Decision Support System Mine -The Management Model

NOT FOR QUOTATION WITHOUT PERMISSION OF THE AUTHOR

DECISION SUPPORT SYSTEM MINE

-

THE MANAG-NT MODEL

S. Kaden I. Michels K. Tiemer

February

1

986 CP-86-9

Cbllaborative P a p e r s r e p o r t work which has not been performed solely

at

t h e International Institute f o r Applied Systems Analysis and which has received only limited review. Views o r opinions expressed h e r e i n do not necessarily r e p r e s e n t those of t h e Insti- tute, i t s National Member Organizations, o r o t h e r organizations supporting t h e work.

INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS 2361 Laxenburg, Austria

PREFACE

The Regional Water Policies project of IIASA

w a s

focused on inten- sively developed regions where both groundwater and s u r f a c e

water

r e s o u r c e s are integrating elements of t h e environment. The r e s e a r c h w a s directed towards t h e development of methods and models

to

support t h e resolution of conflicts within such socio-economic environmental systems.

For t h a t reason Decision Support Systems have been developed and imple- mented for important

test

areas.

The complex problems of such regional policy analysis

are

not

tract-

able in one model using any of existing computational methods. That is why

a

heuristic two-level model approach has been applied. Simplified first-level models t o g e t h e r with interactive procedures f o r multi-criteria analysis are used f o r screening analysis of rational long-term policies. The more comprehensive second-level models s e r v e f o r t h e verification and specifi- cation of t h e r e s u l t s of screening analysis. They a r e used

to

check t h e managerial feasibility of estimated strategies.

One of o u r

case

studies deals with open-pit lignite mining

areas.

The developed Decision Support System MINE has been implemented for

a test

region in t h e Lusatian Lignite District of t h e GDR. The p a p e r describes t h e approaches f o r t h e second-level models (Management Model) of t h a t DSS.

This r e s e a r c h h a s been done within t h e framework of a collaborative agree- ment between IIASA and t h e Institute for

Water

Management in Berlin. This p a p e r i s t h e final r e p o r t for t h e third (last) stage of collaboration.

Sergei Orlovski P r o j e c t Leader

Regional

Water

Policies P r o j e c t

ABSTRACT

The Decision Support System MINE has been developed f o r t h e analysis of regional water policies in open-pit lignite mining

areas.

I t is based on

a

two-level model approach. The first-level p l a n n i n g model is used f o r t h e estimation of rational s t r a t e g i e s of long-term development applying dynamic multi-criteria analysis. Therefor simplified submodels

are

used for

a

rough time discretization (yearly time s t e p s and l a r g e r ) . The second-level management model considers managerial/operational a s p e c t s f o r s h o r t e r time s t e p s (monthly and yearly) employing more comprehensive submodels.

I t i s a classic simulation model. For selected submodels stochastic simulation (Monte Carlo method) is used in o r d e r t o consider random inputs (e.g.

hydrological inflow and

water

demand). This model serves for t h e verifica- tion of s t r a t e g i e s obtained in t h e planning model, f o r t h e verification of simplified submodels used in t h e first-level model, and for t h e specification of strategies.

Starting with t h e description of t h e position of t h e management model within t h e DSS MINE t h e s t r u c t u r e of t h e management model is given. The used submodels f o r s u r f a c e water/groundwater interaction and

water

qual- ity are described. In t h e Appendix computer subroutines of

some

submodels are given being suitable for a

more

general application.

CONTENTS

1. Introduction

1.1 Background and Objectives f o r t h e DSS MINE 1.2 General S t r u c t u r e of t h e DSS MINE

1.3 The GDR Test Area

2. Stochastic Simulation of Management S t r a t e g i e s 2.1 Basics

2.2 Stochastic simulation of input d a t a 2.1.1 Hydrological inflow

2.1.2 Water demand 2.3 Management r u l e s

2.3.1 Balancing of

water

u s e r s 2.3.2 Remaining p i t management 2.4 Simulation of systems development

2.4.1 Remaining pit submodel 2.4.2 Infiltration submodel 2.4.3 Balance submodel

2.5 Monte Carlo simulation and statistical evaluation 2.6 Numerical

tests

3. Deterministic Simulation of Long-term Policies References

Appendix

1. SUBROUTINE REMPIT

-

remaining pit submodel of t h e management model 2. SUBROUTINE INFI

-

infltration submodel of t h e management model 3. SUBROUTINE BALANC

-

balanc submodel of t h e management model

DECISION SUPPORT S Y S T M

-

THE MANAGEMENT MODEL

S.

ade en',

I.

h!ichels2 and

K.

~ i e m e r '

1. I n t r o d u c t i o n

1.1. Background and

Objectives f o r

the

_DSS JllINE

Regions with open-pit lignite mining a r e characterized by complex and grave interactions in the socio-economic environmental system with special regard t o groundwater and surface water resources. To illustrate this f o r the German Demo- cratic Republic as t h e country with t h e greatest lignite production (about one third of t h e world production):

1.

The annual output of lignite amounts t o more then

³⁰⁰

mill. tons/annum.

Thereby

it is

necessary t o pump out more then

1.7

bill. mg/annum water f o r dewatering t h e open-pit mines. This amounts t o about

^20% of

t h e stable runoff of the 'whole country.

2.

The dewatering results in regional cone shaped groundwater depressions and consequently in extensive changes of the hydrological regime and of t h e con- ditions f o r water resources use and management, also in down-stream r i v e r basins.

- Infiltration losses of s&face water caused by mine dewatering reduce t h e water supply f o r down-stream water users and increase t h e groundwater pumpage necessary f o r dewatering

of

t h e lignite mines.

- significant alterations of natural groundwater recharge

are

caused by t h e extensive changes of geographical and ecological conditions in open-pit mining

areas.

For example, t h e natural groundwater r e c h a r g e of

a

typical agricultural a r e a is changing under t h e climatic conditions of t h e GDR from about

²⁰⁰

mm/yr. up t o

⁴⁰⁰

mm/yr., Kaden et

al.

1 9 8 5 ~ .

')~nternational I n s t i t u t e f o r Applied S y s t e m s A n a l y s i s Laxenburg, Austria q n s t i t u t e f o r Water Management, Berlin, CDR

-

The rate of

water

pumped from t h e mining area into t h e s u r f a c e

water

system amounts t o about 30-50 % of t h e total r i v e r discharge (70% under low flow conditions).

3. In lignite mining areas t h e groundwater quality and consequently t h e quality of mine drainage water, as well as t h e water quality in remaining pits i s strongly affected by t h e oxidation of f e r r o u s minerals (e.g. pyrite) in t h e sub- soil. With t h e n a t u r a l groundwater r e c h a r g e t h e oxidation products

are

flushed out, and t h e percolated

water

becomes v e r y acid. Consequently t h e acidity of t h e groundwater increases. In t h e post-mining period t h e

same

effect o c c u r s by t h e raising of groundwater t a b l e and t h e leaching of acid products.

From t h e mentioned processes caused by open-pit lignite mining originate signifi- cant conflicts between different i n t e r e s t groups. Figure 1 illustrates t h e most important interdependencies between

water

u s e r s and t h e

water

r e s o u r c e s subsys-

t e m s

in a n impact diagram.

Nature

'y-L-y'

Figure 1: Water r e s o u r c e s impact diagram f o r lignite mining regions

Due t o t h e complexity of t h e socio-economic environmental prooesses in mining a r e a s , t h e design

of

regional water policies and

water

use technologies

as

w e l l as mine drainage can only done properly based on a p p r o p r i a t e mathematical models.

From a c r i t i c a l analysis of t h e state-of-the-art of modeling in lignite mining areis i t h a s been concluded, t h a t above a11 methods and models are r e q u i r e d t o s u p p o r t t h e analysis and implementation of r a t i o n a l long-term r e g i o n a l w a t e r policies in open-pit lignite mining a r e a s , t o achieve a p r o p e r balance between economic

welfare and t h e

state

of t h e environment, Kaden

et

al. 1985b.

Towards t h a t goal t h e r e s e a r c h of t h e Regional Water Policies p r o j e c t of IIASA, in collaboration with r e s e a r c h institutes in t h e GDR, and in Poland, in t h e period 1984-1985

w a s

directed. One of i t s major products i s t h e

Decision

Support

System MINK see Kaden

et

al. 1985a, 1985c, Kaden 1986.

1.2.

General Structure of

the

DSS MINE

The analysis of regional

water

policies in mining regions i s a problem of dynamic multi-criteria choice. I t i s embedded in a complicated policy making pro- cess. An advanced system of decision aids i s needed which allows:

-

t o consider t h e controversy among different water u s e r s and i n t e r e s t groups,

-

t o include multiple c r i t e r i a some of which c a n not b e evaluated quantitatively,

-

t o t a k e into t h e account t h e uncertainty and t h e stochastic c h a r a c t e r of t h e system inputs

as

w e l l as t h e limited possibilities t o analyze all t h e decisive n a t u r a l and socibeconomic p r o c e s s e s and impacts,

-

t o o f f e r a

set

of decision alternatives, demonstrating t h e n e c e s s a r y trade-offs between d i f f e r e n t

water

u s e r s and i n t e r e s t groups.

A t p r e s e n t no mathematical methods are available o r p r a c t i c a l applicable consid- e r i n g all t h e s e problems in o n e single model. E.g. t h i s holds

true

f o r a n y nonlinear stochastic multi-criteria analysis. Cmly hierarchic& model systems c a n satis*

all requirements.

In general, dynamic problems of regional

water

management

are

approached by time-discrete dynamic systems models. The step-size and t h e available mathematical methods are t h e s t r u c t u r a l f a c t o r s of t h e n e c e s s a r y model h i e r a r - chy. Frequently a l r e a d y

a

two-level m o d e l h i e r a r c h y satisfies most requirements.

F o r t h e D S S MINE such a two-level system h a s been realized, combining

a

f i r s t - level Planning Model with

a

second-level Management Model.

The first-level Planning Model realizes a dynamic multi-criteria analysis f o r a relatively small number of planning periods , j 4 , .

. .

^,J

^as

t h e time s t e p f o r principal

management/technological

decisions. The time s t e p depends on t h e vari- ability in time of r e l e v a n t processes, on t h e r e q u i r e d c r i t e r i a and t h e i r reliability, and o n t h e frequency of decisions. A s

a

compromise between a c c u r a c y and both, d a t a p r e p a r a t i o n and computational e f f o r t , f o r t h e D S S MINE v a r i a b l e time s t e p s

are

used, s t a r t i n g with o n e y e a r and increasing with time up t o 15 y e a r s . This h a s been done taking into account t h e uncertainties in predicting model inputs and t h e r e q u i r e d a c c u r a c y of model r e s u l t s , decreasing with time.

The planning m o d e l s e r v e s f o r t h e estimation of rational s t r a t e g i e s of long-

term

systems development. These s t r a t e g i e s

are

selected by multi-criteria analysis considering a number of criteria. The c r i t e r i a have t o ' b e chosen from a given

set

of indicators, e.g. c o s t of water supply, cost of mine drainage, satisfaction of

water

demand and environmental requirements. These indicators

are

assumed t o b e integral values o v e r t h e whole planning horizon.

In Figure 2 a block scheme of t h e planning model i s given. According t o t h e Figure t h e systems

state

i s c h a r a c t e r i z e d by state variables depending on previ- ous systems

state

and by state descriptive parameters. The

latter are

auxiliary p a r a m e t e r s with r e s p e c t t o t h e multi-criteria analysis but although r e s u l t s of t h a t analysis being of i n t e r e s t f o r t h e m o d e l user. The

state

variables are t r e a t e d

as

control variables (decis!ons) in t h e multi-criteria analysis.

Indiators of systems dowlopmsnt O(

...,

l(j),D(j),Sv(j),Sd(j)

,..-

¹

<

m x 0

--.. ^-.-.

Hydrological/socio- economic input

I ( i )

Figure 2: Block schema of t h e planning model

I

With t h e purpose of a unified model being independent on t h e chosen c r i t e r i a all indicators are bounded and t r e a t e d

as

constraints. Based on t h a t t h e following multi-criteria problem f o r a s u b s e t Ol L EL of t h e indicators 0 ( Q

, , L

=I,.

. . ^,L)

^{i s}

defined:

Or

=

Minimum !

L

EL,^ (1.1) s u b j e c t

to

inequality constraints

0 s maxO (1.2)

& ( j ) S O , j = l ,

...,

J equality constraints

C , , ( j )

=

0 , j = 1 ,

...,

^J

&(j)

-mu) =

^{0 ,} j = 1 ,

...,

J bounds

b j -1

The planning model as a first-level screening model i s based on a s e r i e s of more

o r

less s t r o n g simplifications in o r d e r

to

obtain a manageable system being suitable f o r multi-criteria analysis. The major simplifications a r e :

+

Staeoftbsyrtem

State descriptive parameters Sd(jl = fSd(j, I. D.SVI

4 7

S m variables j + . l +I '

+ ^t

r

Constraints

I

Decisions D ( j ) ; D,

t w

S,,W =fsV(i,sv(j

-

11, D ~ s ~ ) .

-

t h e discretization of t h e planning horizon into a small number of planning periods; all model data, e.g. decisions. s t a t e variables

are

assumed

to

be con- stant within t h e planning period,

-

t h e neglection of uncertainties in model inputs,

-

t h e application of simplified environmental submodels based on comprehensive models,

-

t h e neglection of relevant environmental subprocesses as t h e interaction between groundwater and surface

water

depending on t h e surface

water

table.

That i s why a second-level h a g e m e n t

Model

for t h e simulation of systems behavior f o r

a

l a r g e r number of smaller management periods (monthly and yearly time steps) is applied. I t is used

to

analyze managerial decisions by t h e help of sto- chastic simulation and

to

verify results obtained with t h e planning model.

In t h e given p a p e r t h e Management Model will be described in detail. This r e s e a r c h has been c a r r i e d out in t h e framework of t h e collaborative agreement between IIASA and t h e Institute f o r

Water

Management in Berlin, GDR.

1.3. The

GDR T e s t A r e a

The DSS MINE h a s been developed with special r e g a r d

to a test

region in t h e German Democratic Republic. It is a n about 500 kme large

area

in t h e Lusatian Lig- nite District. A detailed description is given in Kaden

et

al., 1985a. W e consider

a

planning horizon of 50 years, divided into 1 0 planning periods. In Figure 3

a

scheme of t h e

test

region i s depicted, illustrating t h e essential decisions on sys-

t e m s

development.

The following decisions are taken into t h e account (the indices are explained in Figure 3):

B.P

-

^flux

f r o m

a

to 6

C q a

-

supply of lime hydrate for water treatment

Atmd

-

duration of mine drainage mine D before starting i t s operation

maxh, -

^maximum

water

level in t h e remaining pit The systems s t a t e is characterized by t h e following parameters '1:

water table in t h e remaining pit

concentration of component 1 in t h e remaining pit L=I + f i e + , 1=2 -,

H +

s t o r a g e volume in t h e remaining pit.

groundwater flow

to

a

infiltration balance segment

As

a,p representative groundwater table

concentration of component

L

in t h e flow

to

a concentration of componerit

L

in drainage

water

a f t e r treatment

flux/

water

table

at

balance profile bp ^a concentration of component L in t h e flux through balance profile bp a

quantity of industrial waste water

concentration of component

L

in t h e industrial

waste water.

9

Paremetere t y p e d bold a r e s t a t e v a r i a b l e s o f t h e planning model.

Figure 3: Detailed scheme of t h e

test

region

We consider a planning horizon of 50 y e a r s , divided into 10 planning periods. The long-term development is above all determined by t h e mine drainage. This i s a con- tinuous process without relevant medium- and short-term (within t h e y e a r ) varia- tions. Therefor i t is assumed t h a t all decisions and systems descriptive values related

to

mine drainage are sufficiently described by mean values o v e r planning periods (or linear interpolated between planning periods).

The systems variability within t h e y e a r s r e s u l t s from t h e hydrological inflow into t h e region and t h e fluctuating water demand. In this case t h e r e l a t e d deci- sions, s t a t e variables and systems descriptive values depend on managerial a s p e c t s

to

b e considered o n a monthly basis within t h e management model. In t h e Figure 3

those parameters being of interest f o r t h e management model are special signed.

2. Stochastic Simulation of Management Strategies

2.1.

Basics

According t o t h e f i r s t simplifications t h e planning model considers principal

management/technological

decisions f o r estimated input values (expectation values). The feasibility of t h e estimated decisions is checked only in t h e mean f o r planning periods (by t h e help of constraints C,(j), C,, (j) and bounds, compare Eq. (1.2)-(1.4)).

Problems a r i s e if t h e principal decisions are superimposed by managerial decisions f o r s h o r t e r time intervals, depending on t h e actual partly random sys-

t e m s

development. This is especially typical f o r

water

demand/supply. Both, t h e models f o r t h e actual

water

demand, and f o r t h e available

water

r e s o u r c e s have t o consider autocorrelated and random components. The

water

demand has t o b e satisfied according t o its variations between and within y e a r s . I t i s not sufficient t o satisfy t h e water demand in t h e mean o v e r planning periods. E.g.

water

f o r sup- plementary irrigation is needed in t h e vegetation period but not even distributed o v e r t h e year.

Consider t h e

water

u s e r s l

,

l = I , .

. .

^,L with t h e water demand demr and t h e

water

supply supl. For t h e planning model t h e following c r i t e r i a i s used:

Result of t h e multi-criteria analysis is some rational supply s t r a t e g y [ s u p l ( j ) ,

1

=l

,...,

J , l =l

,...,L 1.

This strategy has t o b e transformed by a n a p p r o p r i a t e management r u l e into t h e actual

water

supply strategy f o r all month k in t h e y e a r s i , i d l . . . , I: [ s u p i ( i ,k ), i =1,

...

^{, I , k =1,}

...,

^{1 2}

1.

The common c r i t e r i a f o r t h e satisfaction of water demand - f o r long-term

water

management and planning i s as follows:

with i

-

y e a r , k

-

^month.

Now it has t o b e checked whether t h e strategy obtained based on c r i t e r i a (2.1) satisfies c r i t e r i a (2.2). And this i s t h e f i r s t task of t h e second-level management model. By t h e help of stochastic simulation based on t h e Monte Carlo method t h e j k a s i b i l i t y of s t r a t e g i e s

is

verified and t h e s t r a t e g i e s a r e statistically evaluated.

The model realizes t h e following steps:

1. Stochastic simulation of uncertain hydrological/socio-economic inputs, i.e.

inflow and water demand.

2. Simulation of monthly systems development based on stochastic inputs and management r u l e s considering rational s t r a t e g i e s estimated with t h e plan- ning model.

3. Statistical analysis of selected decisions,

state

variables, descriptive values and indicators f o r probabilistic assessment of t h e management strategy.

The statistical reliability of r e s u l t s depends on t h e number of realizations of t h e Monte Carlo simulations and t h e d e g r e e of influence of stochastic inputs. In most c a s e s 100 realizations should b e sufficient. Nevertheless t h e numerical e f f o r t is high. For t h e 50-years planning horizon in this case t h e simulation has t o b e done

f o r 60000 month.

This a s p e c t has

to

be considered in t h e model f o r stochastic simulation as i t i s illustrated in Figure 4.

Figure 4: Block scheme of t h e management model

p a r t 1

-

stochastic simulation of management s t r a t e g i e s

Hydrologiallcocio-

r ~ n o r n i c Input N m d k b l e uncmain hydro-

I U ) l o g l a l l ~ m i c input

O(i.k) =fO(l,k.O(i.k - 1)

....

¹

Only those decisions + ( i , k ) and submodels

are

included in t h e Monte Carlo simula- tion strongly depending on t h e stochastic inputs @ ( i ,k). For t h e remaining deci- sions, inputs and submodels t h e r e s u l t s of t h e planning model are used as mean values f o r planning periods. Based on t h e r e s u l t s of t h e planning model (decisions) a management ruLe

+ ( i , k )

=

^{~ (},k ,+(i ,k - i ) , @ ( i ,k - i ) , r ( i ,k -1)) ⁱ (2.3)

7

i s defined f o r t h e estimation of t h e m a n a g e r i a l d e c i s i o n s +(i ,k). Based on these decisions and t h e uncertain inputs O(i ,k ) t h e

state

variables r ( i , k ) are estimated ( f o r t h e management model is no need

to

distinguish between

state

variables and

state

descriptive parameters):

r ( i , k )

=

fI'(i,k,+(i,k), O ( i , k ) , r ( i , k ) , I ' ( i , k -1)

,...)

(2.4) Again, only those

state

^variables are considered strongly depending on uncertain inputs and managerial decisions.

7 -

--

Stne of nM rymm _,

4

period j

smte of the rynsm y w r i, month k State -@tire pnametora

Sd(jl = fSd(i.l.D,Sv)

Unwrtain nrbbbs

1 + 1 b

-

Deciriom D(I).D,

b W-nt ruln

W(i,k) =W(i,k,Wi.k

-

^ll,#(i,k - 1)

+

(i,k - 1))

+

ⁱ

.. . ...

-+

^i,k + ¹

-

--

r1i.k) = flYi,k,*,O,r[i.k), r(i,k - 1). ... ⁾

A i.k - 1-+

1 - 1

,

State warimbler

1

~ " ( 1 ) = ~ ~ ( l . s ~ f i - ~ ) . D . s ~ )

In Figure 5

a

simplified scheme of t h e

test

region i s given illustrating t h e decisions, inputs and

state

variables being considered in t h e stochastic simulation

(compare Figure 3). In compewrison

to

^Figure 3

a

few additional balance points have been introduced.

0

Balance points

0

Simulated inflow

0

^Fixed external inflow Water allocation from a to 8

Figure 5: Simplified scheme of t h e

test

region f o r stochastic simulation qi2,3

qc,s qd,s

bp 2 ^qs,i'qi,s REMAINING PIT

(RESERVOIR) TRIBUTARY

The major simplifications are:

1

@1,2

-

-

all mining activities are assumed

to

b e constant during planning periods.

S h o r t

term

variations in mine drainage and mine drainage

water

allocation are neglected.

p

qi5,6

STREAM(S1 q s a

0,

P P

-

(0 P ' P

+

8

- ^water

quality processes are neglected; I t is assumed t h a t

water

quality processes a r e damped and violations of

water

quality requirements

are

less significant a s t h e dissatisfaction of

water

demand in

t e r m s

of

water

quantity.

Water

quality alterations a r e above all caused by mine drainage, and t h a t i s taken as constant during planning periods.

-

groundwater flow variations during planning periods are neglected due

to

t h e damped groundwater flow processes.

That means

all

monthly varying water requirements have

to

b e satisfied from t h e stream.

2.2. Stochastic simulation of input data

2.2.1.

Hydrological inflow

The inflow into t h e region is assumed

to

be

a

natural hydrological process. A comprehensive analysis of s e v e r a l long duration time s e r i e s of runoff h a s shown, t h a t natural runoff under t h e climatic conditions of t h e GDR and with monthly time s t e p s posses t h e following properties, see Schramm 1975:

-

i t i s nonstationary and cyclic with t h e period one y e a r ,

-

i t s monthly one-dimensional distribution function can sufficiently w e l l b e approximated by

a

transformed normal distribution function, e.g. a three- parametric log-normal distribution

with

Q -

mean monthly runoff

X

-

transformed N(O,l)-distributed runoff q o,q, o

-

parameters of t h e distribution function

-

t h e process h a s Markovian c h a r a c t e r .

Starting with t h e transformation

F

of t h e runoff and estimates of t h e auto- and cross-correlation a multi-dimensional runoff process i s simulated. General pur- pose programs f o r t h i s simulation:

-

program SIKO f o r time s e r i e s analysis including parameter estimation

-

program SIMO f o r runoff generation

are

explained and listed in Kaden

et

al., 1985c.

For t h e

test

a r e a t h e t h r e e inflows qs

,,

qs,, qs, have

to

b e simulated. This can not b e done directly because t h e balance points b p l , bp 5, bp7

are

not identically with r i v e r gauges.

In t h e

test

a r e a f o u r r i v e r gauges

are

located close t o t h e s e balance points.

The - above mentioned assumptions have been proven for t h e runoff q

=

(q ,, q el ^Q

s,

q J r through t h e gauges (30-years time s e r i e s of observation).

Based on t h a t t h e parameters of three-parametric log-normal distributions have been estimated.

For t h e N(0.1) transformed runoff in t h e month k t h e following simulation model holds:

f o r k

=

1,

. - .

,12 with

A

-

₀

-

matrices of r e g r e s s i o n coefficients -

-

r e s i d u a l s t a n d a r d deviation

E

-

M(0,l)-distributed random v e c t o r . The a c t u a l r u n o f f s are estimated by t h e retransformation

f o r k

=

1,

- . .

,12 with

qo,s, -

p a r a m e t e r s of LN-3 distribution.

The inflows qs q s 5, qs are weighted sums of t h e simulated runoffs, taking into t h e account t h e a c t u a l catchment areas.

Besides t h e simulated inflows in t h e s u r f a c e water system a few fixed inflows have to b e t a k e n into a c c o u n t (compare Figure 5 and s u r f a c e

water

balances in Kaden

et

al., 1985a). Those are e i t h e r small t r i b u t a r i e s , waste or mine water allocations not being explicitely considered in t h e model system. Detailed informations on fluctua- tions of t h o s e inflows are not available. T h e r e f o r e t h e y are c o r r e l a t e d

to

t h e simulated inflow of t h e r e s p e c t i v stream o r t r i b u t a r y , compare t h e balance model in Appendix 3.

2.2.2. Water

demand

For t h e monthly w a t e r demand of any water u s e r t h e following g e n e r a l

sto-

c h a s t i c model may b e used:

d e m ( i , k )

=

( t r e n d ( i , k )

+

o s c i ( k )

+

a u t o ( i , k ) ) . r a n d [ms/ s e c ] (2.9) with

t r e n d ( i , k )

-

deterministic t r e n d

osci(k)

-

deterministic oscillation component depending on typical seasonal behaviour of water u s e r s

auto(i, k)

-

a u t o c o r r e l a t e d component r a n d

-

random component (noise)

In t h e

GDR test

region t h e following water u s e r have t o b e considered (compare Figure 3): municipal water supply (m), industrial

water

supply (i), a g r i c u l t u r a l water supply (ag), downstream

water

u s e r (ds), environmental p r o t e c t i o n area (e).

The a g r i c u l t u r a l water demand and t h e demand f o r environmental p r o t e c t i o n depend on t h e a c t u a l water t a b l e s in t h e s e regions. The models are given in Kaden

et

al.; 1905a. Random components are neglected.

The model f o r t h e m u n i c i p a l w a t e r d e m a n d h a s been developed according

to

Eq. (2.9). The t r e n d i s d e s c r i b e d as a l i n e a r model, t h e a u t o c o r r e l a t e d component as a f i r s t o r d e r model. The oscillation component i s approximated by a Fourier- s e r i e s , see Kaden

et al.

1985a.

The industrial

water

demand is assumed t o be constant. Seasonal oscillation com- ponents

are

negligible. W e consider only a random component.

The

water

demand of downstream u s e r s is slightly increasing in time. For t h e time being seasonal components are neglected.

1 1

dem*(i,k)

=

[ 8.0

+

O . 1 . i

1

- r a n d [ms/sec] ^(2.12) Besides t h e

water

demand f o r downstream u s e r s a minimum flow has t o be guaranteed with r e s p e c t t o environmental aspects.

For t h e r a n d o m component t h e following model is used:

r a n d

=

(1. - j a c . ~ ) (2.14)'

E is a N(O.1)-distributed random number, j a c a scaling coefficient (for numerical

tests

j a c

=

0.4 has been used).

In o r d e r

to

realize a negative correlation between t h e water demand and t h e hydrological inflow (usually low inflow means d r o u g h t and consequently high

water

demand), f o r t h e random number E t h e number used f o r t h e stochastic inflow gen- e r a t i o n is taken.

2.3.

Management rules

The management r u l e s f o r managerial decisions have t o b e defined in o r d e r

to

satisfy t h e monthly varying

water

demand of t h e above mentioned

water

u s e r s as good as possible. In case of

water

deficits t h e u s e r s are ranked with r e s p e c t

to

t h e i r socio-economic importance. The remaining pit can b e used

as

a r e s e r v o i r

to

minimize deficits.

2.3.1.

Balancing

of

water usera

For t h e management model w e are only interested in t h e

water

requirements

to

t h e

stream

and t h e remaining pit. Keeping in mind t h a t t h e o t h e r supply

com-

ponents (mine drainage water and groundwater) are assumed

to

be constant during a planning period t h e following balance equation holds:

L

dq,,,(f , i l k )

=

d e m , ( j , i , k )

-

a , , ( j ) (2.15)

.

^{L = 1}

with

dem, (j , i ,k )

-

total demand of u s e r

u ,

planning period j , y e a r i, month k

q , , ( j )

-

supply component from s o u r c e 1

to

u s e r

u ,

planning period j

d ( j i

,

k )

-

demand of u s e r

u

f o r water allocation from t h e

stream

( o r t h e remaining pit),

in month k

,

y e a r i , planning period j.

Based on this equation and on Figure 5 t h e balance equations f o r each u s e r can be given (downstream requirements can only be satisfied by t h e stream):

Thus, t h e supply requirements t o t h e

stream

and t h e remaining pit are defined.

The extend t o whiqh t h e s e requirements are satisfied i s used as a c r i t e r i o n t o determine in how f a r t h e long-term s t r a t e g y estimated with t h e planning m o d e l c a n b e implemented under c o n c r e t e conditions with monthly o r seasonal fluctuations of d i s c h a r g e (inflow) and demand.

In case t h e requirements c a n not b e

m e t

in a given month t h e following lexico- g r a p h i c o r d e r i n g (ranking) i s considered:

Highest priority: Municipal

water

supply Minimum downstream flow Industrial

water

supply Down-stream

water

supply Agricultural w a t e r supply

Lowest priority:

Water

supply f o r environmental protection.

A

more

detailed lexicographic o r d e r i n g might b e introduced splitting t h e u s e r s into s u b u s e r s as i t is usually b e dolle in long-term

water

management models,

see

Kozerski 1981.

2.3.2.

Remaining pit management

In t h e

test

^region a remaining pit originating a f t e r abandoning mine A in t h e planning period j , =7 c a n b e used as a r e s e r v o i r f o r

water

supply and flow augmen- tation.

In o r d e r t o u s e t h e remaining p i t as a r e s e r v o i r

it

is n e c e s s a r y

to

fill i t up

to

t h e lower s t o r a g e limit. Both, t h e filling and t h e a c t u a l management of t h e p i t are c h a r a c t e r i z e d by extensive exchange relations between s u r f a c e

water

( t h e reser- voir) and t h e surrounding groundwater (aquifer).

Due t o t h e s e exchange r e l a t i o n s t h e c o n t r o l of t h e filling p r o c e s s and t h e management of t h e remaining pit had

to

b e included as decisions into t h e planning m o d e l because of conflicting i n t e r e s t s between various

water

u s e r s and t h e mining authority. The

water

u s e r s

are

i n t e r e s t e d in a n e a r l y usage of t h e remaining pit

as

a r e s e r v o i r ; t h a t

m e a n s

a f a s t a r t i f i c i a l filling of t h e pit. This, however, contrad- i c t s

to

t h e i n t e r e s t s of t h e mining authority. An a c c e l e r a t e d rise of t h e

water

level in t h e remaining pit c a u s e s a considerable i n c r e a s e in

cost

of mine drainage in neighboured mines. Very illustrative examples f o r t h a t are given by P e u k e r t

et

al., 1985.

Depending on t h e p r e f e r e n c e s of m o d e l u s e r s t h e planning m o d e l w i l l g e n e r a t e some compromise solution f o r t h e remaining pit filling and management in

t e r m s

of mean values f o r planning periods.

The obtained long-term s t r a t e g y h a s

to

b e transformed into

an

adequate monthly management r u l e , hoth, f o r t h e filling, and f o r t h e management.

f i l l i n g phase

During t h e filling p r o c e s s t h e remaining pit

can

be considered as a common

water

u s e r . The demand equals

to

t h e estimated allocation from t h e

stream to

t h e p i t dur- ing t h e planning periods.

Instead of t h e constant values t h e monthly demand could b e interpolated between values f o r planning periods. In t h e given case t h e ''user" remaining pit is ranked between t h e agriculture and t h e environmental protection

area.

The management r u l e is t h e

s a m e

as f o r any user. The possible allocation is compared with t h e

water

demand. If t h e possible allocation i s l a r g e r then t h e demand t h e demand i s satisfied, otherwise a deficit o c c u r s (and is recorded f o r statistical evaluation). This

rule

i s a "pessimistic" one, because any deficit can not be compensated

later.

This means

for

t h e remaining pit, t h a t t h e filling goal can not b e satisfied.

In difference t o common

water

u s e r s f o r t h e remaining pit deficits can b e

com-

pensated, because a surplus of allocation can be realized (if i t i s available). In this case t h e allocation is not controlled by t h e

water

demand according t o Eq. (2.20) but by t h e

water

level.

Define J + ( i , k ) t h e

water

level in t h e remaining pit estimated in t h e planning model (the monthly values

are

obtained by linear interpolation between t h e solu- tions f o r planning periods). The monthly allocation

to

t h e remaining pit i s aimed towards t h e realization of this water level. Therefor t h e required amount of inflow dq:,(i .k) has t o b e estimated in o r d e r

to

increase t h e

water

level in t h e remaining pit from t h e actual value h,'(i ,k -1) in month k -1

to

t h e goal

4

⁽ⁱ .k ). Now t h e remaining p i t i s considered as a u s e r with t h e demand

dq;'

⁽ⁱ ,k ).

In Figure 6 t h e different outcome of t h e given management r u l e s is illustrated.

Both alternatives can b e checked with t h e simulation model.

Water table rem. pit

"mharge control led"

1

Artificial

-

^recharge

"water table controlled"

1 I I b

Year

Po.-- I I I

7 I

I I

---A I L,,-

[ m 3 / ~ . l

Figure 6: Management r u l e s f o r t h e filling phase of t h e remaining pit

Management phase

If t h e

water

level in t h e remaining pit has reached t h e

lower

s t o r a g e limit t h e pit c a n b e managed

as

a r e s e r v o i r . T h e r e is a l a r g e amount of concepts and models f o r r e s e r v o i r management available, both, f o r flood protection, and f o r leveling of

water

deficits. In t h e given study directed towards rational long-term s t r a t e g i e s t h e use of t h e s t o r a g e f o r flood protection i s less important. For long-term management modeling, periods of low flow conditions are considered as t h e signifi- cant events. A s a f i r s t alternative t h e following simple management r u l e is imple- mented:

In case of downstream

water

deficits t h e r e s e r v o i r is used f o r flow augmentation in o r d e r t o level up t h e deficit. Any surplus of runoff in t h e

stream

i s used f o r filling up t h e remaining pit

to

t h e upper s t o r a g e limit. Consequently, i t i s

a

strategy of maximum s t o r a g e parsimony on t h e one hand and of possibly full compensating of deficits on t h e o t h e r one.

But, t h e r e i s a significant difference t o common storages. Due t o t h e low groundwater table around t h e remaining pit caused by mine drainage in neigh- boured mines t h e r e s e r v o i r permanently loses

water to

t h e ground. The loss increases with increasing

water

level in t h e remaining pit. That means, high water levels

are

less economically not only because of lost discharge t o t h e pit, but although because of increased pumpage f o r mine drainage in neighbouring mines.

In t h e time being management r u l e s should be studied taking this into t h e account.

Obviously a compromise between t h e reliability of satisfaction of

water

demand and t h e storage volume (the

water

level) has

to

b e found.

2.4. Simulation of syaterns development 2.4.1. W i n i n g pit aubmodel

The submodel of t h e remaining pit has

to

describe t h e essential interrelations between t h e s u r f a c e

water

in t h e pit and t h e surrounding groundmiter in t h e filling phase

as

well

as

in t h e management phase. That is why t h e common balance equation f o r r e s e r v o i r management in its usual form

with

A S -

change of s t o r a g e volume

P -

precipitation

Z

-

^inflow

E -

evapotranspiration

R -

^outflow

can not b e used h e r e . The equation has t o be extended by a term t h a t t a k e s into t h e account t h e infiltration into t h e groundwater o r t h e flux of groundwater into t h e r e s e r v o i r . This i s illustrated in Figure 7. I t demonstrates t h e effect of different management strategies during one y e a r on t h e

state

of t h e r e s e r v o i r

at

t h e end of t h e year.

The deviations depend on t h e difference between t h e

state

variables water Level remaining pit and water tabLe in the aquifkr. Consequently t h e dynamics of t h e groundwater system have

to

b e considered in addition

to

t h e dynamics of t h e storage. This w a s done by computing management alternatives by means of a com- plex comprehensive groundwater flow model and by deducing a reduced grey-box model. The methodology i s described in detail by Kaden

et

91.. 1985c. The result of model reduction are models f o r yearly and f o r monthly time steps. The monthly model has been developed in such a way t h a t i t provides t h e same r e s u l t s

at

t h e end of one y e a r

as

t h e yearly model if t h e inflow i s constant during t h e year.

The monthly model needed f o r t h e management model has t h e following form:

with

Estimation of yearly values (yearly const. recharges)

.--0.-

... ... ..., 1

Estimation of monthly values Years

--. ^... -

4.2 Water level

remaining pit

Artificial recharge remaining pit

Figure 7 : Impact of different management s t r a t e g i e s on t h e water level in t h e remaining pit

$(i,k)

- water

level in t h e remaining pit [ m ] ,

at

t h e end of month k in t h e y e a r i

hi(i ,k

- ^water

level in t h e remaining p i t under n a t u r a l conditions (q,

a), at

t h e end of month k , y e a r i

!lp(i.k)

-

flux between stream and remaining p i t [ m 9 / sec], month i

,

y e a r k

a i * a p b o b i

-

parameters.

Precipitation and evaporation a r e considered in t h e

water

t a b l e under n a t u r a l conditions. Their a l t e r a t i o n during month and due t o different s u r f a c e of t h e pit in

case

of a c c e l e r a t e d filling a r e negligible.

This model i s used in realizing t h e management r u l e s given in Section 2.3.2.

During t h e filling p h a s e t h e m o d e l above i s applied from month

to

month with t h e given inflow. For t h e management phase t h e remaining pit computation h a s t o b e divided into two p a r t s .

In t h e f i r s t s t e p t h e

total

usable s t o r a g e volume i s imaginary added t o t h e n a t u r a l d i s c h a r g e in t h e s t r e a m and considered t o b e available f o r downstream o r o t h e r users. In o r d e r t o consider t h e exchange p r o c e s s e s between groundwater and remaining p i t t h e following algorithm h a s t o b e used, compare Eq. (2.22):

c = h p ~ ( i . k )

+

a l . & ( i . k - 1 )

+

a e . & , ( i . k - 2 )

+

b l - q p ( i , k - 1 ) (2.24) with

qiPf(i * k )

-

potential maximum d i s c h a r g e [ m 3 / s e c ] , month i , y e a r k

hp"" -

^lower s t o r a g e limit [ m ]

~p"p," -

maximum allocation capacity [ m a / s e c ] .

After balancing off all u s e r s in t h e system t h e final r e s e r v o i r

state

i s computed in

terms

of t h e a c t u a l r e q u i r e d d i s c h a r g e t o t h e stream and t h e

water

level

at

t h e end of t h e studied month. This i s based on t h e minmum of t h e f r e e d i s c h a r g e (not used) qs &(i ,k ) of all balance points.

If q s m b n ( i , k )

> c$yi(i

^{, k )} t h e r e i s a s u r p l u s of s u r f a c e

water

( i , k )

=

qs ,h(i ,k )

-

^{qr:(z ,k )}

^to

b e allocated t o t h e stream. For t h e poten- t i a l maximum allocation

to

t h e pit holds, analogously t o Eq. (2.24)

with

q f $ ( i , k )

-

potential maximum inflow [ m 3 / s e c ] , month i , y e a r k

hpmX

-

u p p e r s t o r a g e limit [ m ]

4:pa

-

maximum allocation capacity [ m 3 / s e c ] Using Eq. (2.24) and (2.25)

w e

obtain:

I

d q , , ( i , k ) f o r d q , , ( i , k )

<

q!,;(i,k)

q , , p ( i , k )

=

(2.26)

q f $ ( i , k ) f o r d q , , ( i , k ) r q f $ ( i , k )

If qs*(i , k ) r q,~,:(i , k ) t h e r e i s a deficit of s u r f a c e

water.

For t h e d i s c h a r g e t o t h e s t r e a m holds:

q p . , ( i , k )

=

q r : ( i , k )

-

~ s * ( i , k ) ( 2 2 7 ) With Eq. (2.22) t h e final

water

level in t h e remaining p i t

at

t h e end of month k i s estimated.

In Appendix A t h e computer program f o r t h i s submodel i s given.

2.4.2. Infiltration dmodel

The major p a r t of common long-term

water

management modeling i s t h e balanc- ing of

water

u s e r s according

to

t h e i r local distribution and lexicographic ranking in o r d e r t o

m e e t

t h e i r

water

demand. The ranking is considered by t h e help of a respective temporal sequence of balancing.

This approach causes difficulties if t h e ranking sequence does not coincide with t h e local distribution (upstream user before downstream user) and if t h e satisfaction of t h e requirements of lower-priority upstream u s e r s effect t h e supply of downstream u s e r s with higher priority. And this happens if t h e

stream

i s characterized by discharge dependent infiltration losses ( o r base flow!).

In t h e mining

test

region

water

level alterations in the

stream

cause signifi- cant changes in t h e infiltration and consequently in t h e discharge between various balance profiles. This process and ways f o r modeling have been discussed in detail by Kaden e t al., 1985a. 1985c. For each balance segment (compare Figure 3)

black-box models of t h e foLlowing s t r u c t u r e have been developed:

with

Agi ( i , k )

-

infiltration between

stream

and groundwater due

to

water level changes in t h e

stream

^[m '/ sec ] h 8 ( i , k )

-

^actual

water

level in t h e stream over bottom

(mean value f o r t h e balance segment) [m], y e a r 5 , month k

K8 (i

-

^average

water

level in t h e stream over bottom (mean value for t h e balance segment) [m

1,

y e a r i (mean value of t h e respective planning period).

The impulse

u

, k ) f o r a balance segment [a, gl results f r o m t h e actual discharge

at

t h e respective

stream

profile. Since this profile might change between upstream and downstream balance point f o r t h e effective impulse a weighted mean i s used. The weighting f a c t o r i s y , OSySl,usuaLlyy=0.5.

With Eq. (2.29) a feed-back between infiltration and changes in discharge is real- ized. The infiltration f o r t h e balance segment effects t h e upstream balance profile as a consequence of

water

level changes. Additionally external inflows/outflows within t h e balance segment have

to

be considered f o r t h e infiltration calculation.

For t h e impulse

at

t h e downstream profile holds:

with

q s ,(i , k )

-

^discharge

^at

t h e upstream balance profile, y e a r i , month k

q i ,,&i

1 -

infiltration f o r t h e balance segment

at

mean

water

level, y e a r i

dq &i , k )

-

external inflow/outflow

at

t h e downstream balance profile, y e a r i , month k

I h 8 . p

- ^water

level key function f o r t h e downstream profile.

The actual discharge

at

t h e downstream profile

6

can be estimated iteratively

applying Eq. (2.28)

-

(2.30). The above mentioned difficulty in balancing under con- sideration of infiltration becomes now obvious.

In Appendix 2 t h e computer code f o r t h e infiltration submodel of t h e management model is given.

2.4.3. Balance submodel

The management rules, t h e submodels f o r input simulation, and t h e above given submodels f o r t h e remaining pit and the infiltration have

to

b e combined f o r balancing t h e surface

water

resources.

Due t o t h e discharge dependent infiltration t h e balancing of the e n t i r e system i s only possible by iterative computation. The infiltration in all balance segments has

to

be estimated before balancing of all

water

users. However, through t h e

term

dq ( i , k ) in Eq. (2.30) t h e infiltration depends on t h e u s e r balancing.

The following algorithm has been developed assuming that in t h e majority of realizations t h e requirements of

all

u s e r s can be satisfied. I t consists of

t w o

s e p a r a t e balance computations:

1. balancing of t h e surface

water

system upstream-downstream f o r a given actual

water

demand of all users, considering t h e infiltration,

2. balancing of

water users

according to t h e i r lexicographical ranking.

The computation

starts

with procedure 1 f o r t h e given

water

demand. If t h e water demand i s fully satisfied,

all

parameters have been exactly estimated and an itera- tion i s redundant.

If t h e

water

demand i s not satisfied, in procedure 2 t h e available r e s o u r c e s

are

distributed between t h e users according t o t h e i r priority. After t h a t in procedure 1 t h e system i s balanced considering t h e reduced

water

demand from procedure 2.

This computation i s continued iteratively until t h e discharges f o r all balance pro- files do not change during iteration (within a given accuracy).

In Appendix 3 t h e computer code of the subroutine balance of t h e management model is given.

2.5. Honte Carlo simulation and statistical evaluation

The major problem related

to

t h e Monte Carlo simulation i s i t s high computa- tional e f f o r t depending on t h e number of realizations NREL. Frequently fixed numbers of realizations (e.g. NREL=100) are selected. In this

case

NREL usually will be overdimensioned in o r d e r

to

ensure a certain statistical evidence and t h e numerical e f f o r t will be higher

as

necessary.

Principally, t h e number of realizations depends on t h e required statistical evidence of t h e results. If this evidence i s checked in the course of t h e computa- tion, t h e simulation can be stopped

as

soon as possible. For t h e

DSS

MINE such a

test

has been realized in t h e following simple f o r m :

Every 1 0 realizations t h e mean values f o r selected parameters

5

(decisions and

state

parameters f o r each planning period)

are

compared. If t h e deviation is smaller then E with r e s p e c t

to

t h e mean value of t h e planning model

zp

t h e simula- tion is stopped.

According

to

t h a t t h e number of realizations i s controlled by t h e factor E t o be fixed by t h e u s e r (e.g. 0.05).

In Figure 8 a simplified flow chart of the subroutine controlling the Monte Carlo simulation is depicted.

t

initialization of arrays for registration

c : for all realizations c: for all planning periods

t

input of results of .planning model for period j

I

^{7 i =} ib(j),ie(j) c : for all years of period j

-

^{k = 1,12} I ^{c: for all} months of year i c : monthly water balance

t

registration of

monthly parameters

t

registration of satisfaction water demand

t

registration of density

function of parameters

t

estimation of yearly parameters

t

estimation of parameters of

planning period

t

estimation of total indicators

1 +

registration of total indicators

no

stowtest: statistical evidence of results sufficiently 7

$

standardization of statistical results

t

estimation of distribution function of total indicators

Figure 8: Flow chart of Monte Carlo simulation

An important methodological problem i s the registration and statistical evaluation. The following types of registration a r e common:

-

distribution functions of reliabilities of t h e o c c u r r e n c e of defined events, e.g.

t h e satisfaction of

water

demand,

-

distribution functions of selected parameters, e.g. t h e total c o s t of mine drainage,

-

density functions of selected parameters, e.g.

water

allocation.

These continuous functions c a n only b e r e g i s t e r e d empirically in a d i s c r e t e form f o r defined classes. Define ( s c l a s s (l ),1 = I , .

. .,KC)

t h e scaling f a c t o r of t h e classes, f o r convenience t h e

same

f o r all functions (e.g. 0.

-

^0.5

-

^0.7

-

^0.8

-

^0.9

-

^0.95).

The r e g i s t r a t i o n depends on t h e definition of t h e r e f e r e n c e value. I t i s advan- tageous

to

use

a

r e f e r e n c e value being known in advance. In t h i s case t h e statisti- cal events have not t o b e s t o r e d and t h e empirical functions c a n b e estimated dur- ing t h e simulation. This i s necessary especially then if

a

l a r g e number of parame-

ters

i s

to

b e r e g i s t e r e d , e.g. f o r t h e GDR

test area

2 1 p a r a m e t e r s f o r 1 0 planning periods and 1 2 month. (1.e. f o r 100 realizations 252000 values.)

For t h e

DSS

MINE t h e following empirical probabilistic functions

are

estimated:

S a t i s f a c t i o n @ w a t e r d e m a n d

with dem

- water

demand, sup.

-

water supply.

This function i s estimated f o r all month in all planning periods. In t h i s case w e use probabilities as t h e r e f e r e n c e values f o r r e g i s t r a t i o n and sup i s normalized by dem, consequently t h e d i s c r e t e function values can b e estimated during stochastic simulation.

I n d i c a t o r s of s y s t e m s development

PI( ind0 )

=

R o b [ ind

<

ind0 j

A l l events have t o b e s t o r e d . The empirical distribution function i s estimated

at

t h e end of simulation. The probability i s scaled with s c l a s s , see above.

F b r a m e t e r s of s y s t e m s development

For decisions,

state

p a r a m e t e r s and

state

variables

a

density function i s estimated.

p p ( p a r O ) = R o b [ p a r 0 s p a r < p a r 0

+

Apar j (2.34) The function i s estimated f o r all planning periods and all month. A s t h e r e f e r e n c e value

w e

use t h e known r e s u l t of t h e planning m o d e l (mean value f o r e a c h period).

In Figure 9 t h e above defined probabilistic functions and t h e i r scaling are illustrated.

2.6. Numerical tests

Basis of t h e numerical

test w a s

a typical r e s u l t of t h e planning model obtained f o r a multi-criteria analysis f o r t h e c r i t e r i a :

dev -m

-

^deviation

^water

demand/supply municipality dev i

-

^deviation

^water

demand/supply industry cost - m i

- total

mine drainage c o s t

cost --m

- ^cost

municipal w a t e r supply cost i

-

c o s t industrial

water

supply.

F o r e a c h c r i t e r i a t h e utopia-point h a s been selected as r e f e r e n c e point. These r e s u l t s have been used

as

initial values f o r t h e management model.

a) Reliability of satisfaction water demand

4

^Scaling:

b) Distribution function of indicator

C) Density distribution of parameter

/

I

I

^{Scaling :}

--

/ / / /

par : (sclass(l), I = 1

,...,

KL;

-

(2-sclars(l)), I = KL,

...,

2) r par

/

/

/ Scaling:

/

/ p, : (sclass(l), I = 1

,...,

KL)

Figure 9: Statistical evaluation

1

+

^ind

The simulation has been performed with 60 realizations. Therefor about 6 Min.

CPU-time

at

t h e VAX

11/780

w a s consumed. A detailed evaluation of t h e numerical results can not be given in this paper. This has

to

be done by t h e e x p e r t s of t h e

water

authority responsible f o r t h e

test

region. In t h e following some aspects will be discussed.