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Hindcasting Water-Surface Elevations for Water Conservation Area 3A South

Poster presented July 2010, at the Greater Everglades Ecosystem Restoration Conference

Paul Conrads1, Zhixiao Xie2, Bryan J. McCloskey3

1USGS, Columbia, SC; 2Florida Atlantic University, Boca Raton, FL; 3USGS, St. Petersburg, FL

Introduction

map showing results from dynamic time-series clustering and group assignments of the 31 stations used in the study
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]
There is interest among principal investigators and water-resource managers for the Everglades Depth Estimation Network (EDEN) project team to generate water-surface and water-depth maps for periods prior to 2000. These maps would provide hydrologic data previously unavailable for assessing biological and ecological impacts over longer time periods. As one moves back in time, the quantity and quality of available data diminishes. An objective of the EDEN hindcasting effort is to identify periods and regions where long-term hydrologic time series will support hindcasting. One approach for generating water-surface maps prior to 2000 is to hindcast particular sub-domains of EDEN where data supports multi-decadal hindcasting rather than the entire freshwater EDEN domain.

Approach

Thirty-one stations from the EDEN network were used to generate water-surface elevation maps for Water Conservation Area 3A South (WCA3AS) using a sub-domain of the EDEN water-surface model. The EDEN sub-domain model was designed to divide the single EDEN water-surface model (Pearlstine and others, 2007) into a set of compartment-based models with unique inputs and interpolation algorithms. A sub-domain model has the potential to better suit the hydrologic characteristics of a specific compartment, and the flexibility to evolve with new data and understanding of an individual compartment's behavior. It also eliminates the need to represent water-level discontinuities across compartment boundaries with pseudo canal stations.

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).

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

Hindcasting Results

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).

Table 1. Hindcast model performance statistics for 16 stations.
Station Data points Percent Record (1990-2010) Minimum observed, cm Maximum observed, cm Coefficient of Determination, R2 Mean Error, cm Root mean square error, cm Percent Model Error Model Extrapolation, percent
S343B_T 5482 75.0 197.82 308.12 0.904 5.68 7.52 6.8 1.3
S343B_H 5482 75.0 222.50 361.61 0.997 2.06 2.54 1.8 0.1
S343A_H 5241 71.7 223.30 360.15 0.968 3.25 4.23 3.1 0.6
3AS3W1 3524 48.2 245.82 350.73 0.993 1.98 2.54 2.4 5.7
W2 1422 19.5 202.69 292.30 0.968 2.40 3.36 3.7 5.5
W11 1394 19.1 211.84 314.25 0.986 2.55 3.68 3.6 6.6
W5 1391 19.0 206.04 299.31 0.997 1.17 1.62 1.7 4.5
W14 1298 17.8 214.27 314.55 0.994 1.59 2.38 2.4 9.4
EDEN_8 1297 17.8 199.64 310.59 0.995 1.91 2.40 2.2 8.3
EDEN_12 1265 17.3 186.23 323.09 0.978 3.99 5.25 3.8 2.3
W15 1245 17.0 227.69 322.17 0.974 2.82 3.62 3.8 5.0
EDEN_4 1233 16.9 191.11 338.63 0.988 2.28 3.60 2.4 4.4
3A-5 1164 15.9 248.41 333.76 0.996 1.29 1.71 2.0 10.9
W18 1159 15.9 241.10 317.30 0.985 2.83 3.59 4.7 9.1
EDEN_5 1133 15.5 245.97 331.32 0.986 2.31 3.20 3.8 8.1
EDEN_14 1022 14.0 250.55 326.75 0.988 1.85 2.80 3.7 13.0

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.

graph of cumulative Z-scores for stations Site 65 and W14.
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]

Sub-Domain Surface-Water Model Results

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).

water surfaces for Water Conservation Area 3A South for October 1, 2003 from the current Everglades Depth Estimation Network surface-water model and the sub-domain model
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.

water surfaces for Water Conservation Area 3A South using the sub-domain model for April 8, 1992 and February 9, 1995
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]

References:

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



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