High Resolution Real Time Simulation Model

3.3 High Resolution Real Time Simulation Model

Regular monitoring of stage and other variables has been in place at a number of locations in the ENP. Directly using this data to fit a statistical model for the response of stage at target locations to releases from control structures and rainfall is of interest. Over the last 8 years the range of annual rainfall at the ENP has been [49,67 in] as compared to the range of [38, 81 in] over the previous 68 years. Consequently, only a limited range of conditions has been seen, limiting the validity and utility of a regression based approach for long-term use at this stage. Further, building such a regression model completely empirically is a daunting task, even if a larger data set were available. One would need to develop a vector regression model for s stage values at the target locations conditional on r releases. Both s and r could be quite large, and one may need to include past stage, rainfall and releases as potential predictors. This translates into a large vector regression problem.

Baldwin and Lall (2004) were faced with a similar problem when trying to develop an approximation to the NSM in the context of developing a Rainfall Driven Operation strategy for the ENP. In that context, a Neural Network approach applied to the prediction of stage at a single site using rainfall and stage at that site and a few neighbors was effective in reproducing the model predictions as well as the across-site correlations. We plan to explore a similar approach to develop a functional estimation strategy to relate control structure releases, stage at control locations, rainfall, and stage at target locations. The smaller length of available data, and the use of real rather than model data may make it difficult to get results that are as impressive as those obtained in Baldwin and Lall (2004).

An alternate approach would be to consider building a model to relate the bias between the SFWMM time series and the observed response time series to the same predictors. A Kalman Filter-like approach that allows one to examine the time and space correlation structure of the prediction errors may allow for a real time correction of the SFWMM (or similar model) predicted stage values.

We expect to evaluate these choices through discussions with appropriate ENP and SFWMD hydrologic modelers.

3.4 Synthesizing a Reduced Set of PMs

An examination of the equations for the HSIs and for some of the PMs reveals that they are often functions of the same underlying variable (e.g., hydroperiod duration). In this sense, the PMs are nonlinear functions of the underlying NSM stage, and hence the NSM stage (or some suitable statistic of the difference between NSM stage and stage achieved under operations) could also be considered to be a PM. One can compute a annual time series for each PM at each target location from an NSM (or other model simulation). Given the mutual functional dependence of many of the PMs, we expect that their time series at a given location may be highly correlated (some correlations may be negative). Further, PMs at nearby target sites may also be highly correlated. These observations suggest that a reduction in the dimension of the number of PMs to consider may be possible without significantly sacrificing their individual merit.

An approach in this direction could be to consider the design of a few new indices that are linear combinations of the PMs. Tarboton (2001) considers a similar idea by averaging the HSI's of three different species into a single index. One approach to reducing the dimension of the PMs that relies on their mutual correlation is Principal Components Analysis (PCA). The Principal Components of the PM data matrix would represent linear combinations of the PMs such that the each successive component explains the maximum remaining variance in the PM data matrix. Then, if the first few components explain the bulk of the PM variance, they can be used as independent indices or measures with a similar information content. Unfortunately, PCA allows negative and positive weights in the process of forming the linear combinations, and hence mixes positively and negatively correlated variables into the same index. In our context this would assemble the PMs which show positive changes into the same index as the PMs that concurrently show negative changes. A similar, but alternative approach that addresses this problem is archetype analysis (Cutler and Stone, 1997).

Archetype Analysis (AA) is similar to PCA, with the exception that the linear combinations of the PM variables are formed with weights that are strictly between 0 and 1. As the name implies, each archetype then represents a weighted average of the PMs that are most alike and also contribute to a maximal explanation of the variance of the PM data matrix. Thus, the first archetype may capture all PMs that are highly positively correlated with each other, and the second one a group of PMs that are highly negatively correlated with the first archetype, but highly positively correlated with each other. If the leading 4 or 5 archetypes were to capture most of the information in the PM matrix, then computationally and conceptually one could look at a much more tractable decision and performance assessment problem.

We shall explore this approach to see if we can demonstrate how NSM targets, PM estimates from NSM simulations, and PM estimates from SFWMM simulations under a selected operating rule can be systematically compared both in terms of the reduced index and its original components.