Figure 1: Management areas South Florida

      The purpose of this analysis is to understand the relationship between rain fall input and stage height in various regions of South Florida. The hypothesis is that in regions such as Big Cypress National Preserve (BCNP) which have relatively few man made water control structures the effect of rain fall on hydrology is greater than in areas such as the water conservation areas where human control dominates patterns of hydrology. A number of analyses are presented below which look at the correlation of hydrology and rain fall at different temporal scales and for different regions within South Florida.

Data and Software
      The hydrology values come from the SFWMD Calibration/Validation run. Details about this data set can be found here. The rain fall data comes from the SFWMD and was provided to us as part the Natural Systems Model (NSM) which was sent us by the SFMWD. This data covers the SFWMM simulation area, and includes some additional area which are outside the SFWMM study area and of no interest here. This data is provided to us in inches of rain fall per day for each 2x2 mile cell in the landscape. The rain fall data is converted using ATLSS convert to change the format into something which is more easily manipulated with PV-Wave (V 6.10). The change includes transforming the data from the SFWMD in-house format to standard BSQ format, and a conversion of units from inches of rain fall to 10^-4 m (1/10 of a mm) of rain fall. The target units ( 10^-4 mm) was chosen to capture the precision and variability in the original data and still store the values as an integer. The SFWMM data is stored as a 4-byte float and converted to a 2-byte integer by ATLSS convert. The values reported in the tables and graphs below have been converted to cm by the PV-Wave scripts used to carry out the analysis. This conversion was performed for ease of comparison with the stage height data. The rain fall data from the SFWMD provides values on a daily time step for the period between 1/1/1965 to 12/31/1995 inclusive. To make the time frame of the rain fall data match the time frame of the hydrology data the ATLSS pull program was used to extract rain fall data for the time period between 1/1/1979 to 12/31/1995 inclusive. All other manipulations and analyses were carried out with PV-Wave (version 6.10).
      The analyses described below were performed on a number of regions within South Florida. These regions reflect division by management boundaries. The areas include Big Cypress National Preserve (BCNP), Water Conservation Areas (WCA) 1,2A,2B,3A,3B and Everglades National Park (ENP). In addition WCA-3A was divided into two regions. The portion of WCA-3A north of I-75 is called WCA-3A North while the portion below I-75 is called WCA-3A south. This division reflects past experience by the ATLSS group that the northern and southern portions of WCA-3A frequently display different dynamics. Figure 1 shows the area used to define each area. Due to the coarseness of the hydrology data and rain fall data, use of a finer representation of each area would be difficult and it is not clear such a refinement would increase accuracy.

Description
      The results shown here compare monthly averaged rain fall data and monthly averaged stage heights for the basins which appear in figure 1. Table 1 shows the correlation coefficients (Pearson's r), regression line slopes and r² values for monthly averaged rain fall plotted against monthly averaged stage height. You may click on any of the values in a row of the table to view graphs associated with a basin. The r² value provides the amount of variation in the data explained by the regression. The value of r² is between 0 (zero) to 1. A r² of 0 (zero), means none of the variation in the data is explained by the regression; a value of 1 means all of the variation is explained by the regression. The regression is performed with least squares fit, and the r² value is the square of Pearson's r.

Results
      The values in Table 1 indicate that correlation between monthly rain fall average and monthly stage height averages is weak. The r² values show that the regression between rain fall averages and stage height describes only a small amount of variation in the data.

      The results shown below compare yearly averaged rain fall data for the entire study area and yearly averaged stage height for each management area. Table 2 shows correlation coefficient, the slope of the regression line between the yearly averaged rain fall the yearly average stage heights for each management area along with the square of Pearson's r. You may click on the entries of each row to view graphs associated with a region. The yearly averaged rain fall data used in the comparison was computed as the total rain fall which fell into the study area divided by the number of days in a year. This average can be expressed as:

      The results of the analysis using yearly average rain fall and stage height are shown in Table 2. With yearly averages the Pearson's r r value show a good correlation between rain fall and stage height for most regions in Figure 1. Each of these r value indicate a significant positive correlation at the 0.01 level except WCA-2A which is significant at the 0.05 level. WCA-2A also shows the weakest correlation between rain fall and stage height. Most values fall within one standard deviation of the mean of the r values. The slope of the regression lines indicate that variation in rain fall has the largest impact on stage height in the conservation areas and has a lesser effect on stage height in areas such as BCNP and ENP. The r² values indicate that the linear regression explains a large portion of the variation in the data. In the best case the linear regression accounts for 62% of the variation in BCNP. However for most other areas the linear regression accounts for only about 50% of the variation. Overall, while rain fall accounts for a large portion of the variation in stage heights it does not account for all of the variation.