Abstract

A general approach for modeling wind speed and wind power is described. Because wind power is a function of wind speed, the methodology is based on the development of a model of wind speed. Values of wind power are estimated by applying the appropriate transformations to values of wind speed. The wind speed modeling approach takes into account several basic features of wind speed data, including autocorrelation, non-Gaussian distribution, and diurnal nonstationarity. The positive correlation between consecutive wind speed observations is taken into account by fitting an autoregressive process to wind speed data transformed to make their distribution approximately Gaussian and standardized to remove diurnal nonstationarity.

As an example, the modeling approach is applied to a small set of hourly wind speed data from the Pacific Northwest. Use of the methodology for simulating and forecasting wind speed and wind power is discussed and an illustration of each of these types of applications is presented. To take into account the uncertainty of wind speed and wind power forecasts, techniques are presented for expressing the forecasts either in terms of confidence intervals or in terms of probabilities.

Abstract

The use of a concept called a precipitation “event” to obtain information regarding certain statistical properties of precipitation time series at a particular location and for a specific application (e.g., for modeling erosion) is described. Exploratory data analysis is used to examine several characteristics of more than 31 years of primitive precipitation events based on hourly precipitation data at Salem, Oregon. A primitive precipitation event is defined as one or more consecutive hours with at least 0.01 inches (0.25 mm) of precipitation. The characteristics of the events that are considered include the duration, magnitude, average intensity and maximum intensity of the event and the number of hours separating consecutive events.

By means of exploratory analysis of the characteristics of the precipitation events, it is demonstrated that the marginal (i.e., unconditional) distributions of the characteristics are positively skewed. Examination of the conditional distributions of some pairs of characteristics indicates the existence of some relationships among the characteristics. For example, it is found that average intensity and maximum intensity are quite dependent on the event duration. The existence and forms of these relationships indicate that the assumption commonly made in stochastic models of hourly precipitation time series that the intensities (i.e., hourly amounts within an event) are independent and identically distributed must be violated. Again using exploratory data analysis, it is shown that the hourly intensities at Salem are, in fact, stochastically increasing and positively associated within a precipitation event.

Abstract

Abstract

The methodology of decision analysis is used to investigate the economic value of frost (i.e., minimum temperature) forecasts to orchardists. First, the fruit-frost situation and previous studies of the value of minimum temperature forecasts in this context are described. Then, after a brief overview of decision analysis, a decision-making model for the fruit-frost problem is presented. The model involves identifying the relevant actions and events (or outcomes), specifying the effect of taking protective action, and describing the relationships among temperature, bud loss, and yield loss. A bivariate normal distribution is used to model the relationship between forecast and observed temperatures, thereby characterizing the quality of different types of information. Since the orchardist wants to minimize expenses (or maximize payoffs) over the entire frost-protection season and since current actions and outcomes at any point in the season are related to both previous and future actions and outcomes, the decision-making problem is inherently dynamic in nature. As a result, a class of dynamic models known as Markov decision processes is considered. A computational technique called dynamic programming is used in conjunction with these models to determine the optimal actions and to estimate the value of meteorological information.

Some results concerning the value of frost forecasts to orchardists in the Yakima Valley of central Washington are presented for the cases of red delicious apples, bartlett pears, and elberta peaches. Estimates of the parameter values in the Markov decision process are obtained from relevant physical and economic data. Twenty years of National Weather Service forecast and observed temperatures for the Yakima key station are used to estimate the quality of different types of information, including perfect forecasts, current forecasts, and climatological information. The orchardist's optimal actions over the frost-protection season and the expected expenses associated with the use of such information are determined using a dynamic programming algorithm. The value of meteorological information is defined as the difference between the expected expense for the information of interest and the expected expense for climatological information. Over the entire frost-protection season, the value estimates (in 1977 dollars) for current forecasts were $808 per acre for red delicious apples, $492 per acre for bartlett pears, and $270 per acre for elberta peaches. These amounts account for 66, 63, and 47%, respectively, of the economic value associated with decisions based on perfect forecasts. Varying the quality of the minimum temperature forecasts reveals that the relationship between the accuracy and value of such forecasts is nonlinear and that improvements in current forecasts would not be as significant in terms of economic value as were comparable improvements in the past.

Several possible extensions of this study of the value of frost forecasts to orchardists are briefly described. Finally, the application of the dynamic model formulated in this paper to other decision-making problems involving the use of meteorological information is mentioned.

Abstract

Most climate impact studies rely on changes in means of meteorological variables, such as temperature, to estimate potential climate impacts, including effects on agricultural production. However, extreme meteorological events, say, a short period of abnormally high temperatures, can have a significant harmful effect on crop growth and final yield. The characteristics of daily temperature time series, specifically mean, variance and autocorrelation, are analyzed to determine possible ranges of probabilities of certain extreme temperature events [e.g., runs of consecutive daily maximum temperatures of at least 95°F (35°C)] with changes in mean temperature of the time series. The extreme temperature events considered are motivated primarily by agricultural concerns, particularly, the effects of high temperatures on corn yields in the U.S. Corn Belt. However, runs of high temperatures can also affect, for example, energy demand or morbidity and mortality of animals and humans.

The relationships between changes in mean temperature and the corresponding changes in the probabilities of these extreme temperature events are quite nonlinear, with relatively small changes in mean temperature sometimes resulting in relatively large changes in event probabilities. In particular, the likelihood of occurrence of a run of five consecutive daily maximum temperatures of at least 95°F under a 3°F (1.7°C) increase in the mean (holding the variance and autocorrelation constant) is about three times greater than that under the current climate at Des Moines, Moreover, by allowing either the variance or the autocorrelation as well as the mean to change, this likelihood of a run event varies over a relatively wide range of values. These changes in the probabilities of extreme events need to be taken into consideration in order to obtain realistic estimates of the impact of climate changes such as increases in mean temperature that may arise from increases in atmospheric carbon dioxide concentration.

Abstract

North Atlantic atmospheric blocking conditions explain part of the winter climate variability in Europe, being associated with anomalous cold winter temperatures. In this study, the generalized extreme value (GEV) distribution is fitted to monthly minima of European winter 6-hourly minimum temperatures from the ECHAM5/MPI-OM global climate model simulations and the ECMWF reanalysis product known as ERA-40, with an indicator for atmospheric blocking conditions being used as covariate. It is demonstrated that relating the location and scale parameter of the GEV distribution to atmospheric blocking improves the fit to extreme minimum temperatures in large areas of Europe. The climate model simulations agree reasonably with ERA-40 in the present climate (1961–2000). Under the influence of atmospheric blocking, a decrease in the 0.95th quantiles of extreme minimum temperatures can be distinguished. This cooling effect of atmospheric blocking is, however, diminished in future climate simulations because of a shift in blocking location, and thus reduces the chances of very cold winters in northeastern parts of Europe.

This paper reports some results of a descriptive study of the value of weather information used by fruit growers in the Yakima Valley of central Washington to decide when to protect their orchards against freezing temperatures. Specifically, the study provides data concerning the decision-making procedures of individual orchardists, the growers' use of weather information including frost (i.e., minimum temperature) forecasts, and the dimensions of the value of such forecasts.

Results from the descriptive study regarding the orchardists' information-processing and decision-making procedures are compared with the procedures included in a previous prescriptive study of the fruit-frost problem in the same geographical area (Katz et al., 1982). The prescriptive study employed a dynamic decision-making model and yielded estimates of the economic value of frost forecasts under the assumption (inter alia) that the orchardists' decisions were based solely on these forecasts. On the other hand, the descriptive study with which the current paper is primarily concerned indicates that growers use temperature and dew point observations available after the frost forecast has been issued, as well as the frost forecasts themselves, to make frost protection decisions. Furthermore, while the results of the descriptive study show that the grower makes a series of decisions to protect or not to protect during the night, the model assumed that an irreversible commitment is made early in the night. The results of an initial effort to modify the original prescriptive model in accordance with the descriptive findings to obtain more realistic estimates of the value of frost forecasts also are reported in this paper.

Some implications of this study for the further development of prescriptive models of the decision-making process in the fruit-frost context and in other weather-information-sensitive contexts are discussed.

The so-called fallowing/planting problem is an example of a decision-making situation that is potentially sensitive to meteorological information. In this problem, wheat farmers in the drier, western portions of the northern Great Plains must decide each spring whether to plant a crop or to let their land lie fallow. Information that could be used to make this decision includes the soil moisture at planting time and a forecast of growing-season precipitation. A dynamic decision-making model is employed to investigate the economic value of such forecasts in the fallowing/planting situation.

Current seasonal-precipitation forecasts issued by the National Weather Service are found to have minimal economic value in this decision-making problem. However, relatively modest improvements in the quality of the forecasts would lead to quite large increases in value, and perfect information would possess considerable value. In addition, forecast value is found to be sensitive to changes in crop price and precipitation climatology. In particular, the shape of the curve relating forecast value to forecast quality is quite dependent on the amount of growing-season precipitation.

Abstract

The purposes of this paper are to describe a dynamic model for repetitive decision‐making in the cost–loss ratio situation and to present some theoretical and numerical results related to the optimal use and economic value of weather forecasts within the framework of the model. This model involves the same actions and events as the standard (i.e., static) cost–loss ratio situation, but the former (unlike the latter) is dynamic in the sense that it possesses characteristics (e.g., decisions, events) that are related over time. We assume that the decision maker wants to choose the sequence of actions over an n‐occasion time period that minimizes the total expected expense. A computational technique known as stochastic dynamic programming is employed to determine this optimal policy and the total expected expense.

Three types of weather information are considered in studying the value of forecasts in this context: 1) climatological information; 2) perfect information; and 3) imperfect forecasts. Climatological and perfect information represent lower and upper bounds, respectively, on the quality of all imperfect forecasts, with the latter considered here to be categorical forecasts properly calibrated according to their past performance. Theoretical results are presented regarding the form of the optimal policy and the relationship among the total expected expenses for these three types of information. In addition, quality/value relationships for imperfect forecasts are described.

Numerical results are derived from the dynamic model for specific values of the model parameters. These results include the optimal policy and the economic value of perfect and imperfect forecasts for various time horizons, climatological probabilities, and values of the cost–loss ratio. The relationship between the accuracy and value of imperfect forecasts also is examined.

Several possible extensions of this dynamic model are briefly discussed, including decision‐making problems involving more actions and/or events, more complex structures of the costs and losses, and more general forms of imperfect forecasts (e.g., probability forecasts).

Abstract

Reliable estimates of future changes in extreme weather phenomena, such as tropical cyclone maximum wind speeds, are critical for climate change impact assessments and the development of appropriate adaptation strategies. However, global and regional climate model outputs are often too coarse for direct use in these applications, with variables such as wind speed having truncated probability distributions compared to those of observations. This poses two problems: How can model-simulated variables best be adjusted to make them more realistic? And how can such adjustments be used to make more reliable predictions of future changes in their distribution?

This study investigates North Atlantic tropical cyclone maximum wind speeds from observations (1950–2010) and regional climate model simulations (1995–2005 and 2045–55 at 12- and 36-km spatial resolutions). The wind speed distributions in these datasets are well represented by the Weibull distribution, albeit with different scale and shape parameters.

A power-law transfer function is used to recalibrate the Weibull variables and obtain future projections of wind speeds. Two different strategies, bias correction and change factor, are tested by using 36-km model data to predict future 12-km model data (pseudo-observations). The strategies are also applied to the observations to obtain likely predictions of the future distributions of wind speeds. The strategies yield similar predictions of likely changes in the fraction of events within Saffir–Simpson categories—for example, an increase from 21% (1995–2005) to 27%–37% (2045–55) for category 3 or above events and an increase from 1.6% (1995–2005) to 2.8%–9.8% (2045–55) for category 5 events.