Proposal Cover Page Research Area Restoration Goal 1: Get the Water Right; Sub-goals (e) and (j) Program Area

3.1 Climate and Weather Scenarios

The monthly ENP rain time series (1927-2002) is illustrated in Figure 3.1.1, along with its decomposition into seasonal and trend components using Loess (Cleveland et al, 1990). Note that the 1965-95 conditions appear to be drier than those in the balance of the record. A Fourier and a wavelet spectrum of the annual rainfall are provided in Figure 3.1.2. It shows low frequency behavior with a peak around 6-8 years, as well as an inter-decadal peak. The “risk” posed by using the 1965-95 record to develop the NSM scenarios as a guide for restoration is illustrated in Figure 3.1.3 through kernel density plots of the annual rainfall. We note that the difference in the probability distribution of the 1965-1995 rainfall record and of the 1927-64; 1996-2002 rainfall records is statistically significant at the 5% level, suggesting that the 1965-1995 period was anomalously dry relative to the balance of years, consistent with the suggestion from Figure 3.1.1.

These features in the time series suggest that the regional climate is likely to be marked by recurring, persistent multi-year droughts (wet periods). Methods that can generate such scenarios are needed for an effective risk/reliability assessment. A variety of methods have been proposed in the literature. These include linear time series models with periodic terms identified using sophisticated spectral analysis methods, nonlinear time series models that can generate oscillatory dynamics, Hidden Markov Models, and change point or threshold autoregressive models. We propose to explore a subset of these methods for their applicability to the ENP rainfall data.

For the ENP applications, we may be interested in developing long-term simulations of seasonal rainfall, and then disaggregating the seasonal to daily values using an appropriate weather generator. Rainfall at many locations (that may be spatially correlated to different degrees) may be of interest. A useful paradigm in this setting is provided by the Hidden Markov Model construct (Hughes and Guttorp, 1994; Hughes et al, 1999). Here, it is assumed that an unobserved mechanism influences regional precipitation. This mechanism may be represented as a binary (e.g., corresponding to wet or dry) process that has a Markovian dependence structure or memory. Since this is an unobserved process, we can only infer its state from the rainfall data. This effectively translates into a process that classifies the rainfall data into these two states and models the transition probability between these states, as well as the (daily or seasonal) rainfall distribution associated with each state. Thus multi-year shifts in regimes as well as their subscale attributes can be modeled. Multiple rainfall sites are treated by considering their mutual correlation structure under each regime. This procedure is described here since it provides a useful paradigm for how a more general framework for rainfall simulation at daily to seasonal scales could be developed for the ENP. For instance, instead of considering a hidden Markov process, we could explicitly try to condition simulations on a large-scale climate variable that may be informative as to local rainfall. As indicated earlier, several researchers in Florida have found connections (predominantly in the winter season) between ENSO, NAO, Atlantic Multi-Decadal Oscillation Indices. Thus, one could build a multi-stage long-term simulator by first developing a univariate (or low dimensional) time series model for relevant climate indices, and then conditioning the regional rainfall process on the state of such an index. A limiting case of this approach could be the existing Hidden Markov Model (or its nonhomogeneous version).

For seasonal climate scenarios we can take a very similar approach. In this case, we can identify useful predictors of seasonal or monthly rainfall, and then develop a conditional probability model for the prediction of the rainfall field. As potential predictors we consider, (a) historical, observed Sea Surface Temperature, Sea Level Pressure and Wind fields; (b) General Circulation Model (GCM) forecasts of the same fields and of rainfall for the upcoming season, and (c) current rainfall and/or Lake Okeechobee inflows. Data on all these fields is available to us either through the ENP/SFWMD or the IRI (all major GCMs) at Columbia University. Our initial analyses suggest that this may be a promising research direction. Selected results are presented in Table 3.1.1 and Figures 3.1.4 and 3.1.5. Once a robust set of predictors is identified, a variety of methods (e.g., De Souza and Lall, 2003) could be used to generate forecast ensembles.

For near real time operation, weather forecasts or weather scenarios need to be generated. We have been in touch with Dr Zoltan Toth, who heads the National Weather Services Ensemble Forecasting group. A preliminary assessment of weather forecast skill in the S. Florida region suggests that the ensemble forecast from the current generation of models has statistically significant skill at the 0-24 hour lead time, but that this skill degrades rapidly thereafter. Consequently, it is not clear whether a direct use of the ensemble forecast system would be worth considering at this time. However, Dr. Toth suggests that it may be useful to explore a Model Output Statistics (MOS) correction scheme to see if significant skill can be achieved via statistical correction for the 1-7 day lead time. This is the lead-time of primary interest for near real time or weekly operation, and successful forecasts of impending storms may be very useful for flood control storage and release management. We consider this of interest and plan a limited exploration of the attributes of the weather forecasts at this time scale.

Even in the absence of weather forecasts for the 1-7 day ahead period, we feel that a risk analysis of floods and not meeting ENP performance targets is feasible by running daily weather scenarios through the real time release and stage response simulation model to be developed. These scenarios can be developed using a regional daily weather generator that has the right seasonal structure. We propose to consider an updated version of the k-nearest neighbor resampling model described by Rajagopalan and Lall (1999). The updates allow for spatial rainfall field simulation and for improved selection of the conditioning vector.

In summary, we feel that the proposed development of robust climate and weather scenario generators for unconditional, long term simulations, and for seasonal to daily forecasts will be a valuable contribution to the ENP restoration analyses and operations. We identified that the regional rainfall time series have (a) long memory attributes (nonstationary behavior) and (b) correlate well with selected large scale slowly evolving climate indicators, and (c) appear to be predictable (with spatial and temporal bias?) using climate/weather forecast models. By using and extending existing techniques of statistical modeling, we anticipate being able to provide representative scenarios that could be used for seasonal as well as near real time decision analysis through system simulation and assessment.

The proposed climate and weather analyses will be conducted in collaboration with Dr. Robertson at the IRI, Drs. Ahn and Kim at the ENP, and Drs Ali, Trimble and Obeyesekare at the SFWMD.