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T H E UNIVERSITY O F NORTH CAROLINA i s comprised ofthe sixteen public senior insti tutions in N o r t h Carol ina

UNC-WRRI-90-254

ANALYSIS OF STORKWATER INFILTRATION PONDS ON THE NORTH CAROLINA OUTER BANKS

G . M. Chescheir, G . Fipps, and R. W. Skaggs

Department of Biological and Agricultural Engineering North Carolina State University

Raleigh, NC 27695-7625

The research on which this publication is based was supported in part by funds provided by The University of North Carolina Water Resources Research Institute. Additional support was provided by the North Carolina Agricultural Research Service.

V‘RFU Project No. 70080

ACKNOhZEDGKENTS

This research was conducted in the Biological and Agricultural Engineering Department at North Carolina State University. The research was supported in part by funds provided by The University of North Carolina Water Resources Research Institute. Our appreciation is expressed to Dr. David Moreau for his constant support and advice during this project. Additional support was provided by the North Carolina Agricultural Research Service.

Field research for this project was conducted on property managed by Bald Head Island Management, Inc. and S u r f Units Owners Association, Inc. We thank these groups for allowing us access to their property and for providing support and assistance for our research effort. Special thanks go to Barbara Canaday at Surf Units, and to Daniel Cutler and Donna Ray at Bald Head Island for their personal assistance.

Our gratitude is expressed to the Groundwater Section of the N. C. Division of Environmental Kanagement for funding and conducting the groundwater investigation at the Surf City research site. Jay Bennett for leading this investigation. We are also grateful to Norma Hall for allowing us access to her property for the investigation.

We appreciate the efforts of

We thank the Water Quality Section of the N. C . Division of Environmental Management for expressing the need for this research and for assistance in locating and evaluating the field research sites. Special thanks to Alan Klimek for his advice and support for the project.

Special thanks are expressed to Wilson Huntley for resisting the constant temptation of the beach to carry out the valuable field work needed to complete this project. effort in organizing, digitizing, and graphing the data collected for the research.

Special thanks also go to Linda Leigh for her tireless

DISCLAIMER STATEMENT

Contents of this publication do not necessarily reflect the views and policies of The University of North Carolina Water Resources Research Institute nor does mention of trade names or commercial products constitute their endorsement or recommendation for use by the Institute or the State of North Carolina .

iii

ABSTRACT

The State of North Carolina adopted the current Stormwater Runoff Disposal Rules ( 1 5 A NCAC 2H.1050) in 1988 requiring stormwater management plans for new development in 20 coastal counties. Stormwater infiltration pond systems are approved by the State as an option for retaining stormwater on the developed site; however, the long-term performance of these systems has not been measured or determined. This study was conducted to monitor the hydrology of stormwater infiltration ponds on the North Carolina barrier islands and to develop a model that continuously simulates the performance of these ponds. The hydrology of two operating infiltration ponds systems was evaluated in an 18-month field study. Rainfall, pond stage, and water table elevations at selected locations were monitored continuously. Water table elevations at additional locations were monitored on a biweekly basis. Soil hydraulic conductivities and soil water characteristic relationships were determined at both field sites. The subsurface geology was described at one site and an aquifer pump test was performed to determine aquifer transmissivity and specific yield. Both of the infiltration ponds in the field studies effectively served their primhry purpose of retaining on site the stormwater runoff from the first 38 mm (1.5.) of rainfall. In nearly every case, the pond seepage rate was sufficient to completely draw down the pond within 5 days. very different. on which there was a shorter distance between the pond and the river and a greater elevation of the pond bottom above mean sea level.

The hydrology of the infiltration ponds at the two research sites was Greater pond drawdown rates were observed at the field site

A numerical solution to the Richards equation for combined saturated and unsaturated flow in three dimensions was developed to determine seepage rates from infiltration ponds. The solution used the Gauss-Seidel finite difference method with successive over-relaxation. To increase the rate of convergence, the numerical solution was modified for the multigrid method. The numerical solutions were used to develop an approximate analytic solution for calculating three-dimensional pond seepage rates. The approximate analytic solutions were incorporated into a computer model to simulate the hydrology of stormwater infiltration systems over long periods of climatological record. The resulting model predicted pond stage, drawdown time, and pond overflow. The model was used to simulate the hydrology of one of the monitored infiltration pond systems for 1988. Predicted values for pond stage and drawdown time compared well to measured values except during an extended period of unusually high tides. effects of island width, island length, pond bottom elevation, pond length to width ratio, pond volume, distance from pond to sink, and impervious area on pond performance. length, and elevation to pond bottom produce better pond performance. Lower values for island width, distance between pond and sink, and impervious area also improve pond performance. surface area reduces pond overflow but increases the time that water is in the pond.

Simulations were conducted to evaluate the

Higher values for pond length to width ratio, island

Increasing pond volume by increasing the

V

TABLE OF CONTENTS

ACKNOWLEJXXENTS O . . . . . . . . . . ~ . O O . . . . . . . . . . e iii

ABSTRACT * . . . 0 0 . e O . . 0 . 0 0 . . . . . * . ~ * ~ ~ . v

TABLEOFCONTENTS e a . . ., e e . . . . . . . . e vii

LIST OF FIGURES * . . . O O . B B . . O . . O . * . . . . . . . e ' . ix

LIST OF TABLES . . . . . . . . . . . . . e O . . . . . . . e . e . xiii SUMMARY AND CONCLUSIONS . e ., a e . . ., . . . . + . e . e xvii

RECOMMENDAT I ON8 . . . . 0 . 0 1 e . s . . 0 0 . . . . . . . . . * * xxi

INTRODUCTION * . . . e e . B B . . . . O . . O . . O . . ~ * . . ~ 1

FIELD STUDY OF TWO INFILTRATION PONDS ON THE NORTH CAROLINA . . - . . 2 BARRIER ISLANDS

SITE DESCRIPTION e e o o e e e

Surf City . . * . . . . . Bald Head Island e . . . .

KETHODS . . . e 0 0 1 0 0 . 0 . .

Soil Analysis e . . . Groundwater Investigation at Surf Pond Hydrology . e .

o o * e . . . . . . . . . . 2 . . * * . . . . . . + r e . a . . . . . . . . . . . . . - z

e . . . . . . . . . . . e . a . . . . . . . . . . . . e e 2 City Site . . . . . . a .. 5 . e . . . * . . . e . . . . 5

RESULTS O . . . . . . . . D O O . O . . . . . . . O . . . . 6 Soil Analysis e . . . . . . . . . e . . . . . e . . . 6 Groundwater Investigation at Surf City Site . . . . . . . . e 8 Hydrology of the Infiltration Ponds ., . . . . . . . . . e e 11

MODELING TKREE-DIMENSIONAL, SATURATED AND UNSATUFtATED FLOW . . * . . e . 33 USING MULTIGRIDS

GOVERNING EQUATIONS AND SOLUTION HETHOD e . . . . . . . . . e . 33 The Richards Equation . . ., . . . . a . . . . . . . . e e . 33 Numerical Solution e . . . e e e . + . . . . . ., . 34

THE MULTIGRID METHOD . . . a . . . . e ,, . . . . . . . . . 35 Linear Two-level Deecription . . . e e . . . . . . . . . 35 Non-linear Two-level Description . . e . e . . . . . . . . 37

MG3D SIMULATION MODEL . . . e . e . . . . . ., e e . . . . . a e 38

vii

Page

SAMPLESOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . 39 Problem A : Flow Between Two Ditches . . . . . . . . . . . . . 39 Problems B and C: Pond Seepage . . . . . . . . . . . . . . . 4 0

SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

POND SEEPAGE IN TWO AND THREE DIXENSIONS . . . . . . . . . . . . . . . . 46 PROBLEM DEFINITION . . . . . . . . . . . . . . . . . . . . . . . . 46

PONDS AT THE ISLAND MIDPOINT . . . . . . . . . . . . . . . . . . . 4 6 Two-dimensional Analysis . . . . . . . . . . . . * * * * * 49 Three-dimensional Analysis . . . . . . . . . . . . . . . . . 5 1

APPROXIMATE SOLUTION . . . . . . . . . . . . . . . . . . . . . . . 51 Deep Profile . . . . . . . . . . . . . . . . . . . . . . . . 56

SPECIALCASES . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Single Pond On Island . . . . . . . . . . . . . . . . . . . . 57 Pond Located Near a Canal . . . . . . . . . . . . . . . . . . 58

SU"Y . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

SIMULATION MODEL FOR INFILTRATION PONDS ON . . . . . . . . . . . . . . . 63 BARRIER ISLANDS

MODEL DESCRIPTION . . . . . . . . . . . . . . . . . . . . . . . 63 MODEL CALIBRATION . . . . . . . . . . . . . . . . . . . . . . . . . 68

SIMULATION OF POND PERFOWMCE AT SURF CITY . . . . . . . . . . . . 7 0

ANALYSIS OF SITE P W S T E R S AND DESIGN VARIABLES . . . . . . . . . 75 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

LIST OF REFERENCES . . . . . . . . . . . . . . LIST OF PUBLICATIONS . . . . . . . . . APPENDIX TABLES . . . . . . . . . . . . . . . . . 89

viii

LIST OF FIGURES

page

Figure 1. Diagram of infiltration pond research site at Surf . . * . . e 3 City showing locations of xr<onitoring wells, pond, sinks, watershed area, and pervious and impervious surface areas.

Figure 2 . Diagram of infiltration pond research site at Bald . . . . . e 4 Head Island showing 1ocatior.s of monitoring wells, pond, sinks, watershed area, and pervious and impervious surface areas.

Figure 3 . Diagram of continuous monitoring system located in the . . . 6 infiltration pond.

Figure 4. Soil water characteristic curves for soil samples collected 9 at the Surf City site.

Figure 5 . Soil water characteristic curves €or soil samples collected e . 9 at the Bald Head Island site.

Figure 6 . Response of the water table and pond surface elevations . ., 92 to rainfall and tides at the Surf City infiltration pond field site. The data are for the first quarter of 1988,

Figure 9 , Response of the water table and pond surface elevations . 13 to rainfall and tides at the Surf City infiltration pond field site. The data are for the second quarter of 1988.

Figure 8 . Response of the water table and pond surface elevations e . 14 to rainfall and tides at the Surf City infiltration pond field site. The data are €or the third quarter of 1988.

Figure 9 , Response of the water table and pond surface elevations . e e 15 to rainfall and tides at the Surf City infiltration pond field site. The data are for the fourth quarter of 1988.

Figures 10. Response of the water table and pond surface elevations . . e 16 to rainfall and tides at the Surf City infiltration pond field site. The data are for the first quarter o f 1989.

Figure 11. Response of the water table and pond surface elevations e 17 to rainfall and tides at the Surf City infiltration pond field site. The data are for the second quarter of 1989.

Figure 12. Response of pond water surface elevation to water table e . . 18 near the pond and to tides.

Figure 13. Response of pond drawdown before and after removal of . . . 19 the sediment layer on the pond bottom at Surf City.

Figure 14. Water table profiles along island length and island width . . 20 at the Surf City field site.

Figure 15. Response of the water table elevation under the pond to . . . 21 rainfall events at Bald Head Island comparing recorded hourly data to the 25 hour moving average data.

Figure 1 6 . Response of the water table and pond surface elevations . . . 23 to rainfall and tides at the Bald Head Island infiltration pond field site. The data are for the first quarter of 1988.

Figure 17. Response of the water table and pond surface elevations . . . 24 to rainfall and tides at the Bald Head Island infiltration pond field site. The data are for the second quarter of 1988.

Figure 18. Response of the water table and pond surface elevations . . . 25 to rainfall and tides at the Bald Head Island infiltration pond field site. The data are for the third quarter of 1988.

Figure 19. Response of the water table and pond surface elevations . . 26 to rainfall and tides at the Bald Head Island infiltration pond field site. The data are for the fourth quarter of 1988.

e of the water table and pond surface elevations . . . 27 fall and tides at the Bald Head Island infiltration eld site. The data are for the first quarter of 1989.

Figure 21. Response of the water table and pond surface elevations . . . 28 to rainfall and tides at the Bald Head Island infiltration pond field site. The data are for the second quarter of 1989.

Figure 22 . Re6 se of the water table and pond surface elevations . . . 29 fall and tides at the Bald Head Island infiltration

pond field site (April, 1988).

Figure 23. Res of the water table and pond surface elevations , , . 30 all and tides at the Bald Head Island iniiltratisn

pond field site (August 17 to September 16, 1988).

Figure 24. Water table profiles along island length and island width . . 31 at the Bald Head Island field site,

uction by relaxation for local and global errors . 36 (taken from HcKeon and Chu, 1987).

Figure 26. Schematic of the flow regime used for flow between two . . . . 40 ditches (Problem A ) ,

Figure 27. Grid levels used in the multigrid solution for Problem A. . . 41

X

lz!22E

Figure 28, Schematic ob the flow regime used for pond seepage a ., a 63 (Problems B and C).

Figure 29. Water table elevations fox pond seepage (Problem C ) , e o o o 43

Fi gu r .e 30, Water table elevations for the two-dimensional flow case * ., 44 (Problem B) compzred the the 3-D flow case (Problem C ) along three transects taken at y = 0, 10, 19, and 4 0 m.

Figure 31, Definition of the 3-0 problem simulated. Shown are identical 47 ponds of constant size, spated at distances of 2 L-

Figure 32, Schematic of the flow regime for the case of ponds located e 48 at the island midpoint.

Figure 33, Water table elevations (m) for W = 16 m, d = 8 m, tind 52 L = 5, 15, and 55 m for the problem shown in Figure 32,

Figure 34. Water table contours for the cases shown in Figure 33. * 53

Figure 35. Pond seepage rates per unit pond length (Q/Ep) for ., ., 5 4 d = 2 m (top), d = 8 m (bottom), and all values of W and L considered.

Figure 36, Division of the solution domain into two regions: radial 55 flow near the pond and 1-D lateral flow away from the pond.

Figure 3 9 . Schematic of the flow regime for a pond end a three-sink system

159

Figure 38. Water table elevations for the three-sink system Ehi3Wn e .. 60 in Figure 37 using H = 82 m, L = 35 m, and d = 8 m.

Figure 39. Water table contours €or the three-sink system shown in ., e 61 Figures 37 and 38 using W = 82 m and d = 8 m.

Figure 40, Flow chart o f interaction between the three model components used in DP’OND.

63

Figure 41. Plan view of model infiltration pond system showing the areal input variables used by DPSOND.

64

Figure 42. Plan view of model infiltration pond system showing the four quadrants (Q,) used for pond seepage calculations by DHPOND.

Figure 43. Elevation view of model infiltration pond system showing the elevation input variables used by DKPOND.

64

6 5

Figure 44. Predicted and measured water table elevations near the infiltration pond a t Surf City.

69

xi

paqe

. . . 71 Figure 4 5 . Predicted and measured water surface elevations in the infiltration pond a t Surf City for the f i r e t quarter of 1988.

Figure 46. Predicted and measured water surface elevations in the , . . 72 infiltration pond at Surf City for the second quarter of 1988.

Figure 47. Predicted and measured water surface elevations in the . . . 7 3 infiltration pond at Surf City for the third quarter of 1988.

Figure 48. Predicted and measured water surface elevations in the . . . 74 infiltration pond a t Surf City for the fourth quhrtet of 1988.

LIST OF TABLES

Table 1. Effective saturated vertical hydraulic conductivity in . . . . 7 7 . 5 cm undisturbed soil samples collected from the surface layer inside and outside of infiltration ponds.

Table 2. Field measurements of horizontal hydraulic conductivity at . . . 8 Surf City and Bald Head Island determined by the auger hole method.

Table 3. Results of aquifer pump test conducted near Surf City Site. . . 10 Data are corrected for tidal fluctuations.

Table 4. Comparison of horizontal and vertical hydraulic conductivity . 10 values measured at the Surf City Site.

Table 5 . Gradients near the infiltration pond at Surf City in response . 21 to a 50 mm rainfall event occurring on 5/15/89.

Table 6. Water table elevations for Problem ' A u predicted by the . . . . 42 Gauss-Seidel SOR solution (GS-SOR), the multigrid solution (MG3D), and an analytic solution (Harino and Luthin, 1982)

Table 7, CPU time required to obtained solutions for three problems . . 45 using the Gauss-Seidel SOR (GS-SOR) method and the multi- grid method (MG3D) as run on a IBM 4381 computer.

Table 8 . Two-dimensional flow rates obtained from the numerical . . . . SO solutions, MG3D, and Eq. 6 for the case of identical ponds located at the island midpoint (Fig. 32b).

TrSle 9. Two-dimensional flow rates for W = 82 m, d = 8 m, and . . . . 51 various q values for the flow regime shown in Fig. 32b.

Tible 10. Three-dimensional seepage rates obtained from the numerical . . 57 solutions, MG3D (+ 5 % ) and as determined with E q s . 26 and 31 for the problem shown in Fig. 32.

Tiible 11. Se tea for a single pond located at the center of . . . 58 the island obtained from the numerical solutions, MG3DI for L=95 m and d = 8 m and calculated with Eq. 22.

le 12. Seepage rates from the left, front, and right sides of a . . . 62 pond (Top View, Fig. 37) located near a canal (along

m, d = 8 m, and Hs = 7 m.

elevations at Surf City used . . . 68

: e 14. Pond performance at Surf City site as simulated by DMPOND . . . 75 for 30 year period using climatological data for the years 1950 to 1979.

xiii

Table 15. Baseline site dimensions, areas, and elevations used in . . . 76 DMPOND simulations evaluating different pond system designs and scenarios.

Table 96. The effect of pond bottom elevation on the number and . . .+ . 76 length of pond drawdown delay incidents during 30 year simulations using Wilmington, N.C. weather data.

Table 17, The effect of pond bottom elevation on the number, total . e 77 volume, and maximum volume of pond overflow incidents during 30 year simulation using Wilmington, N.C. weather data.

Table 98. The effect of pond length to width ratio on the number . e 77 and length of pond drawdown delay incidents during 30 year simulations using Wilmington, N.C. weather data.

Table 19. The effect of pond length to width ratio on the number, . e 78 total volume, and maximum volume of pond overflow incidents during 30 year simulation using Wilmington, N.C, weather data.

Table 2 0 . The effect of length offset on the number and length of . . 38 pond drawdown delay incidents during 30 year simulations using Wilmington, N.C. weather data.

Table 21. The effect of length offset on the number, total volume, II e 7 9 and maximum volume of pond overflow incidents during 30 year simulation using Wilmington, N.C. weather data.

Table 22, The effect of width offset on the number and length of . . . 39 pond drawdown delay incidents during 30 year simulations using Wilmington, N.C. weather data,

Table 23. The effect of width offset on the number, total volume, 80 and maximum volume of pond overflow incidents during 30 year simulation using Wilmington, N.C. weather data.

Table 24. The effect of island width on the number and length of ., . . 80 pond drawdown delay incidents during 30 year simulations

mington, N.C. weather data.

Table 25. The effect of island width on the number, total volume, . . . 81 and maximum volume sf pond overflow incidents during 30 year simulation using Wilmington, N.C. weather data.

Table 26. The effect of island length on the number and length of , pond drawdown delay incident8 during 30 year simulations using Wilmington, N.C. weather data.

e 81

xiv

Table 27. The effect of island length on the number, total volume, . . 82 and maximum volume of pond overflow incidents during 30 year simulation using Wilmington, N.C. weather data.

Table 28. The effect of impervious area on the number and length of . e 82 pond drawdown delay incidents during 30 year simulations using Wilmington, N.C. weather data.

Table 2 9 . The effect of impervious area on the number, total . . . . . 83 volume, and maximum volume of pond overflow incidents during 30 year simulation using Wilmington, N.C. weather data.

Table 30. The effect of pond volume on the number and length of . e . . 83 pond drawdown delay incidents during 30 year simulations using Wilmington, N.C. weather data.

Table 31. The effect of pond volume on the number, total volume, and . . 84 maximum volume of pond overflow incidents during 30 year simulation using Wilmington, N.C. weather data.

xv

SUMMARY AND CONCLUSIONS

The State of North Carolina adopted the current Stormwater Runoff Disposal Rules ( 1 5 A NCAC 2H.1000) in 1988 requiring stormwater management plans for new development in 20 coastal counties. Stormwater infiltration pond systems are approved by the State as an option for retaining storm water on the developed site; however, the long-term performance of these systems has not been measured or determined. Likewise, computer models or other predictive techniques to describe the performance of stormwater infiltration ponds over long periods of time have not been developed and tested. Such models and techniques would provide valuable assistance in evaluating and designing these infiltration systems.

The overall objective of this project was to develop a model that continuously simulates the performance of stormwater infiltration ponds on the North Carolina barrier islands. The hydrology of two operating infiltration ponds systems was studied in an 18-month field study. A three-dimensional numerical simulation model for combined unsaturated and saturated groundwater flow was developed and used to analyze pond seepage under geometries characteristic of the North Carolina barrier islands. The numerical solutions were used to modify and test approximate methods for quantifying pond seepage. The approximate methods were incorporated into a reservoir model for monitoring pond stage and overflow. The reservoir model was included in a hydrologic simulation to predict water table elevation, runoff, and pond performance over a long period of time. The reliability of the model was tested using data collected from the field experiments.

Two stormwater infiltration ponds in operation at Surf City, N.C. and Bald Head Island, N.C. were used for field study. The water table elevations at selected locations along the transect of the island were monitored continuously. Water table elevations at additional locations were monitored on a biweekly basis. The water surface elevations in the infiltration ponds were also monitored on a continuous basis as was the rainfall at the site. Soil hydraulic conductivities and soil water characteristic relationships were determined at both field sites. The subsurface geology was described at the Surf City site and an aquifer pump test was performed to determine aquifer transmissivity and specific yield.

The hydrology of the infiltration ponds at the two research sites was very different. The runoff water stood in the pond at Bald Head Island for much shorter periods than at Surf City. rates, less impervious area in the watershed, and a more shallow pond depth at Bald Head Island. from the shorter distance between the pond and the river and the greater elevation of the pond bottom above the water table and mean sea level.

Both of the infiltration ponds in the field studies effectively served their primary purpose of retaining on site the stormwater runoff from the first first 38 mm (1 .5 in) of rainfall, During the field study, there was no evidence that any stormwater runoff from either developed site flowed overland

Thie was due to greater pond drawdown

The higher pond drawdown rate at Bald Head Island resulted

xvii

to the sounds. Zn nearly every case, the pond seepage rate was sufficient to completely draw down the pond in 5 days. The single case during the 18-month study when drawdown was greater than 5 days occurred during a period of high tides. Even with sufficient drawdown rates, water did stand in the pond for as much as 18 consecutive days due to successive rainfall events. effects to property, environment, or pond performance were observed during these periods.

A numerical solution to the Richards equation for combined saturated and unsaturated flow in three dimensions was developed to determine seepage rates from infiltration ponds. method with successive over-relaxation (GS-SOR). To increase the rate of convergence, the numerical solution was modified for the multigrid method (MG3D). Details of the multigrid method were presented for a two-level description of linear and non-linear systems of equations. Solutions for three sample problems were obtained with the GS-SOR and MG3D algorithms. multigrid solutions resulted in a reduction of total CPU time ranging from 71% to 82% over GS-SOR.

The three-dimensional numerical simulation model for combined unsaturated and saturated groundwater flow was used to analyze pond seepage under geometries characteristic of the North Carolina barrier islands. Ponds of constant size spaced from 10 to 190 m apart were simulated using varying distances from the ponds to the sinks and to the restricting layer. For the geometries and soil properties considered, pond seepage was dominated by flow in the saturated zone. The spacing between adjacent ponds affected seepage rates, having a greater effect for large island widths.

No adverso

The solution used the Gauss-Seidel finite difference

The

The numerical solutions were used to develop an approximate analytic solution for calculating three-dimensional pond seepage rates. The solution is for ponds located at the island midpoint and is based on radial flow theory in the vicinity of the pond and an equation for one-dimensional lateral flow in the remainder of the flow domain. approximating the increase in the length of the flow path due to flow out of the bottom of the pond. pond seepage rates as determined from the numerical solutions for the geometries considered.

For deep profiles, a method is presented for

The approximate solution predicted nearly the same

A computer model, DKPOND, was developed to simulate the performance of stormwater infiltration systems over long periods of climatological record, DMPOND was composed of three components: a seepage component using the approximate method for calculating three dimensional pond seepage, a hydrologic component for calculating stormwater runoff and water table elevation in the pond watershed, and a reservoir component for predicting pond age, storage, and overflow. DMPOND also evaluated pond performance by

predicting the number of pond overflow events and drawdown delays (water standing in the pond more than 5 days) occurring during the simulation period.

DMPOND was used to simulate the hydrology of the Surf City infiltration pond system for 1988. that compared well to measured values except during an extended period of unusually high tides.

DMPOND predicted values for pond stage and drawdown time

xviii

DMPOND simulations were conducted to evaluate the effects of the following design variables on pond performance: island width, island length, pond bottom elevation, pond length to width ratio, pond volume, distance from pond to sink, and impervious area. The performance of a pond was evaluated by several parameters: the number of d r a w d ~ w ~ delays, the maximum time period that water stands in the pond, the number of overflow events, and the percent of total runoff that is retained on site. The simulations indicated that higher values for pond length to width ratio, island length, and elevation to pond bottom produced better pond performance. Lower values for island width, distance between pond and sink, and impervious area also improved pond performance. Increasing pond volume by increasing the surface area reduced pond overflow but increased the time that water is in the pond.

The sensitivities of the pond performance parameters to the design variable6 were different for the set of conditions used in this study. The number of drawdown delays was most sensitive to pond bottom elevation and pond length to width ratio. The number of pond overflow events was most sensitive to pond volume and impervious area. Only three variables (elevation of pond bottom, island width, and impervious area) significantly affected the maximum time period that water was in the pond. Only two variables (pond volume and impervious area) significantly affected the percent of total runoff retained and the total and maximum overflow volumes. The sensitivities reported here may not apply for all conditions encountered on the barrier islands; therefore, infiltration pond systems should be designed using design variables encountered on the specific site.

xix

RECOMMEKDATIONS

Properly designed stomwater infiltration ponds on the North Carolina barrier islands will effectively retain on site the stormwater runoff from the first 38 mm (1.5.) of rainfall. Eoth infiltration ponds analyzed in this field study and most of the hypothetical ponds simulated for a 30-year period using a long-term simulation model performed within the limits of North Carolina regulations. We recommend the use of stormwater infiltration ponds for reducing the volume of runoff from developed areas to coastal waters. recommendation is based on the hydrology of the pond system; however, the effects of infiltration ponds on the water pality of the groundwater has not been considered and should be the topic of future research.

This

Stormwater infiltration ponds must be properly designed in order to perform effectively. The island width (distance from ocean to sound) and island length (perpendicular to width ie. distance between property boundaries or hydraulic sources) are specific for each situation and cannot be easily changed by design. Other variables that affect pond performance can be controlled in the design of a pond system. These variables are the distance of the pond from the ocean or sound, the distance between adjacent ponds, the elevation of the pond bottom above mean sea level, the length-to-width ratio of the pond, and the amount of impervious area. engineer should consider that pond performance improves by

When designing a pond the

1. 2. 3.

4.

5 . decreasing the area of impervious surfaces.

increasing the elevation of the pond bottom above mean sea level, increasing the ratio of pond length to pond width, increasing the distance along the island length between the pond and adjacent ponds or other hydraulic sources, decreasing the distance between the pond and the sound or the ocean, and

The models (DMPOND and MG3D) and equations developed in this project will be very useful to engineers for designing effective stormwater infiltration pond systems. oriented and toward developing simple design methods.

Work is continuing toward making these design tools more user-

x x i

INTRODUCTION

Increasing development along the North Carolina coast has been linked to the deterioration of water quality in adjacent sounds and estuaries. Stormwater runoff from buildings and parking lots has been found to contain particulates, heavy metals, pesticides, inorganic salts, organic matter, micro-organisms, and other pollutants (Bryan, 1970; Sartor Stauffer et al., 1984; USEPA, 1983). Degradation of water and estuaries threatens the coastal ecology which provides area's fishing and tourism industries.

The State of North Carolina adopted the current Stormwater

pathogenic and Boyd, 1972; quality in sounds resources for the

Runoff Disposal Rules (15A NCAC 2H.1000) in 1988 requiring stormwater management plans for new development in 20 coastal counties. The regulations apply to residential, commercial, industrial, or institutional development on land areas greater than 1 acre. If more than 2 5 % of the land adjacent to designated shellfish waters is built upon, stormwater runoff from the first 1.5' (38 mm) of rainfall must be retained on site. If more than 30% of the land near other coastal waters is built upon, runoff from the first 1' ( 2 5 rrun) of rainfall must be retained or detained such that 8 5 % of total suspended solids is removed.

Stormwater infiltration systems are the only retention systems approved by the State that are not considered innovative. In these systems, runoff from the developed area is routed to shallow ponds or swales where particulate matter and micro-organisms are filtered out as the water seeps underground. Although the concept is straightforward, the factors controlling the operation of these systems are not well understood. Intensive long-term monitoring of the water table and pond stage elevations in these systems has not been undertaken. Likewise, computer models have not been developed and tested that continuously simulate the performance of stormwater infiltration ponds over long periods of time . The overall objective of this project was to develop a model that will continuously simulate the performance of a stormwater infiltration pond on the North Carolina Outer Banks. The specific objectives were as follows:

1. To obtain numerical solutions for seepage from infiltration ponds for the range of conditions encountered on the N. C. barrier islands

To use the numerical solutions to test and modify approximate methods for quantifying pond seepage

2 .

3 . To modify a hydrologic simulation model to predict water table depth and runoff from developed areas and to develop a reservoir model to monitor the water elevation in the infiltration pond

To test the reliability of the models using data collected from two field sites

4.

FIELD STUDY OF TWO INFILTRATION PONDS ON THE NORTH CAROLINA EARRIER ISLANDS

SITE DESCRIPTION

The stormwater i n f i l t r a t i o n ponds analyzed i n t h i s s t u d y a r e l o c a t e d on Topsail I s l a n d a t Surf C i t y and on Bald Head I s l a n d . are shown i n F i g s . 1 and 2,

Diagrams of t h e si tes

Surf C i t y . T o p s a i l I s l a n d is a developed barrier i s l a n d 35 km l o n g and v a r y i n g i n w i d t h from 0.3 t o 2.0 km. p r o p e r t y of S u r f U n i t s , Inc. , a 180-uni t condominium development l o c a t e d on NC 210 1.5 km east of t h e i n t e r s e c t i o n of NC 50. The i s l a n d w i d t h a t t h e r e s e a r c h site i s 352 m. Ground e l e v a t i o n a t t h e s i te r a n g e s from 1.7 m above msl a t SI1 t o 3.4 m above means sea l e v e l (MSL) a t S9 on t h e dunes. The v e g e t a t i o n on t h e s i te is a m i x t u r e of lawn g r a s s e s ( f e s c u e and c e n t i p e d e ) , n a t u r a l v e g e t a t i o n and ornamental p l a n t i n g s . undeveloped on t h e w e s t and n o r t h s i d e and developed w i t h beach c o t t a g e s on t h e east s ide. The i n f i l t r a t i o n pond h a s a depth of 1.2 m and a s u r f a c e area a t maximum s t a g e of 0.05 ha w i t h s i d e Slopes of approximately 2 : 1. Pond s t o r a g e i s 600 m3, enough t o store 54 inm of runoff from r a i n f a l l on t h e impervious a r e a s . ha w i t h 1.1 h a of t h a t area b e i n g covered wi th impervious s u r f a c e s . The e l e v a t i o n of t h e bottom of t h e pond is 1.1 m.

Bald Head I s l a n d . Bald Head I s l a n d i s t h e S-km-long b a r r i e r i s l a n d t h a t forms Cape Fear. The i s l a n d is be ing developed as a resort area w i t h beach houses , condominiums, and r e c r e a t i o n a l f a c i l i t i e s . The r e s e a r c h si te is l o c a t e d on a narrow p e n i n s u l a on t h e northwest t i p of t h e i s l a n d . The d i s t a n c e across t h e p e n i n s u l a from t h e Cape Fear r i v e r t o a t i d a l marsh i s 120 m. e x t e n d s a n o t h e r 220 m t o Bald Head creek . Due t o t i d a l f l u c t u a t i o n s , i s l a n d wid th v a r i e s from 340 m a t low w a t e r t o 120 m a t h i g h water . a t t h e site r a n g e s from 1.6 m above HSL a t B7 t o 2 . 8 m above HSL a t B2 o n t h e dunes. ornamental p l a n t i n g s . i s i n c o n n e c t i o n w i t h t h e ocean. d e p t h of 0.46 m and a s u r f a c e area a t maximum s t a g e of 0.05 ha. resembles a n a t u r a l swale w i t h g r a d u a l and v a r i a b l e s i d e slopes. is 107 m3, capable of h o l d i n g 51 mm of runoff from r a i n f a l l on t h e imperv ious areas. The watershed d r a i n i n g t o t h e pond i s approximately 0.51 ha w i t h 0 .21 ha of t h a t area covered by impervious surfaces. t h e pond is 1.6 m

The Surf C i t y s i t e i s located on t h e

The l a n d a d j a c e n t t o t h e si te is

The watershed area d r a i n i n g t o t h e pond i s approximate ly 3

The marsh

Ground e l e v a t i o n

The v e g e t a t i o n on t h e s i te i s a mixture of n a t u r a l v e g e t a t i o n and

The i n f i l t r a t i o n pond on t h e s i te h a s a The pond

The site i s bordered on t h e n o r t h s i d e by a marina t h a t

Pond s t o r a g e

E l e v a t i o n of t h e bottom of

METHODS

Soil Analvsie . Undisturbed s o i l sur rounding areas for l a b o r a t o r y

samples were c o l l e c t e d from t h e ponds and t h e d e t e r m i n a t i o n of ve r t i ca l h y d r a u l i c

c o n d u c t i v i t y and t h e s o i l w a t e r c h a r a c t e r i s t i c . c o n d u c t i v i t y w a s determined u s i n g t h e c o n s t a n t head method (Xlu te , 1965a) . Soil water c h a r a c t e r i s t i c c u r v e s w e r e determined u s i n g a m o d i f i c a t i o n of t h e p r e s s u r e plate method d e s c r i b e d by X l u t e (1965b).

The v e r t i c a l h y d r a u l i c

2

. . P .

. . * : - * *

- 0 * . - :. SI . * . * . f

* . - . .

Figure 1. Diagram of i n f i l t r a t i o n pond research s i te a t Surf City showing l o c a t i o n s of pond, s inks , watershed area, and pervious and

( 0 ) water l e v e l recorders are also shown, ous surface areas . Monitoring w e l l s wi th (0 ) and without

Figure 2 . Diagram of i n f i l t r a t i o n pond research site a t Bald Head Island showing locat ion5 of pond, s inks , watershed area, and pervious and impervious surface areas , Monitoring w e l l s w i t h (0) and without ( 0 ) water l e v e l recorder8 are also shown.

4

Field measurement of horizontal hydraulic conductivities were made at the Surf City site using the auger hole method (Van Beers, 1970). The loose sands at both sites made the augered holes very unstable below the water table; therefore, the holes were augered inside a screened thin walled PVC tube.

Groundwater Investisation at Surf Citv Site. conducted near the Surf City site by the Groundwater Section of the Division of Environmental Management in the North Carolina Department of Natural Resources and Community Development. The investigation site was located 70 m west of the Surf Units property line and 150 m from the ocean. Eight borings were drilled using mud-rotary and hollow stem techniques. Sediment samples were collected by wet grab and split spoon techniques from 4 of the 8 borings. Vertical hydraulic conductivity values were determined by grain size analysis (Hazen, 1893).

A groundwater investigation was

Monitoring wells were installed in 6 of the borings. Five of the wells were screened from MSL to just above an aquitard 7.9 m below MSL. The other well was screened from 11.7 m to 13.2 m below MSL (below the aquitard). A 24-hour aquifer pump test was conducted at a pumping rate of 2.15 l/s (34 gpm). The aquifer transmissivity, horizontal hydraulic conductivity, and specific yield were determined using the type curve method outlined by Boulton (1963), and Prickett (1965).

Pond Hvdrolosv. Shallow monitoring wells were installed at locations shown in Fig. 1. Monitoring wells consisted of PVC pipe jetted to a depth of 3 m and screened from a depth of 2 . 7 m to 3.0 m. Water table elevations were recorded continuously in wells equipped with automatic recorders and biweekly in wells not equipped with recorders. After determining that the water table under the ponds did not accurately reflect the stage of the pond, automatic recorders (B9 & 512) were installed to directly measure the stage of the ponds. A diagram of the monitoring wells installed in the ponds is shown in Fig. 3 . After the pond stage recorders were installed, continuous and biweekly water table elevation data were collected for 18 months. Two months before the end of monitoring, the continuous monitoring station at S9 was moved to station S13.

A layer of sediment and organic matter was removed from the pond bottom at Surf City when it was suspected that this layer might be restricting pond seepage. removed by a small tractor equipped with a scraper blade and a front end loader. The layer removal took place on 12/7/88, after 11 months of monitoring. Monitoring continued for 7 months after the scraping operation.

Vegetation was cleared from the pond and a 0.04 - 0.05 m layer was

Recorder chart data from the continuously monitored wells were read into computer file using a digitizing pad. Breakpoint data were converted to hourly water table elevation by simple interpolation. This conversion simplified analyses of head differences between wells, average pond drawdown rates

Water table elevation observed at station S9 at Surf City and at B3, B6, and B7 at Bald Head Island were strongly influenced by tidal fluctuations. affect the performance of the infiltration system; however, oscillations over longer periods due to meteorological influences may affect pond performance. Since the semidiurnal fluctuations obscured long-term plots of the data, they

The semidiurnal fluctuations were not believed to significantly

5

I 1

Figure 3. Diagram o f cont inuous moni tor ing system l o c a t e d i n t h e i n f i l t r a t i o n pond. t h e o t h e r s t a t i o n moni tors t h e h y d r a u l i c head below t h e pond.

One s t a t i o n mon i to r s t h e s t a g e of t h e pond and

w e r e f i l t e r e d o u t by u s i n g a 25 hour f l o a t i n g ave rage of t h e hour ly d a t a .

t h e 25 hour p e r i o d c e n t e r e d wi th respect t o t h e hour. ach hour ly d a t a p o i n t i n t h e smoothed data r e p r e s e n t e d t h e average of

t + 1 2 I: Hi

i= t -12

where :

H, is t h e e l e v a t i o n a t hour t

Hi is t h e e l e v a t i o n a t hour i and

RESU

S o i l A n a l y s i s . The soi1s ove r most of t h e r e s e a r c h s i te c o n s i s t e d of fine marine sands w i t h small s h e l l f ragments . t h e ponds con ta ined f i n e sed iments t h a t had been washed o f f t h e impervious surfaces. A t Surf C i t y , t h i s sediment l a y e r w a s 3 to 5 c m t h i c k and con ta ined a dense root mass from t h e v e g e t a t i o n growing i n t h e pond. The sediment l a y e r a t Bald Head I s l a n d was 0.5 t o 1.5 cm t h i c k and did not c o n t a i n many roots due t o a s p a r s e populat ion of dune grasses.

The s o i l s u r f a c e in t h e bottom of

6

Vertical hydraulic conductivities of the upper 7.5 em of the soils in the ponds were lower than those of the sands elsewhere on the sites (Table 1). Preliminary analyses showed an order of magnitude difference in conductivity between the surface and subsurface layers; however, subsequent analysis showed less difference and greater variability in the surface layer. The greatest variability in conductivity values occurred on the surface of the Surf City pond. matter in the layer. The roots and organic matter would increase the frequency of macropores which greatly increase conductivity. conductivities of the sands outside the ponds varied little with location and depth. Conductivities at the Surf City site were higher than at the Bald Head Island site. The sand below the surface of the ponds had conductivity values very close to those outside the pond.

This was most likely due to the mass of roots and decaying organic

The vertical

The horizontal hydraulic conductivities as measured by the auger hole method are shown in Table 2. and 64.2 cm/hr outside the pond at Surf City. sea level was noted in the profile descriptions from 4 of the 5 augered holes in the pond. This layer was described in only one of the auger holes outside the pond. Lower conductivity values in the pond at Surf City were probably due to the presence of the silt layer.

Mean values were 29.6 cm/hr in the pond at Surf City A dark silty sand layer near

Horizontal conductivities at Bald Head Island were lower than those outside the pond at Surf City. This was consistent with the observation that lower vertical conductivities occurred outside the pond at Bald Head Island than

Table 1. Effective saturated vertical hydraulic conductivity in 7.5 cm undisturbed soil samples collected from the surface layer inside and outside of infiltration ponds. (SD = standard deviation, n = number of samples)

Site

Surf City

Mean Surface SD

n

Mean Subsurf ace SD

n

Inside Pond Outside Pond

77.6 79.2 13.2 7.0

5 3

Mean 11.6 69.5 Surface SD 8 .7 9 .6

n 5 3

Mean 58.6 65.1 Subsurf ace SD 17.2 10.0

n 5 3

Bald Head Island

7

Table 2, Field measurements of horizontal hydraulic conductivity at Surf City and Bald Head Island determined by the auger hole method.

Site Inside Pond Outside Pond

------------ cm/hr------------

Mean 29.6 64.2

n 5 7 Surf City SD 12.2 30.0

Bald Head Island Mean 39.7 SD 15.1 R 3

43.9 12.7

4

occurred outside the pond at Surf City, Head Island did not differ between inside and outside of the pond. layer was not encountered on the Bald Head Island site.

Horizontal conductivities at Bald A silt

The soil water characteristic data of the soils at Surf City and Bald Head Island are shown i n Figs. 4 and 5 , Between pressure heads of 2 and 60 em, 0.22 and 0.33 cmJ/cm3 of soil water was released from the soils. Very little water was released at pressure heads greater than 75 cm. The surface soil samples from the pond at Surf City retained more water at high pressure heads than the other samples, due to higher organic matter content.

Groundwater Investiqation at Surf Citv Site. The general subsurface geology of the Surf City site consisted of unconsolidated to partially consolidated marine sedimentary deposits from middle Tertiary to the Recent time period. Four geologic formations were encountered in the deep borings of the groundwater investigation, The Castle Hayne limestone formation was encountered from 23.5 m below MSL to the bottom of the boring (29 m below MSL). Sediments from this formation were gray limestone with clayey, silty, fine sand and small mollusk shell layers. The River Bend formation occurred from 11.6 to 23.5 m below HSL and consisted of gray, silty, fine sand with limestone layers. The Belgrade formation lay between 7 . 9 and 11.6 m below MSL. This formation consisted of gray-blaek, clayeyI silty fine sand w i t h shell hash of mollusk shell overlain by a thin very dense bed of gray-black, clayey, silty coarse-to-fine sand and osteriea shells, possibly of the Haywood Landing member, The Waccamaw formation occurred between 3.3 and 7.9 m below MSL and consisted of gray, slightly silty, medium-to-fine sand with shell hash of osteriea, mollusk, and gastropods, and small rounded pebbles. Surficial deposits occurred over the Waccamaw formation to an elevation of 2.7 m above MSL. These deposits consisted of dense-to-medium-dense, light orange and tan to gray, fine, very uniform sand.

The hydrogeology of the site was characterized by three units. unconfined aquifer down to 7.9 m below MSL overlying an aquitard from 7 . 9 to 8.8 m below MSL. deepest point investigated.

A surficial

A semi-confined aquifer lay under the aquitard to beyond the

8

Figure 4 . Soil water characteristic curves for soil samples collected at the Surf City site. below the soil surface. were taken 0.60 m below the soil surface.

Subsurface samples in the pond were taken 0.30 m Subsurface samples outside of the pond

""_ .... _-.. ...- i - SURFACE OUTSIDE P O N D

--- SUBSURFACE OUTSIDE P O N D - SURFACE INSIDE P O N D _...-. SUBSURFACE INSIDE P O N D 0.3 6

I- s

I . . . . l . . . . , . . , ~ , * * , * 0.0 0 -200 -150 -100 -50

PRESSURE HEAD (cm)

Figure 5. Soil water characteristic curves for soil samples collected at the Bald Head Island site. 0.30 m below the soil surface. pond were taken 0.60 m below the soil surface.

Subsurface samples in the pond were taken Subsurface samples outside of the

9

Table 3 . Results of aquifer pump test conducted near Surf City Site. are corrected for tidal fluctuations.

Data

AA26s8 7.6 0 .66 0.008 230 27.1

AA26s3 13.7 0.32 0.010 201 23.7

The results of the aquifer pump test are shown in Table 3 . reacted as an unconfined anisotropic aquifer (NC DEH, 1989). Unrealistically high values for specific yield were observed in wells AA26s6 and AA26s8. Possible reason8 for the high values are recharge from the semi-confined aquifer below, tidal recharge, or aquifer pore pressure reduction near the pumping well. soil water characteristic curves in Fig. 4.

Horizontal and vertical hydraulic conductivity values as measured by different methods at the Surf City site are compared in Table 4. conductivity values are high when compared to other soils. between the methods exist; however, the range of the values within each method overlap the ranges of the other methods. The conductivity values fo r the methods employed in the groundwater investigation are higher than those for the methods using shallow borings,

The aquifer

The specific yield value at well AA26s3 was consistent with the

All of the hydraulic Some variation

Table 4, Comparison of horizontal and vertical hydraulic conductivity values measured at the Surf City Site

Met hod Mean SD Range n ---c--------------------------------------------------------------------------

Horizontal Conductivity (cm/hr)

Auger Hole 50 29 12 - 100 12

Aquifer Pump 127 37 99 - 170 3

Vertical Conductivity (cm/hr)

81 * Soil Core 13 64 - 107 11

Grain Size 112 11 101 - 127 4

* Surface layer samples from the pond are not included

10

Hvdroloav of the Infiltration Ponds. An overview of the hydrology of the infiltration pond systems at the research sites is shown in the quarterly plots of water table elevations, rainfall and tidal fluctuations (Figs. 6 - 11 and 16 - 21). The rainfall data are hourly data collected on the field site and the tide data are the four point moving average of the tides measured by NOAA at Duke Marine Lab in Beaufort, NC. These plots show the response of the water table elevations to rainfall and tidal fluctuations, and the response of pond stage to rainfall and to water table near the pond. Pond performance at the two research sites differed greatly due to island dimensions and to pond location and design.

Water table elevations near the pond at Surf City are shown by the S2 and S11 data on Figs. 6 - 11. Both wells were located 30 m from the pond edge. Water table elevations ranged from 0.63 to .47 m at well S11 and from 0.66 to 1.47 m at well S2. During periods of no in, the water table at S11 (located nearer to the creek) was usually 2 to 3 em lower than at the S2 well. Water table elevations at both wells responded similarly to rainfall events. The elevation at S11 rose slightly higher during some of the larger events. During very large events the water table elevation was greater than the elevation of the pond bottom. This situation occurred 6 times over the 18 month period. At the highest recorded elevation, the water table was 1.22 m below the soil surface (2.69 m) at well S2, and 0.33 m below the soil surface (1.80 m) at well S11. Response of the water table at both wells to tidal fluctuations is small.

The 55 well was located in the pond and measured the hydraulic head 1 m below the pond. Hydraulic heads ranged from 0.65 to 1.77 m (Fig. 6 - 11). Hydraulic heads at the pond were up to 0.3 m higher than at S2 and S11 when water was standing in the pond. These head differences were greatest after large rainfall events and rapidly declined to less than 0.02 m. within 10 days. Hydraulic heads at S5 were greater than the elevation of the pond bottom during larger events. This situation occurred 21 times over the 18 month period.

The response of pond surface elevation to rainfall and to water table elevations near the pond is shown as S12 in Figs. 6 - 11. Surface elevations ranged from the pond bottom (1.12 m for 1988 and 1.08 m for 1989) to 2.35 m. The pond elevation rose very rapidly in response to rainfall. the watershed was in the pond within 1 hour of the rainfall event. Pond drawdown was much slower, averaging 9.41 m/d. 0.50 m/d to 0.05 m/d, with higher rates occurring immediately after large rainfall events when the pond surface elevations were much higher than the surrounding water table elevations. The lower rates occurred toward the end of the pond drawdown when the pond surface elevations were low and the water table elevations near the pond were high. Complete pond drawdown from rainfall events took up to 7 days; consequently, events frequently occurred while water from a previous event was still in the pond. This situation prolonged the period that water stood in the pond. that water stood in the pond due to successive rainfall events was 18 days.

All runoff from

Pond drawdown rates ranged from

The longest period of time

The fluctuations of the water table elevation at well S9 are quite different than at the other wells (Figs. 6 - 11). pond and 50 m from the ocean. Water table elevations at S9 were strongly

Well S9 was located 180 m from the

11

P h)

2.50 E

0 2.00

U

I

d 1.50

m 41

3 1.00

I- Q

6.50

TIME (days)

Figure 6. Responee of t h e water t a b l e and pond surface e l evat ions to r a i n f a l l and t i d e s at t h e Surf C i t y

The data i n t h i s f igure are f o r t h e f i r s t quarter of 1988. i n f i l t r a t i o n pond f i e l d aLte. elevation,

The data for w e l l S9 are t h e moving 25 hr average water table

I I I I

I 1

e 2.50 E I I

W

1 0

3.5

1.0

-500 0 -400 C I

200 2 ,300 5 c

100 73

z 2 n 3 3 v

z! c7 m m I- m <

0 Z

- 3

-0.5 T I I I I I 2

190 - 130 150 170 90 110

TIME (days)

Figure 7 . Response of t h e water t a b l e and pond surface e l e v a t i o n s to r a i n f a l l and t i d e s a t

he Surf City

i n f i l t r a t i o n pond f i e l d site. The data for w e l l S9 are t h e moving 25 hr average water t a b l e e l e v a t i o n . The data i n t h i s figure are for t h e second quarter of 1988.

500 400 5 300 5

.,.I. .__ " ._..._. ...._. ..".. ..- ...... ..... ........................ ..... "-........-.....'.... a-- .-... ..... ...... "...-W..*..--...- I "--

/-c 2.50 E v

5 0.0 3 - - 0 z

-0.5

z I- o 2.00 2 d 1.5(

I 0 I I

h 11

n I \ I

s11 - s12 -

=!

m

.... -0.5 I I 1 I I

22

3 3

z A

U

I I . . - I

I -In

I I

1 80 200 1

37n 260 280 - L4U (La"

TIME (days)

Figure 8. Response of t h e water t a b l e and pond surface e l evat ions to r a i n f a l l and t i d e s at the Surf City i n f i l t r a t i o n pond f i e l d site. The data f o r w e l l S9 are t h e moving 25 hr average water t a b l e e l e v a t i o n . The data i n t h i s f igure are f o r t h e th ird quarter of 1988.

A 2.50 E z 0 2.00 I-

U

2

I

I I I I

52 --- -- s5 - sg .......

s11 -

I

0

0.5

0.0

-500 0 C

,400 3 c 300 6 200 2 100 ~

m

2, Z n 3 3 W

-4 CJ m m r m e

0 z

-

r; -0.5 T I I 1 I I

310 330 350 270 290

TIME (days)

Figure 9. Response of t h e water t a b l e and pond surface e l e v a t i o n s t o r a i n f a l l and t i d e s at t h e Surf C i t y

The data i n t h i s f i g u r e are for t h e fourth quarter of 1988. i n f i l t r a t i o n pond f i e l d site. e l evat ion .

The data for w e l l S9 are t h e moving 25 hr average water t a b l e

c cn

--400 5Z c

2.50 E

0 2.00

W

z I-

2 d 1.50

m 5 1.oc a w

I- d: 3 0.5c

0 I 1 I I

#

m -- 100 ~

0 2 Z n 3 3 W

zl! 1 I I I -0.5

m r- m <

0 z

0.0 3 -

I I I ! -0.5 I

100 - 40 60 80 0 20

TIME (doys)

Figure 10. Reeponee of t h e water t a b l e and pond eurface e l evat ions t o r a i n f a l l and t i d e s a t the Surf City

The data i n t h i s f igure are for the f i r s t quarter of 1989. i n f i l t r a t i o n pond f i e l d e i t e . e l evat ion .

The data for w e l l S9 are the moving 25 hr average water t a b l e

c. U

I f

n 2-50 E

I 1 I I

U

I 1 s2 --- s5 - sg .......

-500 0 c -400 I

c-

-300 -200 2 -100

L n 3 3 v

m I- m

0.0 2! 0 Z

c 1 I 1 I I -0.5 7 90 110 130 150 170 190 -

TIME (days)

Figure 11. Response of t h e water t a b l e and pond surface e l evat ions t o r a i n f a l l and t i d e s a t t h e Surf C i t y in f i l t ra t ion pond f i e l d site. The data for w e l l S9 are t h e moving 25 hr average water t a b l e e l e v a t i o n . The data i n t h i s f i g u r e are for t h e second quarter of 1989.

n E L/

z 0 I- 6

J W W J

6 I- 111 W I-

c

z

m

s

TIME FOR 3/9/88 EVENT (days) 67.5 70.0 72.5 75.0 77.5 80.0

I " ' "

I

3 0 m m I- m <

0 Z n

3

3 I

0.50 - . . . . '

c

65.0

TIME FOR 3/8/89 EVENT (days)

F i g u r e 12. Response o f pond water surface e l e v a t i o n t o water t ab le nea r t h e pond and t o tides. Th i s f i g u r e compares pond drawdown d u r i n g moderate t i d e s t o drawdown dur ing h igh t ides . The r a i n f a l l even t0 preceding pond drawdown w e r e s i m i l a r (30 mm f o r 3/9/88 and 25 f o r 3/8/89).

i n f l u e n c e d by t i d a l f l u c t u a t i o n s and w e r e t h e o n l y cont inuous ly monitored wa te r table e l e v a t i o n s a t Surf C i t y t h a t showed t h e semidiurna l r e sponse of t h e t i d e s . The r e sponse of t h e water table t o r a i n f a l l w a s less t h a n observed

he o t h e r w e l l s . a t i o n s , water table e l e v a t i o n s a t S9

During periods of h i and Inoderate tide During p e r i o d s of low r a i n f a l l and h igh t i d e e e l e v a t i o n s , lower than water at table and

e l e v a t i o n s a t S9 w e r e h i g h e r t h a n at 52 and S11.

The performance of t h e pond a t Surf C i t y w a s n o t s i g n i f i c a n t l y a f f e c t e d by t i d e e l e v a t i o n s d u r i n g most even t s ; however, a period of h igh t i d e i n March 1989 s i g n i f i c a n t l y de l ayed pond drawdown. F igu re 32 compares t h e wa te r table and t i d e e l e v a t i o n s f o r an even t du r ing t h i s period t o t h o s e o f a similar

18

TIME FOR 1 7 /O 1 /88 EVENT (days)

304 306 308 310 - 2.00 E v

z O 1.75 i=

2

I

- BEFORE

TIME FOR 6/75/89 EVENT (doys)

F i g u r e 13. Response of pond drawdown b e f o r e and a f t e r removal o f t h e sediment l a y e r on t h e pond bottom a t Surf Ci ty . The r a i n f a l l e v e n t s preceding pond drawdown w e r e similar ( 2 7 mm f o r 11/1/88 and 31 mm for 6/15/89).

e v e n t d u r i n g moderate t i d e s . pond w i t h i n 3 . 5 days when t h e t i d e e l e v a t i o n s w e r e moderate. The r u n o f f from t h e 2 5 mm r a i n f a l l r e q u i r e d o v e r 7 days t o comple te ly seep from t h e pond when averaged t i d e e l e v a t i o n s were 2 5 c m above KSL. t h e pond d u r i n g t h e period o f h i g h t i d e w a s h i g h e r t h a n d u r i n g t h e moderate t i d e . t h e pond s u r f a c e e l e v a t i o n and t h e w a t e r table t h e r e b y reducing t h e seepage r a t e from t h e pond.

Pond drawdown r a t e s w e r e n o t s i g n i f i c a n t l y a f f e c t e d by t h e removal of t h e sediment layer from t h e bottom o f t h e pond o n 12/7/88. quarterly plots before and after l a y e r removal, t h e o v e r a l l perf pond was n o t changed b y t h e l a y e ean (0.0077 m / h pond drawdown rates af ter t h e l a m/hr) before l a y e r removal, b u t t h i s d i f f e r e n c e was n o t s i g n i f i c a n t due t o v a r i a t i o n s i n t h e s e rates. An example comparing before and after t h e sediment l a y e r removal i s s h drawdown rates w e r e v e r y s

r o f i l e s a l o n g

Runoff from t h e 30 mm r a i n f a l l seeped f r o m t h e

The w a t e r table e l e v a t i o n near

The h i g h w a t e r table n e a r t h e pond reduced t h e head d i f f e r e n c e between

udging from t h e

ower t h a n t h e mean (0.0097

d l e n g t h and Lsland wid th a t S shown i n Fig. 14 for v a r i o u s h y d r o l o g i c a l s i t u a t i o n s . between t h e m o n i t o r i n g w e l l 8 w a s ob6erved d u r i n g d r y o d s (32/8/88). a r a i n f a l l e v e n t , a groundwater mound formed around t h e pond i runoff c o l l e c t i n g i n t h e pond. For t h e first 2 t o 4 days a f t e steeper g r a d i e n t w a s toward t h e area under impervious s u r f a c e s ( 5 / 2 6 / 8 8 and

ry l i t t l e g r a d i

19

DISTANCE ALONG IStAND WIDTH (m) -120 -60 0 60 120 180 240

1.500

1.250

1.000

0.750

0.500 S l l 54 S5 S6 57 sa

0 250

0 000

1.250

1 .WD

0.750

o m

0.250

0 WO

*~o-o-o-o-

0 - 0 8/31/88 (244) A - A 4/15/88 (106)

V - V 8/04/68 (217) 0 - 0 12/6/68 (343)

*-e MEAN N-35

n - D 5/26/86 (147)

0-0-

s5 s3 52 s1

-120 -60 0 60 120 180 240

DISTANCE XONG ISLAND LENGTH (m)

Figure 14. Water table p r o f i l e s a long i s l a n d l e n g t h and i s l a n d wid th a t t h e Sur f C i t y f i e l d site. hydro log ic cond i t ions . r e f e r t o F igures 6 - 11 t o de termine hydro log ic c o n d i t i o n .

P r o f i l e s w e r e measured for a v a r i e t y o f U s e day of y e a r v a l u e s i n p a r e n t h e s i s and

8/31/88). T h i s st impervious s u r f a c e s would not have been recharged by t h e i n f i l t r a t i n g

r g r a d i e n t i s l o g i c a l s i n c e t h e wa te r table under t h e

t h e ground wat mound decayed and t h e water t ab le under t h e ed, t h e g r a d i e n t toward t h e impervious surface

e q u i l i b r a t e d w i t h t h e g r a d i e n t toward t h e sound (8/4/88 and 4/15/88) .

Changes i n g r a d i e n t s nea r t h e i n f i l t r a t i o n pond a t Surf C i t y i n r e sponse t o a re shown in Table 5 . T h i s e v e n t occur red a f t e r t h e mon i to r ing

as moved t o S13. Grad ien t s i n a l l t h r e e d i r e c t i o n s i n c r e a s e d t e l y a f t e r t h e a sed to below p -event va lues . As d i s c u s s e d p r e v i o u s l y , t h e d t h e area under t h e impervious s u r f a c e s w e r e g r e a t e s t fo r t h e

e g r a d i e n t toward t h e sound w a s g r e a t e s t s i n c e

i n f a l l event . Over t h e nex t 5 days t h e

a8 t h e neares

Water t a b l e f l u c t u a t i o n s observed at Bald Head I s l a n d d i f f e r e d g r e a t l y from t h o s e obse rved a t Surf City. The water table e l e v a t i o n s i n a l l o f t h e

le w e r e s t r o n g l y i n f l u e n c e d by t i d a l f l u c t u a t i o n s on6 w e r e observed i n a l l of t h e con t inuous ly osc i l la t ions obscured t h e q u a r t e r l y p l o t s an

t o s i g n i f i c a n t l y e f f e c t t h e o v e r a l l performance o f t h e pond, t h e y

20

Table 5 . Gradients near the infiltration pond at Surf City in response to a 50 mm rainfall event occurring on 5/15/89 (see day 135 on Fig. 11). Rainfall during the event was distributed a5 follows: 39 mm @ day 135.2 and 11 mm @ day 135.9

Gradient (m/m) calculated from S5 to: ........................................ Day s2 513 s11

135.0 .0025 .0025 .0030 135.5 .0110 .0113 .0082 136.5 .0077 .0088 .0060 137.5 ,0044 .0057 .0040 138.5 .0028 .0039 .0028 139.5 .0017 e 0021 0020 140 5 .0003 .0003 .0009

were filtered using the 25 hour floating average. elevation data at station 33 comparing filtered data to unfiltered data is shown in Fig. 15. The filter effectively smoothed the semidiurnal tidal fluctuations while preserving the longer period tidal fluctuations that could affect pond performance. The filtered data did not reflect the transient response of the water table elevation to large rainfall events; therefore, some plo ts of unfiltered data are presented in addition to the quarterly plot to more accurately depict the short-term response of the water table

An example of water table

Figure 15. Response of the water table elevation under the pond to rainfall events at Bald Head Island. This figure compares the recorded hourly data to the 25 hour moving average data.

21

The w a t e r table e l e v a t i o n s n e a r t h e pond are shown by w e l l s B2 and B6 (F igs . 16 - 21). F l u c t u a t i o n s o f t h e w a t e r table a t b o t h w e l l s are v e r y s imilar , w i t h e l e v a t i o n d i f f e r e n c e s between t h e t w o w e l l s less t h a n 0.03 m. Water table f l u c t u a t i o n s a t w e l l s B2 and B6 w e r e more complex t h a n t h o s e n e a r t h e pond a t t h e Surf C i t y s i te s i n c e t h e y w e r e s i g n i f i c a n t l y a f f e c t e d by t i d e s i n a d d i t i o n t o r a i n f a l l . Water table f l u c t u a t i o n s i n t h e f o u r t h q u a r t e r of 1988 when v e r y l i t t l e r a i n f e l l d e p i c t t h e i n f l u e n c e o f t h e t i d e s . q u a r t e r , w a t e r t ab le e l e v a t i o n f l u c t u a t i o n s w e r e v e r y s i m i l a r t o t i d a l f l u c t u a t i o n s (F ig . 1 9 ) . The range o f water t a b l e e l e v a t i o n s n e a r t h e pond a t Bald Head I s l a n d (0.15 t o 0.80 m above HSL) w a s lower t h a n t h a t a t Surf C i t y (0.65 t o 1.47 m ) . Unl ike a t S u r f C i t y , t h e water t a b l e e l e v a t i o n s n e a r t h e pond never exceeded t h e e l e v a t i o n of t h e pond bottom, always remaining a t l e a s t .70 m below pond bottom.

During t h i s

The w e l l a t s t a t i o n B3 w a s l o c a t e d i n t h e pond and measured t h e h y d r a u l i c head e l e v a t i o n 1.5 m below t h e pond s u r f a c e . Hydraul ic heads a t B3 were u s u a l l y w i t h i n 0.03 t o 0.04 m of t h o s e measured a t B2 and a t B6 e x c e p t a f t e r r a i n f a l l e v e n t s . Heads rose s h a r p l y i n r e s p o n s e t o r a i n f a l l t h e n r a p i d l y f e l l t o w i t h i n 0.04 m o f B2 and B6 heads i n less t h a n 36 h o u r s ( F i g s . 22 and 23)- Unl ike a t S u r f C i t y t h e h y d r a u l i c heads below t h e pond never exceeded t h e e l e v a t i o n o f t h e pond bottom. That is, t h e water table never rose t o t h e e l e v a t i o n of t h e pond bottom.

The w e l l a t s t a t i o n B9 (F ig . 2) was l o c a t e d on t h e edge of t h e marsh and recorded w a t e r table f l u c t u a t i o n s t h a t were g r e a t e r t h a n t h o s e e l sewhere o n t h e si te. Water table e l e v a t i o n s w e r e lower t h a n a t o t h e r w e l l s d u r i n g p e r i o d s of lower t i d e e l e v a t i o n s ; however d u r i n g h i g h e r h i g h t i d e s ( u s u a l l y d u r i n g s p r i n g t i d e s ) t h e marsh w a s f looded r e s u l t i n g i n h i g h e r water table e l e v a t i o n s t h a n a t o t h e r w e l l s (F ig . 22 and 23). A f t e r e a c h f l o o d i n g , t h e water table would r e t u r n r a p i d l y t o e l e v a t i o n s n e a r t h o s e a t o t h e r w e l l s . Water table e l e v a t i o n s a t B7 f e l l below e l e v a t i o n s e l s e w h e r e when p e r i o d s of marsh f l o o d i n g ended. table a t w e l l B6. n e a r l y equal t o or s l i g h t l y exceeded t h a t a t B3. When t h e marsh was n o t p e r i o d i c a l l y f looded , t h e water t ab le e l e v a t i o n a t B6 w a s 0.03 t o 0.04 m less t h a n a t B3.

The f l u c t u a t i o n s a t B7 had a s m a l l a f f e c t on t h e w a t e r During p e r i o d s of marsh f l o o d i n g , t h e water table a t B6 w a s

The s u r f a c e e l e v a t i o n o f t h e water i n t h e pond was monitored by w e l l B 9 . Water surface e l e v a t i o n s ranged from 1.57 m (pond bottom) t o 1.80 w, and pond drawdown averaged 0.88 m/day. The maximum d e p t h r e c o r d e d i n t h e Bald Head I s l a n d pond was a b o u t one-s ix th t h a t a t Surf C i t y (0,23 m compared t o 1 . 2 7 in) and t h e average pond drawdown ra te a t Bald Head I s l a n d w a s 4 t i m e s greater t h a n a t S u r f C i t y (0.88 mjday compared t o 0.21 m/day). Consequently, w a t e r s t o o d i n t h e pond a t Bald Head I s l a n d for v e r y s h o r t p e r i o d s . The l o n g e s t period t h a t w a t e r s t o o d i n t h e pond was only 18 haure. rates v a r i e d l i t t l e d u r i n g pond drawdown. Drawdown rates d u r i n g t h e l a r g e e v e n t on 3/21/89 v a r i e d from 2.38 m/day a t t h e beginning o f drawdown t o 0 .77 m/day a t t h e end of drawdown. w e r e a t l e a s t 0.70 m below t h e pond bottom, t h e complex f l u c t u a t i o n e of t h e water table had l i t t l e effect on pond drawdown.

The pond drawdown

S i n c e t h e w a t e r table e l e v a t i o n s n e a r t h e pond

22

Iv w

3 -300 c

w I

1 z I- 0 1.50

2 w" 1.00

h L 1

82 .-__ 83 - 86 - 87 ....... 89 - 41 I

0.5

...... * b o . * .............................................................. " .................... ................................................................

TIME (days)

F i g u r e 16. Response of t h e water t a b l e and pond surface e l evat ions to r a i n f a l l and t i d e the Balcn Head

Is land i n f i l t r a t i o n pond f i e l d site. The data €or w e l l s B2, B3, B6, B7 are t h e moving 251 hr average water table e l evat ion . The data i n t h i s f igure are for the f irst quarter of 198

Po P

TIME (days)

Figure 17. Response of t h e w a t e r t a b l e and pond surface elevat ions t o r a i n f a l l and t i d e s a t t h e Bald Head Island i n f i l t r a t i o n pond f ie ld site. average water table elevation. The da ta i n t h i s f igure a re f o r t h e second quarter of 1988,

The da ta f o r w e l l s 82 , B3, B6, and B7 are t h e moving 25 hr

n 2.00 € v

1 I I

280 220 240 260

Z 2 1.50 c

2 e: 1.00

-0.5

W J

Q m

0.50 8 9 0.00 I- Q

J' I 1 I I

l1.I 1 1 1 11 I

82 --- 83 - 86 - 87 .._....

I I I I

- 400 ' 300

200

100

0

0.5

0.0

n 3 3 U

=! U m m r- m s =! 0 z

Figure 18. Response of t h e water t a b l e and pond surface e l evat ion8 to r a i n f a l l and t i d e 8 a t Is land i n f i l t r a t i o n pond f i e l d site. average water t a b l e e l evat ion .

The data for w e l l s B2, 83, 86, and B7 are t h e moving 25 hr The data in t h i s f igure are for t h e t h i r d quarter of 1988.

N 0-l

I I I I I

- 2.00 I I I I I I

370 w

U € 1

'4 3 0.00

s I

I I I I

86 - 87 ....... 89 -

9 w 1.00

m

4i

W A

4

e 0.50

00

'5

j0

!5

3

0.5

c!

- -0.5

TIME (days)

Figure 19. Reeponee of t h e water t a b l e and pond surface elevation6 t o r a i n f a l l and t i d e s a t t h e Bald Head Ieland i n f i l t r a t i o n pond f i e l d site. The data fo r w e l l s B2, B3, 86, and B7 are t h e moving 25 h r average w a t e r t a b l e elevation. The da ta i n t h i s f igure are f o r t h e fourth quarter of 1988,

I

n 2.00 - € z 0 1.50- I-

U

2 w” 1.00 -- w

I I

I I 82 .--_ a3 - 86 - 87 .......

I - 1 1 I

U 20 40 60 80

,400 2 3

300 c ).

< 200

100

0

0.5

0.0

-0.5 7 TIME (days)

Figure 20. ReSponSe of the water table and pond eurface elevation8 to rainfall and tides at the Bal Island infiltration pond field site. The data for wells B2, B3, B6, and B7 are the moving 25 hr average water table elevation. The data in this figure are for the first quarter of 1989.

100 1 J

- 2.00 E z - O 1 .SO --

i;j 1.00 -- 9

-. I I I I

W

- 92 .--- 83 - 86 - 97 B9 -

I-

2 .......

OD

cx 0.50

!!! a 2: 0.00 I 1 I I

..................................... ....... ......................................................................................................................................... w I

300

200

100

0

0.5

* 0.0

0 c K C

=! € m

5;

2J

Z 22

3 3 A

W

5 CJ m

<

0 Z

3

I 1 1 I ! -0.5 7 I

190 - 130 1 50 170 90 110

TIME (doys)

Figure 21. Response of t h e water t a b l e and pond surface e l evat ione to r a i n f a l l and t i d e s a t t h e Bald Head Island i n f i l t r a t i o n pond f i e l d site. average water t a b l e e l evat ion .

The data for welle B2, 83, B 6 , B7 are t h e moving 25 hr The data i n t h i s f igure are for the second quarter of 1989.

n 2.0C E

W

I 1 I

100 110 120

z 0 1.50 I-

2

-.I -

ii 1.00 W J m ' 0.50

Q 8 I-

0.00

!

rJ c I I

1 I

83 - 86 - 87 ......

y..-..-.-.-.- .... "..."._."."." ........ "..." ........... \...*.i

100 0 c

75

50

25

0

D.5

9.0

70 b Z -

-0.5 ??

Figure 22. Response of the water table and pond surface elevations to rainfall and tides at the Bald Head Island infiltration pond field site. All well data are hourly recorded data for the mont April, 1988.

w 0

2.00 c t U

z 1. hL h 8 0 1.50 -- B3 - 86 - 97 ....... B9 - Itl

f5 m 2 0.50

c s 0.00 I

I I

240 250

TIME (days)

160

120

80

40

0

0.5

0 C 3 C

n 3 3 W

=! U m

12 i l

0.0 ij - 0 Z

* -0.5 T d

260 - 230

Figure 23. Responae of the water table and pond aurface elevatione to rainfall and tides at the Bald Head Island infiltration pond field site. September, 16, 1988.

All w e l l data are hourly recorded data from August, 17 to

1 .w

- o . m - - E v J om-- m I w 0 . a

m 4 0.200 z 0

l3 -I w 0.800--

B

2 0.w

4: s p o*oo- -

3

m 0600.-

CK

0 200 -- 0 W - r

Figure 24. Water table profiles along island length and island width at the Bald Head Island field site. Profiles were measured for a variety of hydrologic conditions. Use day of year values in parenthesis and refer to Figures 16 - 2 1 to determine hydrologic condition.

Water table profiles along island length and island width at Bald Head Island are shown in Fig. 24 for various hydrological situations. The highest water table elevations occurred during a period of high tide and high rainfall (4 /14/89) . tide and low rainfall (2/15/89). The mean profile along the island width depict gradients from the pond toward the ocean and the marsh with the largest gradient toward the ocean. The mean profile along the island length depicts a gradient from the wider part of the island toward the end of the peninsula.

The lowest water table profile occurred during a period of low

CONCLUSIONS

Both of the infiltration ponds in the field studies effectively served their primary purpose of retaining on site the stormwater runoff from the first 38 mm of rainfall. runoff from either developed site flowed overland to the sounds, every case, the pond seepage rate was sufficient to completely drain the pond in 5 days. The single case during the 18 month study when drawdown was greater than 5 days occurred during a period of high tides. sufficient drawdown rates, water did stand in the pond for as much as 18 days due to successive rainfall events. environment, or pond performance were observed during these periods.

There was no evidence during the study that any stormwater In nearly

Even with

No adverse effects to property,

-55 0 55 70 105 I I I

e d " 0

A\.& / -- E===U------4-8

0- O------O

82 83 96 87 -- I I

0-0 4/14/88 (105) A - A 8/31/88 (244) Ill-0 5/11/89 (313)

V--0 3/16/89 ( 7 5 ) 0 - 0 2/t5/&9 ( 46 )

o - - - 3 - - - - 4 A - - - A I A

L A -- 0-* MEAN N-56

E1 BJ B4 85 0

-0 ---O-----.-~

I I +

31

The hydrology of t h e i n f i l t r a t i o n ponds a t t h e r e s e a r c h sites w a s v e r y d i f f e r e n t . The r u n o f f water s tood i n t h e pond a t Bald Head I s l a n d f o r much s h o r t e r p e r i o d s t h a n a t Surf City . rates, less impervious area i n t h e waterehed, and a more sha l low pond a t Bald Head I s l a n d . The h i g h e r drawdown rate a t Bald Head I s l a n d r e s u l t e d from t h e s h o r t e r d i s t a n c e between t h e pond and t h e r i v e r and t h e g r e a t e r e l e v a t i o n of t h e pond bottom above t h e water t a b l e and mean sea l e v e l .

The i n f i l t r a t i o n pond a t Bald Head Xsland was l o c a t e d on a p e n i n s u l a w i t h s h o r t e r i s l a n d wid th and a t h i r d s ink . Consequently, t h e r e sponse o f t h e wa te r t a b l e t o r a i n f a l l and d ra inage was more r a p i d t h a n a t Surf Ci ty . t h e water table a t Bald Head f e l l r a p i d l y a f t e r r a i n f a l l e v e n t s , it w a s less l i k e l y t o be h e l d a t a h ighe r e l e v a t i o n due t o s u c c e s s i v e r a i n f a l l even t s . Thus pond drawdown w a s ve ry r a p i d and una f fec t ed by t h e water table r i s i n g above t h e e l e v a t i o n of t h e pond bottom. Water never s t o o d i n t h e pond for more t h a n 18 consecu t ive hours. more slowly and was h e l d a t h ighe r e l e v a t i o n s du r ing s u c c e s s i v e e v e n t s , wa te r table r o s e above t h e e l e v a t i o n of pond bottom 21 times and slowed t h e pond drawdown r a t e . r e s u l t e d i n t h e wa te r s t and ing i n t h e pond a t S u r f C i t y for up t o 18 days due t o s u c c e s s i v e r a i n f a l l even t s .

Th i s was d u e t o g r e a t e r pond drawdown

S i n c e

A t t h e Surf C i t y site, t h e wa te r t a b l e f e l l The

The h igher wa te r table and t h e slower drawdown r a t e

The shor te r i s l a n d wid th and t h e t h i r d s i n k a t Bald Head I s l a n d caused t h e water t a b l e t o respond t o t i d a l f l u c t u a t i o n s more t h a n a t Surf C i t y . S ince t h e e l e v a t i o n o f t h e pond bottom was h igh enough t o p reven t t h e w a t e r t a b l e from r i s i n g i n t o t h e pond, f l u c t u a t i o n s of t h e wa te r t ab le due t o t h e t i d e s d i d n o t s i g n i f i c a n t l y a f f e c t t h e pond performance.

t h e wa te r t a b l e t o t h e t i d e s was n o t as g r e a t . t h e wa te r table w a s n e a r enough t o t h e pond bottom t h a t t h e pond perform- once a t Surf C i t y w a s a f f e c t e d by t h e t ides on a t l e a s t one occas ion . Had t h e e l e v a t i o n o f t h e pond bottom a t Bald Head I s l a n d been 0,70 m lower, t i d a l f l u c t u a t i o n s might have a f f e c t e d pond performance.

The r e s u l t s from t h e f i e l d sites demonstrated t h e importance of si te pa rame te r s and pond d e s i g n v a r i a b l e s on t h e performance o f i n f i l t r a t i o n pond systems. The impor t an t s i t e parameters t h a t a f f e c t e d pond performance i n the

A t t h e Surf C i t y s i te t h e i s l a n d wid th was g r e a t e r t h a n a t t h e Bald Head site, t h e r e sponse c

Even w i t h t h i s lower response

were i s l a n d width and t h e presence of a t h i r d s ink . Pond improved w i t h s m a l l e r i s l a n d width and w i t h a t h i r d s i n k .

a n t pond d e s i g n v a r i a b l e s t h a t a f f e c t e d pond performance w e r e d i s t a n c e from t h e pond t o t h e s i n k , e l e v a t i o n of t h e pond bottom, and amount of impervious area i n t h e watershed. d i s t a n c e from t h e pond t o t h e s i n k , i nc reased pond bottom e l e v a t i o n , and dec impervious area.

Other site parameters t h a t could a f f e c t pond performance are i s l a n d l e n g t h a

Pond performance improved w i t h dec reased

u l i c c o n d u c t i v i t y . Other d e s i g n v a r i a b l e s t h a t cou ld a f f e c t pond e are pond volume and t h e ra t io of pond l e n g t h t o pond width.

can t d i f f e r e n c e s between t h e sites i n t h e s e parameters and variables bserved i n t h i s f i e ld s tudy . The i r e f f e c t s can be e v a l u a t e d u s i n g

32

MODELING TgtlEE-DIMESSIONA, SATURATED AND UNSATURATED F’LOW USING MULTICRIDS

Modeling combined saturated and unsaturated groundwater flow in three dimensions is appropriate for analyzing seepage from infiltration ponds; however, it is difficult due to the complexity of the mathematical formulation. The governing equation characterizing such flow is a non-linear, second order partial differential equation that, for most problems, can only be solved using numerical methods. A few three-dimensional numerical solutions have been developed for flow under partially saturated conditions (Freeze, 1971; Frind and Verge, 1978; Huyakorn et al., 1986). The application of these solutions to a wide range of flow problems tended to be limited by high computer (CPU) time requirements. In this chapter, a three-dimensional numerical solution for steady, combined saturated and unsaturated flow is presented. The Gauss-Seidel finite difference method with successive over- relaxation (GS-SORI was used to obtain numerical solutions. A variation of the full approximate storage (FAS) (Brandt, 1977) multigrid method (MG3D) was incorporated into numerical solution procedures in order to accelerate the rate of convergence. The multigrid method is a relatively new technique that is able to reduce the high computation costs associated with problems having a large number of unknowns. approaches a linear function of the number of unknowns (Brandt 1977), and the convergence rate can equal or exceed that obtainable with other iterative solution techniques (Stuber and Trottenberg, 1982). The solutions to three sample problems are obtained and used to compare the rates of convergence with and without multigrids. Results of this chapter are summarized in a paper by Fipps and Skaggs (1989)

With this method, the required computation time

GOVERNING EQUATIOSS AND SOLUTION METHOD

The Richards Equation. L. A. Richards (1931) derived an equation describing the flow of water in the unsaturated zone by combining the Darcy-Buckingham equation for unsaturated flow with the continuity equation. The equation has been expanded to include both flow in the saturated and unsaturated zones and may be written for three-dimensional flow in an isotropic, homogeneous, and slightly deformable soil as:

where C(h) = de/dh, soil water capacity; R(h) is the hydraulic conductivity, written as a function of the soil water pressure head, h; H = hiz, total hydraulic head; 8 is the volumetric water content; z is the vertical distance above the datum; and x and y represent the horizontal dimensions. Hysteresis and temperature gradients are neglected. For steady state conditions the left side of Eq. 2 is equal to zero, resulting in the elliptic equation:

33

Numerical Solution. Gauss-Seidel finite difference method (Smith, slow to converge, requires minimum computer core storage and is very stable. With a node-centered scheme and variable node spacings in x , y and z, the finite difference approximation to Eq. 3 may be written for an interior node (i,j,k) located at the coordinates x i ' yjf zk as:

Numerical solutions to Eq. 3. were obtained using the 1978). This method, although

A H?+l,j ,k + B H F l , j , k + c H!,j+t,k D H T ] - l , k E H?,j,k+l

C e -

where Axi, byj, and Azk are the average grid spacings in the x t y and z directions at node (i, j ,k); A X ~ + ~ = ( X ~ + , - X ~ ) , Ayj+l=(yj+l-yj) , the iteration level; and n++ is the half-step solution.

and 80 forth; n is

34

- The function R(h) defines both the saturated and unsaturated hydraulic conductivity in the space between adjoining nodes and was determined here by the harmonic mean (Wuntoon, 1974). The conductivity between node (i,j,k) and node (i+l,j,k), for instance, may be written

The new solution (SOR), expressed

is improved by iteration with successive over-relaxation as :

where o is the acceleration factor, usually defined experimentally for non- linear equations by varying its value and comparing the rate of convergence. For the present solution the optimum value for o was 1.7. A computer program, GS-SORI was written in Fortran 77 to solve E q s . 4-6.

THE MULTIGRID KETHOD

The multigrid method is based on the idea that convergence of systems with a large number of unknowns can be significantly accelerated by combining error smoothing by relaxation with a method of calculating corrections on coarser grids and recursive application. Brandt (1977) first introduced the mathematical framework for the multigrid method. Since then, the method has gained attention from researchers in many fields (see Hackbusch and Trottenberg, 1982). The following discussion on the multigrid method is based on the presentations by Walsh (1987), Brandt (1977, 1982), and McKeon and Chu (1987). Hackbusch (1982) and Hackbusch and Trottenberg (1982) provide further details on the method and mathematical proofs on convergence of linear multigrid systems.

The multigrid idea is based on an analysis of the error in iterative solutions by Fourier series. Two types of errors are identified: local errors which

rder of the grid size3 and han the grid size. Standard

are effective in smoothing the local or high frequency quency errors can be quickly smoo

s of decreasing node density, with the ef

n be most easily

e grid by 9-1. near system of equat

Given a

L u = F (7)

where L is a linear operator, u ie the solution variable, and F is the inhomogeneous term on the right-hand side of the differential equation, the discrete approximation to Eq. 7 on the finer grid, Gg can be written

35

BEFORE RELAXATION

GLOBAL ERRORS LOCAL ERRORS

AFTER RALAXATION

SLIGHT REDUCTION SIGNIRCANT REDUCTION

1N AMPLITUDE it4 AMPLITUDE

F i g u r e 25, E r r o r r e d u c t i o n by r e l a x a t i o n f o r local and global e r r o r s ( t a k e n from HcKeon and Chu, 1987)-

Lg ug = Fg

A f t e r a f e w s t e p s o f t h e smoothing p r o c e s s a n approxhnate s o l u t i o n u*@ is ob ta ined . The d e f e c t or r e s i d u a l , r, is a measure o f how w e l l t h e c u r r e n t approximat ion of t h e s o l u t i o n s a t i s f i e e t h e d i f f e r e n t i a l e q u a t i o n , and may be c a l c u l a t e d on t h e f i n e g r id u s i n g

The r e s i d u a l is t r a n s f e r r e d t o t h e c o a r s e g r i d , Gg", by a r e s t r i c t ion operator Rgi', t h e r e b y d e f i n i n g a mesh-funct ion a t t h e p o i n t s o t r a n s f e r s t r a t e g i e s are commonly used. c o a r s e gr id be a s u b s e t of tho f i n e grid. The f i n e - g r i d v a l u e is t h e n s lmpfy a s s i g n e d t o t h e co r re spond ing node on t h e coarse g r i d . referred t o as i n j e c t i o n . The o t h e r s t r a t e g y u s e s a smoothing o o p e r a t o r , and is r e q u i r e d when t h e coarse g r i d p o i n t s do n o t cor f i n e g r id p o i n t s . we igh t ing f u n c t i o n even when t h e i n j e c t i o n s t r a t e g y is Chu, 11987).

On t h e c o a r s e g r i d , r e l a x a t i o n sweeps are used t o reduce t h errors and to d e f i n e a c o r r e c t i o n t o t h e f i n e g r i d s o l u t i o n u'g. The equation on G9-l which d e f i n e s t h e c o r r e c t i o n , vgP1, s a t i s f i e s

The easiest i s t o l e t nodes on t h e

T h i s s t r a t e g y is

I n some problems convergence is enhanced by u s i n g a

36

The correction is then transferred from the coarse grid to the fine grid using a prolongation or interpolation operator, Ig?, The solution on the fine grid Gg is then corrected using

(11)

Erandt (1977), Walsh (1987), and Stuber and Trottenberg (1982) discuss practical multigrid algorithms for solving E q s . 8-11 and methods of defining the interpolation and restriction operators.

Non-linear Two-level Description. For non-linear systems, although convergence cannot be established mathematically, the multigrid method has been applied effectively for elliptic problems (see Hackbusch and Trottenberg, 1982). approximate storage) method presented by Brandt (1977). Instead of 'storing' a correction vg (designed to correct the fine-level approximation u'g) , the f u l l current approximation ug is retained or stored for use in the next stage of the procedure. Substituting the correction and the residual into the non- linear form of Eq. 8 yields

L~(uS + vg) - LB ug = rg

Most non-linear multigrid algorithms are based on the FAS {full

- ( 1 2 1

- where is now a non-linear operator. With L substituted €or L, Eq. 12 is in the same form as Eq. 8 , except that it is rewritten to explicitly incorporate the correction and residual terms.

When represented on the coarse grid level Gg'l, Eq. 12 may be written

9- 1 9-1 - g-1 i;g-'(Rg ug + vg-') - Lg-l(Rg us) = Rg rg (13)

The notation can be simplified by defining two additional variables

g-l u9 +. v9'1 R9

u9-1 p

Then Eq. 13 may be written

Equation 16 is in the same form as Eq. 8 and standard iterative methods can be used to solve it. correction is defined by

Once the approximate solution to Eq. 16 is obtained, the

and added to the fine grid solution to obtain the next approximation

37

Brandt (1977) presented algorithms for solving E q s . 12-18. These algorithms contain controls which allow for the automatic switching between grid levels. If the convergence rate is slow, the solution is transferred to the next coarser grid; if the convergence criteria are met, the solution is interpolated to the next finer grid. Brandt (1982) discusses the defining of parameters that can be used to control the switching between the grid levels.

McKeon and Chu (1987) had good success in adapting the FAS algorithm for a two-dimensional solution to the pressure head form of the Richards equation for steady unsaturated flow. However, the FAS algorithm is a very general formulation €or the solution of differential equations. with smoothing and transfer strategies is still required to obtain good convergence rates (Walsh, 1987). Brandt (1982) discusses some of the practical aspects of optimizing non-linear multigrid solutions.

Much experimentation

MG3D SIMULATION MODEL

A numerical simulation model, WG3D, was developed using a variation of the multigrid FAS method outlined above. Taking advantage of the fact that the total hydraulic head varies little from point to point in many solution

jection of the solution variable on the coarser grids without a operator, R, and linear interpolation of the correction to the

finer grids were used. To simplify programming, the multigrid method was implemented using a single 'V' cycle (one cycle of fine to coarse to fine grid transfers) (Walsh, 1987). In addition, the residuals were not explicitly transferred to the coarser grids but were included in the value of the solution variable injected to the coarser grids,

The steps used in HG3D can be summarized as follows. on the fine grid is improved by a fixed number of relaxation sweeps (usually five). Standard coarsening is used, where the number of nodes is reduced by half, alternately in x and z, and then in y. remain a subset of the finest grid. A fixed number of relaxation sweeps is used on each succeeding grid. At the coarsest grid level, relaxation sweeps are carried out until the solution is within the convergence criteria. correction is then transferred to the next finer grid using linear interpolation. On each succeeding finer grid, relaxation sweeps are performed until the convergence criteria are met,

We had the best results using an absolute convergence error defined as the largest change in the prediction of hydraulic head at any node between successive iterations. Generally, increasing the number of nodes on the finest grid required smaller convergence criteria. for the solutions presented here were in the range of 0 .5 mm to 0.1 mm.

The MG3D computer code is given by Fipps (1988) and is composed of the following six separate algorithms:

First, the initial guess

The solution is then transferred to the next coarser grid.

In each case, the node points on the coarser grids

The

The convergence criteria

1, SETUP: reads in finest grid, sets boundary conditions, and defines the initial guess;

38

2 .

3.

4.

5.

6 .

REDXZ: forms next coarser grid by reducing the number of node points in x and z by a factor of two, transfers finer grid solution by injection;

REEX: performs either a fixed number of relaxation sweeps or continues until convergence criterion are met;

REDY: forms the next coarser grid by reducing the number of nodes in y by a factor of two;

ZNTERPXZ: transfers the correction from the coarser to the next finer grid using linear interpolation in x and z; and

INTERPY: transfers the correction from the coarser to finer grid using linear interpolation in y.

Special attention is required in the design of the grids with variable node spacing to ensure that appropriate spacings will be maintained near the specified head boundaries in the coarser grids. Although variable node spacing complicates the programming, we found that it enhanced convergence and significantly reduced the required mesh density at the finest grid level.

SAMPLE SOLUTSONS

The reduction in CPU t h e with the multigrid method is illustrated here using solutions to three problems: steady flow between two ditches; seepage from a pond in two dimensions; and seepage from a pond in three dimensions. Brooks and Corey (1964) equations were used to define the conductivity as a function of soil water pressure head (h) in Eq. 2 ; expressed as

The

where K, is the saturated conductivity, hb is the bubbling pressure head, and fl is a soil dependent parameter. The parameters used in E q s . 19 were determined from the Soil water characteristic obtained by Skaggs and Wardak (1981) for a coastal sandy loam: K, = 0.25 m/h, hb = 0.043 m and q = 3.146.

Problem A: Flow Between Two Ditches. Figure 26 illustrates the flow regime used to represent two-dimensional flow between two parallel ditches. Two- dimensional flow was simulated with the three-dimensional numerical solutions by using a unit width of 1 m in the y-direction. face can be neglected, the boundary conditions for this problem may be written :

Assuming that the seepage

x = 0, ( z ( 2 m

aH/ax = 0 x = 0, O S Y L l m 2 < z 5 3 m

H = 2 . 6 m x = 30 m, y m 8 0 5 z 5 2 . 6 m

a H / a x = 0 x = 30 m, O S Y i S 1 m r 2 .6 < z 3 m

39

I. 30 m c

water table

Z

------T

3 m 2.6 m I

F i g u r e 2 6 . Schemat ic of t h e f l o w regime used f o r f low between t w o d i t c h e s (Problem A ) .

Three g r i d l e v e l s w e r e used (Fig. 271, w i t h t h e f i n e s t g r i d c o n t a i n i n g 31 node6 i n x, 2 nodes i n y, and 19 nodes i n z; r e p r e s e n t i n g t h e 30 m by 1 m by 3 m flow regime.

The r e s u l t i n g s t e a d y water table e l e v a t i o n s are l i s t e d i n Table 6 a long w i t h a n a n a l y t i c s o l u t i o n (Matino and Zuth in , 1982) for t h e same problem. As expec ted , b o t h numer i ca l s o l u t i o n s : HG3D (wi th m u l t i g r i d s ) and GS-SOX ( w i t h o u t m u l t i g r i d s ) , p r e d i c t e d n e a r l y t h e same w a t e r table e l e v a t i o n s , and t h e s e e l e v a t i o n s are i n agreement w i t h %he a n a l y t i c s o l u t i s n ,

Problems 8 and C : Pond Seepaae, Figure 28 (Sec t ion V i e w ) i l l u s t r a t e s t h e f l o w reg ime used t o s i m u l a t e pond seepage i n t w o dimensions, w i d e and 1 m deep, located 82 m from a d i t c h w i t h a water l e v e l of 7 m above t h e imperv ious barrier, and 4 1 m from a d i t c h wi th a water l e v e l of 7 . 9 m above t h e barrier, The w a t e r depth i n t h e 1 m deep pond is 0.9 m, or 7 . 9 m above t h e barrier, As before, twn-dimensional f low a n a l y s i s is s i m u l a t e d w i t h t h e th ree -d imens iona l numerical s o l u t i o n s by s p e c i f y i n g a u n i t w id th of y = 1 m, Three grid l e v e l s w e r e used. The f i n e s t g r i d con ta ined 7 9 nodes in x f 2 nodes i n y, and 17 nodes i n z; r e p r e s e n t i n g t h e 133 m by 1 m by 8 m f low regime.

Shown is a pond 10 m

4 0

GRID LEVEL G-2

Figure 27. Grid l e v e l s used i n t h e mul t igr id s o l u t i o n for Problem A. f i n e s t g r i d conta ins 1378 nodes represent ing t h e 30 m by 1 m by 3 m f l o w regime.

the

4 1

Table 6. Water table elevations for Problem *A8 predicted by the Gauss- Seidel SOR solution (GS-SOR), the multigrid solution (MG3D), and an analytic solution (Marino and Luthin, 1982).

x (m) WATER TABLE ELEVATION (m) --------------------____c_________

analytic MG3D GS-SOR

0 2.00 2.00 2.00 2 2.05 2.05 2.05 4 2.09 2.09 2.09 6 2.13 2.13 2.14 8 2.18 2.18 2.18

12 2.26 2.26 2.26 14 2.30 2.30 2.30

16 2.34 2.34 2.34 18 2.38 2.38 2.38 20 2.42 2.42 2.41 22 2.45 2.45 2.45 24 2.49 2.49 2.49 26 2.53 2.53 2.53 28 2.56 2.56 2.56 30 2.60 2.60 2.60

10 2.22 2.22 2.22

For the three-dimensional analysis, the flow regime is expanded to include the y-dimension as illustrated in Fig. 28 (Top View). length of the pond (Lp) and the length (L) from the pond to the no-flow boundary at y = 0. The boundary conditione for this problem may be written

Shown are two lengths: the

H 7 . 9 82 5 x 5. 92 m i E 5 Y I L’Lp 2’7”

H = 7 . 9 m x = 133 m, 0 5 Y s L+Lp, Q z z s S m

aH/ay = 0 0 x 5 133 m, y = O , y=L+Lp, O ( z 5 8 m

aH/az = 0 0 5 x 5 133 m, 0 s y I L+Lp, z = O , 2 = 8 m

where for the two-dimensional flow analysis: L = Q and Lp = 1 m; €or the three-dimensional flow analysis: L 5: 35 m and Lp = 5 m. dimensional solution, nine lines of nodes were added to the finite difference grid in the y-direction to represent the 40 m profile length (L$L). Five grid levels were used, with the grids alternately coarsened in x and z, and then in Y*

In the three-

42

A pond

TOP VIEW

H

7%

.PI

E - 760

m .- 0" 2 iii 7.45

t

c

a

723 - 5

7.K. 70

Y X no-flow boundary

Figure 29. Water table elevations for pond seepage (Problem C).

43

..I - - SECTION VIEW . 10.9 m

1, t 'Tf 7.9 m 8 m

7 m 2 I

t X I impervious I 1

79 -t

7.8 -

7.7 - E . 5 7.6 - F . UJ 7.5 - J w . w

7.4 -

v

5

3 E 7.3 - G ' 92-

7.1 -

2 - D

l- y - 0

DISTANCE IN X (m)

F i g u r e 30. Water table e l e v a t i o n s f o r t h e two-dimensional f low c a s e 3-1) f l o w case (Problem C ) along = 0, 10, 19, and 40 m e

d 30- F i g u r e 29 shows t h e s teady t h r e table e l e v a t i o n s . I n F ig . 30, t h e w a t e r table e l e v a t i o n two-dimensional f low c a s e are com t o those of t h e t h r e e re shown f o r t h e th ree -d imens iona l solu 0 m. The t h r e e -

s o l u t i o n e due t o f l o w i n t h e y-di

Table 9 l is ts t h e CPU time for t h e

two-dimensional

e q u i r e d by t h e t h o u t m u l t i g r i d s ) .

e between 71% and 82%.

44

Table 7. CPU time required to obtained solutions for three problems using the Gauss-Seidel SOR (GS-SOR) method and the multi-grid method (MG3D) as run on a IBM 4381 computer.

Problem Number of Nodes

1178

2844

25590

6 . 5 1.1

57.0 14.3

Time Reduct ion

%

71

82

75

SUMMARY

A numerical solution to the Richards equation for combined saturated and unsaturated flow in three dimensions was obtained using the Gauss-Seidel finite difference method with successive over-relaxation (GS-SOR). To increase the rate of convergence, the numerical solution was modified for t h e multigrid method (MG3D). Details of the multigrid method were presented for a two-level description of linear and non-linear systems of equations. Solutions for three sample problems were obtained with the GS-SOR and MG3D algorithms. The multigrid solutions (HG3D) resulted in a reduction of total CPU time ranging from 71% to 82% over GS-SOR.

POND SEEPAGE IN TWO ANI) THREE DIMENSIONS

PROBLEM DEFINITION

In this chapter the three-dimensional solution method, MG3D was used to analyze pond seepage under geometries characteristic of the North Carolina barrier islands. Results presented in this chapter are summarized in a paper by Fipps and Skaggs (1990)

The North Carolina barrier islands differ from many sea isles in that a clay and silt restricting layer usually exists at a small depths (6 to 21 m) which produces a shallow unconfined fresh water formation that is separated from the deeper confined aquifers. The shallow unconfined sand aquifer is underlain by 'upper" and 'lower" confined limestone and sandstone aquifers of fresh to brackish water (Kimrey, 1961). On some islands an additional restricting layer is found at a depth corresponding to sea level, often as close as 2 m below the surface. barrier islands are formed over salt marshes (Hoyt, 1967) and effectively separate the unconfined sand aquifers from daily tidal fluctuations of the deeper confined aquifers, except in the area in the immediate vicinity of the ocean.

Due to the existence of the shallow restricting layers, the problem is simplified to that of freshwater flow only. However, this simplification is not strictly valid in the area immediately adjoining the ocean, particularly for deep depths to the restricting layers.

The boundary conditions were chosen to represent typical barrier island geometries and are based on the studies mentioned above and on the critical dimensions given in the North Carolina stormwater rules. Some parameters were held constant for all simulations in order to provide a basis for comparison. These are illustrated in Fig. 31 and include the pond dimensions (10 m long by 10 m wide by 1 m deep), the water level in the pond (0.6 m), and the distance from the bottom of the pond to the water level in the ocean and sound (1 m). Water flows from the pond to the sound and ocean, which are referred to as "6inks' in this study. The distances from the pond to the sinks, to the island midpoint, and to the underlying impervious layer were varied, as were the distances between ponds.

Such shallow restricting layers are common in areas where

The soil property data used in this study were obtained by Skaggs and Wardak (1981) €or a previous study on Bogue Banks, N.C., with K, = 0.192 m/h, hb = 0.043 m and r ] = 3.15.

PONDS AT THE ISLAND MIDPOINT

The first case analyzed was f o r infiltration ponds located at the center of the island (Fig. 32). Assuming that the island midpoint correspnds to the groundwater flow divide, an axis of symmetry passes through the center of the pond; thus, only half of the pond (W,) is considered. Solutions were obtained for four widths: W i= 16, 42, 82, and 195 m; and for two depths: d = 2 and 8 m - For the three-dimensional flow analysis, t h e solution domain includes the distances in the y-direction illustrated in Fig. 32a. Two dimensions are

4 4

+J (d

(d a a

0 h n

I I I I I

W I 0 1

m I

0 1

S I : I

E l I

' I I I 1 I I I I 1 I I I I

4 m

W 0

a a r: 0 a

a 01 U (d d z 4 m

E rl P 0 Ll a CJ I m

47

- - A -1

----- axis of symetry - - I I

L 1 1 - - - - -

a H

P

G TOP View

B b. Elevation View

Schematic of t h e flow regbe for t h e c a s e of ponds l o c a t e d a t t h e i s l a n d midpoint. Axes of symmetry pass through t h e c e n t e r of t h e

Figure 32.

pond i n both t h e x- and y- d i r e c t i o n s . -

48

shown: the length of the no-flow boundary at y = 0. The no-flow boundary at y = 0 implies that identical ponds are spaced at distances of 2 L. be written

pond, Lp, and the length, L, from the pond to the

The boundary conditions may

H = Hp x = w, L 5 y 5 L+Lp, d < z 4 c+d (20f)

H = Hp W 5 x 5 W+Wp, L 5 y 5 L+Lp, z = d (2%)

where c = 1 m and Wp = L and at the sink, respectively, expressed in terms of total hydraulic head fm). For the case of d = 2 m: H = 2.6 m and m: Hp = 8 . 6 m and H, = 7 m.

Two-dimensional Analvsis. Results from a two-dimensional analysis are presented first in order to identify some important factors that affect pond seepage and to introduce an analytic expression for seepage from which a three-dimensional solution will be derived. The flow regime used for two- dimensional flow is illustrated in Fig. 32b. Such a regime would represent a continuous pond of width 2 Wp located along the longitudinal axis at the center of the island. Two-dimensional solutions were obtained with the three- dimensional numerical code by specifying a unit length in the y-direction and Lp = 1 m and L = 0. regime illustrated in Fig. 32b are listed in Table 8 . seepage from the front, back, and bottom of the pond, but not from the ends (in the y-direction) which is only considered in a three-dimensional analysis.

For saturated flow between a line source and sink, the Dupuit-Forchheber (DF) assumptions can be used to obtain an approximate solution (Marino and Luthin, 1982) :

= 5 m. Hp and H, are the water levels in the pond

H, = 1 m; and for the case of d = 8

f?

P

Predicted pond seepage rates for the half-pond and flow These rate8 include

where Q, is the flow rate per unit length (m3/m/h). While Eq. 21 neglects unsaturated flow and head losses due to vertical flow near the source and sink, it is sufficiently accurate and commonly used for many design applications.

49

Table 8, Two-dimensional flow rates obtained from the numerical solutions, MG3D, and Eq. 6 for the case of identical ponds located at the island midpoint (Fig. 32b).

FLOW RATE PER UNIT LENGTH (m3/m/h)

16 0.034 0.035

42 0,014 0.013

a2

195

0.007

0.003

0.007

0.003

MG3D EQ 21

0.100 0.150

0.054 0.057

0.028 0.029

0.012 0.012

Both the predicted two-dimensional flow rates calculated with Eq. 21 and obtained from the numerical solutions are listed in Table 8 for the two profile depths. For the deep profile (d = 8 m), both methods predicted nearly the same flow rates for W > 42 m. For W 5 42 m, the streamlines are less horizontal and convergence head losses due to vertical flow near the pond become more important due to the DF assumptions. introduced into the flow rates calculated with Eq. 21 for decreasing values ob W. For the shallow profile (d = 2 m), the seepage rates are nearly identical for all values of W, indicating that this convergence head losses can be neglected fo r shallow profiles,

Pond seepage €or the geometries and soil simulated here is dominated by flow in the saturated zone. This is indicated because Eq. 21, which does not consider unsaturated flow, predicted nearly the same flow rates as did the numerical solution for all values of W for the ease of d = 2 m and €car large W values for the case of d = 8 m (Table 8),

Thus, increasing error is

The effect of soil properties on the amount of flow occurring in the unsaturated zone can be demonstrated by varying the value of q in Eq. 19b. varied the valves for q from 0.5 to 6.3 while holding K, and hb constant. A lower q produces an unsaturated condu'ctivity function that decreases less rapidly with Soil water pressure head (h)# thereby increasing the amount of unsaturated flow; conversely, a larger q produces less unsaturated flow. The predicted 2-1) flow rates and the percentage of flow occurring in the unsaturated zone are given in Table 9 for the case of W = 82 m and d = 8 m. Note that only 2.3% of the flow occurs in the unsaturated zone for the soil considered in this study ( 0 = 3.2).

We

50

Table 9 . Two-dimensional flow rates for W = 82 m, d = 8 m, and various q values for the flow regime shown in Fig. 32b.

Total Seepage Flow in unsaturated rl "/" zone ( % of total)

0.5 0.O300 13.7 1.0 0.0291 10.1 1.6 0.0286 7.6 3.2 0.0278 2.3 6.3 0.0263 1.4

Three-dimensional Analysis. A three-dimensional analysis is needed to determine the effect on seepage rates of the spacing between ponds (2 L, Fig. 31). For this case, we held the length of the ponds constant at Lp = 5 m and used four profile lengths: L = 15 m, 35 m, 55 m, and 95 m (Fig. 32a) along with the widths and depths given above. Increasing L while keeping the other dimensions constant results in higher seepage rates and lower water table elevations in the profile.

Figure 33 shows the three-dimensional water table elevations for the case of W = 16 m, d = 8 m, and L = 5 m, 15 m, and 35 m. Figure 34 shows the corresponding water table contours. As L increases, the water table is lowered throughout the region, reaching its lowest level at L = 35 m for this value of W. For wider profile widths (W), larger pond spacings are required fo r the water table to reach its lowest level fo r each geometry considered. The results show that for large values of W and small L, flow is primarily two-dimensional in most of the domain. As expected, three-dimensional aspects become more important as L increases and W decreases.

The predicted pond seepage rates for each L and d considered are plotted as a function of W in Fig. 35. The three-dimensional seepage rates are given in terms of flow per unit pond length (Q/L ) with units of m3/m/h. A l s o shown in P Fig. 35 are the seepage rates obtained in the two-dimensional analysis. Generally, the seepage rates increase as the spacing between ponds (L) increases and the profife width (W) decreases. The rates are lower for the shallow profi -sectional area of flow and in the amount

APPROXIMATE SOL

The water table he total flow system can be divided into two component flow 8 illustrated in Fig. 36: radial flow near the pond and linear or one-dimensional flow away from the pond. Dividing the flow regime into component systems was also used by Dachler and Ernst (see Bouwer, 1969) in developing expressions for two-dimensional seepage from canals. For deep profiles (d > Wp), an additional vertical flow component exists due to flow out of the bottom of the pond as discussed below.

51

21.00

al

21.00

21 .oo

Figure 33. Water table e l e v a t i c ' r s ( m ) for W = 16 m, d = 8 m, and L = 5, 15, and 35 m for t h e prc:>:,lem shown i n Figure 32.

52

Y

0 . 0 0 . 0 0 8 . 1 8

X

Y

0.00 5 .25 10.50 15.75 21 -00

Y

30

20

10

X

0.00 - 5.25 10.50

X

15.75 21.00

Figure 34. Water t a b l e contours for t h e cases shown i n Figure 33 ( y - a x i s no t to scale). Contours range from 7 . 1 to 8.6 m ( t o t a l head).

53

0 IO?

8 0 8 -

c

f 006- m' E n J

0

- 0.04 -

002 *

SHALLOW PROFILE d =2m

1

0.25 I

0 20

c I 0.15 E m' E 4

n i

0.10

0.05

0.0

LE15 L - 5

* 2-D

DEEP PROFILE d=8m

I 160 200 00 I20 0 So

Figure 35. Pond seepage rates per unit pond length (Q/Lp) for d = 2 m (top), d = 8 m (bottom), and all values of W and L considered.

54

F i g u r e 36. D i v i s i o n of t h e s o l u t i o n domain i n t o t w o r eg ions : r a d i a l flow n e a r t h e pond and 1-D l a t e r a l flow away from t h e pond.

The e q u a t i o n for r a d i a l flow u s e d i n t h e r e g i o n n e a r t h e pond may be w r i t t e n

where HaVg = ( H p + H R ) / 2 , t h e average d e p t h of f l o w ; (Hp-HR) is t h e head drop i n t h e r a d i a l flow r eg ion ; r i s t h e r a d i u s of t h e pond, t a k e n as r = W = Lp; and R i s t h e h o r i z o n t a l e x t e n t of t h e r a d i a l flow region (F ig . 36) whicg can be e s t i m a t e d as

R = Lp + L / 2 (23)

For t h e r e g i o n of one-dimensional flow, Eq. 2 1 i s u s e d i n t h e form

K, fL+Lp)

2 we

Q = (HZ - H , z ) ( 2 4 )

where HR is t h e head a t t h e r a d i a l d i s t a n c e R or a t x = We; and We i s t h e e f f e c t i v e w i d t h of t h e l i n e a r flow r e g i o n ( F i g . 36), approximated as

We = W + Wp - R cos a

Equat ing Eqs. 2 2 and 24 and e l i m i n a t i n g HR, t h e a p p r o x h a t e s o l u t i o n for pond seepage can be w r i t t e n

t h e

55

where

L+Lp

Equation 26 is valid for We > 0.

In Table 10 the pond seepage rates calculated with Eq. 26 are listed along with the rates obtained from the numerical solution. Due to the interrelationship between Le and We, the maximum seepage rates calculated with Eq. 2 6 occur at values for L which are slightly larger than W.

Deep Profiles. assumed in Eq. 26 due to vertical flow of water out of the bottom of the pond. This increase in the length of the flow path, Wv, reduces the amount of seepage with the effect being particularly significant for deep profiles (d > Wp). pond (Wp and Lp) , and the horizontal lengths of the flow paths out of the pond (WR and L,, Fig. 36). following empirical equations:

The average length of the flow path is greater than that

The magnitude of Wv depends on the profile depth (d), the size of the

The length of the flow path may be approximated by the

where

where WR = W + W becomes

- We (Fig. 36). The approximate solution for pond seepage P

2 (We + Wv)

Eq. 31 is valid for positive values of We and Wv and predicts a maximum seepage rate at values of L which are slightly less than W.

In Table 10 the seepage rates calculated with Eq. 31 are listed along with those obtained from the numerical solutions for the deep profile (d Both methods predict nearly the same seepage rates for all values of W and L a

56

Table 10. Three-dimensional seepage rates obtained from the numerical solutions, MG3D (+ 5 % ) and as determined with Eqs. 26 and 31 for the problem shown in Fig. 32. (Rates represent 1 / 4 of the total pond seepage.)

POND SEEPAGE RATES (m3/h)

d = 2 m d = 8 m

MG3D EQ 26 MG3D EQ 31 ---------------- ----------------

W = 1 6 m Ir ( m l

5 0.31 0.30 0.97 0 . 9 8 1 5 0.47 0.46 1 .24 1 .24 35 0.51 - 1.24 -

0.51 - 1.24 - 55 0 .51 - 1.24 - 95

W = 4 2 m

5 0.12 0.12 0.47 0.48 1 5 0.23 0.22 0.77 0.76 35 0.34 0.32 0 .95 0.94 55 0.37 0.34 1 .05 -

0.37 - 1.06 - 95

W = 8 2 m

5 0.06 0.06 0.27 0.27 1 5 0.12 0.12 0.47 0.47 35 0.20 0.20 0.67 0.69 55 0.25 0.25 0.78 0.77 95 0.28 0.28 0.86 -

W I= 195 m

5 0.04 0.03 0.12 0.12 15 0.05 0.05 0.25 0.22 35 0 . 0 9 0.10 0.41 0 . 3 9 5 5 0.13 0.13 0 .50 0.49 9 5 0.17 0.17 0.60 0 . 5 9

SPECIAL CASES

Sinale Pond On Island. located at the center of a rectangular island. will provide the maximum seepage rates obtainable for the geometries considered here. The no-flow boundary located at y = 0 (GH, Fig. 32) was changed to a specified head boundary, expressed as

One special case considered is that of a single pond Analysis of this extreme case

57

H = H, 0 5 x 5 W+Wp, y = 0, 0 5 z 5 H, (32a)

aH/az = 0 0 5 x 5 W+Wp, y = 0, H, < z c+d (32b)

The other boundary conditions remain as given in E q s . 20 with H, = 7 m, c = 1 m, d = 8 m, W = 5 m, and L = 5 m. A single length of L = 95 m was

P P used along with the four widths: W = 16, 42, 82 and 195 m.

Seepage rates obtained from the numerical solution and calculated with the radial flow equation (Eq. 22) are listed in Table 11. These rates represent 1/4 of the total flow out of the pond. As expected, flow becomes nearly radial fo r larger widths (W). For the narrowest width (W = 16 m) there was no increase in seepage over the rates given in Table 11, as nearly all of the flow was towards boundary AG (Fig. 32). As W increases, more of the flow is toward boundary GH, Table 11, The largest increase in total seepage occurred for the case of W = 195 m.

Pond Located Near a Canal. or canals, the flow patterns will be different from the results presented above- To analyze such a situation, a set of solutions was obtained for the three-sink system illustrated in Fig. 37. A total island width of w = 174 m was considered with the four lengths: L = 15, 35, 5 5 , and 9 5 m. In addition to the two sinks at x = 0 and x = w, a third sink representing a canal extending to the impervious layer was assumed to be located at y = 0 and to extend to the center of the island (IJ, Fig. 37)- The boundary conditions for this case may be written

and the total seepage rates increase over those given in

In areas where ponds are located near tidal creeks

Table 11. Seepage rates for a single pond located at the center of the island obtained from the numerical solutions, MG3D, for L=95 m and d = 8 m and calculated with E q . 22. Rates represent 1 / 4 of the total pond seepage.

POXD SEEPAGE RATE (m3/h)

MG3D Eq. 22

w (m) d = 2 m

16 0.50 0.75 42 0.41 0.41 82 0.32 0.31 195 0.29 0.30

d - 8 m 16 1.24 3.24 42 1.24 1.77 82 1.15 1.35 195 1.14 1.28

58

A -

sink

I I I I I

E -

sink

I sink J no flow boundary K a TopViw

Figure 37. Schematic of the flow regime for a pond and a three-sink system. Sinks are located along boundaries AI, IJ, and KE.

5 9

aH/az = 0 O < X ( W , Q 5 y 5 L+Lp, z = c+d ( 3 3 i )

H = Hp x = W, x = W+WP, L 5 y 5 L+Lp, d < z 5 c+d ( 3 3 j 9

H = Hp W 5 x 5 w+2wp, L 5 y 5 L+Lp, a. = d 133k)

where H, = 7 m, W = 82 m, Lp = 5 m, W = 5 m, c = 1 m, and d = 8 m. P

The w a t e r t a b l e e l e v a t i o n s for L = 35 m are g i v e n i n F ig . 38, and t h e wa te r table c o n t o u r s f o r L = 15, 35, and 55 m are g i v e n in Fig . 39. As b e f o r e , t h e s p a c i n g between ponds a f f e c t s t h e wa te r table e l e v a t i o n s beyond t h e canal (JK, Fig . 38). t h e narrow spac ings , most of t h e flow occurs from t h e f r o n t ( 8 2 5 x 5 92 m and y = 5 m ) and l e f t s i d e ( a t x = 82 m and y 5 5 m ) o f t h e pond. d i s t a n c e from t h e pond t o t h e c a n a l i n c r e a s e s , t h e f low p a t t e r n s change as more flow o c c u r s from t h e left s i d e and lese f r o m t h e f r o n t o f t h e pond. s eepage rates for L = 95 m f a l l between t h e rates g i v e n i n Tab le s 10 and 11.

The pond seepage rates f o r each case are l i s t e d i n Table 12. For

As t h e

The

474,o

F i g u r e F i g u r e 38. Water t a l >le e l e v a t i o n s for t h e t h r e e - s i n k system shown i n 37 using W = 82 m, L = 35 m, and d = 8 m.

60

0 44 87 131

X

.. Y

0 87 131 174

X

Figure 39. Water table contours for the three-sink system shown in Figures 37 and 38 using W = 82 n and d = 8 n. Contours range from 7.1 to 8.6 n (total head).

61

Table 12. Seepage rates from the left, front, and right sides of a pond (Top

Rates represent 112 of total View, Fig. 37) located near a canal (along boundary IJ, Fig. 38) and W = 82 m, d = 8 m, and M, = 7 m. pond seepage.

POND SEEPAGE (m3/h)

Left Side Front Right Side Total

15 0 . 4 5 9.10 0.69 2.23 35 0.53 0.94 0.62 2.10 555 0.90 0.54 0.59 2.05 95 0.92 0.53 0.57 2.00

Ir (m)

S U ” R Y

A three-dimensional numerical simulation model for combined unsaturated and saturated groundwater flow (Fipps and Skaggs, 1989) was used to analyze pond seepage under geometries characteristic of the North Carolina barrier islands. Ponds of constant size (1 m deep x 10 m x 10 m) and spaced from 10 to 190 m apart were simulated using varying distances from the ponds to the sinks and to the restricting layer. For the geometries and soil properties considered, pond seepage was dominated by flow in the saturated zone. adjacent ponds affected seepage rates, having a greater effect for large island widths.

The spacing between

The numerical solutions were used to develop an approximate analytic solution for calculating three-dimensional seepage rates. The solution is for ponds located at the island midpoi vicinity of the pond and an equation for one-dimensional lateral flow in the remainder of the flow domain. presented for approximating the increase in the length of the flow path due to flow out of the bottom of the pond. The approximate solution predicted nearly the same pond seepage rates as determined from the numerical solutions for the geometries considered.

Two special cases were also analyzed to determine the limits of pond seepage for different geometries: a single pond located at the center of rectangular island, and a pond in a three sink system. The limits of flow were found to lie between the approximate solution and a solution assuming total radial flow. More work is needed to develop analytic methods to accurately predict seepage rates for these conditions.

d is based on radial flow theory in the

For deep profiles (d > Wp), a method is

a

62

SIMULATION MODEL FOR INFILTRATION PONDS ON BARRIER ISLANDS

RESERVO I R MODEL -

MODEL DESCRIPTION

WATER SURFACE

ELEVATION

A long-term continuous simulation model was developed to evaluate the performance of stormwater infiltration pond systems. This type of model was selected since pond performance was influenced by successive rainfall events during prolonged wet periods as well as by single large events. A model was developed capable of determining the response of a proposed system to the variety of weather conditions that occurred at a specific location over a 20 to 30 year time period. Other factors that would affect pond performance such as changes in land use or watershed boundaries over time were neglected.

The model, DMPOND, was composed of three parts: (1) a seepage component for calculating seepage from an infiltration pond, ( 2 ) a hydrology component for calculating stormwater runoff and water table elevations, and (3) a reservoir component for calculating reservoir stage and storage given output from parts 1 and 2. A flow chart of this procedure is shown in Fig. 40.

DKPOND considers a specific area of influence ( A t ) of the infiltration pond system delineated by the island width and island length (Fig. 41). Island width (W,) is the distance between the ocean and the sound. Island length ( L t ) is the distance between property boundaries or one half of the combined

INPUT DATA

WATER TABLE ELEVAT I ON

HYDROLOGY

MODEL

R W F F RATES

RESERVO I R STAGE

A

SEEPAGE RATES

Figure 40. Flow chart of interaction between the three model components used in DMPOND

w

63

_I

) SEEPAGE

MODEL

I

I I I 1

- -

*P

1 1 I

Figure 41. Plan view of model infiltration pond system showing the areal input variables used in DMPOND (see text on pages 63 and 65 for explanation).

Figure 42. Plan view of model infiltration pond system showing the four quadrants (Q,) used for pond seepage calculations by DMPOND. variables for the seepage equations are shown for each quadrant (see text on page 65 for explanation).

The

64

Figure 43. Elevation view of model infiltration pond system showing the elevation input variables used by DMPOND

distance between surrounding sources (ie. other infiltration ponds or septic systems). Within the area of influence is a watershed area that drains to the pond. This watershed area is divided into pervious surface area ( A ) and

P impervious surface area (Ai) . The center of a rectangular pond (2W X 2L ) is P P located relative to the center of the area of influence by the distances, W,

and Lo. Four quadrants are delineated from the pond center as shown in Fig. 42.

Elevation variables considered by DMPOND are shown in Fig. 43. These variables are average land elevation above MSL (D), elevation of MSL above impermeable layer (H,), elevation of pond bottom above impermeable layer (d), elevation of pond water surface above impermeable layer (H ), and maximum pond stage (S,,,).

The seepage component of DMPOhI calculates the seepage rate using the equations ( E q s 26 and 31) developed in the previous chapter. Pond seepage is the sum of the seepage rates calculated in each quadrant of Fig. 42.

P

Q, ?= C Qn (35) n-1

where Q, is the total pond seepage rate, and Qn is the seepage rate from quadrant n calculated f equation 26 for d 4 Wp and by equation 31 for d > wP*

During pond seepage, the elevation of the pond water surface was never allowed to be lese than the elevation of water table (calculated by the hydrology part of the model). elevation of the pond bottom and equal to the elevation of the pond water

When the elevation of water table was greater than the

6 5

surface, seepage from the pond was calculated as the change in pond storage in response to the change in water table elevation. That is, the pond water surface drops at the same rate as the water table-

The hydrology component of DKPOND is a modified version of the water management model, DRAINMOD (Skaggs, 1980). DrViINMOD performs a water balance in the soil-water regime at the midpoint between two drains of equal elevation. The model is capable of calculating hourly values for water table depth, surface runoff, subsurface drainage, infiltration, and actual evapotranspiration over many years of climatological data. simulations are conducted for 20 to 4 0 years of climatological record.

Typically

The water balance in DRAINMOD involves t w o basic equations. An equation for the soil profile,

AV, = D + ET + DS - F ( 3 6 )

where AV, is the change in air volume, E) is the drainage from the profile, ET is the actual evapotranspiration from the profile, D S is the deep seepage from the profile, and F is infiltration into the profile; and an equation for a water balance at the soil surface,

AS = P - F - RO (379

where AS is the change in water volume stored at the soil surface, P is precipitation, F is the infiltration volume, and RO is the surface runoff, Methods for evaluating equation variables are discussed in detail in Skaggs (1980).

The modifications of DRAINMOD for DMPOND involve changes in the water balance equation in the soil profile (Eq 36). These changes are the addition of recharge from pond seepage and adjustment of ET and F for the impervious surface area. between two parallel sinks (ie. ocean and sound) is

The modified equation for the water balance at the midpoint

AV, = D + PF(ET - F) + DS - PS ( 3 8 )

where PS is the pond seepage volume divided by the area of influence, and PF is the fraction of the area of influence that is pervious.

The assumption that the seepage from the pond recharges the soil profile as opposed to being lost to the sinks is conservative. justified by the observation at the Surf City field site that the water table under the impervious surfaces was recharged by some of the pond seepage.

The water balance equation at the soil surface is unchanged in DHPOND. The values for infiltration, surface runoff, and precipitation are not adjusted €or the fraction of pervious surface. Surface storage is interpreted a0 Only occurring on the pervious surfaces. There is no surface storage on the impervious surfaces, and surface runoff from the impervious surfaces is calculated in the reservoir component of the model.

The reservoir component of DMPOND calculates the change in pond storage Using the water balance equation:

The assumption is

66

APSTO = P * Ai + RO * Ap - PS - OW7 (39)

where PSTO is the volume of water stored in the pond, Ai is the area of the impervious surfaces in the watershed (see Fig. 41), A is the area of the pervious surfaces in the watershed (see Fig. 41), and OVR is the volume of water that overflows the pond. The overflow volume, O W , is the volume of water in excess of the maximum storage capacity of the pond. This volume is assumed to be lost to the receiving water.

The reservoir model has two options for calculating reservoir stage. The first option assumes the stage-storage relationship as a simple linear function.

P

PSTO = 2Lp * 2Wp * PSTA ( 4 0 )

where PSTA is pond stage, and 2Lp and 2Wp are pond length and width respectively (see Fig. 41). This option is most useful when using DMPOND simulations to estimate optimum pond location and volume.

The second option assumes a power function to describe the stage - storage relationship (Malcom, 1989).

PSTO = c, PSTA~ ( 4 1 )

where C, and b are parameters that are constant for a given pond and vary with pond shape. The power function option is used for accurately simulating pond stage in actual designs with specific pond shapes.

DHPOND uses hourly time steps on days when precipitation occurs and when water is in the pond. For other conditions DKPOND uses the 2 hour and 24 hour time steps as used by DRAINMOD.

Two objective functions are calculated in DMPOND for evaluating the performance of the infiltration pond system over a long period of time. These objective functions evaluate pond drawdown and pond overflow within the guidelines established by the North Carolina coastal stormwater regulations.

DMPOND determines the frequency and volume of pond overflow in response to rainfall events. For this determination, a rainfall event is defined as a

11 period separated from other rainfall periods by at least 2 4 hours of nfall. Hourly amounts of rainfall and volumes of pond overflow are over each rainfall event. If pond overflow occurs during an event, the

date, total rainfall amount, and total pond overflow volume are stored and are available as model output. The model determines the number of overflow events occurring during the simulation period in response to rainfall events of any

1 events less than 38 mm ( 1 . 5 in). The total volume of nd during the simulation period is also calculated.

nd drawdown times and the number of delays in pond drawdown . When pond stage is greater than zero, the model sums the nd rainfall amounts. If the number of consecutive hours is

an 120 ( 5 days), the model stores the number of hours, the rainfall the date as model output. The model determines the number of

times that water remains in the pond €or more than 5 consecutive days (drawdown delays) during the simulation period in response to rainfall events of any size and to rainfall events less than 38 nun.

67

Table 13. S i t e dimensions, a r e a s , and e l e v a t i o n s a t Surf C i t y used i n DM?ONB c a l i b r a t i o n s i m u l a t i o n s (see F ig 41 and 43).

-~~

Dimensions in ID

I s l a n d wid th , W, = 352 I s l a n d l e n g t h , Lt = 235 Pond width , 2Wp = 19 Pond l e n g t h , 2Lp = 2 5 Width o f f s e t , Wo = 60 Length o f f s e t , Lo = 30 Max pond s t a g e , S, = 1.2

Stage - storage constants C, = 472 b = 1.34

Areas in ha

T o t a l area o f i n f l u e n c e , Perv ious area i n watershed,

At = 8.3 Ap = 2 . 0

Impervious are i n watershed, A i = 1.1

Elevations i n m above impermeable l a y e r

Elev o f water s u r f a c e i n s i n k , H, = 1.35 Elev o f pond bottom, d = 2 .48 Elev of l and surface, E) = 3.68

S o i l Hydraul ic Conduct iv i ty , mjhr K, = 0.75

MODEL CALIBFiATION

BMPOND w a s c a l i b r a t e d u s i n g t h e c o n d i t i o n s e x i s t i n g a t t h e Surf C i t y f i e ld si te. S i t e dimensions and parameters used i n t h e s i m u l a t i o n s are shohm i n Table 13. boundary t o a l i n e midway between t h e pond and a t r a i l e r pa rk on t h e w e s t boundary. wa te r surface area of t h e pond a t one h a l f s t a g e . measured pond l e n g t h a t one h a l f of maximum s t a g e .

DMPOND w a s c a l i b r a t e d by a d j u s t i n g t h e e f f e c t i v e dep th t o t h e impermeable l a y e r , H,. d i f f e r e n c e between t h e d a i l y water t a b l e e l e v a t i o n p r e d i c t e d by t h e model, and t h e d a i l y water table e l e v a t i o n measured a t t h e S2 moni tor ing w e l l . D i f f e r e n c e s i n t h e water table e l e v a t i o n s were averaged f o r t h e y e a r o f 1988. The ave rage d i f f e r e n c e w a s minimized t o 0.106 m when t h e depth t o t h e impermeable l a y e r w a s 1.35 m below MSL.

The c a l i b r a t e d e f f e c t i v e dep th t o t h e impermeable l a y e r w a s c o n s i d e r a b l y less t h a n t h e d e p t h t o t h e aqu ic lude (7,9 m below HSL) measured i n t h e groundwater i n v e s t i g a t i o n . of a s i l t y o r g a n i c l a y e r a t HSL, or t h e convergence o f f l o w a t t h e ocean or sound due to t h e s a l t w a t e r i n t e r f a c e .

A plot comparing p r e d i c t e d t o measured w a t e r table e l e v a t i o n s is shown in Fig. 44. e v e n t s and faster drawdown rate. e l e v a t i o n was probably near enough t o t h e pond t o be a f f e c t e d by t h e format ion and decay of t h e mound near t h e pond. by OMPOND ie averaged o v e r t h e e n t i r e area of i n f l u e n c e and would be less t h a n t h a t measured near t h e pond. larger rise t h a n p r e d i c t e d on day 305. which w a s not cons ide red by t h e model. table between days 225 and 235 occur red d u r i n g a p e r i o d o f v e r y l o w t ide.

The i s l a n d l e n g t h was measured f r o m t h e p r o p e r t y l i n e on t h e e a s t

Pond l e n g t h and wid th were chosen such t h a t t h e i r p roduct was t h e The pond l e n g t h w a s t h e

C a l i b r a t i o n w a s ach ieved by minimizing t h e average absolute

P o s s i b l e e x p l a n a t i o n s for t h i s are t h e i n t e r m i t t e n t p re sence

The measured water table e l e v a t i o n shows a g r e a t e r response t o r a i n f a l l The l o c a t i o n of t h e measured w a t e r table

The response of water table p r e d i c t e d

The measured w a t e r table e l e v a t i o n had a much T h i s w a s a p e r i o d of v e r y h i g h t i d e The v e r y rapid drawdown of t h e wa te r

68

2.5 n € z 2.0 W

0 gr ‘a: 2 1.5 -J W W

Q b-

1.0 m

E w 0.5

0.0

I 100.0

,............*.I.. * ............. * ........... . ..............I * .............. * ...............I.. ... ..... * ................................... * ............ . ..... * ....................................................... GROUND ELEVATION AT S2

e---- MEASURED

- PREDICTED I

I I I 1 I

0 61 122 183 244

TIME (day) 305 366

1

Predicted and meaeured water t a b l e e l e v a t i o n s near t h e i n f i l t r a t i o n pond a t Surf C i t y . pred ic ted e l e v a t i o n s a r e from a DMPOND s imulat ion of t h e Surf C i t y site for 1988. v a l u e s are d a i l y water t a b l e e l e v a t i o n s recorded a t w e l l S2 for 1988.

Dai ly The measured

Predicted and measured water surface elevations in the pond are compared for 1988 in Figs. 45 - 48, The model predicted the water surface elevation in the pond very well for most events. The steady state equations for pond seepage predicted the average pond drawdown rate very accurately; however, these equations did not mimic the decrease in pond drawdown re te during drawdown from larger events. Thus the reservoir component underpredicted pond drawdown rate during and immediately after rainfall and overpredicted the drawdown rate toward the end of pond drawdown. Prediction of lower drawdown rates during and shortly after rainfall caused the model to predict higher water surface elevations for longer events (day 2 0 5 ) and for rainfall events occurring within 2 or 3 days of previous events (day 179). Agreement between measured and predicted water surface elevation8 in the pond was generally good with an average deviation of only 0.14 m fo r days when water was in the pond.

DMPOND predicted the time that water was in the pond to within 0.5 days for all but two events. The event on day 105 was during a period of high tides which decreased drawdown rates, particularly at the end of the drawdown period. that water was in the pond by 3.3 days.. DMPOND predicted that the water table was above the pond bottom between day 242 and 258. The model overpredicted the time that water was in the pond during this period by 3.5 days. during 1988 a total of 92.1 days compared to 8 8 . 5 days actually observed.

DMPOND predicted higher seepage rates and underestimated the time Toward the end of a wet period,

DMPOND predicted that water was in the pond

DMPOND did a reasonable job of simulating the performance of the pond at the Surf City site after it was calibrated for water table elevations. the calibration did not involve adjustments of the input parameter to match predicted and observed pond elevations or time that water was in the pond. Both of these variables are important and were predicted quite accurately by DMPOND. most likely due to the model neglecting the influence of the tides. to account for the effect of the tides would be a valuable addition to the model; however, we find that the present model is sufficiently accurate to evaluate the performance of infiltration pond designs similar to that at the Surf City site over long periods of climatological data.

Note that

Some errors between predicted and measured results did exist and were A routine

S I M U L A T I O N OF POND PERFOREBNCE AT SURF CITY

nfiltration pond system at the Surf City site was simulated fo r the 30 period from 1950 to 1979 using climatological data for Wilmington, NC.

The input data are shown in Table 13 (same as for calibration). The performance of the pond during this simulation is summarized in Table 34.

The simulated pond system at Surf City performed well retaining 90.8% of the total runoff from the developed area over the 30-year period. the 42000 m3 of runoff not retained on the site over the 30-year period was from rainfall in excess of 38 mm. events less than 38 mm were infrequent and of little consequence to the environment and the pond system. rainfall events of any size was excessive in some cases, when water was standing in the pond occurred when the water table elevation was greater than the pond bottom elevation during extended wet periods with many successive rainfall events. could cause mosquito problems or result in sealing of the pond bottom,

All but 5 ut3 of

Drawdown delay and overflow incidents for

The length of drawdown delays in response to These long periods

These long periods when water is in the pond

7 0

F i g u r e 45. Predicted and measured w a t e r e u r f a c e e l e v a t i o n s i n t h e i n f i l t r a t i o n pond a t Surf C i t y for t h e f irst q u a r t e r of 1988. s i m u l a t i o n o f t h e S u r f C i t y s i te f o r 1988. e l e v a t i o n s recorded i n t h e pond f o r 1988. The recorder measuring t h e pond water e l e v a t i o n s d id n o t b e g i n f u n c t i o n i n g u n t i l day 37.

Predicted v a l u e e are h o u r l y w a t e r s u r f a c e e l e v a t i o n s from a DMPOWD The measured v a l u e s are t h e h o u r l y w a t e r s u r f a c e

n

E W

Z 0 F=

2 -J W W 0 4 LL a: 3 v, a: W I- Q 3

2.250

2.000

1.750

1.500

1.250

- MEASURED

.. .. * . .. . . . . . . ! . . . . . . . I . . * . . : : i ! . . . . . . . . . . . . . . . . . . . . . .

500 E 400 z 300 200 -?’

0

P i 100 ;D

I I 1 1 1.000 1 110 130 90

TIME (days)

2

3 3

21 n

W

F i g u r e 46. P r e d i c t e d and measured w a t e r s u r f a c e e l e v a t i o n s i n t h e i n f i l t r a t i o n pond a t Surf C i t y f o r t h e second q u a r t e r o f 1988. s i m u l a t i o n o f t h e Sur f C i t y site f o r 1988. e l e v a t i o n s recorded i n t h e pond f o r 1988.

Predicted v a l u e s are h o u r l y w a t e r s u r f a c e e l e v a t i o n s from a DMPOND

The r e c o r d e r measuring t h e pond water e l e v a t i o n s The measured v a l u e s are t h e h o u r l y water s u r f a c e

ma l func t ioned from day 148 t o day 162.

73

‘41 P

2.500 A

E W

i - -

I -- I I I I

- MEASURED

500 L

400 x c 300 5 200 2 100 75 m

0 2

3 3

Z n

v

I 1 I I

31 0 330 350 370 1.000 I

270 290

TIME (days)

Figure 48. Predicted and measured water surface e l evat ions i n t h e i n f i l t r a t i o n pond a t Surf C i t y for t h e fourth quarter o f 1988. s imulat ion o f t h e Surf C i t y site for 1988. e l e v a t i o n s recorded i n t h e pond for 1988.

Predicted valuee are hourly water surface e l evat ions from a DMPOND The measured values are t h e hourly water surface

Table 14, Pond performance at Surf City site as simulated by DMPOND for 30 year period using climatological data for the years 1950 to 1979.

Drawdown Delay Incidents

For A l l Events For Events Less than 38 mm Elev of pond bottom above Delays Max 5 YRI Delays Max 5 YRI average WT over Delay Delay over Delay Delay

5 days days days 5 days days days

0.29 174 106.5 71.0 6 6.6 5.0

Overflow Incidents

For All Events For Events Less than 38 mm

total runoff Number Maximum 5 YRI Number Maximum 5 YRI Percent of

ret a ined of Volume of Volume % Incidents n3 n3 Incidents n3 n3 ------- ......................... ..........................

90.8 123 2002 1135 1 5 0

ANALYSIS OF SITE PARAMETERS AND DESIGN VARIABLES

Pond performance is affected by many different variables. Eight sets of DMPOND simulations were conducted to evaluate the effects of island width, island length, pond bottom elevation, pond length to width ratio, pond volume, impervious area, length offset, and width offset on pond performance. Pond performance was evaluated by the frequency and length of pond drawdown delays and by the frequency and volume of pond overflows. DFLPOND simulations were

ormed over the 30-year period from 1950 through 1979 using weather data Wilmington, N.C.

A pond system similar to that at Surf City was used as a baseline system. site dimensions, areas, and elevations for this system are shown in Table 15. Specific variables were changed for each set of simulations. each set of simulations are shown in Appendix tables A 1 - A8.

ed that these simulations no longer represent conditions at the Surf City site, as different parameter values are used to examine their effect on the pond performance.

Pond performance in response to pond bottom elevation is shown in Tables 16 and 17. As the elevation of pond bottom increased, pond performance was greatly improved due to greater head difference between the pond and the sinks, and greater separation between the pond bottom and the water table. The number of drawdown delay incidents from all events decreased from 216 to 15. Drawdown delay incidents from events less than 38 mm occurred only for

The

Variables for It should be

75

Table 15. B a s e l i n e site dimensions, a r e a s , and e l e v a t i o n s used i n DKPOND s i m u l a t i o n s e v a l u a t i n g d i f f e r e n t pond system d e s i g n s and s c e n a r i o s (see Figs . 41 and 43).

Dimensions in m

I s l a n d width, W, = 352 I s l a n d l e n g t h , L, = 235 Pond width, 2Wp = 21.9 Pond l e n g t h , 2~~ = 28.9 Width o f f s e t , w, = 88 Length o f f s e t , Lo = 0 Max pond s t a g e , S, = 0.9

Pond volume (m3), PV = 570

Areas in Ea

T o t a l a r e a of i n f l u e n c e , P e r v i o u s area i n watershed, Impervious area i n watershed,

A, = 8.72 Ap = 2.00 Ai = 1.49

Elevations in IP above impermeable layer

Elev of impermeable layer, H, = 1.35

E l e v of l a n d s u r f a c e , D = 3.68 E l e v of pond bottom, d = 2.78

S o i l h y d r a u l i c c o n d u c t i v i t y (m/hr) , K, = 0.75

t h e lowest pond bottom e l e v a t i o n . The number of over f low i n c i d e n t s in response t o e v e n t s less t h a n 38.1 nun decreased from 8 t o 1 as pond bottom e l e v a t i o n i n c r e a s e d . t h a t was r e t a i n e d on t h e s i te i n c r e a s e d from 83.2% t o 87.1%. The t o t a l volume of water over f lowing t h e pond d u r i n g t h e 30-year s i m u l a t i o n s d e c r e a s e d from 103000 t o 99000 m3*

The p e r c e n t of t h e t o t a l r u n o f f o v e r t h e 30-year p e r i o d

The d e c r e a s e i n maximum d e l a y p e r i o d from 126.7 t o 7 . 5 d a y s is of p a r t i c u l a r i n t e r e s t i n t h i s se t of s i m u l a t i o n s . Thia d e c r e a s e is much g r e a t e r t h a n observed i n t h e o t h e r sets of s i m u l a t i o n s . Long p e r i o d s of w a t e r s t a n d i n g i n t h e ponds are caused by t h e water table r i s i n g above t h e e l e v a t i o n of t h e pond bottom; consequent ly , i n c r e a s i n g t h e e l e v a t i o n of t h e pond bottom is t h e most e f f e c t i v e d e s i g n s t r a t e g y for a v o i d i n g long drawdown d e l a y s . I n c r e a s i n g the e l e v a t i o n of t h e pond bottom r e s u l t s i n d e c r e a s i n g pond depth and i n c r e a s i n g pond s u r f a c e area which may n o t be possible i n some i n s t a n c e s .

Table 16. The e f f e c t of pond bottom e l e v a t i o n on t h e number and l e n g t h of pond drawdown d e l a y i n c i d e n t s d u r i n g 30-year s i m u l a t i o n s u s i n g Wilmington, N.C. weather d a t a , ( 5 YRP s t a n d s for 5 yeas recurfench? i n t e r v a l . )

For All Events ’ For Events L e s s t h a n 38 nun Pond Ele,r of ...................... -------------c------------

B o t t o m pond above Delays Wax 5 YRI Delays Max 5 YRI Elev avg WT o v e r Delay Delay o v e r Delay Delay

m m 5 days days d a y s 5 d a y s days day8 ----- ------- ----------^----------- .......................... 2.48 0.27 216 126.7 81.2 4 7.5 0 2.78 0.57 118 53.5 20 .6 0 0 0 3.08 0.86 52 14.8 8 . 5 0 0 0 3.38 1.16 1 5 7.5 5.9 0 0 0

76

Table 17. The effect of pond bottom elevation on the number, total volume, and maximum volume of pond overflow incidents during 30-year simulations using Wilmington, N.C. weather data. (5 YRI stands for 5 year recurrence interval.)

Percent For All Events For Events Less than 38 nun Pond of Total ------_-------------___L_

..........................

Elev Retained of Volume of Volume Bottom Runoff Number Maximum 5 YRI Number Maximum 5 YRI

m % Incidents m3 m3 Incident6 m3 m3 ----- ------- ......................... ..........................

2.48 83.2 237 3070 1840 8 2 60 30 2.78 84.5 216 3040 1750 4 240 0 3.08 85.6 2 02 3000 1610 1 180 0 3.38 87.1 186 2910 1560 1 20 0

Tables 18 and 19 show pond performance in response to pond length (2L ) to width (2Wp) ratio (see Fig. 41). simulations. more linear and less radial, resulting in improved pond performance. The number of drawdown delay incidents from all events decreased from 327 to 31 over the range of ratios. The maximum delay for the 30-year simulations only changed from 57.0 to 53.3 days. Drawdown delay greater than 5 days from events less than 38 mm occurred only for the two lowest ratios. overflow incidents in response to events less than 38 mm decreased from 15 to 1 as pond length to width ratio increased. The percent of the total runoff over the 30-year period that was tetained on the site increased from 81.5% to 87.4%. The total volume of water overflowin simulations decreased from 113000 to 77000 m .

P

Increasing the length-to-width ratio made the flow near the pond The pond volume was fixed for these

The number of

the pond during the 30-year P

Table 18, The effect of pond length to width ratio on the number and length of pond drawdown delay incidents during 30-year simulations using Wilmington, N.C. weather data. (5 YRI stands for 5 year recurrence interval,)

1:8 1:4 1:2 1:l 2:l 4:l 8:l

0.57 0.57 0.57 0.57 0.56 0.56 0.56

327 57.0 20.6 261 53.7 21.0 202 53.7 20.4 144 53.8 20.7 85 53.4 20.7 50 53.8 20.8 31 53.3 21.0

For Events Less than 38 nun

over Delay Delay 5 days days days

20 2 0 0 0 0 0

5.5 5.3 5.1 0 0 0 0 0 0 0 0 0 0 0

77

Table 19. The effect of pond length to width ratio on the number, total volume, and maximum volume of pond overflow incidents during 30- year simulations using Wilmington, N.C. weather data. (5 YRI stands for 5 year recurrence interval.)

Eengt h io

Width Ratio

1:8 1:4 1:2 1:l 2 : l 4:l 8: 1

-----

Percent of Total Runoff Retained

%

81.5 82.3 83.2 84.1

86 .2 8 3 - 4

-------

85.1

For All Events

Number Maximum 5 YRI .........................

of Volume Incidents m3 m3

--------------------___^_

256 3180 2040 246 3150 1970 236 3110 1890 222 3060 1790 211 3000 1670 199 2920 1 5 7 0 188 2800 1520

For Events Less than 38 mn

Number Maximum 5 YRI ..........................

of Volume Incidents m3 m3 ..........................

15 320 90 10 300 60

7 280 2 0 5 250 0 1 220 0 1 130 0 1 20 0

The effects of pond length offset, Lo (see Fig.41) on pond performance are shown in Tables 20 and 21. lengthwise on the site. the length boundaries, thereby increasing pond seepage. Pond performance improved as length offset decreased. from all events decreased from 267 to 118 over the range of length offset values. The maximum delay for the 30-year simulations did not change for different length offsets. Drawdown incidents from events less than 38 mm occurred only for the highest length offset value. incidents in response to events less than 38 mm decreased from 12 to 4 as length offset decreased, period that was retained on the site increased from 84.5% to 82.3%. volume of water overflowing the pond during the 30-year simulations decreased from 109000 to 95000 m3.

Decreasing length offset centers the pond Centering the pond reduced the restriction of flow at

The number of drawdown delay incidents

The number of overflow

The percent of the total runoff over the 30-year The total

Table 20 . The effect of length offset on the number and length of pond drawdown delay incidents during 30-year simulations using Wilmington, N.C. weather data. (5 YRI stands for 5 year recurrence interval )

For All Events For Events Less than 38 mm Elev of ...................... ..........................

Length pond above Delays Max 5 YRI Delays Max 5 YRI Offset avg WT over Delay Delay over Delay Delay m m 5 days days days 5 days days days ----- ------- ...................... p - - - - - - - - - - - - - - - - ^ - - - - - - - ~

0 0.57 118 53.5 20.6 0 0 0 29 0.57 134 53.5 20.6 0 0 0 59 0 . 5 7 168 53.4 20.8 0 0 0 88 0 .56 267 53.6 21.0 2 5 . 1 0

7 8

Table 21. The effect of length offset on the number, total volume, and maximum volume of pond overflow incidents during 30-year simulations using Wilmington, N.C. weather data. ( 5 YRI stands for 5 year rec~rrence interval.)

Length Off set m

0 29 59 88

-----

Percent of Total Runoff Retained

%

84.5 84.3 83 .7 82.3

-------

For All Events

Number Maximum 5 Y R I .........................

of Volume 3 Incidents m3 m .........................

216 3040 1 7 5 0 2 19 3050 1770 228 3080 1840 249 3150 1980

Pond performance in response to pond width offset is shown in Tables 22 and 23. Increasing width offset moved the pond closer to one of the sinks and farther away from the other sink. Pond seepage increased as the distance between the pond and sink decreased. The increase in seepage as the pond moved toward the nearer sink was greater than the decrease in seepage as the pond moved away from the farther sink. Pond performance improved as width offset increased. The number of drawdown delay incidents from all events decreased from 193 to 57 over the range of width offset values. delay for the 30-year simulations did not change for different width offsets.

Drawdown incidents from events less than 38 mm occurred only for the lowest width offset value. The number of overflow incidents in response to events less than 38 nun decreased from 6 to 1 as width offset decreased. The percent of the total runoff over the 30-year period that was retained on the site increased from 83.4% to 86.0%. The total volume of water overflowing the pond during the 30-year simulations decreased from 101000 to 86000 m3

The maximum

Table 22. The effect of width offset on the number and length of pond drawdown delay incidents during 30-year simulations using Wilmington, N.C. weather data. ( 5 Y R I stands for 5 year recurrence interval.)

For All Events Elev of -----_--_-------------

Width nd above Delays M a x 5 YRI Offset avg WT Over Delay Delay

m m 5 days days days

0 0.57 193 53.9 20.4 44 0.57 172 53.4 20.6 88 0.57 118 53.5 20.6

132 0.56 57 53.9 20.9

----- ------- ......................

For Events Less than 38 mm

Delays Max 5 Y R I over Delay Delay

5 days days days .......................... 1 5 . 2 0 0 0 0 0 0 0 0 0 0

79

Table 23. The effect of width offset on the number, total volume, and maximum volume of pond overflow incidents during 30-year simulations using Wilmington, N.C. weather data. ( 5 YRI stands fo r 5 year recurrence interval,)

Percent For All Event8 For Events Less than 38 mm of Total ......................... ..........................

Width Runoff Number Haximum 5 YRI Number Maximum 5 YRI Offset Retained of Volume of Volume m % Incidents m3 m3 Incidents m3 m3 ----- ------- ......................... .......................... 0 83.4 233 3100 1870 6 270 lo

44 83.7 228 3090 1840 5 2 60 0 88 84.5 216 3040 1750 4 240 0 132 86.0 201 2940 1580 1 150 0

Tables 24 and 25 show pond performance in response to island width. width decreased, the water table elevation decreased. This increased the separation between the pond bottom and water table and improved pond performance. Also, the distance from the pond to the sink decreased with decreased island width, which increased the pond seepage rate and improved pond performance. The maximum delay for the 30-year simulations decreased from 126.9 to 15.0 days. The number of drawdown delay incidents from all events decreased from 156 to 81 over the range of width values. Drawdown incidents from events less than 38 mm occurred for the two highest island width values. than 38 mm decreased from 6 to 1 as island width decreased. The percent of the total runoff over the 30-year period that was retained on the site increased from 83.4% to 86.0%. during the 30-year simulations decreased from 102000 to 91000 m3

As island

The number of overflow incidents in response to events less

The total volume of water overflowing the pond

Table 24. The effect of island width on the number and length of pond drawdown delay incidents during 30-year simulations using Wilmington, N-C. weather data. (5 YRI stands for 5 year recurrence interval.)

For All Events For Events Less than 38 mm Elev of ...................... ..........................

Island pond above Delays H a x 5 Y R I Delays Max 5 Y R I Width avg WT over Delay Delay over Delay Delay

m m 5 days days days 5 days days days ----- ------- ------^--------------~ .......................... 282 0.81 81 15.0 10.5 0 0 0 317 0.69 PO6 22.2 13.1 0 0 0 352 0.57 118 53.5 20.6 0 0 0 387 0.44 144 88.0 40.3 1 5.2 0 422 0.31 156 126.9 54.4 5 6 . 6 0

80

Table 25. The effect of island width on the number, total volume, and maximum volume of pond overflow incidents during 30-year simulations using Wilmington, N.C. weather data. (5 YRI stands for 5 year recurrence interval.)

Percent For All Events For Events Less than 38 nun of Total ---c--------------c-_c___ ..........................

Island Runoff Number Maximum 5 YRI Number Maximum 5 YRI Width Retained of Volume of Volume m Incidents m3 m Incidents m3 m 3 3

282 85.2 210 3000 1670 1 220 0 317 84.8 2 12 3020 1710 3 230 0 352 84.5 216 3040 1750 4 240 0 387 84 .0 221 3350 1770 5 2 5 0 0 422 83.4 227 4170 1800 6 2 SO 30

The effects of island length on pond performance are shown in Tables 26 and 27. Increased island length improved pond performance by reducing flow restriction at the length boundaries. from all events decreased from 280 to 89 over the range of length values. The maximum delay for the 30-year simulations decreased from 56.6 to 52.5 days.

Drawdown incidents from events less than 38 mm occurred for the lowest island length value . The number of overflow incidents in response to events less than 38 mm decreased from 12 to 2 as island length increased. The percent of the total runoff over the 30-year period that was retained on the site increased from 82.0% to 85.0%. during the 30-year simulations decreased from 110000 to 92000 m3

The number of drawdown delay incidents

The total volume of water overflowing the pond

Table 26. The effect of island length on the number and length of pond drawdown delay incidents during 30-year simulations using Wilmington, N.C. weather data. (5 YRI stands for 5 year recurrence interval.

Elev of Island pond above Length avg W T

m m

f 18 0.45 176 0.53 235 0.57 294 0.59 3 52 0.61

280 56.6 25.5 164 54.8 21.0 118 53.5 20.6 98 53.0 20.1 89 52.5 20.3

For Events Less than 38 nun

4 5 . 2 0 0 0 0 0 0 0 0 0 0 0 0 0

81

Table 2 9 , The effect of island length on the number, total volume, and maximum volume of pond overflow incidents during 30-year simulations using Wilmington, N.C. weather data. ( 5 YRI stands for 5 year recurrence interval.)

Percent For All Events For Events Less than 38 mm

Island Length m

118 176 235 294 352

-----

of Tot a1 Runoff Retained

%

82.0 83.8 84.5 84.9 85.0

-------

......................... Number Maximum 5 YRI of Volume

Incidents m3 m3 ......................... 249 3160 2000 228 3080 1830 216 3040 1750 212 3020 1710 212 3010 1680

Number Haximum 5 YRI of Volume

Incidents m3 m3 ___------p-----------------

12 300 70 5 260 0 4 240 0 2 230 0 2 220 0

Pond performance in response to impermeable area is shown in Tables 28 and 29. Pond volume for these simulations was increased with impermeable area such that the pond could hold the runoff of a 38 mm rainfall event. performance declined as impermeable area increased. elevation increased because of a reduction in evapotranspiration. This decreased the separation between the pond bottom and the water table, increasing the maximum delay for the 30-year simulations from 53.5 to 116.5 days. 118 to 412 over the range of impermeable area values. Drawdown incidents from events less than 38 mm occurred for the three highest impermeable values. The number of overflow incidents in response to events less than 38 mm increased from 4 to 139 as impermeable area increased. The percent of the total runoff over the 30-year period that was retained on the site decreased from 84.5% to 71.4%. The total volume of water overflowin the pond during the 30-year simulations increased from 95000 to 729000 m

Pond The average water table

The number of drawdown delay incidents from all events increased from

P

Table 28. The effect of impervious area on the number and length of pond drawdown delay incidents during 30-year simulations using Wilmington, N, C . weather data. 5 YRI stands for 5 year recurrence interval.

Imperv For All Events For Events Less than 38 mm Elev of ...................... .......................... Area

% of pond above Delays Hax 5 YRI Delays Max 5 YRI Total avg WT over Delay Delay over Delay Delay Area m 5 days days days 5 days days days ----- ------- --------------------_q ..........................

18 8.57 118 53.5 2 0 . 6 0 0 0 25 0 . 5 2 251 54.8 22.7 0 0 0 38 0.46 389 61.9 36.6 89 6.9 6.4 50 0.41 412 63.3 4 2 . 5 117 8 .7 8.2 95 0.34 348 116.5 74.5 221 11.7 10.9

82

Table 29. The effect of impervious area on the number, total volume, and maximum volume of pond overflow incidents during 30-year simulations using Wilmington, N.C. weather data. (5 YRI stands for 5 year recurrence interval.)

Imperv Percent For All Events For Events Less than 38 mm Area % of

Total Area

18 25 38 50 75

-----

of Total Runoff

Retained %

84.5 82.5 79.3 76.6 71.4

--------

......................... Number Maximum 5 YRI of Volume

Incidents m3 m3 ......................... 216 3040 1750 244 4350 2720 290 6880 4510 334 9560 6340 429 15000 9640

.......................... Number Maximum 5 YRI

of Volume Incidents m3 m3 ..........................

4 240 0 8 410 70 34 720 310 66 1050 590

139 1700 1200

Pond performance in response to pond volume is shown in Tables 30 and 31. Impermeable area remained constant for these simulations. The number of drawdown delay incidents from all events increased from 118 at pond volume of 570 m3 to 178 at pond volume of 950 m3 then decreased to 156 at a pond volume of 1710 m3. to 71.2 days as pond volume increased. The number of drawdown delays and the maximum drawdown delays increased since more of the runoff from larger events had to seep through the pond. No drawdown incidents from events less than 38 mm occurred for these simulations. Overflow incidents in response to events less than 38 mm occurred only at pond volumes of 570 and 760 m3. The number of overflow incidents in response to events of any size decreased from 216 to 17 as pond volume increased. The percent of the total runoff over the 30-year period that was retained on the site increased from 84.5% to 98.1%. The total volume of water overflowing the pond during the 30-year simulations decreased from 95000 to 11000 m3. Pond volume was the only variable tested that showed an improvement in one pond performance factor while the other factor worsened.

Table 30. The effect of pond volume on the number and length of pond drawdown delay incidents during 30-year simulations using Wilmington, N.C. weather data. (5 YRI stands for 5 year recurrence interval.)

The maximum delay for the 30-year simulations increased from 53.5

For All Events For Events Less than 38 mm Elev of ...................... ..........................

Pond pond above Delays Max 5 YRI Delays M a x 5 YRI Volume avg WT over Delay Delay over Delay Delay

m3 m 5 days days days 5 days days days ----- ------- ...................... .......................... 570 0.57 118 53.5 20.6 0 0 0 7 60 0.55 162 54.5 21.8 0 0 0 950 0.55 178 55.2 25.1 0 0 0 1140 0.55 173 56.0 25.8 0 0 0 1330 0.54 168 57.0 26.7 0 0 0 1710 0.54 156 71.2 27.5 0 0 0

83

Table 31. The effect of pond volume on the number, total volume, and maximum volume of pond overflow incidents during 30-year simulations using Wilmington, N.C. weather data. ( 5 YRI stands for 5 year recurrence interval.)

-~ - ~

Percent For All Events For Events Less than 38 mm of Total ......................... ...........................

Pond Runoff Number Maximum 5 Y R I Number Maximum 5 Y R I Volume Retained of Volume of Volume m3 % Incidents m3 m 3 Incidents m3 m3 _---- ------- ......................... ...........................

570 84 .5 2 16 3040 1750 1 240 0 7 60 89.4 136 2830 1650 1 90 0 950 92.6 97 2620 1570 0 0 0 1140 94.7 66 2470 1380 0 0 0 1330 96.3 45 2360 1190 0 0 0 1710 98.1 17 2090 890 0 0 0

CONCLUSIONS

All of the variables tested in these eight sets of simulations affected the number of drawdown delay and pond overflow incidents. Variables, except fos pond volume, affected drawdown delay more than pond overflow. Only three variables (elevation of pond bottom, island width, and impervious area) significantly affected the maximum drawdown delay time. (pond volume and impervious area) significantly affected the percent of total runoff retained and the total and maximum overflow volumes.

The island width and island length variables are island specific and can not be easily changed during the design process. controlled during the design of a pond system, engineer should consider that increasing pond length to width ratio, width offset, and elevation to pond bottom improves pond performance. Decreasing length offset and impervious area also Improve pond performance. Increasing the elevation to the pond bottom is the most effective way of improving pond performance since it decreases the maximum delays in pond drawdown in addition to improving the other performance factors. Increasing the elevation of the pond bottom is achieved by decreasing pond depth; however this increases the area required by the pond which may not be possible in some instances. Fortunately, decreasing the pond depth makes the pond less conspicuous because a smaller and more gradual change in elevation from outside of the pond to the

Only two variables

Other variables tested can be When designing a pond the

inside of the pond can be achieved. A smaller change in result in more uniform vegetation inside and outside the soil moisture conditions.

elevation Gill often pond due to similar

LIST OF REFERENCES

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Bouwer, H. 1969. Theory of seepage from open channels. In: Advances in Hydroscience, Edited by V. T. Chow, Academic Press, NY. 305 pp.

Brandt, A. 1977. Multi-level adaptive solutions to boundary value problems. Math. Comput. 31:333-390.

Brandt, A. 1982. Guide to multi-grid development. In: Multi-grid Methods, Lec. Notes in Math., Ser. 960, edited by Hackbusch, W. and U. Trottenberg. Springer Verlag, New York.

Brooks, R. H. and A. T. Corey. 1964. Hydraulic properties of porous media. Hydraul. Pap. 3, Colo. State Univ., Ft. Collins.

Bryan, E. H. 1970. Quality of stormwater drainage from urban land areas in North Carolina. University of North Carolina Water Resources Research Institute Report No. 37, Raleigh, NC.

Fipps, G . 1988. Numerical solutions to the Richards equation in two and three dimensions. Ph.D. Dissertation, North Carolina State University, Raleigh. 117 pp.

Fipps, G . and R. W. Skaggs. 1989. Hodeling three-dimensional, saturated and unsaturated flow using multigrids, Trans. her. SOC. Rar. Enq. 32(4):1263- 1268.

Fipps, G . and R. W. Skaggs. 1990. Pond seepage in two and three dimensions. Journal of Hvdrolouv. In Press

Freeze, R. A. 1971. Three-dimensional, transient, saturated-unsaturated flow in a groundwater basin. Water Resourc. Res. 7(2):347-366.

Frind, E. 0. and M. J. Verge. 1978. Three dimensional modeling of groundwater flow systems. Water Resourc. Res. f4(5):844-856.

Hackbusch, W. 1982. Multi-grid convergence theory. In: Multi-grid Methods, Lec. Notes in Math., Ser. 960, edited by Hackbusch, W. and U. Trottenberg. Springer-Verlag, Berlin.

Hackbusch, W. and U. Trottenberg. 1982. Multf-grid methods. Lec. Notes in Math., Ser. 960. Springer-Verlag, Berlin.

Hazen, A. 1893. Some physical properties of sands and gravels with special reference to their use in filtration. 24th Annual Report of the Massachusetts State Board of Health, Boston, MA. 541 pp.

Hoyt, J. H. 1967. Barrier Island formation. Geol. SOC. Am. 78:1125-1136.

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Huntoon, R. W. 1974. Finite Difference Methods As Applied to the Solution of Groundwater Flow Problems. Wyoming Water Resources Research Institute, Univ. of Wyoming, Laramie, WY. 98 pp.

Huyakorn, P. S., E. P. Springer, V. Guvanasen, and T. D. Wadsworth. 9986. A three-dimensional finite-element model for simulating water flow in variably saturated porous media. Water Resourc. Res, 22(13):1790-1801.

Kimrey, J. 0. 1961. Ground-water supply for the Dare Beaches Sanitary D District, Invest. No. 3. NC. Dept. of Water and Air Res., Div. Groundwater, Raleigh, NC.

Klute, A. 1965a. Laboratory measurement of hydraulic conductivity of saturated s o i l . In: Methods of Soil Analvsis, C. A. Black, ed. American Society of Agronomy, Madison, WI. pp. 210-221.

Klute, A. 1965b. Water capacity. In: Methods of Soil Analysis. C. A. Black, ed. American Society of Agronomy, Hadison, WI. pp. 273-278,

Malcom, H. R. 1989. Elements of Urban Stormwater Design. Industrial Extensiofl Service, North Carolina State University, Raleigh, NC. p. 111-4

Marino, M. A. and 9. N. Luthin. 1982, Seepaae and aroundwater. Elsevier Scientific Publishing Co., Amsterdam, The Netherlands. 489 pp.

McKeon, T. Y. and W.-S. Chu. 1987. A multigrid model for steady flow in partially saturated porous media. Water Resourc. Res. 23(4):542-550.

North Carolina Groundwater Section of the Division of Environmental Management. 1989. Report of investigation for the stormwater infiltration pond study,

Prickett, T. A, 1965. Type curve solution to aquifer tests under water table conditions. Groundwater, 3(3):5-14.

Richards, L. A. 1931. Capillary conduction of liquids through porous mediums. Phvsics, 1:318-324.

Sartor, J. 0. and G . B. Boyd, 1992. Water pollution aspects of street surface contaminates. USEPA Report No. EPA-RZ-72-83.

Skaggs, R . W. 1980. DRAINMOD Reference Report. USDA-SCS, South National Technical Center, Fort Worth, TX. 329 pp.

Skaggs, R.W. 1982. Field evaluation of a water management simulation model, Trans. her. SOC. Aar. Enq. 25:666-674.

Skaggs, R. W. and J. G . Wardak. 1981. Highway construction in coastal areas. Project ERSD-110-96-1, NC. Dept. Transportation, Federal Highway Admine, May.

Smith, G . D. 1978. Numerical Solution of Partial Differential Eauations: Finite Difference Methods. Clarendon Press, Oxford, 304 pp.

06

Stauffer, M, K., G . S. Herman, and T. A. Burstynsky. 1984. Oil and grease in urban stormwater. J. Envirn. Bnq. 110(1):58-72.

Stuber, R. and U. Trottenberg. 1982. Multigrid methods: fundamental algorithms, model problem analysis and applications. In: Multi-grid Methods, Lec. Notes in Math., Ser, 960, edited by Hackbusch, W. and U. Trottenberg, Springer Verlag, Berlin.

United State Environmental Protection Agency ( U S E P A ) . 1983. Results of the nationwide urban runoff program. Kater Planning Division, Washington, DC,

van Beers, W.F.J. 1970. The auger hole method, a field measurement of the hydraulic conductivity of soil below the water table. Bulletin 1. International Institute for Land Reclamation and Improvement. Wageningen, The Netherlands.

h'alsh, J. 1987. Multigrid methods for elliptic equations, In: The State of the Art in Numerical Analysis. Edited by Iserles, A. and M . J . D . Powell, Clarendon Press, Oxford. 315 pp.

87

LIST OF PUBLICATIONS

Fipps, G . and R. W. Skagge, 1989. Modeling three-dimensional, saturated and unsaturated flow using multigrid@, Trans. Amer. Soc. A a r . Ena., 32(4):1263-1268

Fipps, G . and R. W. Skaggs, 1990. Pond seepage in two and three dimensions. Journal of Hvdroloay. In Press.

Chescheir, 0. M., G. Fipps and R. W. Skaggs, 1988. Hydrology of two stormwater infiltration ponds on the North Carolina barrier islands. In: Proceedings of the Coastal Water Resources Conference, Wilimington, NC. pp. 313-320

Fipps, G . , G . M. Chescheir and R. W. Skaggs, 1988. Modeling seepage from stormwater infiltration ponds, In: Proceedings of the Coastal Water Resources Conference, Wilimington, NC. pp. 321-332

Development and testing of DMPOND and associated hydrologic models is the subject of the senior author’s Ph. D. dissertation, which will be completed in 1990. and further document the models developed in this study.

Completion of that work will extend the results given in this report

APPENDIX TABLES

Table A l . Site dimensions, areas, and elevations used in DMPOND simulations evaluating the effect of elevation of pond bottom on pond performance

Dimensions in m

Island width, W, = 352 Island length, L, = 235 Pond width, 2w =

38.0, 26.9, 21.6, 19.0 Pond length, 2L =

50.0, 35.4, 28.6, 25 .0 Width offset, Wo = 88 Length offset, Lo = 0 Max pond stage, S, =

0.3, 0.6, 0 .9 , 1 .2

Areas in ha

Total area of influence, Pervious area in watershed, Impervious area in watershed,

A, = 8 .3 Ap = 2.0 Ai = 1.49

Elevations in IP above impermeable l a y e r

Elev of water surface in sink, H, = 1.35 Elev of pond bottom, d =

Elev of land surface, D = 3.68 3.38, 3.08, 2 .78, 2.48

T a b l e A2. Site dimensions, areas, and elevations used in DNPOND simulations evaluating the effect of t h e length-width ratio on pond performance

Dimensions in m Areas i n ha

Island width, = 352 Total area of influewee, a, = 8.3 Island length, L, = 235 Pervious area in watershed, % = 2.0 Pond width, 2Wp = Impervious area in watershed, Ai = 1.49

8 .9 , 12.6, 17.8, 25.2, 35.6, 50.3, 71.2

71.2, 50.3, 35.6, 25.2, 17.8, 12.6, 8.9

Width offset, Wo = 88.0 Elev of water surface in s i n k , Xs = 1.35 Length offset, Le = 0 Elev of pond bottom, d = 2.78 Max pond stage, S, = 0.9 Elev of land surface, B = 3,68

Pond length, 2Lp = Elevations in IP above impermeable l a y e r

89

Table 243. S i t e dimensions, a r e a s , and e l e v a t i o n s used i n DMPOND s i m u l a t i o n s e v a l u a t i n g t h e e f f e c t of l e n g t h o f f s e t on pond performance

Dimensions in m

I s l a n d wid th , W, = 352 I s l a n d l e n g t h , L, = 235 Pond width , 2Wp = 21.9 Pond l e n g t h , 2Lp = 28.9 Width o f f s e t , Wo = 88 Length o f f s e t , Lo =

Max pond e t a g e , S, = 0, 29, 59, 08

0.9

Areas in ba

Total area of i n f l u e n c e , Perv ious area i n watershed, Impervious area i n watershed,

E l e v a t i o n s i n m above impermeable layer

At = 8.3 Ap = 2.0 Ai = 3.49

Elev of water s u r f a c e i n s i n k , H, = 1.35 Elev of pond bottom, d = 2.78 Elev o f l a n d s u r f a c e , D = 3.68

Table A 4 * Site dimensions, z r e a s , and e l e v a t i o n s used i n DHPOND s i m u l a t i o n s e v a l u a t i n g t h e e f f e c t of wid th offset on pond performance

Dimensions i n IP Areas in ha

I s l a n d wid th , W, = 352 I s l a n d l e n g t h , L, = 235 Pond width , 2Wp = 21.9 Pond l e n g t h , 2Lp = 20.9 Width o f f s e t , Wo =

Length o f f s e t , Lo = 0 Wax pond s t a g e , S, = 0.9

0, 44, 88, 132

T o t a l area o f i n f l u e n c e , Perv ious area i n watershed, Imperv ious area i n watershed,

E l e v a t i o n s in m above impermeable layer

Elev o f water s u r f a c e i n s i n k , H, = 1.35 Elev of pond bottom, d = 2.78 Elev of l a n d s u r f a c e , D = 3.68

A, = 8.3 % = 2.0 Ai = 1.49

Table A5. S i t e dimensions, areas, and e l e v a t i o n s used i n DMPOND s i m u l a t i o n 8 e v a l u a t i n g t h e e f f e c t of i s l a n d wid th on p n d performance

Dimensions i n P

I s l a n d wid th , W, =

I s l a n d l e n g t h , L, = 235 Pond width , 2Wp = 21.9 Pond l e n g t h , 2Lp = 28.9 Width offset, W, = 53, 70, 88, 106, 123 Length o f f s e t , Lo = 0 Max pond s t a g e , S, =

282, 317, 352, 387, 422

0.9

Areas in ha

Total area o f i n f l u e n c e ,

Perv ious area i n watershed, Ap

A, -- 6.6, 7.4, 8.3, 9.3, 9.9

area i n watershed,

Elevations in a above bpenneable layer

Elev o f water surface i n s i n k , H, = 1.35 Elev o f pond bottom, d = 2.78 Elev of l a n d surface, D = 3.68

90

Table A6. Site dimensions, areas, and elevations used in DKPOND simulations evaluating the effect of island length on pond performance.

Dimensions i n 1p Areas fn

Island width, W, = 352 Island length, L, =

117, 176, 235, 294, 352 Pond width, 2Wp = 21.9 Pond length, 2Lp = 28.9 Width offset, Wo = 88 Length offset, Lo = 0 Max pond stage, S, = 0.9

Total area of influence, 4.1, 6.2, 8.2, 10.3, 12.4

Pervious area in watershed, Impervious area in watershed,

A, =

Ap = 2.0 Ai = 1.49

Elevations i n P above impermeable l a y e r

Elev of water surface in sink, H, = 1.35 Elev of pond bottom, d = 2.78 Elev of land surface, D = 3.68

Table A?. Site dimensions, areas, and elevations used in DKPOND simulations evaluating the effect of impervious surface area on pond performance

Dimensions in m Areas i n ha

Island width, W, = 352 Island length, L, = 235 Pond width, 2Wp =

Pond length, 2Lp =

Width offset, Wo = 88 Length offset, Lo = 0 M a x pond stage, S, = 0.9

21.9, 25.8, 31.6, 36.5, 44.7

28.9, 33.9, 41.6, 48.0, 58.8

Total area of influence, Pervious area in watershed, Impervious &rea in watershed, 1.49, 2.07, 3.10, 4.14, 6.20

A, = 8.3 Ap = 2 . 0

Ai =

Elevations in m above impermeable l a p e r

Elev of water surface in sink, H, = 1.35 Elev of pond bottom, d = 2.78 Elev of land surface, D = 3.68

Table AB. S i t e dimensions, areas, and elevations used in DFiOND simulations evaluating the effect of pond volume on pond performance

Dhens ions in m Areas in ha

Island width, W, = 352 Total area of influence, A, = 0.3 Island length, Lt = 235 Pervious area in watershed, % = 2.0 Pond width, 2Wp = Impervious area in watershed, Ai = 1.49

Pond length, 2Lp = Elevations i n II above impermeable l a y e r

Width offset, Wo = 88 Elev of water surface in sink, H, = 1.35 Length offset, 2, = 0 Elev of pond bottom, d = 2.78 M a x pond stage, Sa = 0.9 Elev of land surface, D = 3.68

25.3, 28.3, 31.0, 33.5, 38.0

33.3, 37.3, 40.8, 44.1, 50.0

91