Point and Area Precipitation Probability Forecasts: Some Experimental Results

An experiment was conducted at the National Weather Service Forecast Office in St. Louis, Missouri, to investigate the ability of forecasters to differentiate among different points in a forecast area with regard to the likelihood 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 to 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 are a 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

Credible Interval Temperature Forecasting: Some Experimental Results

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 forecasters to express the uncertainty inherent in their temperature forecasts in probabilistic terms and to compare two approaches (variable-width and fixed-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 degree F and 9 degree 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 forecasts derived from climatology. The fixed-width intervals, on the other hand, were assigned probabilities that were, on the average, considerably larger than 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

Probability Forecasts: A Survey of National Weather Service Forecasters

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

Subjective Probability Forecasting Experiments in Meteorology: Some Preliminary Results

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 ill a series of forthcoming papers

The Use of Credible Intervals in Temperature Forecasting: Some Experimental Results

Probability can be thought of as the language of uncertainty, and, as such, it provides forecasters with a means of describing the uncertainty inherent in their forecasts in a formal, quantitative manner. Probability forecasts, in turn, provide potential users of forecasts with information required to make rational decisions in uncertain situations. Since 1965, the National Weather Service (NWS) in the United States has routinely issued precipitation probability forecasts to the general public. Forecasts of maximum and minimum temperature, however, are still expressed in categorical terms (i.e., in terms of a specific temperature or a range of temperatures). In this paper we describe and compare the results of two recent experiments in which NWS forecasters used credible intervals to describe the uncertainty inherent in their temperature forecasts. A credible interval temperature forecast is simply an interval forecast accompanied by the forecaster's subjective probability that the temperature of concern will fall in the interval. The experiments were conducted in the NWS forecast offices in Denver, Colorado and Milwaukee, Wisconsin and involved four and five forecasters, respectively. In each experiment, one group of forecasters made variable-width interval forecasts and the other group made fixed-width interval forecasts. In the variable-width approach, the forecasters determined 50% and 75% central credible intervals using the "method of successive sub-divisions" (i.e., they assessed the median, 25th percentile, 12.5th percentile, 75th percentile, 87.5th percentile of their probability distributions, in that order). In the fixed-width approach, the forecasters first determined a median and then assessed probabilities for 5 degrees F and 9 degrees F intervals centered at the median. In evaluating the results of the experiments, several properties of the forecasts (i.e., the medians and the intervals) were of interest, including their reliability and precision. Reliability refers to the degree of correspondence between the probabilities associated with the forecasts and the sample relative frequencies (i.e., the distribution of observed temperatures), while precision relates to the degree of correspondence between the forecasts and the observed temperatures on an individual basis. The latter can be measured by computing the average absolute error (and similar quantities) in the case of the medians and average scores based upon one or more "proper" scoring rules in the case of the (fixed-width) intervals. The forecasts formulated by the forecasters were also compared with forecasts based solely upon climatological data. The results of the experiments indicate that NWS forecasters can formulate reliable and precise credible interval temperature forecasts and that these forecasts are generally better (in the sense of these two properties) than forecasts based upon climatological data. The influences of a number of variables were considered in the process of evaluating the forecasts. These variables included: 1) location of experiment (Denver, Milwaukee); 2) type of interval (variable-width, fixed-width); 3) type of temperature (maximum, minimum); 4) forecast length (12 hours, 24 hours, 36 hours) ; and 5) forecaster. In addition, factors such as forecasting experience, training, and learning effects were investigated within the constraints imposed by the number of forecasters and the length of the experiments. Finally, we briefly discuss the implications of these experiments and the results for probability forecasting in general and probability forecasting in meteorology in particular

Subjective Probability Forecasting in the Real World: Some Experimental Results

Three experiments in subjective probability forecasting were designed, and these experiments were conducted in four forecast offices of the U.S. National Weather Service. The first experiment involved credible interval temperature forecasts, the second experiment involved point and area precipitation probability forecasts, and the third experiment involved the effect of guidance forecasts on precipitation probability forecasts. In each case, some background material is presented; the design of the experiment discussed; some preliminary results of the experiment are presented; and some implications of the experiment and the results for probability forecasting in general and probability forecasting in meteorology in particular are discussed

Long-term degradation of optical devices on the moon

Forty years ago, Apollo astronauts placed the first of several retroreflector arrays on the lunar surface. Their continued usefulness for laser-ranging might suggest that the lunar environment does not damage optical devices. However, new laser ranging data reveal that the efficiency of the three Apollo reflector arrays is now diminished by a factor of ten at all lunar phases and by an additional factor of ten when the lunar phase is near full moon. These deficits did not exist in the earliest years of lunar ranging, indicating that the lunar environment damages optical equipment on the timescale of decades. Dust or abrasion on the front faces of the corner-cube prisms may be responsible, reducing their reflectivity and degrading their thermal performance when exposed to face-on sunlight at full moon. These mechanisms can be tested using laboratory simulations and must be understood before designing equipment destined for the moon.Comment: 9 pages; 4 figures; accepted for publication in Icaru

Pupil diameter tracks lapses of attention

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