A Systems Approach to Eutrophication Management with Application to Lake Balaton

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NOT F O R QUOTATION WITHOUT P E R M I S S I O N O F THE AUTHOR

A SYSTEMS APPROACH T O E U T R O P H I C A T I O N MANAGEMENT

WITH A P P L I C A T I O N T O LAKE BALATON

L . S o m l y o d y

S e p t e m b e r 1 9 8 2 W P - 8 2 - 7 9

W o r k i n g P a p e r s a r e i n t e r i m r e p o r t s o n w o r k of t h e I n t e r n a t i o n a l I n s t i t u t e f o r A p p l i e d S y s t e m s A n a l y s i s a n d have r e c e i v e d o n l y l i m i t e d r e v i e w . V i e w s o r o p i n i o n s e x p r e s s e d h e r e i n do n o t n e c e s s a r i l y r e p r e - s e n t t h o s e of t h e I n s t i t u t e o r of i t s N a t i o n a l M e m b e r O r g a n i z a t i o n s .

I N T E R N A T I O N A L I N S T I T U T E FOR A P P L I E D SYSTEMS A N A L Y S I S

A - 2 3 6 1 L a x e n b u r g , A u s t r i a

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PREFACE

One of t h e main r e s e a r c h e f f o r t s o f t h e R e s o u r c e and E n v i r o n - ment Area o f IIASA d u r i n g t h e p a s t few y e a r s was t h e Lake B a l a t o n E u t r o p h i c a t i o n S t u d y , u n d e r t a k e n i n c o o p e r a t i o n w i t h t h e Hungarian Academy of S c i e n c e s and o t h e r Hungarian i n s t i t u t i o n s . The s t u d y was i n i t i a t e d b e c a u s e o f t h e r e c o g n i t i o n t h a t o u r u n d e r s t a n d i n g on e u t r o p h i c a t i o n w a s m u c h l e s s s a t i s f a c t o r y f o r s h a l l o w l a k e s t h a n f o r d e e p l a k e s . Lake B a l a t o n was s e l e c t e d f o r s e v e r a l r e a - s o n s , o n e o f them b e i n g t h e pronounced economic i n t e r e s t i n s o l v - i n g t h e r e a l - l i f e p r o b l e m s o f t h e l a k e and t h e s u r r o u n d i n g r e g i o n . The s t u d y c o v e r e d v a r i o u s s c i e n t i f i c i s s u e s ( c o u p l e d b i o c h e m i c a l - h y d r o p h y s i c a l m o d e l i n g o f a l a k e , s e d i m e n t - w a t e r i n t e r a c t i o n , t h e d e r i v a t i o n o f n u t r i e n t l o a d s , u n c e r t a i n t i e s and s t o c h a s t i c i n f l u - e n c e s , e t c . ) on one s i d e , and t h e management o f t h e l a k e ' s w a t e r q u a l i t y - - a much more n a c r o s c o p i c i s s u e - - o n t h e o t h e r .

T h i s p a p e r o f f e r s a swtunary, a l b e i t b r i e f , o f t h e e n t i r e e f f o r t , r e f l e c t i n g a s t a g e s h o r t l y b e f o r e t h e c l o s e o f t h e s t u d y . More d e t a i l e d r e s u l t s on t h e a p p l i c a t i o n o f t h e w a t e r q u a l i t y manage- ment model w i l l b e s e t o u t i n t h e f o r t h c o m i n g book on E u t r o p h i c a - t i o n Management f o r L a k e - r e g i o n S y s t e m s , and t h e p r o c e e d i n g s o f t h e c o n f e r e n c e on t h e E u t r o p h i c a t i o n o f S h a l l o w Lakes: N o d e l i n g , M o n i t o r i n g and Managenent (The Lake B a l a t o n Case S t u d y ) , 29 August t o 3 S e p t e m b e r , 1982, Veszprem, Hungary, b o t h L > u b l i c a t i o n s t o a p p e a r i n f a l l 1983.

~ A s z l 6 somly6dy L e a d e r

B a l a t o n Case S t u d y

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A SYSTEMS APPROACH TO EUTROPHICATION MANAGEMENT WITH APPLICATION TO LAKE BALATON"

LAszlb Somlybdy 3

Abstract.--The problem o f t h e l a k e - r e g i o n system s t u d - i e d is c h a r a c t e r i z e d by complexity, u n c e r t a i n t y , and by t h e need t o i n c o r p o r a t e d i f f e r e n t l e v e l s o f a n a l y s i s such a s s c i e n t i f i c u n d e r s t a n d i n g and p o l i c y making. The a p p r o a c h a d o p t e d i s based o n d e c o m p o s i t i o n and a g g r e g a t i o n . D e t a i l e d s t u d i e s were made o n s u b p r o c e s s e s (sediment-water i n t e r a c - t i o n , b i o c h e m i c a l and h y d r o p h y s i c a l phenomena, n u t r i e n t l o a d s , e t c . ) . The e s s e n t i a l f e a t u r e s o f t h e s e p r o c e s s e s were p r e s e r v e d a t t h e l e v e l of w a t e r q u a l i t y management and

i n c o r p o r a t e d i n a n o p t i m i z a t i o n model a c c o u n t i n g f o r uncer- t a i n t i e s .

INTRODUCTION

The a r t i f i c i a l e u t r o p h i c a t i o n of l a k e s and r e s e r - v o i r s is recognized worldwide a s a s e r i o u s problem; i t encompasses b o t h t h e physico-chemical changes o f w a t e r q u a l i t y and t h e economic and s o c i a l p r o c e s s e s t h a t un- d e r l i e t h e s e changes. E x c e s s i v e a l g a l blooms, provoked by augmented n u t r i e n t l o a d s of a g r i c u l t u r a l , m u n i c i p a l , and i n d u s t r i a l o r i g i n , r e d u c e t h e r e c r e a t i o n a l poten- t i a l o f t h e w a t e r b o d i e s and h a v e s e r i o u s a d v e r s e e f - f e c t s o n t h e i r s u i t a b i l i t y a s s o u r c e s o f d r i n k i n g w a t e r . Furthermore, e u t r o p h i c a t i o n e n t a i l s u n d e s i r e d changes i n t h e ecology o f t h e system, making i t g e n e r a l l y l e s s s t a b l e and more v u l n e r a b l e .

To c o n t r o l e u t r o p h i c a t i o n i s n o t a n e a s y t a s k . Although i n most c a s e s a s o l u t i o n would i n c l u d e r e - d u c i n g n u t r i e n t l o a d s i n one form o r another--in i t s e l f a d i f f i c u l t t a s k - v a r i o u s u n c e r t a i n t i e s i n e v i t a b l y e x i s t r e g a r d i n g t h e e x t e n t o f t h e r e d u c t i o n s r e q u i r e d t o a c h i e v e d e s i r a b l e improvements i n t h e l a k e ' s w a t e r q u a l - i t y . Thus, t h e e f f e c t i v e n e s s o f a l t e r n a t i v e s o l u t i o n s measured by t h e i r r e s p o n s e s i n t h e l a k e (and consequent- l y w i t h r e s p e c t t o i t s d e s i r e d f u n c t i o n s ) c a l l s f o r t h e e x p l i c i t t r e a t m e n t of t h e p r o b l e m - r e l a t e d u n c e r t a i n t i e s ( r a n g i n g from d a t a u n c e r t a i n t y t o u n c e r t a i n t y due t o a l i m i t e d u n d e r s t a n d i n g of t h e p r o c e s s e s i n v o l v e d ) .

Thus, u s i n g a systems appmach t o a n a l y z e and e v a l - u a t e a l t e r n a t i v e m g e m e n t s t m t e g i e s o f f e r s p a r t i c u l a r a d v a n t a g e s . I n f a c t , t h i s i s perhaps t h e o n l y way t o perform a n i n t e g r a t e d s t u d y encompassing t h e l a k e , t h e r e g i o n , and t h e r e l a t e d p h y s i c a l . b i o l o g i c a l , c h e m i c a l , economic, and s o c i a l p r o c e s s e s . T h i s approach s t r u c - t u r e s i n f o r m a t i o n i n a f o r m a t a p p r o p r i a t e f o r b o t h t h e research phase and t h e s u b s e q u e n t phase o f policy i n r plementatwn. ^{A t}t h e c o r e o f t h e approach, m d e l s p l a y a n i m p o r t a n t r o l e and a r e e f f e c t i v e t o o l s . Model re- s u l t s c a n be f e d back t o f i e l d workers t o f o c u s t h e i r a t t e n t i o n on a r e a s where o u r knowledge of t h e r e a l world i s s t i l l i n s u f f i c i e n t . Model r e s u l t s a l s o e n a b l e managers t o v i s u a l i z e t h e e f f e c t s o f p o s s i b l e management o p t i o n s .

The n a j o r f e a t u r e o f man-caused e u t r o p h i c a t i o n i s t h a t , a l t h o u g h t h e consequences a p p e a r w i t h i n t h e l a k e , t h e cause-the g r a d u a l i n c r e a s e of n u t r i e n t s ( v a r i o u s phosphorous and n i t r o g e n compounds) r e a c h i n g t h e lake-- l i e s i n t h e r e g i o n . Consequently, e u t r o p h i c a t i o n man- agement r e q u i r e s a n a l y s i s o f t h e complex i n t e r a c t i o n s between the water body v u l n e r a b l e t o e u t r o p h i c a t i o n and

i t s surrounding region. I n t h e l a k e , d i f f e r e n t b i o l o g - i c a l , chemical and h y d r o p h y s i c a l p r o c e s s e s a r e impor- t a n t , w h i l e i n t h e r e g i o n t h e r e a r e human a c t i v i t i e s g e n e r a t i n g n u t r i e n t r e s i d u a l s t h a t a r e u l t i m a t e l y wash- ed t o t h e l a k e s and r e s e r v o i r s .

The r e l a t i o n o f c a u s e and e f f e c t of e u t r o p h i c a t i o n i s s i m i l a r b o t h f o r deep and s h a l l o w l a k e s . S t i l l t h e u n d e r s t a n d i n g of p r o c e s s e s i n s h a l l o w l a k e s i s much

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lpaper presented a t the Third International Con- l e s s s a t i s f a c t o r y t h a n f o r deep l a k e s . I n c o n t r a s t t o f e r e n c e o n State-of-the-Art i n E c o l o g i c a l Modelling. deep l a k e s , t h e r e l a t i v e l y f a s t and i r r e g u l a r dynamics Colorado S t a t e U n i v e r s i t y . May 24-28, 1982. i n f l u e n c e d by t h e n e a r l y complete a b s e n c e of tempera-

,,

t u r e s t r a t i f i c a t i o n , and c l i m a t i c and h y d r o l o g i c f a c -

% i s s t u d y was i n i t i a t e d by IIASA's Resources and t o r s b e i n g s t r o n g l y s t o c h a s t i c i n n a t u r e s h o u l d b e men- Environment Area and c a r r i e d o u t i n c o o p e r a t i o n w i t h t i o n e d . Because t h e l a k e i s s h a l l o w , wind-induced s e d i - t h e Hungarian Academy o f S c i e n c e s and o t h e r Hungarian m e n t l w a t e r i n t e r a c t i o n and s p a t i a l mass exchange p l a y i n s t i t u t i o n s . i m p o r t a n t r o l e s . The l i g h t c o n d i t i o n s i n t h e w a t e r

3Dr. L. Somly6dy ( o n leave f r o m the Research Cen- f l u c t u a t e a g r e a t d e a l more, owing t o changes i n t h e ter f o r

water

Resources Development (VITUKI), Budapest, c o n c e n t r a t i o n o f suspended s o l i d s - As a s p e c i a l i s s u e . Hungary) is a t present leader of the Balaton Case Study t h e gap between h y d r o p h y s i c a l and e c o l o g i c a l modeling o f t h e Besources and Environment Area a t t h e I n t e r n a - s h o u l d a l s o b e n o t e d , t h e r e a s o n b e i n g t h a t b i o l o g i c a l , t i o n a l I n s t i t u t e f o r Applied Sys terns A n a l y s i s , Laxen- c h e m i c a l , and p h y s i c a l p r o c e s s e s of q u i t e d i f f e r e n t

burg, A u s t r i a . time and s p a t i a l s c a l e s a r e i n v o l v e d .

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To a n a l y z e a l l t h e s e i s s u e s , Lake Balaton, t h e l a r g e s t l a k e i n C e n t r a l Europe, was s e l e c t e d a s t h e sub- j e c t of a c a s e s t u d y . T h i s l a k e i s t h e most important r e c r e a t i o n a l a r e a i n Hungary and has e x h i b i t e d t h e un- f a v o r a b l e s i g n s of a r t i f i c i a l e u t r o p h i c a t i o n . There i s n o t only a s c i e n t i f i c , b u t a l s o a s t r o n g economic i n t e r e s t i n t h e s t u d y (roughly 40% of t h e income from tourism i n Hungary stems from t h e Balaton r e g i o n ) . T h i s paper gives a sumnary of t h e s t u d y , which is now n e a r i n g completion. For f u r t h e r d e t a i l s on t h e c a s e s t u d y , t h e r e a d e r i s r e f e r r e d t o van S t r a t e n e t a 1

.,

1979. van S t r a t e n and Somlybdy 1980. Somlybdy 1981a.

and Somlyddy and van S t r a t e n , forthcoming.

MAJOR CHARACTERISTICS OF THE SYSTEM

The l a k e and i t s watershed a r e i l l u s t r a t e d i n f i g - u r e 1. The l e n g t h of t h e l a k e i s 78 km, t h e average width around 8 km ( s u r f a c e a r e a n e a r l y 600 km2) and

t h e average depth 3.1 m. The major inflow of t h e l a k e is t h e River Zala a t t h e southwestern end of t h e l a k e which d r a i n s h a l f of t h e t o t a l catchment a r e a (- 5800 km2). There i s a s i n g l e outflow a t t h e o t h e r end of t h e l a k e , Sidfok, through a c o n t r o l g a t e . The mean r e s i d e n c e time of water is about 2 y e a r s .

The f l u c t u a t i o n i n t h e w a t e r ' s temperatufe is h i g h . There i s a r e l a t i v e l y long ice-covered period

(around two months), w h i l e t h e temperature i n s m e r may exceed 25O C. Concerning t h e chemical composition of t h e w a t e r , t h e high calcium c a r b o n a t e c o n t e n t and pH v a l u e (8.3 t o 8.7) should be mentioned. Wind a c t i o n i s important r e s u l t i n g i n f a v o r a b l e oxygen c o n d i t i o n s and a permanent back and f o r t h motion ( s e i c h e ) along t h e l a k e and a complicated c i r c u l a t i o n p a t t e r n . Wind s t r o n g l y i n f l u e n c e s s e d i m e n t a t i o n and r e s u s p e n s i o n of t h e sediment ( i t s o r g a n i c m a t e r i a l c o n t e n t is low) which i s a s s o c i a t e d w i t h an e f f e c t i v e adsorption-desorp-

t i o n p r o c e s s . The y e a r l y n e t d e s o r p t i o n a s i n t e r n a l load has t h e same o r d e r of magnitude a s t h e e x t e r n a l one ( s e e Gelencskr e t a l . , 1982).

I n r e c e n t y e a r s , remarkable changes have been observed i n t h e water q u a l i t y due t o t h e r a p i d i n c r e a s e i n tourism, sewage d i s c h a r g e s , f e r t i l i z e r use, and oth- e r f a c t o r s . The a l g a l biomass ( a l g a e is t h e most i n r p o r t a n t primary producer i n t h i s c a s e ) i n c r e a s e d by a

' i g u r e 1.-Major c h a r a c t e r i s t i c s of t h e system K

-

Keszthely. T

-

Tihany. S

-

S i d f o k I . . . I V t y p i c a l b a s i n s of t h e l a k e

- . -

boundary of t h e catchment

=== boundary of t h e r e c r e a t i o n a l a r e a sewage d i s c h a r g e s i n t h e r e g i o n

f a c t o r of 10 when compared y i t h t h e p a s t 15-20 y e a r s . The t r e n d i n primary production i s s i m i l a r and a t the most p o l l u t e d western b a s i n , peaks of up t o 13.6gc/m2d were observed, a h y p e r t r o p h i c v a l u e (Herodek and Tamds.

1975). I n s h o r t . t h e average l a k e c o n d i t i o n s moved from mesotrophic t o e u t r o p h i c , thus endangering t h e use of t h e l a k e f o r r e c r e a t i o n a l purposes, t h e prime water u s e i n t h i s c a s e .

Phosphorus p l a y s a dominant r o l e i n the e u t r o p h i - c a t i o n of the l a k e . Thus. both f r o m t h e p o i n t of view of understanding and managing t h e system, t r a c i n g t h e phosphorus compounds i n t h e l a k e and on t h e watershed is of primary i n t e r e s t . The t o t a l phos horus load of

S

t h e l a k e i s around 1000 kgld (0.52 mgfm d i n a lake- wide average) ( J o l l n k a i and Somlyddy, 1981). h a l f of which is estimated t o be a v a i l a b l e f o r a l g a l uptake.

The load has many components: 33% i s derived from sewage. 27% from d i f f u s e s o u r c e s . 22% is r e l a t e d t o run- o f f p r o c e s s e s i n t h e d i r e c t v i c i n i t y of t h e l a k e , while

t h e c o n t r i b u t i o n of atmospheric p o l l u t i o n i s 18%. The r a t i o of s w a g e d i s c h a r g e s i n t h e a v a i l a b l e load i s h i g h e r ; o n l y t h e sewage r e l e a s e d i n t h e r e c r e a t i o n a l a r e a ( f i g u r e 1 ) a c c o u n t s f o r 36% of t h e a v a i l a b l e l o a d . This d i r e c t load v a r i e s q u i t e a l o t i n time, f o l l o w i n g

t h e f l u c t u a t i o n s i n p o p u l a t i o n due t o tourism, and h a s a 2-4 times h i g h e r v a l u e i n suarmer than d u r i n g t h e o f f - s e a s o n . The load d i s t r i b u t i o n along t h e l a k e i s approx- i m a t e l y uniform ( t h e t r i b u t a r y l o a d is higher f o r t h e Western end of t h e l a k e , w h i l e t h e sewage load is q u i t e t h e o p p o s i t e ) ; however, t h e volume r e l a t e d v a l u e i s twelve times h i g h e r a t t h e Keszthely Bay ( f i g . 1) t h a n a t t h e o t h e r end of t h e l a k e , due t o d i f f e r e n c e s i n t h e volume of t h e f o u r main b a s i n s . T h i s f a c t i s a l s o r e f l e c t e d i n t h e pronounced l o n g i t u d i n a l g r a d i e n t of v a r i o u s water q u a l i t y parameters, e.g.. f o r Chloro- phyll-a t h e r a t i o of t h e maximum and minimum v a l u e s ranges between 4 and 20 (van S t r a t e n e t a l . . 1979).

The g r a d i e n t observed a t t h e same time i n d i c a t e s t h a t t h e s t r o n g wind a c t i o n and t h e mixing a s s o c i a t e d w i t h i t a r e s t i l l n o t s u f f i c i e n t f o r l e v e l i n g o u t t h e spa- t i a l n o n u n i f o r m i t i e s

.

From a n a n a l y s i s of t h e d a t a i t i s c l e a r t h a t t h e r e is n o t o n l y a c r i t i c a l s t a t e of t h e water q u a l i t y a t Keszthely Bay, b u t a l s o a s p r e a d i n g d e t e r i o r a t i o n process which extends towards o t h e r a r e a s of t h e l a k e where t h e water q u a l i t y i s s t i l l good. Thus a c t i o n is u r g e n t l y r e q u i r e d from t h e view of t h e e n t i r e l a k e .

Based on h y d r o l o g i c and water q u a l i t y considera- t i o n s , t h e l a k e was d i v i d e d i n t o f o u r b a s i n s , a s i n d i - c a t e d i n f i g u r e 1. The a p p l i c a t i o n of t h e p r i n c i p l e of segmentation proved t o b e a u s e f u l t o o l f o r modeling.

d a t a c o l l e c t i o n , and d a t a handling.

Concerning d a t a , e x t e n s i v e r e c o r d s a r e a v a i l a b l e on hydrology and meteorology. Regular w a t e r q u a l i t y monitoring s t a r t e d t e n y e a r s ago, i n two network sys-

tems c o n s i s t i n g of 9 and 16 s p a t i a l sampling p o i n t s . r e s p e c t i v e l y (10-20 measurements per y e a r ) , b u t i r r e g u - l a r d a t a a r e a l s o a v a i l a b l e d a t i n g back t o t h e e a r l y s i x t i e s . S e v e r a l o t h e r i n s i t u and l a b o r a t o r y measurements were a l s o taken (primary production, e x t i n c t i o n , sediment-water i n t e r a c t i o n , v e l o c i t y . e t c .)

.

A survey was done on t h e n u t r i e n t load between 1975-1979, which

involved 20 t r i b u t a r i e s and 27 sevage d i s c h a r g e p o i n t s (JolAnkai and Somlyddy. 1981) ( i n d i c a t e d i n f i g . 1 ) . On t h e major t r i b u t a r y , d a i l y o b s e r v a t i o n s were made d u r i n g t h i s p e r i o d .

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THE APPROACH

As mentioned i n S e c t i o n 1 t h e s t u d y s h o u l d c o v e r s e v e r a l i n t e r r e l a t e d b u t s t i l l q u i t e d i v e r s e i s s u e s and p r o c e s s e s s u c h a s s c i e n t i f i c u n d e r s t a n d i n g and p o l i c y making, t h e l a k e and i t s r e g i o n , w a t e r s h e d p r o c e s s e s , b i o c h e m i s t r y , hydrodynamics, e t c . Thus t h e d i l e a m a i s which approach c a n b e used f o r t h e r e s e a r c h and w i t h i n

t h i s , f o r modeling. Two e x t r e m e s a r e a s f o l l o w s : ( i ) t o b a s e i t o n i n t u i t i o n and t o d r a s t i c a l l y

s i m p l i f y t h e problem a p r i o r i ;

( i i ) t o e s t a b l i s h o n e l a r g e , d e t a i l e d model which a c c o u n t s f o r a l l t h e s u b p r o c e s s e s and t h e d i f - f e r e n t l e v e l s ( u n d e r s t a n d i n g and management)

.

As t h e f i r s t a p p r o a c h i s n o t a c c e p t a b l e and t h e second is u n r e a l i s t i c , a d i f f e r e n t approach was worked o u t which i s based on t h e i d e a o f d e c o m p o e i t i o n and a g g r e g a t i o n (Somlyddy. 1 9 8 1 a ) .

The a p p r o a c h b e g i n s by decomposing t h e s y s t e m i n t o s m a l l e r , t r a c t a b l e u n i t s f o r m i n g a h i e r a r c h y o f i s s u e s s u b j e c t t o s t u d y . One c a n make d e t a i l e d i n v e s t i g a t i o n s o f each o f t h e s e i s s u e s , u s i n g i n s i t u and l a b o r a t o r y o b s e r v a t i o n s , models and o t h e r a v a i l a b l e i n f o r m a t i o n . T h i s s t e p is f o l l o w e d by a g g r e g a t i o n , t h e aim o f which

i s t o p r e s e r v e and i n t e g r a t e o n l y t h e i s s u e s t h a t a r e e s s e n t i a l f o r t h e h i g h e r s t r a t a o f t h e h i e r a r c h y ( a t t h e u p p e r m s t l e v e l , u l t i m a t e l y f o r a n s w e r i n g q u e s t i o n s o f management), r u l i n g o u t t h e u n n e c e s s a r y d e t a i l s . Prom a s t r u c t u r a l v i e v p o i n t , t h i s i s a n off-line approach, which a l l o w s a p p l i c a t i o n o f d i f f e r e n t t e c h n i q u e s and p r i n c i p l e s a t v a r i o u s l e v e l s a s d e s i r e d , a c c o u n t s f o r u n c e r t a i n t i e s , and l e a d s t o a r e a l i s t i c , y e t s i m p l e . model a t t h e h i g h e s t l e v e l of t h e h i e r a r c h y , where e v a l - u a t i n g management a l t e r n a t i v e s is t h e o b j e c t i v e .

I t is n o t e d t h a t i n e c o l o g i c a l modeling. t h e r e i s a c e r t a i n gap between " l a r g e r " models and " s m a l l e r " mod- e l s ( s e e Beck. 1 9 8 2 ) . I n t h e f i r s t c a s e t h e r e is n e a r l y no hope f o r a p r e c i s e c a l i b r a t i o n , b u t " s m a l l e r " models c a n a l s o b e j u s t a s u n r e a l i s t i c f o r complex problems b e c a u s e of t h e i r s i m p l i c i t y . The a p p r o a c h o u t l i n e d o f - f e r s a r e a s o n a b l e a l t e r n a t i v e f o r s u c h c a s e s .

The a p p l i c a t i o n o f t h i s a p p r o a c h f o r t h e Lake Bala- t o n problem i s e x p l a i n e d w i t h t h e h e l p of f i g u r e 2.

The f i r s t d e c o m p o s i t i o n t h a t d i r e c t l y comes t o mind is t h e d i s t i n c t i o n between l a k e and w a t e r s h e d , s i n c e , a s

F i g u r e 2.-The method o f d e c o m p o s i t i o n : h i e r a r c h y of models

(1) submodels f o r u n i f o r m segments ( d o t t e d a r e a s ) (2) c o u p l i n g o f t h e submodels

.

mentioned b e f o r e , t h e w a t e r q u a l i t y problem l i e s i n t h e l a k e , b u t t h e c a u s e s , and p r a c t i c a l l y 211 c o n t r o l pos- s i b i l i t i e s , a r e t o b e found i n t h e w a t e r s h e d .

The p r o c e d u r e , i n v o l v i n g f i v e s t r a t a , w i l l b e d i s - c u s s e d i n g r e a t e r d e t a i l f o r t h e Lake E u t r o p h i c a t i o n Model (LEM), w i t h r e f e r e n c e t o t h e models which h a v e b e e n e l a b o r a t e d . The p a r a l l e l s i n t h e N u t r i e n t Loading Model (NLM) c a n b e s e e n i n f i g u r e 2.

S t r a t u m 5

F i r s t , t h o s e segments o f t h e l a k e s h o u l d b e i s o l a t - ed which can b e c o n s i d e r e d a p p r o x i m a t e l y u n i f o r m from t h e v i e w p o i n t of w a t e r q u a l i t y ( c o m p l e t e mixing i n s i d e each u n i t ) and from t h e f a c t o r s i n f l u e n c i n g them. The o b j e c t i v e o f t h e m o d e l s o n t h i s s t r a t u m i s t o d e s c r i b e t h e a l g a l dynamics and n u t r i e n t c y c l i n g f o r a l l t h e segments, i n v o l v i n g b o t h t h e w a t e r body and t h e s e d i m e n t . s i n c e t h e l a t t e r i s a s i n k and s o u r c e of v a r i o u s mate- r i a l s and t h e i r i n t e r a c t i o n p l a y s a n i m p o r t a n t r o l e i n s h a l l o w l a k e s . These k i n d s o f models b a s e d o n t h e mass c o n s e r v a t i o n p r i n c i p l e and f o r m u l a t e d t h r o u g h a s e t o f n o n l i n e a r o r d i n a r y d i f f e r e n t i a l e q u a t i o n s (ODES) a r e well-known i n t h e l i t e r a t u r e ( S c a v i a and Robertson.

1 9 7 9 ) . I n t h e frame o f t h e p r e s e n t s t u d y . t h r e e submodels. BPI. BALSECT, and SPlBAL w e r e developed (Hero- d e k e t a l . , 1980; L e o m v . 1980; and v a n S t r a t e n . 1980).

w i t h r e s p e c t t o t h e i r comparison ( v a n S t r a t e n and Somly- ddy. 19801 which d i f f e r s b a s i c a l l y i n t h e number o f s t a t e v a r i a b l e s (between 4 and 7) and e s s e n t i a l para- m e t e r s (10-17). a s w e l l a s i n t h e m a t h e m a t i c a l formula- t i o n o f v a r i o u s p r o c e s s e s and i n t h e p a r a m e t e r e s t i m a - t i o n t e c h n i q u e a d o p t e d . I t is n o t e d h e r e t h a t some o f t h e p a r a m e t e r s c a n b e d e r i v e d from f u r t h e r i s o l a t i o n up t o a lower l e v e l w i t h a p p r o p r i a t e l y d e s i g n e d e x p e r i - ments. As examples, t h e e s t i m a t i o n o f a l g a l growth p a r a m e t e r s from v e r t i c a l p r i m a r y p r o d u c t i o n measurements ( v a n S t r a t e n and Herodek. 1981) and t h e s t u d y o f wind induced sediment-water i n t e r a c t i o n ( s e e t h e sec- t i o n o n wind induced s e d i m e n t w a t e r i n t e r a c t i o n ) may b e mentioned

.

S t r a t u m 4

On t h e n e x t l e v e l t h e s e g m e n t - o r i e n t e d b i o c h e m i c a l and sediment models a r e c o u p l e d by i n v o l v i n g mass in- and o u t f l o w s a t t h e b o u n d a r i e s of t h e u n i t s . F o r t h i s p u r p o s e , a h y d r o d y n a m i c - t r a n s p o r t model c a n b e u s e d . I n l i g h t o f t h e e x p e r i e n c e s g a i n e d from t h e s t u d y of t h e G r e a t Lakes (Boyce e t a l . . 1979). i t was d e c i d e d m t t o u s e a c o u p l e d m u l t i - d i m e n s i o n a l hydrodynamic- t r a n s p o r t model i n c o r p o r a t i n g t h e submodels o f t h e . 1 0 ~ e r s t r a t u m : t h e g a i n i n i n f o r m a t i o n is n o t p r o p o r t i o n - a l t o t h e i n c r e a s e i n c o m p l e x i t y . Here a g a i n , a n o f f - l i n e t e c h n i q u e is a p p l i e d . The b a s i c a s s u m p t i o n i s t h a t it is s u f f i c i e n t t o s u b d i v i d e t h e l a k e i n a l o n g i - t u d i n a l d i r e c t i o n o n l y . T h i s i s s u p p o r t e d by t h e r i v e r - i n e s h a p e of t h e l a k e and t h e presumably e x t e n s i v e t r a n s v e r s a l mixing. s i n c e t h e p r e v a i l i n g wind d i r e c t i o n i s n e a r l y p e r p e n d i c u l a r t o t h e l a k e ' s a x i s ( t h e d e s c r i p - t i o n of t h e s h o r e l i n e e f f e c t s is n o t t h e o b j e c t i v e h e r e ) . C o n s e q u e n t l y , t h e p a r a l l e l development o f a n u n s t e a d y three-. two-, and one-dimensional hydrodynamic model was d e c i d e d o n (Shanahan e t a l . , 1981; Shanahan, 1981; Somlyddy. 1982; Somlyddy and V i r t a n e n . 1 9 8 2 ) . The f i r s t two c a n b e used t o d e r i v e c o n v e c t i o n and t h e l o n g i t u d i n a l d i s p e r s i o n c o e f f i c i e n t ( e i t h e r d i r e c t l y o r i n d i r e c t l y a s a n " e m p i r i c a l " f u n c t i o n of t h e major wind p a r a m e t e r s ) , w h i l e t h e 1-D model c o u l d d e s c r i b e convec- t i o n o n l y ( i t s a d v a n t a g e l i e s i n i t s s i m p l i c i t y and s h o r t e x e c u t i o n t i m e o n t h e c o m p u t e r ) . S u b s e q u e n t l y , t h e s u b m d e l s of s t r a t u m 5 w i l l b e i n c o r p o r a t e d i n a

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s t r a i g h t f o r w a r d way i n t o a s e t of l o n g i t u d i n a l d i s p e r - s i o n equations on s t r a t u m 4 .

A t t h i s l e v e l , t h e 1-D model was aggregated from t h e 3-D v e r s i o n . A f u r t h e r a g g r e g a t i o n can be a r r i v e d a t through t h e u s e of t h e coupled dispersion-biochemical m d e l ( s e e t h e s e c t i o n on a p p l i c a t i o n of hydrodynamic models). O r i g i n a l l y , i n a l l t h r e e biochemical m d e l s ( s e e "Major C h a r a c t e r i s t i c s of t h e System") f o u r segments ( s r mixed r e a c t o r s , s e e f i g . 1 ) a r e assumed; t h e i r c o u p l i n g is based on hydrologic throughflow and a wind i n f l u e n c e d mass exchange process d e s c r i b e d g l o b a l l y . S i n c e t h e model s t r u c t u r e based on ODES has many advan- t a g e s , one of t h e o b j e c t i v e s of t h e s t u d y on t h e 1-D coupled model is whether t h e f o u r b a s i n s concept can be maintained o r n o t .

Stratum 3

The involvement of mass exchange among segments a s d e s c r i b e d b e f o r e w i l l r e s u l t i n t h e Lake E u t r o p h i c a t i o n Model (LPI) ( f i g . 2) which has s e v e r a l f o r c i n g f u n c t i o n s . such a s s o l a r r a d i a t i o n , w a t e r temperature, wind, e t c . ,

( n a t u r a l o r u n c o n t r o l l a b l e f a c t o r s ) and t h e n u t r i e n t l o a d . S i n c e t h e l a t t e r is the only f a c t o r which can be c o n t r o l l e d , i t plays a d i s t i n g u i s h e d r o l e . A thorough d a t a c o l l e c t i o n and t h e d e r i v a t i o n of a n u t r i e n t bal- ance f o r t h e whole l a k e gave a s o l i d background ( f o r d e t a i l s s e e J o l d n k a i and Somlyddy, 1981). The main c o n c l u s i o n s have been sumsarized i n '!Major C h a r a c t e r i s - t i c s of t h e System". Because of t h e high c o n t r i b u t i o n of t h e sewage Load and t h e i n s u f f i c i e n t amount of watershed d a t a o n l y l i m i t e d e f f o r t was expended on non-point s o u r c e modeling ( ~ o g d r d i and Duckstein, 1979). Rather, t h e a n a l y s i s of h i s t o r i c a l r i v e r load d a t a was pre- f e r r e d , which then s a t i s f a c t o r i l y r e s u l t e d i n u n c e r t a i n - t i e s i n t h e load ( s e e t h e s e c t i o n on n u t r i e n t l o a d un- d e r u n c e r t a i n t y and s t o c h a s t i c i t y ) due t o t h e stochas- t i c c h a r a c t e r of t h e h y d r o l o g i c regime and d a t a s c a r c i - t y . The r e s e a r c h a l s o allowed t h e d e r i v a t i o n of t h e temporal and s p a t i a l p a t t e r n of t h e load components, both f o r LEM and t h e Water Q u a l i t y Management Model

(WQMM) on Stratum 2.

Stratum 2

The o b j e c t i v e of WQMM i s t o g e n e r a t e a l t e r n a t i v e management o p t i o n s and s t r a t e g i e s ( t h e e f f e c t of t h e s e being expressed through NLM which should be used h e r e

i n a planning m d e ) and t o s e l e c t from among t h e s e a l - t e r n a t i v e s , on t h e b a s i s of one o r m r e o b j e c t i v e s . Both w a t e r q u a l i t y and c o s t s can b e used a s o b j e c t i v e f u n c t i o n s o r c o n s t r a i n t s , and q u i t e o f t e n t h e i r weight- ing i s r e q u i r e d . Frequently t h e load c a n r e p l a c e t h e l a k e ' s w a t e r q u a l i t y i n t h e o p t i m i z a t i o n , i n which c a s e LEM i s used merely t o check t h e r e a c t i o n of t h e l a k e and WQKM may have a s i m p l e r s t r u c t u r e . Admittedly h o w e v e r , t h e i n c l u s i o n of water q u a l i t y is = r e obvious because of t h e n a t u r e of t h e problem. This f o r m u l a t i o n however l e a d s t o t h e dilemma: how should a complex mod- e l be i n c o r p o r a t e d i n t o t h e o p t i m i z a t i o n framework?

A t t h i s s t e p a g g r e g a t i o n i s a l s o needed. T h i s s t a r t s w i t h t h e s e l e c t i o n of c e r t a i n w a t e r q u a l i t y in- d i c a t o r s c h a r a c t e r i z i n g t h e l a r g e s c a l e and long-term behavior of t h e system s e r v i n g a s a b a s i s f o r d e c i s i o n making. D i f f e r e n t parameters ( y e a r l y peak, d i f f e r e n t averages, d u r a t i o n of c r i t i c a l c o n c e n t r a t i o n s , frequen- cy d i s t r i b u t i o n s , e t c . ) of t y p i c a l v a t e r q u a l i t y components (primary production, a l g a l biomass, Chloro- phyll-a, e t c . ) can be employed a s i n d i c a t o r s . S u b s e q u e n t l y t h e dynamic model LEM can be used i n t e r m of

i n d i c a t o r s e s t a b l i s h e d , I , under reduced l o a d i n g con- d i t i o n s o r i n another way under s e v e r a l l o a d i n g s c t n a r - i o s . L . S i n c e t h e d e f i n i t i o n of i n d i c a t o r s i n t r o d u c e s temporal a v e r a g i n g , i t i s expected t h a t t h e l a k e ' s re- sponse w i l l be l e s s complex compared t o t h e dynamic s i m u l a t i o n and a simple, d i r e c t I ( L ) type r e l a t i o n s h i p can be found f o r t h e new e q u i l i b r i u m . I f such a solu- t i o n has a l r e a d y been a t t a i n e d , LEM could be r e p l a c e d by 1(L) i n WQm; an e s s e n t i a l a g g r e g a t i o n ( s e e t h e sec- t i o n on t h e w a t e r q u a l i t y management model).

Among t h e management a l t e r n a t i v e s , o n l y t h e two most important o p t i o n s a r e mentioned here: ( i ) t e r t i a r y t r e a t m e n t ( p o i n t s o u r c e l o a d r e d u c t i o n ) , ( i i ) e s t a b l i s h - ing r e s e r v o i r s ( c o n s i s t i n g of two segments s e r v i n g f o r t h e removal of both p a r t i c u l a t e and d i s s o l v e d n u t r i e n t forms, r e s p e c t i v e l y (van S t r a t e n e t a 1

.,

1979) a t t h e mouth of r i v e r s which a r e t h e r e c i p i e n t s of p o i n t and non-point s o u r c e p o l l u t a n t s . The o p t i m i z a t i o n should t h e n be based on t h e trade-off between t h e tvo b a s i c a l t e r n a t i v e s , with r e s p e c t t o t h e i r l o c a t i o n s and t h e s p a t i a l v a r i a t i o n of t h e l a k e ' s w a t e r q u a l i t y .

S t r a t u m 1

For t h e sake of completeness i t has t o be mentioned t h a t WQMM could be thought of a s being a p a r t of a r e g i o n a l development p o l i c y model forming the top of t h e pyramid, a f i e l d which i s beyond t h e scope of t h i s s t u d y .

ILLUSTRATION OF THE DIFFERENT STEPS OF THE APPROACH Wind Induced Sediment Water I n t e r a c t i o n (Stratum 5 )

For s t u d y i n g t h e sediment-water i n t e r a c t i o n i n l a k e s , s e v e r a l approaches a r e p o s s i b l e (Sheng and Lick.

1979). I n t h i s s t u d y , y e t a n o t h e r method was chosen (Somlyddy, 19801, i n r e c o g n i t i o n t h a t when eutrophica- t i o n i s c o n s i d e r e d , more than j u s t t h e p h y s i c a l pro- c e s s e s should be examined. Daily measurements were taken f o r 6 months, a t t h e mid-point of t h e Szemes ba- s i n (Basin 2, f i g . 1 ) . The measurements included S e c c h i depth, temperature, suspended s o l i d s (SS), Chloro- phyll-a, and phosphorus f r a c t i o n s a t d i f f e r e n t v e r t i c a l l o c a t i o n s . Wind v e l o c i t y and d i r e c t i o n were recorded c o n t i n u o u s l y , from which hourly averages were c a l c u l a t e d . The o b j e c t i v e of t h e f i r s t p a r t of t h e a n a l y s i s was t o d e s c r i b e t h e dynamics of t h e suspended s o l i d s a s a func- t i o n of wind. T h i s then allowed f o r a c h a r a c t e r i z a t i o n of t h e temporal changes i n t h e l i g h t c o n d i t i o n s , t h e d e p o s i t i o n , and r e s u s p e n s i o n of p a r t i c u l a t e m a t e r i a l and t h e a s s o c i a t e d s o r p t i o n phenomenon. Here t h e be- h a v i o r of SS w i l l be d i s c u s s e d .

The a n a l y s i s s t a r t e d from a s i m p l i f i e d t r a n s p o r t e q u a t i o n f o r d e s c r i b i n g t h e temporal and v e r t i c a l changes of t h e average SS c o n c e n t r a t i o n f o r t h e b a s i n , n e g l e c t i n g inflow and outflow (Somlyddy, 1980).

Afterward t h e e q u a t i o n was i n t e g r a t e d a l o n g t h e depth l e a d i n g t o a n o r d i n a r y d i f f e r e n t i a l e q u a t i o n in- c o r p o r a t i n g the unknovn f l u e s of deposition, Qd, and resuspenswn, Qe, on t h e r i g h t hand s i d e . The objec-

t i v e is t o e s t i m a t e these f l u x e s from the o b s e r v a t i o n s . I n o r d e r t o do t h i s , hypotheses were made based on t h e l i t e r a t u r e : Qd i s p r o p o r t i o n a l t o t h e depth i n t e g r a t e d SS c o n c e n t r a t i o n

,

w h i l e Qe t o some power of t h e wind speed, Wn ( f o r d e t a i l s . s e e Somlyddy. 1980 and 1981b).

This procedure l e d t o t h e e q u a t i o n f o r SS c o n c e n t r a t i o n

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h e r e K1 and K 2 comprise t h e unknovn c o e f f i c i e n t s , de- r i v e d from t h e hypotheses. Consequently, t h e s t r u c t u r e of t h e model should be i d e n t i f i e d and t h e parameter val- ues K 1 , K2, and n, e s t i m a t e d from measurements. The f e a s i b i l i t y of Equation ( 1 ) can be a p p r e c i a t e d from f i g u r e 3a. vhich c l e a r l y shovs t h e i n f l u e n c e of vind v e l o c i t y on t h e c o n c e n t r a t i o n .

F i r s t a non-recursive d e t e r m i n i s t i c e s t i m a t i o n technique v a s adopted t o d e r i v e t h e unknovn c o e f f i c i e n t s v h i c h r e s u l t e d i n r e a l i s t i c v a l u e s , b u t v i t h o u t proving

t h e c o r r e c t n e s s of t h e hypotheses ( a p o s t e r i o r i model s t r u c t u r e i d e n t i f i c a t i o n . s e e Beck. 1982).

For t h i s purpose, a s a second s t e p , t h e Extended Kalman F i l t e r ( E m ) method vas a p p l i e d (Beck and Somly- ddy, 1982). For t h e pover n a v a l u e near t o 1 vas de- r i v e d v h i c h corresponded t o the small Richardson number

(Somlyddy, 1981b). Subsequently n v a s f i x e d t o 1 s i n c e i n t h i s c a s e t h e p h y s i c a l i n t e r p r e t a t i o n of t h e r e s u l t s i s more obvious. The r e c u r s i v e e s t i m a t i o n s t a r t e d from t h e e s t i m a t e s of t h e d e t e r m i n i s t i c technique. The re- s u l t s a r e i l l u s t r a t e d i n f i g u r e 3a. A s is apparent.

the agreement between o b s e r v a t i o n s and model c a l c u l a - t i o n is reasonably good. and the parameters become ap- proximately c o n s t a n t a f t e r t h e f i r s t 40-50 days ( f i g . 3 b ) , proving t h a t t h e w d e l s t r u c t u r e is adequate and t h e d a t a do n o t c o n t a i n more information t h a n d e s c r i b e d by t h e model. Some s l i g h t parameter changes can be ob- s e r v e d a t t h e end of t h e p e r i o d ; t h i s may be caused.

e.g.. by t h e e x c l u s i o n of i n f l o r o u t f l o v p r o c e s s e s ( o r by o t h e r phenomena such a s a l g a l blooms). T h i s s u g g e s t s t h a t t h e i s o l a t i o n of subprocesses is g e n e r a l l y n o t c o p p l e t e . From t h e a n a l y s i s , a r e a l i s t i c o r d e r of magnitudes follows f o r a l l t h e e s s e n t i a l p h y s i c a l q u a n t i t i e s ; i n t h i s connection s e e Somlyddy, 1981b.

A s can be observed i n f i g u r e 3, f o r one w n t h i n t h e middle of t h e t o t a l p e r i o d , no measurements v e r e a v a i l a b l e . so t h e model v a s used f o r p r e d i c t i o n . The a p p r o p r i a t e n e s s of t h e model is a l s o i l l u s t r a t e d by t h e f a c t t h a t a f t e r g e t t i n g nev d a t a , t h e parameter v a l u e s d i d n o t change. T h i s second period s e r v e d f o r v a l i d a - t i o n , f o l l o w i n g t h e i d e n t i f i c a t i o n and c a l i b r a t i o n procedure.

The advantage of t h e simple i n t e r a c t i o n model a r - r i v e d a t i s t h a t i t can be e a s i l y i n c o r p o r a t e d i n t o t h e modeling approach ( f i g . 2). f o r ( i ) c h a r a c t e r i z i n g transparency c o n d i t i o n s i n t h e water and ( i i ) f o r de- s c r i b i n g t h e r e l e a s e of t h e sediment l a y e r a s t h e in- t e r n a l P s o u r c e . A s v a s shovn i n t h e r e p o r t by Gelenc- s & r e t a l , (1982) t h e d e s o r p t i o n of resuspended p a r t i - c l e s i s t h e primary cause of t h e sediment phosphorus

F i g u r e 3a .--1dentif i c a t i o n and parameter e s t i m a t i o n of a model f o r wind induced sediment-water i n t e r a c t i o n f o r Lake Balaton: r e c u r s i v e e s t i m a t e of t h e suspended s o l i d s c o n c e n t r a t i o n ; W

-

d a i l y average wind speed, c

-

suspended s o l i d s c o n c e n t r a t i o n .

* -

o b s e r v a t i o n s .

Figure 3b .-Recursive parameter e s t i m a t e s f o r t h e s e d i - ment-vater i n t e r a c t i o n model.

r e l e a s e ( d i f f u s i o n and convection of pore v a t e r c o n t r i - b u t e t o a l e s s e r e x t e n t ) ; thus, vind-induced i n t e r a c -

t i o n i s r e a l l y of importance.

A p p l i c a t i o n of Hydrodynamic Models (Stratum 4) The r e s u l t s gained from t h e t r a n s i e n t 3-D, 2-0 ( h o r i z o n t a l ) . and 1-D models (Shanahan e t a l . , 1981;

Somlyddy and Virtanen. 1982; and Somlyddy. 1982) shoved t h a t t h e models could be e q u a l l y c a l i b r a t e d a g a i n s t t h e dynamic water l e v e l d a t a . For a n example of t h e a p p l i - c a t i o n of t h e 1-D model, s e e f i g u r e 4. The model was a l r e a d y used i n t h e v a l i d a t i o n phase. The storm v a s c h a r a c t e r i z e d by a l o n g - l a s t i n g l o n g i t u d i n a l wind f o l - lowed by s m a l l e r shocks from d i f f e r e n t d i r e c t i o n s ( f i g . 4 a ) . The agreement between measured and simulated wa- t e r l e v e l s a t t h e tvo ends of t h e l a k e is e x c e l l e n t ( f i g . 4 b ) . The d i s c h a r g e a t t h e Tihany p e n i n s u l a shovs a s t r i k i n g o s c i l l a t i o n between -2000 and 3000 m3/s ( f i g . 4c) a s s o c i a t e d w i t h t h e s e i c h e phenomenon. T h i s back and f o r t h motion is higher by two o r d e r s of magnitude t h a n t h e h y d r o l o g i c t h r o u g h f l o v .

A s mentioned p r e v i o u s l y , t h e 1-D model alone does n o t g i v e s a t i s f a c t o r y i n f o r m a t i o n f o r a v a t e r q u a l i t y s t u d y a s i t s e r v e s t h e l o n g i t u d i n a l convection term o n l y , b u t n o t d i s p e r s i o n . S t i l l t h i s model ver- s i o n , t h e s i m p l e s t , is extremely u s e f u l . Two examples d i s c u s s e d subsequently i l l u s t r a t e t h i s statement:

( i ) To f i n d a more s a t i s f a c t o r y agreement between model s i m u l a t i o n and o b s e r v a t i o n t h a n t h a t given i n f i g u r e 4 i s o f t e n impossible. The r e a s o n i s q u i t e s i r p l e : a small e r r o r i n t h e vind d i r e c t i o n may cause a d r a s t i c change i n t h e vind f o r c e , i f t h e d i r e c t i o n i s f a r from t h e l o n g i t u d i n a l one. I n f a c t , t h e r e a r e many kinds of u n c e r t a i n t i e s i n t h e vind d i r e c t i o n , such a s random f l u c t u a t i o n ( t u r b u l e n c e ) , the i n f l u e n c e of h i l l s on t h e n o r t h e r n s i d e of the l a k e , which cause nonuni- f o r m i t i e s i n t h e vind f i e l d , measurement e r r o r s , e t c . F i g u r e 5 i l l u s t r a t e s t h e c a s e ( t r a n s v e r s a l vind condi-

t i o n s ) . A d e t e r m i n i s t i c s i m u l a t i o n d i d n o t prove ac- c e p t a b l e . Bearing i n mind t h e p o s s i b l e r o l e of uncer- t a i n t i e s , a random component v a s subsequently added to t h e wind d i r e c t i o n (Gaussian d i s t r i b u t i o n , zero mean,

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f o r a two-dimensional model, Somlyddy 1982)

.

F i g u r e 4.-Simulation of a h i s t o r i c a l event: l o n g i t r r d i n a l wind c o n d i t i o n s . ( a ) wind r e c o r d (Muszka- l a y , 1979), W speed, ALFA a n g l e (North s o O ) ; (b) comparison of s i m u l a t e d and observed water l e v e l s (T

-

0 corresponds t o 16/11/1966, 8 a.m.).

Dots i n d i c a t e measurements (Muszkalay, 1979);

(c) computed streamflow r a t e a t Tihany.

Figure 5.-The i n f l u e n c e of wind d a t a u n c e r t a i n t y on t h e d i s c h a r g e a t t h e Tihany p e n i n s u l a (T = 0 corresponds to 8/7/1963. 8 a.m.);

d i s c h a r g e d e r i v e d from measurements (Muszkalay, 1979).

17' s t a n d a r d d e v i a t i o n : a modest v a l u e ) and a Monte Carlo simulation was performed ( f o r d e t a i l s , s e e Somly- ddy, 1982). F i g u r e 5, which smnuarizes t h e r e s u l t s of 100 r u n s , does not r e q u i r e d e t a i l e d d i s c u s s i o n : i t s t r e s s e s t h e eztreme s a s t i v i t y to input data uncer- t a i n t y (compared t o t h i s , t h e parameter s e n s i t i v i t y is n e g l i g i b l e ) and i l l u s t r a t e s how d i f f i c u l t i t i s t o v a l i - d a t e a d e t e r m i n i s t i c model ( t h e s t i u a t i o n is s i m i l a r

( i i ) A t a given l o c a t i o n i n t h e l a k e t h e i n t e n - s i v e back and f o r t h motion causes an o s c i l l a t i o n of v a r i o u s c o n s t i t u e n t s w i t h i n a day, which a l s o s t r o n g l y depends on t h e l o n g i t u d i n a l g r a d i e n t . T h i s may r e s u l t i n q u i t e a l a r g e e r r o r i n t h e c o n c e n t r a t i o n determined through i n s t a n t a n e o u s sampling. For such a s h o r t time s c a l e a s a . d a y , b i o l o g i c a l r e a c t i o n s can be n e g l e c t e d and t h e c o n c e n t r a t i o n f l u c t u a t i o n can be analysed through a coupled 1-D hydrodynamic-transport model as- suming c o n s e r v a t i v e meter i a l

.

Through t h i s model a n u n c e r t a i n t y range of h i s t o r i c a l o b s e r v a t i o n s can be s p e c i f i e d . S i m u l a t i o n s showed t h a t f o r t h i s p a r t i c u l a r l a k e t h e sampling s t r a t e g y f o r Basin I1 ( f i g . 1 ) is of major importance; t h e e r r o r range of a s i n g l e sample a t a f i x e d l o c a t i o n can r e a c h f30%, depending on t h e a c t u a l g r a d i e n t and streamflow p a t t e r n .

The c a l i b r a t i o n of t h e rwo-dimensional hydrodynamic model (Shanahan, 1981) r e s u l t e d i n t h e same wind d r a g c o e f f i c i e n t and bottom f r i c t i o n parameter a s t h e 1-D model v e r s i o n . The s i m u l a t i o n s showed a pronounced c i r - c u l a t i o n p a t t e r n observed a l s o on some s a t e l l i t e photo- graphs and a p h y s i c a l model (GyBrke. 1975)

.

It i s noted t h a t the t r a n s i e n t 3-D model (Shanahan e t a l . . 1981) and a l s o o t h e r s t e a d y s t a t e models t e s t e d . (van S t r a t e n and Somlyddy, 1980) r e f l e c t e d m c h l e s s c i r c u l a t i o n i n t h e l a k e , c l e a r l y showing t h a t o u r understanding o f t h e three-dimensional water notion i n shallow lakes (and w i t h i n t h i s , of t h e v e r t i c a l eddy v i s c o s i t y ) i s far f r o m complete.

I n o r d e r t o couple t h e h o r i z o n t a l l y 2-D hydrodynam- i c model t o a uhosphorus c y c l e model through a s e t of l o n g i t u d i n a l d i s p e r s i o n e q u a t i o n s ( s e e "The Approach"

and "The Lake E u t r o p h i c a t i o n Model (Stratum 3)"), Shana- han (1981) computed t h e d i s p e r s i o n c o e f f i c i e n t ( a s a f u n c t i o n of time and space) from t h e v e l o c i t y f i e l d through extending t h e method of F i s c h e r (1979). D i s - p e r s i o n i s t h e h i g h e s t near t h e ^twoends of t h e l a k e and a t t h e v i c i n i t y of t h e p e n i n s u l a , due t o s t r o n g changes i n geometry and t h e a s s o c i a t e d secondary cur- r e n t s and g y r e s . The l a r g e d i s p e r s i o n c o e f f i c i e n t (up

to 40 m2/s) is due t o s t r o n g winds. A s a temporal and s p a t i a l average, 1 m2/s was found by Shanahan t o be a p p r o p r i a t e enough f o r water q u a l i t y s i m u l a t i o n s .

The c r o s s s e c t i o n a l l y averaged streamflow ( o r ve- l o c i t y ) f o r t h e 1-D d i s p e r s i o n model was d e r i v e d from t h e 2-D hydrodynamic model a f t e r i n t e g r a t i o n . The same p a t t e r n and magnitudes were a r r i v e d a t a s suggested i n f i g u r e s 4 and 5. The f a s t dynamics l e a d t o a small s e i c h e e x c u r s i o n ( l e s s than 1-2 h). This means t h a t t h e r e is an o s c i l l a t o r y t r a n s l a t i o n of water p a r t i c l e s of a s h o r t time s c a l e , w i t h i n which biochemical reac- t i o n s can be p r a c t i c a l l y n e g l e c t e d and thus t h e concen- t r a t i o n averaged over a s e i c h e type event is unchanged ( s e e item ( i i ) ) . From t h i s f e a t u r e i t follows (Shana- han, 1981) t h a t convection w i t h i t s u n c e r t a i n t i e s ( s e e item ( i ) ) can be neglected and only d i s p e r s i o n and hy- d r o l o g i c throughflow should be accounted f o r i n t h e coupled l a k e e u t r o p h i c a t i o n model ( S e c t i o n 4.4).

The N u t r i e n t Load under U n c e r t a i n t y and S t o c h a s t i c i t y (Stratum 3)

The d e t e r m i n i s t i c load e s t i m a t e and t h e s p a t i a l d i s t r i b u t i o n f o r a s p e c i f i c h i s t o r i c a l y e a r (1975-79) i s d e r i v e d on the b a s i s of t h e d a i l y o b s e r v a t i o n s on t h e Zala R i v e r ' s d r a i n i n g 50% of t h e t o t a l watershed, t h e survey on d a t a f o r o t h e r r i v e r s and sewage treatment p l a n t s , on p i l o t zone s t u d i e s , watershed c h a r a c t e r i s - t i c s , e t c . (JolAnkai and Somlyddy, 1 9 8 1 ) . The temporal

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p a t t e r n i s derived from t h e dynamics of t h e Zala River l o a d , o b s e r v a t i o n s made i n t r e a t m e n t p l a n t s d u r i n g t h e off-season and s m e r p e r i o d , r e s p e c t i v e l y , and popula- t i o n f l u c t u a t i o n r e l a t e d t o tourism. Such a load es- t i m a t e i s a c c e p t a b l e f o r t h e d e s c r i p t i v e use of t h e l a k e model, LEH, but c e r t a i n l y n o t f o r planning purposes.

For management of t h e system, t h e s t o c h a s t i c char- a c t e r of t h e load and o t h e r e x i s t i n g u n c e r t a i n t i e s should be accounted f o r . I n o r d e r t o develop a load scenario generator, f i r s t t h e a l l o w a b l e i n t e g r a t i o n period of t h e load i n p u t was t e s t e d through t h e dynamic l a k e model. The a n a l y s i s showed t h a t monthly averages f o r a l l t h e fozeing ftmctwns can be s a t i s f a c t o r i l y used; an important f i n d i n g , a s i t a l l w s g e n e r a t i o n of t h e load on a monthly b a s i s . T h i s can be r e a s o n a b l y d e r i v e d from t h e d a t a a v a i l a b l e , w h i l e t h e procedure f o r a s h o r t e r time s c a l e m u l d be u n r e a l i s t i c .

With t h i s c o n c l u s i o n , t h e Zala River d a t a were a p r i o r i aggregated t o monthly averages and a simple re- g r e s s i o n a n a l y s i s was done between phosphorus l o a d s

(TP and P04-P) and streamflow r a t e . Acceptable ex- p r e s s i o n s were a r r i v e d a t (of c o u r s e , with e r r o r t e r m s ) . D e r i v i n g t h e s t a t i s t i c s of t h e monthly a v e r a g e s t r e a u r flow from long-term o b s e r v a t i o n s (Baranyi. 1979). t h e load can be c a l c u l a t e d i n a s t o c h a s t i c f a s h i o n . F i g u r e 6 shows t h e c h a r a c t e r i s t i c s of t h e load p a t t e r n f o r 1976-79 (from o b s e r v a t i o n s ) and t h e 90% c o n f i d e n c e lev- e l s d e r i v e d f o r t h e long-term l o a d . For i l l u s t r a t i n g t h e i n f l u e n c e of t h e h y d r o l o g i c regime a n e v e n t of l w p r o b a b i l i t y i n J u l y . 1975, is l i k e w i s e i n d i c a t e d . The s t o c h a s t i c i n f l u e n c e of t h e h y d r o l o g i c regime f o r o t h e r subwatersheds was d e r i v e d from t h e a n a l y s i s o u t l i n e d and a v a i l a b l e d a t a f o r t h e s e catchments. The d a i l y ob- s e r v a t i o n s a t t h e mouth s e c t i o n of t h e Zala River were a l s o used t o s t u d y t h e implication o f infrequent obser- vations t y p i c a l f o r most of t h e t r i b u t a r i e s (one o r two samples per month). Due t o s c a r c i t y of d a t a , t h e con- t r i b u t i o n of f l o o d s t o t h e l o a d a r e p a r t i a l l y unob- s e r v e d . A s t h e " a c c u r a t e load" f o r a c e r t a i n p e r i o d (e.g., long-term monthly o r y e a r l y a v e r a g e s ) f o r t h e Zala River c a n be gained from t h e o r i g i n a l d a t a , i t allows one t o s t u d y t h e e r r o r caused by s c a n t y obser- v a t i o n s . The procedure is a s t r a i g h t f o r w a r d M n t e Carlo type technique which s t a r t s v i t h a random s e l e c -

t i o n on t h e d e t a i l e d d a t a s e t f o l l o w i n g t h e sampling s t r a t e g y of t h e o t h e r t r i b u t a r i e s and c a l c u l a t e s t h e

F i g u r e 6.--Influence of t h e h y d r o l o g i c regime on t h e monthly average load. Zala River: 3

-

average load

(1976-79). 4 and 2

-

minimum and maximum v a l u e s ( o b s e r v e d ) , 5 and 1

-

90% confidence l e v e l s .

load of t h e period i n q u e s t i o n . A f t e r making a s u f f i - c i e n t number o f random s e l e c t i o n s t h e s t a t i s t i c a l parameters of t h e load can be determined. The r e s u l t s f o r

t h e long-term monthly a v e r a g e load (on t h e b a s i s of a four y e a r long o b s e r v a t i o n p e r i o d ) a r e i l l u s t r a t e d i n f i g u r e 7 . A s can be s e e n from f i g u r e 7, which shows t h e mean and extreme v a l u e s , a s w e l l a s the domain of 2 s t a n d a r d d e v i a t i o n , t h e e r r o r i s q u i t e high and i t s f l u c t u a t i o n f o l l o w s t h e change i n t h e mean v a l u e . On t h e b a s i s of t h i s study. a random component was added t o t h e monthly average load component (Somlyddy and E l o r a n t a . 1982)

.

From f i g u r e 7, t h e q u e s t i o n a u t o m a t i c a l l y a r i s e s : how can t h e u n c e r t a i n t y domain be reduced? I n a d i f - f e r e n t way, what scmrpling strategy should be followed?

This i s s u e was a l s o s t u d i e d . Besides, f i r s t o r d e r a n a l y s i s (Cochran. 1963). d i f f e r e n t sampling s t r a t e g i e s ( r e g u l a r , random, s t r a t i f i e d , e t c .)

,

were r e a l i z e d i n a Monte Carlo type f a s h i o n . Also, v a r i o u s kinds of e s t i m a t e s (simple, r a t i o , e t c . . s e e e.g., Dolan e t a1

..

1981) were t e s t e d i n o r d e r t o reduce b i a s and v a r i a n c e of t h e load e s t i m a t e . Without going i n t o d e t a i l , ( t h e r e a d e r i s r e f e r r e d t o Somlyddy and van S t r a t e n , f o r t h - coming), i t should be noted t h a t , w i t h proper s t r a t i - f i e d sampling ( f e v samples when t h e v a r i a n c e is small-- l o r f l o w conditions-and f r e q u e n t sampling f o r f l o o d s c h a r a c t e r i z e d by l a r g e v a r i a n c e (Cochran. 1965)). t h e t o t a l amount of samples can be reduced t o one f o u r t h o r one f i f t h . An important c o n c l u s i o n of t h e s t u d y is t h a t t h e v a r i a n c e of t h e l o a d can be r e p l a c e d by t h a t of t h e d i s c h a r g e , Q. ^{A s}Q is a n e a s i l y measureable q u a n t i t y , a r e a l i s t i c s t r a t i f i e d sampling s t r a t e g y can be vorked o u t i n p r a c t i c e , on t h i s b a s i s .

Returning t o t h e development of t h e load genera- t o r , f o r sevage l o a d , t h e same p a t t e r n i s used as i n t h e d e s c r i p t i v e f a s h i o n , but i n a d d i t i o n , an u n c e r t a i n - t y component i s i n t r o d u c e d , which e x p r e s s e s t h e over- load i n t h e t r e a t m e n t p l a n t s due t o t h e p o p u l a t i o n in- c r e a s e i n t h e main t o u r i e t season.

A s a f i n a l o u t p u t of t h e r e s e a r c h o u t l i n e d i n t h i s s e c t i o n , a l o a d s c e n a r i o g e n e r a t o r was developed f o r t h e v h o l e l a k e , which accounted f o r both u n c e r t a i n t y and s t o c h a s t i c i t y . d i s c u s s e d above. For f u r t h e r de- t a i l s s e e Somlyddy and E l o r a n t a (1982).

It i e noted h e r e t h a t u s i n g h i s t o r i c a l d a t a , a s i m i l a r a n a l y s i s was made on c l i m a t i c ( u n c o n t r o l l a b l e ) f a c t o r s , which allowed t h e water temperature and s o h radiation t o be generated i n harmony w i t h each o t h e r .

i n a random fashion. Thus, f u t u r e s c e n a r i o s can be generated f o r a l l t h e e s s e n t i a l f o r c i n g f u n c t i o n s of t h e l a k e model--an e s s e n t i a l t o o l f o r planning purposes ( s e e "The Lake E u t r o p h i c a t i o n Model (Stratum 3)" and

"Water Q u a l i t y Management Model (Stratum 2)") _{T P b d}

.

lWdl

I . .

* J C Y A Y . I J . S O N O

-

Finure 7.--Monthlv

-

averaRe TP load: u n c e r t a i n t y caused by infrecpen; o b s e r v a t i o n s ( Z a l a River, 1976-79) : 3

-

mean value. 4 and 2

-

^fs t a n d a r d d e v i a t i o n . 5 and 1

-

extreme v a l u e s .

(10)

The Lake E u t r o p h i c a t i o n Model ( S t r a t u m 3) R e s u l t s g a i n e d w i t h t h e s i m p l e s t model, SIMBAL ( v a n S t r a t e n . 1980). d e v e l o p e d f o r Lake B a l a t o n . a r e g i v e n below. The model i s a phosphorus c y c l e model.

t h a t i s , a l l t h e s t a t e v a r i a b l e s ( t h e e s s e n t i a l s a r e two a l g a l g r o u p s , d e t r i t u s , and d i s s o l v e d i n o r g a n i c p h o s p h o r u s ) a r e e x p r e s s e d i n t e r m s o f p h o s p h o r u s , f o r t h e f o u r b a s i n s i n d i c a t e d i n F i g u r e 1. A Monte C a r l o s i m u l a t i o n i s i n c o r p o r a t e d i n t o t h e model t o f i n d a r c a s i n p a r a m e t e r s p a c e where t h e model p r o d u c e s r e s u l t s f u l l y w i t h i n s p e c i f i e d b o u n d a r i e s drawn around t h e d a t a t o a c c o u n t f o r d a t a u n c e r t a i n t y and t h u s , i s e a s i l y ap- p l i c a b l e f o r t e s t i n g v a r i o u s h y p o t h e s e s ( v a n S t r a t e n . 1980; F e d r a e t a l . . 1981; H o r n b e r g e r and S p e a r . 1 9 8 0 ) .

Among t h e c a l i b r a t i o n r u n s , r e s u l t s f o r t h e phyto- p l a n k t o n phosphorus, PPP, f o r t h e f o u r b a s i n s , a r e g i v - e n i n f i g u r e 8 ( a s 1977 f o r c i n g s d a t a was u s e d ) t o g e t h - e r w i t h t h e c o r r e s p o n d i n g o b s e r v a t i o n v a r i a b l e , Chloro- p h y l l - a ( b a s i n a v e r a g e v a l u e s ) . It i s p o i n t e d o u t t h a t C h l o r o p h y l l - a and PPP c a n n o t b e d i r e c t l y compared t o e a c h o t h e r ; however, s i n c e a more o r l e s s l i n e a r measurement e q u a t i o n i s e x p e c t e d among them, PPP s h o u l d f o l l o w t h e p a t t e r n o f C h l o r o p h y l l - a : a t r e n d which c a n b e gen- e r a l l y o b s e r v e d . F o r i l l u s t r a t i o n , t h e s t a n d a r d d e v i a - t i o n a r o u n d t h e t r a j e c t o r y f o r B a s i n 2 e s t i m a t e d t h r o u g h t h e Monte C a r l o s i m u l a t i o n i s a l s o i n d i c a t e d ( p a r a m e t e r u n c e r t a i n t y ) . F u r t h e r d i s c u s s i o n o n t h e c a l i b r a t i o n and model improvement r e q u i r e d c a n b e found i n v a n S t r a t e n

( 1 9 8 0 ) .

The r e s u l t s p r e s e n t e d h e r e w e r e from t h e f o u r box model ( f i g . 1 and "The Approach"). Whether t h e c o n c e p t o f t h e f o u r box model c a n b e p r e s e r v e d o r n o t , was t e s t - ed t h r o u g h t h e coupled hydrodynamic-dispersion-P c y c l e m d e l ( s e e " A p p l i c a t i o n o f Hydrodynamic Models ( S t r a t u m 4 ) " ) . I n t h e l i n k e d model, t h e p a r a m e t e r v a l u e s of t h e o r i g i n a l model w e r e m a i n t a i n e d . From t h e c o m p a r i s o n o f t h e s i m u l a t i o n r e s u l t s o f t h e " c o n t i n u o u s " and f o u r box model ( s e e Shanahan, 1981 and Shanahan and Harleman i n t h e s e p r o c e e d i n g s ) , we may c o n c l u d e a s f o l l o w s :

( i ) t h e c o u p l e d t r a n s p o r t - w a t e r q u a l i t y model o b v i o u s l y b e t t e r r e f l e c t s t h e s p a t i a l d e t a i l s and l o c a l i n f l u e n c e s ;

( i i ) t h e f o u r box model u n d e r e s t i m a t e s t h e v a r i - o u s phosphorus c o n c e n t r a t i o n s f o r o n e o f t h e b a s i n s . w h i l e t h e b a s i n wide a v e r a g e s a r e s a t i s f a c t o r y f o r t h e r e s t o f t h e l a k e ;

( i i i ) t h e r e t u r n f l o w v e l o c i t y c a n n o t b e u s e d s i n c e t h e f o u r box f o r m u l a t i o n i n t r o d u c e s a p r i o r i a r t i f i c i a l d i s p e r s i o n , which i s h i g h e r t h a n t h e wind i n d u c e d d i s p e r s i o n .

- _'-

_T¹ ⁴ ¹ ^.1 ^-v _-1¹ ⁴ ¹ ^w

nm vm

F i g u r e 8.--Results from SIMBAL. Comparison of f i e l d d a t a f o r f o u r b a s i n s ( l e f t ) and a v e r a g e model f o r r u n s s a t i s f y i n g t h e b e h a v i o r d e f i n i t i o n ( r i g h t ) , ( 1 ) .

. .

^{( 4 ) .} B a s i n s 1 . . . 4 . Adopted from v a n S t r a t e n ( 1 9 8 0 ) .

( i v ) t h e four boz model w i t h i t s ODE s t r u c t u r e and a l l t h e a d v a n t a g e s a s s o c i a t e d w i t h t h i s can be rea- sonably maintained for practical purposes and s u b s e q u e n t a n a l y s i s .

For management p u r p o s e s t h e s i m u l a t i o n of h i s t o r i c - a l e v e n t s c a n n o t be u s e d . E i t h e r some c r i t i c a l . unfa- v o r a b l e e n v i r o n m e n t a l c o n d i t i o n s s h o u l d be i n t r o d u c e d o r t h e model s h o u l d b e c o n s i d e r e d s t o c h a s t i c t h r o u g h i n p u t d a t a . Here t h e l a t t e r a p p r o a c h was a d o p t e d and t h e g e n e r a t o r s o u t l i n e d i n t h e p r e v i o u s s e c t i o n c o u p l e d t o t h e l a k e model. Tvo e s s e n t i a l r e s u l t s f o r B a s i n I a r e p r e s e n t e d i n f i g u r e s 9 and 1 0 .

I n t h e f i r s t c a s e , u n c e r t a i n t i e s c a u s e d by natural factors were c o n s i d e r e d and t h e 1977 l o a d was m a i n t a i n e d . The summary o f 100 Monte C a r l o r u n s (mean,

+

s t a n d a r d d e v i a t i o n , and t h e e x t r e m e s o f PPP) s u g g e s t s t h e r e l a - t i v e l y l a r g e s e n s i t i v i t y o f t h e l a k e ' s w a t e r q u a l i t y t o m e t e o r o l o g i c a l f a c t o r s and e x p l a i n s t h e e s s e n t i a l y e a r t o y e a r changes o b s e r v e d i n t h e b e h a v i o r o f t h e l a k e e v e n when t h e l o a d remained u n a f f e c t e d . The s e c o n d c a s e ( f i g . 1 0 ) i n v o l v e d t h e random generation o f both natural and c o n t r o l l a b l e f a c t o r s . While f o r t h e p r e v i - ous example t h e s p e c i f i c 1977 l o a d was a d o p t e d , h e r e t h e mean l o a d of t h e i n p u t g e n e r a t o r was d e r i v e d from d a t a f o r t h e p e r i o d 1975-1979 ("The N u t r i e n t Load u n d e r

F i g u r e 9.--The i n f l u e n c e of m e t e o r o l o g i c f a c t o r s o n t h e w a t e r q u a l i t y . B a s i n 1: 3

-

mean v a l u e , 4 and 2 -

+

s t a n d a r d d e v i a t i o n s , 5 and 1

-

extreme v a l u e s .

F i g u r e 10.--The combined i n f l u e n c e of u n c e r t a i n t y and s t o c h a s t i c i t y i n t h e m e t e o r o l o g y and l o a d i n g , r e - s p e c t i v e l y , o n t h e w a t e r q u a l i t y . B a s i n 1 : 3

-

mean v a l u e . 4 and 2

- +

s t a n d a r d d e v i a t i o n s , 5 and 1

-

e x t r e m e v a l u e s .

A Systems Approach to Eutrophication Management with Application to Lake Balaton

NOT F O R QUOTATION WITHOUT P E R M I S S I O N O F THE AUTHOR