Numerical Model of the Salt-Wedge Reach of the Duwamish River Estuary, King County, Washington GEOLOGICAL SURVEY PROFESSIONAL PAPER 990 Prepared in cooperation with the Municipality of Metropolitan Seattle Numerical Model of the Salt-Wedge Reach of the Duwamish River Estuary, King County, Washington By Edmund A. Prych, W. L. Haushild, and J. D. Stoner GEOLOGICAL SURVEY PROFESSIONAL PAPER 990 Prepared in cooperation with the Municipality of Metropolitan Seattle UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1976 UNITED STATES DEPARTMENT OF THE INTERIOR THOMAS S. KLEPPE, SVm/rm GEOLOGICAL SURVEY V. E. McKelvey, Director Library of Congress Cataloging in Publication Data Prych, Edmund. A. Numerical model of the salt-wedge reach of the Duwamish River Estuary, King County, Washington. (Geological Survey Professional Paper 990) Bibliography: p. 25-26. Supt.ofDocs.no.: 119.16:990 1. Oceanography-Washington (State)-Duwamish River estuary-Mathematical models. 2. Estuarine pollution-Washington (State)-Duwamish River estuary-Mathematical models. 3. Phytoplankton-Washington (State)-Duwamish River estuary. I. Haushild, W. L., joint author. II. Stoner, J. D., joint author. III. Seattle. IV. Title. V. Series: United States Geological Survey Professional Paper 990. GC856.P77 551.4'66'32 76-608136 For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 Stock Number 024-001-02886-7 CONTENTS Page Page Abstract ___________________________ 1 Application of the model to the Duwamish Introduction __________________________________ 1 River estuary Continued Acknowledgments _________________________ 3 Input data Continued Flow model _____________________________ 3 Constituent models Continued General description.._____________________ 3 Salinity _________________________ 14 Flow in the wedge ___________________________ 4 Temperature _________________ ___ 14 Flow in the upper layer____________________ 5 Phytoplankton ___ _____ ____ 15 Transport model _______________________ g Biochemical oxygen demand __________________ 16 General description _____________________ 6 Dissolved oxygen ______ __ _ 17 Transport in the wedge __________________ g Model verification ________ _ _ ___ _ 17 Transport in the upper layer ______________ 6 General remarks _____________ __ ___ 17 Advection __________________________ 6 Temperature __________ __ _______ 20 Diffusion _________________________ 8 Chlorophyll a ____________________________________ 21 Constituent models ___________________________ 8 Dissolved oxygen _________ ___ _____ 23 General description______________________ 8 Prediction of future dissolved-oxygen concentrations ___ 23 Salinity ______________________________ 8 Summary and conclusions--______--- _ 24 Temperature _____________________________ 8 References _______-____ __ __ ____ 25 Phytoplankton _________________________________ 10 Supplemental information Biochemical oxygen demand _______________ 11 Phytoplankton _______________ __ __ 28 Dissolved oxygen _______________________ 12 General ____________ __ -- 28 Application of the model to the Duwamish River Sample collection, preparation, and analysis __ ____ 28 estuary _____________________________ 12 Abundant phytoplankton taxa___ __ _ _ 28 General ________________________ 12 Production and consumption of oxygen by phyto­ Input data ______________________________ 12 plankton_________________ 29 Flow model _____________________________ 12 Estimated influence of nutrients on phytoplankton Constituent models______________________ 14 growth __________ __ __ 31 Boundary conditions _________________ 14 Herbivores--___________- - 33 ILLUSTRATIONS Page FIGURE 1. Map of Green-Duwamish River study area_________________________ _____ __ _ __ 2 2-5. Diagrams showing: 2. Longitudinal profiles of salinity, temperature, and dissolved-oxygen concentration in Duwamish River es­ tuary ______________________ ________________________ __ 3 3. Probable circulation pattern in Duwamish River estuary __________________________ 4 4. Definition of elements in Duwamish River estuary model __________ __ _ 4 5. Definition of elements in the volume-transfer matrix, U ___ - 7 6. Graph showing solar-radiation and temperature functions for computing phytoplankton growth rates __ 11 7-23. Graphs showing computed and observed data for Duwamish River estuary for: 7. Water temperatures and tide stages during July 1967 __ _ _____ __ 17 8. Water temperatures and tide stages during August 1967 ______ _ -- 17 9. Chlorophyll a concentrations during July 1967, 16th Avenue South Bridge 18 10. Chlorophyll a concentrations during July 1967, First Avenue South and Spokane Street Bridges 18 11. Chlorophyll a concentrations during August 1967 _______________ _ - - -- 18 12. Dissolved-oxygen concentrations during July 1967, 16th Avenue South Bridge - -- 19 13. Dissolved-oxygen concentrations during July 1967, Spokane Street Bridge _____ 19 14. Dissolved-oxygen concentrations during August 1967, 16th Avenue South Bridge _ ______ __ 19 15. Dissolved-oxygen concentrations during August 1967, Spokane Street Bridge -___ -- 19 16. Water temperatures and tide stages during July 1968 ____________ __ _ 20 17. Water temperatures and tide stages during August 1968 __ _ -- -- 20 18. Chlorophyll a concentrations during July 1968 _____________ __ _ -- 20 19. Chlorophyll a concentrations during August 1968 ____________________ _ __ 20 20. Dissolved-oxygen concentrations during July 1968 ______ - - 21 IV CONTENTS Page FIGURES 7-23. Graphs showing computed and observed data for Duwamish River estuary for Continued 21. Dissolved-oxygen concentrations during August 1968 _________________________________ 21 22. Water temperatures and tide stages during September 1971 ____________________________ 21 23. Dissolved-oxygen concentrations during September 1971________________________________ 22 24-29. Graphs showing: 24. Computed dissolved-oxygen concentrations in top sublayer of Duwamish River estuary during September 1971 for 1971 and future RTF effluent discharges ________________________________ 24 25. Longitudinal distributions ofCyclotella sp ________________________________________ 31 26. Longitudinal distribution of oval flagellates.._______________________________________ 32 27. Longitudinal distribution of "coccoids" plus "coccoid" clusters ___________________________ 32 28. Relation between concentrations of excess dissolved oxygen and chlorophyll a __________________ 33 29. Relations between Michaelis-Menton factors and concentrations of nutrients __________________ 33 TABLES Page TABLE 1. Data required for computing flow in the Duwamish River estuary ______________________________ 13 2. Relation of width to elevation at cross sections for computing geometry of the Duwamish River estuary ______ 13 3. Equations for computing location of wedge toe in Duwamish River estuary_______ _________________ 13 4. Data required for the phytoplankton model ____________________________________________ 15 5. Data for the BOD Model _______________________________________________________ 16 6. Miscellaneous BOD inflows to the Duwamish River estuary from upstream BODT, and downstream, BODM, from First Avenue South Bridge _________________________________________________ 16 7. Data required for the DO model___________________________________________________ 17 8. Estimated decreases in the monthly averages of computed DO concentrations in the Duwamish River estuary during June-September 1971 for an increase in the RTF effluent discharge to the probable future maximum _____ 24 9. Abundant taxa in samples collected at four stations in Elliott Bay near Seattle during 1967-69 ___________ 29 10. Abundant taxa in freshwater samples collected in 1967 at two stations on the Green-Duwamish River _______ 29 11. Five most abundant taxa in freshwater samples obtained at two stations on the Green-Duwamish River during March-August 1967 _______________________________________________________ 29 12. Abundant taxa during two blooms in the Green-Duwamish River ______________________________ 30 13. Concentration of herbivores in water samples from the Green-Duwamish River for 3 days during phytoplankton blooms in 1967 and 1968 _____________________________________________________ 33 DEFINITION OF SYMBOLS average cross-sectional area of wedge element i, in constituent concentration in wedge element i. square feet. constituent concentration in wedge element i before average width of interface between a wedge element i computation. and the upper layer, in feet. constituent concentration in sublayer element i, j. 5-day biochemical oxygen demand of sublayer element constituent concentration in sublayer element i, j be­ i, j, in milligrams per litre. fore a computation. 5-day biochemical oxygen demand of sublayer element Cf constituent concentration in freshwater inflow at wedge i, j before a computation, in milligrams per litre. toe. BOD/ 5-day biochemical oxygen demand of freshwater inflow cr a coefficient used to compute incident long-wave radia­ to the estuary, in milligrams per litre, tion, dimensionless. BODM miscellaneous 5-day biochemical oxygen demand added Cs constituent concentration in seawater. to the estuary downstream from First Avenue South ct constituent concentration in water flowing into up­ Bridge, in pounds per day. stream end of sublayer./. 5-day biochemical oxygen demand of Green River water chlorophyll a concentration in sublayer element i, j, in at Tukwila gage, in milligrams per litre. micrograms per litre. 5-day biochemical