3.0   MODEL CALIBRATION AND RESULTS

3.1   Initial depth

     For purposes of initializing the simulation, the water surface profile of the system was assumed to be at the bottom of the canals.  This assumption generated zero initial depths in the canal system.  Thus, all initial rainfall contributed to filling the empty canals.  Using this assumption and implementing the cold restart option that provides very minimal continuity errors.

3.2   Infiltration

     Infiltration from pervious areas is computed using the Horton equation. Its parameters were set to the following values, based on review of the soil surveys:

Max infiltration rate                                             2 inch/hour

Min (asymptotic) infiltration rate                       0.1 inch/hour

Decay rate of infiltration                                     0.00115 sec^-1

3.3   Imperviousness percentages

     The project area has been subdivided and assigned six different imperviousness percentages based on the projected 1993 functional population [3] computed using the New Jersey equation:

I = 9.6 PD ^{(0.53 – 0.0391 log 10 PD)}                                                                 (3.1)

Where:

I = imperviousness [%]

PD = population density in developed portion of the urbanized area (persons/acre)

     The New Jersey equation generated very low estimates of impervious percentages therefore alternate estimates were sought.  A literature survey of urban area development suggested appropriate imperviousness between 5% and 30% for the Cape Coral area.  Only a limited area (751 acres) was designated as high-populated area corresponding to an imperviousness percentage of 34%.  These values from the literature survey were used in preference to the New Jersey equation estimates.

3.4   Manning’s factor (n)

     The canal Manning’s factors were determined based on the information and photo documentation received from Lee County Environmental Services.  The n factors used for the channels in tidal reaches of the conveyances were set as 0.03. Generally these conveyances are wide with minimal plant growth in the channel.  The n factors in the freshwater channel portion of the conveyances located east of Nelson Road was set as 0.07.  Fresh water areas tend to be narrower and have more plant growth in the channel than the tidal portions of channels.  From Nelson Road due west until Weir #11, 13, 14 and 15 the factors were set as 0.06 or 0.05 [1].  For the overland flow within each subcatchment Manning’s “n” factors are 0.05 for the impervious portion and 0.20 for the pervious portion.

3.5   Groundwater flow

     The XP-SWMM Groundwater option in the present study was used in a less detailed analysis to evaluate its hydrology, focusing overall on the correct evaluation of the interflow/base flow contribution in the outflow hydrograph shape and total volume.

     In the City of Cape Coral the aquifer system is comprised of unconsolidated sand or silty sand deposits interbedded with sandy limestone, shell fragments, and sandy clay.  It is not under artesian pressure [1], [2].  The aquifer is reported to be approximately 20 feet thick and is under-laid with a thick (59 feet or more) layer of sandy clay.  Its hydraulic conductivity varies due to lithologic changes.  Results found in literature indicate that the hydraulic conductivity ranges from 10^-5 and 2*10^-2 feet/sec.  The higher values would indicate sand deposits, while the lower values would indicate limestone (References [4]). 

     The water level in this aquifer rises in response to recharge by local rainfall and seepage from the extensive network of drainage canals.  The levels fall in response to losses by evapotranspiration and seepage into the canals, the Caloosahatchee River, and the Bay.  Recharge of this aquifer by vertical percolation of rainwater is inhibited in many of the undeveloped and undisturbed parts of Cape Coral because of layer of silt and clay, which exist in places at very shallow depths.  This results in areas with locally perched water tables from which much of the rainfall is lost to evapotranspiration rather than infiltration to the water table aquifer.

     Groundwater movement is generally radial flow in the Cape Coral area, with flow moving to the west towards Matlacha Pass, and flow directions to the south and east towards the Caloosahatchee River, the canal system, and again Matlacha Pass [4].

     Groundwater elevations vary within the watershed. Adjacent to the main canals and their tributaries, water levels are low.  This provides for well-drained soil conditions.  This well-drained condition is evident from the dry conditions near the canals.  Localized ponding of water is often attributable to the fine grain soils rather than an overall high water table.  The localized ponding is usually of short duration, typically less than six hours.  Wet season water levels farther from the canal, including the area east of U.S. 41, are close to the ground surface as expected.  This is especially true in the areas that are not developed with canals and have not had land elevations raised [1].

     In the present study the water table was assumed to be 2.0 feet below the natural ground level, to run a steady state groundwater outflow calibration.  The groundwater rate that can be withdrawn from the water table aquifer into the canal system by horizontal seepage has been evaluated according to the Dupuit-Forchheimer formula resulting from a head differential of 2.5 feet between the furthermost area of the sub basins and the canals, a distance of approximately ¼ mile.

     Vertical percolation is more effective than seepage from the canals in reaching the water table aquifer.  The potential rate of this vertical percolation is up to 5 cfs/acres.  The canal system, however, has a potential recharge rate of less than 0.01 cfs/acre with a head of 1 foot [2].

     There are tributary conveyances on the north side of the Gator Slough canal. These conveyances have no control structures to maintain water levels.  The net effect is to expand the overdrained areas that exist adjacent to the main canal. Control structures on these and future connections to the canal could be designed to minimize the area of overdrainage.

     The City of Cape Coral Utility Master Plan Update, Final Report prepared by Dames & Moore in association with Black and Veatch August 1999 [4], describes a groundflow simulation performed in the area.  The MODFLOW model results presented in the report have been used as a calibration target to fix the groundwater parameters of the XP-SWMM options.  The Dames & Moore model showed that the base flow attainable rate would vary from 43 to 62 cfs.  The XP-SWMM model has finally reached the amount of a constant 50 cfs during the simulated period (September, 1996).

Groundwater outflow data

     Groundwater discharge represents lateral flow from the saturated zone to the receiving water.  The Dupuit Forcheimer flow equation takes on the following general form (with reference to Figure. 8):

        (cfs per linear foot of canal)                                    (3.2)

where

K = hydraulic conductivity (range 10^-5 to 2*10^-2 feet/sec)

L = maximum flow distance at the upstream end of the aquifer

L is determined by the average distance of the canals reaches, and is set

to about 0.25 mile

                                    Figure 8.  Definition sketch for Dupuit-Forcheimer approximation for                 

                 drainage to adjacent channel.

The XP-SWMM general groundwater equation takes the form:

                            (3.3)

                             Figure 9.  XP-SWMM sketch for the groundwater component.

Comparison of equations (3.2) and (3.3) gives:

     To route the groundwater simulation it is necessary to enter the name of the node or conduit to where groundwater from this subcatchment will drain.  The drainage name may or may not be the current node name. In the model the rate of ground flow coming from each single subcatchment (node) is chosen to drain in the subcatchment itself.  A summary table with the complete set of groundwater data is provided in Table 3.

                            Table 3.  Groundwater Required Parameters in XP-SWMM2000.

3.6   Tidal Boundary Conditions

     The Cape Coral City canals system bounded by the Lee-Charlotte County line on the north limit and by Pine Island road to the south, flows through Basins 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 eventually discharging to the North Spreader Canal System.  The spreader system is composed of saltwater canals not used for the City withdraws because of the high salinity and the detrimental impact this type of water has on the vegetation.  It originally was a body of fresh water isolated from salt water by a berm between the waterway and the saline Matlacha Pass. However, breaches and channels in the berm currently allow salt water to flow from the Pass to the waterway [4].

     The Spreader Canal System was designed to intercept discharge of freshwater from the Cape Coral network.  The main objective of the waterway is to prevent point discharge of the canal network into the mangrove fringe along the west and southwest coastline of Cape Coral, distributing the canal discharges over all the existing mangroves.  The mangroves were to be maintained by the waterway providing sheet flow through existing tidal wetlands.

     Other purposes of the Spreader are to provide additional salinity control for the canals which discharge into it and to maintain higher groundwater elevations upstream during the dry season [2].  The existing Spreader Canal consists of the North Spreader Waterway to the north of Pine Island Road, taken into account in this study, and the South Spreader Waterway to the south of Pine Island Road.  Both systems are physically separated and can be considered to be distinct entities [4].

     Breaks exist in the berm that separates the waterway from the Matlacha Pass. Currently, saltwater flows through these breaks from the pass to the Spreader System.  Therefore downstream of Burnt Store Road, in the North Spreader Waterway, the conveyance is controlled by the same tidal conditions of Matlacha Pass, also considering the capacity of the perimeter canal system in the Cape Coral and connections seaward, and it was assumed the water elevations would be similar to those in Matlacha Pass station.  Each of the four main canals of the network has a weir along Burnt Store Road: Weir 11 (Gator Slough Canal), 13 (Horseshoes Canal), 14 (Hermosa Canal) and 15 (Shadroe Canal).

     Matlacha Pass tide level historical information was provided by Lee County Environmental Services-Natural Resources Division, Florida Department of Environmental Protection and the U.S. Department of Commerce-National Oceanic and Atmospheric Administration National Ocean Service.  The model has been assigned a constant Mean High Water Level over the full period of the calibration event.  The unique node (#1756) assigned with the Outfall option and a “User Stage History” is located in the last southwest most position.  The level is taken from the Tidal Bench Mark “Matlacha Pass” (Latitude: 26^o37.9’N, Longitude: 082^o04.1’W, USGS Quad: Matlacha).  The calibration event (1 year Return Interval) has been assigned with a tide elevations of 2.0 feet NGVD.  The project events (5, 25, 100 years Return Interval) were assigned with a tide elevations of 2.7 feet NGVD.  The backwater analysis only accounts for conditions created by the design rainfall events. 

3.7   Upstream Inflow Data

     The only data available for calibration and verification was for the Gator Slough canal watershed.    Insufficient data were available for Horseshoe, Hermosa and Shadroe canals.  Therefore the conceptual methodology adopted to calibrate the model has been to use one year of data for only one sub watershed, the Gator Slough canal watershed, and assume that the calibrated parameters are applicable to other basins.

     Upstream inflow to Gator Slough originating from the portion of the watershed located north and east at U.S. 41 (33 square miles undeveloped watershed of wildlife management area) are inserted as a “User Inflow” input in node 31 of the model.  Data are from gauging station located 0.5 miles west of U.S. 41, named Gator Slough at US 41 near Ft. Myers, FL.

     The period selected for model calibration includes 24 days from September 5^th to 28^th, 1996.  This is consistent with the 1-year return interval (RI) event selected based on Gumbel statistical analysis performed over the outflow historical period of record for Weir #11, downstream of Gator Slough Canal.  The peak Gumbel 1-year RI flow for this section is 42 cfs (daily average value)

3.9   Outflow Data and Statistical Analysis  

     The main criteria used in selecting the calibration period of record was the Gumbel statistical analysis applied to the outflow data for the station located near S.R. 765, corresponding to Weir #11.  The analysis was conducted for Weir #11 outflow data to identify that period of record most closely matching a 1-year RI runoff event and for which a concurrent rainfall record and upstream inflow record were also available.

Gumbel Statistical Analysis

     The annual maximum flood flow value, in daily mean series, detected in a water stream section, is an extreme event. Since the watershed was not submitted to relevant hydrologic modifications during the period of years under analysis, those series can be treated as homogeneous and independent values. These conditions allow us to associate the probable frequency and then the return interval to a given discharge event and to apply those values to the statistical analysis methods.  Gumbel analysis has been proved to be one of the most reliable methods for hydrologic series.  A double exponential probability distribution allows assignment of an expected flow rate for all return periods.

     The U.S. Geological Survey monthly maximum values of daily average discharge on S.R. 765 corresponding to Weir #11 are shown in Table 5.

Table 5.  USGS monthly maximums of discharge (cfs) for location: 

               264139082022100 Gator Slough at SR 765 Near Fort Myers, FL.

     Some of the annual series were not populated with all monthly values.  In these cases an annual event maximum value was taken into account only when the values for the whole period between June and October were available.  This is because the peak flow rates for all years occurred in this interval.  A return period was then associated to each of the extreme values as shown in the following Table 6.

                     Table 6.  Event with Gumbel associated return time for Gator Slough at S.R. 765.

     After the Gumbel analysis it is possible to find out a discharge value for every given return period as an independent variable (Table 7).

                        Table 7.  Return period with associated discharge values for Gator Slough at S.R. 765.

     Given the logarithmic nature of the final Gumbel equation, the 1-year event is obtained from an interpolation trend line of the other data.  Figure 13 shows the data distribution and the logarithmic trend line used to associate the discharge value to 1 year.

3.10   Model Calibration Results

     September 1996 was selected as the period of record to calibrate the Cape Coral canals model.  The period selected included all of the following basic data sets for a one-year recurrence interval storm event were available: (1) Inflow data for the Gator Slough at U.S. 41 USGS station, (2) Outflow data for the Gator Slough at S.R. 765 USGS station, and (3) Rainfall data at the Lee County Lake Fairways station.

     The one-year recurrence interval event was identified based on Gumbel statistical analysis of discharge data at S.R. 765.  Thus, the period of record used for the calibration run represents a documented flow event with a peak near to the statistical one-year recurrence interval flow magnitude.  The calibration event was not selected on the basis of the one-year rainfall magnitude.

       The historical outflow hydrograph in Figure 15 presents the measured flow rates from September 5 to September 28, 1996.  The hydrograph rises to a double peak value and recedes to the completion of the complex event.  The duration of the one-year event used for calibrations purposes was limited to 24 days (from 5^th to 28^th of September, 1996) to be consistent with the requirement that the system achieve the same conditions at the end of the event as it had at the beginning.  The runoff data for September 1-4 and September 29-30 included either a falling or rising hydrograph limbs and therefore were eliminated from consideration.

     The canal system calibration was also evaluated by comparison with the Johnson Engineering design water surface profile along the Gator Slough Canal for the one-year event [1]. The mass balance is summarized in the Table 8.  Figures 14-16 describe the model calibration results. These figures show an underestimation of total runoff of approximately 10% over the 24-day period when compared to USGS discharge data. However an internal budget analysis shows approximately two additional inches of system outputs (runoff + ET) when compared to system inputs (rainfall + U.S. 41 inflow). This difference is assumed to be the result of base flow.  Table 9 is a comparison of the model calibration results with USGS measured data.

                                  Table 8.  Mass balance table for XP-SWMM calibration event.

                    Table 9.  Flow comparison between model calibration results and 

                                   USGS measurements at S.R. 765.

     As these distilled results show, the model appears to be performing well.  The record of a single rain station is applied to the whole model area, whereas much of the regional rainfall occurs as thunderstorms, which strike unpredictably and locally. Is therefore reasonable to consider acceptable the 20% error in some points of the outflow hydrograph comparison and the mismatch of the two main event peaks.  The fact that the first event is over predicted and the second event under predicted suggests that the model performance is correct, on average, and is limited by rainfall data.  The overall agreement between the calibrated XP-SWMM model and the USGS data were acceptable.  While limited rainfall data make event-by-event comparisons difficult, agreement over the 24-day period shows a model peak flow of 346 cfs compared to the USGS measured of 331 cfs, an overestimation of only 4.3%. The model underestimated discharge volume by 10% (7.2 inches were measured by the model while USGS measured 8.0 inches).