Seasonal Simulation-Optimization Model

3.2 Seasonal Simulation-Optimization Model

The seasonal simulation-optimization model is intended to develop a seasonal operating rule conditional on either long run climate ensembles, or on seasonal climate forecast ensembles. At this time we envisage using the NSM and SFWMM for seasonal simulations. First, we consider simulating the NSM with an m member climate ensemble of length n years. For the sake of discussion, consider that bootstrapping historical years of data has generated each climate ensemble. These NSM simulations would inform us as to the range of variation in performance measures at each target location if the NSM were an accurate representation of the underlying dynamics, and natural conditions were maintained. This then provides a benchmark against which the long-term performance of a particular operational plan (e.g., Lake Okeechobee release policy or IOP rules) can be judged.

The potential outcomes under the proposed operational plan could be evaluated by implementing the plan in SFWMM (or equivalent) and running the simulations through the same climate bootstrap samples that were used with the Natural System simulations. Now, since we have m (e.g., 100) ensembles of outcomes in each case, we can empirically compute the likelihood that the probability distribution of PM/HSI outcomes for a particular operational plan simulated with SFWMM, matches the corresponding probability distribution of the same PM/HSI outcomes as simulated for the natural conditions. This approach gets around the rather tenuous problem of trying to compare the time series of PM values computed from a short set of measured values with the corresponding PM values computed from the NSM, SFWMM or other models/policies. If we are only concerned with achieving the desired long-term outcomes without regard to their time ordering, then the operating policy that leads to the probability distribution of PMs that best matches what is projected for the natural system under the same climate is a useful goal. We do better than the natural system in some years, worse in others, but overall deliver the same services. Note that if time ordering across years is important for ecological outcomes, we need to ensure that an appropriate PM is defined that recognizes the year to year dependence, and that the climate scenario generation procedure accounts for the inter-annual or regime dependence.

Now consider a seasonal climate forecast represented as an ensemble. We can engage in the same exercise, and compare alternate macro level release policies by simulating them scenarios through the SFWMM, and comparing the resulting PM outcomes for each candidate operating plan against what would be expected for the PMs from the climate ensemble run through the NSM model. It is possible that a particular operating policy emerged as the best choice for matching natural conditions in terms of the PMs specified based on the long term climate scenarios. However, if an effective climate forecast were available (e.g., biased bootstrap of the historical years of record to reflect the current state of the climate predictors), then one could re-evaluate the ranking of competing operating policies for the upcoming season. Thus, a new operating rule could show up as being superior in a given season if the forecast indicates conditions that are quite different from those in the historical climatology. This is a secondary optimization of the operating policy.

Thus far we have considered a comparison of two or more clearly defined operating rules through simulations, and selected the best one. Clearly, an extension of this idea is to consider the formulation of an operating policy in terms of seasonal and monthly targets for reservoir storage and release. Here, the decision variables would be these targets, and we would seek to optimize over the PMs from the ensemble simulations. Thus the best operating rule would now be defined by the values of these targets rather than by the choice between two discrete operation rules.

The potentially large state space and the simulation time required to run the models is likely to be a computational constraint for solving such a stochastic optimization problem. We plan to explore a hybrid simulation-optimization approach to address such a problem. The formulation of such a model is best done in the context of a pilot application to an area of the Everglades, where the specific issues can be clearly defined and the complexity is controllable. We expect to collaborate with Dr. Ahn (ENP), and Drs. Ali, Obeyesekare, Tarboton, and Neidrauer at the SFWMD to develop and exemplify this strategy.

F
igure 3.1.1 1927-2002 ENP monthly rain time series, with a long-term trend (301 month filter), two quasi-oscillatory inter-annual and decadal components (filtered at 101 and 45 months respectively), the annual cycle with amplitude varying over the period of record, and residuals of these components.

Figure 3.1.2 Fourier and Wavelet Spectrum of the Annual ENP Rain. Note the peak around 7 years in both and the episodic interdecadal variability in the wavelet spectrum.


Figure 3.1.3 Kernel density plots of (a) Annual ENP Rain from 1965-1995 (marked as e and as dotted line), (b) Annual ENP Rain from 1927-1964, 1996-2002 (marked as o and dash-dot line), and (c) Annual ENP Rain from 1927-2002 (marked as f and solid line).

Table 3.1.1 Rank correlations of ENP seasonal rainfall with selected indices from the preceding season (3 months prior). The previous season’s ENP rain is shown for comparison. The correlations in the winter are quite strong, while those in the other seasons are statistically significant but not nearly as dramatic.

Figure 3.1.4 Rank correlation of selected monthly ENP rainfall with preceding month’s estimated vertical velocity (surrogate for convection). Note that while the traditional climate indices are not highly correlated with the ENP summer rainfall, this diagnostic suggests that identifying appropriate areas of tropical and equatorial convection in the Atlantic and Pacific may provide greater predictability for ENP rainfall in this season.

F
igure 3.1.5 Rank correlation between observations and precipitation forecast issued in (a) May for July rain, and (b) in August for November rain. The forecasts are the simple averages of precipitation forecasts from 3 GCMs. In both cases note that there are areas of high correlation that are spatially shifted from Florida. The models exhibit a systematic spatial bias that may be corrected, or they can provide a useful predictand for ENP rain.

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