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1 Supporting Documentation for PercPackTM A Groundwater - Surface Water Interface for ICPR Prepared by Peter J. Singhofen, Streamline Technologies, Inc. 1900 Town Plaza Court Winter Springs, Florida 32708 407-679-1696 April, 2008 Copyright 2008, Streamline Technologies, Inc. All Rights Reserved This document may not be reproduced, copied, distributed or electronically transmitted without written permission from Streamline Technologies, Inc. Supporting Documentation for PercPackTM, A Groundwater Surface Water Interface for ICPR 2008, Streamline Technologies, Inc. TABLE OF CONTENTS Introduction ..1 Theoretical Basis ..5 Unsaturated Vertical Flow for Constant Surface Areas .. 5 Unsaturated Vertical Flow for Variable Surface Areas .. 7 Saturated Horizontal 9 Soil Storage Recovery and Aquifer Recharge ..13 Green-Ampt Method for Drainage Basins.

2 14 exfiltration Trenches ..15 Filter Hydraulics ..16 Input Parameters for Green-Ampt Rainfall Excess Option ..19 Percolation Options and Input Parameters for Percolation Links ..23 Examples ..30 Slug Loads and Pollution Abatement Recovery ..30 Ditch in Close Proximity to a Multiple Ponds in Close Proximity ..43 Percolation from Base Flow Calculations ..56 Radius of Influence ..59 exfiltration Trench Links ..63 Parameters Related to the Unconfined Aquifer ..64 Parameters Related to the Trench and Pipe ..65 Parameters Related to the Computational Framework ..66 Examples ..67 exfiltration Trenches without Pipe Hydraulics ..70 exfiltration Trenches with Pipe Hydraulics.

3 81 Filter Links ..89 Input Parameters ..90 Example ..91 References ..95 Supporting Documentation for PercPackTM, A Groundwater Surface Water Interface for ICPR 2008, Streamline Technologies, Inc. APPENDICES Appendix A. Verification of the Modified Green-Ampt Method for Unsaturated Vertical Flow .. A-1 Appendix B. Verification of the Saturated Horizontal Flow Algorithm for Use with exfiltration Trenches .. B-1 Appendix C. Verification of the Saturated Horizontal Flow Algorithm for Pond Draw Down Analysis .. C-1 Appendix D. Comparisons of ICPR with MODRET ( ) And PONDS ( ).. D-1 Input D-2 Comparison of Runoff Hydrographs .. D-8 Comparison of Infiltration D-10 Comparison of Stage Hydrographs.

4 D-17 Appendix E. A Refined Infiltration Method in ICPR .. E-1 Introduction ICPR, since its inception more than 25 years ago, has always been an unsteady state one-dimensional single event stormwater model. Its mathematical framework is based on a link-node concept where stages are calculated at nodes through conservation of mass principles and flows are calculated for links based on stages at the nodes. Although it has always been possible to approximate percolation from ponds using rating curves, there was never a true groundwater - surface water interface in ICPR. Until now, other software programs such as PONDS and MODRET had to be used separately from ICPR in order to model the interaction between surface water and groundwater. However, PONDS and MODRET are limited to a single pond and pond configurations must be idealized into equivalent rectangles in order to blend with the rectangular finite difference grid used for groundwater modeling.

5 If multiple ponds are hydraulically connected on the surface and interdependent, then a tedious if not impossible task of iterating models is required. PercPackTM is an optional plug-in for ICPR and provides a true groundwater - surface water interface for interconnected ponds and other complex surface drainage systems. The main focus of ICPR continues to be surface water modeling and although the new PercPackTM features are quite powerful, we wanted them to compliment the surface model rather than drive it. Our goals were to make the new groundwater algorithms technically rigorous, computationally robust and fast, flexible and capable of handling a wide range of problems. Yet, it was important that these new features fit easily into the mathematical framework of ICPR without unduly burdening the surface water algorithms. Given the goals cited above, the main features of PercPackTM have been implemented in the form of three new link types: 1.

6 Percolation Links 2. exfiltration Trench Links 3. Filter Links (both side bank and bottom filters) Data forms for each of these new link types are accessed the same as all other links in ICPR as shown in Figure Figure Accessing the New Link Types in ICPR 2 Supporting Documentation for PercPackTM, A Groundwater Surface Water Interface for ICPR 2008, Streamline Technologies, Inc. These new links work very similar to other link types in ICPR and are used to move water from one node to another. For example, a percolation link can be used to connect a pond ( , a stage-area node type designated as Pond in Figure ) to a groundwater sink ( , a time-stage node designated as Soil Column in Figure ). The Pond receives inflow from runoff hydrographs like any other node in ICPR. Also, surface connections can be made in the same manner as always. The flow rate for the percolation link depends on the water level in the pond and also the location of the water table below the pond.

7 Percolation links can be used for a variety of applications including: storage recovery for ponds; estimates of base flow for ditches, roadway under drains, wetlands, ponds and lakes; percolation from swales; and, many other applications. Figure Link-Node Schematic for Single Pond with Percolation and Weir Links exfiltration trenches are used to dispose of stormwater runoff underground. A trench is excavated and backfilled with gravel and perforated pipe as shown in Figure Stormwater enters the trench and then percolates into the soil column. These link types are actually a special case of percolation links and use the same algorithms for groundwater flow. However, storage in the trench is automatically calculated based on trench dimensions and pipe size and assigned to the from node for the link. The groundwater flow algorithms in ICPR for Percolation and exfiltration Trench link types include unsaturated vertical flow and saturated horizontal flow.

8 The basics of these methods are discussed in the following section. 3 Supporting Documentation for PercPackTM, A Groundwater Surface Water Interface for ICPR 2008, Streamline Technologies, Inc. Figure exfiltration Trench Schematic Filters, placed in either the side banks of a pond or on the bottom of the pond, are used to treat stormwater runoff before it is released offsite. A typical side bank filter is shown in Figure Figure Side Bank Filter PercPackTM includes other features like the Green-Ampt method for drainage basins, XML import/export options, and new reporting capabilities. 4 Supporting Documentation for PercPackTM, A Groundwater Surface Water Interface for ICPR 2008, Streamline Technologies, Inc. This Page Intentionally Left Blank 5 Supporting Documentation for PercPackTM, A Groundwater Surface Water Interface for ICPR 2008, Streamline Technologies, Inc. Theoretical Basis Unsaturated Vertical Flow for Constant Surface Areas This method applies to exfiltration trench links since the surface area at the trench soil interface is always constant ( , vertical sides).

9 It also applies to percolation links when the Surface Area Option is set to either User Specified or Use 1st Point in Stage/Area Table as illustrated below. Consider the schematic depicted in Figure As water infiltrates through the bottom of a pond or trench and percolates into the soil column, a wetting front advances downward through an unsaturated zone at the propagation speed Uprop. During each time step, t, the head, H, is constant and the wetting front advances a vertical distance, Zf, a variable to be integrated. Figure Schematic for Vertical Percolation from a Pond 6 Supporting Documentation for PercPackTM, A Groundwater Surface Water Interface for ICPR 2008, Streamline Technologies, Inc. From Darcy s Law: q = Ky I (eq. ) where, q is the apparent velocity Ky is the vertical conductivity I is the hydraulic gradient The hydraulic gradient is expressed as follows: I = (H + Zf + ) / Zf (eq.)

10 Where, H is the water depth in the pond Zf is the vertical distance from the pond bottom to the edge of the wetting front is the wetting front capillary suction head The propagation velocity of the wetting front is defined by the following equation: Uprop = dZf / dt = q / F (eq. ) where, F is the effective or fillable porosity Combining equations yields the following differential equation: dZf / dt = (Ky / F) (H + Zf + ) / Zf (eq. ) Letting H = H + and rearranging terms yields: dt = [ F Zf dZf ] / [ Ky (H + Zf) ] (eq. ) Eq. can now be integrated between times 0 and t0 and Zf between 0 and Z0 to obtain the total vertical distance, Z0, advanced by the wetting front after time, t0. t0 = (F H / Ky) [ (Z0 / H ) ln(1 + Z0 / H ) ] (eq. ) Eq. is an implicit function of Z0 and must be solved iteratively. It simulates the well-known logarithmic decay of infiltration rate with time and is similar to the Green-Ampt equation except flooding above the ground surface is incorporated into H.