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- Author or Editor: Francis W. Zwiers x
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Abstract
Resampling procedures include hypothesis testing methods based on Permutation Procedures and interval estimation methods based on bootstrap procedures. The former are widely used in the analysis of climate experiments conducted with general circulation models (GCMs) and in the comparison of the simulated and observed climates. The latter are used less frequently than their flexibility and utility warrants. Both resampling techniques are powerful tools, which provide elegant means of overcoming fundamental statistical difficulties encountered in the analysis of observed and simulated climate data. Unfortunately, inference based on both resampling schemes are as sensitive to the effects of serial correlation as classical statistical methods. These tools must therefore be used with the same amount of caution as other statistical methods when it is suspected that the data might be serially correlated.
Abstract
Resampling procedures include hypothesis testing methods based on Permutation Procedures and interval estimation methods based on bootstrap procedures. The former are widely used in the analysis of climate experiments conducted with general circulation models (GCMs) and in the comparison of the simulated and observed climates. The latter are used less frequently than their flexibility and utility warrants. Both resampling techniques are powerful tools, which provide elegant means of overcoming fundamental statistical difficulties encountered in the analysis of observed and simulated climate data. Unfortunately, inference based on both resampling schemes are as sensitive to the effects of serial correlation as classical statistical methods. These tools must therefore be used with the same amount of caution as other statistical methods when it is suspected that the data might be serially correlated.
Abstract
The climate literature contains a considerable amount of indirect evidence that there is a connection betweenthe size of the spring Tibetan snowpack and the strength of the subsequent Asian summer monsoon. This paperreports on a study that was conducted to search for evidence of a direct snow-monsoon interaction in a simulatedclimatology derived from two long integrations of the Canadian Climate Centre's GCM version 1. Statisticalmethods based on a combination of empirical orthogonal function analysis and canonical correlation analysiswere the primary investigative tools. Only a weak signal was found. It is therefore concluded that either thesimulated variability ofthe snow on Tibet is too small, the model does not react appropriately to the simulatedvariability, or the true natural snow-monsoon mechanism is weak and any snow-monsoon connection reliesupon a third factor. The first possibility is considered to be remote: the model simulates substantial interannualvariability of Tibetan snow. The second and third possibilities are more likely. In particular, the physical mechanism that is thought to connect Tibetan snow with the Asian monsoon may not be properly simulated inthe model.
Abstract
The climate literature contains a considerable amount of indirect evidence that there is a connection betweenthe size of the spring Tibetan snowpack and the strength of the subsequent Asian summer monsoon. This paperreports on a study that was conducted to search for evidence of a direct snow-monsoon interaction in a simulatedclimatology derived from two long integrations of the Canadian Climate Centre's GCM version 1. Statisticalmethods based on a combination of empirical orthogonal function analysis and canonical correlation analysiswere the primary investigative tools. Only a weak signal was found. It is therefore concluded that either thesimulated variability ofthe snow on Tibet is too small, the model does not react appropriately to the simulatedvariability, or the true natural snow-monsoon mechanism is weak and any snow-monsoon connection reliesupon a third factor. The first possibility is considered to be remote: the model simulates substantial interannualvariability of Tibetan snow. The second and third possibilities are more likely. In particular, the physical mechanism that is thought to connect Tibetan snow with the Asian monsoon may not be properly simulated inthe model.
Abstract
Recurrence analysis was introduced to infer the degree of separation between a “control” and an “anomaly” ensemble of, say, seasonal means simulated in general circulation model (GCM) experiments. The concept of recurrence analysis is described as a particular application of a statistical technique called multiple discriminant analysis (MDA). Using MDA, univariate recurrence is easily generalized to multicomponent problems. Algorithms that can be used to estimate the level of recurrence and tests that can be used to assess the confidence in a priori specified levels of recurrence are presented.
Several of the techniques are used to reanalyze a series of El Niño sensitivity experiments conducted with the Canadian Climate Centre GCM. The simulated El Niño response in DJF mean 500 mb height are all estimated to be more than 94% recurrent in the tropics and are estimated to be between 90% and 959b recurrent in the Northern Hemisphere between 20° and 60°N latitude.
Discrimination rules that can be used to classify individual realizations of climate as members of the control or “experimental” ensemble are obtained as a by-product of the multiple recurrence analysis. We show that it is possible to make reasonable inferences about the state of the eastern Pacific sea surface temperature by classifying observed DJF 500 mb height fields with discrimination rules derived from the GCM experiments.
Abstract
Recurrence analysis was introduced to infer the degree of separation between a “control” and an “anomaly” ensemble of, say, seasonal means simulated in general circulation model (GCM) experiments. The concept of recurrence analysis is described as a particular application of a statistical technique called multiple discriminant analysis (MDA). Using MDA, univariate recurrence is easily generalized to multicomponent problems. Algorithms that can be used to estimate the level of recurrence and tests that can be used to assess the confidence in a priori specified levels of recurrence are presented.
Several of the techniques are used to reanalyze a series of El Niño sensitivity experiments conducted with the Canadian Climate Centre GCM. The simulated El Niño response in DJF mean 500 mb height are all estimated to be more than 94% recurrent in the tropics and are estimated to be between 90% and 959b recurrent in the Northern Hemisphere between 20° and 60°N latitude.
Discrimination rules that can be used to classify individual realizations of climate as members of the control or “experimental” ensemble are obtained as a by-product of the multiple recurrence analysis. We show that it is possible to make reasonable inferences about the state of the eastern Pacific sea surface temperature by classifying observed DJF 500 mb height fields with discrimination rules derived from the GCM experiments.
Abstract
In this paper log–linear analysis and analysis of variance methods were used to analyze the interannual variability and potential predictability of precipitation as simulated in an ensemble of six 10-yr Atmospheric Model Intercomparison Project climate simulations conducted with CCC GCM2, the second-generation general circulation model of the Canadian Centre for Climate Modelling and Analysis. Since observed 1979–88 sea surface temperatures (SSTs) and sea ice extent were prescribed as lower boundary conditions in all six simulations, it is possible to diagnose the extent to which the variability of the seasonal frequency, seasonal mean intensity, and seasonal total of precipitation is affected by the prescribed boundary conditions. The specified SST–sea ice forcing was found to significantly affect both the frequency and intensity of precipitation, particularly in the Tropics, but also in the temperate latitudes. Precipitation frequency appears to be more sensitive to the external forcing than precipitation intensity, especially over land areas. Potential predictability from internal sources such as land surface variations is generally small.
Abstract
In this paper log–linear analysis and analysis of variance methods were used to analyze the interannual variability and potential predictability of precipitation as simulated in an ensemble of six 10-yr Atmospheric Model Intercomparison Project climate simulations conducted with CCC GCM2, the second-generation general circulation model of the Canadian Centre for Climate Modelling and Analysis. Since observed 1979–88 sea surface temperatures (SSTs) and sea ice extent were prescribed as lower boundary conditions in all six simulations, it is possible to diagnose the extent to which the variability of the seasonal frequency, seasonal mean intensity, and seasonal total of precipitation is affected by the prescribed boundary conditions. The specified SST–sea ice forcing was found to significantly affect both the frequency and intensity of precipitation, particularly in the Tropics, but also in the temperate latitudes. Precipitation frequency appears to be more sensitive to the external forcing than precipitation intensity, especially over land areas. Potential predictability from internal sources such as land surface variations is generally small.
Abstract
The relative operating characteristic (ROC) is a measure of the quality of probability forecasts that relates the hit rate to the corresponding false-alarm rate. This paper examines some aspects of the ROC curve for probability forecasts of three equiprobable categories (below normal, near normal, and above normal) in the framework of a simple analog of a climate forecasting system. The insensitivity of the ROC score to some types of forecast biases is discussed and the link to deterministic potential predictability is established in the context of the simple forecasting system. The findings are illustrated with a collection of 24-member ensemble hindcasts of seasonal mean 700-hPa temperature produced with the second-generation general circulation model of the Canadian Centre for Climate Modelling and Analysis.
Abstract
The relative operating characteristic (ROC) is a measure of the quality of probability forecasts that relates the hit rate to the corresponding false-alarm rate. This paper examines some aspects of the ROC curve for probability forecasts of three equiprobable categories (below normal, near normal, and above normal) in the framework of a simple analog of a climate forecasting system. The insensitivity of the ROC score to some types of forecast biases is discussed and the link to deterministic potential predictability is established in the context of the simple forecasting system. The findings are illustrated with a collection of 24-member ensemble hindcasts of seasonal mean 700-hPa temperature produced with the second-generation general circulation model of the Canadian Centre for Climate Modelling and Analysis.
Abstract
Using an optimal detection technique, the extent to which the combined effect of changes in greenhouse gases and sulfate aerosols (GS) may be detected in observed surface temperatures is assessed in six spatial domains decreasing in size from the globe to Eurasia and North America, separately. The GS signal is detected in the annual mean near-surface temperatures of the past 50 yr in all domains. It is also detected in some seasonal mean temperatures of the past 50 yr, with detection in more seasons in larger domains.
Abstract
Using an optimal detection technique, the extent to which the combined effect of changes in greenhouse gases and sulfate aerosols (GS) may be detected in observed surface temperatures is assessed in six spatial domains decreasing in size from the globe to Eurasia and North America, separately. The GS signal is detected in the annual mean near-surface temperatures of the past 50 yr in all domains. It is also detected in some seasonal mean temperatures of the past 50 yr, with detection in more seasons in larger domains.
Abstract
The extremes of surface temperature, precipitation, and wind speed and their changes under projected changes in radiative forcing are examined in an ensemble of three transient climate change simulations for the years 1900–2100 conducted with the global coupled model of the Canadian Centre for Climate Modelling and Analysis. The evolution of the greenhouse gases and aerosols in these simulations is consistent with the Intergovernmental Panel on Climate Change 1992 scenario A. The extremes are analyzed in three 21-yr time periods centered at years 1985, 2050, and 2090.
The model simulates reasonably well the extremes of the contemporary near-surface climate. Changes in extremes of daily maximum and daily minimum temperature are distinctively different and are related to changes in the mean screen temperature, soil moisture, and snow and sea-ice cover. Extreme precipitation increases almost everywhere on the globe. Relative change in extreme precipitation is larger than change in total precipitation. Extreme wind speed in the extratropics changes only modestly. Changes in duration of extended wet and dry periods are consistent with changes in total precipitation. There are temperature-related changes in cooling and heating degree days.
Abstract
The extremes of surface temperature, precipitation, and wind speed and their changes under projected changes in radiative forcing are examined in an ensemble of three transient climate change simulations for the years 1900–2100 conducted with the global coupled model of the Canadian Centre for Climate Modelling and Analysis. The evolution of the greenhouse gases and aerosols in these simulations is consistent with the Intergovernmental Panel on Climate Change 1992 scenario A. The extremes are analyzed in three 21-yr time periods centered at years 1985, 2050, and 2090.
The model simulates reasonably well the extremes of the contemporary near-surface climate. Changes in extremes of daily maximum and daily minimum temperature are distinctively different and are related to changes in the mean screen temperature, soil moisture, and snow and sea-ice cover. Extreme precipitation increases almost everywhere on the globe. Relative change in extreme precipitation is larger than change in total precipitation. Extreme wind speed in the extratropics changes only modestly. Changes in duration of extended wet and dry periods are consistent with changes in total precipitation. There are temperature-related changes in cooling and heating degree days.
Abstract
A difficulty with the statistical techniques which are ordinarily used in the analysis of climate sensitivity experiments is that they do not identify the stable, or recurrent, aspects of the experimental response. Therefore, a new concept called “recurrence” is proposed. With this concept it is possible to identify the parts of the response which are likely to recur with an a priori likelihood each time a new experimental realization is obtained. A variety of statistical tests which may be used to assess an a priori level of recurrence by means of limited samples is suggested.
A recurrence analysis is performed with data simulated by the Canadian Climate Centre general circulation model forced with climatological sea surface temperatures (SSTs) and with several El Ninño SST anomalies. All considered SST anomalies, a positive and a negative doubled standard Rasmusson and Carpenter anomaly and the winter 1982/83 anomaly excite a globally significantly response in terms of height and temperature. However, only part of the significant response is also recurrent. In the cold SST anomaly experiment, recurrence is confined to a minor part of the tropics. In the warm SST anomaly runs, recurrence is found in most of the tropics and partly over the northeastern Pacific. These results indicate that equatorial Pacific SST anomalies are associated with a rather limited predictive value, even if the anomalies are very strong.
Abstract
A difficulty with the statistical techniques which are ordinarily used in the analysis of climate sensitivity experiments is that they do not identify the stable, or recurrent, aspects of the experimental response. Therefore, a new concept called “recurrence” is proposed. With this concept it is possible to identify the parts of the response which are likely to recur with an a priori likelihood each time a new experimental realization is obtained. A variety of statistical tests which may be used to assess an a priori level of recurrence by means of limited samples is suggested.
A recurrence analysis is performed with data simulated by the Canadian Climate Centre general circulation model forced with climatological sea surface temperatures (SSTs) and with several El Ninño SST anomalies. All considered SST anomalies, a positive and a negative doubled standard Rasmusson and Carpenter anomaly and the winter 1982/83 anomaly excite a globally significantly response in terms of height and temperature. However, only part of the significant response is also recurrent. In the cold SST anomaly experiment, recurrence is confined to a minor part of the tropics. In the warm SST anomaly runs, recurrence is found in most of the tropics and partly over the northeastern Pacific. These results indicate that equatorial Pacific SST anomalies are associated with a rather limited predictive value, even if the anomalies are very strong.
Abstract
A simple statistical model of seasonal variability is used to explore the properties of probability forecasts and their accuracy measures. Two methods of estimating probabilistic information from an ensemble of deterministic forecasts are discussed. The estimators considered are the straightforward nonparametric estimator defined as the relative number of the ensemble members in an event category, and a parametric Gaussian estimator derived from a fitted Gaussian distribution. The parametric Gaussian estimator is superior to the standard nonparametric estimator on seasonal timescales. A statistical skill improvement technique is proposed and applied to a collection of 24-member ensemble seasonal hindcasts of northern winter 700-hPa temperature (T 700) and 500-hPa height (Z 500). The improvement technique is moderately successful for T 700 but fails to improve Brier skill scores of the already relatively reliable raw Z 500 probability forecasts.
Abstract
A simple statistical model of seasonal variability is used to explore the properties of probability forecasts and their accuracy measures. Two methods of estimating probabilistic information from an ensemble of deterministic forecasts are discussed. The estimators considered are the straightforward nonparametric estimator defined as the relative number of the ensemble members in an event category, and a parametric Gaussian estimator derived from a fitted Gaussian distribution. The parametric Gaussian estimator is superior to the standard nonparametric estimator on seasonal timescales. A statistical skill improvement technique is proposed and applied to a collection of 24-member ensemble seasonal hindcasts of northern winter 700-hPa temperature (T 700) and 500-hPa height (Z 500). The improvement technique is moderately successful for T 700 but fails to improve Brier skill scores of the already relatively reliable raw Z 500 probability forecasts.
Abstract
Several methods of combining individual forecasts from a group of climate models to produce an ensemble forecast are considered. These methods are applied to an ensemble of 500-hPa geopotential height forecasts derived from the Atmospheric Model Intercomparison Project (AMIP) integrations performed by 10 different modeling groups. Forecasts are verified against reanalyses from the European Centre for Medium-Range Weather Forecasts. Forecast skill is measured by means of error variance. In the Tropics, the simple ensemble mean produces the most skillful forecasts. In the extratropics, the regression-improved ensemble mean performs best. The “superensemble” forecast that is obtained by optimally weighting the individual ensemble members does not perform as well as either the simple ensemble mean or the regression-improved ensemble mean. The sample size evidently is too small to estimate reliably the relatively large number of optimal weights required for the superensemble approach.
Abstract
Several methods of combining individual forecasts from a group of climate models to produce an ensemble forecast are considered. These methods are applied to an ensemble of 500-hPa geopotential height forecasts derived from the Atmospheric Model Intercomparison Project (AMIP) integrations performed by 10 different modeling groups. Forecasts are verified against reanalyses from the European Centre for Medium-Range Weather Forecasts. Forecast skill is measured by means of error variance. In the Tropics, the simple ensemble mean produces the most skillful forecasts. In the extratropics, the regression-improved ensemble mean performs best. The “superensemble” forecast that is obtained by optimally weighting the individual ensemble members does not perform as well as either the simple ensemble mean or the regression-improved ensemble mean. The sample size evidently is too small to estimate reliably the relatively large number of optimal weights required for the superensemble approach.
