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Water Resource Predictions from Meteorological Probability Forecasts
The National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Center now provides each month US seasonal forecasts (Climate Outlooks) of air temperature and precipitation, consisting of one-month outlooks for the next month and 13 three-month outlooks, going into the future in overlapping fashion in one-month steps. Each outlook estimates probabilities of average air temperature and total precipitation falling within the lower, middle, and upper thirds of observations from 1961-1990 for an upcoming period.
Users of climate outlooks can interpret meteorological probability forecasts through "Operational Hydrology" approaches to assess the risk of extreme conditions and of variability in general. Possibilities for the future are identified that resemble past meteorology (preserving observed spatial and temporal relationships) yet are compatible with climate outlook probabilities. One important approach considers historical meteorology as possibilities for the future by segmenting the historical record and using each segment with models to simulate a hydrologic possibility for the future. The approach then considers the resulting set of hydrologic possibilities as a statistical sample and infers probabilities and other parameters, associated with both meteorology and hydrology, through statistical estimation from this sample.
The operational hydrology approach uses statistical sampling tools as if the set of possible future scenarios were a single "random sample" (i.e., the scenarios are independent of each other and equally likely). Unfortunately, the relative frequencies of selected events are fixed at values different (generally) from those specified as climate outlook probabilities. We can restructure the set of possibilities, by duplicating each possibility a select number of times, to give relative frequencies of average air temperature and total precipitation (over each outlook period) satisfying a priori probability settings of available climate outlooks. This restructuring violates the implicit assumption of independent and equally likely possibilities in our statistical sample (it is not a "random sample") from the point of view of the historical record ("a priori" information). However, the restructured set can be viewed as a random sample ("posterior" information) of possibilities conditioned on climate outlooks. There are many methods for restructuring the set of possible future scenarios.
The use of this hypothetical restructured set corresponds to the weighted use of the unstructured set from the (original) historical data and weighted statistics are derived to use the unstructured set. These weights are determined by constructing boundary equations for the weights, setting the relative importance of each equation in case incompatibilities arise, and solving them for physically-relevant values. Their solution becomes an optimization problem for the general case. The computation of these weights, the use of them in statistics to estimate hydrological variable probabilities, and an example are available in the reference. The corresponding weighted hydrological possibilities are used to infer water resource probabilities and other parameters. See the example hydrological outlook.
Computer code is available, to make all computations (outside of the hydrological modeling), for use by others in utilizing NOAA's Climate Prediction Center Climate Outlook. The code finds all necessary reference quantiles, for using a climate outlook, from a user-supplied file of historical daily air temperature and precipitation, sets up equations, formulates the optimization of equations, and performs sequential optimizations (either to use all historical data or to maximize use of a priori climate outlook settings). Both a stand-alone FORTRAN implementation, for use under a variety of operating systems, and a specially-designed user interface Windows application are available . The latter allows understandable interpretation of the Climate Outlooks and assignment of relevant priorities.
One- & Three-Month Climate Outlooks for Average Air Temperature & Total Precipitation (made 15 November 1995):
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An Operational Hydrology Approach
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A Simple Example of Building a Structured Set
Consider structuring a set of possible future scenarios that gives relative frequencies of average air temperature and total precipitation (over various times in the scenarios) satisfying a priori settings of climate outlooks. We can arbitrarily construct a very large structured set of size N by adding (duplicating) each of the available scenarios (in the original set of n possible future scenarios); each scenario numbered i, (i = 1, ..., n) is duplicated ri times. By judiciously choosing these duplication numbers, (r1, r2, ..., rn), it is possible to force the relative frequency of any arbitrarily-defined "group" of scenarios in the structured set to any desired value. For example, suppose only five of 50 (10%) twelve-month scenarios beginning in April have a total April precipitation exceeding 80 mm, and our a priori setting (from a climate outlook) for this exceedance is 20%.
We could repeat each of these 5 scenarios 9 times and repeat the other 45 scenarios 4 times to build a structured set. This structured set of size 225 (= 5 9 + 45 4) would then have a relative frequency of 20% of total April precipitation exceeding 80 mm (5 9 / 225 = 0.2). For sufficiently large N, we can approximate a priori settings at any precision by using integer-valued duplication numbers, ri. Note that the n duplication numbers sum to N.
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Croley, T. E., II (1996) Using NOAA's new climate outlooks in operational hydrology. J. Hydrol. Eng. 1(3):93-102.
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An Example Hydrological Outlook
Example probabilistic hydrological outlooks for March 1996 through March 1997:
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Last updated: May 24, 2002 mbl