of themodel. There is no single universal solution procedurethat will efficiently solve all optimization models. Hence,model builders tend to model water resources systemsby using mathematical expressions that are of a formcompatible with one or more known solution procedures.

Approximations of reality, made to permit model solution

by a chosen optimization solution procedure (algorithm),may justify a more detailed simulation to check andimprove on any solution obtained from that optimization.Simulation models are not restricted to any particular formof mathematics, and can define many relations includingthose not easily incorporated into optimization models.

One of many challenges in the use of optimizationmodelling is our inability to quantify and express


mathematically all the planning objectives, the technical,economic, and political constraints and uncertainties, andother important considerations that will influence thedecision-making process. Hence at best a mathematical-model of a complex water resources system is only anapproximate description of the real system. The optimalsolution of any model is optimal only with respect to theparticular model, not necessarily with respect to the realsystem. It is important to realize this limited meaning of theword optimal, a term commonly used by water resourcesand other systems analysts, planners and engineers.

Figure 3.5 illustrates the broad differences between

simulation and optimization. Optimization models needexplicit expressions of objectives. Simulation models do not.Simulation simply addresses what-if sceanarios what mayhappen if a particular scenario is assumed or if a particulardecision is made. Users must specify the values of designand operating decision-variables before a simulation can beperformed. Once these values of all decision-variables aredefined, simulation can help us estimate more precisely theimpacts that may result from those decisions. The difficultywith using simulation alone for analysing multiple alterna-tives occurs when there are many alternative, and potentially

attractive, feasible solutions or plans and not enough time orresources to simulate them all. Even when combined withefficient techniques for selecting the values of each decision-variable, an enormous computational effort may still lead toa solution that is still far from the best possible.

For water resources planning and management, itis often advantageous to use both optimization andsimulation modelling. While optimization will tell us

water resources system

water resources system

simulation

optimization

system design and operating policy

system design and operating policy

system inputs

system inputs

system outputs

system outputs

E011

217

o

Figure 3.5. Distinguishing

between simulation and

optimization modelling.Simulation addresses what if

questions; optimization can

address what should be

questions. Both types of models

are often needed in water

resources panning and

management studies.



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what we should do what the best decision is thatsolution is often based on many limiting assumptions.Because of this, we need to use optimization not as a wayto find the best solution, but to define a relatively smallnumber of good alternatives that can later be tested,evaluated and improved by means of simulation. This

process of using optimization to reduce the large numberof plans and policies to a few that can then be simulatedand better evaluated is often called preliminary screening.

3.5. Types of Models

3.5.1. Types of Simulation Models

Simulation models can be statistical or process oriented,or a mixture of both. Pure statistical models are basedsolely on data (field measurements). Pure process-oriented models are based on knowledge of the funda-

mental processes that are taking place. The examplesimulation model just discussed is a process-orientedmodel. It incorporated and simulated the physicalprocesses taking place in the system. Many simulationmodels combine features of both of these extremes.

The range of various simulation modelling approachesapplied to water resources systems is illustrated inFigure 3.6.

Regressions, such as that resulting from a least-squanalysis, and artificial neural networks are examplepurely statistical models. As discussed in Chapter relationship is derived between input data (cause) output data (effect), based on measured and obserdata. The relationship between the input and the out

variable values is derived by calibrating a black-boxstatistical model with a predefined structure unrelatethe actual natural processes taking place. Once calibrathe model can be used to estimate the output varivalues as long as the input variable values are withinrange of those used to calibrate the model.

Hybrid models incorporate some process relationshinto regression models or neural networks. These rtionships supplement the knowledge contained in calibrated parameter values based on measured data.

Most simulation models containing process relationsh

include parameters whose values need to be estimated. Tis called model calibration. Calibration requires measufield data. These data can be used for initial calibration verification, and in the case of ongoing simulations, continual calibration and uncertainty reduction. The lais sometimes referred to as data assimilation.

Other simulation model classifications are possiSimulation models can be classified based on what

regression

and

neural

networks

hybrid

models

process

models

& data

assimilation

process

based

simulation

models

fully process orientedfully data oriented

process

knowledge

measured

data

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110

s

Figure 3.6. Range of simulat

models types based on the

extent to which measured fiedata and descriptions of syst

processes are included in the

model.



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model simulates: on the domain of application. Todayone can obtain, or develop, computer programs written tosimulate a wide variety of water resources system compo-nents or events. Some of these include:

water quantity and/or quality of rivers, bays, estuaries

or coastal zones reservoir operation for quantity and/or quality saturated and/or unsaturated zone groundwater quan-

tity and/or quality precipitation runoff, including erosion and chemicals water system demands, supply distribution and treat-

ment high-water forecasting and control hazardous material spills morphological changes wastewater collection systems

wastewater purification facilities irrigation operations hydropower production ecological habitats of wetlands, lakes, reservoirs and

flood plains economic benefits and costs.

Simulation models of water resources systems generallyhave both spatial and temporal dimensions. These dimen-sions may be influenced by the numerical methods used,if any, in the simulation, but otherwise they are usually

set, within the limits desired by the user. Spatial resolu-tions can range from 0 to 3 dimensions. Models are some-times referred to as quasi 2- or 3-dimensional models.These are 1 or 2-dimensional models set up in a way thatapproximates what takes place in 2- or 3-dimensionalspace, respectively. A quasi-3D system of a reservoircould consist of a series of coupled 2D horizontal layers,for example.

Simulation models can be used to study what mightoccur during a given time period, say a year, sometime inthe future, or what might occur from now to that given

time in the future. Models that simulate some particulartime in the future, where future conditions such asdemands and infrastructure design and operation arefixed, are called stationary or static models. Models thatsimulate developments over time are called dynamicmodels. Static models are those in which the externalenvironment of the system being simulated is not chang-ing. Water demands, soil conditions, economic benefit


and cost functions, populations and other factors do notchange from one year to the next. Static models provide asnapshot or a picture at a point in time. Multiple years ofinput data may be simulated, but from the output statis-tical summaries can be made to identify what the valuesof all the impact variables could be, together with their

probabilities, at that future time period.Dynamic simulation models are those in which the

external environment is also changing over time.Reservoir storage capacities could be decreasing due tosediment load deposition, costs could be increasing dueto inflation, wastewater effluent discharges could bechanging due to changes in populations and/or waste-water treatment capacities, and so on.

Simulation models can also vary in the way they aresolved. Some use purely analytical methods while othersrequire numerical ones. Many use both methods, asappropriate.

Finally, models can also be distinguished according tothe questions being asked and the level of informationdesired. The type of information desired can range fromdata of interest to policy-makers and planners (requiringrelatively simple models and broader in scope) to that ofinterest to researchers desiring a better understandingof the complex natural, economic and social processestaking place (requiring much more detailed models andnarrower in scope). Water management and operational

models (for real-time operations of structures, for exam-ple) and event-based calamity models are somewherebetween these two extremes with respect to model detail.The scope and level of detail of any modelling study willalso depend on the time, money and data available forthat study (see Chapter 2).

3.5.2. Types of Optimization Models

There are many ways to classify various types of con-strained optimization models. Optimization models can

be deterministic or probabilistic, or a mixture of both.They can be static or dynamic with respect to time. Manywater resources planning and management models arestatic, but include multiple time periods to obtain astatistical snapshot of various impacts in some planningperiod. Optimization models can be linear or non-linear.They can consist of continuous variables or discrete orinteger variables, or a combination of both. But whatever



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type they are, they have in common the fact that they aredescribing situations where there exist multiple solutionsthat satisfy all the constraints, and hence, there is thedesire to find the best solution, or at least a set of verygood solutions.

Regardless of the type of optimization model, they all

include an objective function. The objective function ofan optimization model (such as Equation 3.11 in theexample problem above) is used to evaluate multiplepossible solutions. Often multiple objective functionsmay be identified (as will be discussed in Chapter 10). Butat least one objective must be identified in all optimizationmodels. Identifying the best objective function is often achallenging task.

Optimization models can be based on the particulartype of application, such as reservoir sizing and/or opera-tion, water quality management, or irrigation develop-ment or operation. Optimization models can also beclassified into different types depending on the algorithmto be used to solve the model. Constrained optimizationalgorithms are numerous. Some guarantee to find thebest model solution and others can only guarantee locallyoptimum solutions. Some include algebraic mathematicalprogramming methods and others include deterministicor random trial-and-error search techniques. Mathematicalprogramming techniques include Lagrange multipliers,linear programming, non-linear programming, dynamic

programming, quadratic programming, fractional pro-gramming and geometric programming, to mention afew. The applicability of each of these as well as otherconstrained optimization procedures is highly dependenton the mathematical structure of the model. The follow-ing Chapter 4 illustrates the application of some ofthe most commonly used constrained optimization tech-niques in water resources planning and management.These include classical constrained optimization usingcalculus-based Lagrange multipliers, discrete dynamicprogramming, and linear and non-linear programming.

Hybrid models usually include multiple solutionmethods. Many generic multi-period simulation modelsare driven by optimization methods within each timeperiod. (The CALSIM II model used by the State ofCalifornia and the US Bureau of Reclamation to allocatewater in central California is one such model.)

Each of a variety of optimization modelling typesand solution approaches will be discussed and illustrated

in more detail in subsequent chapters. In some cases,can use available computer programs to solve optimtion models. In other cases, we may have to write own software. To make effective use of optimization, even simulation, models one has to learn some mosolution methods, since those methods often dictate

type of model most appropriate for analysing a particplanning or management problem or issue.

To date, no single model type or solution procedhas been judged best for all the different types of issand problems encountered in water resources plannand management. Each method has its advantages limitations. One will experience these advantages limitations as one practices the art of model developmand application.

4. Model Development

Prior to the selection or development of a quantitasimulation model, it is often useful to develop a conctual one. Conceptual models are non-quantitative repsentations of a system. The overall system structurdefined but not all its elements and functional relatiships.

Figure 3.7 illustrates a conceptual model, withindicating what each box represents, defining relati

ships between what land and water managers can do the eventual ecological impacts of those actions.

Once a conceptual model has been quanti(expressed in mathematical terms), it becomes a mamatical model. The models equations typically inclstate and auxiliary variables, parameters and other mocomponents.

The values of the models parameters need to be demined. Model calibration involves finding the best vafor these parameters. It is based on comparisons of model results with field measurements. Optimiza

methods can sometimes be used to identify the valueall model parameters. This is called model calibrationidentification. (Illustrations of the use of optimizationestimating model parameter values are containedChapters 4 and 6).

Sensitivity analysis (Chapter 9) may serve to identhe impacts of uncertain parameter values and shwhich parameter values substantially influence



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models results. Following calibration, the remaininguncertainties in the model predictions may be quantifiedin an uncertainty analysis as discussed in Chapter 9.

In addition to being calibrated, simulation models

should also be validated or verified. In the validation orverification process the model results are compared withan independent set of measured observations that werenot used in calibration. This comparison is made to verifywhether or not the model describes the system behavioursufficiently correctly.

5. Managing Modelling Projects

There are some steps that, if followed in modelling

projects, can help reduce potential problems and lead tomore effective outcomes. These steps are illustrated inFigure 3.8 (Scholten et al., 2000).

Some of the steps illustrated in Figure 3.8 may notbe relevant in particular modelling projects. If so, theseparts of the process can be skipped. Each of thesemodelling project steps is discussed in the next severalsections.


5.1. Creating a Model Journal

One common problem of model studies once they areunderway occurs when one wishes to go back over a

series of simulation results to see what was changed, whya particular simulation was made or what was learned. Itis also commonly difficult if not impossible for thirdparties to continue from the point at which any previousproject terminated. These problems are caused by a lackof information on how the study was carried out. Whatwas the pattern of thought that took place? Which actionsand activities were carried out? Who carried out whatwork and why? What choices were made? How reliableare the end results? These questions should be answerableif a model journal is kept. Just like computer-programming

documentation, this study documentation is oftenneglected under the pressure of time and perhaps becauseit is not as interesting as running the models themselves.

5.2. Initiating the Modelling Project

Project initiation involves defining the problem to bemodelled and the objectives that are to be accomplished.

land and water management practices and policies

hydrological consequences

ecosystem habitat & function impacts

impacts on specific species

E020

110t

Figure 3.7. An example of a

conceptual model without its

detail, showing the cause andeffect links between

management decisions and

specific system impacts.



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There can be major differences in perceptions betweenthose who need information and those who are going toprovide it. The problem as stated is often not the prob-

lem as understood by either the client or the modeller. Inaddition, problem perceptions and modelling objectivescan change over the duration of a modelling project.

The appropriate spatial and time scales also need to beidentified. The essential natural system processes must beidentified and described. One should ask and answerthe question of whether or not a particular modellingapproach, or even modelling in general, is the best way toobtain the needed information. What are the alternativesto modelling or a particular modelling approach?

The objective of any modelling project should be

clearly understood with respect to the domain and theproblem area, the reason for using a particular model,the questions to be answered by the model, and thescenarios to be modelled. Throughout the project theseobjective components should be checked to see if anyhave changed and if they are being met.

The use of a model nearly always takes place within abroader context. The model itself can also be part of a

larger whole, such as a network of models in which mare using the outputs of other models. These conditimay impose constraints on the modelling project.

Proposed modelling activities may have to be justiand agreements made where applicable. Any client at time may wish for some justification of the model

project activities. Agreement should be reached on hthis justification will take place. Are intermediate reprequired, have conditions been defined that will indian official completion of the modelling project, is vecation by third parties required, and so on? It is partlarly important to record beforehand the events or tiwhen the client must approve the simulation resuFinally, it is also sensible to reach agreements with respto quality requirements and how they are determior defined, as well as the format, scope and contentmodelling project outputs (data files) and reports.

5.3. Selecting the Model

The selection of an existing model to be used in any pect depends in part on the processes that will be mode(perhaps as defined by the conceptual model), the davailable and the data required by the model. The avable data should include system observations for comison of the model results. They should also inclestimates of the degree of uncertainty associated w

each of the model parameters. At a minimum this monly be estimates of the ranges of all uncertain paramvalues. At best it could include statistical distributionthem. In this step of the process it is sufficient to knwhat data are available, their quality and completenand what to do about missing or outlier data.

Determining the boundaries of the model is an esstial consideration in model selection. This defines whto be included in a model and what is not. Any moselected will contain a number of assumptions. Thassumptions should be identified and justified, and l

tested.Project-based matters such as the computers to

used, the available time and expertise, the modellers psonal preferences, and the clients wishes or requiremmay also influence model choice. An important practcriterion is whether there is an accessible manual operating the model program and a help desk availabladdress any possible problems.

report model results

step 7

interpret model results

implement the model

analyse the model

select the model

initiate modeling project

establish project journal

step 6

step 5

step 4

step 3

step 2

step 1

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Figure 3.8. The modelling project process is an iterative

procedure involving specific steps or tasks.



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The decision to use a model, and which model to use,is an important part of water resources plan formulation.Even though there are no clear rules on how to selectthe right model to use, a few simple guidelines can bestated:

Define the problem and determine what information isneeded and what questions need to be answered.

Use the simplest method that will yield adequate accu-racy and provide the answer to your questions.

Select a model that fits the problem rather than tryingto fit the problem to a model.

Question whether increased accuracy is worth theincreased effort and increased cost of data collection.(With the advances in computer technology, compu-tational cost is rarely an issue except perhaps for somegroundwater management problems.)

Do not forget the assumptions underlying the modelused and do not read more significance into the simu-lation results than is actually there.

5.4. Analysing the Model

Once a modelling approach or a particular model hasbeen selected, its strengths and limitations should bestudied in more detail. The first step is to set up a plan fortesting and evaluating the model. These tests can includemass (and energy) balance checks and parameter sensitivity

analyses (see Chapter 9). The model can be run underextreme input data conditions to see if the results are asexpected.

Once a model is tested satisfactorily, it can be cali-brated. Calibration focuses on the comparison betweenmodel results and field observations. An important prin-ciple is: the smaller the deviation between the calculatedmodel results and the field observations, the better themodel. This is indeed the case to a certain extent, asthe deviations in a perfect model are only due to measure-ment errors. In practice, however, a good fit is by no

means a guarantee of a good model.The deviations between the model results and the field

observations can be due to a number of factors. Theseinclude possible software errors, inappropriate modellingassumptions such as the (conscious) simplification ofcomplex structures, neglect of certain processes, errors inthe mathematical description or in the numerical methodapplied, inappropriate parameter values, errors in input


data and boundary conditions, and measurement errorsin the field observations.

To determine whether or not a calibrated model isgood, it should be validated or verified. Calibratedmodels should be able to reproduce field observations notused in calibration. Validation can be carried out for

calibrated models as long as an independent data set hasbeen kept aside for this purpose. If all available data areused in the calibration process in order to arrive atthe best possible results, validation will not be possible.The decision to leave out validation is often a justifiableone especially when data are limited.

Philosophically, it is impossible to know if a model ofa complex system is correct. There is no way to prove it.Experimenting with a model, by carrying out multiplevalidation tests, can increase ones confidence in thatmodel. After a sufficient number of successful tests, onemight be willing to state that the model is good enough,based on the modelling project requirements. The modelcan then be regarded as having been validated, at least forthe ranges of input data and field observations used in thevalidation.

If model predictions are to be made for situations orconditions for which the model has been validated, onemay have a degree of confidence in the reliability of thosepredictions. Yet one cannot be certain. Much less confi-dence can be placed on model predictions for conditions

outside the range for which the model was validated.While a model should not be used for extrapolations

as commonly applied in predictions and in scenarioanalyses, this is often exactly the reason for the modellingproject. What is likely to happen given events we have notyet experienced? A models answer to this questionshould also include the uncertainties attached to thesepredictions. Beck (1987) summarized this dilemma in thefollowing statement: using scientifically based models,you will often predict an incorrect future with great accu-racy, and when using complex, non-identifiable models,

you may be capable of predicting the correct future withgreat uncertainty.

5.5. Using the Model

Once the model has been judged good enough, it may beused to obtain the information desired. One shoulddevelop a plan on how the model is to be used, identifying



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the input to be used, the time period(s) to be simulated,and the quality of the results to be expected. Again, closecommunication between the client and the modeller isessential, both in setting up this plan and throughout itsimplementation, to avoid any unnecessary misunderstand-ings about what information is wanted and the assump-

tions on which that information is to be based.Before the end of this model-use step, one should

determine whether all the necessary model runs havebeen performed and whether they have been performedwell. Questions to ask include:

Did the model fulfill its purpose? Are the results valid? Are the quality requirements met? Was the discretization of space and time chosen well? Was the choice of the model restrictions correct?

Was the correct model and/or model program chosen? Was the numerical approach appropriate? Was the implementation performed correctly? Are the sensitive parameters (and other factors) clearly

identified? Was an uncertainty analysis performed?

If any of the answers to these questions is no, then thesituation should be corrected. If it cannot be corrected,then there should be a good reason for this.

5.6. Interpreting Model Results

Interpreting the information resulting from simulationmodels is a crucial step in a modelling project, especiallyin situations in which the client may only be interested inthose results and not the way they were obtained. Themodel results can be compared to those of other similarstudies. Any unanticipated results should be discussedand explained. The results should be judged with respectto the modelling project objectives.

The results of any water resources modelling project

typically include large files of time-series data. Only themost dedicated of clients will want to read those files, sothe data must be presented in a more concise form.Statistical summaries should explicitly include anyrestrictions and uncertainties in the results. They shouldidentify any gaps in the domain knowledge, thus generat-ing new research questions or identifying the need formore field observations and measurements.

5.7. Reporting Model Results

Although the results of a model should not be the sole bfor policy decisions, modellers have a responsibilitytranslate their model results into policy recommendatioPolicy-makers, managers, and indeed the participa

stakeholders often want simple, clear and unambiguanswers to complex questions. The executive summary report will typically omit much of the scientifically justidiscussion in its main body regarding, say, the uncertties associated with some of the data. This execusummary is often the only part read by those responsfor making decisions. Therefore, the conclusions of model study must not only be scientifically correct complete, but also concisely formulated, free of jargand fully understandable by managers and policy-makThe report should provide a clear indication of

validity, usability and any restrictions of the model resuThe use of visual aids, such as graphs and GIS, can be vhelpful.

The final report should also include sufficient detaallow others to reproduce the model study (includingresults) and/or to proceed from the point where this stended.

6. Issues of Scale

Scaling aspects play an important role in many modelprojects. Four different types of scales can be disguished: the process scale, the information scale, model scale and the sampling scale. Each of thesdiscussed below.

6.1. Process Scale

Most hydrological processes vary over space and tiThe scale on which the process variations manifest thselves is referred to as the process scale. Spatially, pro

scale can vary from the movement of small granulesediment, for example, to the flooding of large river baor coastal zones. All kinds of intermediary scale procecan be found, such as drainage into ditches of runoff frparcels of land, transport of sediment in brooks and fmovements in aquifers.

Various temporal scales can also be distinguishvarying from the intensity of rain in less than a minut



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the change in landscape in geological time. Many processdescriptions require a spectrum of scales. Such is the case,for example, in the simulation of interdependent surfaceand groundwater quantity and quality processes takingplace in a watershed.

6.2. Information Scale

Information scale is the spatial and temporal scale of theinformation required. Generally, a strategic water resourcesmanager (for example the local, regional or nationalgovernment) needs information on a scale relative to theirresponsibilities and authorities. This level of information islikely to differ from the level desired by operational watermanagers dealing with day-to-day issues.

Information at scales smaller than what is needed isseen as being noise. Information at scales larger thanwhat is needed is not relevant or helpful. For localorganizations (e.g., water boards) concerned with runoff,for example, there is no need to collect information onindividual raindrops. The important spatial variancesare usually within a range varying from hundreds ofmetres to hundreds of kilometres. Larger-scale variations(differences between precipitation in the Netherlandsand Russia or between North and South America, forexample) are rarely if ever relevant. The informationscale depends on the task set for the water planner or

manager.

6.3. Model Scale

Model scales refer to their spatial and temporal discretiza-tion. The model scales determine the required data inter-polation and aggregation.

If the temporal and spatial scales of the problem havenot been defined clearly enough, this can affect the laterphases of the modelling process negatively. If the modelscale chosen is too large, this may result in too general a

schematization and relevant details might not be derivedfrom the results. If the chosen model scale is too small,irrelevant small-scale variations can lead to non-optimalcalibrations for the large-scale variations.

In large, spatially distributed models in particular, it isvital that the scale and the number of independentparameters (degrees of freedom) are chosen on the basisof the available data. If too many parameters are included


in a model, there is a risk of it appearing to work well butbeing unsuitable for interpolation or prediction. This canactually only be determined if adequate measuring dataare available having a measurement frequency at leastequal to the chosen modelling time step. This must betaken into account when selecting or constructing themodel, as there is otherwise the risk that the modelcannot be calibrated adequately.

6.4. Sampling Scale

Sampling scale is the scale at which samples are taken.The sampling spatial scale can vary from point observa-tions (for example, a temperature measurement at acertain location at a certain time) to area observations(using, for example, remote sensing images). The densityof the measuring network and the sampling or measuring

and recording frequency determine the sampling spatialand temporal scales.

6.5. Selecting the Right Scales

Modellers must choose the model scale in such a mannerthat the model provides information at the requiredinformation scale, taking into account the process scalespresent, in combination with the spatial and temporalsampling scales. It is possible that situations will occurthat are impossible to model just because of these scale

issues.The relationship between the types of scales is repre-

sented in Figure 3.9. The relative level of detail is given onthe horizontal axis, from considerable detail on the left tomuch less detail on the right.

To show that the various types of scales may not bemutually compatible, consider the following threeexamples.

sampling

scale

small scale

process

scale

information

scale

large scale

E020

110

v

Figure 3.9. Relationships among various scale types.



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Example 1: The information scale is different from the processscale

Water resources planning studies are typically carried outat a river basin or watershed scale. From a hydrological(process) point of view, this makes sense because it enablesa comprehensive analysis (including upstream and down-stream impacts), makes it easier to develop a water balancefor the study area, and reduces the amount of informationneeded at the borders of the study area. However, mostdecision-makers are not interested in results at river basinor watershed scale; they want to know what these resultsmean for their province, municipality or city. This conflictof scales can be solved by a well-considered selection of the(sub)watersheds that will be considered in the study and apost-processor that translates the results at these processscales into the required administrative scales.

Example 2: The information scale is smaller than the processscale

Imagine that a water resources manager wants to evaluatealternative anti-dehydration measures on the groundwaterlevel over a period of five years. Thus the requiredinformation scale is a five-year period. However, thegroundwater level is characterized by a very slow response.The relevant temporal groundwater-level process scale isaround fifteen to twenty years. Whatever managementalternative is implemented, it will take fifteen to twenty

years to determine its impact. Thus, regardless of the choiceof measuring frequency (sampling scale) and the modelscale, it is impossible within the five-year period of interestto arrive at information on the groundwater-level changes asa consequence of anti-dehydration measures.

Example 3: The sampling scale is larger than the process scaleand information scale

Assume it is necessary to estimate the change in concen-trations of certain substances in the soil and groundwaterin an urban area. The information spatial scale is one to

two decimetres. This corresponds to the spatial variationof cohesion processes that take place in the soil andgroundwater aquifer. However, logistic and budgetaryconsiderations make it impossible to increase the spatialsampling density to less than a measurement site everyfew hundred metres. As the spatial sampling scale ismuch larger than the spatial process scale, useful inter-polations cannot be made.

7. Conclusions

This chapter has reviewed some basic types of models presented guidelines for consideration when undertaka modelling project. Generic models for water resousystem analyses are increasingly becoming available, savmany organizations that need model results from havindevelop their own individual models. While many readerthis book may get involved in writing their own modmost of those involved in water resources planning and magement will be using existing models and analysing presenting their results. The information provided in chapter is intended to help model users plan and maneffective modelling projects as well as improve the repducibility, transferability and usefulness of model results

8. References

BECK, M.B. 1987. Water quality modeling: a reviewthe analysis of uncertainty. Water Resources ReseaNo. 23, pp. 13931442.

SCHOLTEN, H.; WAVEREN, R.H. VAN; GROOT,GEER, F.C. VAN; WSTEN, J.H.M.; KOEZE, R.D. NOORT, J.J. 2000. Good modelling practice in water manment, proceedings hydroinformatics 2000. Cedar Rapids, IoInternational Association for Hydraulic Research.

Additional References (Further Reading)

ABBOTT, M.B. 1999. Introducing hydroinformatJournal of Hydroinformatics, Vol. 1, No. 1, pp. 320.

BISWAS, A.K. (ed.). 1997. Water resources: environmeplanning, management, and development. New YoMcGraw-Hill.

BOBBA, A., GHOSH, S.; VIJAY, P. and BENGTSSON2000. Application of environmental models to diffehydrological systems. Ecological Modelling, Vol. 1pp. 1549.

BOOCH, G. 1994. Object-oriented analysis with apptions. Redwood City, Benjamin Cummings.

CHAN, H.W. and LAM, P.F. 1997. Visualizing Input output analysis for simulation. Simulation Practice Theory, Vol. 5, No. 5, pp. 42553.



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EDSALL, R.M.; HARROWER, M. and MENNIS, J.L. 2000.Tools for visualizing properties of spatial and temporalperiodicities in geographic data. Computers & Geosciences,

Vol. 26, No. 1, pp. 10918.

FEDRA, K. and JAMIESON, D.G. 1996. An object-orientedapproach to model integration: a river basin informationsystem example. In: K. Kowar and H.P. Nachtnebel (eds.),Proceedings of the HydroGIS96 Conference, No. 235,

Vienna, IAHS Press. pp. 66976.

GUARISO, G. and WERTHNER, H. 1989. Environmentaldecision support systems. New York, Ellis Horwood-Wiley.

HO, J.K.K. and SCULLI, D. 1997. The scientific approachto problem solving and decision support systems.International Journal of Production Economics, Vol. 48,No. 3, pp. 24957.

HUFSCHMIDT, M.M. and FIERING, M.B. 1966. Simulationin the design of water resource systems. Cambridge, Mass.,Harvard University Press.

LAM, D.C.L.; MAYFIELD, C.I. and SAWYNE, D.A. 1994.A prototype information system for watershed manage-ment and planning. Journal of Biological Systems, Vol. 2,No. 4, pp. 499517.

LAM, D. and SWAYNE, D. 2001. Issues of EIS softwaredesign: some lessons learned in the past decade. Environ-mental Modeling and Software, Vol. 16, No. 5, pp. 41925.

LAW, A.M. and KELTON, W.D. 2000. Simulation modelingand analysis, 3rd edn. Boston, Mass., McGraw-Hill.

LOUCKS, D.P.; STEDINGER, J.S. and HAITH, D.A. 1981.Water resources systems planning and analysis. EnglewoodClifts, N.J., Prentice Hall.

MAASS, A.; HUFSCHMIDT, M.M.; DORFMAN, R.;THOMAS, H.A.; MARGLIN, S.A. and FAIR, G.M. 1966.Design of water resources systems. Cambridge, UK, HarvardUniversity Press.

REITSMA, R.F. and CARRON, J.C. 1997. Object-orientedsimulation and evaluation of river basin operations.Journal of Geographic Information and Decision Analysis,Vol. 1, No. 1, pp. 924.

RIZZOLI, A.E. and YOUNG, W.J. 1997. Deliveringenvironmental decision support systems: software toolsand techniques. Environmental Modeling & Software,

Vol. 12, No. 23, pp. 23749.


RIZZOLI, A.E.; DAVIS, J.R. and ABEL, D.J. 1998. Modeland data integration and re-use in environmental decisionsupport systems. Decision support systems, Vol. 24, No. 2,pp. 12744.

SARGENT, R.G. 1982. Verification and validation ofsimulation models. In: F.E. Cellier (ed.), Progress inmodelling and simulation, pp. 15969. London andelsewhere, Academic Press.

SARGENT, R.G. 1984a. A tutorial on verification andvalidation of simulation models. In: S. Sheppard,U. Pooch and D. Pegden (eds.), Proceedings of the 1984winter simulation conference, pp. 11521. Piscataway, N.J.,Institute of Electrical and Electronics Engineers.

SARGENT, R.G. 1984b. Simulation model validation. In:T.I. ren, B.P. Zeigler and M.S. Elzas (eds.), Simulation and

model-based methodologies: an integrative view, pp. 53755.Berlin and elsewhere, Springer-Verlag (No. 10 in the series:NATO ASI Series F: Computer and Systems Sciences).

SINGH, V.P. (ed.). 1995. Computer models of watershedhydrology. Littleton, Colo., Water Resources Publications.

SUN, L. and LIU, K. 2001. A method for interactive artic-ulation of information requirements for strategic decisionsupport. Information and Software Technology, Vol. 43,No. 4, pp. 24763.

VAN WAVEREN, R.H.; GROOT, S.; SCHOLTEN, H.;VAN GEER, F.C.; WSTEN, J.H.M.; KOEZE, R.D. andNOORT, J.J. 1999. Good modelling practice handbook: STOWAreport 9905. Lelystad, the Netherlands, Dutch Dept. ofPublic Works, Institute for Inland Water Management and

Waste Water Treatment (report 99.036).

YOUNG, P. 1998. Data-based mechanistic modeling ofenvironmental, ecological, economic and engineeringsystems. Environmental Modeling & Software, Vol. 13,pp. 10522.

YOUNG, W.J.; LAM, D.C.L.; RESSEL, V. and WONG,J.W. 2000. Development of an environmental flowsdecision support system. Environmental Modeling &Software, Vol. 15, pp. 25765.

ZEIGLER, B.P. 1976. Theory of modelling and simulation.Malabar, Fla, Robert E. Krieger.

ZEILER, M. 1999. Modeling our world: the ESRI guide togeodatabase design. Redlands, Calif., ESRI.



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