Evaluation of Pesticides in Ground Water - American Chemical Society

21 Field Validation of Ground Water Models

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Mary P. Anderson Department of Geology and Geophysics, University of Wisconsin-Madison, Madison, WI 53706

Rigorous field validation or calibration of a groundwater model is often impossible because of uncertainties in input parameters. Nevertheless, an attempt should always be made to demonstrate that a model is capable of predicting concentrations measured in the field. The biggest uncertainty in model input often lies in quantifying the source function. The amount and concentration of contaminants entering the groundwater system depend not only on the amount infiltrating the land surface but also on uptake and chemical reactions occurring in the unsaturated zone. Ideally, a groundwater model should be linked to a model of the unsaturated zone. Other uncertainties typically arise owing to a lack of information on the degradation characteristics of the contaminant in the subsurface and the heterogeneous nature of the porous material that constitutes the aquifer. Heterogeneities influence the configuration of the velocity field and may be critical to proper quantification of contaminant movement but there is no consensus among researchers on the proper way to simulate dispersion of contaminants in groundwater. Moreover, modelers must confront the fact that most groundwater models are designed to simulate two-dimensional flow fields when in reality many groundwater contamination problems are three-dimensional. Whereas, groundwater flow problems generally can be simplified to two dimensions, it appears doubtful that three-dimensional contaminant plumes can be adequately represented by two-dimensional models. The expense of collecting sufficient three-dimensional field data to validate a three-dimensional model will be prohibitive for most studies. These points are demonstrated through discussion of a case example involving the application of a two-dimensional contaminant transport model to simulate the movement of aldicarb in groundwater in Wisconsin. 0097-6156/ 86/ 0315-0396S06.00/ 0 © 1986 American Chemical Society

Garner et al.; Evaluation of Pesticides in Ground Water ACS Symposium Series; American Chemical Society: Washington, DC, 1986.

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P r e d i c t i n g the f u t u r e i s n o t an easy t a s k . Based on e n g i n e e r i n g and g e o l o g i c judgement, i t i s c e r t a i n l y p o s s i b l e to make p r e d i c t i o n s a b o u t the n a t u r e and e x t e n t o f the m i g r a t i o n o f c h e m i c a l s i n groundwater. However, i t i s o f t e n p r e f e r a b l e to use a m a t h e m a t i c a l model i n o r d e r to remove some o f the s u b j e c t i v i t y i n h e r e n t i n making p r e d i c t i o n s . A m a t h e m a t i c a l model c o n s i s t s o f a s e t o f e q u a t i o n s t h a t have been demonstrated to mimic the e f f e c t s o f v a r i o u s p h y s i c a l p r o c e s s e s o p e r a t i v e i n the r e a l w o r l d . However, the d e r i v a t i o n and s o l u t i o n o f the e q u a t i o n s always r e q u i r e a number o f assumptions t h a t s i m p l i f y the way i n which p r o c e s s e s o c c u r i n the r e a l w o r l d . F o r t h i s r e a s o n , models a r e n e v e r c o m p l e t e l y a c c u r a t e and c a n n o t be e x p e c t e d to p r e d i c t the f u t u r e with certainty. The degree o f c o n f i d e n c e t h a t c a n be p l a c e d i n m o d e l i n g p r e d i c t i o n s depends on: 1. how w e l l the r e a l w o r l d s i t u a t i o n conforms to the assumptions imposed by the model; 2. the c e r t a i n t y w i t h which v a r i o u s i n p u t parameters a r e known from f i e l d d a t a . F o r the purposes o f t h i s paper, groundwater models c a n be c l a s s i f i e d i n t o two g e n e r a l c l a s s e s : flow models and c o n t a m i n a n t t r a n s p o r t models. Among groundwater h y d r o l o g i s t e , a t t e n t i o n i s c u r r e n t l y f o c u s e d on c o n t a m i n a n t t r a n s p o r t models. However, the c o n f i g u r a t i o n o f the groundwater flow f i e l d i s n e c e s s a r y i n p u t to these models and thus i t i s e s s e n t i a l to have i n f o r m a t i o n on the head d i s t r i b u t i o n . A groundwater flow model i s o f t e n used as an a i d i n c o n c e p t u a l i z i n g t h e f l o w f i e l d and d e f i n i n g the head distribution. The v e l o c i t y d i s t r i b u t i o n , which i s used d i r e c t l y i n a contaminant t r a n s p o r t model, i s c a l c u l a t e d from the head distribution. C a l i b r a t i o n o f models r e f e r s to the p r o c e s s by which the v a l u e s o f c e r t a i n parameters a r e a d j u s t e d by t r a i l and e r r o r u n t i l the model y i e l d s r e s u l t s which approximate a s e t o f f i e l d d a t a . When c a l i b r a t i n g a groundwater flow model, the o b j e c t i v e i s to match the o b s e r v e d head d i s t r i b u t i o n . When c a l i b r a t i n g a contaminant t r a n s p o r t model, a t t e m p t s a r e made to r e p r o d u c e the measured c o n c e n t r a t i o n d i s t r i b u t i o n o f a g i v e n c h e m i c a l c o n s t i t u e n t . The p r o c e s s o f c a l i b r a t i o n has a l s o been c a l l e d h i s t o r y matching (1). L o o s e l y s p e a k i n g , f i e l d v a l i d a t i o n o f models i s synonymous with c a l i b r a t i o n . S t r i c t l y s p e a k i n g , f i e l d v a l i d a t i o n r e f e r s to a model p r e d i c t i o n made s e v e r a l y e a r s i n t o the f u t u r e , which i s l a t e r v e r i f i e d i n the f i e l d . Under t h i s s t r i c t d e f i n i t i o n , no groundwater contaminant t r a n s p o r t model has been f i e l d v a l i d a t e d to d a t e . I n t h i s paper, p r o c e d u r e s f o r c a l i b r a t i n g flow models and c o n t a m i n a n t t r a n s p o r t models a r e o u t l i n e d and some o f the d i f f i c u l t i e s f r e q u e n t l y encountered during c a l i b r a t i o n a r e discussed. An example o f a c o n t a m i n a n t t r a n s p o r t model a p p l i e d to a problem i n v o l v i n g a l d i c a r b m i g r a t i o n i n groundwater i n W i s c o n s i n i s a l s o presented. Dimensionality R e a l w o r l d problems a r e t h r e e - d i m e n s i o n a l i n n a t u r e b u t t h r e e d i m e n s i o n a l models a r e seldom used i n p r a c t i c e because i t i s r a r e


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to have adequate t h r e e - d i m e n s i o n a l f i e l d d a t a . Moreover, t h r e e d i m e n s i o n a l models a r e cumbersome to use. T h e r e f o r e , a key c o n c e r n i n s e l e c t i n g a m a t h e m a t i c a l model i s whether the problem a t hand c a n be s i m p l i f i e d to one o r two d i m e n s i o n s . Most flow problems c a n be r e a d i l y s i m p l i f i e d t o two-dimensions and most o f the s t a n d a r d methods f o r t r e a t i n g groundwater s u p p l y problems a r e b u i l t around two-dimensional a n a l y s e s . I t i s less easy to j u s t i f y the use o f two-dimensional a n a l y s e s f o r contaminant t r a n s p o r t problems. However, because t h r e e - d i m e n s i o n a l contaminant t r a n s p o r t models a r e p a r t i c u l a r l y unwieldy, most r e a d i l y a v a i l a b l e t r a n s p o r t models and most r e p o r t e d a p p l i c a t i o n s a r e two-dimensional i n nature. Flow Models The two-dimensional g o v e r n i n g groundwater flow i s :

+

e q u a t i o n used

Ιτ

( Τ

Λ7

>

"

S

i n most s i m u l a t i o n s o f

f t "

W

(1)

where h i s head; T and T a r e components o f the t r a n s m i s e i v i t y t e n s o r ; S i s s t o r a g e c o e f f i c i e n t and W i s the r e c h a r g e r a t e . The c a l i b r a t i o n p r o c e s s f o r flow models i d e a l l y c o n s i s t s o f two s t e p s — a s t e a d y s t a t e c a l i b r a t i o n phase and a t r a n s i e n t c a l i b r a t i o n phase, sometimes c a l l e d model v e r i f i c a t i o n ( 2 ) . D u r i n g the s t e a d y s t a t e c a l i b r a t i o n phase, the t r a n s m i s e i v i t y d i s t r i b u t i o n and the r e c h a r g e r a t e a r e a d j u s t e d w i t h i n a p r e - d e t e r m i n e d r e a s o n a b l e range u n t i l the s t e a d y s t a t e heads o b s e r v e d i n the f i e l d a r e matched. Boundary c o n d i t i o n s may a l s o be a d j u s t e d . I d e a l l y , the parameters determined d u r i n g the s t e a d y s t a t e c a l i b r a t i o n phase a r e v e r i f i e d d u r i n g a t r a n s i e n t c a l i b r a t i o n phase. D u r i n g t r a n s i e n t c a l i b r a t i o n , the s t o r a g e c o e f f i c i e n t i s a d j u s t e d and minor adjustments may a l s o be made i n the t r a n s m i s s I v i t y d i s t r i b u t i o n . However, t r a n s i e n t d a t a s e t s such as drawdown d a t a from w e l l pumping, o r a r e c o r d o f the d e c l i n e o f water l e v e l s d u r i n g a drought, a r e seldom a v a i l a b l e and i t i s common to s k i p the v e r i f i c a t i o n phase. A good d i s c u s s i o n o f the s t e p s i n v o l v e d I n c a l i b r a t i o n o f a flow model c a n be found i n (3). x

y

T r a n s m i s s i v i t y and s t o r a g e c o e f f i c i e n t a r e s t a n d a r d a q u i f e r parameters t h a t c a n be e s t i m a t e d from g e o l o g i c d a t a . Recharge r a t e i s one o f the most d i f f i c u l t parameters to e s t i m a t e w i t h c o n f i d e n c e and i t i s s t a n d a r d p r a c t i c e to l e t r e c h a r g e e q u a l a f r a c t i o n o f the average annual p r e c i p i t a t i o n . The r a t i o o f r e c h a r g e to p r e c i p i t a t i o n w i l l v a r y w i t h the g e o g r a p h i c l o c a t i o n o f the study s i t e . Groundwater r e c h a r g e i n W i s c o n e i n i e r o u g h l y e e t i m a t e d to be onet h i r d o f p r e c i p i t a t i o n , o r a b o u t 10 i n / y r (254 mm/yr). However, i t i e l i k e l y t h a t a c t u a l a v e r a g e a n n u a l r e c h a r g e variée w i t h i n the e t a t e from c l o e e to z e r o i n p a r t e o f e a e t e r n Wieconein, where t h e r e


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a r e n e a r l y i m p e r v i o u s s o i l s , to perhaps as much as 15 i n / y r (381 mm/yr) i n the c e n t r a l and n o r t h e r n p o r t i o n s o f the s t a t e , where t h e r e a r e sandy g l a c i a l deposit's a t the s u r f a c e . I d e a l l y the e n t i r e s u b s u r f a c e s h o u l d be t r e a t e d i n a s i n g l e model. The g o v e r n i n g e q u a t i o n f o r groundwater flow c a n be g e n e r a l i z e d to i n c l u d e the u n s a t u r a t e d zone and a model based on t h i s g o v e r n i n g e q u a t i o n a l l o w s the r e c h a r g e p r o c e s s to be s i m u l a t e d d i r e c t l y w i t h i n the model ( 4 - 6 ) . However, these types o f models a r e unwieldy and u s u a l l y a r e a v o i d e d f o r p r a c t i c a l a p p l i c a t i o n s . O t h e r i n v e s t i g a t o r s (7) a d v o c a t e d the use o f l i n k e d models i n which a o n e - d i m e n s i o n a l u n s a t u r a t e d column model i s used to c a l c u l a t e amounts o f r e c h a r g e a r r i v i n g a t the water t a b l e . T h i s a p p r o a c h has r e c e n t l y been a p p l i e d to a problem i n v o l v i n g p e s t i c i d e movement i n the s u b s u r f a c e ( 8 ) . The o u t p u t o f a flow model c o n s i s t s o f the head d i s t r i b u t i o n i n time and space. D a r c y ' s Law i s used to c o n v e r t the head d i s t r i b u t i o n to a v e l o c i t y d i s t r i b u t i o n s u i t a b l e f o r Input to a c o n t a m i n a n t t r a n s p o r t model. I n a two-dimensional a p p l i c a t i o n , D a r c y ' s Law i s used to compute two s e t s o f v e l o c i t y components: K

~ x 9_h 9

η

* (2)

K

" y 3h η

3y

where v and v a r e the components o f the average l i n e a r v e l o c i t y ; K and Ky a r e components o f the h y d r a u l i c c o n d u c t i v i t y t e n s o r and η i s effective porosity. H y d r a u l i c c o n d u c t i v i t y i s r e l a t e d to t r a n s m i s s i v i t y as f o l l o w s : x

y

x

T

x

- K b x

(3) Ty = Kyb where b i s the s a t u r a t e d t h i c k n e s s o f the a q u i f e r . The e f f e c t i v e p o r o s i t y i s a measure o f the i n t e r c o n n e c t e d v o i d space and g e n e r a l l y ranges between 0.15 and 0.35. F o r sandy m a t e r i a l s , e f f e c t i v e p o r o s i t y can be taken e q u a l to s p e c i f i c y i e l d . A compilation of r e p r e s e n t a t i v e v a l u e s f o r groundwater flow parameters f o r use i n m o d e l i n g c a n be found i n ( 9 ) . Contaminant

T r a n s p o r t Models

The t w o - d i m e n s i o n a l g o v e r n i n g e q u a t i o n used i n most contaminant transport applications i s : 3 /~ T&>\\

9c , _ a x" °12 3cv 3y> +

+,

3

9721

- ^(cVy) = R _

+

3c , ^ 3c + °22

37) - 3 â /^ c v* )

a7

XcR -

x

x

_


(4)

400

E V A L U A T I O N O F P E S T I C I D E S IN G R O U N D W A T E R

D

l l

=

2

°L c o s 6 D

1 2

s i n 8 ; D 2 2 = &L s i n 6 + 2

+

= D i =

2

(OL-0 )

2

T

s i n Q c o s

2

cos e;

e

where c i s c o n c e n t r a t i o n and c' i s the s o u r c e c o n c e n t r a t i o n ; i s the 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 and Dr i s the t r a n s v e r s e d i s p e r s i o n c o e f f i c i e n t ; θ i s the a n g l e o f r o t a t i o n between the l o c a l and g l o b a l c o o r d i n a t e systems and R i s the r e t a r d a t i o n f a c t o r . When s u f f i c i e n t f i e l d data a r e a v a i l a b l e , c a l i b r a t i o n c o n s i s t s of a t t e m p t s to r e p r o d u c e the c o n f i g u r a t i o n o f an o b s e r v e d plume o f c o n t a m i n a t e d water. Unknown parameters s u b j e c t to adjustment d u r i n g c a l i b r a t i o n i n c l u d e the d i s p e r s i o n parameters known as l o n g i t u d i n a l and t r a n s v e r s e d i s p e r s i v i t y ( 1 0 ) . D i s p e r s i v i t i e s a r e r e l a t e d to the d i s p e r s i o n c o e f f i c i e n t s as f o l l o w s : D

L

D

T

= =

* I νI a J ν J L

T

ν = / v

x

+ v

+ D* + D*

(5)

y

where a^ and a? a r e the d i s p e r s i v i t i e s and D* i s the c o e f f i c i e n t o f molecular d i f f u s i o n . R e p r e s e n t a t i v e v a l u e s f o r parameters used i n c o n t a m i n a n t t r a n s p o r t models c a n be found i n ( 9 ) . A key c o n s i d e r a t i o n d u r i n g model c a l i b r a t i o n i s the dimen s i o n a l i t y o f the problem. I f a two-dimensional model i s used to s i m u l a t e a t h r e e - d i m e n s i o n a l plume, some d i s c r e t i o n must be used i n s e l e c t i n g c o n c e n t r a t i o n d a t a a g a i n s t which to c a l i b r a t e the model. For example, i n a t w o - d i m e n s i o n a l a r e a l modeling a p p l i c a t i o n i t i s g e n e r a l l y assumed t h a t the contaminant i s u n i f o r m l y d i s t r i b u t e d t h r o u g h o u t the e n t i r e s a t u r a t e d t h i c k n e s s o f the a q u i f e r . I f the plume i s s t r a t i f i e d o r does n o t p e n e t r a t e the f u l l t h i c k n e s s o f the a q u i f e r , c o n c e n t r a t i o n d a t a o b t a i n e d from v e r t i c a l l y n e s t e d w e l l s s h o u l d be a v e r a g e d b e f o r e comparing f i e l d d a t a to model r e s u l t s . A n o t h e r s t r a t a g e m may be n e c e s s a r y i f t h e r e a r e n o t enough f i e l d d a t a to c a l c u l a t e r e l i a b l e v e r t i c a l l y averaged c o n c e n t r a t i o n s . Examples o f model c a l i b r a t i o n a r e c i t e d i n (11) and (12) and an example o f an a t t e m p t to f i e l d v a l i d a t e a model i s d i s c u s s e d i n (13). An example o f a t w o - d i m e n s i o n a l model a p p l i c a t i o n f o r a case i n which the f i e l d d a t a were i n s u f f i c e n t f o r c a l c u l a t i n g r e l i a b l e v e r t i c a l a v e r a g e s and were a l s o i n s u f f i c i e n t f o r d e f i n i n g the a r e a l e x t e n t o f the plume, i s p r e s e n t e d below. Case Study Introduction. A problem i n v o l v i n g the movement o f a l d i c a r b i n groundwater i n the c e n t r a l sand p l a i n a r e a o f W i s c o n s i n ( F i g u r e 1) w i l l be p r e s e n t e d to i l l u s t r a t e the d i f f i c u l t i e s i n v o l v e d i n model calibration. A l d i c a r b i s a s y s t e m i c p e s t i c i d e manufactured by U n i o n C a r b i d e under the t r a d e name Temik. I n W i s c o n s i n , Temik i s a p p l i e d i n p o t a t o f u r r o w s d u r i n g p l a n t i n g to c o n t r o l a v a r i e t y o f i n s e c t s , m i t e s and nematodes. The f i e l d study which s u p p l i e d the f i e l d d a t a


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or

Figure

1.

L o c a t i o n map

o f the C e n t r a l Sand P l a i n

i n Wisconsin.


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E V A L U A T I O N O F P E S T I C I D E S IN G R O U N D W A T E R

f o r t h i s s i m u l a t i o n was p a r t o f an i n v e s t i g a t i o n of a l d i c a r b c o n t a m i n a t i o n o f groundwater beneath s e v e r a l a g r i c u l t u r a l f i e l d s i n W i s c o n s i n (14-17). The f i e l d d a t a r e p o r t e d i n t h i s paper were taken from these s o u r c e s . The computer code used i n t h i s problem s o l v e s the a d v e c t i o n d i s p e r s i o n e q u a t i o n i n two dimensions u s i n g a random walk t e c h n i q u e (18). The code a l s o c o n t a i n s a two-dimensional flow model component t h a t i n t e r f a c e s w i t h the random walk model. The g r i d shown i n F i g u r e 2 was adapted from p r e l i m i n a r y m o d e l i n g s i m u l a t i o n s (16) and was used f o r a l l the s i m u l a t i o n s r e p o r t e d h e r e . A l d i c a r b was a p p l i e d i n 1979 and 1980, to the p o r t i o n o f the f i e l d shaded i n F i g u r e 2, a t a r a t e of 3 l b s / a c r e of a c t i v e i n g r e d i e n t o f Temik. A l d i c a r b was a p p l i e d to the e n t i r e shaded a r e a i n 1979, but to o n l y the w e s t e r n h a l f o f the shaded a r e a i n 1980. A l d i c a r b was detected i n f o u r o b s e r v a t i o n w e l l s e t s , C2, C7, C4 and C9, l o c a t e d b e n e a t h and downgradient o f the a l d i c a r b - t r e a t e d p o r t i o n o f the f i e l d . The l o c a t i o n s o f the w e l l s e t s a r e shown i n F i g u r e 2. A well set (or w e l l n e s t ) c o n s i s t s of two o r more p i e z o m e t e r s f i n i s h e d a t d i f f e r e n t depths below the water t a b l e . E a c h p i e z o m e t e r was c o n s t r u c t e d w i t h a 3 f o o t (0.91 m) w e l l s c r e e n . A bundle p i e z o m e t e r s i m i l a r to the type d e s c r i b e d i n (19) was l o c a t e d n e a r the c o n v e n t i o n a l n e s t e d p i e z o m e t e r s a t s i t e 4. The bundle p i e z o m e t e r ( o r m u l t i l e v e l s a m p l e r ) c o n s i s t e d o f 9 s a m p l i n g p o r t s , each open to a p p r o x i m a t e l y 6 i n c h e s o f the a q u i f e r . The d i s t a n c e between sampling p o r t s was a b o u t 1.5 f e e t (0.46 m). Flow M o d e l i n g . The flow component of the random walk model was used to produce the head d i s t r i b u t i o n shown i n F i g u r e 3a. The h y d r a u l i c c o n d u c t i v i t y o f the a q u i f e r was s e t e q u a l to 200 f t / d a y (61 m/day). The s a t u r a t e d t h i c k n e s s o f the a q u i f e r i s e q u a l to the e l e v a t i o n o f the water t a b l e above the impermeable bedrock; the water t a b l e e l e v a t i o n i s a d j u s t e d a u t o m a t i c a l l y d u r i n g the i t e r a t i o n p r o c e s s used to s o l v e the flow e q u a t i o n . Boundary c o n d i t i o n s used i n the s i m u l a t i o n c o n s i s t e d o f s p e c i f i e d heads a l o n g the e a s t e r n and w e s t e r n s i d e s o f the modeled a r e a and no flow c o n d i t i o n s a l o n g the n o r t h e r n and s o u t h e r n edges. Under these boundary c o n d i t i o n s water Is s u p p l i e d to the a q u i f e r as a r e s u l t o f an Imposed head g r a d i e n t . Hence, i t was n o t n e c e s s a r y to s u p p l y water to the a q u i f e r v i a r e c h a r g e and the r e c h a r g e r a t e was s e t e q u a l to z e r o f o r the purposes of c r e a t i n g the flow f i e l d shown i n F i g u r e 3a. However, s e t t i n g r e c h a r g e e q u a l to z e r o i n the flow model causes an I n c o n s i s t e n c y between the flow component and the random walk component o f the model. When s o l v i n g the random walk component, i t i s n e c e s s a r y to s p e c i f y a l o a d i n g r a t e , d e f i n e d to be the v o l u m e t r i c r e c h a r g e r a t e to the water t a b l e times the c o n c e n t r a t i o n of the l e a c h a t e . During c a l i b r a t i o n e f f o r t s d e s c r i b e d below, the l o a d i n g r a t e was e s t i m a t e d to be 0.0548 l b / a c r e (6.14 kg/km^) o f a l d i c a r b . I d e a l l y , one s h o u l d s p e c i f y a non z e r o r e c h a r g e r a t e d u r i n g those time p e r i o d s when l e a c h i n g i s assumed to o c c u r and s o l v e f o r the t r a n s i e n t head d i s t r i b u t i o n d u r i n g and a f t e r leaching episodes. S e n s i t i v i t y t e s t i n g o f the flow model assuming a r e c h a r g e r a t e of 10 i n / y r (254 mm/yr) d u r i n g l e a c h i n g e p i s o d e s , demonstrated t h a t t r a n s i e n t head d i s t r i b u t i o n s a r e not a p p r e c i a b l y


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Evaluation of Pesticides in Ground Water - American Chemical Society

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