Nutrient models for engineering management of Pamlico River, NC

NUTRIENT MODELS FOR

ENGINEERING MANAGEWENT

OF

PAMLTCO

ESTUARY, NORTH CAROLINA

Donald

T.

L a u r i a and

C h a r l e s R , O'Melia

Department of Environmental S c i e n c e s and Engineering U n i v e r s i t y of North C a r o l i n a a t Chapel H i l l

The work upon which t h i s p u b l i c a t i o n i s based was s u p p o r t e d i n p a r t by

funds provided by t h e O f f i c e of Water Research and Technology, U.S.

Department of t h e I n t e r i o r , Washington, D . C . , through t h e Water Resources Research I n s t i t u t e of t h e U n i v e r s i t y of North C a r o l i n a a s a u t h o r i z e d by

t h e Water Research and Development Act of 1978.

ACKNOWLEDGEMENTS

T h i s r e p o r t i s t h e r e s u l t of t h e knowledge and work of many p e r s o n s . The most i m p o r t a n t c o n t r f b u t i o n s have been made by s t u d e n t s i n t h e

Department of Environmental S c i e n c e s and Engineering, w i t h s p e c i a l t h a n k s t o Bobby White, B i l l Wright, J i m E r i c s o n , Schoou Yuh Chang, John M a r t i n i e r e , and Dave Green. Drs. William Snodgrass (Canada) and Mehmet Karpuzcu (Turkey) provided a s s i s t a n c e i n sediment p r o c e s s e s and d i s p e r s i o n modeling,

r e s p e c t i v e l y . We a r e i n d e b t e d t o o u r coworkers, Drs, Ed Kuenzler, Don S t a n l e y , and J e f f Koenings f o r s h a r i n g t h e i r time and knowledge of

b i o l o g i c a l p r o c e s s e s . The d a t a o b t a i n e d by D r . John Hobbie and coworkers a t North C a r o l i n a S t a t e U n i v e r s i t y were i n v a l u a b l e , We a r e a l s o g r a t e f u l f o r t h e generous a s s i s t a n c e of D r . Graham Davis ( E a s t C a r o l i n a U n i v e r s i t y ) and Doug Mercer of Texasgulf.

DISCLAIMER STATEMENT

Contents of t h i s p u b l i c a t i o n do n o t n e c e s s a r i l y r e f l e c t t h e views and p o l i c i e s of t h e O f f i c e of Water Research and Technology, U, S . Depart- ment of t h e I n t e r i o r , n o r does mention of t r a d e names o r commercial

p r o d u c t s c o n s t i t u t e t h e i r endorsement o r recommendation f o r u s e by t h e U.S.

ABSTRACT

The s p e c i f i c o b j e c t i v e s of t h i s r e s e a r c h a r e f o u r i n number: t o develop p r e d i c t i v e models f o r n u t r i e n t s and a s s o c i a t e d w a t e r q u a l i t y p a r a m e t e r s i n t h e Pamlico E s t u a r y f o r u s e i n managing t h a t a q u a t i c

system, t o c a l i b r a t e and v e r i f y t h e s e models u s i n g a v a i l a b l e d a t a , t o u s e t h e models t o s i m u l a t e o r p r e d i c t w a t e r q u a l i t y i n t h e Pamlico E s t u a r y under d i f f e r e n t n u t r i e n t l o a d i n g s , and t o u s e t h e model t o e v a l u a t e t h e s i g n i f i c a n c e of s e l e c t e d p h y s i c a l , chemical and b i o l o g i c a l p r o c e s s e s i n t h e e s t u a r y .

Two s t e a d y - s t a t e

,

one-dimensional models have been developed and v e r i f i e d . One model, designed f o r w i n t e r c o n d i t i o n s , c o n s i d e r s

phosphorus a s t h e n u t r i e n t l i m i t i n g a l g a l growth d u r i n g t h a t s e a s o n . The second model, developed f o r summer s e a s o n s , i s based on n i t r o g e n a s t h e l i m i t i n g n u t r i e n t .

S i m u l a t i o n s u s i n g t h e s e models i n d i c a t e t h a t p a s t i n d u s t r i a l d i s c h a r g e s of phosphorus have had s i g n i f i c a n t e f f e c t s on w a t e r q u a l i t y i n t h e e s t u a r y , A d d i t i o n a l s i m u l a t i o n s i n d i c a t e t h a t r e d u c t i o n of

phosphorus i n p u t s t o l e v e l s s p e c i f i e d i n p r e s e n t d i s c h a r g e p e r m i t s w i l l produce s u b s t a n t i a l improvements i n w a t e r q u a l i t y .

The r e s e a r c h a l s o i n d i c a t e s t h a t n i t r o g e n i n c o r p o r a t e d i n t o

a l g a l blooms d u r i n g a w i n t e r s e a s o n i s d e t a i n e d i n e s t u a r y s e d i m e n t s u n t i l t h e f o l l o w i n g summer, when i t can b e used a g a i n a s a n u t r i e n t s o u r c e

under t h e n i t r o g e n - l i m i t e d c o n d i t i o n s t h a t p r e v a i l a t t h a t t i m e . The r e s u l t s a l s o i n d i c a t e t h a t r e l e a s e of n i t r o g e n from e s t u a r y s e d i m e n t s i s

a major f a c t o r i n summer a l g a l blooms,

TABLE OF CONTENTS

. . .

Acknowledgements

A b s t r a c t

. . .

. . .

L i s t o f F i g u r e s

. . .

L i s t of T a b l e s

Summary and C o n c l u s i o n s

. . .

. . .

1

.

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

2

.

O b j e c t i v e s

. . .

3

.

E s t u a r y C o n d i t i o n s

. . .

. . .

.

4 Model F o r m u l a t i o n

5

.

Hydrodynamic P a r a m e t e r s

. . .

. . .

.

6 W i n t e r Model

. . .

.

7 S u ~ m e r Model

8

.

S i m u l a t i o n s

. . .

. . .

.

9 D i s c u s s i o n s

1 0

.

R e f e r e n c e s

. . .

11

.

Appendices

. . .

Appendix 1

.

W i n t e r Model Computer Program

. . .

Appendix 2

.

Summer Model Computer Program

Appendix 3 . User's Guide f o r P a m l i c o Models

. . .

P a g e

.

ii

.

iii

.

vii

.

i x

.

x i

1

.

8

.

11

.

1 5

.

24

.

33

.

45

.

5 8

.

76

.

86

.

88

.

8 8 102

LIST OF FIGURES

Page

. . .

.

1 The Tar-Pamlico Drainage Basin 2

. . .

.

2 T a r R i v e r Flows a t Tarboro (1971) 3

. . .

3

.

S a l i n i t y i n Pamlico E s t u a r y a t Midpoint (1971) 3

. . .

4

.

Temperature i n Pamlico E s t u a r y a t Midpoint (1971) 3

. . .

5

.

Sampling S t a t i o n s of Hobbie and Coworkers

6

. . .

6

.

Flow Diagram of t h e Modeling P r o c e s s 1 0

. . .

7

.

E s t u a r y Segments f o r t h e F i n i t e S e c t i o n Models 18

. . .

8

.

Map of E s t u a r y Segments and F i e l d Sampling S t a t i o n s 25

. . .

.

9 Schematic of P r o c e s s e s i n F i n a l W i n t e r Model 38

. . .

10

.

Schematic of E q u a t i o n s i n F i n a l Winter Model 4 1

. . .

11

.

C a l i b r a t i o n of Winter Model (1972) 44

. . .

12

.

V e r i f i c a t i o n of Winter Model (1970) 46

. . .

1 3

.

V e r i f i c a t i o n of Winter Model (1971) 47

. . .

14

.

V e r i f i c a t i o n of Winter Model (1973) 48

15

.

Schematic of P r o c e s s e s i n F I n a l Summer Model

. . .

52

. . .

16

.

Schematic of E q u a t i o n s i n F i n a l Summer Model 55

1 7

.

C a l i b r a t i o n of Summer Model (1970)

. . .

57

. . .

18. V e r i f i c a t i o n of Summer Model (1971) 60

. . .

1 9

.

V e r i f i c a t i o n of Summer Model (1972) 6 1

20

.

P r e d i c t e d E f f e c t s of Changes i n Texasgulf Phosphorus I n p u t s

on E s t u a r i n e Water Q u a l i t y

.

W i n t e r . 1970 C o n d i t i o n s

. . .

63 2 1

.

P r e d i c t e d E f f e c t s of Changes i n Texasgulf Phosphorus I n p u t s

. . .

.

on E s t u a r i n e Water Q u a l i t y Summer. 1970 C o n d i t i o n s 64 22

.

P r e d i c t e d E f f e c t s of Allowable Average and Weekly Maximum

Texasgulf Phosphorus Tnputs on E s t u a r i n e Water Q u a l i t y

-

Winter. 1970 C o n d i t i o n s

. . .

67

Page 2 3 . P r e d i c t e d E f f e c t s of Allowable Average and Weekly Maximum

Texasgulf Phosphorus I n p u t s on E s t u a r i n e Water Q u a l i t y

-

Summer,

1 9 7 0 C o n d i t o n s , . . . , . , , , , . , . ,

. . , . . .

68 2 4 . P r e d i c t e d E f f e c t s of Allowable Average Combined I n d u s t r i a l

Phosphorus I n p u t s on E s t u a r i n e Water Q u a l i t y

-

W i n t e r , 1970

C o n d i t i o n s . .

. . .

70 25, P r e d i c t e d E f f e c t s of Allowable Average Combined I n d u s t r i a l

Phosphorus I n p u t s on E s t u a r i n e Water Q u a l i t y

-

Summer,

1970 C o n d i t i o n s

. . .

7 1 2 6 . P r e d i c t e d E f f e c t s of Allowable Weekly Maximum Combined

I n d u s t r i a l Phosphorus I n p u t s on E s t u a r i n e Water Q u a l i t y

-

W i n t e r , 1 9 7 0 C o n d i t i o n s

. . .

7 2 2 7 . P r e d i c t e d E f f e c t s of A l l o w a b l e Weekly Maximum Combined I n d u s t r i a l

Phosphorus I n p u t s on E s t u a r i n e Water Q u a l i t y

-

Surnmer, 1970

C o n d i t i o n s

. . .

73

2 8 . Comparison of P r e d i c t e d E f f e c t s of Allowable Average and Weekly Maximum Combined I n d u s t r i a l Phosphorus I n p u t s w i t h H i s t o r i c a l

. . .

Response

-

W i n t e r , 1970 7 4

2 9 . Comparison o f P r e d i c t e d E f f e c t s of Allowable Average and Weekly Maximum Combined I n d u s t r i a l Phosphorus I n p u t s and H i s t o r i c a l

. . .

Response

-

Summer, 1970 7 5

v i i i

LIST OF TABLES

Page

. . .

1. Pamlico River Analyses by Hobbie e t a l . 7

. . .

.

2 Average E s t u a r y C o n c e n t r a t i o n s 13

. . .

.

3 Approximate N u t r i e n t Loads on Pamlico E s t u a r y 1 6

. . .

.

4 C h a r a c t e r i s t i c s of Pamlico R i v e r S e c t i o n s 26

. . .

.

5 I n c r e a s e i n Drainage Area Along Pamlico R i v e r 29

. . .

6

.

Winter Model P a r a m e t e r s and Boundary C o n d i t i o n s 43

Summary and Conclusions

The models developed i n t h i s r e s e a r c h a r e made p o s s i b l e by e x t e n s i v e f i e l d d a t a f o r t h e Pamlico E s t u a r y o b t a i n e d by Hobbie and coworkers d u r i n g t h e y e a r s 1970 t o 1973, and by d a t a f o r t h e Texasgulf d i s c h a r g e o b t a i n e d over t h e same p e r i o d by p e r s o n n e l a t T e x a s g u l f ,

Two s t e a d y - s t a t e , one-dimensional models f o r t h e Pamlico E s t u a r y have been developed. One i s f o r w i n t e r s e a s o n s , and i s based on phosphorus b e i n g

t h e l i m i t i n g n u t r i e n t f o r p h o t o s y n t h e t i c p r o c e s s e s , I t p e n n i t s p r e d i c t i o n s of c o n c e n t r a t i o n s of such w a t e r q u a l i t y p a r a m e t e r s a s r e a c t i v e n i t r o g e n , r e a c t i v e phosphorus, and c h l o r o p h y l l a a s f u n c t i o n s of t h e i n p u t s of n u t r i e n t s and r i v e r flow t o t h e e s t u a r y system. The second model i s f o r summer s e a s o n s , and c o n s i d e r s n i t r o g e n a s t h e l i m i t i n g n u t r i e n t . I t a l s o p e r m i t s p r e d i c t i o n s of e s t u a r y q u a l i t y a s a f u n c t i o n of i n p u t s t o t h e e s t u a r y system. The s e l e c t i o n of t h e s u i t a b l e l i m i t i n g n u t r i e n t f o r each s e a s o n was f i r s t made on t h e b a s i s of e v a l u a t i o n s of t h e i n p u t s of N and P t o t h e e s t u a r y , and t h e n t e s t e d by comparing t h e r e s u l t i n g model w i t h f i e l d o b s e r v a t i o n s .

Based on t h e s e models, t h e f o l l o w i n g c o n c l u s i o n s and i n t e r p r e t a t i o n s a r e made.

1. During a w i n t e r s e a s o n , i n o r g a n i c n i t r o g e n ( l a r g e l y n i t r a t e ) e n t e r s t h e e s t u a r y from upstream s o u r c e s i n t h e Tar R i v e r flow, This

produced t h e n s e t t l e s and i s d e t a i n e d i n t h e e s t u a r y , The f i e l d d a t a a r e c o n s i s t e n t w i t h t h e assumption of phosphorus l i m i t a t i o n . During summer s e a s o n s , t h e e s t u a r y i s s e v e r e l y n i t r o g e n l i m i t e d . The i n p u t s of n i t r o g e n t o t h e e s t u a r y from upstream s o u r c e s a r e much l e s s i n summer t h a n i n w i n t e r , The c a u s e s of t h i s r e d u c t i o n

a r e n o t known w i t h c e r t a i n t y . I t i s proposed h e r e t h a t n i t r o g e n i s r e t a i n e d on t h e l a n d by p h o t o s y n t h e t i c p r o c e s s e s t o a much g r e a t e r e x t e n t i n summer than i n w i n t e r , s o t h a t i t cannot b e washed away i n r u n o f f . I n a d d i t i o n , runoff i s lower i n summer

t h a n i n w i n t e r , T h i s combination of low s o l u b l e n i t r o g e n a v a i l - a b i l i t y on l a n d and low runoff from upstream s i g n i f i c a n t l y

r e d u c e s n i t r o g e n i n p u t s t o t h e e s t u a r y d u r i n g summer s e a s o n s . 3 . A s i g n i f i c a n t s o u r c e of n i t r o g e n i n p u t s t o t h e e s t u a r y d u r i n g t h e

summer a r i s e s from t h e e s t u a r y sediments. A s u b s t a n t i a l p o r t i o n of t h i s sedimentary n i t r o g e n a r i s e s from o r g a n i c n i t r o g e n d e p o s i t e d d u r i n g w i n t e r s e a s o n s , T h i s n i t r o g e n i s r e l e a s e d t o t h e o v e r l y i n g w a t e r s p r i m a r i l y a s

NH3

a s warm summer t e m p e r a t u r e s p r o v i d e

c o n d i t i o n s f o r h e t e r o t r o p h i c b i o l o g i c a l a c t i v i t y i n t h e s e d i m e n t s .

4 . During t h e summer, t h e b a l a n c e between displacement of water down-

s t r e a m by a d v e c t i v e f r e s h w a t e r i n p u t s and l o n g i t u d i n a l mixing by wind and o t h e r f a c t o r s c a u s e s s i g n i f i c a n t upstream t r a n s p o r t of

s a l i n i t y . I t a l s o p e r m i t s upstream t r a n s p o r t of phosphorus from t h e i n d u s t r i a l d i s c h a r g e . The i n o r g a n i c n i t r o g e n a r r i v i n g a t t h e head of t h e e s t u a r y r e a c t s w i t h phosphorus i n t h e upper r e a c h e s of

t h e e s t u a r y and i s r a p i d l y d e p l e t e d . A l g a l biomass i s h i g h e s t a t upstream l o c a t ions d u r i n g t h e summer,

5 . There i s some eviden .ce t h a t sudden i n c r e a s e s

i n

f l o w d u r i n g t h e summer c a n produce temporary s t r a t i f i c a t i o n i n t h e e s t u a r y , T h i s c a n produce a n o x i c c o n d i t i o n s i n t h e bottom waters. I t i s proposed h e r e t h a t t h e s e a n o x i c c o n d i t i o n s a r e r e l a t e d t o t h e decomposition of o r g a n i c m a t t e r produced and s e t t l e d i n t h e e s t u a r y , F a c t o r s which i n c r e a s e s o r d e c r e a s e t h i s p r o d u c t i o n of biomass would t h e n

i n c r e a s e o r d e c r e a s e t h e o c c u r r e n c e and s e v e r i t y of t h e s e a n o x i c c o n d i t i o n s .

6 . The primary f a c t o r a f f e c t i n g w a t e r q u a l i t y i n a q u a t i c systems i s t h e i n p u t of c r i t i c a l s u b s t a n c e s t o t h o s e systems. Hence, t h e w a t e r q u a l i t y i n t h e Pamlico E s t u a r y i s p r i m a r i l y a f f e c t e d by

i n p u t s of n i t r o g e n and phosphorus t o t h a t system, For c o n d i t i o n s r e p r e s e n t a t i v e of 1970-73, p r o d u c t i v i t y i s s e v e r e l y l i m i t e d by n i t r o g e n i n t h e summer and moderately l i m i t e d by phosphorus i n t h e w i n t e r , S u b s t a n t i a l changes i n i n p u t s of e i t h e r of t h e s e n u t r i e n t s could c a u s e changes i n t h e s e r e l a t i o n s h i p s , For example, doubling t h e i n d u s t r i a l d i s c h a r g e of phosphorus c o u l d c a u s e t h e e s t u a r y t o

b e n i t r o g e n l i m i t e d i n t h e w i n t e r . E x t e n s i v e phosphorus removal

m i g h t c a u s e t h e system t o b e l i m i t e d by phosphorus i n t h e summer.

Use of t h e s e models f o r management purposes should c o n s i d e r t h e s e p o s s i b l e changes.

7 . Severe r e d u c t i o n s i n t h e i n p u t s of n i t r o g e n d u r i n g t h e w i n t e r , such a s may have o c c u r r e d d u r i n g t h e c o l d and r e l a t i v e l y d r y

w i n t e r s of 1976 and 1977, may c a u s e t h e e s t u a r y t o become n i t r o g e n l i m i t e d d u r i n g t h e w i n t e r .

8 , The development of e x t e n s i v e a n o x i c c o n d i t i o n s d u r i n g t h e summer, such a s t h o s e i n d i c a t e d i n t h e sumner of 1973, can cause t h e p r e s e n t n i t r o g e n - l i m i t e d model t o b e i n e r r o r , T h i s i s p a r t i c u l a r l y t r u e f o r p r e d i c t i n g t h e r e a c t i v e phosphorus i n

t h e e s t u a r y w a t e r s , s i n c e phosphorus can b e r a p i d l y r e l e a s e d from sediments under a n o x i c c o n d i t i o n s .

9. Model s i m u l a t i o n s i n d i c a t e t h a t i n d u s t r i a l d i s c h a r g e s of phosphorus had s u b s t a n t i a l e f f e c t s on e s t u a r i n e w a t e r q u a l i t y i n t h e e a r l y 1 9 7 0 ' s , and t h a t r e d u c t i o n of t h e s e phosphorus i n p u t s t o a v e r a g e l e v e l s s p e c i f i e d i n p r e s e n t d i s c h a r g e p e r m i t s w i l l y i e l d s i g n i f i c a n t improvements.

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

The Pamlico R i v e r shown i n F i g u r e 1 is an e s t u a r y i n North C a r o l i n a t h a t e x t e n d s from Washington t o Pamlico Sound, a d i s t a n c e of about 60

km.

The width of t h e e s t u a r y a t Washington

i s

a b o u t 1

km,

and a t i t s mouth i s about 7

h.

The d e p t h r a n g e s from about 2 t o 7 m , w i t h a n a v e r a g e of 3.4 m . The t i d a l e f f e c t s i n t h e e s t & a r y a r e modest because of t h e Outer Banks which form a b a r r i e r between Pamlico Sound and t h e A t l a n t i c Ocean; t h e average l u n a r t i d e

i s

only aBout 0.2 m. Wind t i d e s , however, may c a u s e water s u r f a c e v a r i a t i o n s of 1 m o r more.

The p r i n c i p a l t r i b u t a r y of t h e e s t u a r y i s t h e Tar R i v e r whose mouth i s a t Washington, T h i s r i v e r d r a i n s mostly a g r i c u l t u r a l and f o r e s t e d l a n d s i n e a s t e r n North C a r o l i n a . The d r a i n a g e area of t h e r i v e r a t

2

Washington i s about 8300 km

.

Approximately 8 0

km

upstream a t Tarboro, t h e U. S. G e o l o g i c a l Survey (USGS) m a i n t a i n s a permanent gauging s t a t i o n ,

2

t h e d r a i n a g e a r e a of which i s about 5800

km

.

Flows i n t h e Tar R i v e r a r e t y p i c a l l y high i n w i n t e r months when r a i n f a l l i s heavy and low i n t h e summer; i n s p r i n g and f a l l , t h e f l o w s a r e v a r i a b l e . F i g u r e 2 shows t h e monthly runoff a t Tarboro f o r 1971, a f a i r l y t y p i c a l y e a r . I n t h e v i c i n i t y

of Washington, t h e USGS m a i n t a i n s a gauging s t a t i o n on a small t r i b u t a r y

of t h e Tar River c a l l e d H e r r i n g Run, t h e d r a i n a g e a r e a of which i s a b o u t

40 Ian2. The p a t t e r n of i n f l o w s t o t h e Tar from t h i s t r i b u t a r y is probably r e p r e s e n t a t i v e of i n p u t s t o t h e Pamlico R i v e r between Washington and i t s mouth.

The s a l i n i t y c o n c e n t r a t i o n a t Washington

i s

g e n e r a l l y less t h a n 500 mg/L. Pamlico Sound on t h e o t h e r hand i s h a l f sea water, w i t h a v e r a g e

J

F

M

A

M

J

J

A

S

O

N

D

F i g u r e 2 . T a r R i v e r Flows a t T a r b o r o ( 1 9 7 1 )

0

I I I I I I I I I 1 . I

J

F

M

A

M

J

J

A

S

O

N

D

F i g u r e 3 . S a l i n i t y i n Pamlico E s t u a r y a t M i d p o i n t ( 1 9 7 1 )

J

F

M

A

M

J

J

A

S

O

N

D

F i g u r e 4. Temperature i n Pamlico E s t u a r y a t Midpoint ( 1 9 7 1 )

of t h e e s t u a r y i s about 300 m g / ~ p e r

km.

S a l i n i t y c o n c e n t r a t i o n s i n t h e e s t u a r y v a r y w i t h f r e s h w a t e r i n f l o w and o t h e r c o n d i t i o n s . The a v e r a g e monthly s a l i n i t y p r o f i l e approximately midway Along t h e l e n g t h of t h e e s t u a r y i n 1971 i s shown i n F i g u r e 3; d a t a a r e from Hobbie e t a l . (1972). F i g u r e 4 shows t h e 1971 monthly v a r i a t i o n i n temperatures.

As

i n d i c a t e d , summer t e m p e r a t u r e s a r e between 25 and

30°C,

and t h o s e i n w i n t e r r a n g e from a b o u t 6 t o 10°C.

The Pamlico R i v e r i s n o t used e x t e n s i v e l y f o r r e c r e a t i o n a l purposes. However, i t s u p p o r t s modest commercial f i s h i n g and is a l s o used f o r n a v i g a t i o n . One of i t s

main

u s e s

i s

f o r r e c e i v i n g wastewater d i s c h a r g e s from T e x a s g u l f , Inc., a f e r t i l i z e r manufacturer engaged i n phosphate

mining and p r o c e s s i n g

a t

Aurora, NC, approximately midway between Washington and Pamlico Sound.

I n t h e e a r l y 1 9 6 0 1 s , e x t e n s i v e phosphate d e p o s i t s were d i s c o v e r e d i n t h i s p a r t of North C a r o l i n a , E s t i m a t e s p l a c e t h e s e d e p o s i t s between

1 and 1 0 b i l l i o n m e t r i c t o n s , which r a n k them a s one of t h e w o r l d ' s major phosphorus r e s o u r c e s . I n 1965, T e x a s g u l f , I n c . ( t h e n c a l l e d Texas Gulf

S u l f u r Corp.) began mfning t h e a p a t i t e o r e and p r o c e s s i n g i t i n t o f e r t i l i z e r ( a t p r e s e n t p r o d u c t i o n r a t e s , t h e e s t i m a t e d l i f e of t h e d e p o s i t s i s about 300 y e a r s ) . They u s e s t r i p mining methods i n which t h e overburden w i t h t h i c k n e s s of about 20

m

i s removed t o expose t h e 15-m t h i c k l e n s of a p a t i t e . Because t h e w a t e r t a b l e i s s o c l o s e t o t h e ground s u r f a c e , i t must b e

lowered, which i s done through u s e of wells. The r a t e of w e l l water d i s c h a r g e remains f a i r l y c o n s t a n t a t about 2.0m3/s (72 c f s ) . A f t e r u s i n g

I n t h e mid 1 9 6 0 ' s when Texasgulf was f i r s t b e g i n n i n g o p e r a t i o n , t h e S t a t e of N o r t h C a r o l i n a became concerned a b o u t t h e impact of t h i s d i s c h a r g e on e s t u a r y q u a l i t y , I n p a r t i c u l a r , t h e c o n c e r n was o v e r p o t e n t i a l problems of e u t r o p h i c a t i o n . A s a r e s u l t , D r . John Hobbie and coworkers a t NC S t a t e U n i v e r s i t y i n R a l e i g h were funded t h r o u g h t h e NC Water R e s o u r c e s R e s e a r c h I n s t i t u t e t o m o n i t o r e s t u a r y q u a l i t y (Hobbie 1970a, 1970b, 1971, 19743 Hobbie e t a l . 1972; Copeland and Hobbie, 1972; H a r r i s o n and Hobbie, 1 9 7 4 ) . About 30 sampling s t a t i o n s were e s t a b l i s h e d i n t h e e s t u a r y s t a r t i n g a b o u t

8 km below Washington and e x t e n d i n g t o t h e mouth. Except i n t h e u p p e r r e a c h e s where t h e e s t u a r y i s r e l a t i v e l y narrow, two o r t h r e e s t a t i o n s were l o c a t e d a t e a c h of 1 4 t r a n s e c t s a c r o s s t h e w i d t h of t h e e s t u a r y , a s shown i n F i g u r e 5. During a n i n t e n s i v e s a m p l i n g p e r i o d from l a t e 1969 t o e a r l y 1974, samples were c o l l e c t e d and a n a l y z e d o n c e o r t w i c e monthly. The l o c a t i o n of samples and r o u t i n e a n a l y s e s a r e shown i n T a b l e 1. I n

a d d i t i o n t o p r e s e n t i n g f i n d i n g s i n I n s t i t u t e r e p o r t s , d a t a were s t o r e d i n a computer f i l e a t t h e T r i a n g l e U n i v e r s i t i e s Computation C e n t e r . The work by Hobbie and c o l l e a g u e s c o n s t i t u t e s t h e most e x t e n s i v e fund of a v a i l a b l e i n f o r m a t i o n on t h e q u a l i t y of t h e Pamlico R i v e r .

I n r e c e n t y e a r s , p l a n s have been made f o r expanding p h o s p h a t e p r o d u c t i o n from t h e d e p o s i t s a t Aurora. W i t h i n t h e n e x t two y e a r s , North C a r o l i n a P h o s p h a t e Corp. w i l l b e g i n o p e r a t i o n u s i n g s t r i p mining and p r o c e s s i n g p r a c t i c e s s i m i l a r t o t h o s e of T e x a s g u l f . I n l i g h t of

t h i s i n c r e a s e d a c t i v i t y , t h e S t a t e of North C a r o l i n a would l i k e t o know t h e e f f e c t of a d d i t i o n a l phosphorus d i s c h a r g e s o n e s t u a r y q u a l i t y .

They a l s o want t o know t h e l e v e l a t which phosphorus d i s c h a r g e s a r e l i k e l y t o c a u s e problems w i t h e x c e s s i v e a l g a e g r o w t h s , B a s i c a l l y , t h e S t a t e i s l o o k i n g f o r a t o o l t o a s s i s t i n managing e s t u a r y q u a l i t y , I n 1975,

T a b l e 1

Pamlico R i v e r Analyses by Hobbie e t a l . A n a l y s i s

Temperature D i s s o l v e d Oxygen S a l i n i t y

pH

Sample Locat i o n S u r f a c e and Bottom S u r f a c e and Bottom S u r f a c e and Bottom S u r f a c e and Bottom

Ammonia S u r f a c e Only

N i t r i t e N i t r a t e

T o t a l U n f i l t e r e d N i t r o g e n T o t a l F i l t e r e d N i t r o g e n T o t a l U n f i l t e r e d Phosphorus T o t a l F i l t e r e d Phosphorus R e a c t i v e Phosphorus

Chlorophyll-a

t h e r e s e a r c h r e p o r t e d h e r e i n was funded by t h e NC Water Resources Research I n s t i t u t e f o r t h e purpose of developing such a t o o l .

2. O b j e c t i v e s

The o v e r a l l g o a l of t h i s r e s e a r c h i s t o develop a p r e d i c t i v e mathematical model t h a t can be used by t h e S t a t e of North Carolina and o t h e r s i n

managing t h e q u a l i t y of t h e Pamlico River. The s p e c i f i c o b j e c t i v e s under t h i s goal a r e a s f o l l o w s :

1; Develop p r e d i c t i v e models f o r v a r i o u s c o n s t i t u e n t s i n t h e Pamlico River a s s o c i a t e d w i t h e u t r o p h i c a t i o n .

2 . C a l i b r a t e and v e r i f y t h e models u s i n g a v a i l a b l e d a t a .

3 . Use t h e models t o s i m u l a t e Pamlico River q u a l i t y under a l t e r n a t i v e n u t r i e n t loadings.

4 . I n t e r p r e t t h e d a t a and f i n d i n g a t o e x p l a i n t h e p r i n c i p a l

phenomena o c c u r r i n g i n t h e system.

The f i r s t o b j e c t i v e makes i t c l e a r t h a t t h e model i s t o focus on

problems of e u t r o p h i c a t i o n , n o t

BOD

o r oxygen which have been t h e t r a d i t i o n a l concerns of water q u a l i t y modeling. Major i n t e r e s t , t h e n , i s w i t h such

water c o n s t i t u e n t s a s n i t r o g e n , phosphorus,chlorophyll,and a l g a l biomass. Also of importance i s t h e purpose f o r whrch t h e model i s intended: i t must

t o d e l i v e r t o t h e S t a t e and o t h e r u s e r s a c a r d deck o r t a p e of t h e computer program, t o g e t h e r w i t h u s e r i n s t r u c t i o n s ,

Under t h e second o b j e c t i v e , t h e p r e d i c t i v e model i s t o b e b o t h c a l i - b r a t e d and v e r i f i e d

.

C a l i b r a t i o n i m p l i e s parameter e v a l u a t i o n , a l s o

c a l l e d parameter i d e n t i f i c a t i o n , That i s , t h e mathematical symbols t h a t d e s c r i b e t h e s t a t e of t h e system s u c h a s t h e c r o s s s e c t i o n a l a r e a of t h e e s t u a r y , t h e d i s p e r s i o n c o e f f i c i e n t t h a t t a k e s accound of mixing, and t h e r e a c t i o n r a t e c o n s t a n t s t h a t d e s c r i b e n u t r i e n t c y c l i n g must b e a s s i g n e d numerical v a l u e s , e i t h e r based on i n f o r m a t i o n i n t h e t e c h n i c a l l i t e r a t u r e o r from f i e l d o b s e r v a t i o n s , V e r i f i c a t i o n i m p l i e s t h e comparison of

p r e d i c t e d v a l u e s from t h e c a l i b r a t e d model w i t h f i e l d o b s e r v a t i o n s t h a t have i n no way been used f o r model c a l i b r a t i o n . Under t h i s obj e c t i v e , b o t h c a l i b r a t i o n and v e r i g i c a t i o n a r e t o b e done u s i n g a v a i l a b l e d a t a

from such s o u r c e s a s Hobbie, Texasgulf, and t h e USGS. A flow c h a r t of t h e c a l i b r a t i o n and v e r i f i c a t i o n p r o c e s s i s shown i n F i g u r e 6 ,

S i n c e f i e l d d a t a c o l l e c t i o n i s n o t a p a r t of t h i s s t u d y , t h e water q u a l i t y c o n s t i t u e n t s t h a t can b e modeled a r e l i m i t e d t o t h o s e f o r which d a t a a r e a l r e a d y a v a i l a b l e . For example, s u f f i c i e n t d a t a do n o t e x i s t on g r o s s biomass c o n c e n t r a t i o n s o r c o n c e n t r a t i o n s of s p e c i f i c a l g a l s p e c i e s i n Pamlico R i v e r , and hence t h e s e c o n s t i t u e n t s cannot b e modeled d e s p i t e t h e f a c t t h a t they a r e p o t e n t i a l i n d i c a t o r s of e u t r o p h i c a t i o n . I t should b e mentioned t h a t under t h i s o b j e c t i v e , c l o s e c o o p e r a t i o n was planned w i t h P r o f e s s o r E . J . Kuenzler of t h e U n i v e r s i t y of North C a r o l i n a who was

s i m u l t a n e o u s l y engaged i n a s t u d y of n u t r i e n t k i n e t i c s i n t h e Pamlico R i v e r ,

1

DEVELOP MODEL

I

I

SELECT SET OF FIELD DATA

I

I

EVALUATE PARAMETERS

I

I

MODEL I S CALIBRATED

I

-

-

MAKE PREDl CTIONS

I

SELECT ANOTHER SET OF F l ELD DATA

I

CHANGE

MODEL

AND/OR

PARAMETERS

I

SET PARAMETERS TO APPROPRIATE

VALUES

I

DO

A

NO

PREDI CTIONS

Y

-

-

OBSERVATIONS

I

I

MAKE PREDICTIONS

I

PREDICTIONS

_-

\

\

OBSERVATIONS

/

Figure

6.

Flow Diagram of

the Modeling Process

1

YES

The t h i r d o b j e c t i v e i n v o l v e s u s e of t h e model f o r s i m u l a t i n g Pamlico River q u a l i t y under a l t e r n a t i v e n u t r i e n t l o a d i n g s . T h i s

i s

t h e p e n u l t i m a t e s t e p i n t h e g e n e r a l p r o c e s s of modeling, t h e f i n a l one b e i n g u s e of t h e model f o r d e c i d i n g waste l o a d a l l o c a t i o n s (which was n o t a p a r t of t h i s p r o j e c t )

.

The v a l u e of a mathematical model i s t h a t i t e n a b l e s p r e d i c t i o n of r i v e r q u a l i t y under a wide v a r i e t y of c o n d i t i o n s . I n t h i s work, o n l y a few s i m u l a t i o n s were made based on a l t e r n a t i v e phosphorus l o a d s from

Texasgulf and N . C . Phosphate. However, t h e p o s s i b i l i t i e s f o r a d d i t i o n a l s i m u l a t i o n s a r e enormous and a r e expected t o b e performed by t h e S t a t e of North C a r o l i n a .

Under t h e l a s t o b j e c t i v e , work i s r e q u i r e d t o "explain" t h e system. Recognizing t h a t a model i s b a s i c a l l y a s t a t e m e n t of c a u s e and e f f e c t i n mathematical language, i t p e r m i t s ( o r r a t h e r i s ) a n e x p l a n a t i o n of what

o c c u r s i n t h e system. I n t h e c a s e of t h i s modal, t h e e x p l a n a t i o n s a r e of two t y p e s , one t h a t d e a l s w i t h t h e u p t a k e and c y c l i n g of n u t r i e n t s t h a t go i n t o t h e p r o d u c t i o n and decay of a l g a l biomass, and t h e o t h e r t h a t d e a l s w i t h how t h e e s t u a r y w i l l respond under a l t e r n a t i v e n u t r i e n t l o a d i n g s from t h e i n d u s t r i e s ,

E s t u a r y Conditions

e n t r a t i o n was a b o u t 2.5 pM _{( p a r t i c u l a t e phosphorus i s c o n t a i n e d i n a l g a l} c e l l s and i n d i c a t e s t h e p r e s e n c e of biomass). Correspondingly,

t h e chlorophyll-a c o n c e n t r a t i o n i n w i n t e r was about 40 pg/L whereas i n summer i t was a b o u t 25 p g / ~ . Hobbie (1971) r e p o r t e d t h a t t h e d i n o f l a g e l l a t e Heterocapsa was p r i n c i p a l l y r e s p o n s i b l e f o r t h e w i n t e r bloom. H i s d a t a

showed t h a t t h e w i n t e r bloom o c c u r r e d about midway a l o n g e s t u a r y l e n g t h , whereas t h e summer bloom was f u r t h e r upstream n e a r Washington.

R e a c t i v e n i t r o g e n (NH3

+

NO;

+

NO-)

and r e a c t i v e phosphorus ( o r t h o )

3

c o n c e n t r a t i o n s were a l s o d i f f e r e n t i n summer and w i n t e r , I n t h e w i n t e r , r e a c t i v e n i t r o g e n ranged a l o n g t h e l e n g t h of t h e e s t u a r y from about 5 t o 45

pM,

w i t h an a v e r a g e of about 3 0 p M , whereas i n summer, t h e r a n g e was from about 3 t o 1 5 w i t h an average of 6 pM. The peak n i t r o g e n concen- t r a t i o n s i n b o t h w i n t e r and summer o c c u r r e d upstream i n t h e v i c i n i t y of Washington (near t h e mouth of t h e Tar R i v e r ) . Winter r e a c t i v e phosphorus

c o n c e n t r a t i o n s v a r i e d a l o n g t h e e s t u a r y from a b o u t 0.5 t o 3 pM w i t h an a v e r a g e of 1

yM

whereas i n summer, t h e r a n g e was from a b o u t 1 t o 1 0 yM w i t h an average of 5 pM. Unlike n i t r o g e n , t h e peak r e a c t i v e phosphorus c o n c e n t r a t i o n s occurred about midway a l o n g e s t u a r y l e n g t h n e a r t h e Texasgulf o u t f a l l . I n g e n e r a l , Hobbie found t h e d i s s o l v e d oxygen c o n c e n t r a t i o n s i n b o t h w i n t e r and summer t o b e above 5 m g / ~ , a l t h o u g h p e r i o d i c a l l y ( e s p e c i a l l y i n summer 1973), lower v a l u e s were encountered. The above c o n d i t i o n s a r e summarized i n Table 2.

I n an a t t e m p t t o d e t e r m i n e whether t h e system might b e e i t h e r

n i t r o g e n o r phosphorus l i m i t e d , a v e r a g e d a t a on n u t r i e n t l o a d i n g s d i s c h a r g e d t o t h e e s t u a r y were examined. The a v e r a g e w i n t e r flow of t h e Tar R i v e r a t Tarboro d u r i n g t h e y e a r s when Hobbie

e t

a l . c o l l e c t e d t h e i r d a t a was

3 3

Table 2

Average Estuary C o n c e n t r a t i o n s

Ranee Average Tar

over i n River

Length Estuary Mouth

R e a c t i v e Nitrogen (pM) Winter

Summer

Reactive Phosphorus (yM) Winter

Summer

P a r t i c u l a t e Phosphorus (vM) Winter

Summer

Chlorophyll-a ( ~ g /L) Winter

Assuming t h a t t h e r u n o f f c o e f f i c i e n t o v e r t h e e n t i r e d r a i n a g e b a s i n a t any t i m e was e s s e n t i a l l y c o n s t a n t , t h e f l o w s a t t h e mouth of t h e T a r R i v e r can be e s t i m a t e d by m u l t i p l y i n g Tarboro f l o w s by 1 . 5 , t h e approximate r a t i o of d r a i n a g e a r e a s , The corresponding a v e r a g e w i n t e r and summer f l o w s

3

e n t e r i n g t h e Pamlico R i v e r n e a r Washington were a b o u t 170 m /s (6000 c f s ) 3

and 30 m /s (1000 c f s ) , r e s p e c t i v e l y . Using t h e c o n c e n t r a t i o n d a t a a t t h e mouth of t h e Tar R i v e r shown i n T a b l e 2 , t h e r e a c t i v e n i t r o g e n i n p u t s t o t h e Pamlico n e a r Washington i n w i n t e r and summer were a b o u t 7 . 7 m o l l s and 0.5 m o l / s , r e s p e c t i v e l y . C o r r e s p o n d i n g l y , t h e r e a c t i v e phosphorus i n p u t s from t h e T a r R i v e r were a b o u t 0 . 3 m o l / s i n w i n t e r and 0 . 1 m o l l s i n summer, Hence, t h e molar r a t i o of l o a d i n g s of r e a c t i v e n i t r o g e n t o r e a c t i v e

phosphorus i n w i n t e r and summer a t t h e head of t h e e s t u a r y were a b o u t 2 5 and 5 , r e s p e c t i v e l y . Based on t h e s o - c a l l e d R e d f i e l d r a t i o ( R e d f i e l d e t a l . , 1965) which i n d i c a t e s t h a t a b o u t 1 5 moles of n i t r o g e n a r e t a k e n up i n t h e p r o d u c t i o n of a l g a l biomass f o r each mole of phosphorus when n e i t h e r n u t r i e n t limits p r o d u c t i v i t y , t h e s e v a l u e s i n d i c a t e t h a t t h e e s t u a r y n e a r Washington was somewhat phosphorus l i m i t e d i n t h e w i n t e r and s e v e r e l y n i t r o g e n l i m i t e d i n summer.

N u t r i e n t s e n t e r t h e Pamlico R i v e r from s o u r c e s o t h e r t h a n t h e T a r R i v e r . T r i b u t a r i e s a l o n g t h e l e n g t h of t h e e s t u a r y c o n t r i b u t e i n p u t s , b u t t h e s e

*

a p p e a r t o b e r e l a t i v e l y s m a l l . Phosphorus l o a d s from T e x a s g u l f , however, 3 a r e s i z e a b l e and c a n n o t b e i g n o r e d , With a n a v e r a g e d i s c h a r g e of 2 m /s

(72 c f s ) and a c o n c e n t r a t i o n of 280 pM, t h e i n d u s t r i a l l o a d of r e a c t i v e 2

phosphorus was a b o u t 0.6 m o l l s , which i s a p p r o x i m a t e l y t w i c e t h e T a r R i v e r i n p u t i n w i n t e r and s i x times i t s i n p u t i n summer. Adding t h i s amount t o t h a t from T a r R i v e r , t h e t o t a l e s t u a r y l o a d of r e a c t i v e phosphorus was

a b o u t 0 . 9 m o l / s i n winter, and 0.7 mol/s i n summer, The c o r r e s p o n d i n g molar r a t i o s of r e a c t i v e n i t r o g e n t o phosphorus w e r e a b o u t 9 i n w i n t e r and 1 i n summer. These r e s u l t s a r e shown i n T a b l e 3 ,

These rough e s t i m a t e s a r e n o t c o n c l u s i v e e v i d e n c e r e g a r d i n g n u t r i e n t l i m i t a t i o n s i n Pamlico R i v e r . However, t h e y s u g g e s t t h a t i n w i n t e r , t h e upper r e a c h e s of t h e e s t u a r y a r e phosphorus l i m i t e d , b u t by midway a l o n g

i t s l e n g t h , n i t r o g e n i s no l o n g e r i n e x c e s s and may even b e l i m i t i n g , I n summer, on t h e o t h e r hand, t h e e s t u a r y a p p e a r s t o b e s e v e r e l y n i t r o g e n l i m i t e d t h r o u g h o u t i t s e n t i r e l e n g t h . Based on t h e s e p r e l i m i n a r y c o n c l u s i o n s , p l a n s were made t o d e v e l o p two s t e a d y - s t a t e models f o r t h e P a m l i c o , one

p e r t a i n i n g t o w h t e r c o n d i t i o n s when a t l e a s t p a r t of t h e e s t u a r y i s

phosphorus l i m i t e d , and t h e o t h e r f o r summertime when n i t r o g e n is t h e l i m i t i n g n u t r i e n t .

4 . Model Formulation*

Themodeling a p p r o a c h of t h i s p r o j e c t was p a t t e r n e d a f t e r t h e f i n i t e d i f f e r e n c e f o r m u l a t i o n s f i r s t developed by Thomann (1972). Based o n t h e f i e l d d a t a of Hobbie e t a l . f o r t h e Pamlico R i v e r , i t was d e c i d e d t h a t v e r t i c a l and l a t e r a l c o n c e n t r a t i o n g r a d i e n t s were n o t s u f f i c i e n t l y g r e a t

Table 3

Approximate N u t r i e n t Loads on Pamlico Estuary

F ~ ? W RN* RP

*

RN RP RN/RP

(m / s )

(1.m

) _(F.M

_---

_{(molls (rhol/s)}

-

_(mol/mol)

WINTER

Tar River 170 45 1.5 7.7 0.3 2 5

Texasgulf 2 0 280 0 0.6 0

T o t a l 7.7 0.9 9

SUMMER

Tar River 3 0

Texasgulf 2

T o t a l

c o n c e n t r a t i o n s i n any p l a n e a c r o s s t h e w i d t h , A s m e n t i o n e d a b o v e , t h e model assumed s t e a d y - s t a t e c o n d i t i o n s .

I n Thomann's a p p r o a c h , model f o r m u l a t i o n b e g i n s by d T v i d i n g t h e e s t u a r y i n t o s e v e r a l s e g m e n t s , n o t n e c e s s a r i l y of e q u a l l e n g t h , Assume t h a t t h e main body o f t h e e s t u a r y c o n t a i n s n s e g m e n t s as shown i n F i g u r e 7 , w i t h segment 0 t h e u p s t r e a m b o u n d a r y s e c t i o n and segment n-tl t h e

downstream boundary s e c t i o n . Assume t h a t e a c h segment i s c o m p l e t e l y mixed s o t h a t i t c o n t a i n s no c o n c e n t r a t i o n g r a d i e n t s . Changes i n c o n c e n t r a t i o n c a n t h e r e f o r e o c c u r o n l y from o n e segment t o t h e n e x t .

T h e t a s k now i s t o w r i t e a mass b a l a n c e e q u a t i o n f o r e a c h w a t e r c o n s t i t u e n t of i n t e r e s t i n e a c h of t h e main body s e g m e n t s , I n w o r d s , t h e

mass b a l a n c e e q u a t i o n f o r any segment i s

[ A c c u m u l a t i o n ] = [ I n p u t by A d v e c t i o n ]

-

[ O u t p u t by A d v e c t i o n ]

+

[ I n p u t by D i s p e r s i o n ]

-

[ O u t p u t by D i s p e r s i o n ]

+

[ S o u r c e s ]

-

[ S i n k s ] ( 1 )

I n t h i s e q u a t i o n , a d v e c t i o n i s assumed t o b e t h e mechanism whereby a w a t e r c o n s t i t u e n t i s t r a n s p o r t e d from u p s t r e a m t o downstream s e g m e n t s d u e t o f r e s h w a t e r i n p u t t o t h e e s t u a r y , S i m i l a r l y , d i s p e r i s o n i s assumed t o b e t h e mechanism t h a t a c c o u n t s f o r a l l m i x i n g , t h e m a j o r c a u s e s of w h i c h a r e l u n a r a n d wind t i d e s . The S o u r c e s and S i n k s t e r m s r e s p e c t i v e l y a c c o u n t f o r t h e i n c r e a s e s and d e c r e a s e s of t h e c o n s t i t u e n t i n t h e segment d u e t o s u c h t h i n g s as c h e m i c a l r e a c t i o n s , s e d i m e n t a t i o n , a n d d i r e c t i n p u t s from

MAIN

BODY

Eq. (1) can be rewritten in mathematical symbols by treating its

terms one by one. Assume that the equation applies to the i-th segment

of the estuary in which the concentration of the constituent of interest

is s

The accumulation term on the left hand side is simply

i '

where Vi is the volume of the segment and the derivative represents the

rate of concentration change with time. The units of Eq. (2) are mass/time.

Under the assumption of steady-state, no accmulation occurs in section

i, and thus

Eq. (2) is zero.

Input into section i by advection through the upstream boundary

between sections i-1 and i is simply equal to the concentration at the

boundary times the flow at the boundary. Using the symbol

Q

to indicate

flow and s to indicate concentration, and with the subscript i-I+. to

indicate the boundary, advection into the i-th section is

where the units are maasjtime, as before. Note, however, that the dependent

variables for this model are the concentrations within segments, not at

the boundaries. Hence,

si-]ri

in

Eq. (3) must be rewritten in terms of

concentrations in segments. For this purpose, assume that the concentration

at the boundary is a linear combination of concentrations in the adjacent

segments. Hence, we can write

8

-

i - y

-

%-I+

1

+ i -

si

shows how n u m e r i c a l v a l u e s f o r t h e s e p a r a m e t e r s c a n be e s t i m a t e d from t h e

l e n g t h s of t h e segments. I n g e n e r a l ,

and

where

R .

and

R .

a r e t h e l e n g t h s of t h e u p s t r e a m and downstream segments,

1 J

r e s p e c t i v e l y ? S u b s t i t u t i n g Eq. ( 4 ) i n t o Eq. ( 5 ) , t h e a p p r o p r i a t e e x p r e s s i o n

f o r a d v e c t i o n i n t o s e c t i o n i i s

t h e p a r a m e t e r s of which a r e Q ,

a

and

6.

S i m i l a r l y , t h e e x p r e s s i o n i n

mass b a l a n c e E q . (1) f o r a d v e c t i o n o u t of t h e segment i s

Q&i+l +1 " i + l ) (8)

The u n d e r l y i n g assumption of d i s p e r s i o n i s t h a t t h e r a t e of t r a n s p o r t through a u n i t a r e a normal t o t h e c o n c e n t r a t i o n g r a d i e n t i s p r o p o r t i o n a l t o

t h e g r a d i e n t . That i s , t h e r a t e of t r a n s p o r t p e r u n i t a r e a ( w i t h u n i t s m a s s / t i m e / a r e a ) i s p r o p o r t i o n a l t o d s / d x , t h e c o n c e n t r a t i o n g r a d i e n t , where

x i n d i c a t e s d i s t a n c e a l o n g t h e l e n g t h of t h e e s t u a r y . The r a t e of t r a n s p o r t i n t o s e c t i o n i a c r o s s t h e upstream f a c e by d i s p e r s i o n i s t h e r e f o r e t h e pro- d u c t of t h e c o n c e n t r a t i o n g r a d i e n t , t h e c r o s s s e c t i o n a l a r e a A, and t h e

p r o p o r t i o n a l i t y c o n s t a n t E ( c a l l e d t h e d i s p e r s i o n c o n s t a n t h e r e i n ) ,

e v a l u a t i o n of which i s d e s c r i b e d i n t h e n e x t s e c t i o n of t h i s r e p o r t .

The u n i t s of E q . (9) a r e m a s s l t i m e , a s b e f o r e . However, t h e g r a d i e n t a t t h e boundary must b e r e w r i t t e n i n terms of c o n c e n t r a t i o n s w i t h i n segments, s i n c e t h e s e a r e t h e dependent v a r i a b l e s of t h e model; t h i s c a n b e done a s f o l l o w s

where t h e denominator i s t h e d i s t a n c e between t h e m i d p o i n t s of s e c t i o n s

i-1 and i. S u b s t i t u t i n g Eq. (10) i n t o Eq. ( 9 ) and combining t h e a r e a , d i s p e r s i o n , a n d l e n g t h p a r a m e t e r s i n t o a s i n g l e term E' y i e l d s t h e f o l l o w i n g e x p r e s s i o n f o r d i s p e r s i o n i n t o s e c t i o n

i

E

I

i-y

('1-1.

-

si>

where

Similarly, t h e e x p r e s s i o n f o r t r a n s p o r t by d i s p e r s i o n o u t of segment i i s

o b t a i n e d by combining Eqs. ( 2 ) , ( 7 ) , ( 8 ) , (11) and (13) t o y i e l d (under s t e a d y - s t a t e c o n d i t i o n s and a £ t e r r e a r r a n g e m e n t )

Note t h a t a l l t h e terms i n p a r e n t h e s e s a r e p a r a m e t e r s ; t h e i r e v a l u a t i o n f o r t h e Pamlico R i v e r i s d e s c r i b e d i n t h e n e x t s e c t i o n of t h e r e p o r t . The s terms on t h e o t h e r hand, a r e t h e dependent v a r i a b l e s whose v a l u e s a r e

Using t h e symbols a

- 1 i an"i,i+~ f o r t h e c o e f f i c i e n t s of

and s

i+l

'

r e s p e c t i v e l y , Eq. (14.) can b e r e w r i t t e n a s f o l l o w s

unknown.

s S

i-1' i

(15)

A few o b s e r v a t i o n s a b o u t Eq. (15) a r e i m p o r t a n t b e f o r e p r o c e e d i n g f u r t h e r w i t h model f o r m u l a t i o n and s o l u t i o n . T h i s e q u a t i o n a p p l i e s t o o n l y one segment of t h e e s t u a r y , v i z . s e c t i o n i. With n main-body segments,

i t i s n e c e s s a r y t o w r i t e an e x p r e s s i o n l i k e Eq. (15) f o r each. T h i s r e s u l t s i n n l i n e a r e q u a t i o n s i n terms of n+2 c o n c e n t r a t i o n s . The con- c e n t r a t i o n s i n t h e boundary segments, however, (So and S ) must b e

n + l

known, t h u s r e d u c i n g t h e problem t o one w i t h n e q u a t i o n s and n unknowns, which can be s o l v e d . I f i n f a c t t h e y a r e known, t h e model i s s a i d t o have " f i x e d b o u n d a r i e s . " A l t e r n a t i v e l y , t h e model c o u l d have " g r a d i e n t b o u n d a r i e s " wherein i t i s n e c e s s a r y t o have m a t h e m a t i c a l e x p r e s s i o n s f o r s ₀ i n terms

of s (and p o s s i b l y s ) and s ~ + ~ i n terms of sn (and p o s s i b l y sn

1 2

-

Note t h a t Eq. (15) h a s t h r e e unknowns, s ~ - ~ , si and s ~ + ~ . Assume t h a t n u m e r i c a l v a l u e s a r e a v a i l a b l e f o r a l l a ' s , W ' s , s and s,+~. The

0

s e t of n e q u a t i o n s , t h e n , f o r t h e e n t i r e e s t u a r y can b e w r i t t e n a s foLlows, where knowns have been brought t o t h e r i g h t hand s i d e and unknowns a r e on t h e l e f t

I n m a t r i x form, Eq. (16) can b e w r i t t e n

where W' i s t h e d i r e c t i n p u t t o t h e f i r s t o r l a s t main body segment a d j u s t e d f o r t h e (known) c o n c e n t r a t i o n i n t h e boundary s e c t i o n . Note t h a t t h e m a t r i x of a ' s i s t r i d i a g o n a l , which makes i t p o s s i b l e t o u s e s p e c i a l s o l u t i o n t e c h n i q u e s £ o r e v a l u a t i n g t h e c o n c e n t r a t i o n s .

5 . Hydrodynamic P a r a m e t e r s

The model of t h i s r e s e a r c h r e q u i r e d e v a l u a t i o n of f i v e hydrodynamic p a r a m e t e r s ( 1 ) t h e l e n g t h of e a c h segment, ( 2 ) t h e c r o s s - s e c t i o n a l a r e a of b o u n d a r i e s between segments, ( 3 ) t h e a v e r a g e d e p t h ( o r w i d t h ) of b o u n d a r i e s ,

( 4 )

f l o w s a t b o u n d a r i e s , and (5) d i s p e r s i o n c o e f f i c i e n t s a t b o u n d a r i e s .

The f i r s t t a s k i n e v a l u a t i n g p a r a m e t e r s was t o d i v i d e t h e e s t u a r y i n t o segments. Based p r i m a r i l y on t h e l o c a t i o n of major t r i b u t a r i e s and Hobbie's sampling s t a t i o n s , 1 3 main-body segments were s e l e c t e d , a s shown i n F i g u r e 8.* _{The upstream boundary of s e c t i o n 1 and t h e down-} s t r e a m boundary of s e c t i o n 1 3 a r e 1 2 . 5

km

and 64.1 Ian below Washington, r e s p e c t i v e l y . The l e n g t h of segments v a r i e s from about 2.6 t o 6.6 km, w i t h a n a v e r a g e of a b o u t 4.0

km;

l e n g t h d a t a f o r e a c h segment a r e i n T a b l e 4.

S e c t i o n 0 i s t h e end segment upstream of s e c t i o n 1; t h e l e n g t h s of t h e s e two s e c t i o n s a r e i d e n t i c a l , S i m i l a r l y , s e c t i o n 14 is t h e end seg- ment downstream of t h e l a s t main-body segment; b o t h of them have t h e same

l e n g t h . The segments were s e l e c t e d s u c h t h a t e a c h s e c t i o n e x c e p t 11 c o n t a i n s a t l e a s t one of Hobbie's sampling s t a t i o n s . T h i s i s shown i n F i g u r e 8 and T a b l e 4. The upstream end s e c t i o n (0) c o n t a i n s H o b b i e ' s s t a t i o n 1, and t h e downstream end s e c t i o n (14) c o n t a i n s Hobbie's s t a t i o n 30. The a p p r o x i m a t e c o o r d i n a t e s of t h e m i d p o i n t of t h e u p s t r e a m boundary of e a c h s e c t i o n a r e shown i n T a b l e 4.

Once segment b o u n d a r i e s were s e l e c t e d , t h e i r c r o s s s e c t i o n a l a r e a s were measured from n a v i g a t i o n c h a r t s p u b l i s h e d by t h e N a t i o n a l Oceanic

T a b l e 4

S e c t i o n

Hobbie

'

s S t a t i o n s

1

2 , 3 4 5 6 7 , 8 , 9 10,11,12 1 3 , 1 4 , 1 5 16,17,18 19,20 21,22,23

-

24,25,26 27,28.29 30

Char a c t e r i

C o o r d i n a t e s of Upstream Longitude

s t i c s of Pamlico R i v e r S e c t i o n s _{C h a r a c t e r i s t i c s of} Upstream Boundary Average C r o s s - S e c t i o n a l

Length Volume Surf ace-Area Depth Area

Boundaries a t Midpoints

( 1 0 ~ ~ ) ( 1 0 % ~ ) ( 106m2

(4

(103m2)

h his

i s t h e downstream boundary of s e c t i o n 13.

2 ~ h e

a

v a l u e s f o r s e c t i o n s 1 and 14 a r e e a c h 0.5 which i m p l i e s Q,, = 3.38 lun and g14 = 6.60

km.

and Atmospheric A d m i n i s t r a t i o n

(NOAA)

of t h e U . S. Department of Commerce.* These c h a r t s a l s o provided i n f o r m a t i o n on t h e a v e r a g e d e p t h a t each

3 2 t r a n s e c t . Areas were found t o v a r y from about 6 x 1 0 ~ t o 35x10 m

,

and a v e r a g e d e p t h s v a r y from 3.5 t o 4.5 m; s p e c i f i c d a t a f o r e a c h s e c t i o n a r e shown i n Table 4 , which a l s o l i s t s s e c t i o n volumes and s u r f a c e a r e a s .

Once t h e d a t a on segment geometry were compdled, a t t e n t i o n was d i r e c t e d toward e v a l u a t i n g flow and d i s p e r s i o n p a r a m e t e r s . Unlike e s t u a r y geometry which changes v e r y l i t t l e over t i m e , flows a r e h i g h l y v a r i a b l e and cannot be simply r e a d i n t o t h e model a s a s i n g l e s e t of v a l u e s .

R a t h e r , a model was needed f o r p r e d i c t i n g t h e a v e r a g e w i n t e r and summer flow a t each segment boundary of t h e model.

With o n l y t h e USGS flow d a t a a t t h e Tarboro, H e r r i n g Run, and a few o t h e r gauging s t a t i o n s a v a i l a b l e f o r a n a l y s i s , s u f f i c i e n t i n f o r m a t i o n d i d n o t e x i s t f o r developing and v e r i f y i n g a s o p h i s t i c a t e d f l o w model.

Consequently, i t was assumed t h a t Tar R i v e r f l o w s a t Washington could b e e s t i m a t e d simply by m u l t i p l y i n g Tarboro flows by 1 . 5 1 , t h e r a t i o of t h e d r a i n a g e a r e a a t Washington t o t h a t a t Tarboro. To t h i s must b e added t h e flow from t r i b u t a r i e s below Washington p l u s t h e d i s c h a r g e from Texasgulf. The flow from t r i b u t a r i e s was e s t i m a t e d by multPplying the r u n o f f c o e f f i c i e n t a t H e r r i n g Run by t h e i n c r e m e n t a l d r a i n a g e a r e a s between Washington and t h e boundaries of each segment. The r e s u l t i n g g e n e r a l e q u a t i o n f o r e s t i m a t i n g

t h e flow a t any boundary j i s

[Flow a t Boundary j] = 1 . 5 1 x [Flow a t Tarboro]

+

[Flow from T e x a s g u l f ]

+

[Drainage Area Between Washington and Boundary j] x [Herring Run Flow]/[Herring Run Drainage Area]

(18)

I n t h i s e q u a t i o n , t h e flow from Texasgulf i s i n c l u d e d o n l y f o r p o i n t s below t h e upstream boundary of s e c t i o n 6 , t h e segment i n t o which t h e i n d u s t r y d i s c h a r g e s i t s waste. Above 6, t h e model assumes t h a t t h e Texasgulf flow i s z e r o . During t h e p e r i o d when Hobbie e t a l . c o l l e c t e d t h e i r d a t a ,

3

t h e Texasgulf flow was e s s e n t i a l l y c o n s t a n t a t 2nl / s (72 c f s ) . Also 2

c o n s t a n t i s t h e 40 km d r a i n a g e a r e a of H e r r i n g Run. From USGS maps, t h e i n c r e m e n t a l d r a i n a g e a r e a s between Washington and segment b o u n d a r i e s were measured; t h e d a t a a r e shown i n Table 5 . The r e s u l t i n g e q u a t i o n s

f o r e s t i m a t i n g t h e flow a t each boundary of t h e model are a s f o l l o w s

= QWASH

= QWASH = QWASH

= QWASH

= QWASH

= QWASH = QWASH

= QWASH

= QWASH

= QWASH = QWASH

= QWASH = QWASH

= QWASH

+

6.4 QHER

+

7 . 2 QHER

+

10.7 QHER

+

10.7 QHER

+

1 3 . 0 QHER

+

16.0 QHER

+

16.0 QHER

+

16.0 QHER

+

22.0 QHER

+

22.0 QHER

+

22.0 QHER

+

65.0 QHER

+

80.0 QHER

+

80.0 QHER

+

QTGS

+

QTGS

+

QTGS

+

QTGS

+

QTGS

+

QTGS

+

QTGS

Table 5

I n c r e a s e i n Drainage Area Along Pamlico River

Sect i o n

I n t h e c a l i b r a t i o n and v e r i f i c a t i o n work f o r t h e w i n t e r and summer q u a l i t y models d e s c r i b e d i n t h e n e x t two s e c t i o n s of t h i s r e p o r t , a v e r a g e s e a s o n a l f l o w s were o b t a i n e d by i n s e r t i n g i n t o Eq$.(19) t h e s p e c i f i c Tarboro and H e r r i n g Run f l o w s on t h e d a t e s when Hobbie e t a l . t o o k f i e l d samples, and t h e n a v e r a g i n g t h e r e s u l t s . T h i s p r o c e d u r e d i d n o t a l l o w f o r t h e p o s s i b i l i t y of a l a g i n t h e time of t r a v e l between Tarboro and t h e e s t u a r y . However, i t d i d n o t c a u s e d i s c e r n i b l e problems. When u s i n g t h e f l o w model f o r p r e d i c t i n g f u t u r e c o n d i t i o n s , Eqs..(19) o f f e r a

r e a s o n a b l e approach t h a t i s c o n s i s t e n t w i t h t h e o t h e r a b s t r a c t i o n s i n t h e model.

S i m i l a r t o f l o w s , d i s p e r s i o n c o e f f i c i e n t s a r e n o t c o n s t a n t o v e r t i m e o r l o c a t i o n and hence c a n n o t be simply i n s e r t e d i n t h e q u a l i t y models

a s a s i n g l e s e t of d a t a . R a t h e r , a p r e d i c t i v e d i s p e r s i o n model was needed. The g e n e r a l approach t o d e v e l o p i n g such a model was t o e v a l u a t e d i s p e r s i o n c o e f f i c i e n t s from Hobbie's s a l i n i t y d a t a i n Pamlico R i v e r and t h e n t o r e l a t e them t o e s t u a r y c o n d i t i o n s u s i n g r e g r e s s i o n a n a l y s i s .

The p r e v i o u s s e c t i o n of t h i s r e p o r t p r e s e n t s a f i n i t e d i f f e r e n c e model f o r a c o n s e r v a t i v e s u b s t a n c e (such a s s a l i n i t y ) i n a n e s t u a r y . The b a s i c e x p r e s s i o n i s Eq. ( 1 4 ) . I n s t e a d of making t h i s model f o r a r e l -

a t i v e l y l a r g e segment of t h e e s t u a r y a s was d o n e , i t c o u l d have been developed f o r a n i n f i n i t e l y t h i n s l i c e of t h e system, which would have r e s u l t e d i n

t h e f o l l o w i n g d i f f e r e n t i a l e q u a t i o n

u n i t s a r e a l t i m e , s i s c o n c e n t r a t i o n and d s / d x i s t h e c o n c e n t r a t i o n g r a d i e n t .

Eq. (20) i s c a l l e d t h e s t e a d y s t a t e c o n t i n u i t y e q u a t i o n f o r a

c o n s e r v a t i v e s u b s t a n c e i n an e s t u a r y . It p r o v i d e s a b a s i s f o r e v a l u a t i n g t h e d i s p e r s i o n c o e f f i c i e n t u s i n g s a l i n i t y d a t a . Note t h a t by i n t e g r a t i n g Eq. (20) over t h e l e n g t h of t h e e s t u a r y ( i . e . , over a l l x ) , an e q u a t i o n i s o b t a i n e d f o r p r e d i c t i n g t h e s a l i n i t y c o n c e n t r a t i o n a t any p o i n t i n t h e system. Assuming t h e flow Q , d i s p e r s i o n c o e f f i c i e n t E, and c r o s s s e c t i o n a l a r e a A a r e everywhere c o n s t a n t i n t h e e s t u a r y , t h e r e s u l t i n g e q u a t i o n upon i n t e g r a t i o n i s

where s i s t h e c o n c e n t r a t i o n a t any p o i n t i n t h e system, x i s d i s t a n c e below t h e upstream boundary of t h e e s t u a r y , L i s t h e d i s t a n c e from t h e upstream boundary t o t h e mouth, and so i s t h e s a l i n i t y c o n c e n t r a t i o n a t t h e mouth. U s u a l l y , f i e l d d a t a a r e a v a i l a b l e f o r a l l of t h e terms i n E q .

(21) except E. Hence, t h i s parameter can b e e v a l u a t e d u s i n g semilog graph paper by p l o t t i n g s a l i n i t y v a l u e s ( s ) on t h e l o g s c a l e v e r s u s (Q/A) (x-L). I f t h e assumptions of t h e model a p p l y , t h e r e s u l t i n g graph i s a s t r a i g h t l i n e , t h e s l o p e of which i s

11~:

The problem i n u s i n g Eq. (21) i n t h i s r e s e a r c h was t h a t t h e assumptions do n o t apply t o Pamlico R i v e r . I n t h e f i r s t p l a c e , t h e c r o s s s e c t i o n a l a r e a i s n o t c o n s t a n t b u t r a t h e r i n c r e a s e s s i g n i f i c a n t l y w i t h d i s t a n c e

downstream. Also, t h e flow i n t h e e s t u a r y i s n o t c o n s t a n t . Most i m p o r t a n t , however, E v a r i e s a l o n g e s t u a r y l e n g t h . It i s l a r g e s t n e a r