Figure 1. Map showing results from dynamic time-series clustering and group assignments (Group 1 - red, Group 2 - blue, or Group 3- green) of the 31 stations used in the study. [larger image]

To generate hindcasted water-surface maps prior to 1990, a database was built with the measured and hindcasted data and used as input for the sub-domain model. Of the 31 stations used in the sub-domain model, 15 stations had records 95 percent (%) or greater complete back to 1990. Sixteen of the stations had short-term records and were hindcasted to create records concurrent with the long-term records. A dynamic time-series cluster technique (Roehl and others, 2006) was used to group stations with similar behaviors (fig.1). Each group had at least two stations with data records prior to 1990. The long-term stations were used to hindcast the short-term data back to 1990 using either linear regression or artificial neural network models (fig 2).

Figure 2. Example of water-level record hindcasted to 1990. Station S333_H is shown for reference to a long-term station. [larger image]

The average coefficient of determination (R²) and root mean square error of the hindcast models were 0.98 and 3.38 centimeters (cm), respectively (table 1). Models, both empirical and mechanistic, are more accurate when interpolating within the historical range of the data used to develop the model than extrapolating beyond the range of the data used to develop the model. To hindcast back to 1990, the models only extrapolated an average of 6% of the time or are interpolating within the historical range of the data 94% of the time (table 1).

Cumulative Z-scores are useful to find subtle changes in time-series data. The Z-score is the value (measured or hindcasted) minus the mean divided by the standard deviation. Changes in the slope of the cumulative Z-scores indicate a change in the behavior, or dynamics, of the time-series data. Cumulative Z-scores were computed and plotted for the long-term and hindcasted water level to evaluate whether the predicted water levels had dynamic behavior similar to the measured data. The cumulative Z-score for measured station Site 65 and hindcasted station W14 are shown in figure 3, along with the water-level for Site 65. Site 65 was not used in the hindcast model for W14. The "saw tooth" character of the plot is a result of the wet-dry season cycle. The larger changes in the slope, for example from 1990 to 1992 and 1994 to 1996, are a result of change in the hydrologic dynamics of the system. The Z-scores of the hindcasted data for W14 show similar dynamics as the Z-scores for the measured data at Site 65.

Figure 3. Cumulative Z-scores for stations Site 65 and W14. The majority of the time-series (82.2%) for W14 is hindcasted. [larger image]

An important difference in the sub-domain model is that only measured canal data are used, rather than using the additional interpolated canal data that the current EDEN model uses. Using a single day in the current EDEN database (2000-present), the EDEN sub-domain model for WCA3AS was statistically compared to the current (2010) EDEN model for October 1, 2003 (fig. 4). The sub-domain model had a lower cross-validation root mean squared error than the same sub-area of the EDEN model (13.74 and 39.75 cm, respectively) and a lower mean error (0.12 and 0.33 cm, respectively).

Figure 4. Water surfaces for WCA3AS for October 1, 2003 from (A) the current EDEN surface-water model and (B) the sub-domain model. [larger image]

The measured and hindcasted data were used as inputs to the sub-domain model to generate water surfaces for WCA3AS for a day of lower water levels (April 8, 1992; fig. 5A) and a day of higher water levels (February 9, 1995; fig. 5B). For the lower-water day, the majority of the cross validation errors are less than 5 cm with higher errors occurring to the north and northwest. For the higher-water day, the majority of the cross validation errors are less than 6 cm with higher errors occurring to the northeast and northwest.

Figure 5. Water surfaces for WCA3AS using the sub-domain model for (A) April 8, 1992 and (B) February 9, 1995. Numbers on the surfaces are results of cross validation (centimeters). [larger image]

Roehl, E., Risley, J., Stewart, J., Mitro, M., 2006-1, Numerically optimized empirical modeling of highly dynamic, spatially expansive, and behaviorally heterogeneous hydrologic systems - Part 1, iEMSs 2006 Summit on Environmental Modelling and Software, Burlington VT, June, 2006, 6p.

Pearlstine, L., Higer, A., Palaseanu, M., Fujisaki, I., and Mazzotti, F., 2007, Spatially Continuous Interpolation of Water Stage and Water Depths Using the Everglades Depth Estimation Network (EDEN): Gainesville, FL, Institute of Food and Agricultural Sciences, University of Florida, CIR 1521, 18 p., 2 apps.

For more information about EDEN, please visit our website at: http://sofia.usgs.gov/eden