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- Author or Editor: Richard W. Katz x
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Abstract
Kraus (1977) has demonstrated that subtropical African droughts exhibit statistically significant persistence. It is emphasized, through a further analysis of annual subtropical African rainfall, that the data are highly variable with only a small degree of persistence. These results have significant implications concerning the appropriate characterization of the likelihood of drought for dissemination to decision-makers.
Abstract
Kraus (1977) has demonstrated that subtropical African droughts exhibit statistically significant persistence. It is emphasized, through a further analysis of annual subtropical African rainfall, that the data are highly variable with only a small degree of persistence. These results have significant implications concerning the appropriate characterization of the likelihood of drought for dissemination to decision-makers.
Abstract
Statistical problems that may be encountered in fitting autoregressive-moving average (ARMA) processes to meteorological time series are described. Techniques that lead to an increased likelihood of choosing the most appropriate ARMA process to model the data at hand are emphasized. One specific meteorological application of ARMA processes, the modeling of Palmer Drought Index time series for climatic divisions of the United States is considered in detail. It is shown that low-order purely autoregressive processes adequately fit these data.
Abstract
Statistical problems that may be encountered in fitting autoregressive-moving average (ARMA) processes to meteorological time series are described. Techniques that lead to an increased likelihood of choosing the most appropriate ARMA process to model the data at hand are emphasized. One specific meteorological application of ARMA processes, the modeling of Palmer Drought Index time series for climatic divisions of the United States is considered in detail. It is shown that low-order purely autoregressive processes adequately fit these data.
Abstract
One particular index has been commonly used to monitor precipitation in drought-prone regions such as the West African Sahel and the Brazilian Northeast. The construction of this index involves standardizing the annual total rainfall for an individual nation and then averaging these standardized rainfall deviations over all the stations within the region to obtain a single value. Some theoretical properties of this “Standardized Anomaly Index” are derived. By studying its behavior when applied to actual rainfall data in the Sahel, certain aspects of the practical utility of the index are also considered. For instance, the claim that the Sahel has recently experienced a long run of relatively dry years does not appear to be sensitive to the exact form of index that is employed. On the other hand, it is shown by means of principal components analysis that no single index can “explain” a large portion of the variation in Sahelian rainfall, implying that much information, that is at least potentially useful, is lost when one relies only on a single index. The implications of these results for assessments of the impact of drought on society in arid and semiarid regions are discussed.
Abstract
One particular index has been commonly used to monitor precipitation in drought-prone regions such as the West African Sahel and the Brazilian Northeast. The construction of this index involves standardizing the annual total rainfall for an individual nation and then averaging these standardized rainfall deviations over all the stations within the region to obtain a single value. Some theoretical properties of this “Standardized Anomaly Index” are derived. By studying its behavior when applied to actual rainfall data in the Sahel, certain aspects of the practical utility of the index are also considered. For instance, the claim that the Sahel has recently experienced a long run of relatively dry years does not appear to be sensitive to the exact form of index that is employed. On the other hand, it is shown by means of principal components analysis that no single index can “explain” a large portion of the variation in Sahelian rainfall, implying that much information, that is at least potentially useful, is lost when one relies only on a single index. The implications of these results for assessments of the impact of drought on society in arid and semiarid regions are discussed.
Abstract
A relative measure of actual, rather than potential, predictability of a meteorological variable on the basis of its past history alone is proposed. This measure is predicated on the existence of a parametric time series model to represent the meteorological variable. Among other things, it provides an explicit representation of forecasting capability in terms of the individual parameters of such time series models.
As an application, the extent to which the Southern Oscillation (S0), a major component of climate, can be predicted on a monthly as well as a seasonal time scale on the basis of its past history alone is determined. In particular, on a monthly time scale up to about 44% of the variation in SO can be predicted one month ahead (zero months lead time) and about 35% two months ahead (one month lead time), or on a seasonal time scale about 53% one season ahead (zero seasons lead time) and about 31% two masons ahead (one season lead time). In general, the degree of predictability naturally decays as the lead time increases with essentially no predictability on a monthly time scale beyond ten months (nine months lead time) or on a seasonal time scale beyond seasons (two seasons lead time).
Abstract
A relative measure of actual, rather than potential, predictability of a meteorological variable on the basis of its past history alone is proposed. This measure is predicated on the existence of a parametric time series model to represent the meteorological variable. Among other things, it provides an explicit representation of forecasting capability in terms of the individual parameters of such time series models.
As an application, the extent to which the Southern Oscillation (S0), a major component of climate, can be predicted on a monthly as well as a seasonal time scale on the basis of its past history alone is determined. In particular, on a monthly time scale up to about 44% of the variation in SO can be predicted one month ahead (zero months lead time) and about 35% two months ahead (one month lead time), or on a seasonal time scale about 53% one season ahead (zero seasons lead time) and about 31% two masons ahead (one season lead time). In general, the degree of predictability naturally decays as the lead time increases with essentially no predictability on a monthly time scale beyond ten months (nine months lead time) or on a seasonal time scale beyond seasons (two seasons lead time).
Abstract
An index consisting of the difference of normalized sea level pressure departures between Tahiti and Darwin is used to represent the Southern Oscillation (SO) fluctuations. Using a time-domain approach, autoregressive-moving average (ARMA) progress are applied to model and predict this Southern Oscillation Index (SOI) on a monthly and seasonal basis. The ARMA process which is chosen to fit the monthly SOI expresses the index for the current month as a function of both the SOI one month and seven (or nine) mouths ago, as well as the current and previous month's random error. A purely automotive (AR) process is identified as representative of the seasonal SO fluctuations, with the SOI for the current season being derived from the index for the immediate past three seasons and a single random disturbance term for the current season. To allow for the phase locking of the SOI with the annual cycle, ARMA processes with seasonally varying coefficients are also considered.
As one example of how these models could be used, seasonal SO variations have been forecast. When SOI observations from 1935 through the summer of 1983 are employed, the seasonal model indicates forecast of positive SOI from fall 1983 through fall 1984. Forecasts based only on SOI observations from 1935 through spring 1982 show a low predictive skill for the SOI values from summer 1982 through winter 1984, whereas one-season-ahead forecasts starting with summer 1982 agree reasonably well with the actual SOI observations. These examples help illustrate the degree to which the future behavior of the SOI is predictable on the basis of its past history alone.
Abstract
An index consisting of the difference of normalized sea level pressure departures between Tahiti and Darwin is used to represent the Southern Oscillation (SO) fluctuations. Using a time-domain approach, autoregressive-moving average (ARMA) progress are applied to model and predict this Southern Oscillation Index (SOI) on a monthly and seasonal basis. The ARMA process which is chosen to fit the monthly SOI expresses the index for the current month as a function of both the SOI one month and seven (or nine) mouths ago, as well as the current and previous month's random error. A purely automotive (AR) process is identified as representative of the seasonal SO fluctuations, with the SOI for the current season being derived from the index for the immediate past three seasons and a single random disturbance term for the current season. To allow for the phase locking of the SOI with the annual cycle, ARMA processes with seasonally varying coefficients are also considered.
As one example of how these models could be used, seasonal SO variations have been forecast. When SOI observations from 1935 through the summer of 1983 are employed, the seasonal model indicates forecast of positive SOI from fall 1983 through fall 1984. Forecasts based only on SOI observations from 1935 through spring 1982 show a low predictive skill for the SOI values from summer 1982 through winter 1984, whereas one-season-ahead forecasts starting with summer 1982 agree reasonably well with the actual SOI observations. These examples help illustrate the degree to which the future behavior of the SOI is predictable on the basis of its past history alone.
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
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).
