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Allan H. Murphy
and
Robert L. Winkler

Abstract

An experiment was conducted at the National Severe Storms Forecast Center during 1976 and 1977 in which National Weather Service forecasters formulated probabilistic forecasts of several tornado events in conjunction with both severe weather outlooks and severe thunderstorm and tornado watches. The results indicate that the probabilistic forecasts associated with the outlooks were quite reliable and exhibited positive skill, relative to forecasts based on sample climatological probabilities. The probabilistic forecasts associated with the watches, however, were less reliable and skillful. In view of the lack of prior experience at making probabilistic tornado forecasts, as well as the absence of feedback, comparable objective probabilistic guidance, and even appropriate past data on which to base climatological probabilities, the results of the experiment are quite encouraging. Some suggestions for further work in probabilistic tornado forecasting are provided.

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Seijo Kruizinga
and
Allan H. Murphy

Abstract

The purpose of this paper is to describe some results of a study in which an analogue procedure developed in The Netherlands is used to formulate objective probabilistic temperature forecasts on an experimental basis. As currently employed, the procedure routinely provides forecasters at the Royal Netherlands Meteorological Institute with guidance information that summarizes, for days 11 through 6, the weather conditions associated with the best thirty analogues of the corresponding forecast situation. In the work reported here, the empirical frequency distribution of maximum temperature corresponding to these thirty analogues is used to generate both categorical and probabilistic forecasts of this element. Attention is focused on three types of probabilistic forecasts of maximum temperature: 1) a discrete distribution for five temperature classes 2) a variable-width credible interval., and 3) a fixed-width credible interval.

Results of the experiment indicate that all three types of probabilistic temperature forecasts are quite reliable, in the sense that the forecast probabilities correspond closely to the relative frequencies of observed temperatures associated with these class/intervals. Moreover, the forecasts generally are more accurate and precise, according to several different measures of performance, than forecasts based on standards of reference such as climatology and persistence. Thus, these experimental objective probability forecasts usually exhibit positive skill. As expected, the level of skill decreases markedly from day 1 to day 6 for all three types of probability forecasts. Evaluation of two types of categorical forecasts—the median and mean temperatures derived from the empirical frequency distribution—reveals similar results.

The implications of the results of this study for operational temperature forecasting are discussed briefly, and some possible refinements and/or improvements in objective probabilistic temperature forecasting are described.

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Robert L. Winkler
and
Allan H. Murphy

Abstract

An experiment was conducted at the National Weather Service Forecast Office in St. Louis, Mo., to investigate the ability of forecasters to differentiate among different points in a forecast area with regard to the livelihood of the occurrence of measurable precipitation and the relative ability of forecasters to make point and area precipitation probability forecasts. On each forecasting occasion in the experimental period (November 1972–March 1973), the forecasters made an average point probability forecast for the St. Louis metropolitan area, point probability forecasts for five specific points in the area, an area probability forecast, and an expected areal coverage forecast.

The results indicate that the forecasters did not differentiate among the five points very often, but that this absence of differences among the point probabilities was justified by the lack of variability exhibited by the observations of precipitation occurrence at these points during the experimental period. Evaluations of the average point probability forecasts, individual point probability forecasts, and expected areal coverage forecasts reveal that these forecasts were quite reliable and accurate and that they were also internally consistent. The area probability forecasts, however, tended not to be consistent with the other forecasts, and the average area probability forecast was considerably lower than the relative frequency of occurrence of precipitation “somewhere in the area.”

The implications of these results for precipitation probability forecasting in meteorology are briefly discussed.

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Allan H. Murphy
and
Robert L. Winkler

Abstract

This paper describes the results of an experiment involving credible interval temperature forecasts. A credible interval is an interval of values of the variable of concern, in this case maximum or minimum temperature, accompanied by a probability which expresses a forecaster's “degree of belief” that the temperature will fall in the given interval. The experiment was designed to investigate the ability of fore-casters to express the uncertainty inherent in their temperature forecasts in probabilistic terms and to compare two approaches (variable-width and flied-width intervals) to credible interval temperature forecasting.

Four experienced weather forecasters participated in the experiment, which was conducted at the National Weather Service Forecast Office in Denver, Colorado. Two forecasters made variable-width, fixed-probability forecasts using 50% and 75% intervals, while the other two forecasters made fixed-width, variable-probability forecasts using 5°F and 9°F intervals. On each occasion the forecasters first determined a median, and the variable-width and fixed-width intervals were then centered at the median in terms of probability and width, respectively.

The results indicate that, overall, the medians determined by the forecasters were good point forecasts of maximum and minimum temperatures. Further, a comparison of the average errors for the forecasters’ medians with the average errors for the medians derived from climatology reveals that the forecasters were able to improve greatly upon climatology. The variable-width credible intervals were very reliable in the sense that the observed relative frequencies corresponded very closely to the forecast probabilities. Moreover, the variable-width intervals were more reliable and much more precise than the corresponding climatological forecasts. The fixed-width intervals, on the other hand, were assigned probabilities that were, on the average, larger that the corresponding relative frequencies.

In summary, the results indicate that weather forecasters can use credible intervals to describe the uncertainty contained in their temperature forecasts. The implications of these experimental results for probability forecasting in general and temperature forecasting in particular 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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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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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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