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Supporting Documentation

for

PercPackTM A Groundwater - Surface Water

Interface for ICPR

Prepared by

Peter J. Singhofen, P.E.

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 1.0 Introduction........................................................................................1

2.0 Theoretical Basis.................................................................................5

2.1 Unsaturated Vertical Flow for Constant Surface Areas ........................ 5

2.2 Unsaturated Vertical Flow for Variable Surface Areas ......................... 7

2.3 Saturated Horizontal Flow.............................................................. 9

2.4 Soil Storage Recovery and Aquifer Recharge ...................................13

2.5 Green-Ampt Method for Drainage Basins ........................................14

2.6 Exfiltration Trenches ....................................................................15

2.7 Filter Hydraulics ..........................................................................16

3.0 Input Parameters for Green-Ampt Rainfall Excess Option.................19

4.0 Percolation Links...............................................................................23

4.1 Options and Input Parameters for Percolation Links..........................23

4.2 Examples ...................................................................................30

4.2.1 Slug Loads and Pollution Abatement Recovery .......................30

4.2.2 Ditch in Close Proximity to a Pond........................................36

4.2.3 Multiple Ponds in Close Proximity .........................................43

4.2.4 Percolation from Swales .....................................................48

4.2.5 Base Flow Calculations .......................................................56

4.2.6 Radius of Influence ............................................................59

5.0 Exfiltration Trench Links ...................................................................63

5.1 Parameters Related to the Unconfined Aquifer .................................64

5.2 Parameters Related to the Trench and Pipe .....................................65

5.3 Parameters Related to the Computational Framework .......................66

5.4 Examples ...................................................................................67

5.4.1 Exfiltration Trenches without Pipe Hydraulics .........................70

5.4.2 Exfiltration Trenches with Pipe Hydraulics .............................81

6.0 Filter Links ........................................................................................89

6.1 Input Parameters ........................................................................90

6.2 Example ....................................................................................91

References ..................................................................................................95


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 (v6.1) And PONDS (v3.2).................................................................D-1

D.1 Input Data...................................................................... D-2

D.2 Comparison of Runoff Hydrographs .................................... D-8

D.3 Comparison of Infiltration Hydrographs............................. D-10

D.4 Comparison of Stage Hydrographs ................................... D-17 Appendix E. A Refined Infiltration Method in ICPR ................................... E-1

1.0 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. 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. 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 1.1.

Figure 1.1 Accessing the New Link Types in ICPR

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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 (e.g., a stage-area node type designated as “Pond” in Figure 1.2) to a groundwater sink (e.g., a time-stage node designated as “Soil Column” in Figure 1.2). 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. 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 1.2 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 1.3. 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. The basics of these methods are discussed in the following section.

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Figure 1.3 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 1.4.

Figure 1.4 Side Bank Filter PercPackTM includes other features like the Green-Ampt method for drainage basins, XML import/export options, and new reporting capabilities.

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2.0 Theoretical Basis 2.1 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 (i.e., vertical sides). 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 2.1. 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 2.1 Schematic for Vertical Percolation from a Pond

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From Darcy’s Law:

q = Ky I (eq. 2.1) 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 + Ψ) / Zf (eq. 2.2) 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 Ψ 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. 2.3) where, F is the effective or fillable porosity Combining equations yields the following differential equation: dZf / dt = (Ky / F) (H + Zf + Ψ) / Zf (eq. 2.4) Letting H’ = H + Ψ and rearranging terms yields: dt = [ F Zf dZf ] / [ Ky (H’ + Zf) ] (eq. 2.5) Eq. 2.5 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. 2.6) Eq. 2.6 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’. Therefore, the percolation rate depends on both the location of the wetting front and depth of water in the pond or trench. The time marching scheme in ICPR calculates the maximum potential infiltration amount, Z0, at any point in time based on the location of the wetting front from the previous time step and the current stage in the pond. If an adequate supply of water is available in the pond, then the potential infiltration can be satisfied completely. Otherwise, an adjustment must be made to Z0 based on the available water in the pond. Once the final infiltration rate is known, it is applied to the area at the surface – soil interface to determine the current discharge rate for the link.

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For an exfiltration trench, the area is the length of the trench multiplied by its width. For percolation links, the user can specify the area. This flow rate then becomes an outflow component for the node it is attached “from” and works the same as any other link with regard to determining the mass balance and change in storage for the node. 2.2 Unsaturated Vertical Flow for Variable Surface Areas The Green-Ampt method described in the previous section cannot be used for applications involving variable surface areas. When the “Surface Area Option” for a percolation link is set to “Vary based on Stage/Area Table” as shown below, then an alternate method to the modified Green-Ampt equation is needed.

ICPR uses the stage-area table provided for the node at the upstream end (i.e., the “from” node) of the link when this option is selected. A surface area is easily obtained for any elevation based on the stage-area table. The potential infiltration rate is calculated by multiplying the current surface area by the vertical conductivity. Water is then transferred from the pond to the soil column. Storage in the unsaturated zone of the soil column depends on how much area is exposed to the wetted surface of the pond, which in turn varies with depth. Consider the three unsaturated soil zones depicted in Figure 2.2. Zone 1 is directly below the bottom of the pond. If the inflow rate of water to the pond is less than the potential infiltration rate, then unsaturated flow would be confined to zone 1 and stages in the pond would not rise above the bottom. As inflow rates increase and exceed the potential infiltration rate, water levels in the pond rise above the bottom of the pond and the surface area expands exposing additional unsaturated areas below the pond. ICPR calculates the available soil storage at every computational time increment, continuously adjusting it as the simulation proceeds. The entire unsaturated zone must be completely filled or saturated before horizontal flow can take place.

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Figure 2.2. Unsaturated Soil Zone Between Pond Bottom and Water Table

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2.3 Saturated Horizontal Flow The saturated horizontal flow algorithm is automatically triggered once the soil column below the pond is saturated (see Figure 2.3). In other words, when the wetting front reaches the water table, vertical flow ceases and horizontal flow commences. This algorithm is applied to both percolation links and exfiltration trenches.

Figure 2.3 Saturated Horizontal Flow Schematic

The computational scheme for horizontal flow in ICPR is similar to that presented by Hull (1983) and as originally proposed by Prickett and Lonnquist (1971 and 1973). However, ICPR uses a quasi two-dimensional formulation instead of a full two-dimensional formulation for ease of implementation and computational speed. It models the outward radial advancement of the groundwater mound away from the pond (or trench). This is accomplished by segmenting the area beyond the edge of the pond into a number of finite difference cells. Water movement from one cell to the next is tracked based on continuity principles and Darcy’s Law as described in this section. Consider the schematic shown in Figure 2.4 with groundwater flow moving horizontally away from the pond. In order for mass to be conserved in the control volume associated with node i, the change in storage must equal the inflow volume to the node minus the outflow volume. This can be expressed as follows:

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Qs = Qin – Qout (eq. 2.7) where, Qs is the change in storage Qin is the inflow to the node control volume Qout is the outflow from the node control volume Darcy’s law (Q = KIA) can be used to calculate flows in an aquifer and letting the gradient I=∆h/∆x yields the following: Q = (Kh) • (I) • (A) = (Kh) • (∆h/∆x) • (∆h∆y) (eq. 2.8) where, Kh is the horizontal conductivity I is the hydraulic gradient A is the cross sectional area of flow ∆h is the change in head ∆x is the length (away from the pond) ∆y is the width of flow Qin and Qout can now be expressed in finite difference form: Qin = (K) • [ (hi-1 – hi) / ∆xi-1 ] • [ hi-1 ∆yi-1 ] (eq. 2.9) Qout = (K) • [ (hi – hi+1) / ∆xi ] • [ hi ∆yi ] (eq. 2.10) The change in storage for a given cell can also be written in differential form as the change in head with respect to time multiplied by the effective surface area of the cell. Qs = [dh/dt] • [F Asurf] (eq. 2.11) where, dh/dt is the change in head with respect to time F is the effective or fillable porosity Asurf is the cell surface area By rearranging terms, equation 2.12 can be written for each differential cell to form a system of equations that must be solved simultaneously. dhi /dt = [Qin – Qout]i / [F • Asurf] = [Qin – Qout]i / [F • ∆yi (∆xi-1+∆xi)/2)] (eq. 2.12)

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Figure 2.4 Schematic of the Computational Framework For Saturated Horizontal Flow

The ambient water table elevation (an input parameter) is used to initialize all heads in the model. The two boundaries for this model are located at the edge of the pond or trench and at the outer edge of the computational grid. These are handled as follows:

1. A fixed head boundary condition is used at the outer edge of the computational grid equal to the ambient water table elevation unless recharge (an input parameter) is applied to the unconfined aquifer. In that case, a zero flow boundary condition is used at the outer edge and the water level there is allowed to fluctuate based on the recharge volumes.

2. A variable head boundary condition based on current stages in the pond or

trench is used at the upper edge of the computation grid to calculate Qin (see eq. 2.9). This is a horizontal flow component. The vertical flow, based on surface area and vertical conductivity, is simultaneously calculated and if the vertical flow is less than the horizontal flow, then Qin is set to the vertical flow.

Also known are all of the heads, h, at the previous time step. Equation 2.12 is solved for head at the interior nodes for the current time step due to changes in stage at the pond or trench and water is transferred from the pond or trench to the adjacent unconfined aquifer. The final percolation rate assigned to the pond is the flux across the interface between the pond or trench and the surrounding unconfined aquifer. As discussed in the following paragraphs, three computational rings are

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required and the flux across the innermost ring (i.e., Qin for the first finite difference cell) becomes the percolation rate for the pond or trench. This one-dimensional finite difference algorithm becomes a quasi two-dimensional scheme by allowing the width, ∆y, to vary with x. In addition to the much faster computational performance of the quasi two-dimensional finite difference algorithm used by ICPR, it has several other advantages. Since the spacing and widths of individual cells can be varied, non-rectangular and irregular pond shapes can be modeled. For percolation links, perimeters must be specified for three “computational rings”, as well as the distance and number of finite difference cells to be used between the rings. For example, consider the circular pond depicted in Figure 2.5 with radius “r1”. The perimeter at the edge of the pond is P1 = 2∏(r1). Therefore, the width, say ∆y1, at the edge of the pond is equal to P1. If an outer concentric ring with radius “r2” is placed beyond the pond’s edge for computational purposes, its perimeter would be P2 = 2∏(r2) and correspondingly its width, say ∆y2, would be equal to P2. The distance between the two rings is ∆x12 = r2 – r1. Now imagine groundwater flowing horizontally from the pond’s edge in a radial direction outward away from the pond. From a computational standpoint, the distance ∆x12 could be further divided into a number of concentric rings each a distance ∆x = (∆x12/n) apart, where n is the number of cells. The width of each cell, ∆y, would expand proportionally from ∆y1 to ∆y2.

Figure 2.5 Circular Pond Schematic with Two Concentric

Outer Computational Rings

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This concept is easily applied to other pond configurations. Three perimeter lengths (P1, P2 and P3) must be specified. P1 is located at the edge of the pond, or better said, at the edge of the unsaturated vertical flow zone. The other two can be placed anywhere beyond the first one, but far enough away from the pond to allow the groundwater mound to dissipate into the ambient water table. All points along a given outer perimeter must be offset an equal distance from the first perimeter. In addition to the three perimeter lengths, the distances from P1 to P2 and from P2 to P3 must be specified. These do not have to be equal. As a matter of fact, the distance from P1 to P2 is typically less than P2 to P3. Also, the number of computational cells between P1 and P2 and between P2 and P3 must be specified. 2.4 Soil Storage Recovery and Aquifer Recharge As water enters a pond (or trench), the wetting front advances vertically downward through the unsaturated zone. If the potential infiltration rate exceeds the inflow rate to the pond, then all water will percolate downward and the stages in the pond will not build up. However, when the inflow rates exceed the potential infiltration rates, then stages increase in the pond. As soon as the supply is exhausted (i.e., the moment the pond becomes dry) then a queuing period ensues whereby the water in the soil column is held for a period of time equal to the travel time from the edge of the wetting front down to the current water table position. If additional water comes into the pond during this queuing period, then it is considered part of the original event and infiltration proceeds as it did before. If no other water enters the pond during the queuing period, then the water in the unsaturated zone (i.e., from the bottom of the pond to the edge of the wetting front) is transferred to the water table directly below the pond and is factored into the horizontal flow computations. Leaky unconfined aquifers can also be modeled with the use of an annual recharge rate (an input parameter). Water is removed from or added to the unconfined aquifer depending on the sign of the recharge rate. Positive values remove water from the unconfined aquifer (and send it o the deep aquifer) and negative values add water to the unconfined aquifer. The user specified annual rate is in inches per year. This annual recharge rate is also subtracted or added from the water table at each finite difference cell and at every time step in the simulation. If the annual recharge rate is something other than zero, then a zero flow boundary condition is used at the outer edge of the computational grid as explained in the previous section. If the annual recharge rate is set to zero, then a fixed head boundary condition equal to the ambient water table is used. A time variable recharge rate can also be applied to the unconfined aquifer by setting the annual recharge rate to –9999. This is a trigger that tells ICPR to use the time-stage relationship at the downstream node for the percolation or exfiltration link to determine recharge rates. This feature is most applicable to long term simulations that cross over wet and dry seasons. As an example, assume that the water table begins the rainy season on June 1 at its lowest point and then rises 4 feet by August 31 (92 days or 2,208 hours). It then stays at the seasonal high for two more months (61 days or 1,464 hours) before receding gradually back to the seasonal low on May 31 (212 days later or 5,088 hours). The time-stage relationship would be:

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Time Stage -hrs- -ft-

0 0 2,208 4 3,672 4 8,760 0

Although depths are used above, actual elevations could also be used. Recharge rates at any point in time are based on differential stages from one time step to the next. For example, the water table rises 4 feet in 92 days. For a porosity of 0.25, the recharge rate during this period is –4 x 0.25 / 92 = -0.01087 fpd. The negative value is used for inflow to the unconfined aquifer. A detailed example using this feature can be found in Section 4.2.5. 2.5 Green-Ampt Method for Drainage Basins PercPackTM includes the Green-Ampt rainfall excess method as an option with either the SCS Unit Hydrograph Method or the Santa Barbara Urban Hydrograph Method. Furthermore, a drainage basin can be segmented into multiple “sub-basins” or “sub-catchments”. There is no practical limit as to the number of sub-basins that can be used for a given basin, but at least one sub-basin must be specified. ICPR calculates the rainfall excess from each sub-basin independently and then sums them up to obtain the total rainfall excess for the entire basin. The time of concentration and unit hydrograph (or Santa Barbara method) are applied to the total rainfall excess rather than to each individual sub-basin. Rainfall excess for each sub-basin is calculated in 3 parts:

1. Rain falling on directly connected impervious areas (DCIA). After subtracting an initial abstraction of 0.1” for each independent rainfall event, 100% runoff occurs from the DCIAs.

2. Impervious areas that are not directly connected are assumed to drain onto

pervious areas. This area is equal to the % impervious minus the % DCIA. Like DCIA, 0.1” is subtracted from each independent rainfall event for initial abstraction.

3. The Green-Ampt equation (refer to equation 2.6) is used to determine

infiltration rates for pervious areas. Rainfall excess is the amount of rainfall plus flow from impervious areas draining onto pervious areas minus the amount of infiltration. If the wetting front, as calculated by the Green-Ampt method, reaches the “cutoff depth” (an input parameter), then infiltration ends.

Soil Storage Recovery: For long term or multi-event simulations, it is important to be able to recover soil storage and to determine if a particular rainfall event is independent of the previous event. The location of the wetting front is tracked continuously with the Green-Ampt method. If precipitation ceases, then a queuing

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time is calculated equal to the effective porosity times the thickness of the saturated zone divided by the conductivity. This is an estimate of how long it would take for the saturated zone to drain to field capacity. If no rainfall occurs during that period, then the soil column is evacuated and infiltration can begin again as an independent event. If rainfall occurs during the queuing period, then the queue time is reset to zero and infiltration is calculated as if no delay occurred. 2.6 Exfiltration Trenches There are two key components to an exfiltration trench: storage in the trench and groundwater flow from the trench. Pipe hydraulics are not included with exfiltration trench links. However, they can be modeled by combining standard pipe links with exfiltration links as is described in section 5.4.2 of this document. Storage in the trench is straightforward. The key input parameters are: (1) trench bottom elevation, length, width and height; (2) pipe size and invert elevation; and, (3) gravel porosity. From these, a wetted surface area is easily calculated at any depth by the following equation: Atrench = L x [(Wt - Wp)x Fg + Wp] (eq. 2.13) where, Atrench is the wetted surface area in the trench L is the trench length (input parameter) Wt is the trench width (input parameter) Wp is the width of pipe at the current water depth Fg is the porosity of the gravel (input parameter) As already discussed, unsaturated vertical and saturated horizontal groundwater flow are both calculated for exfiltration trenches. The Green-Ampt method described in section 2.1 is used for unsaturated flow. The saturated horizontal groundwater flow algorithm used for exfiltration trenches is based on the finite difference scheme described in section 2.3. A computational grid must to be established. In addition to the trench length, there are 3 parameters that are used to establish the grid as described below: Cell Spacing: The cell spacing is the distance outwardly perpendicular to the trench for each finite difference computational cell. A typical value for this parameter is 5 feet, but can be smaller or larger if warranted. Number of Cells: This parameter provides the total number of finite difference computational cells to be used for saturated horizontal groundwater flow. The total distance away from the edge of the exfiltration trench is equal to the cell spacing multiplied by the number of cells. For example, if the cell spacing is 5 feet and the number of cells is 50, then the total distance away from the edge of the trench is 250 feet. The fixed head boundary condition equal to the ambient water table elevation would be applied at the 250 feet location in this example. The objective is to place the outer boundary far enough away from the trench so that it’s influence is minimal. Basically, water moving away from the trench will dissipate into the water table. In most typical applications, this might be between 200 and 400 feet.

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End Treatment: Typically, exfiltration trenches are much longer than they are wide and little or no flow would be expected out of the ends of the trenches. For situations like this, the end treatment option should be set to “Exclude”. However, the “Include” option can be used if the trench is relatively short and significant flow is expected through the ends. From a computational standpoint, if the ends are excluded, then the “width” (y) of each computational finite difference cell remains constant regardless of the distance from the edge of the trench. This “width” (y) would be equal to twice the length of the trench since water would flow from both sides of the trench. y = 2 x L (exclude ends) (eq. 2.14) If the ends are included, then the computational “width” expands as flow progresses outward from the trench. The following equation is used to compute the computational width (y) y = 2 x L + 2∏d (include ends) (eq. 2.15) where, d is the distance from the edge of the trench 2.7 Filter Hydraulics Like many groundwater flow applications, Darcy’s equation is used to calculate flow through filters. Q = (K) • (I) • (A) = (K) • (∆h/∆x) • (A) (eq. 2.16) where, K is the conductivity or permeability of the filter media I is the hydraulic gradient A is the cross sectional area of flow ∆h is the change in head ∆x is the average distance through the filter media The challenge in applying Darcy’s equation to filters is determining the appropriate values of A, ∆h, and ∆x. The methods vary somewhat depending on whether the filter is placed in the side bank or on the bottom of the pond. Each is discussed below. Side Bank Filters: Based on the geometric input parameters for a side bank filter, ICPR builds a computational framework similar to that depicted in Figure 2.6. A line is projected from the bottom surface edge of the filter and tangent to the outer edge of the pipe (designated as “Tangent 1” in the figure). A second line is projected from the upper surface edge of the filter and tangent to the outer edge of the pipe (designated as “Tangent 2” in the figure). These two tangent lines intersect behind the pipe and the intersection point becomes the center of an arc that swings from

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the lower surface edge of the filter to the upper surface edge of the filter. As water levels increase in the pond, more of the filter media is exposed. The filter media extends from the surface at the pond down to the edge of the gravel envelope. When the water level in the pond is at or below Z2, water can only seep through the left side of the gravel envelope. Water levels above Z2 can seep through both the left face and top face of the gravel. ICPR applies Darcy’s equation separately to the left and top faces of the gravel, depending on water levels in the pond. When the water level in the pond is at or below Z2, ∆x is calculated by passing three flow lines from the pond to the tangent intersection point. The first is always the lower tangent line (Tangent 1). The second is a line connecting the tangent intersection point to a point on the surface where the water intersects the filter media. The third flow line connects the tangent intersection point with a point on the surface at an elevation halfway between the current water level and the bottom edge of the filter. The lengths of three lines between the surface and the left face of the gravel envelope are determined and then averaged. This average length is then used as ∆x in Darcy’s equation. A similar approach is used for the upper face of the gravel envelope when the water level in the pond exceeds Z2. The average cross sectional area is determined by taking the cross sectional area of the filter media in the “seepage trapezoid” and dividing it by the average seepage length, ∆x. For example, if the water level in the pond is at or above Z3, then areas A1 and A2 as shown in Figure 2.6 would be divided by the average flow lengths, ∆x1 and ∆x2. The change in head, ∆hleft, for the left face of the gravel envelope is set as difference between the water surface elevation in the pond minus the elevation at the point where the “third” flow line described previously intersects the gravel envelope or the downstream tailwater condition, whichever is higher. The change in head, ∆htop, for the top face of the gravel envelope is set as difference between the water surface elevation in the pond minus the elevation of the top face of the gravel envelope or the downstream tailwater condition, whichever is higher.

Figure 2.6 Side Bank Filter Schematic

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Bottom Filters: A schematic of a bottom filter is depicted in Figure 2.7. ICPR assumes that the gravel envelope is placed in native soils and that select filter media is placed on top of the gravel envelope. A “seepage trapezoid” is formed from the outer edges of the filter media at the surface to the top corners of the gravel envelope as shown. No seepage is permitted through the sides of the gravel envelope. The average flow length, ∆x, is the average of three seepage lines (designated L1, L2 and L3 in Figure 2.8) through the filter media from the surface to the top face of the gravel envelope. The average seepage cross sectional area of flow, A, is the area of the seepage trapezoid divided by the average seepage length, ∆x. The change in head, ∆h, is the difference in elevations between the water level in the pond and the top face of the gravel envelope or the tailwater elevation if it’s higher than the gravel envelope.

Figure 2.7 Bottom Filter Schematic

Figure 2.8 Seepage Lines for Bottom Filter

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3.0 Input Parameters for Green-Ampt Rainfall Excess Option Rainfall excess for drainage basins can be by the Green-Ampt method (refer to section 2.5 and 2.1 for details of the Green-Ampt method) when using either the SCS Unit Hydrograph Method or the Santa Barbara Urban Hydrograph Method (SBUH). It is invoked by setting the “Type” field to either “SCS Unit Hydrograph GA” or “Santa Barbara GA” as shown in Figure 3.1.

Figure 3.1 Basin Data Form for the Green-Ampt Rainfall Excess Mehtod When using the Green-Ampt rainfall excess method, a drainage basin can be segmented into multiple “sub-basins” or “sub-catchments”. There is no practical limit as to the number of sub-basins that can be used for a given basin, but at least one sub-basin must be specified. ICPR calculates the rainfall excess from each sub-basin independently and then sums them up to obtain the total rainfall excess for the entire basin. The time of concentration and unit hydrograph (or Santa Barbara method) is applied to the total rainfall excess rather than to each individual sub-basin. Each of the input parameters are described below. Typical Green-Ampt parameters can be found in Table 3.1.

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Area (acres or hectares): Each sub-basin must be assigned its own area. % Impervious (percentage): The % Impervious is the total amount of impervious area within a sub-basin (not the total drainage basin area). This parameter can be set to zero for sub-basins with no impervious area. It should never be less than zero or greater than 100. Furthermore, the % Impervious parameter should never be less than the % DCIA. % DCIA (percentage): The DCIA ("directly connected impervious area") is the impervious area within a basin that is hydraulically connected to the discharge point. For example, if a paved road in a sub-division drains by way of curb and gutter into a storm sewer system, then the roadway would be considered a DCIA. Furthermore, if paved driveways and a portion of the roofs drain directly into the roadways without passing over pervious areas, then they would also be considered part of the DCIA. However, if a portion of the roofs drain onto the lawn, then that portion would not be considered DCIA even though they are impervious. The DCIA is expressed as the percentage of the sub-basin area. For example, if the area of a sub-basin is 40 acres and the DCIA is set to 25, then 10 acres (i.e., 25% of the 40 acres) would be DCIA. The % DCIA is applied only to the sub-basin and not to the total drainage basin. This parameter can be set to zero for sub-basins with no DCIAs. It should never be less than zero or greater than 100 and it should never be greater than the “% Impervious”. Cutoff Depth (feet or meters): The Green-Ampt method in ICPR is used to track an advancing saturated wetting front through an unsaturated zone in the soil column. When the wetting front reaches a depth equal the cutoff depth, infiltration ceases and 100% runoff occurs. The cutoff depth is often set to the depth to the seasonal high water table. However, it can also be set to the depth of a hydraulically restrictive layer. If infiltration should continue regardless of the location of the wetting front, then set this parameter to a large number (e.g., 999 feet). Hydraulic Conductivity (feet or meters per day): The hydraulic conductivity is the vertical permeability of the soil. Bouwer (“Groundwater Hydrology”, McGraw-Hill, 1978, page 45) suggests reducing measured saturated vertical conductivities by 50% to account for air entrapment. Hydraulic conductivity (K) can vary significantly depending on site-specific conditions. Effective Porosity (decimal): The effective porosity (a decimal value between 0 and 1) is the fractional amount of moisture that can be stored in the soil column at the onset of infiltration. It is the porosity of the soil minus the initial soil moisture or residual moisture and is often termed “fillable porosity”. Wetting Front Suction Head (inches or centimeters): Suction head is a capillary effect. The drier and finer textured the soil, the greater the suction.

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Table 3.1 Typical Green-Ampt Parameters Based on Soil Class

Effective Porosity

Wetting Front Suction Head

Saturated Hydraulic Conductivity

Soil Class (decimal) (inches) (centimeters) (feet/day) (meters/day)

Sand 0.417 4.17 10.6 16.5362 5.0400

Loamy Sand 0.402 5.59 14.2 4.8113 1.4664

Sandy Loam 0.412 8.74 22.2 2.0395 0.6216

Loam 0.436 12.40 31.5 1.0394 0.3168

Silt Loam 0.486 15.91 40.4 0.5355 0.1632

Sandy Clay Loam 0.330 17.68 44.9 0.3386 0.1032

Clay Loam 0.389 17.56 44.6 0.1811 0.0552

Silty Clay Loam 0.431 22.87 58.1 0.1181 0.0360

Sandy Clay 0.321 25.04 63.6 0.0945 0.0288

Silty Clay 0.423 25.47 64.7 0.0709 0.0216

Clay 0.385 28.11 71.4 0.0472 0.0144

Source: U.S. Army Corps of Engineers, EM 1110-2-1417, August 31, 1994 (Table 6-2)

Notes: (1) Parameters in this table were originally published by Rawls and Brakensiek, 1982

and Rawls, Brakensiek, and Saxton, 1982.

(2) The effective porosities presented in this table were derived by subtracting mean residual

saturation from mean total porosity.

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4.0 Percolation Links The percolation link data form is accessed from the Routing pull down menu as shown in Figure 4.1. Percolation links can be used for a number of applications including recovery of storage in ponds, estimates of drawdown times, and base flow estimates among others.

Figure 4.1 Accessing the Percolation Link Data Form For example, a percolation link can be used to connect a pond node (e.g., Pond 2) to an unconfined aquifer or groundwater sink (e.g., GW_Sink) as shown on the data form in Figure 4.2. Node “Pond 2” is a typical stage-area (or stage-volume) node type and “GW_Sink” is a time-stage node type. The percolation link is completely independent of “GW_Sink” in that the time-stage data specified for it are not used for any hydraulic calculations associated with the percolation link. Multiple percolation links can be attached to “GW_Sink” and the “Total Inflow” to node “GW_Sink” is the sum of all links connected to it. 4.1 Options and Input Parameters for Percolation Links A typical data form for percolation links is shown in Figure 4.2. There are a few options associated with percolation links that must be set and data requirements change somewhat depending on the option that is selected. Specific input parameters for percolation links are described in this section.

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Figure 4.2 Typical ICPR Percolation Link Data Form Surface Area Option: The surface area option controls how unsaturated vertical flow computations are to proceed. There are three options for setting the surface area as indicated Figure 4.3. The first option (“Use 1st Point in Stage/Area Table”) and third option (“User Specified”) hold the surface area to a constant value relative to unsaturated vertical flow computations. The modified Green-Ampt method as described in section 2.1 is used for these two cases. The second option (“Vary based on Stage/Area Table”) varies the surface area with water levels in the pond based on the user provided stage-area table. However, the modified Green-Ampt method is not applicable for this situation and unsaturated vertical flow is calculated by multiplying the current surface area by the vertical conductivity as described in section 2.2.

Figure 4.3 Surface Area Options for Percolation Links

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The “Use 1st Point in Stage/Area Table” option will automatically extract the first value from the stage-area table at the “from node” for the percolation link and the bottom elevation and corresponding surface area are set accordingly.

The second option, “Vary based on Stage/Area Table”, uses the first elevation in the stage-area table as the bottom elevation, but, as previously mentioned, it will vary the surface area (relative to unsaturated flow calculations) based on water levels in the pond. This is the typical setting for most applications. The last option, “User Specified”, allows the user to set both the pond bottom elevation and the surface area to be used for unsaturated vertical flow computations. This option is used for special situations. For example, if a portion of the pond has a partial impermeable lining, then this option can be used for the non-lined portion of the pond. Also, a refined infiltration method as described in Appendix E of this document can be implemented by stair-stepping multiple percolation links along the side slopes of a pond. The “User Specified” surface area option must be used in this case. Bottom Elevation (feet or meters above datum): As mentioned above, if the surface area option is set to “User Specified”, then a bottom elevation is required (see Figure 4.4). This is the elevation at the interface between the surface and the soil column. The head used in the modified Green-Ampt equation is calculated as the water level in the pond minus this bottom elevation. Surface Area (acres or hectares): The modified Green-Ampt equation used for vertical flow computations results in an infiltration rate (fps or mps). The rate is then applied to this “surface area” to arrive at a flow rate (cfs or cms).

Figure 4.4 Bottom Elevation and Surface Area Settings

Vertical Flow Termination: Once the wetting front associated with unsaturated vertical flow reaches either the water table or the “Layer Thickness”, whichever is closer, vertical flow is shut off and percolation can continue (or not) in three ways as shown in Figure 4.5. Typically, groundwater flow transitions to horizontal saturated flow and the “Horizontal Flow Algorithm” should be selected for this option.

Figure 4.5 Vertical Flow Termination Options

However, there may be situations when horizontal flow is either not appropriate or not desired. The other two options include a user specified constant rate in feet (or meters) per day (note: this can be set to zero to stop infiltration completely). The other option is to set the final infiltration rate as a percentage of the rate when the wetting front reaches the water table (or layer thickness).

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Aquifer Base Elevation (feet or meters above datum): This is the elevation of the hydraulically restrictive layer or impermeable layer at the base of the unconfined aquifer (see Figure 4.6). Water Table Elevation (feet or meters above datum): This parameter is used to set the initial heads for each of the finite difference computational cells. It also serves as a fixed head boundary condition at the outer edges of the computational grid when the annual recharge rate is set to zero. If the ambient water table elevation is located above the pond bottom and there is another outlet for the pond such as a weir overflow, then groundwater levels will eventually move toward this lower elevation. Base flow calculations are modeled this way. This parameter is typically set to the seasonal high water table for single event modeling. However, for long term or multi-event modeling (e.g., a year-long simulation), it might be better to start the simulations in the drier months and set the water table to a seasonal low rather than high. Annual Recharge Rate (inches or centimeters per year): For single event modeling, this parameter is typically set to zero. If it is set to zero, then the ambient water table becomes a fixed head boundary condition at the outer edge of the computational grid.

Figure 4.6 Schematic of the Unconfined Aquifer The annual recharge rate can be set to either a positive value to remove water from the unconfined aquifer or to a negative value to add water to it. It is treated as a constant steady-state flow. Another option is to set it to –9999, which serves as a trigger for ICPR to base the recharge rate on the time-stage table used at the downstream node of the link (i.e., the “to node”). A detailed example of this feature is explained in Section 4.2.5. It is also described in Section 2.4.

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Horizontal Conductivity (feet or meters per day): The average soil permeability in the horizontal direction. This parameter is used for the saturated horizontal flow computations. If you want to apply a factor of safety, you should do so by reducing the conductivity accordingly. Site-specific soils testing should be conducted to determine this parameter. Vertical Conductivity (feet or meters per day): The average soil permeability in the vertical direction. This parameter is used for the unsaturated vertical flow computations. If you want to apply a factor of safety, you should do so by reducing the conductivity accordingly. Site-specific soils testing should be conducted to determine this parameter. Effective Porosity (decimal): The effective porosity (a decimal value between 0 and 1) is the fractional amount of moisture that can be stored in the soil column at the onset of infiltration. It is the porosity of the soil minus the initial moisture or residual moisture and is often referred to as the “fillable porosity”. Site-specific soils testing should be done to determine this parameter. Suction Head (inches or centimeters): This is the wetting front suction head. Refer to Table 3.1 for typical values by soil class. Layer Thickness (feet or meters): Typically, this parameter can be set as the distance between the bottom of the pond and the ambient water table elevation (see Figure 4.6). However, some options are available to you, depending on what your objectives are. For example, if you want to model slug flow (a case where the pond is assumed to be instantly filled to some pre-determined level), then it is likely that the soil column directly below the pond is fully saturated yet the ambient water table might be well below the pond. In this case, if you set the layer thickness to zero and the water table to its seasonal high level, unsaturated flow cannot occur and ICPR proceeds directly to the horizontal flow computations. While the ambient water table can be thought of as a fixed head boundary condition on the edge of the outer computational ring (for the no recharge scenario), the bottom elevation minus the layer thickness can be thought of as an initial water table elevation directly below the pond. Another scenario for setting the layer thickness to something different that the distance to the water might be where a deep water table exists (say, 50 feet below the surface), but it is desired for the unsaturated vertical flow computations to cease at say 10 feet. In that case, the layer thickness would be set to 10 feet and the water table to 50 feet below the surface. Perimeters, Distances and Cells: Three perimeter lengths (P1, P2 and P3) must be specified for saturated horizontal flow computations. P1 is located at the edge of the pond, or better said, at the edge of the unsaturated vertical flow zone. The other two can be placed anywhere beyond the first one, but far enough away from the pond to allow the groundwater mound to dissipate into the ambient water table. All points along a given outer perimeter must be offset an equal distance from the first perimeter.

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In addition to the three perimeter lengths, the distances from P1 to P2 and from P2 to P3 must be specified. These do not have to be equal. As a matter of fact, the distance from P1 to P2 is typically less than P2 to P3. Also, the number of computational cells between P1 and P2 and between P2 and P3 must be specified. Irregular Shaped Ponds: Consider the percolation pond depicted in Figure 4.7. The bottom is at approximately elevation 78 feet. As water fills the pond, the surface area expands. Assume that the water level in the pond reaches approximately elevation 83 feet and lingers there long enough to saturate the soils beneath it down to the water table. Now imagine a cylinder passing through the pond down to the base of the aquifer with a cross sectional area equal to the surface area of the pond at elevation 83 feet. Saturated horizontal groundwater flow is perpendicular to this cylinder and would move outward away from the pond. The perimeter around this cylinder becomes the first of the three required computational rings. The second ring is offset an equal distance from the first and the third ring is offset an equal distance from the second, similar to that shown in Figure 4.7. Perimeters for each are measured and become input for the model. In this example, P1, P2 and P3 are 335 feet, 960 feet and 3780 feet, respectively. The offset distance between P1 and P2 is 50 feet and 450 feet between P2 and P3. Typically, the second ring is placed between 50 and 100 feet from the first and the third ring is usually 500 to 1000 feet from the first. The objective is to place the outermost ring far enough away so that water moving outward from the pond can dissipate into the ambient water table. The last thing that needs to be done is to set the number of computational cells between adjacent rings. Typically, a 5-foot spacing works well between the first two rings and then a 10-foot spacing between the second third rings. Therefore, the number of cells should be 10 and 45 from P1 to P2 and from P2 to P3, respectively. The data form is shown in Figure 4.8.

Figure 4.7 Computational Rings for Percolation Pond

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Figure 4.8 Perimeter, Distance and Cell Settings Rectangular Ponds: Since rectangular ponds are used frequently in stormwater design, it is worth mentioning how perimeters are established for them. Let’s say we have a 200-foot by 100-foot rectangular pond. The first perimeter is set to P1=600 feet (2x200 + 2x100). Now offset the second perimeter 100 feet away from the first. If another rectangle is simply offset 100 feet from the first, a perimeter of 1,400 feet ( 2 x (200 + 100 + 100) + 2 x (100 + 100 + 100)) is calculated. However, this would be incorrect because in order to be equidistant from the first rectangle, a corner radius must be applied. Therefore, the second perimeter would be P2 = 600 + 2∏(100) = 1,228 feet. Therefore, for rectangles, the following applies: P1 = 2(L + W) P2 = P1 + 2∏(x1-2) P3 = P1 + 2∏(x1-2 + x2-3) The rectangular pond concept is depicted in Figure 4.9. Notice that the shape begins to look more circular the farther away from the original rectangular pond.

Figure 4.9 Computational Rings for a Rectangular Pond

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Circular Ponds: Many natural depressions can be approximated with circular geometry. An inner radius (say “r1”) can be estimated by dividing the surface area at the desired elevation by 2∏. Once “r1” is known, P1 can be determined from P1 = 2∏(r1). If an outer concentric ring with radius “r2” (see Figure 4.10) is placed beyond the pond’s edge for computational purposes, its perimeter is P2 = 2∏(r2). The distance between the two rings is ∆x1-2 = r2 – r1. P3 and ∆x2-3 are determined in a similar manner.

Figure 4.10 Circular Pond Schematic with Two Concentric Outer Computational Rings

4.2 Examples A detailed example of a closed retention system with percolation as the only outfall is presented in Appendix D. Also, a refined infiltration method is presented in Appendix E for the same retention system. This section covers numerous other examples including slug loads and pollution abatement recovery, multiple ponds in close proximity, ponds in close proximity to a ditch, percolation from a swale, estimates of base flow, and a radius of influence calculation. 4.2.1 Slug Loads and Pollution Abatement Recovery Stormwater retention ponds are often used for pollution abatement. A certain volume of water, based on features of the drainage basin, is required to be held in a pond and percolated into the soil column. Typically, the pollution abatement volume

31


must be recovered within a stipulated time frame (e.g., 72 hours). The calculations proceed by assuming that the water level in the pond is equal to the pollution abatement level. This approach is referred to as a “slug load”. Then draw down calculations are performed to determine the length of time required to fully recover the pollution abatement storage. Recovery in retention ponds from slug loads can be easily performed in ICPR using percolation links. Although it is possible to model unsaturated vertical flow, it is unreasonable to assume that the pollution abatement volume can instantly fill the pond without some percolation taking place. The approach presented here assumes that the recovery will take place well after the soil column below the pond has been saturated and after all other inflows to the pond have ceased including runoff from the drainage basin. The setup for this type of problem is similar to most other percolation problems. Two nodes are required, one representing the pond and the other representing the groundwater table. A stage-area or stage-volume node is used for the pond and a stage-time node is used for the groundwater table. These two nodes are connected together with a percolation link. The parameters are set as normal except for two things as shown in Figure 4.11.

1. The layer thickness for the percolation link must be set to zero. This will force the soil column between the bottom of the pond and the ambient water table to be fully saturated at the onset of the simulation.

2. The initial stage in the pond should be set at the required pollution

abatement level.

Figure 4.11 Modeling Slug Loads in ICPR

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To illustrate how this works, an example is used from the St. Johns River Water Management District Applicant’s Handbook, Section 26.5. In that example, a pollution abatement volume of 6,807 cubic feet is stored in a small retention pond between the bottom (elevation 20.0 feet) and the overflow structure (21.22 feet). Rather than repeat all of the input data in tables, the corresponding ICPR data forms are provided in Figures 4.12, 4.13 and 4.14. Also, the pertinent parameters in the routing control data form are provided in Figure 4.15. Note in Figure 4.13 that the initial stage is set to elevation 21.22, the pollution abatement level and that the layer thickness is set to zero in the percolation link data form (Figure 4.14). Also notice that the “Hydrology Sim” data field in the routing control data form is left blank since a draw down analysis is to be performed after all runoff has occurred.

Figure 4.12 The Nodal Network

Figure 4.13 Excerpts from the Node Data Forms

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Figure 4.14 Excerpt from the Percolation Link Data Form

Figure 4.15 Excerpt from the Routing Control Data Form There are numerous reports in ICPR that could be reviewed to evaluate the timing of full recovery of the pollution abatement volume. For example, the mass balance report indicates that 6,803 cubic feet of water (slightly less than the 6,807 due to interpolation differences) has left the system at hour 48.52 as shown in Figure 4.16.

Figure 4.16 Excerpt from the Mass Balance Report

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It is interesting to note that in the original SJRWMD example, hand calculations indicated that 53 hours is needed to recover the storage, which is inline with the ICPR calculations. A stage-time graph can be plotted for the node as shown in Figure 4.17 and the groundwater mounding impacts can be assessed as shown in Figure 4.18.

Figure 4.17 Pond Recovery from Slug Load

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Figure 4.18 Groundwater Mounding Impact

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4.2.2 Ditch in Close Proximity to a Pond Ponds are often located near ditches as shown in Figure 4.19. The ditch can be controlled lower than the adjacent ambient water table and potentially impact the water table immediately below the pond. This scenario can be modeled in ICPR by creating two separate percolation links. The first link, say Perc-A, connects the pond to the ambient water table away from the ditch. The second link, say Perc-B, connects the pond to the water table impacted by the ditch.

Figure 4.19 Cross Section of Pond in Close Proximity to Ditch

Although not a requisite, if the basic soil properties are assumed to be the same for both percolation links, then there are three other primary considerations with regard to the input parameters for each link that must be addressed:

1. Distributing the surface area of the pond available for infiltration to each link. 2. Setting the water table elevation and the layer thickness parameters. 3. Setting the computational perimeters and distances.

For discussion purposes, assume that the pond has an average surface area of 1 acre and that the length to width ratio is 2 to 1. The average length and width of the pond would then be 295.2 feet and 147.6 feet, respectively. The “Surface Area Option” for both percolation links should be set to “User Specified” and the “Bottom Elevation” for both links should be set to elevation 26 feet. The surface area must be split between the two links. This will impact unsaturated vertical flow computations mostly, but could also impact the saturated horizontal flow component somewhat. Consider the sketch shown in Figure 4.20. Most of the groundwater flow from the pond to the ditch occurs along the face of the pond nearest to the ditch. As the flow progresses toward the ditch, it will expand in width. Assuming a 45-degree angle of expansion, and then projecting it backward to the center of the pond, the surface area associated with each link can be calculated. In this example, the ratio is 0.375 toward the ditch and 0.625 away from the ditch.

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Therefore, the corresponding surface areas for Perc-A and Perc-B are 0.625 acres and 0.375 acres, respectively. The “Vertical Flow Termination” option should be set to “Horizontal Flow” for both links. The water table elevation for Perc-A should be set to the ambient water table elevation of 23 feet and serve as a fixed head boundary condition at the outer computational ring. Flow through this link will seep away from the ditch and blend into the ambient water table. The water table elevation for Perc-B should be set to the ditch control elevation, 20 feet. The layer thickness for Perc-A should be the distance between the bottom of the pond and the ambient water table. Doing so assumes that the ambient water table extends under the pond – at least for that portion of the pond away from the ditch. A decision has to be made regarding the layer thickness on the other side of the pond. If a value of 6 feet is used (i.e., the distance between the pond bottom and the ditch control elevation), then the full affect of the ditch will be “felt” at the pond. This probably would not occur. Setting it to 4.5 feet splits the difference between the water level in the ditch and the ambient water table.

Figure 4.20 Adjustments to Computational Rings for Pond in Close Proximity to Ditch

The last thing to consider is the computational perimeters and distances for each percolation link. Consider the schematic again in Figure 4.20. Perimeters P1a, P2a and P3a should be used for Perc-A and P1b, P2b and P3b should be used for Perc-B. Let the distance xA

1-2 from P1a to P2a be 100 feet and let the distance xA2-3 from P2a

to P3a be 900 feet. The perimeters for Perc-A are as follows:

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P1a = 2W + L = 2(147.6) + 295.2 = 590.4 feet P2a = P1a + ∏(xA

1-2) = 590.4 + ∏(100) = 904.5 feet P3a = P1a + ∏(xA

1-2 + xA2-3) = 590.4 + ∏(1000) = 3,732.0 feet

Now let the distance xB

1-2 from P1b to P2b be 100 feet and let the distance xB2-3 from

P2b to P3b be 50 feet (the remaining distance to the ditch). The perimeters for Perc-B are as follows: P1b = L = 295.2 feet P2b = P1b + ∏(xB

1-2)/2 = 295.2 + ∏(100)/2 = 452.3 feet P3b = P1b + ∏(xB

1-2 + xB2-3)/2 = 295.2 + ∏(75) = 530.8 feet

The ICPR nodal network for this example is shown in Figure 4.21. A single 11-acre drainage basin called “Catchment” drains into the pond. The pond has two links leaving it, Perc-A and Perc-B as already described. Input data forms for basin “Catchment”, node “Pond” and links “Perc-A” and “Perc-B” are provided in Figures 4.22 through 4.25. The SCS Type II Florida Modified (Flmod) rainfall distribution is used with 8.6 inches of rain over a 24-hour period. The resulting stage-hydrograph for the pond is shown in Figure 4.26. The peak stage is 29.5 feet, 3.5 feet above the bottom of the pond. The runoff hydrograph into the pond along with the total infiltration from the pond (the sum of links Perc-A and Perc-B) are depicted in Figure 4.27. A maximum combined infiltration rate of about 5 cfs occurs. The individual infiltration hydrographs are shown in Figure 4.28. Although more water overall is seeping outward away from the ditch and blending back into the ambient water table, a substantial amount of water is flowing toward the ditch. The groundwater mounding impacts both away from the ditch to the ambient water table and toward the ditch are presented in Figures 4.29 and 4.30.

Figure 4.21 Network Schematic

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Figure 4.22 Basin Data Form

Figure 4.23 Node Data Form for Pond

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Figure 4.24 Percolation Link Data Form (Connected to Water Table Away From Ditch)

Figure 4.25 Percolation Link Data Form (Connected to Water Table Toward Ditch)

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Figure 4.26 Stage Hydrograph for Pond

Figure 4.27 Inflow-Outflow Hydrographs for Pond

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Figure 4.28 Infiltration Hydrographs for Individual Percolation Links

Figure 4.29 Groundwater Mounding Impact Away From Ditch

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Figure 4.30 Groundwater Mounding Impact Toward Ditch

4.2.3 Multiple Ponds in Close Proximity Hydraulically speaking, percolation links act independent of one another. Therefore, when ponds are in close proximity, some adjustments are needed for computational perimeters. For example, consider the two rectangular ponds depicted in Figure 4.31 along with the computational rings associated with each pond. Since the computational rings for each pond are separated, no adjustments are required.

Figure 4.31 Two Independent Ponds

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Now consider Figure 4.32 where the two ponds are in close proximity to one another. Since each pond has its own independent percolation link connecting it to the unconfined aquifer, an adjustment to the computational rings is necessary to account for the influence of one on the other. If an adjustment is not made to the three perimeters for both links, percolation from each pond will be over predicted.

Figure 4.32 Two Ponds in Close Proximity with Overlapping Computational Rings

The computational rings for the two individual ponds must be blended together as shown in Figure 4.33. Once they are blended together, the perimeters must be divided along an axis that separates the two ponds. For example, if P2 and P3 represent the total perimeter length for the outer two computational rings, then they should be split equally in this case between Pond 1 and Pond 2 since they are symmetrical and of equal size. If one pond were larger than the other, then appropriate adjustments would have to be made. The innermost perimeter, P1, for each pond must be adjusted as well. P1 should exclude the common edge between the two ponds. In other words, P1 = 2L + W. If both ponds were allowed to flow across this common boundary, a double accounting would take place. This is equivalent to passing an impermeable wall between the two ponds downward to the base of the aquifer.

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Figure 4.33 Blended Computational Rings

The example in the previous section can be used to illustrate the impact of ponds in close proximity. Assume that two identical 1-acre ponds with the same dimensions as that used in the previous section are placed 100 feet apart similar to that shown in Figure 4.33. The ditch from the previous example is not included in this example. The only things that would change between a simulation where the ponds are independent of one another and in close proximity are the computational perimeters, P1, P2 and P3. These are calculated as follows: Independent Ponds: P1 = 2(L + W) = 2(295.2 + 147.6) = 885.6 feet P2 = P1 + 2∏(xA

1-2) = 885.6 + 2∏(100) = 1,513.9 feet P3 = P1 + 2∏(xA

1-2 + xA2-3) = 885.6 + 2∏(500) = 4,027.2 feet

Ponds in Close Proximity: P1 = 2L + W) = 2x295.2 + 147.6 = 738 feet P2 = P1 + 2(50) + ∏(xA

1-2) = 738 + 100 + ∏(100) = 1,152 feet P3 = P1 + 2(50) + ∏(xA

1-2 + xA2-3) = 885.6 + 100 + ∏(500) = 2,409 feet

The data forms for these two scenarios are shown in Figures 4.34 and 4.35. Notice that the only changes are to the perimeters. All other parameters stay the same. A comparison of stages is presented in Figure 4.36. Maximum stages increase slightly when the ponds are in close proximity. However, the recovery times are increased significantly due to the influence of the ponds on one another. This could be significant in terms of recovery of either flood storage for the next event or for

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pollution abatement recovery. The infiltration hydrographs for the first 60 hours are depicted in Figure 4.37.

Figure 4.34 Percolation Link Data Form for Independent Ponds

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Figure 4.35 Percolation Link Data Form for Ponds in Close Proximity

Figure 4.36 Comparison of Stage Hydrographs for Independent Ponds and Ponds in Close Proximity

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Figure 4.37 Comparison of Infiltration Hydrographs for Independent Ponds and Ponds in Close Proximity

4.2.4 Percolation from Swales Ditch blocks are often used in roadside swales (see Figure 4.38) to trap a portion of the stormwater runoff and then percolate it into the soil column. Notice that the bottom of the channel is two feet below the weirs providing storage in the swale. This type of stormwater management system can be modeled in ICPR with a set of channel, weir and percolation links.

Figure 4.38 Swale with Ditch Blocks

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A nodal network of the swale and ditch block system depicted in Figure 4.38 is shown in Figure 4.39. Links “Chan_1” and “Chan_2” are used to connect nodes “2” to “1” and “4” to “3”, respectively. “Weir_1” connects node “1” to the surface boundary node “Bndy-Surface” and “Weir_2” connects node “3” to “2”. There are also two drainage basins included in the nodal network assigned to nodes “2” and “4”, respectively. A total of four percolation links (“Perc_1a”, “Perc_1b”, “Perc_2a” and “Perc_2b”) are used to move water from the swale system to the soil column (represented as node “Bndy-GWT”). This approach distributes the percolation along the entire length of each swale segment rather than concentrating it at the lowest end. Drainage Basin Data: Basins 1 and 2 are identical, both having areas, curve numbers, DCIAs and TCs of 2.2 acres, 70, 75% and 10 minutes, respectively. A unit hydrograph and peaking factor of 323 is used. The SCS Type II Florida Modified Rainfall Distribution (Flmod) is used with a total rainfall amount of 8.6 inches in a 24-hour period. A typical basin data form is provided in Figure 4.40. Node Data: Stage-Area node types are used for nodes 1, 2, 3 and 4. No stage-area tables are necessary since storage is automatically obtained by ICPR from the connecting channels. Initial stages are set at the bottom of the channel (see Figure 4.38). Time-Stage node types are used for the boundaries Bndy-Surface and Bndy-GWT. The stage for Bndy-Surface is set below the weir invert for the entire simulation. A typical stage-area node data form is provided in Figure 4.41. Weir Data: Weir links are used to model the ditch blocks. The inverts of the weirs are 2 feet above the upstream channel invert elevations and are shown in Figure 4.38. A trapezoidal section is used with a 4-foot bottom width and 8:1 side slopes. A typical weir data form is provided in Figure 4.42.

Figure 4.39 Nodal Network of the Swale and Ditch Block System

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Channel Data: A trapezoidal section (4-foot bottom width, 4:1 side slopes) is used for the two channel links. Invert elevations and lengths are provided in Figure 4.38. A Manning n of 0.03 is used. A typical channel data form is provided in Figure 4.43. Percolation Data: A total of 4 percolation links are used in this example, one at each end of both channel links. A typical percolation link data form is shown in Figure 4.44. Since stage-area tables are not provided for the various nodes and because ICPR derives storage data automatically from the channel links that are attached either to or from each respective node, a “User Specified” surface area is needed for the percolation links. Multiplying an average width of 12 feet (1 foot deep in the channel) by half the channel length (100 feet) gives a surface area of 1,200 square feet (0.02755 acres) per percolation link. The bottom elevation for each percolation link corresponds to the bottom of the channel at each respective location. The water table is set to 3 feet below the bottom elevation. Groundwater will mound directly below the swale and then flow outward along both sides of the swale perpendicular to flow in the swale. Therefore, the perimeters, P1, P2 and P3 are all set to 200 feet which corresponds to two times half the length of a swale segment. All other parameters related to the soil column and unconfined aquifer are the same for each percolation link: Aquifer Base Elevation: 85 feet Annual Recharge Rate: 0 ipy Horizontal Conductivity: 15 fpd Vertical Conductivity: 10 fpd Effective Porosity: 0.3 Suction Head: 4 inches Layer Thickness: 3 feet

Figure 4.40 Typical Basin Data Form

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Figure 4.41 Typical Stage-Area Node Data Form

Figure 4.42 Typical Weir Data Form

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Figure 4.43 Typical Channel Data Form

Figure 4.44 Typical Percolation Link Data Form

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Results: Maximum stages for nodes 1 through 4 are presented in Figure 4.45. There is very little head loss (about 0.01 feet) along each channel segment at peak conditions. An argument could be made to replace the channels segments with a stage-area table that reflects the storage in the channels. The peak stage immediately upstream of Weir_1 (node “1”) is 102.85 feet and is 0.85 feet above the invert of the weir. The peak stage immediately upstream of Weir_2 (node “3”) is 103.61 feet and is 0.61 feet above the weir invert. Weir_1 receives more runoff than Weir_2 and consequently results in a higher stage.

Figure 4.45 Excerpt from Node Maximum Conditions Report

Stage hydrographs for nodes 1 and 3 are presented in Figure 4.46. As previously discussed, the average surface area set for the percolation links was based on a depth of 1 foot in the channels. For node 1, a 1-foot depth corresponds to elevation 101 feet. The amount of time that node 1 is at or above elevation 101 is approximately half the time the stage is above the bottom elevation. The same is true for node 3. Therefore, basing the average surface area on a depth of 1 foot is reasonable. The swales have fully recovered by about hour 60 in the simulation or 36 hours after the rainfall has ended.

Figure 4.46 Stage Hydrographs at Nodes 1 and 3

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The volume of stormwater sent to the surface and groundwater boundaries is presented in Figure 4.47. The total volume of runoff (25-year 24-hour storm event) is approximately 121,690 cubic feet. Of that, approximately 36.3% percolates into the ground and 63.7% is released to the surface system.

Figure 4.47 Volume Hydrographs for Surface and Groundwater Boundaries

The resulting groundwater mound as a function of time for link “Perc_1b” is depicted in Figure 4.48. Perc_1b is used to account for percolation from the upper half of the downstream-most channel link, Chan_1. The water level in the swale is shown as well as water table levels at various perpendicular distances from the edge of the swale to hour 150. The impact is minor at a distance of about 200’ from the edge of the swale. The water table directly below the swale is at about elevation 99 feet at hour 150, or 1.5 feet below the swale. Link Perc_1a is shown in Figure 4.49. Since the water levels are deeper at this point for a longer period of time and more water flows to this location, the draw down times in the swale are longer by about 10 hours or so.

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Figure 4.48 Groundwater Mounding Impacts for Link Perc_1b

Figure 4.49 Groundwater Mounding Impacts for Link Perc_1a

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4.2.5 Base Flow Calculations Base flow to a pond or trench occurs when the outfall is placed below the ambient water table elevation. It is often useful or necessary to know the base flow rate. This is a relatively simple analysis in ICPR and can be performed by connecting two time-stage nodes together with a percolation link as shown below in Figure 4.50. Node “Underdrain” in this example represents a roadway underdrain and node “GWT” represents the unconfined aquifer adjacent to the underdrains. Node Underdrain is connected to node GWT with a percolation link designated “Perc-1”.

Figure 4.50 Simple Nodal Schematic for Base Flow Calculation

The stage at the underdrains is forced to remain at the control elevation (i.e., the invert elevation of the pipe) by setting a time-stage relationship as shown in Figure 4.51.

Figure 4.51 Time-Stage Relationship Used for Node “Underdrain” The water table in this example is expected to fluctuate from the seasonal low elevation of 100 feet to a seasonal high elevation of 104 feet. This fluctuation occurs over a 92-day period (2208 hours) and then remains at the seasonal high for another 61 days (to hour 3672) before gradually falling back to the seasonal low elevation 100 feet at the onset of the next rainy season. The time-stage table for node GWT is set up accordingly as shown in Figure 4.52. (Note: Although these have been input as actual elevations, depths could have also been specified.) The data form for the percolation link is shown in Figure 4.54. The base of the aquifer is at elevation 96 feet and the water table elevation is set to 100 feet. This is the initial water table level and will fluctuate as the simulation progresses. The conductivity and porosity are 7 fpd and 0.25, respectively. Note that the annual

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recharge is set to “–9999”. This is a flag that tells ICPR to retrieve the time-stage data at the downstream node (node “GWT” in this example) and use it to determine recharge rates. Recharge rates at any point in time are based on the differential stages from one time step to the next as determined from the time-stage table. For example, the water table would change from elevation 100 feet to elevation 104 feet over a 2,208-hour period (92 days). Therefore, the average recharge rate (for a porosity of 0.25) during this period is -4 x 0.25 / 92 = -0.01087 fpd. A negative value is used as inflow to the unconfined aquifer and a positive value is used as outflow from the aquifer. Anytime recharge is used with a percolation link, a zero flow boundary condition is invoked at the outer computational edge.

Figure 4.52 Time-Stage Relationship for Unconfined Aquifer The perimeters, P1, P2 and P3, are each set to 2,000 feet. There will be seepage along both sides of the underdrain, so a perimeter of 2,000 feet is used for 1,000 feet of underdrain. Since the only two nodes used in this example are both time-stage nodes, a larger than normal calculation time increment can be used. As shown in Figure 4.53, the min and max calc times are both set to 300 seconds (5 minutes). The simulation is run for a full year (8,760 hours). There is no need to run hydrology with this example.

Figure 4.53 Routing Control Data

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Figure 4.54 Percolation Link Data Form

The resulting infiltration hydrograph is depicted in Figure 4.55. Since the percolation link is connected “from” the underdrain “to” the groundwater table and because the water table rises above the invert of the underdrain, infiltration rates are negative in value, meaning groundwater is flowing from the water table to the underdrain. A peak infiltration rate of 0.0259 cfs occurs 92 days into the simulation, the moment the water table reaches its highest level. The impact to the water table at various distances from the edge of the underdrain is shown in Figure 4.56.

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Figure 4.55 Infiltration Hydrograph

Figure 4.56 Groundwater Draw Down Impacts

4.2.6 Radius of Influence If a pond is controlled at an elevation below the ambient water table, then the water table near the pond will be pulled downward toward the control elevation of the pond. The impact depends on both distance away from the pond and time. Radius of influence calculations can be performed in a manner similar to the base flow calculations described in Section 4.2.5. Assume that a 200-foot by 100-foot pond is to be controlled at elevation 100 feet and that the ambient water table is at elevation 103 feet. Two time-stage nodes are connected together with a percolation link as shown in Figure 4.57. The time-stage table for the pond (see Figure 4.58) is set to force stages to match the control elevation (100 feet in this example). The time-stage table for the groundwater node “GWT” is arbitrarily set to elevation zero and will not factor into the calculations. The

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percolation link data form is provided in Figure 4.59. The water table elevation is set to elevation 103 feet and the perimeters are based on the dimensions of the pond and at distances 100 feet and 2000 feet away from the pond.

Figure 4.57 Nodal Network

The model is executed for a 20,000-hour period (over 2 years). The resulting draw down curves are included in Figure 4.60. These are accessed from the link graphs, 1 link per page (report 2b). As expected, the largest impacts are closest to the pond. Also, the steepest rate of draw down occurs early in the simulation and then the curves flatten with time.

Figure 4.58 Pertinent Node Data

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Figure 4.59 Percolation Link Data Form

Figure 4.60 Groundwater Draw Down Curves

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5.0 Exfiltration Trench Links The exfiltration trench link data form is accessed from the Routing pull down menu as shown in Figure 5.1. A typical data form is provided in Figure 5.2. There are three primary categories of input data required for exfiltration trenches: (1) data related to the unconfined aquifer adjacent to and below the trench; (2) data related to the trench and pipe; and (3) data related to the computational framework for saturated horizontal flow.

Figure 5.1 Accessing the Exfiltration Trench Link Data Form

Figure 5.2 The Exfiltration Trench Link Data Form

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5.1 Parameters Related to the Unconfined Aquifer Aquifer Base Elevation (feet or meters above datum): This is the elevation of the hydraulically restrictive layer or impermeable layer at the base of the unconfined aquifer (see Figure 5.3).

Figure 5.3 Exfiltration Trench in Relation to Unconfined Aquifer

Water Table Elevation (feet or meters above datum): This parameter is used to set the initial heads for each of the finite difference computational cells. It also serves as a fixed head boundary condition at the outer edges of the computational grid when the annual recharge rate is set to zero. If the ambient water table elevation is located above the trench bottom and there is another outlet for the pond such as a weir overflow, then groundwater levels will eventually move toward this lower elevation. Base flow calculations are modeled this way. This parameter is typically set to the seasonal high water table for single event modeling. However, for long term or multi-event modeling (e.g., a year-long simulation), it might be better to start the simulations in the drier months and set the water table to a seasonal low rather than high. Annual Recharge Rate (inches or centimeters per year): For single event modeling, this parameter is typically set to zero. If it is set to zero, then the ambient water table becomes a fixed head boundary condition at the outer edge of the computational grid. The annual recharge rate can be set to either a positive value to remove water from the unconfined aquifer or to a negative value to add water to it. It is treated as a constant steady-state flow. Another option is to set it to –9999, which serves as a trigger for ICPR to base the recharge rate on the time-stage table used at the

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downstream node of the link (i.e., the “to node”). A detailed example of this feature is explained in Section 4.2.5. It is also described in Section 2.4. Horizontal Conductivity (feet or meters per day): The average soil permeability in the horizontal direction. This parameter is used for the saturated horizontal flow computations. If you want to apply a factor of safety, you should do so by reducing the conductivity accordingly. Site-specific soils testing should be conducted to determine this parameter. Vertical Conductivity (feet or meters per day): The average soil permeability in the vertical direction. This parameter is used for the unsaturated vertical flow computations. If you want to apply a factor of safety, you should do so by reducing the conductivity accordingly. Site-specific soils testing should be conducted to determine this parameter. Effective Porosity (decimal): The effective porosity (a decimal value between 0 and 1) is the fractional amount of moisture that can be stored in the soil column at the onset of infiltration. It is the porosity of the soil minus the initial moisture or residual moisture and is often referred to as the “fillable porosity”. Site-specific soils testing should be done to determine this parameter. Suction Head (inches or centimeters): This is the wetting front suction head. Refer to Table 3.1 for typical values by soil class. 5.2 Parameters Related to the Trench and Pipe Refer to Figure 5.4 for the various geometric parameters needed for exfiltration trenches.

Figure 5.4 Exfiltration Trench Schematic

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Trench Bottom Elevation (feet or meters): The lowest elevation of the trench – located at the bottom of the gravel envelope. Trench Width (feet or meters): The distance across the gravel envelope. Trench Length (feet or meters): The longitudinal distance of trench to be used. Trench Height (feet or meters): The distance from the bottom of the trench to the top of the gravel envelope. Gravel Porosity (decimal): The porosity of the gravel rock in the trench – must be a decimal value between 0 and 1. Pipe Diameter (inches): Pipes are always assumed to be circular. Enter the pipe diameter. Special Note on Pipe Diameter: This parameter can be positive, negative or zero. A positive value means the pipe is part of the trench and hollow. A zero value means there is no pipe in the gravel envelope. A negative value means there is a solid pipe with no storage available in the trench. Pipe Invert Elevation (feet or meters): The elevation of the bottom of the pipe, usually above the bottom of the trench. 5.3 Parameters Related to the Computational Framework The horizontal groundwater flow algorithm used for exfiltration trenches is based on a finite difference scheme that requires a computational grid be established. There are 3 parameters that are used to establish the grid as described below: Cell Spacing (feet or meters): The cell spacing is the distance outwardly perpendicular to the trench for each finite difference computational cell. A typical value for this parameter is 5 feet, but can be smaller or larger if warranted. Number of Cells (integer): This parameter provides the total number of finite difference computational cells to be used for saturated horizontal groundwater flow. The total distance away from the edge of the exfiltration trench is equal to the cell spacing multiplied by the number of cells. For example, if the cell spacing is 5 feet and the number of cells is 50, then the total distance away from the edge of the trench is 250 feet. The fixed head boundary condition equal to the ambient water table elevation would be applied at the 250 feet location in this example. The objective is to place the outer boundary far enough away from the trench so that it’s influence is minimal. Basically, water moving away from the trench will dissipate into the water table. In most typical applications, this might be between 250 and 500 feet. End Treatment: Typically, exfiltration trenches are much longer than they are wide and little or no flow would be expected out of the ends of the trenches. For situations like this, the end treatment option should be set to “Exclude”. However, the “Include” option can be used if the trench is relatively short and significant flow is expected through the ends.

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From a computational standpoint, if the ends are excluded, then the “width” (y) of each computational finite difference cell would remain constant regardless of the distance from the edge of the trench. This “width” (y) is equal to twice the length of the trench since water flows from both sides of the trench. y = 2 x L (exclude ends) If the ends are included, then the computational “width” expands as flow progresses outward from the trench. The following equation is used to compute the computational width (y) y = 2 x L + 2πd (include ends) where, d is the distance from the edge of the trench 5.4 Examples There are two ways to model exfiltration trenches with ICPR. The first is a simple approach that ignores pipe hydraulics and the second includes the pipe hydraulics of the exfiltration system. Both approaches are described in this section. Consider the exfiltration trench layout depicted in Figure 5.5. This is a 17.2-acre commercial site and 1,750 feet of exfiltration trench is proposed as shown. Six inlets/catch basins are used to collect the surface runoff from the site and distribute it to the exfiltration trench. A weir is used at the downstream end of the exfiltration trench to hold water in the trench and force it to percolate into the soil. Excess runoff flows over the weir and into a detention pond that is controlled by another structure before discharging to a canal. Pollution abatement is provided in the trench and attenuation is provided in the pond.

Figure 5.5 Exfiltration Trench Layout

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A detail of the exfiltration trench is presented in Figure 5.6. The trench is 4.5 feet wide and 4 feet high with a 24-inch circular pipe embedded in the trench between elevations 12 and 14 feet. The control structure used to hold water in the trench is shown in Figure 5.7. The weir crest is set at elevation 15.0 feet and corresponds to the top of the trench. Water spills over the weir and then flows through a pipe to the detention pond. The weir/pipe combination is modeled as a drop structure in ICPR.

Figure 5.6 Exfiltration Trench Detail

Figure 5.7 Control Structure for Exfiltration Trench

Surface drainage patterns are shown in Figure 5.8. The site has been delineated into six drainage basins labeled 1 through 6. Each basin has an area of 2.87 acres, a CN

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of 85 and a TC of 10 minutes. The Santa Barbara Urban Hydrograph Method is used to compute the hydrographs with a computational time increment of 2.5 minutes. A typical basin data form is included in Figure 5.9. The pond has a drainage area of 3 acres, a CN of 95 and a TC of 10 minutes. Some flooding is anticipated above the pavement. Stage-area data are provided for a single inlet/catch basin in Table 5.1 as well as the combined total area for all six inlets.

Stage (feet)

Area for Single Inlet (acres)

Combined Area (acres)

16.5 0.1148 0.6888 17.0 0.3444 2.0664 17.5 0.6887 2.7548 18.0 1.1478 6.8868

Table 5.1 Stage-Area Data

Figure 5.8 Surface Drainage Patterns

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Figure 5.9 Typical Drainage Basin Data Form

5.4.1 Exfiltration Trenches without Pipe Hydraulics As already mentioned, the simple approach to modeling exfiltration trenches presented in this example ignores the hydraulics of the pipe embedded in the trench. Consequently, the entire trench system can be lumped together as a single exfiltration trench link. A schematic of the nodal network for this approach is shown in Figure 5.10. A node designated as “4” in the schematic receives runoff from all six drainage basins (“1”, “2”, “3”, “4”, “5”, and “6”). Node “4” is connected to node “Pond” with a drop structure link labeled “4-Pond”. Node “4” is also connected to node “GWSink” with an exfiltration trench link. A second drop structure (“Pond-Canal”) is used to connect the detention pond to the outfall canal.

Figure 5.10 Nodal Network Schematic for Simple Approach

Stage-Area relationships for node “4” and “Pond” are provided in Figure 5.11 along with other relevant node data. Notice that the stage-area table for node “4” includes the combined surface area for all six inlets. The first elevation, 16.49 feet is just inside the inlet while elevation 16.5 feet extends onto the pavement. No additional

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storage is needed inside the inlet or exfiltration trench since that is automatically calculated based on the exfiltration trench link data. Time-Stage relationships for nodes “Canal” and “GWSink” are included in Figure 5.12. Note that “GWSink” is set to elevation zero. This is arbitrary and since the exfiltration link is independent of the downstream stage, the stage values are inconsequential. It is only necessary to have at least two points. Node “Canal” is set at elevation 6.0 feet and is assumed to be constant for this simulation.

Figure 5.11 Stage-Area and Other Pertinent Node Data for Nodes “4” and “Pond”

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Figure 5.12 Time-Stage Data for Nodes “GWSink” and “Canal”

The data form for the exfiltration trench link is shown in Figure 5.13. Notice that the trench length is 1,750 feet, which is the total length of trench for the site. The trench parameters and aquifer parameters are set accordingly. From a mass balance perspective, the storage in the trench is automatically assigned to the upstream node. It includes the storage in the gravel as well as the storage in the pipe. Data forms for the drop structures are provided in Figures 5.14 and 5.15.

Figure 5.13 Exfiltration Trench Link Data Form

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A 25-year 24-hour storm (8.6 inches of rainfall) was simulated for this system using the SCS Type II (Florida Modified) rainfall distribution. The hydrology and routing control data forms are provided in Figure 5.16. Resulting stage hydrographs for the trench (node “4”), the pond and the canal are shown in Figure 5.17. The peak stage in the parking area of the commercial site is 17.24 feet, which is about 9 inches above the inlets into the pavement areas. The pond reached a maximum elevation of 11.45 feet, 3.45 feet above the control elevation. Discharge hydrographs are shown in Figure 5.18. The control structure for the trench doesn’t begin to flow until hour 10.53. At that point, 0.6427 acre-feet (0.448 inches for the entire site) have percolated into the soil column (refer to Figure 5.19) and there is still 0.365 acre-feet stored in the trench. The combined treatment volume at this point is 1.008 acre-feet or 0.70 inches from the entire site. As indicated in Figure 5.19, 2.36 acre-feet (1.65 inches) have percolated into the ground after 24 hours and 2.57 acre-feet (1.79 inches) after 40 hours. If additional pollution abatement storage is required, the trench width can be expanded. Groundwater mounding impacts are presented in Figure 5.20.

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Figure 5.14 Drop Structure Data Forms for Exfiltration Trench Control

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Figure 5.15 Drop Structure Data Form for Pond Outfall

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Figure 5.16 Hydrology and Routing Control Data

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Figure 5.17 Stage Hydrographs for “Simple Approach”

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Figure 5.18 Discharge Hydrographs for “Simple Approach”

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Figure 5.19 Volume Percolated into the Soil from the Trench for “Simple Approach”

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Figure 5.20 Groundwater Mounding Impacts for “Simple Approach”

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5.4.2 Exfiltration Trenches with Pipe Hydraulics The “simple approach” to modeling exfiltration trenches presented in the previous section ignores the hydraulics of the pipe embedded in the trench. The pipe hydraulics can be incorporated into the model simultaneously with the exfiltration trench, but a little more work is required. First, more nodes are needed – one for each inlet/catch basin. Next, the various nodes need to be connected together with pipe links. For example, node 1 is connected to node 2 with a 24-inch circular pipe. Node 2 is connected to node 4 with a pipe. And, so on. Finally, exfiltration trench links need to be connected from each of the inlets/catch basins to the groundwater sink. A schematic of the resulting nodal network is depicted in Figure 5.21. Separate drainage basins are assigned to each of the nodes. There are two tricky parts to this more rigorous approach. Since both pipe links and exfiltration trenches have storage associated with them, a potential double accounting of the pipe storage can occur unless a special provision is made. Setting the pipe diameter to a negative value on the trench data form eliminates the storage in the pipe that is embedded in the exfiltration trench. For example, if the pipe diameter is 24 inches, then it should be set to –24 inches. The negative value tells ICPR to create a solid pipe in the trench that removes space from the gravel envelope but provides no storage. The pipe storage is accounted for separately in the pipe links instead of the exfiltration links. The other issue is related to setting the trench lengths. Remember that the storage associated with an exfiltration trench is automatically assigned to the upstream node for that link. Water is pulled from the node and transferred to the groundwater table adjacent to the trench. It would be inappropriate to simply set the trench length equal to the length of each pipe. Instead, the trench extends halfway upstream and downstream of any pipe connected to or from each respective node. The trench lengths in this example should be set as follows: Link Length

Exfil-1 125 feet Exfil-2 375 feet Exfil-3 125 feet

Exfil-4 625 feet Exfil-5 125 feet Exfil-6 375 feet

Total 1,750 feet A typical pipe link data form and an exfiltration trench link data form are shown in Figures 5.22 and 5.23, respectively. The exfiltration trench link is identical to that used in the simple approach except the length has been adjusted in accordance with the table above and the pipe diameter is set to a negative value. All other parameters are the same as before. Since a storm sewer system is being modeled, the routing control parameters should be adjusted to reduce the computational time increment. The adjusted values are highlighted in Figure 5.24.

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Figure 5.21 Schematic of Nodal Network

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Figure 5.22 Typical Pipe Link Data Form

Figure 5.23 Typical Exfiltration Trench Link Data Form

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Figure 5.24 Routing Control Data Form

An excerpt from the node maximum conditions report is provided in Figure 5.25. The peak stage at node 4 for this simulation is 16.34 feet as compared to a peak stage of 17.24 for the simple approach used in the previous section. The rim elevation for the inlet at node 4 is 16.5 feet. Therefore, no flooding takes place at this particular node using the rigorous hydraulic approach. However, due to head losses in the various pipes, flooding occurs at the other inlets/catch basins and the magnitude increases from downstream to upstream. For example, one of the pipe runs goes from node 1 to node 2 to node 4. The peak stages are 17.70 feet, 17.55 feet and 16.34 feet, respectively. A comparison of water levels at each of the inlets for the entire simulation is shown in Figure 5.26. Also, a comparison of stages at node 4, the location immediately upstream of the control structure for the trench system, between the simple approach and the rigorous approach is provided in Figure 5.27. The reason the stages are lower at this point for the rigorous approach is because higher flooding occurs upstream and consequently more storage and flood attenuation occurs. Discharge hydrographs for the total inflow to the pond, flow from the pond to the canal and flow from the trench to the groundwater table are shown in Figure 5.28. The peak flow to the canal is about 20 cfs. Comparisons of discharge hydrographs for the simple and rigorous approaches from the trench to the pond and from the pond to the canal are depicted in Figures 5.29 and 5.30. Water leaves the trench system and enters the pond at a higher rate for the simple approach. This is directly attributable to the higher stages at node 4 for the simple approach – more water is being driven over the control structure. Since more attenuation occurs in the parking lots at the various inlets for the rigorous approach, lower flow rates to the pond occur and an overall lower peak discharge rate to the canal is experienced. Comparisons of infiltration rate and volume hydrographs between the simple and rigorous approaches are shown in Figures 5.31 and 5.32, respectively. The peak infiltration rates are similar in magnitude. There are some timing differences due to the more refined distribution of inflows to the trench system for the rigorous approach. The total volume infiltrated for both approaches is slightly different after 40 hours, but essentially the same.

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Figure 5.25 Node Maximum Conditions Report (Rigorous Approach)

Figure 5.26 Stage Hydrographs for Inlets/Catch Basins (Rigorous Approach)

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Figure 5.27 Comparison of Stages at Node 4

Figure 5.28 Discharge Hydrographs (Rigorous Approach)

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Figure 5.29 Comparison of Discharge Hydrographs from Trench to Pond

Figure 5.30 Comparison of Discharge Hydrographs from Pond to Canal

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Figure 5.31 Comparison of Infiltration Rate Hydrographs

Figure 5.32 Comparison of Volume Hydrographs

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6.0 Filter Links The filter link data form is accessed from the Routing pull down menu as shown in Figure 6.1. Both side bank and bottom filters can be modeled in ICPR (refer to Figures 6.2 and 6.3 for details).

Figure 6.1 Accessing the Filter Link Data Form

Figure 6.2 Side Bank Filter Detail

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Figure 6.3 Bottom Filter Detail

6.1 Input Parameters Side Slope (decimal): The number of horizontal units to one vertical unit. For example, a value of 4 should be used when the side bank is sloped 4 horizontal units for each vertical unit. Flat filters do not need a side slope. Filter Elevation (feet or meters above datum): The lowest elevation at the surface of the filter media. This is the elevation at which the filter begins to drain the pond. Filter Width (feet or meters): The distance at the surface across the filter media. Filter Length (feet or meters): The longitudinal distance of filter to be used. Filter Permeabilty (feet or meters per day): The hydraulic conductivity of the filter media. Pipe Invert Elevation (feet or meters above datum): The elevation of the bottom of the pipe. Pipe Diameter (inches or centimeters): Pipes are always assumed to be circular. Enter the pipe diameter. Gravel Thickness X-Direction (inches or centimeters): If a gravel envelope is used around the pipe, specify the distance of the gravel in the x-direction beyond the right outer edge of the pipe. Gravel Thickness Y-Direction (inches or centimeters): If a gravel envelope is used around the pipe, specify the distance of the gravel in the y-direction beyond the top outer edge of the pipe.

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6.2 Example Assume that a site requires 54,000 cubic feet of pollution abatement and that volume must be recovered in no more than 72 hours. A side bank filter is to be used to recover the pollution abatement volume. Flood attenuation is not a concern for this example. The nodal network for this example is shown in Figure 6.4 and consists of two nodes (the “Pond” and the boundary “Bndy”). The pond is connected to the boundary with a filter link.

Figure 6.4 Schematic of the Nodal Network

The stage-area data for the pond is presented in Figure 6.5. The storage in the pond at elevation 95.5 feet (also the overflow elevation) is 55,830 cubic feet. This is a little more than the required 54,000 cubic feet, but a little buffer is provided because as the stage approaches the bottom of the pond, the filtration rate becomes asymptotic to zero. The initial stage for the pond is set to elevation 95.5 feet and the draw down time will be examined afterward.

Figure 6.5 Stage-Area Data for Pond

A tailwater elevation of 91.0 feet (2 feet below the pond bottom) is used on the filter. The time-stage data for node “Bndy” is included in Figure 6.6. It is not a problem for the tailwater to vary with time. If it does, then it will be included in the hydraulic computations.

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Figure 6.6 Time-Stage Data for Boundary Node

A side bank filter is proposed and the specific parameters are included in Figure 6.7. Determining the actual length is an iterative process, and based on that process, it was determined that 425 feet of filter are needed.

Figure 6.7 Filter Link Data

An excerpt from the node time series report for the Pond is provided in Figure 6.8. At hour 72, the stage is 93.08 feet, slightly above the bottom, and 1.2424 acre-feet (54,119 cubic feet) have passed through the filter. Therefore, the requisite recovery volume and time have been met.

Figure 6.8 Excerpt from Node Time Series Report for the Pond

A stage hydrograph showing the draw down of the pond is presented in Figure 6.9. The last 0.08 feet are drained by hour 120. The filter becomes very inefficient as the

93


water level in the pond approaches the bottom. A volume hydrograph is shown in Figure 6.10.

Figure 6.9 Stage Hydrograph for the Pond

Figure 6.10 Volume Hydrograph for the Filter

94


This Page is Intentionally Left Blank

95


References

1. Anderson, Mary P. and William W. Woessner, Applied Groundwater Modeling, Simulation of Flow and Advective Transport, Academic Press, 2002.

2. Andreyev, N.E., “MODRET v6.1 Program Documentation”. 3. Branscome, Joycelyn and Richard S. Tomasello, “Field Testing of Exfiltration

Systems”, Technical Publication 87-5 DRE-236, Water Resources Division, Resource Planning Department, South Florida Water Management District, December 1987.

4. Chow, Ven Te, David R. Maidment and Larry W. Mays, Applied Hydrology,

International Edition, McGraw-Hill International Editions, 1988.

5. Hull, Laurence C. “Prickett and Lonnquist Aquifer Simulation Program for the Apple II Minicomputer”, Geosciences Branch, Earth and Life Sciences Office, EG&G Idaho, Inc. February 1983.

6. Prickett, T.A. and C.G. Lonnquist, “Selected Digital Techniques for Ground-

Water Resource Evaluation”, Illinois State Water Survey Bulletin 55, Urbana, Illinois, 1971.

7. Prickett, T.A. and C.G. Lonnquist, “Aquifer Simulation Model for Use on Disk

Supoorted Small Computer Systems”, Illinois State Water Survey Bulletin 55, Urbana, Illinois, 1973.

8. Professional Service Industries, Inc. Jammal & Associates Division, “Full-

Scale Hydrologic Monitoring of Stormwater Retention Ponds and Recommended Hydro-Geotechnical Design Methodologies”, Special Publication SJ93-SP10, St. Johns River Water Management District, August 1993.

9. Rawls, W. J., and Brakensiek, D. L. “Estimating Soil Water Retention from

Soil Properties”, Journal Irrigation Drainage Division. American Society of Civil Engineers, Vol 108, No. IR2, pp 166-171.

10. Rawls, W. J., Brakensiek, D. L., and Saxton, K.E. “Estimating Soil Water

Properties”, Transactions American Society of Agricultural Engineers, St. Joseph, MI, Vol 25, No. 5, pp 1316-2320.

11. Seereeram, Devo, “PONDS v3.2 Program Documentation”.

12. St. Johns River Water Management District, “Applicant’s Handbook:

Regulation of Stormwater Management Systems Chapter 40C-42, F.A.C.”, February 1, 2005.

13. U.S. Army Corps of Engineers, “Engineering and Design Flood-Runoff

Analysis”, EM 1110-2-1417, August 31, 1994.

14. Wang, Herbert F., and Mary P. Anderson, Introduction to Groundwater Modeling, Finite Difference and Finite Element Methods, Academic Press, 1982.

96



Appendix A. Verification of the Modified Green-Ampt Method for Unsaturated Vertical Flow The fundamental equation used for modeling vertical percolation in ICPR, when the surface area is held constant, is a modified form of the Green-Ampt equation that accounts for variable head above ground and reflects changing stages in a pond. In order to verify that the method as implemented is performing correctly, a comparison was made using the vertical percolation component in ICPR and the original Green-Ampt equation for infiltration. In particular, Example 5.4.1 from the book “Applied Hydrology” by Chow, Maidment and Mays (International Edition, McGraw-Hill, 1988) was used as a test case. In that example, a 3-hour rainfall hyetograph (see Table A.1) was applied to a sandy-loam soil with a vertical conductivity of 1.09 cm/h (0.8583 fpd), a wetting front suction head of 11.01 cm (4.33464 inches) and an effective porosity of 0.247. In the first hour of the rainfall event, the potential infiltration rate exceeds the rainfall intensity and therefore, all rainfall is infiltrated. Between 60 minutes and 140 minutes, the rainfall intensity increases and exceeds the potential infiltration rate. Consequently, a potion of the rainfall is absorbed into the ground and the remainder appears as rainfall excess. Finally, the potential infiltration rate exceeds the rainfall rate for the remainder of the storm and the rainfall is fully absorbed into the soil column. This is depicted in Figure 5.4.2 of the “Applied Hydrology” textbook and is reproduced here for illustrative purposes. The depth or location of the wetting front below the ground surface in this example is simply the cumulative infiltration divided by the fillable porosity.

Time

(minutes)

Incremental Rainfall (cm)

Cumulative Rainfall (cm)

Cumulative Infiltration

(cm)

Cumulative Rainfall Excess

(cm) 0 0.00 0.00 0.00 0.00 10 0.18 0.18 0.18 0.00 20 0.21 0.39 0.39 0.00 30 0.26 0.65 0.65 0.00 40 0.32 0.97 0.97 0.00 50 0.37 1.34 1.34 0.00 60 0.43 1.77 1.77 0.00 70 0.64 2.41 2.21 0.20 80 1.14 3.55 2.59 0.96 90 3.18 6.73 2.95 3.78 100 1.65 8.38 3.29 5.09 110 0.81 9.19 3.62 5.57 120 0.52 9.71 3.93 5.78 130 0.42 10.13 4.24 5.90 140 0.36 10.49 4.53 5.96 150 0.28 10.77 4.81 5.96 160 0.24 11.01 5.05 5.96 170 0.19 11.20 5.24 5.96 180 0.17 11.37 5.41 5.96

Table A.1 Summary of Rainfall, Infiltration and Rainfall Excess for Example 5.4.1 from Chow, Maidment, and Mays (Table 5.4.2, “Applied Hydrology”, 1988).

A-2


Since the Green-Ampt equation used in the Chow, Maidment, Mays example assumes that the depth of water above the ground surface is negligible and is not a factor in the calculations, an ICPR model had to be devised that would essentially force stages in a pond to remain constant and at ground elevation. A schematic of the model is depicted in Figure A.1. An inflow hydrograph equivalent to the rainfall hyetograph was applied to a node representing the pond. The pond has two links leaving it, one representing the percolation into the ground (a “percolation” link in ICPR) and a weir link representing a surface outlet. A very large weir (10,000 feet in length) was set at the bottom of the pond so that stages in the pond never rise more than a fraction above the bottom. Water flowing through the percolation link is equivalent to the infiltration component in the Chow, Maidment, Mays example. And, water flowing over the weir is equivalent to the rainfall excess amount in that example.

A-3


Figure A.1 ICPR Model Schematic Used for the Chow, Maidment, Mays

Example 5.4.1. The rainfall hyetograph in Table A.1 was applied to a 1-acre (43,560 sqft) surface area and the resulting hydrograph was assigned to node “Pond” via the “Boundary Flow” feature of ICPR. This is equivalent to direct rainfall falling on the pond surface. A stage-area node type was used for node “Pond” with a constant surface area of 1 acre. Time-stage nodes were used for nodes “Soil Column” and “Surface Outlet” and the stages were held constant at elevation zero and do not influence the hydraulics. The invert elevation of the weir link was set at the bottom of the pond (i.e., at an elevation corresponding to the first point of the stage-area table). As previously mentioned, a 10,000-foot long vertical weir was used in an effort to prevent stages from building up above the bottom of the pond. Should the rate of inflow to the pond exceed the percolation rate, excess water will spill over the weir. In essence, flow over the weir in this model is equivalent to the rainfall excess in the Chow, Maidment, Mays example. The input parameters for the percolation link (see Figure A.2) include water table elevation, vertical hydraulic conductivity, fillable porosity and wetting front suction head. If the wetting front reaches the water table, a transition from vertical flow to horizontal flow could occur. However, since the goal in this example is to confirm that the vertical seepage component is working properly, the water table was set well below the pond to insure that the wetting front does not intercept it for this simulation. Also, the “Vertical Flow Termination” option was set to “Constant Rate” instead of “Horizontal Flow” and the constant rate was set to zero. This means that if the wetting front were to reach the water table, then the infiltration rate would automatically be set to zero. All other parameters were set in accordance with the Chow, Maidment, Mays example.

A-4


Figure A.2 Data Form for Percolation Link Used for the Chow, Maidment, Mays Example.

Figure A.3 depicts the equivalent inflow (direct rainfall), rainfall excess and infiltration hydrographs. The infiltration rates are equal to the inflow hydrograph through the first 60 minutes of the simulation. This means that the rainfall was insufficient to satisfy infiltration potential and all of it was absorbed into the soil column. Discharge over the weir begins at the 60-minute mark and continues until 140 minutes. This occurs because the rainfall rate exceeds the infiltration potential and cannot be completely absorbed into the soil column. The flow over the weir, as previously mentioned, is equivalent to the rainfall excess for the storm event. After 140 minutes, the rainfall rate drops below the infiltration potential again and is absorbed into the soil column.

A-5


Figure A.3 Resulting Hydrographs from the ICPR Simulations Figure A.4 shows water elevations in the pond (blue graph) and in the soil column (red graph). The water levels in the pond are essentially flat throughout the simulation as expected. The maximum stage in the pond is only about 0.1079 cm (0.00354 feet) above the bottom of the pond. The wetting front gradually moves downward as more water enters the soil column. A comparison between the Chow, Maidment, Mays example and the ICPR simulations of cumulative infiltration and rainfall excess are provided in Table A.2. There are only minor differences between the two, with cumulative infiltration slightly lower and the rainfall excess slightly higher in the ICPR results. These differences occur because some head is required in order for the weir to flow. Consequently, the water level in the pond rises slightly (0.1079 cm (0.00354 feet) for the worse case) in the pond and pushes some water over the weir even in the earliest part of the storm. One of the primary purposes of the ICPR percolation link is to consider the impact of variable head in the pond on percolation rates. In that regard, a separate simulation was performed with the weir link shut off. Stages in the pond were allowed to rise and the only outlet for this second simulation was the percolation link. Table A.3 compares the cumulative infiltration and as expected, infiltration volumes increase by 13.5% for this scenario. This is a particularly important consideration for land-locked systems that rely on percolation for storage recovery.

A-6


Figure A.4 Advancement of the Wetting Front as Computed in ICPR

Cumulative Infiltration (cm)

Cumulative Rainfall Excess (cm)

Time

(minutes)

Chow, Maidment,

Mays

ICPR via

Percolation Link

Chow, Maidment,

Mays

ICPR via Weir Link

0 0.00 0.00 0.00 0.00 10 0.18 0.18 0.00 0.00 20 0.39 0.38 0.00 0.00 30 0.65 0.64 0.00 0.01 40 0.97 0.96 0.00 0.01 50 1.34 1.32 0.00 0.02 60 1.77 1.74 0.00 0.03 70 2.21 2.18 0.20 0.21 80 2.59 2.57 0.96 0.94 90 2.95 2.93 3.78 3.69 100 3.29 3.27 5.09 5.04 110 3.62 3.60 5.57 5.56 120 3.93 3.91 5.78 5.78 130 4.24 4.22 5.90 5.90 140 4.53 4.51 5.96 5.97 150 4.81 4.79 5.96 5.98 160 5.05 5.03 5.96 5.98 170 5.24 5.21 5.96 5.99 180 5.41 5.38 5.96 5.99

Table A.2 Comparison of Cumulative Infiltration and Cumulative Rainfall Excess for Example 5.4.1 from Chow, Maidment, and Mays (“Applied Hydrology”, 1988) and ICPR Simulations Using a Percolation Link.

A-7


Time (minutes)

Chow, Maidment,

Mays (cm)

ICPR via Percolation Link

(with weir)1

(cm)

ICPR via Percolation Link (without weir)2

(cm) 0 0.00 0.00 0.00 10 0.18 0.18 0.18 20 0.39 0.38 0.39 30 0.65 0.64 0.65 40 0.97 0.96 0.97 50 1.34 1.32 1.34 60 1.77 1.74 1.77 70 2.21 2.18 2.20 80 2.59 2.57 2.60 90 2.95 2.93 2.99 100 3.29 3.27 3.39 110 3.62 3.60 3.78 120 3.93 3.91 4.14 130 4.24 4.22 4.50 140 4.53 4.51 4.84 150 4.81 4.79 5.17 160 5.05 5.03 5.49 170 5.24 5.21 5.80 180 5.41 5.38 6.11

1 Water levels in pond held near bottom with overflow weir. 2 Water levels in pond fluctuate. Table A.3 Comparison of Cumulative Infiltration for Example 5.4.1 from Chow, Maidment, and Mays (“Applied Hydrology”, 1988) and ICPR Simulations Using a Percolation Link.

A-8



Appendix B. Verification of the Saturated Horizontal Flow Algorithm for Use With Exfiltration Trenches A number of tests and comparisons were made with both recorded data and with other similar groundwater-surface water models. In particular, ICPR’s exfiltration trench links were compared with three field tests published in a study by the South Florida Water Management District (SFWMD) entitled “Field Testing of Exfiltration Systems”, (Branscome & Tomasello, 1987). Exfiltration trenches in ICPR use the same vertical and horizontal flow algorithms as those used for percolation links. The primary difference is related to how storage in the trench is calculated and allocated to nodes. These tests are referred to as the “SFWMD TP87-5/DRE-236 Comparisons” In the report “Field Testing of Exfiltration Systems”, two exfiltration trenches, each 10 feet long, 6 feet wide and 6 feet high were constructed. A number of controlled tests were performed whereby flow into the trenches was measured and stages were held constant for a period of time. The amount of water required to maintain constant elevations in the trenches dropped with time as the tests proceeded. Tests 5, 6 and 7 were reproduced in ICPR using exfiltration link types. A stage-area node type and a time-stage node type were established for each test and then connected together with Exfiltration Trench links. Data forms for each of the three trench experiments are provided in Figures B.1, B.2 and B.3. In all three cases, the ambient water table was above the bottom of the trench and therefore, groundwater flow was completely horizontal. Unsaturated vertical flow would not occur under these conditions. As mentioned, the trenches were initially filled to a predetermined elevation during the field tests and then that elevation was maintained by adding water as needed. Records were kept on the amount and timing of water added to the trenches. These “inflow hydrographs” were set up in ICPR as “boundary flows” and assigned to the node at the upstream end (i.e., the “from node”) of each respective exfiltration link. Initial stages were set at the ambient water table elevations. Storage below the maintenance elevations of the tests was automatically derived from the exfiltration trench data (i.e., the void space in the gravel and in the pipe). The only other storage provided in the ICPR simulations was a buffer above the maintenance elevations. In other words, as the trenches were filled, if there was a numerical excess of water, it was held in a buffer at the maintenance elevation and later percolated out of the trench. Since no other link types were included in the model such as weir overflows at the maintenance elevations, 100% of the inflow volume passed through the trenches. An analysis of the amount of water held in the buffer was made and found to be only a few percent of the total volume which is remarkable considering the lack of precision in measuring flows during the field tests and other parameters like the porosity of the gravel (assumed to be 0.5) and the elevation of the base of the aquifer (not measured but assumed in the report to be twice the depth of the trench – 12 feet). Simulation results for each of the three tests are presented graphically in Figures B.4 through B.9. A comparison of the recorded inflow hydrographs and the simulated exfiltration hydrographs for tests 5, 6 and 7 are provided in Figures B.4, B.6 and B.8, respectively. As can be seen from these figures, there is an initial filling period. The inflow rates are held constant during these initial periods. However, as expected,

B-2


the exfiltration rates gradually climb during this period because the elevations and driving head increase with time as the voids in the gravel are filled. Once filled, the amount of water added to the trenches in order to maintain a constant elevation decreases with time. This is because the gradients needed to drive water from the trenches to the surrounding soil column also decrease with time. The ICPR simulations match the recorded inflow rates after the initial filling period quite well, especially considering the uncertainties in the depth to the aquifer base. Simulated stage hydrographs for tests 5, 6 and 7 are shown in Figures B.5, B.7 and B.9. The blue graph in each of these reflects the water level in the trenches. Notice how it climbs in the early part of the simulation and then flattens out. The flat part of these graphs is the maintenance stage used in each of the field tests.

Figure B.1 Exfiltration Trench Data Form for Test 5

B-3



B-4



B-5


Figure B.4 Resulting Hydrographs for Test 5

Figure B.5 Resulting Stage Hydrographs for Test 5

B-6




B-7




B-8



Appendix C. Verification of the Saturated Horizontal Flow Algorithm for Pond Draw Down Analysis In the report “Full-Scale Hydrologic Monitoring of Stormwater Retention Ponds and Recommended Hydro-Geotechnical Design Methodologies” (SJRWMD Special Publication SJ93-SP10, 1993), four existing ponds were monitored during various periods. These included the Airport Warehouses, Tutor Time Day Care Center, Fisherman’s Landing, and the Tom Statham Park. Several models and equations were compared against recorded field data. These included a “Simplified Analytical Method”, “Modified MODRET”, “Hantush”, “Glover’s Equation” and a program called “Pond Flow”. Extensive field tests were performed to determine soil properties at each of the sites. Among other parameters, hydraulic conductivities were estimated using several different methods. Values varied significantly depending on the method used. In general, the “Cased Hole Falling Head – kh Method” seemed to provide the most accurate modeling results in that investigation. Therefore, it was used in the ICPR simulations discussed in this section. Although ICPR simulations were performed for all four of the ponds, the Tom Statham Park site experienced very long draw down times and was affected as much by evaporation as percolation. Evaporation was included in the ICPR simulations, and, very good results were obtained by adjusting the hydraulic conductivity. However, these are not included in this document because the focus here is on percolation and not evaporation. Rainfall and pond stage records were examined in the SJ93-SP10 report. Rainfall events for each of the ponds were identified that caused pond stages to reach the overflow structures. Ambient water table elevations at the start of the draw down period were also recorded. Stages in the ponds were then monitored and the draw down times determined and recorded to either full recovery of the pond storage or to the next event. Then each of the models and equations described in the first paragraph were applied and compared to recorded draw down times. It should be pointed out that slug flow was assumed for the published calculations. In other words, the various simulations began while the stages in the ponds were well above the bottom of the ponds. It was assumed that the soil column directly below the ponds was saturated and consequently only horizontal flow was considered. ICPR was used to model these ponds (Airport Warehouses, Tutor Time Day Care and Fisherman’s Landing) using the information provided in the SJ93-SP10 report. Slug flow is modeled in ICPR by setting the layer thickness to zero. In addition to modeling these three ponds with ICPR, comparisons were made with PONDS (v3.2) and MODRET (v6.1). Slug flow can be modeled in MODRET and PONDS. However, both start at the bottom of the pond and calculate the required volume to fill the pond and any unsaturated soils below the pond to the desired starting elevation. PONDS fills this volume quickly (e.g., a minute or so) while MODRET fills it over a one hour period similar to a short duration storm. ICPR does not need to do this and can begin the simulation at time zero with any elevation and by setting the layer thickness to zero, the soil column begins fully saturated. Although the computational framework for PONDS and MODRET are similar in the sense that both spawn the USGS MODFLOW program which needs a rectangular

C-2


mesh, the two programs go about it differently. An equivalent length and width can be specified in PONDS and gives the user some flexibility in how the mesh is established. MODRET on the other hand back-calculates an equivalent length and width based on specified volumes, design depths and length to width aspect ratios. Consequently, MODRET does not have the same flexibility as PONDS in this regard. ICPR builds its computational framework from three rings beginning at the edge of the pond and extending outward from the pond. ICPR has the most flexibility of the three programs and is not limited to an idealized rectangular pond. Since the computational grid is important and the three models establish this in different ways, it was necessary to use several different methods to develop the computational framework as described below: Method 1 – Equivalent Length and Width from Total Pond Volume: As already mentioned, MODRET does not allow the user to input equivalent lengths and widths directly. Therefore, this first method is based on MODRET’s technique of back-calculating equivalent lengths and widths from the total pond volume. This is not the best approach for either PONDS or ICPR, but is included so that an appropriate comparison can be made of the three models. The calculations proceed as follows: Aavg = (V2 – V1) / (Z2 – Z1) Weq = (Aavg / Raspect)1/2 Leq = Weq x Raspect where,

Aavg = average area V1 = volume at bottom of pond (zero) V2 = volume at commencement of draw down Z1 = elevation of bottom of pond Z2 = elevation at commencement of draw down Raspect = length to width ratio (derived from SJ93-SP10)

Weq = equivalent width Leq = equivalent length

Once Weq and Leq are determined, they are entered directly into PONDS. They are also used to determine the three perimeters (P1, P2 and P3) needed for ICPR. Since both PONDS and MODRET are based on equivalent rectangles, a rectangular shape was assumed for computing P1, P2 and P3 for ICPR as follows: P1 = 2(Weq + Leq) P2 = P1 + 2∏(X12) P3 = P1 + 2∏(X12 + X23) where, X12 = is the offset distance between P1 and P2 (100’ was used)

X23 = is the offset distance between P2 and P3 (650’ was used) Method 2 – Equivalent Length and Width from Draw Down Volume: This method is basically the same as Method 1 except the average area is based strictly

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on the draw down volume rather than the entire volume of the pond. Two of the ponds (Tutor Time and Fisherman’s Landing) were still wet at the end of the recorded draw down period. Therefore, it is more accurate to derive the equivalent lengths and widths from the draw down volume rather than the entire volume of the pond. Unfortunately, there is no mechanism to input these adjusted equivalents into MODRET, so only Method 1 was used for those simulations. Method 3 – Obtain Perimeters from Scaled Drawings: In general, for ICPR, it is better to base the first perimeter, P1, on a scaled drawing rather than using equivalent lengths and widths. This was done for the Airport Warehouses and Fisherman’s Landing sites. It wasn’t necessary for the Tutor Time site since that pond is rectangular. Details of the various simulations, including published results of the 1993 study, are provided on the following pages. A summary is included in Table C.1. In general, the least accurate results are obtained when the computational framework is based on Method 1 described above. The results for PONDS and ICPR improve greatly using Method 2. However, Methods 1 and 2 are both techniques to arrive at an equivalent rectangle. When a pond is highly irregular, such as the Fisherman’s Landing site (see Figure C.1), all three models perform poorly with an equivalent rectangle. However, when the perimeter, P1, is obtained from a scaled drawing as in the case of the Airport Warehouses site and the Fisherman’s Landing site, the ICPR draw down times are within 10% of actual values. Actual MODRET1 PONDS1 ICPR1 PONDS2 ICPR2 ICPR3

Airport

Warehouses

5.3

---

5.1

-3.8%

4.5

-15.1%

4.2

-20.8%

---

---

---

---

4.8

-9.4%

Tutor Time

Day Care

4.0

---

4.5

+12.5%

4.6

+15.0%

4.5

+12.5%

4.4

+10.0%

4.25

+6.3%

---

---

Fisherman’s

Landing

7.8

---

9.8

+25.6%

10.7

+37.2%

10.1

+29.5%

9.3

+19.2%

8.8

+12.8%

8.0

+2.6%

Table C.1 Summary of Simulated Draw Down Times (in days) and Percent Deviation

from Actual Values. Notes: 1 Computational Framework based on Method 1. 2 Computational Framework based on Method 2. 3 Computational Framework based on Method 3.

It might be possible to use better methods to arrive at equivalent lengths and widths based on actual perimeters, volumes and areas and apply them to the PONDS program and obtain more accurate results. However, it does not appear to be possible to modify the equivalent lengths and widths in MODRET as it is currently configured.

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Airport Warehouses

Event: March 25, 1992 Recovery: from +7.0 ft NGVD to +6.0 ft NGVD Time: 5.3 days Aquifer Base: 3.5 ft NGVD Water Table: 4.7 ft NGVD Bottom Elev: 6.0 ft NGVD Kh: 14 fpd Porosity: 20% Published Results (Table 10, SJ93-SP10): Simplified Analytical Method 4.7 days Modified MODRET 4.5 days Hantush 3.5 days Glover’s Equation 4.0 days Pond Flow 4.8 days Simulation Results:

Method 1 & 2: Equivalent Length and Width Based on Draw Down Volume

Draw Down Volume: 2,141 cubic feet Draw Down Depth: 1 foot Length to Width Ratio: 1.33 (from published data) Equivalent Length: 53.3 feet Equivalent Width: 40.1 feet

Perimeters and Offsets for ICPR: P1 = 187 feet P2 = 815 feet X12 = 100 feet N = 20 P3 = 4,899 feet X23 = 650 feet N = 65

ICPR v3.1 4.2 days (-20.8%) PONDS v3.2 4.5 days (-15.1%) MODRET v6.1 5.1 days ( -3.8%)

Method 3: Perimeter, P1, Based on Scaled Drawing P1 = 166 feet (4 x 41.5’) P2 = 795 feet X12 = 100 feet N = 20 P3 = 4,879 feet X23 = 650 feet N = 65

ICPR v3.1 4.8 days ( -9.4%)

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Tutor Time Day Care

Event: May 4, 1992 Recovery: from +6.73 ft NGVD to +5.27 ft NGVD Time: 4.0 days Aquifer Base: 1.5 ft NGVD Water Table: 4.7 ft NGVD Bottom Elev: 4.8 ft NGVD Kh: 18 fpd Porosity: 20% Published Results (Table 10, SJ93-SP10): Simplified Analytical Method 5.0 days Modified MODRET 4.5 days Hantush 3.1 days Glover’s Equation 2.3 days Pond Flow 4.3 days Simulation Results:

Method 1: Equivalent Length and Width Based on Pond Volume Draw Down Volume: 1,978 cubic feet Draw Down Depth: 1.93 feet (4.80 to 6.73) Length to Width Ratio: 2.37 (from published data) Equivalent Length: 49.3 feet Equivalent Width: 20.8 feet


ICPR v3.1 4.5 days (+12.5%) PONDS v3.2 4.6 days (+15.0%) MODRET v6.1 4.5 days (+12.5%)

Method 2: Equivalent Length and Width Based on Draw Down Volume Draw Down Volume: 1,722 cubic feet Draw Down Depth: 1.46 feet (5.27 to 6.73) Length to Width Ratio: 2.37 (from published data) Equivalent Length: 52.9 feet Equivalent Width: 22.3 feet Perimeters and Offsets for ICPR: P1 = 150 feet P2 = 779 feet X12 = 100 feet N = 20 P3 = 4,863 feet X23 = 650 feet N = 65

ICPR v3.1 4.25 days (+6.3%) PONDS v3.2 4.4 days (+10.0%)

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Fisherman’s Landing

Event: May 24, 1992 Recovery: from +2.2 ft NGVD to +1.4 ft NGVD Time: 7.8 days Aquifer Base: -12.0 ft NGVD Water Table: 0.8 ft NGVD Bottom Elev: 1.0 ft NGVD Kh: 5 fpd Porosity: 20% Equivalent Length and Width Based on Draw Down Volume: Draw Down Volume: 4,310 cubic feet Draw Down Depth: 0.80 feet (between 1.4 and 2.2) Length to Width Ratio: 2.18 (from published data) Equivalent Length: 108.4 feet Equivalent Width: 49.7 feet Published Results (Table 10, SJ93-SP10): Simplified Analytical Method 16.4 days Modified MODRET 14.0 days Hantush 11.6 days Glover’s Equation 6.3 days Pond Flow 11.5 days Simulation Results:

Method 1: Equivalent Length and Width Based on Total Pond Volume Draw Down Volume: 4,964 cubic feet Draw Down Depth: 1.20 feet (between 1.0 and 2.2) Length to Width Ratio: 2.18 (from published data) Equivalent Length: 95.0 feet Equivalent Width: 43.6 feet


ICPR v3.1 10.1 days (+29.5%) PONDS v3.2 10.7 days (+37.2%) MODRET v6.1 9.8 days (+25.6%)

Method 2: Equivalent Length and Width Based on Draw Down Volume Draw Down Volume: 4,310 cubic feet Draw Down Depth: 0.80 feet (between 1.4 and 2.2) Length to Width Ratio: 2.18 (from published data) Equivalent Length: 108.4 feet

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Equivalent Width: 49.7 feet


ICPR v3.1 8.8 days (+12.8%) PONDS v3.2 9.3 days (+19.2%)

Method 3: Perimeters Based on Scaled Drawing (see Figure C.1) P1 = 350 feet P2 = 950 feet X12 = 100 feet N = 20 P3 = 5,034 feet X23 = 650 feet N = 65

ICPR v3.1 8.0 days ( +2.6%)

Figure C.1 The First Two Computational Rings Used by ICPR

for the Fisherman’s Landing Pond.

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Appendix D. Comparisons of ICPR with MODRET (v6.1) and PONDS (v3.2) MODRET (v6.1) and PONDS (v3.2) are similar groundwater – surface water models in the sense that both spawn the USGS MODFLOW groundwater program for saturated flow computations. Both also require an equivalent rectangular pond so that a 2-D finite difference grid can be created as required by MODFLOW. MODRET and PONDS have unsaturated vertical flow algorithms and automatically transition to saturated horizontal flow. The following example (Figure D.1) was taken from the MODRET user’s documentation (Example 3) that comes with the program. It was selected because it is a closed retention system and includes both vertical unsaturated flow and horizontal saturated flow. A few adjustments to the input data were necessary to maintain consistency between the models.

Figure D.1 Plan View with Contours of a Closed Retention System

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D.1 Input Data In this example, a runoff hydrograph for a 100-year 24-hour storm from a single drainage basin serves as inflow to the pond. The only means of recovering storage is via percolation. There are no other outfalls for this pond. Drainage Basis Data Catchment Area: 5.2 acres Curve Number: 77 % DCIA: 18.8% Time of Concentration: 23 minutes Storm and Unit Hydrograph Data Distribution: Type II – Florida Modified (1) Rainfall Depth: 8.6 inches Peak Factor & Unit Hydrograph: 323 (1) To minimize inconsistencies, the MODRET rainfall distribution was imported to ICPR and used instead of the standard FLMOD distribution that is provided in ICPR. Pond Data Table D.1 includes stage-area-volume data used in this example. For modeling purposes, the bottom of the pond and starting elevation are assumed to be 78.0 feet.

Stage - ft -

Area - sqft -

Volume - cuft -

Volume - acft -

78.0 6,440 0 0.00

80.0 10,570 18,731 0.43

82.0 14,375 42,253 0.97

84.0 21,675 76,230 1.75

86.0 31,035 128,938 2.96

Table D.1 Stage-Area-Volume Data for the Pond

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Data Used to Establish the Computational Grid for Saturated Flow MODRET: Area at Starting Water Level: 6,440 sqft Volume Between Starting Water Level and Est. High Water: 76,230 cuft Pond Length to Width Ratio: 1.33 Design High Water: 84.00 ft MODRET derives equivalent length and width from the above data. Although not stated in the documentation, these are determined by first dividing the volume (76,230 cuft) by the design depth of 6 feet (84 ft minus 78 ft) to obtain an average area (12,705 sqft). Then, given the length to width aspect ratio of 1.33, L and W values of 130.1 ft and 97.6 ft are obtained, respectively. MODRET has two options for determining flood stages in the pond and recovery. The first is a direct method called the “Infiltration Module” and does not use the actual stage-storage relationship for the pond. The second option is the “Routing Module” which allows the stage-storage relationship to be entered and used for the computations. It is unclear from the documentation exactly how this is accomplished. Both methods are compared with ICPR and PONDS. It should be noted that the maximum allowable infiltration rate in MODRET for this example is limited to the average area (12,705 sqft in this example) multiplied by the vertical conductivity and divided by the safety factor. This applies to both the infiltration module and the routing module. This will be discussed in greater detail in subsequent sections. PONDS: Equivalent Length: 130.1 ft Equivalent Width: 97.6 ft

Maximum Area for Unsaturated Infiltration (at el. 83.82’) 21,000 sq. ft.

Note: The equivalent length and width match the equivalent length and width derived by MODRET. The methodology used by MODRET to derive equivalent lengths and widths might not be the best approach for PONDS. However, for comparison purposes, the MODRET derived values were used. The maximum area for unsaturated infiltration was obtained through multiple iterations such that it matched peak stages reasonably close.

ICPR: The perimeters for three computational rings must be specified in ICPR. Although equivalent rectangles are not required in ICPR and are not the recommended approach, for consistency sake, Perimeter 1 was obtained from the equivalent length and width (P1 = 2W + 2L) defined for PONDS and derived by MODRET. Perimeters 2 and 3 were calculated using corner radii of 100 feet and 1,000 feet, respectively. (Note: P = 2(L+W) + 2∏R, where R is the corner radius) Twenty finite difference cells (5-ft spacing) were used between the first and second computational rings and 90 10-ft cells were used between the second and third

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rings. A total distance of 1,000 feet from the edge of the pond is used for the saturated horizontal groundwater flow computations. Aquifer Data Aquifer Base Elevation: 58.00 ft Water Table Elevation: 73.00 ft Unsaturated Vertical Hydraulic Conductivity: 8.67 fpd Factor of Safety for Kvu: 2.00 Saturated Horizontal Conductivity: 20.00 fpd Effective/Fillable Porosity Unsaturated Analysis: 0.28 Effective/Fillable Porosity Saturated Analysis: 0.30 Average Effective/Fillable Porosity: 0.29 Note: Kvu for PONDS and ICPR was reduced by 50% (4.335 fpd) to incorporate a factor of safety of 2.0. Pertinent input data used for each of the three models are provided in Figures D.2, D.3 and D.4.

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Figure D.2 Pertinent Input Data for MODRET

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Figure D.3 Pertinent Input Data for PONDS

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Figure D.4 Pertinent Input Data for ICPR

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D.2 Comparison of Runoff Hydrographs The computed runoff hydrographs from each of the three models are shown in Figure D.5. There are some minor differences but none that would make an appreciable difference in the routing results. Differences in the first few hours of the storm are believed to be due to the way initial abstraction is handled for DCIAs in each of the models. ICPR assumes 0.1” is lost to initial abstraction over the DCIA. It is unclear if or how the other two models are addressing this. The hydrographs for PONDS and ICPR are almost identical after the first few hours. MODRET seems to shift slightly in time by about 5 minutes.

Figure D.5. Runoff Hydrographs Generated by MODRET, PONDS and ICPR Using the SCS Unit Hydrograph Method (Peak Factor = 323, SCS Type II – Florida Modified Rainfall Distribution, 8.6” of Rainfall in 24-hour Period).

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Figure D.6 Comparison of Runoff Hydrographs for the First 4 Hours of Storm

Figure D.7 Comparison of Runoff Hydrographs at Peak Conditions

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D.3 Comparison of Infiltration Hydrographs Before discussing specific infiltration hydrographs, it would be useful to understand how infiltration for unsaturated flow is handled. Consider the three unsaturated soil zones depicted in Figure D.8. Zone 1 is directly below the bottom of the pond. If the inflow rate of water to the pond is less than the potential infiltration rate, then unsaturated flow would be confined to zone 1 and stages in the pond would not rise above the bottom. As inflow rates increase and exceed the potential infiltration rate, water levels in the pond rise above the bottom of the pond and the surface area expands exposing additional unsaturated areas below the pond.

Figure D.8 Unsaturated Soil Zone Between Pond Bottom and Water Table PONDS calculates potential infiltration rate by multiplying vertical conductivity by the current wetted surface area in the pond. Surface areas are interpolated from a user provided stage-area table. As water levels increase, the potential infiltration rates also increase. Driving head due to increased flood stages is not considered for unsaturated flow. Unsaturated flow in PONDS continues until all of the soil storage between the pond and the water table is filled. The amount of available soil storage is determined by projecting an “imaginary cylinder” through the pond down to the water table. The cross sectional area of this “cylinder” is an input parameter in PONDS and is designated as the “Maximum Area for Unsaturated Infiltration”. It appears as though a guess of the maximum stage must first be made. Then the corresponding area is obtained from a stage-area table to estimate this parameter. If the first guess is too

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high, then the available soil storage in the unsaturated zone would also be too high and it would take longer to fill. Consequently, the transition to horizontal saturated flow would take longer. Conversely, if the guess is too low, then the transition to saturated flow would be quicker than it should be. Therefore, estimating the “Maximum Area for Unsaturated Flow” in the PONDS program is an iterative process. Furthermore, if significant differences in peak stages occur for different storm events or design conditions, then technically, the iterative process should be performed for each storm event and design condition. A few iterations in PONDS were made for this example to determine the “Maximum Area for Unsaturated Flow”. A final value of 21,000 square feet was used and corresponds to an elevation of 83.82 ft. As indicated in Table D.2, the net available soil storage below the pond at this elevation is 44,305 cubic feet. This is the amount of water that must be infiltrated from the pond to the soil column before the transition to saturated flow can occur in PONDS. Based on a few tests, it appears as though PONDS calculates the available soil storage before the simulations begin. In essence, it’s like the volume of an empty bucket and the bucket must be completely filled before saturated flow can occur.

Elevation - ft -

Depth

To W.T. - ft –

Surface

Area - sq ft -

Gross(1) Volume - cu ft -

Pond

Volume - cu ft -

Net Soil(2) Storage - cu ft -

73.00 0.00 0 0 0 0

78.00 5.00 6,440 32,200 0 9,338

80.00 7.00 10,570 73,990 18,731 16,025

81.12(3) 8.12 12,705 103,165 31,766 20,706

82.00 9.00 14,375 129,375 42,253 25,265

83.82(4) 10.82 21,000 227,220 74,444 44,305

84.00 11.00 21,675 238,425 76,230 47,037

86.00 13.00 31,035 403,455 128,938 79,610 Notes: (1) Gross volume is the surface area multiplied by the depth to the water table

(2) Net soil storage is difference between gross volume and pond volume multiplied by average fillable porosity (0.29)

(3) Elevation 81.12 ft corresponds to the average pond area of 12,705 sq ft as computed by MODRET (4) Elevation 83.82 ft corresponds to the “Maximum Area for Unsaturated Flow” used in the PONDS model

Table D.2 Soil Storage Below Pond at Various Depths

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An excerpt from the detailed results report of PONDS is shown Figure D.9. Notice that the flow type changes from “U/P” (unsaturated/pond) to “U/S” (unsaturated/soil) as the cumulative infiltration volume exceeds the available soil storage as described above.

Figure D.9 Excerpt from the PONDS Detailed Results Report

ICPR has a few options for handling unsaturated flow. The most appropriate for this example is to set the “Surface Area Option” to “Vary based on Stage/Area Table” as previously shown in Figure D.4. ICPR works very similar to PONDS when this option is selected. Potential infiltration rates are calculated the same as in PONDS – vertical conductivity multiplied by the current surface area. Available soil storage is determined in a similar manner. However, the user does not have to guess the maximum stage before the simulation takes place. ICPR automatically adjusts the available soil storage below the pond at every time step based on stages in the pond. Unlike the fixed “bucket” example sited for PONDS, ICPR adjusts the bucket size as the simulation proceeds. Consequently, no guesses are required before the simulation takes place and no iterations are necessary. Figure D.10 includes excerpts from the ICPR link and node time series reports. The last three digits of the “Qcode” change from 600 to 620 from hour 20.58 to 20.67 and means the flow has transitioned from unsaturated flow to saturated flow. The infiltration volume through hour 20.58 is 0.94313 acre-feet or about 41,000 cubic feet. By tracking the available soil storage continuously throughout the simulation, a little less overall soil storage is required to be filled in ICPR than in the PONDS model before the transition to saturated flow. Multiple storm events can be run in ICPR without changing any of the input parameters.

Figure D.10 Excerpt from the ICPR Link and Node Time Series Reports

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A comparison of infiltration hydrographs for PONDS and ICPR is shown in Figure D.11. Unsaturated flow occurs in both models prior to hour 20 and as noted in the graphs, they are expectedly quite similar for this period since both models use a relatively simple and similar method for calculating unsaturated flow. ICPR transitions into saturated flow about an hour earlier than PONDS because of how ICPR calculates the available soil storage in the unsaturated zone. The PONDS “bucket” is about 45,000 cubic feet while ICPR’s bucket is 41,000 cubic feet at the moment of transition. At an infiltration rate of 0.9 cfs, PONDS would need about 1.25 hours more to fill the additional 4,000 cubic feet of soil storage.

Figure D.11 Comparison of Infiltration Hydrographs Notable differences occur between PONDS and ICPR at the transition point from unsaturated flow to saturated flow. There is an abrupt spike in the PONDS hydrograph because at the moment the wetting front touches the water table, the full head (i.e., the water surface in the pond minus the ambient water table elevation) is felt at the water table. There does not appear to be any consideration for limitations caused by the vertical conductivity and the pond’s ability to deliver sufficient water to the groundwater table to “feed” the horizontal flow algorithm. After transitioning to saturated horizontal flow, ICPR checks the vertical flow availability from the pond against the horizontal flow demand at the water table. If the pond cannot deliver the amount of water demanded by the horizontal flow

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algorithm, then the horizontal flow is limited to the vertical flow. In essence, the boundary condition for the saturated horizontal flow model is set to a flow rate rather than head condition. Consequently, the abrupt spike in infiltration experienced in the PONDS model is not an issue in the ICPR model. Figure D.12 compares infiltration hydrographs of PONDS and ICPR to MODRET. The infiltration module of MODRET was used in this case. An enlarged view is shown in Figure D.13. The MODRET infiltration rate increases linearly for the first 10 hours up to about 0.25 cfs and then jumps to 0.6375 cfs and remains virtually constant until hour 36. It is interesting to note that the available soil storage directly below the very bottom of the pond is 9,338 cubic feet (refer to Table D.2, elevation 78 feet) and that according to the MODRET results, 9376 cubic feet of water has infiltrated at this transition point. It appears that the flow has transitioned from unsaturated to saturated flow at this point.

Figure D.12 Comparison of Infiltration Hydrographs

The limiting infiltration rate of 0.6375 cfs cited in the previous paragraph corresponds to the vertical unsaturated conductivity rate of 4.335 fpd (the rate of 8.67 fpd with a safety factor of 2) applied over the average surface area of 12,705 square feet. It is noteworthy that the apparent trigger for transition from unsaturated to saturated flow is based on the bottom area of the pond (6,440 square feet) rather than the average surface area of 12,705 square feet, but the limiting

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infiltration rate is based on the average surface area and not the bottom area of the pond. MODRET does not appear to allow the infiltration rate to exceed the vertical conductivity applied over the average surface area.

Figure D.13 Comparison of Infiltration Hydrographs There are several important assumptions in the MODRET infiltration module that warrant further discussion. First, a design high water elevation and corresponding pond volume must be assumed prior to the simulation. From that information and a length to width aspect ratio, a rectilinear box with vertical sides is assumed for the entire simulation. Since stage-area-storage data are not provided (in the infiltration module), the increased infiltration normally expected from increased surface areas is not considered. Consequently, infiltration rates are potentially over-predicted in the earlier part of the storm and under-predicted in the later part. Since the infiltration module of MODRET does not include stage-area data, increasing surface areas with depth in the pond are not considered. Therefore, the routing module, which does include a stage-storage table, was used in hopes of more accurately modeling infiltration rates. The resulting infiltration hydrograph is shown in Figure D.14 superimposed with the runoff hydrograph through hour 40. The infiltration rates match the runoff rates closely up to about hour 10, as expected. Then, the infiltration rates drop suddenly and match the previous simulation results from the “infiltration module”. This behavior begins when the soil column

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immediately below the very bottom of the pond is filled. This point, as already mentioned, is probably the transition point from unsaturated flow to saturated flow. Although stage-storage data, and intrinsically stage-area data, are available to MODRET’s routing module, the limiting infiltration rate of 0.6375 cfs is tied back to the average pond area of 12,705 square feet. Infiltration rates between hours 10 and 20 would be about 60% higher if the vertical conductivity was applied to the actual surface area (as is done in PONDS and ICPR) rather than to the average surface area. Not doing so means higher stages and longer drawdown times.

Figure D.14 Comparison of MODRET Routing Module Runoff and Infiltration Hydrographs

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D.4 Comparison of Stage Hydrographs Stage hydrographs for PONDS, ICPR and MODRET (infiltration module) are depicted in Figure D.15. PONDS and ICPR are remarkably close in both amplitude and duration. MODRET produces higher peak stages and longer drawdown times. This is directly attributable to the way MODRET restricts the infiltration rate to the vertical conductivity applied over the average surface area.

Figure D.15 Comparison of Stage Hydrographs Figure D.16 compares stages for the infiltration and routing modules of MODRET. The peak stages are close, but the recession legs of the hydrographs depart significantly between hours 36 and 120. Since the infiltration hydrographs for both modules are identical beyond about hour 10, the differences in the drawdown curves are likely the result of introducing the stage-storage table for the routing module. The infiltration module uses a rectilinear box with a constant average surface area of 12,705 square feet. The actual surface areas of the pond above about elevation 81.1 feet are greater than the average surface area and less than the average below 81.1 feet. Therefore, given identical infiltration hydrographs, slower drawdown times would be expected for the infiltration module when the pond stage is above elevation 81.1 feet and faster drawdown times should occur for pond stages below 81.1 feet.

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Figure D.16 Comparison of MODRET Stage Hydrographs

Appendix E. A Refined Infiltration Method in ICPR Infiltration during unsaturated vertical flow can be calculated a few different ways in ICPR. In the PONDS-MODRET-ICPR comparison example (see Appendix D), a single percolation link was used to connect the pond (node “ICPR-Pond”) to the groundwater table (node “ICPR-GWT”). That link was used to move water between the surface and the unconfined aquifer. The “Surface Area Option” for the percolation link in that example was set to “Vary based on Stage/Area Table” as shown in Figure E.1. This tells ICPR to extract surface areas from a stage-area table specified for the upstream node of the link (i.e., node “ICPR-Pond” in this example). It also tells ICPR to calculate the infiltration rate at any point in time by multiplying the current surface area in the pond by the vertical conductivity. Consequently, infiltration rates are automatically varied with stage. ICPR also automatically calculates the available soil storage below the pond based on an imaginary cylinder projected through the pond down to the water table with a cross sectional area equal to the current surface area in the pond. The available soil storage is updated at every time step and therefore there is no need to “guess” at a design high water beforehand. Finally, when the wetting front below the pond reaches the water table, a transition to saturated horizontal flow occurs. What happens after that depends on how the “Vertical Flow Termination” option is set. In the PONDS-MODRET-ICPR example, it was set to “Horizontal Flow Algorithm”. Therefore, when available soil storage below the pond is completely filled, horizontal flow commences.

Figure E.1 Surface Area and Vertical Flow Termination Options for Percolation Links in ICPR.

The “Vary based on Stage/Area Table” option is easy to use and allows for infiltration to vary with stage. However, there are a few shortcomings with it. First, the soil storage must be completely filled before a transition to horizontal flow can occur. In reality, water percolating near the bottom of the pond will reach the water table much quicker than along the side slopes. Secondly, the infiltration rates are simplified by applying the vertical conductivity over a surface area without consideration for head in the pond or location of the wetting front. These limitations can be overcome with a little more work when setting up the model as will be described. As previously discussed in this document, ICPR can also calculate infiltration rates for unsaturated vertical flow based on a modified Green-Ampt method (see Section 2.1). The infiltration rates with this method depend on the location of the wetting front in the soil column below the pond and also on the depth of water above the specified bottom elevation. However, due to the fundamental assumptions in the derivation of the Green-Ampt equation, it can only be applied to constant areas. Therefore, when

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the “Surface Area Option” for a percolation link is set to “Vary based on Stage/Area Table”, the Green-Ampt method is not used. To invoke the Green-Ampt method, the “Surface Area Option” must be set to either “Use 1st Point in Stage/Area Table” or “User Specified”. However, invoking either of these two options negates the advantages of using a variable stage-area relationship for the pond relative to infiltration calculations. It would be useful if the two approaches could be combined. It is possible in ICPR to apply the Green-Ampt method to a pond with varying slopes by “stair-stepping” up the slopes of the pond with multiple percolation links as shown in Figure E.2. ICPR was designed since its inception more than 25 years ago to allow for multiple links to be used between any two nodes. Percolation links are no exception.

Figure E.2 Refining Infiltration Calculations in ICPR by Using Multiple Percolation Links

The example depicted in Figure E.2 uses 10 separate percolation links to connect the pond to the unconfined aquifer. The “Surface Area Option” in the percolation link data form is set to “User Specified” for each of the links. A bottom elevation and corresponding surface area must be specified for each one. The bottom elevation is the elevation at which infiltration begins in the link. For example, as water begins to fill the pond shown in Figure E.2, it would first spread across link 1 and then 2 and then 3 and so on. There will be a period when link 1 is “wet” while the other links

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are “dry”. Likewise, as the water level drops below any of the specified bottom elevations, infiltration would cease for that link. Surface areas corresponding to the bottom elevations of each link are also required. These are actually differential areas as the links stair-step up the slope of the pond. They become the “imaginary cylinders” for each link and are projected downward to the water table. Soil storage is calculated in each cylinder so that the wetting front can be tracked independently for each one. Also, the driving head for each link is known. Consequently, the Green-Ampt equation can be applied to each link and therefore a more accurate accounting of the infiltration process can take place. The transition from vertical flow to horizontal flow must be carefully considered when using multiple percolation links to connect a single pond to the unconfined aquifer. Clearly, it would be incorrect to allow each link to transition to horizontal flow. Remember that the horizontal flow algorithm is based on three computational rings that encompass the pond. The horizontal flow algorithm should be invoked by only one of the percolation links – the others should be “shut off” when the wetting fronts reach the water table. Unless there are some special circumstances, the horizontal flow algorithm should only be allowed for the link with the lowest bottom elevation (e.g., link 1 in Figure E.2). This link will be wet longer than any other link and it is the closest to the water table. Consequently, the wetting front for this link is expected to arrive at the water table before any of the others. Figure E.3 shows the settings that would be required for the lowest percolation link. The “Surface Area Option” is set to “User Specified” and a corresponding bottom elevation and surface area are provided. The “Vertical Flow Termination” option is set to “Horizontal Flow Algorithm”. The “Vertical Flow Termination” option for all other percolation links should be set to “Constant Rate” and the constant rate should be set to zero as shown in Figure E.4. This will shut the link off once the wetting front reaches the water table.

Figure E.3 Settings for Bottom-Most Percolation Link in Refined Infiltration Procedure

Figure E.4 Typical Settings for Percolation Links Situated Above the Bottom-Most Link in Refined Infiltration Procedure

The last consideration is that the computational rings for the bottom-most link must be set. This of course requires judgment on the modeler’s part, but a strong case can be made for using the same computational rings as those used when a single

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percolation link is used in conjunction with the “Surface Area Option” set to “Vary based on Stage/Area Table”. In essence, the average surface area can be projected downward to the base of the aquifer and the perimeter of the innermost computational ring calculated. Then offsets for the other two computational rings are made from there. This multi-percolation link approach was used for the PONDS-MODRET-ICPR example discussed at length in Appendix D. A total of 34 percolation links were used to connect the pond to the unconfined aquifer, each stair stepping upward along the slope of the pond at 0.2-foot increments. Table E.1 provides the relationship between stage in the pond and the differential areas. Bottom elevations and corresponding surface areas for each link were set to the stages and differential areas in Table E.1. The “Vertical Flow Termination” option for all links except the bottom-most one were set to a “Constant Rate” of zero. The horizontal flow algorithm was only used for the bottom-most link and the original computational rings were used (P1, P2, P3 = 455.4’, 1,083.7’ and 6,738.6’; X12 = 100’, X23 = 900’; and, N12 = 20, N23 = 90). The resulting infiltration hydrograph for the “multi-link” simulation is shown in Figure E.5 along with the “single-link” run. The peak combined multi-link infiltration rate is 2.12 cfs and occurs at hour 12.9 while the peak infiltration rate for the single link simulation is 1.04 cfs and occurs at hour 16.5. The transition from unsaturated flow to saturated flow occurs at hour 20.58 for the single-link run and 19.00 for the multi-link run. The transition to horizontal flow for the multi-link simulation occurs earlier because the wetting front directly below the pond, as expected, arrives at the water table sooner than the “averaged” wetting front associated with the single link run. The peak infiltration rate for the multi-link simulation is higher than the single-link simulation because the modified Green-Ampt equation is used for unsaturated flow. This equation accounts for head on the soil column and drives water into the soil at a higher rate than simply using the vertical conductivity times a surface area. The infiltration rate computed by the Green-Ampt equation is never less than the vertical conductivity multiplied by surface area. Figure E.6 shows separate infiltration hydrographs for the bottom of the pond and the sides. By hour 25.5, all side infiltration has ceased. This is not entirely because the stage in the pond has dropped below each respective side link. Instead, many of the side links have reached full saturation and the “Vertical Flow Termination” option was set to shut these links off when the wetting front reached the water table. In essence, both vertical and horizontal flows are occurring simultaneously between hours 19 and 25. Prior to hour 19, flow is entirely unsaturated and after hour 25 the flow is entirely saturated. This is believed to be more realistic than being either entirely unsaturated or entirely saturated. Stage comparisons between the multi-link and single link simulations are shown in Figure E.7. The peak stage is lower for the multi-link run – 83.12 feet versus 83.72 feet. The reason is directly related to the increased infiltration rates for the multi-link simulation as discussed in the previous paragraph. Consequently, a higher volume of water is infiltrated in the multi-link simulation and the recovery time is shorter. Intuitively, the multi-link simulation is probably more accurate than the single link simulation. However, the accuracy of one method over the other cannot be definitively concluded in the absence of recorded data.

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Figure E.5 Comparison of Infiltration Hydrographs

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Figure E.6 Comparison of Infiltration Hydrographs for ICPR Multi-Link Simulation

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Figure E.7 Comparison of Stage Hydrographs

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Stage (feet)

Total Area(square feet)

Total Area(acres)

Differential Area (acres)

78.0 6440.0 0.147842 0.147842 78.1 6646.5 0.152583 0.004741 78.3 7059.5 0.162064 0.009481 78.5 7472.5 0.171545 0.009481 78.7 7885.5 0.181026 0.009481 78.9 8298.5 0.190507 0.009481 79.1 8711.5 0.199989 0.009481 79.3 9124.5 0.209470 0.009481 79.5 9537.5 0.218951 0.009481 79.7 9950.5 0.228432 0.009481 79.9 10363.5 0.237913 0.009481 80.1 10760.3 0.247021 0.009108 80.3 11140.8 0.255756 0.008735 80.5 11521.3 0.264492 0.008735 80.7 11901.8 0.273227 0.008735 80.9 12282.3 0.281962 0.008735 81.1 12662.8 0.290697 0.008735 81.3 13043.3 0.299432 0.008735 81.5 13423.8 0.308167 0.008735 81.7 13804.3 0.316902 0.008735 81.9 14184.8 0.325637 0.008735 82.1 14740.0 0.338384 0.012747 82.3 15470.0 0.355142 0.016758 82.5 16200.0 0.371901 0.016758 82.7 16930.0 0.388659 0.016758 82.9 17660.0 0.405418 0.016758 83.1 18390.0 0.422176 0.016758 83.3 19120.0 0.438935 0.016758 83.5 19850.0 0.455693 0.016758 83.7 20580.0 0.472452 0.016758 83.9 21310.0 0.489210 0.016758 84.1 22143.0 0.508333 0.019123 84.3 23079.0 0.529821 0.021488

Table E-1. Stage-Differential Area Values Used for Multi-Link Simulations

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