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- Author or Editor: J. C. Thompson x
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Abstract
Several studies have examined the conditions in the equatorial Pacific basin that lead to the maximum growth over a fixed time period, τ. These studies have the purpose of finding the characteristic precursor to an ENSO warm event, or more generally to explore error growth and predictability of the coupled ocean–atmosphere system. This paper develops a linearized version of the Battisti model (similar to the Zebiak–Cane model) with a time-invariant background state. The optimal initial conditions for time period τ (τ-optimals) were computed for a range of τ and for a selection of background states.
A number of interesting characteristics of the τ-optimals emerged: 1) The τ-optimals grow more quickly than even the most unstable mode (the ENSO mode) of the system. 2) The τ-optimals develop quickly into the ENSO mode—in around 90 days. 3) The ENSO mode produced by a given τ-optimal does not in general peak at time τ. For τ less than 360 days the ENSO modes peak after time τ, and for τ greater than 360 days the ENSO mode first peaks before τ. At 360 days, designated τ max, the ENSO mode peaks at τ: this is also the τ-optimal, which produces the most growth. 4) Optimals were produced that used the SST only (T-optimals) and that used only the ocean dynamics (r-optimals). It is shown that for τ greater than 60 days, these two optimals both produce ENSO modes (of the same phase). This result makes a comparison of the relative importance of the SST versus the ocean dynamics straightforward: A T-optimal pattern with a 0.1 degree anomaly produces the same size ENSO as an r-optimal pattern with 1.2-m thermocline anomaly. 5) It is shown that the full optimal is the linear combination of these two suboptimals, where their relative sizes are determined by their relative weights (in the norm used).
The paper also experiments with a neutral and a damped version of the model and shows that their optimals have similar properties to those listed above; in particular, the shape of the optimal patterns is not overly sensitive to stability. The physical mechanisms for optimal growth are explored in depth.
Abstract
Several studies have examined the conditions in the equatorial Pacific basin that lead to the maximum growth over a fixed time period, τ. These studies have the purpose of finding the characteristic precursor to an ENSO warm event, or more generally to explore error growth and predictability of the coupled ocean–atmosphere system. This paper develops a linearized version of the Battisti model (similar to the Zebiak–Cane model) with a time-invariant background state. The optimal initial conditions for time period τ (τ-optimals) were computed for a range of τ and for a selection of background states.
A number of interesting characteristics of the τ-optimals emerged: 1) The τ-optimals grow more quickly than even the most unstable mode (the ENSO mode) of the system. 2) The τ-optimals develop quickly into the ENSO mode—in around 90 days. 3) The ENSO mode produced by a given τ-optimal does not in general peak at time τ. For τ less than 360 days the ENSO modes peak after time τ, and for τ greater than 360 days the ENSO mode first peaks before τ. At 360 days, designated τ max, the ENSO mode peaks at τ: this is also the τ-optimal, which produces the most growth. 4) Optimals were produced that used the SST only (T-optimals) and that used only the ocean dynamics (r-optimals). It is shown that for τ greater than 60 days, these two optimals both produce ENSO modes (of the same phase). This result makes a comparison of the relative importance of the SST versus the ocean dynamics straightforward: A T-optimal pattern with a 0.1 degree anomaly produces the same size ENSO as an r-optimal pattern with 1.2-m thermocline anomaly. 5) It is shown that the full optimal is the linear combination of these two suboptimals, where their relative sizes are determined by their relative weights (in the norm used).
The paper also experiments with a neutral and a damped version of the model and shows that their optimals have similar properties to those listed above; in particular, the shape of the optimal patterns is not overly sensitive to stability. The physical mechanisms for optimal growth are explored in depth.
Abstract
Long range plans for national and international economic improvements are vitally affected by the influence of weather and climate. It is therefore of interest to examine the magnitude of potential economic gains which may result from meteorological research. In this paper a preliminary study is made of the relative economic gains in weather prediction which may be achieved through further basic scientific studies in meteorology as well as through more operationally-oriented research. Considering the economic model used and sample predictions analyzed, the results suggest that average potential gains are strikingly uniform, ranging from five to ten per cent of the protectable weather losses.
Abstract
Long range plans for national and international economic improvements are vitally affected by the influence of weather and climate. It is therefore of interest to examine the magnitude of potential economic gains which may result from meteorological research. In this paper a preliminary study is made of the relative economic gains in weather prediction which may be achieved through further basic scientific studies in meteorology as well as through more operationally-oriented research. Considering the economic model used and sample predictions analyzed, the results suggest that average potential gains are strikingly uniform, ranging from five to ten per cent of the protectable weather losses.
Abstract
The application of modern statistical methods to the forecasting of rainfall in Los Angeles is discussed. Forecasts are made by graphical integration of a number of objective meteorological variables and the results presented in terms of the probability of rainfall occurring in each of several amount categories. The accuracy of this technique is discussed and compared with that obtained by current conventional forecasting methods, while the precision of the probability estimates is compared with a subjective evaluation of the probability distribution. Both comparisons show a slight, but statistically nonsignificant bias in favor of the numerical method.
The probability forecasts are shown to provide additional information regarding the reliability of each prediction which, by applying the principle of calculated risk, may be used to minimize the cost of carrying on any repetitive operation. An example of the use of this type of forecast is given, showing the saving which would result in a typical industrial operation in Los Angeles during the winter season of 1949–50.
Abstract
The application of modern statistical methods to the forecasting of rainfall in Los Angeles is discussed. Forecasts are made by graphical integration of a number of objective meteorological variables and the results presented in terms of the probability of rainfall occurring in each of several amount categories. The accuracy of this technique is discussed and compared with that obtained by current conventional forecasting methods, while the precision of the probability estimates is compared with a subjective evaluation of the probability distribution. Both comparisons show a slight, but statistically nonsignificant bias in favor of the numerical method.
The probability forecasts are shown to provide additional information regarding the reliability of each prediction which, by applying the principle of calculated risk, may be used to minimize the cost of carrying on any repetitive operation. An example of the use of this type of forecast is given, showing the saving which would result in a typical industrial operation in Los Angeles during the winter season of 1949–50.
A brief general analysis is made of the aims, methods, and uses of applied research in weather forecasting. The relationship between basic research in meteorology and applied forecasting research is discussed and the common ground between the two is pointed out.
A brief general analysis is made of the aims, methods, and uses of applied research in weather forecasting. The relationship between basic research in meteorology and applied forecasting research is discussed and the common ground between the two is pointed out.
A quantitative analysis is made of the range of operations for which conventional categorical weather forecasts are useful. It is shown that, because individual forecasts must of necessity be designed for only a small range of operations, their utility may be severely limited when the operating risks are much different from those to which the forecasts apply. This deficiency may be minimized, either by making categorical forecasts so that the optimum operating decision is provided for each user, or by providing an estimate of the probability of occurrence of critical weather and thus permitting the user to make his own operating decision.
A quantitative analysis is made of the range of operations for which conventional categorical weather forecasts are useful. It is shown that, because individual forecasts must of necessity be designed for only a small range of operations, their utility may be severely limited when the operating risks are much different from those to which the forecasts apply. This deficiency may be minimized, either by making categorical forecasts so that the optimum operating decision is provided for each user, or by providing an estimate of the probability of occurrence of critical weather and thus permitting the user to make his own operating decision.
Abstract
The economic factors involved in the use of weather forecasts are discussed, and procedures for analyzing the economic utility of both probability and categorical forecasts are derived. Some of the considerations involved in making public forecasting decisions are presented, and expressions are suggested for assessing the economic utility of public forecasts. The relationships between these measures of economic usefulness and certain formulae frequently used to assess forecasting accuracy are also pointed out.
Abstract
The economic factors involved in the use of weather forecasts are discussed, and procedures for analyzing the economic utility of both probability and categorical forecasts are derived. Some of the considerations involved in making public forecasting decisions are presented, and expressions are suggested for assessing the economic utility of public forecasts. The relationships between these measures of economic usefulness and certain formulae frequently used to assess forecasting accuracy are also pointed out.
Abstract
In this study the behavior of a linear, intermediate model of ENSO is examined under stochastic forcing. The model was developed in a companion paper (Part I) and is derived from the Zebiak–Cane ENSO model. Four variants of the model are used whose stabilities range from slightly damped to moderately damped. Each model is run as a simulation while being perturbed by noise that is uncorrelated (white) in space and time. The statistics of the model output show the moderately damped models to be more realistic than the slightly damped models. The moderately damped models have power spectra that are quantitatively quite similar to observations, and a seasonal pattern of variance that is qualitatively similar to observations. All models produce ENSOs that are phase locked to the annual cycle, and all display the “spring barrier” characteristic in their autocorrelation patterns, though in the models this “barrier” occurs during the summer and is less intense than in the observations (inclusion of nonlinear effects is shown to partially remedy this deficiency). The more realistic models also show a decadal variability in the lagged autocorrelation pattern that is qualitatively similar to observations.
Analysis of the models shows that the greatest part of the variability comes from perturbations that project onto the first singular vector, which then grow rapidly into the ENSO mode. Essentially, the model output represents many instances of the ENSO mode, with random phase and amplitude, stimulated by the noise through the optimal transient growth of the singular vectors.
The limit of predictability for each model is calculated and it is shown that the more realistic (moderately damped) models have worse potential predictability (9–15 months) than the deterministic chaotic models that have been studied widely in the literature. The predictability limits are strongly correlated with the stability of the models’ ENSO mode—the more highly damped models having much shorter limits of predictability. A comparison of the two most realistic models shows that even though these models have similar statistics, they have very different predictability limits. The models have a strong seasonal dependence to their predictability limits.
The results of this study (with the companion paper) suggest that the linear, stable dynamical model of ENSO is indeed a plausible hypothesis for the observed ENSO. With very reasonable levels of stochastic forcing, the model produces realistic levels of variance, has a realistic spectrum, and qualitatively reproduces the observed seasonal pattern of variance, the autocorrelation pattern, and the ENSO-like decadal variability.
Abstract
In this study the behavior of a linear, intermediate model of ENSO is examined under stochastic forcing. The model was developed in a companion paper (Part I) and is derived from the Zebiak–Cane ENSO model. Four variants of the model are used whose stabilities range from slightly damped to moderately damped. Each model is run as a simulation while being perturbed by noise that is uncorrelated (white) in space and time. The statistics of the model output show the moderately damped models to be more realistic than the slightly damped models. The moderately damped models have power spectra that are quantitatively quite similar to observations, and a seasonal pattern of variance that is qualitatively similar to observations. All models produce ENSOs that are phase locked to the annual cycle, and all display the “spring barrier” characteristic in their autocorrelation patterns, though in the models this “barrier” occurs during the summer and is less intense than in the observations (inclusion of nonlinear effects is shown to partially remedy this deficiency). The more realistic models also show a decadal variability in the lagged autocorrelation pattern that is qualitatively similar to observations.
Analysis of the models shows that the greatest part of the variability comes from perturbations that project onto the first singular vector, which then grow rapidly into the ENSO mode. Essentially, the model output represents many instances of the ENSO mode, with random phase and amplitude, stimulated by the noise through the optimal transient growth of the singular vectors.
The limit of predictability for each model is calculated and it is shown that the more realistic (moderately damped) models have worse potential predictability (9–15 months) than the deterministic chaotic models that have been studied widely in the literature. The predictability limits are strongly correlated with the stability of the models’ ENSO mode—the more highly damped models having much shorter limits of predictability. A comparison of the two most realistic models shows that even though these models have similar statistics, they have very different predictability limits. The models have a strong seasonal dependence to their predictability limits.
The results of this study (with the companion paper) suggest that the linear, stable dynamical model of ENSO is indeed a plausible hypothesis for the observed ENSO. With very reasonable levels of stochastic forcing, the model produces realistic levels of variance, has a realistic spectrum, and qualitatively reproduces the observed seasonal pattern of variance, the autocorrelation pattern, and the ENSO-like decadal variability.
A GENERALIZED STUDY OF PRECIPITATION FORECASTING
PART 1: COMPUTATION OF PRECIPITATION FROM THE FIELDS OF MOISTURE AND WIND
Abstract
For the eventual purpose of developing a generalized method for predicting precipitation from assumed accurate prognoses of the required meteorological elements, a preliminary investigation is made of the contemporary relationship between precipitation and the fields of moisture and wind in the atmosphere. Procedures are developed for calculating the rate of precipitation by computing the divergence of the horizontal wind at 50-mb. intervals from the surface to 300 mb. using a technique suggested by Bellamy. From these values, vertical speeds are determined. Using the vertical speeds in Fulks' formula for the rate of precipitation from pseudo-adiabatically ascending air, but with some modifications to compensate for non-saturated initial conditions, a method is derived for calculating the intensity of precipitation. Computed amounts are compared with observed precipitation.
Abstract
For the eventual purpose of developing a generalized method for predicting precipitation from assumed accurate prognoses of the required meteorological elements, a preliminary investigation is made of the contemporary relationship between precipitation and the fields of moisture and wind in the atmosphere. Procedures are developed for calculating the rate of precipitation by computing the divergence of the horizontal wind at 50-mb. intervals from the surface to 300 mb. using a technique suggested by Bellamy. From these values, vertical speeds are determined. Using the vertical speeds in Fulks' formula for the rate of precipitation from pseudo-adiabatically ascending air, but with some modifications to compensate for non-saturated initial conditions, a method is derived for calculating the intensity of precipitation. Computed amounts are compared with observed precipitation.
