Introduction
      Measuring ground surface elevations in South Florida is a difficult task. As a result the elevation data available for the region exists only at a coarse spatial resolution. This has presented a significant problem when trying the capture the dynamics of biological components. Local hydrologic conditions are an important factor in the behavior and life histories of many of South Florida's flora and fauna. The local elevation of the ground surface is in turn an important part of local hydrologic conditions. Without detailed elevation data there can be no local response by models to hydrology. The ATLSS High Resolution Topography (HRT) model has been produced to provide detailed elevation data as input to various models, both within the ATLSS project and in other projects, at spatial resolutions which are relevant to biological processes.
      The accuracy and sources of errors in the ATLSS HRT are long-standing questions. The lack of any reliable ground surface elevation data against which the model could be tested have made it difficult to find meaningful answers. To date, the problems with the elevation data sets available to us has been the lack of error measurements for either the horizontal or vertical data. In addition, many early data sets either covered very limited regions, or covered large regions at very coarse spatial resolutions.
      The High Accuracy Elevation Data (HAED) project is an effort headed by the US Geological Survey (USGS) to obtain accurate elevation values for the Everglades at a high spatial resolution. The technique used by the HAED to measure both the horizontal and vertical data utilizes differential GPS. The differential GPS technology yields measurment accuracies which previously have been difficult to achieve.
      Measurements are taken on a grid where the nominal longitudinal or latitudinal distance between measurements is 400 meters. This represents a vast improvement in the resolution at which elevations are known for the region. In addition, the error in the horizontal data is less than a centimeter, so the location of each measurment is known to a high degree of accuracy. The vertical data are measured utilizing differential GPS providing 15 centimeters of vertical accuracy. Further information about this data set can be found at: sofia.usgs.gov/projects/elev_data/. The data sets provided by the HAED project are broken into a number of regions. Currently there are 19 regions. The location and names of these regions are shown in Figure 1.
      We have used the data from the USGS project to evaluate the quality of the HRT model outputs and to understand the sources of errors.

Figure 1. Map of south east Florida showing the locations and names of the various regions for which the HAED project has collected elevation data. Each colored box represents a single region, each region is shown with a different color. An index is present in the upper left hand corner of each box which corresponds to one of the indices listed in the upperleft hand corner of the figure. The region names given in this figure reflect the names of the data files obtained from the USGS web site. The red an blue does represent the locations at which the HAED project has surveyed elevation. Red dots represent positive elevations relative to NAVD 88. Blue does represent negative elevation relative the NAVD 88. Zero NAVD 88 can be taken to be approximatly equal to mean sea level.

Method of comparison
      The data provided by the HAED project provides three pieces of information for each data point. The Universal Transect Mercator (UTM) coordinates for each data point are given, providing the longitude and latitude of each data point. The elevation for each point is also given. Elevations are recorded in meters relative to NAVD 88.
      To compare the HRT model output and the HAED data we need HRT elevations for each location given by the HAED data. The HRT model does not make predictions about ground surface elevation in urban areas. For this reason the regions from the HAED project which include urban areas have been excluded from the analysis. Of the 19 regions for which HAED project data is available 11 are used for this analysis. The locations and names of these regions are given in figure 2. The HRT model is partially based on the ground surface elevation given by the South Florida Water Management District (SFWMD). So the elevations given in the SFWMD elevation map were also recorded for each location given by the HAED data. The files from which the HRT and SFWMD data were extracted are located in: /quartz/homes/a/sfla/Nov.4.1997/pseudotopo/NEW/pseudotopo.28m.abs.lan and
/diamond/homes/datafiles/ground/version.2.9/data/ground.surface.elevation.unit-mm.lan
respectively. Each of these files give ground surface elevation in mm relative NGVD 29. This was confimed prior to using the data in two ways. The source code which creates the HRT data as check. The two data files where compared using PVWave to assure the data files had the smae range of values. The units of the HRT and SFWMD elevations for each location were converted to meters relative to NAVD 88. For each region, the distribution of elevations given by the HAED, the HRT model and the SFWMD elevation data were comparied in a number of ways. Scatter plots for each region where created which show the elevations from one data set plotted agains one of the two remaining data sets. This resulted in three scatter plots for each region, one comparing the HAED and SFWMD data, one comparing the SFWMD and HRT data and one comparing the HAED and HRT data. For each region the average elevation and 95% range of elevations given by the HAED and HRT data associated with each habitat type where plotted. For each region the histograms showing the distribution of elevations for each data set are graphed together. For these plots the average and standard deviation were computed for each data set. The normal distribution for each data set was plotted on the same graph. To determine if two or more of the averages differed significantly a one way ANOVA was employed. Even though the standard deviations are not identical the results of the ANOVA should be essentially correct (Triola 1994). The results of this comparison are given in the next section.

Results
      The results of the comparison are shown in Figures 3a-3k. Each figure represents the distribution of elevations for the HAED project, the HRT model and the SFWMD elevation data for a given region. The region represented by each figure is listed at the top of each figure. In each figure the abscissa represents elevation in meters. The ordinate gives the frequency with which each elevation occurs within a region. Elevations were aggregated to the nearest tenth of a meter. The data for the HAED is shown in red, the HRT data is shown in blue and the SFWMD data is shown in green. For each data set the actual distribution of elevations is shown by the thick curve. The thin curve shows the normal distribution based on the mean and variance of the measured data. Each figure also shows the mean and standard deviation for each data set. Each figure shows the value of a one way ANOVA. The number of degrees of freedom for the numerator and denominator are also show in each figure. In all cases ANOVA indicates a significant difference between at least two of the data sets with a 1% chance of a type I error. The statistics for each region have been gathered in Table 1.
      In all regions the average HRT elevations are below the HAED elevation. In at least three of the regions, Blackwater, Joe Bay and West Lake this is the result of low SFWMD elevations and a lack of hydroperiod information of certain of the habitat types present in these regions. The SFWMD elevations are the starting point for the creation of HRT elevation. In the three regions listed above the average SFWMD elevation is below the average HAED elevation. Lower SFWMD elevations are joined with the fact that we do not have hydroperiod values for some of the habitat types present in these regions. In particular we do not have hydroperiods for two of the Red Mangrove (Rhizophora mangle) types. These habitat types consitute a large portion of the area within these regions. Lacking hydroperiod values for these habitat types the HRT model can not adjust their elevations. In these cases the HRT model gives locations occupied by Red Mangrove the same elevation the SFWMD provides. In addition, many of the habitat types in these regions are assigned hydroperiods or 365 days. Since the SFWMD hydrology model already predicts a 365 day hydroperiod for these regions, the model assumes they are already at an appropriate elevation. In this way the majority of locations within Blackwater, Joe Bay and West Lake keep the elevation provided by the SFWMD elevation data. A few sites have hydroperiod shorter than 365 days, and the model raises these site. This results in average HRT elevations higher than the SFWMD, but since most site are not modified the effect is small.
      In most of the regions however the HRT model is decreasing the ground surface elevation by to much. This is the result of assigning hydroperiod values to habitat types which are long compared to the hydroperiod predicted by the SFWMD hydrology model. This problem can be addressed in two ways, which maybe used in concert. The simplest solution is to assign shorter hydroperiods to the habitat types. This may mean shortening the maximum hydroperiod for each range, or moving both the maximum and minimum hydroperiod values. Another solution is to change how the model chooses a hydroperiod value from the range of values available for each habitat type. Currently the HRT model chooses a hydroperiod for a habitat type from the range of hydroperiod values in proportion the hydroperiod predicted by the SFWMD hydrology model (See Box 1).

Box 1 : How the HRT model chooses hydroperiod values for a habitat type.

For each location, the SFWMD hydrology model predicts a hydroperiod between 0 and 365 days. This value is normalized. This normalized value is used to choose a hydroperiod for a habitat type from the range of hydroperiods. A normalized value of zero corresponds to choosing the shortest hydroperiod available for a habitat type. A normalized value of one corresponds to choosing the longest hydroperiod available for a habitat type. Interpolation between the max and min hydroperiod is linear.

In stead of choosing hydroperiod values on a simple proportional basis the model could use other information. The hydroperiod choosen for one habitat type depend on the hydroperiod preferences for the other types. For example if a long hydroperiod type is close to a short hydroperiod type, the model might shift the choose of hydroperiod for the longer type toward the shorter end of the hydroperiod range for that type. Similarly the hydroperiod choosen for the short hydroperiod type might come from the longer end of its range due to its proximity to the long hydroperiod type. Alernatively the model could be designed to choose a hydroperiod with a tendency toward a particular value with in a given range or based on a weighting of the values within the range. A bias in the choice of hydroperiod would be parameterized to reflect the hydroperiod preferences of a habitat type. Both of these approaches add realizem into the HRT model and would allow the model to predict average elevations which are better fit to HAED elevations.
      The difference in the standard deviations between data sets is less consistant from region to region. However some patterns are present. The regions can be broken into two groups. Those where are dominated by positive HAED elevations and those dominated by negative HAED elevations. Recall that HAED elevations are measured relative to NAVD 88, so negative elevation represent elevations below this base line. The regions dominated by positive HAED elevations are Coopertown, Custard, Haileah, Long Island, Pennsuco and Taylor. The regions dominated by negative HAED elevations are Blackwater Joe Bay, Madeira, Mahogany, and West Lake. This partitioning can be seen from figure 1 by observing which regions contain more red (positive elevation) or blue (negative elevation) dots. If we partitioned the regions based on positive or negative SFWMD elevation dominance the groups would be different, since most of the elevations provided by the SFWMD are positive. However the range of SFWMD elevations in the HAED positive group are an order of magnatude larger than the SFWMD elevations for the HAED negative group. Specifically, in regions dominated by negative HAED elevations the SFWMD elevations for those regions are close to zero meters. In regions dominated by positive HAED elevations the SFWMD elevations are at least a meter above NAVD 88. This break is important because it effects the output of the HRT model.
      With the regions partitioned according to positive or negative HAED elevation we see that for positive HAED elevation regions the standard deviation of elevation predicted by the HRT model is larger than both the HAED and SFWMD standard deviations. Infact the standard deviation for the HAED data is between the standard deviation for the SFWMD and HRT data. In these regions the HRT model has created to much diversity in the elevations. While this indicates that the current HRT data set isn't a very good match to the HAED data, it implies that there is enough flexability in the model which can be used to better match the HAED data. In particular the variation in elevations produced by the HRT model can be effected by changing the range of hydroperiods assigned to each region. By making the range of hydroperiods assigned to habitat types more similar the range of elevations produced by the HRT model can be narrowed. The results in a normalization of hydroperiod values. (?) This sort of change to the hydroperiod ranges is possible since it intails narrowing the diversity of hydroperiod ranges within a range of values which is already present with in the data. Narrowing the range of hydroperiod maybe effected by the process of shifting the range of hydroperiods described earlier in as much as moving a hydroperiod range to far in one direction or another may force a narrowing.
      For regions in the negative HAED elevation group the picture is less clear. In many of the regions the standard deviation of HRT elevations is larger than the standard deviation of SFWMD elevations. However, the standard deviation of the HAED elevations is no longer consistantly braketed by the HRT and SFWMD data. In these regions the HRT model under estimates the diversity of elevation. More diveristy can be added to the elevation by diversifing the range of hydroperiod values assigned to each habitat type. There are limits to this diversification since hydroperiod values are constraned to the range 0 to 365. Overlap in hydroperiod ranges can also minimize diversity by allowing differnt habitat types to have similar or identical hydroperiods. The process of diversification can also conflict with the processes or normalization described above. It is not clear if these two processes can be achived simultainiously. In addition this process may not be compatable with shifting the entire range of hydroperiods to improve the fit of average hydroperiods.
      In two of the regions, Madeira and West Lake the standard deviation of the HRT elevations is less than the standard devation of the SFWMD elevations. This result is a consequence of limitation in the input data sets. In these regions the hydroperiod predicted by the SFWMD hydrology model is less than 365 days. For most of the habitat types in these regions 365 days is the given hydroperiod. Under these conditions, the HRT model does not modify the elevation of the habitat types since their hydroperiod requirements are met at the elevation given by the SFWMD elevation data.

Figure 3a: Elevation distribution for region 1, Blackwater (bl990415.cor). In this figure, the spike in the HRT data covers a identical spike in the SFWMD data.

Figure 3b: Elevation distribution for region 2, Coopertown (cooperct.cor).

Figure 3c: Elevation distribution for region 3, Custard (custard.cor).

Figure 3d: Elevation distribution for region 8, Hialeah (hialeah.cor).

Figure 3e: Elevation distribution for region 10, Joe Bay (jb990414.cor).

Figure 3f: Elevation distribution for region 11, Long Island (long_is.cor).

Figure 3g: Elevation distribution for region 12, Madeira (mb990412.cor).

Figure 3h: Elevation distribution for region 13, Mahogany (mh990412.cor).

Figure 3i: Elevation distribution for region 14, Pennsuco (penncoop.cor).

Figure 3j: Elevation distribution for region 18, Taylor Slough (ts990326.cor).

Figure 3k: Elevation distribution for region 19, West Lake (wl990412.cor).

Discussion