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- Author or Editor: T. N. Palmer x
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Abstract
A reduction of computational cost would allow higher resolution in numerical weather predictions within the same budget for computation. This paper investigates two approaches that promise significant savings in computational cost: the use of reduced precision hardware, which reduces floating point precision beyond the standard double- and single-precision arithmetic, and the use of stochastic processors, which allow hardware faults in a trade-off between reduced precision and savings in power consumption and computing time. Reduced precision is emulated within simulations of a spectral dynamical core of a global atmosphere model and a detailed study of the sensitivity of different parts of the model to inexact hardware is performed. Afterward, benchmark simulations were performed for which as many parts of the model as possible were put onto inexact hardware. Results show that large parts of the model could be integrated with inexact hardware at error rates that are surprisingly high or with reduced precision to only a couple of bits in the significand of floating point numbers. However, the sensitivities to inexact hardware of different parts of the model need to be respected, for example, via scale separation. In the last part of the paper, simulations with a full operational weather forecast model in single precision are presented. It is shown that differences in accuracy between the single- and double-precision forecasts are smaller than differences between ensemble members of the ensemble forecast at the resolution of the standard ensemble forecasting system. The simulations prove that the trade-off between precision and performance is a worthwhile effort, already on existing hardware.
Abstract
A reduction of computational cost would allow higher resolution in numerical weather predictions within the same budget for computation. This paper investigates two approaches that promise significant savings in computational cost: the use of reduced precision hardware, which reduces floating point precision beyond the standard double- and single-precision arithmetic, and the use of stochastic processors, which allow hardware faults in a trade-off between reduced precision and savings in power consumption and computing time. Reduced precision is emulated within simulations of a spectral dynamical core of a global atmosphere model and a detailed study of the sensitivity of different parts of the model to inexact hardware is performed. Afterward, benchmark simulations were performed for which as many parts of the model as possible were put onto inexact hardware. Results show that large parts of the model could be integrated with inexact hardware at error rates that are surprisingly high or with reduced precision to only a couple of bits in the significand of floating point numbers. However, the sensitivities to inexact hardware of different parts of the model need to be respected, for example, via scale separation. In the last part of the paper, simulations with a full operational weather forecast model in single precision are presented. It is shown that differences in accuracy between the single- and double-precision forecasts are smaller than differences between ensemble members of the ensemble forecast at the resolution of the standard ensemble forecasting system. The simulations prove that the trade-off between precision and performance is a worthwhile effort, already on existing hardware.
Abstract
Results from a set of nine-member ensemble seasonal integrations with a T63L19 version of the European Centre for Medium-Range Weather Forecasts (ECMWF) model are presented. The integrations are made using observed specified sea surface temperature (SST) from the 5-year period 1986–90, which included both warm and cold El Niño–Southern Oscillation (ENSO) events. The distributions of ensemble skill scores and internal ensemble consistency are studied. For years in which ENSO was strong, the model generally exhibits a relative high skill and high consistency in the Tropics. In the northern extratropics, the highest skill and consistency are found for the northern Pacific–North American region in winter, whereas for the northern Atlantic–European region the spring season appears to be both skillful and consistent. For years in which ENSO was weak, the distributions of ensemble skill and consistency are relatively broad and no clear distinction between Tropics and extratropics can be made.
Applying a t test to interannual fluctuations over various tropical and extratropical regions, estimates of a minimum useful ensemble size are made. Explicit calculations are done with ensemble size varying between three and nine members; estimates for larger sizes are made by extrapolating the t values. Based on an analysis of 2-m temperature and precipitation, the use of relatively large (approximately 20 members) ensembles for extratropical predictions is likely to be required; in the Tropics, smaller-sized ensembles may be adequate during years in which ENSO is strong, particularly for regions such as the Sahel.
The role of the SST forcing in a seasonal timescale ensemble is to bias the probability distribution function (PDF) of atmospheric states. Such PDFs can, in addition, be a convenient way of condensing a vast amount of data usually obtained from ensemble predictions. Interannual variability in PDFs of monsoon rainfall and regional geopotential height probabilities is discussed.
Abstract
Results from a set of nine-member ensemble seasonal integrations with a T63L19 version of the European Centre for Medium-Range Weather Forecasts (ECMWF) model are presented. The integrations are made using observed specified sea surface temperature (SST) from the 5-year period 1986–90, which included both warm and cold El Niño–Southern Oscillation (ENSO) events. The distributions of ensemble skill scores and internal ensemble consistency are studied. For years in which ENSO was strong, the model generally exhibits a relative high skill and high consistency in the Tropics. In the northern extratropics, the highest skill and consistency are found for the northern Pacific–North American region in winter, whereas for the northern Atlantic–European region the spring season appears to be both skillful and consistent. For years in which ENSO was weak, the distributions of ensemble skill and consistency are relatively broad and no clear distinction between Tropics and extratropics can be made.
Applying a t test to interannual fluctuations over various tropical and extratropical regions, estimates of a minimum useful ensemble size are made. Explicit calculations are done with ensemble size varying between three and nine members; estimates for larger sizes are made by extrapolating the t values. Based on an analysis of 2-m temperature and precipitation, the use of relatively large (approximately 20 members) ensembles for extratropical predictions is likely to be required; in the Tropics, smaller-sized ensembles may be adequate during years in which ENSO is strong, particularly for regions such as the Sahel.
The role of the SST forcing in a seasonal timescale ensemble is to bias the probability distribution function (PDF) of atmospheric states. Such PDFs can, in addition, be a convenient way of condensing a vast amount of data usually obtained from ensemble predictions. Interannual variability in PDFs of monsoon rainfall and regional geopotential height probabilities is discussed.
Abstract
The impact of ensemble size on the performance of the European Centre for Medium-Range Weather Forecasts ensemble prediction system (EPS) is analyzed. The skill of ensembles generated using 2, 4, 8, 16, and 32 perturbed ensemble members are compared for a period of 45 days—from 1 October to 15 November 1996. For each ensemble configuration, the skill is compared with the potential skill, measured by randomly choosing one of the 32 ensemble members as verification (idealized ensemble). Results are based on the analyses of the prediction of the 500-hPa geopotential height field. Various measures of performance are applied: skill of the ensemble mean, spread–skill relationship, skill of most accurate ensemble member, Brier score, ranked probability score, relative operating characteristic, and the outlier statistic.
The relation between ensemble spread and control error is studied using L 2, L 8, and L ∞ norms to measure distances between ensemble members and the control forecast or the verification. It is argued that the supremum norm is a more suitable measure of distance, given the strategy for constructing ensemble perturbations from rapidly growing singular vectors. Results indicate that, for the supremum norm, any increase of ensemble size within the range considered in this paper is strongly beneficial. With the smaller ensemble sizes, ensemble spread does not provide a reliable bound on control error in many cases. By contrast, with 32 members, spread provides a bound on control error in nearly all cases. It could be anticipated that further improvement could be achieved with higher ensemble size still. On the other hand, spread–skill relationship was not consistently improved with higher ensemble size using the L 2 norm.
The overall conclusion is that the extent to which an increase of ensemble size (particularly from 8 to 16, and 16 to 32 members) improves EPS performance, is strongly dependent on the measure used to assess performance. In addition to the spread–skill relationship, the measures most sensitive to ensemble size are shown to be the skill of the best ensemble member (particularly when evaluated on a point-wise basis) and the outlier statistic.
Abstract
The impact of ensemble size on the performance of the European Centre for Medium-Range Weather Forecasts ensemble prediction system (EPS) is analyzed. The skill of ensembles generated using 2, 4, 8, 16, and 32 perturbed ensemble members are compared for a period of 45 days—from 1 October to 15 November 1996. For each ensemble configuration, the skill is compared with the potential skill, measured by randomly choosing one of the 32 ensemble members as verification (idealized ensemble). Results are based on the analyses of the prediction of the 500-hPa geopotential height field. Various measures of performance are applied: skill of the ensemble mean, spread–skill relationship, skill of most accurate ensemble member, Brier score, ranked probability score, relative operating characteristic, and the outlier statistic.
The relation between ensemble spread and control error is studied using L 2, L 8, and L ∞ norms to measure distances between ensemble members and the control forecast or the verification. It is argued that the supremum norm is a more suitable measure of distance, given the strategy for constructing ensemble perturbations from rapidly growing singular vectors. Results indicate that, for the supremum norm, any increase of ensemble size within the range considered in this paper is strongly beneficial. With the smaller ensemble sizes, ensemble spread does not provide a reliable bound on control error in many cases. By contrast, with 32 members, spread provides a bound on control error in nearly all cases. It could be anticipated that further improvement could be achieved with higher ensemble size still. On the other hand, spread–skill relationship was not consistently improved with higher ensemble size using the L 2 norm.
The overall conclusion is that the extent to which an increase of ensemble size (particularly from 8 to 16, and 16 to 32 members) improves EPS performance, is strongly dependent on the measure used to assess performance. In addition to the spread–skill relationship, the measures most sensitive to ensemble size are shown to be the skill of the best ensemble member (particularly when evaluated on a point-wise basis) and the outlier statistic.
Abstract
During the winter of 1988/89, a real-time experimental scheme to predict skill of the ECMWF operational forecast was devised. The scheme was based on statistical relations between skill scores (the predictands) and a number of predictors including consistency between consecutive forecasts, amplitude of very short-range forecast errors, and indices of large-scale regime transitions. The results of the experiment are assessed with particular attention to a period with large variations in the skill of the operational forecast.
Abstract
During the winter of 1988/89, a real-time experimental scheme to predict skill of the ECMWF operational forecast was devised. The scheme was based on statistical relations between skill scores (the predictands) and a number of predictors including consistency between consecutive forecasts, amplitude of very short-range forecast errors, and indices of large-scale regime transitions. The results of the experiment are assessed with particular attention to a period with large variations in the skill of the operational forecast.
Abstract
Two ensembles of 90-day forecasts for 1982–83 have been made with the UK Meteorological Office 11-layer atmospheric general circulation model. Each ensemble comprised three integrations initialized one day apart, using analyses from December 1982. The first ensemble used observed SSTs and the second used climatological SSTs. Our objectives were to compare the skill of the two ensembles and to compare the results with a longer climate sensitivity experiment.
The skill of the forecasts for 10-, 30- and 90-day means was assessed using root-mean-square wind errors at 200 mb. In the tropics, the skill was improved with observed SSTs on all time scales. In the extratropics, the skill was improved on the 30-day time scale except at the initial stages of the forecasts, and the skill was also improved for 90-day means. On the 10-day time scale, however, the improvement was not consistent, and there were periods in which the errors were larger with observed SSTs. The response of the model to the observed SSTs was found to be similar to that of a 540-day perpetual January integration with the winter mean SST anomaly for 1982–83.
Abstract
Two ensembles of 90-day forecasts for 1982–83 have been made with the UK Meteorological Office 11-layer atmospheric general circulation model. Each ensemble comprised three integrations initialized one day apart, using analyses from December 1982. The first ensemble used observed SSTs and the second used climatological SSTs. Our objectives were to compare the skill of the two ensembles and to compare the results with a longer climate sensitivity experiment.
The skill of the forecasts for 10-, 30- and 90-day means was assessed using root-mean-square wind errors at 200 mb. In the tropics, the skill was improved with observed SSTs on all time scales. In the extratropics, the skill was improved on the 30-day time scale except at the initial stages of the forecasts, and the skill was also improved for 90-day means. On the 10-day time scale, however, the improvement was not consistent, and there were periods in which the errors were larger with observed SSTs. The response of the model to the observed SSTs was found to be similar to that of a 540-day perpetual January integration with the winter mean SST anomaly for 1982–83.
Abstract
Using 10-day forecast 500 mb height data from the last 7 yr, the potential to predict the skill of numerical weather forecasts is discussed. Four possible predictor sets are described. The first, giving the consistency between adjacent forecasts, is apparently more skillful if the anomaly correlation coefficient, rather than RMS difference, is used as measure of forecast spread and forecast skill. It is concluded that much of this enhanced skill results from the dependence of the anomaly correlation coefficient on the magnitude of the forecast anomaly. It is noted that the spread between “today's” and “yesterday's” forecast is a more reliable estimate of the skill of yesterday's forecast than today's, and the implications of this on lagged-average ensemble forecasts are discussed. The impact of temporal filtering of the data in spread/skill correlations are also described.
The second predictor set is derived from a regression analysis between RMS error skill scores and EOF coefficients of the forecast and/or initial 500 mb heights. The predictors themselves are large-scale anomaly patterns, some of which, towards the end of the forecast period, resemble low-frequency teleconnection patterns of the atmosphere. It is shown that forecast EOF coefficients are more skilful predictors than EOF coefficients of the initial conditions, and that when both sets of coefficients are used in the regression there is a danger of overfitting. The dependence of these patterns on the truncation of the EOF expansion and of temporal filtering is discussed. In particular, it is shown that when a severe EOF truncation is made, some of the forecast flow anomaly patterns become less geographically localized, indicating poorer predictive skill.
The third predictor is defined as the RMS skill of the day-1 forecast. Both upstream and local correlations are studied. It is shown that with day-1 forecast error leading day-3 RMS error by up to 3 days, there appears to be a propagating signal, in addition to a quasi-stationary one. In general, the latter appears to be dominant. The fourth predictor is defined as the RMS difference between the forecast 500 mb height, and the initial 500 mb height. Use of this latter predictor was motivated by diagnostic studies showing relationships between interannual variability of forecast scores and interannual variability of persistence errors. These studies are partly described here. It is shown that the use of forecast persistence as a predictor gives partial skill, at least towards the end of the forecast period.
The skill of the predictors are tested, and the regression coefficients derived, on data from six winters, for both regional and hemispheric skill scores. As an independent test, the predictors are also applied separately to the seventh winter period 1986/87. It is concluded that some aspects of the low-frequency component of forecast skill variability can be satisfactorily predicted, though significant high frequency variability remains unpredicted.
In discussing the physical mechanisms that underlie the use of these predictors, three important components of forecast skill variability are discussed: the quality of the initial analysis, the intrinsic instability of the flow, and the role of model systematic errors.
It is shown that results from the EOF predictor for the European region towards the end of the forecast period are strongly influenced by model systematic error. On the other hand, over the Pacific/North American region, growth of errors on flows with varying barotropic stability characteristics are an important component of medium-range forecast variability. This is discussed using a barotropic model with basic states defined from the results of the regression analyses for various regions. At shorter range it is suggested that growth of errors by baroclinic processes is probably dominant.
Abstract
Using 10-day forecast 500 mb height data from the last 7 yr, the potential to predict the skill of numerical weather forecasts is discussed. Four possible predictor sets are described. The first, giving the consistency between adjacent forecasts, is apparently more skillful if the anomaly correlation coefficient, rather than RMS difference, is used as measure of forecast spread and forecast skill. It is concluded that much of this enhanced skill results from the dependence of the anomaly correlation coefficient on the magnitude of the forecast anomaly. It is noted that the spread between “today's” and “yesterday's” forecast is a more reliable estimate of the skill of yesterday's forecast than today's, and the implications of this on lagged-average ensemble forecasts are discussed. The impact of temporal filtering of the data in spread/skill correlations are also described.
The second predictor set is derived from a regression analysis between RMS error skill scores and EOF coefficients of the forecast and/or initial 500 mb heights. The predictors themselves are large-scale anomaly patterns, some of which, towards the end of the forecast period, resemble low-frequency teleconnection patterns of the atmosphere. It is shown that forecast EOF coefficients are more skilful predictors than EOF coefficients of the initial conditions, and that when both sets of coefficients are used in the regression there is a danger of overfitting. The dependence of these patterns on the truncation of the EOF expansion and of temporal filtering is discussed. In particular, it is shown that when a severe EOF truncation is made, some of the forecast flow anomaly patterns become less geographically localized, indicating poorer predictive skill.
The third predictor is defined as the RMS skill of the day-1 forecast. Both upstream and local correlations are studied. It is shown that with day-1 forecast error leading day-3 RMS error by up to 3 days, there appears to be a propagating signal, in addition to a quasi-stationary one. In general, the latter appears to be dominant. The fourth predictor is defined as the RMS difference between the forecast 500 mb height, and the initial 500 mb height. Use of this latter predictor was motivated by diagnostic studies showing relationships between interannual variability of forecast scores and interannual variability of persistence errors. These studies are partly described here. It is shown that the use of forecast persistence as a predictor gives partial skill, at least towards the end of the forecast period.
The skill of the predictors are tested, and the regression coefficients derived, on data from six winters, for both regional and hemispheric skill scores. As an independent test, the predictors are also applied separately to the seventh winter period 1986/87. It is concluded that some aspects of the low-frequency component of forecast skill variability can be satisfactorily predicted, though significant high frequency variability remains unpredicted.
In discussing the physical mechanisms that underlie the use of these predictors, three important components of forecast skill variability are discussed: the quality of the initial analysis, the intrinsic instability of the flow, and the role of model systematic errors.
It is shown that results from the EOF predictor for the European region towards the end of the forecast period are strongly influenced by model systematic error. On the other hand, over the Pacific/North American region, growth of errors on flows with varying barotropic stability characteristics are an important component of medium-range forecast variability. This is discussed using a barotropic model with basic states defined from the results of the regression analyses for various regions. At shorter range it is suggested that growth of errors by baroclinic processes is probably dominant.
Abstract
From observations and a variety of general circulation modeling evidence, it is suggested that the exceptionally cold weather experienced over much of the United States during some recent winter months (e.g., January 1985, December 1976–February 1977) was associated with enhanced latent heat release over the tropical West Pacific. The mechanism associated with such enhancement may not be unique.
Abstract
From observations and a variety of general circulation modeling evidence, it is suggested that the exceptionally cold weather experienced over much of the United States during some recent winter months (e.g., January 1985, December 1976–February 1977) was associated with enhanced latent heat release over the tropical West Pacific. The mechanism associated with such enhancement may not be unique.
Abstract
Experiments with the atmospheric component of the ECMWF Integrated Forecasting System (IFS) have been carried out to study the origin of the atmospheric circulation anomalies that led to the unusually cold European winter of 2005/06. Experiments with prescribed sea surface temperature (SST) and sea ice fields fail to reproduce the observed atmospheric circulation anomalies suggesting that the role of SST and sea ice was either not very important or the atmospheric response to SST and sea ice was not very well captured by the ECMWF model. Additional experiments are carried out in which certain regions of the atmosphere are relaxed toward analysis data thereby artificially suppressing the development of forecast error. The relaxation experiments suggest that both tropospheric circulation anomalies in the Euro–Atlantic region and the anomalously weak stratospheric polar vortex can be explained by tropical circulation anomalies. Separate relaxation experiments for the tropical stratosphere and tropical troposphere highlight the role of the easterly phase of quasi-biennial oscillation (QBO) and, most importantly, tropospheric circulation anomalies, especially over South America and the tropical Atlantic. From the results presented in this study, it is argued that the relaxation technique is a powerful diagnostic tool to understand possible remote origins of seasonal-mean anomalies.
Abstract
Experiments with the atmospheric component of the ECMWF Integrated Forecasting System (IFS) have been carried out to study the origin of the atmospheric circulation anomalies that led to the unusually cold European winter of 2005/06. Experiments with prescribed sea surface temperature (SST) and sea ice fields fail to reproduce the observed atmospheric circulation anomalies suggesting that the role of SST and sea ice was either not very important or the atmospheric response to SST and sea ice was not very well captured by the ECMWF model. Additional experiments are carried out in which certain regions of the atmosphere are relaxed toward analysis data thereby artificially suppressing the development of forecast error. The relaxation experiments suggest that both tropospheric circulation anomalies in the Euro–Atlantic region and the anomalously weak stratospheric polar vortex can be explained by tropical circulation anomalies. Separate relaxation experiments for the tropical stratosphere and tropical troposphere highlight the role of the easterly phase of quasi-biennial oscillation (QBO) and, most importantly, tropospheric circulation anomalies, especially over South America and the tropical Atlantic. From the results presented in this study, it is argued that the relaxation technique is a powerful diagnostic tool to understand possible remote origins of seasonal-mean anomalies.
Abstract
Experiments with the ECMWF model are carried out to study the influence that a correct representation of the lower boundary conditions, the tropical atmosphere, and the Northern Hemisphere stratosphere would have on extended-range forecast skill of the extratropical Northern Hemisphere troposphere during boreal winter. Generation of forecast errors during the course of the integration is artificially reduced by relaxing the ECMWF model toward the 40-yr ECMWF Re-Analysis (ERA-40) in certain regions. Prescribing rather than persisting sea surface temperature and sea ice fields leads to a modest forecast error reduction in the extended range, especially over the North Pacific and North America; no beneficial influence is found in the medium range. Relaxation of the tropical troposphere leads to reduced extended-range forecast errors especially over the North Pacific, North America, and the North Atlantic. It is shown that a better representation of the Madden–Julian oscillation is of secondary importance for explaining the results of the tropical relaxation experiments. The influence from the tropical stratosphere is negligible. Relaxation of the Northern Hemisphere stratosphere leads to forecast error reduction primarily in high latitudes and over Europe. However, given the strong influence from the troposphere onto the Northern Hemisphere stratosphere it is argued that stratospherically forced experiments are very difficult to interpret in terms of their implications for extended-range predictability of the tropospheric flow. The results are discussed in the context of future forecasting system development.
Abstract
Experiments with the ECMWF model are carried out to study the influence that a correct representation of the lower boundary conditions, the tropical atmosphere, and the Northern Hemisphere stratosphere would have on extended-range forecast skill of the extratropical Northern Hemisphere troposphere during boreal winter. Generation of forecast errors during the course of the integration is artificially reduced by relaxing the ECMWF model toward the 40-yr ECMWF Re-Analysis (ERA-40) in certain regions. Prescribing rather than persisting sea surface temperature and sea ice fields leads to a modest forecast error reduction in the extended range, especially over the North Pacific and North America; no beneficial influence is found in the medium range. Relaxation of the tropical troposphere leads to reduced extended-range forecast errors especially over the North Pacific, North America, and the North Atlantic. It is shown that a better representation of the Madden–Julian oscillation is of secondary importance for explaining the results of the tropical relaxation experiments. The influence from the tropical stratosphere is negligible. Relaxation of the Northern Hemisphere stratosphere leads to forecast error reduction primarily in high latitudes and over Europe. However, given the strong influence from the troposphere onto the Northern Hemisphere stratosphere it is argued that stratospherically forced experiments are very difficult to interpret in terms of their implications for extended-range predictability of the tropospheric flow. The results are discussed in the context of future forecasting system development.
Abstract
Stochastic parameterization provides a methodology for representing model uncertainty in ensemble forecasts. Here the impact on forecast reliability over seasonal time scales of three existing stochastic parameterizations in the ocean component of a coupled model is studied. The relative impacts of these schemes upon the ocean mean state and ensemble spread are analyzed. The oceanic variability induced by the atmospheric forcing of the coupled system is, in most regions, the major source of ensemble spread. The largest impact on spread and bias came from the stochastically perturbed parameterization tendency (SPPT) scheme, which has proven particularly effective in the atmosphere. The key regions affected are eddy-active regions, namely, the western boundary currents and the Southern Ocean where ensemble spread is increased. However, unlike its impact in the atmosphere, SPPT in the ocean did not result in a significant decrease in forecast error on seasonal time scales. While there are good grounds for implementing stochastic schemes in ocean models, the results suggest that they will have to be more sophisticated. Some suggestions for next-generation stochastic schemes are made.
Abstract
Stochastic parameterization provides a methodology for representing model uncertainty in ensemble forecasts. Here the impact on forecast reliability over seasonal time scales of three existing stochastic parameterizations in the ocean component of a coupled model is studied. The relative impacts of these schemes upon the ocean mean state and ensemble spread are analyzed. The oceanic variability induced by the atmospheric forcing of the coupled system is, in most regions, the major source of ensemble spread. The largest impact on spread and bias came from the stochastically perturbed parameterization tendency (SPPT) scheme, which has proven particularly effective in the atmosphere. The key regions affected are eddy-active regions, namely, the western boundary currents and the Southern Ocean where ensemble spread is increased. However, unlike its impact in the atmosphere, SPPT in the ocean did not result in a significant decrease in forecast error on seasonal time scales. While there are good grounds for implementing stochastic schemes in ocean models, the results suggest that they will have to be more sophisticated. Some suggestions for next-generation stochastic schemes are made.
