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Roman Krzysztofowicz

Abstract

Consider an event definable in terms of two subevents as, for example, the occurrence of precipitation within a 24-h period is definable in terms of the occurrence of precipitation within each of the 12-h subperiods. A complete forecast must specify three probabilities; these may be marginal probabilities, one for the period and two for subperiods. Theoretical relations between these probabilities are investigated and solutions are presented to three problems encountered in operational forecasting: (i) guaranteeing that the marginal probabilities jointly obey the laws of probability, (ii) structuring admissible procedures for adjusting the initial (guidance) probabilities by forecasters, and (iii) formulating optimal estimators of the probability for period in terms of the probabilities for subperiods.

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Roman Krzysztofowicz

Abstract

From the theory of sufficient comparisons of experiments, a measure of skill is derived for categorical forecasts of continuous predictands. Called Bayesian correlation wore (BCS), the measure is specified in terms of three parameters of a normal-linear statistical model that combines information from two sources: a prior (climatological) record of the predictand and a verification record of forecasts. Three properties characterize the BCS: (i) It is meaningful for comparing alternative forecasts of the same predictand, as well as forecasts of different predictands, though in a limited sense; (ii) it is interpretable as correlation between the forecast and the predictand; and, most significantly, (iii) it orders alternative forecast systems consistently with their ex ante economic values to rational users (those who make decisions by maximizing the expected utility of outcomes under the posterior distribution of the predictand). Thus, by maximizing the BCS, forecasters can assure a utilitarian society of the maximum potential economic benefits of their forecast.

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Roman Krzysztofowicz and Ashley A. Sigrest

Abstract

The predictand of a probabilistic quantitative precipitation forecast (PQPF) for a river basin has two parts: (i) the basin average precipitation amount accumulated during a fixed period and (ii) the temporal disaggregation of the total amount into subperiods. To assist field forecasters in the preparation of well-calibrated (reliable) and informative PQPFs, local climatic guidance (LCG) was developed. LCG provides climatic statistics of the predictand for a particular river basin, month, and period (e.g., 24-h period beginning at 1200 UTC and divided into four 6-h subperiods). These statistics can be conditioned on information entered by the forecaster such as the probability of precipitation occurrence and various hypotheses regarding the precipitation amount and timing.

This article describes two probability models of the predictand, details guidance products, and illustrates them for the Lower Monongahela River basin in Pennsylvania. The first model provides marginal climatic statistics of the predictand on an “average” day of the month. The second model conditions the statistics on the timing of precipitation within the diurnal cycle. The resultant characterization of the precipitation process allows the forecaster to decompose the complex assessment of a multivariate PQPF into a sequence of feasible judgmental tasks.

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Roman Krzysztofowicz and W. Britt Evans

Abstract

A sequence of meteorological predictands of one kind (e.g., temperature) forms a discrete-time, continuous-state stochastic process, which typically is nonstationary and periodic (because of seasonality). Three contributions to the field of probabilistic forecasting of such processes are reported. First, a meta-Gaussian Markov model of the stochastic process is formulated, which provides a climatic probabilistic forecast with the lead time of l days in the form of a (prior) l-step transition distribution function. A measure of the temporal dependence of the process is the autocorrelation coefficient (which is nonstationary). Second, a Bayesian processor of forecast (BPF) is formulated, which fuses the climatic probabilistic forecast with an operational deterministic forecast produced by any system (e.g., a numerical weather prediction model, a human forecaster, a statistical postprocessor). A measure of the predictive performance of the system is the informativeness score (which may be nonstationary). The BPF outputs a probabilistic forecast in the form of a (posterior) l-step transition distribution function, which quantifies the uncertainty about the predictand that remains, given the antecedent observation and the deterministic forecast. The working of the Markov BPF is explained on probabilistic forecasts obtained from the official deterministic forecasts of the daily maximum temperature issued by the U.S. National Weather Service with the lead times of 1, 4, and 7 days. Third, a numerical experiment demonstrates how the degree of posterior uncertainty varies with the informativeness of the deterministic forecast and the autocorrelation of the predictand series. It is concluded that, depending upon the level of informativeness, the Markov BPF is a contender for operational implementation when a rank autocorrelation coefficient is between 0.3 and 0.6, and is the preferred processor when a rank autocorrelation coefficient exceeds 0.6. Thus, the climatic autocorrelation can play a significant role in quantifying, and ultimately in reducing, the meteorological forecast uncertainty.

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