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Robert T. Clemen
and
Allan H. Murphy

Abstract

This paper addresses two specific questions related to the interrelationships between objective and subjective probability of precipitation (PoP) forecasts: Do the subjective forecasts contain information not included in the objective forecasts? Do the subjective forecasts make full use of the objective forecasts? With respect to the first question, an analysis of more than 11 years of data indicates that the subjective PoP forecasts add information above and beyond that contained in the objective PoP forecasts for all combinations of geographical area, lead time, and season investigated in this study. For longer lead times, this conclusion appears to contradict the results of earlier studies in which the two types of PoP forecasts were compared using aggregate skill scores. With regard to the second question, the statistical results demonstrate that the subjective forecasts generally do not make full use of the objective forecasts. However, these latter results are not as strong, in a statistical sense, as the results related to the first question; moreover, they indicate that it is primarily in the vicinity of the climatological probability (i.e., 0.10 to 0.40) that better use could be made of the objective forecasts. This conclusion suggests that it may be possible to combine the objective and subjective forecasts to produce a PoP forecast with even greater information content.

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Robert T. Clemen
and
Allan H. Murphy

Abstract

This paper reports the results of an empirical investigation of some methods for improving the quality of precipitation probability forecasts. These methods include 1) techniques for adjusting subjective and objective forecasts using past reliability data and 2) techniques for combining these two types of forecasts via both averaging and a more sophisticated statistical aggregation procedure. The empirical results indicate that forecast performance can be improved through such methods, with the greatest improvements arising from averaging forecasts that have previously been adjusted.

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Barbara G. Brown
and
Allan H. Murphy

Abstract

Fire-weather forecasts (FWFs) prepared by National Weather Service (NWS) forecasters on an operational basis are traditionally expressed in categorical terms. However, to make rational and optimal use of such forecasts, fire managers need quantitative information concerning the uncertainty inherent in the forecasts. This paper reports the results of two studies related to the quantification of uncertainty in operational and experimental FWFs.

Evaluation of samples of operational categorical FWFs reveals that these forecasts contain considerable uncertainty. The forecasts also exhibit modest but consistent biases which suggest that the forecasters are influenced by the impacts of the relevant events on fire behavior. These results underscore the need for probabilistic FWFs.

The results of a probabilistic fire-weather forecasting experiment indicate that NWS forecasters are able to make quite reliable and reasonably precise credible interval temperature forecasts. However, the experimental relative humidity and wind speed forecasts exhibit considerable overforecasting and minimal skill. Although somewhat disappointing, these results are not too surprising in view of the fact that (a) the forecasters had little, if any, experience in probability forecasting; (b) no feedback was provided to the forecasters during the experimental period; and (c) the experiment was of quite limited duration. More extensive experimental and operational probability forecasting trials as well as user-oriented studies are required to enhance the quality of FWFs and to ensure that the forecasts are used in an optimal manner.

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Allan H. Murphy
and
Martin Ehrendorfer

Abstract

This paper explores the relationship between the quality and value of imperfect forecasts. It is assumed that these forecasts are produced by a primitive probabilistic forecasting system and that the decision-making problem of concern is the cost-loss ratio situation. In this context, two parameters describing basic characteristics of the forecasts must be specified in order to determine forecast quality uniquely. As a result, a scalar measure of accuracy such as the Brier score cannot completely and unambiguously describe the quality of the imperfect forecasts. The relationship between forecast accuracy and forecast value is represented by a multivalued function—an accuracy/value envelope. Existence of this envelope implies that the Brier score is an imprecise measure of value and that forecast value can even decrease as forecast accuracy increases (and vice versa). The generality of these results and their implications for verification procedures and practices are discussed.

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Allan H. Murphy
and
Robert L. Winkler

This paper describes the preliminary results of three experiments in subjective probability forecasting which were recently conducted in four Weather Service Forecast Offices (WSFOs) of the National Weather Service. The first experiment, which was conducted at the St. Louis WSFO, was designed to investigate both the ability of forecasters to differentiate among points in a forecast area with regard to the likelihood of occurrence of measurable precipitation and their relative ability to make point and area (including areal coverage) precipitation probability forecasts. The second experiment, which was conducted at the Denver WSFO, was designed to investigate the ability of forecasters to use credible intervals to express the uncertainty inherent in their temperature forecasts and to compare two approaches (variable-width intervals and fixed-width intervals) to credible interval temperature forecasting. The third experiment, which was conducted at both the Great Falls and Seattle WSFOs, was designed to investigate the effects of guidance (i.e., PEATMOS) forecasts upon the forecasters' precipitation probability forecasts.

For each experiment, some background material is presented; the design of the experiment is discussed; some preliminary results of the experiment are presented; and some implications of the experiment and the results for probability forecasting in meteorology and probability forecasting in general are discussed. The results of each of these experiments will be described individually and in much greater detail in a series of forthcoming papers.

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Allan H. Murphy
and
Robert L. Winkler

Some results of a nationwide survey of National Weather Service forecasters with regard to probability forecasting in general and precipitation probability forecasting in particular are summarized. Specifically, the questionnaire which was used in the survey, the participants in the survey (i.e., the forecasters), and the nature of the results are briefly described, and some recommendations based upon these results are presented.

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Allan H. Murphy
and
Robert L. Winkler

This paper summarizes the responses of the forecasters of the Travelers Weather Service to a questionnaire concerning probability forecasting. The questionnaire was designed to elicit information from the forecasters relative to the process of precipitation probability forecasting (e.g., the information sources examined, their relative importance and order of examination), the relationship between judgments and forecasts, the effect of the definition of precipitation on the forecasts, the meaning of the forecasts, the effects of feedback and experience on the forecasts, and related matters. The responses to the questionnaire and subsequent discussions with Travelers Weather Service and National Weather Service forecasters suggest the presence of a number of “problems” related to probability forecasting. Several of these “problems” are considered in some detail in a separate paper (Murphy and Winkler, 1971).

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Allan H. Murphy
and
Robert L. Winkler

The responses to a questionnaire which was administered to forecasters actively involved in probability forecasting are summarized in Murphy and Winkler (1971). These responses and subsequent discussions with forecasters reveal the presence of a number of “problems” concerning probability forecasting. In this paper, we identify several of the more important problems, describe their nature, indicate some approaches and results which clarify certain aspects of the problems, and make some recommendations related to research studies and operational practices in probability forecasting. In particular, we discuss the formulation of judgments and the assessment process, the interpretation of probability forecasts, the occurrence of “hedging” by forecasters, and the evaluation of probability forecasts and forecasters.

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Allan H. Murphy
and
Robert L. Winkler

The case for an operational program involving the formulation and dissemination of probabilistic temperature forecasts is presented. First, the need for information concerning the uncertainty in temperature forecasts is discussed, and examples of formal and informal decision-making situations in which such information would be useful are described. The results of experiments in probabilistic temperature forecasting are then reviewed, and it is concluded that experienced weather forecasters can quantify the uncertainty inherent in temperature forecasts in a reliable and skillful manner. Finally, the essential components of an operational probabilistic temperature forecasting program are outlined, and some suggestions are made regarding specific temperature events that should receive probabilistic treatment on an operational basis.

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William R. Bergen
and
Allan H. Murphy

Severe downslope windstorms are an outstanding feature of the winter weather in Boulder, Colo., and property damage associated with these storms averages about $1 million each year. Recently, efforts to develop a numerical model capable of forecasting downslope windstorms have yielded encouraging results. The possibility that short-term forecasts of these storms might become available on an operational basis led to a study of the societal impact of improved windstorm forecasts in the Boulder area, and this paper describes the results of that study.

Surveys were conducted of selected samples of Boulder residents and businesses concerning the potential economic and social benefits and disbenefits of improvements in downslope windstorm forecasts. The survey questions concerned five basic topics: 1) perception of the windstorm hazard; 2) the desire for improved windstorm forecasts; 3) the use of windstorm forecasts; 4) the value of improved forecasts; and 5) possible forecast dissemination techniques. Personal interviews were conducted with local businesses and public service agencies to supplement and extend the results of the surveys.

All segments of the community were found to be concerned about the windstorms because of the possibility of serious injury and/or major property damage. The responses also revealed a strong desire for improved windstorm forecasts, although the level of desire was found to depend upon the accuracy of the forecasts. Moreover, significant increases in the use of a variety of protective actions would occur if accurate (i.e., 80% accurate) windstorm forecasts were available. The results of the surveys and interviews indicated that accurate forecasts could reduce residential property damage by approximately $200 000 annually, and the potential savings to local businesses were estimated to be an additional $150 000. These benefits appear to greatly exceed any incremental costs associated with formulating and disseminating the forecasts and any economic losses suffered by local businesses due to decreased windstorm damage. In addition, the residents expressed a willingness to support a local windstorm forecasting system if governmental funding was not available. Finally, while no completely effective procedure for alerting a significant fraction of the community to an approaching windstorm was identified, it was recognized that this problem is not unique to forecasts of downslope windstorms and requires further study.

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