Considering the limitation of the linear theory of singular vector （SV）, the authors and their collabora- tors proposed conditional nonlinear optimal perturbation （CNOP） and then applied it in the predictability s...Considering the limitation of the linear theory of singular vector （SV）, the authors and their collabora- tors proposed conditional nonlinear optimal perturbation （CNOP） and then applied it in the predictability study and the sensitivity analysis of weather and climate system. To celebrate the 20th anniversary of Chinese National Committee for World Climate Research Programme （WCRP）, this paper is devoted to reviewing the main results of these studies. First, CNOP represents the initial perturbation that has largest nonlinear evolution at prediction time, which is different from linear singular vector （LSV） for the large magnitude of initial perturbation or/and the long optimization time interval. Second, CNOP, rather than linear singular vector （LSV）, represents the initial anomaly that evolves into ENSO events most probably. It is also the CNOP that induces the most prominent seasonal variation of error growth for ENSO predictability; furthermore, CNOP was applied to investigate the decadal variability of ENSO asymmetry. It is demonstrated that the changing nonlinearity causes the change of ENSO asymmetry. Third, in the studies of the sensitivity and stability of ocean＇s thermohaline circulation （THC）, the nonlinear asymmetric response of THC to finite amplitude of initial perturbations was revealed by CNOP. Through this approach the passive mechanism of decadal variation of THC was demonstrated; Also the authors studies the instability and sensitivity analysis of grassland ecosystem by using CNOP and show the mechanism of the transitions between the grassland and desert states. Finally, a detailed discussion on the results obtained by CNOP suggests the applicability of CNOP in predictability studies and sensitivity analysis.展开更多
The uncertainties caused by the errors of the initial states and the parameters in the numerical model are investigated. Three problems of predictability in numerical weather and climate prediction are proposed, which...The uncertainties caused by the errors of the initial states and the parameters in the numerical model are investigated. Three problems of predictability in numerical weather and climate prediction are proposed, which are related to the maximum predictable time, the maximum prediction error, and the maximum admissible errors of the initial values and the parameters in the model respectively. The three problems are then formulated into nonlinear optimization problems. Effective approaches to deal with these nonlinear optimization problems are provided. The Lorenz’ model is employed to demonstrate how to use these ideas in dealing with these three problems.展开更多
Since the last International Union of Geodesy and Geophysics (IUGG) General Assembly (1999), the predictability studies in China have made further progress during the period of 1999-2002. Firstly, three predictability...Since the last International Union of Geodesy and Geophysics (IUGG) General Assembly (1999), the predictability studies in China have made further progress during the period of 1999-2002. Firstly, three predictability sub-problems in numerical weather and climate prediction are classified, which are concerned with the maximum predictability time, the maximum prediction error, and the maximum allowable initial error, and then they are reduced into three nonlinear optimization problems. Secondly, the concepts of the nonlinear singular vector (NSV) and conditional nonlinear optimal perturbation (CNOP) are proposed, which have been utilized to study the predictability of numerical weather and climate prediction. The results suggest that the nonlinear characteristics of the motions of atmosphere and oceans can be revealed by NSV and CNOP. Thirdly, attention has also been paid to the relations between the predictability and spatial-temporal scale, and between the modei predictability and the machine precision, of which the investigations disclose the importance of the spatial-temporal scale and machine precision in the study of predictability. Also the cell-to-cell mapping is adopted to analyze globally the predictability of climate, which could provide a new subject to the research workers. Furthermore, the predictability of the summer rainfall in China is investigated by using the method of correlation coefficients. The results demonstrate that the predictability of summer rainfall is different in different areas of China. Analysis of variance, which is one of the statistical methods applicable to the study of predictability, is also used to study the potential predictability of monthly mean temperature in China, of which the conclusion is that the monthly mean temperature over China is potentially predictable at a statistical significance Ievel of 0.10. In addition, in the analysis of the predictability of the T106 objective analysis/forecasting field, the variance and the correlation coemcient are calculated to explore the distribution characteristics of the mean-square errors. Finally, the predictability of short-term climate prediction is investigated by using statistical methods or numerical simulation methods. It is demonstrated that the predictability of short-terrn climate in China depends not only on the region of China being investigated, but also on the time scale and the atmospheric internai dynamical process.展开更多
Since the last International Union of Geodesy and Geophysics General Assembly （2003）, predictability studies in China have made significant progress. For dynamic forecasts, two novel approaches of conditional nonlin...Since the last International Union of Geodesy and Geophysics General Assembly （2003）, predictability studies in China have made significant progress. For dynamic forecasts, two novel approaches of conditional nonlinear optimal perturbation and nonlinear local Lyapunov exponents were proposed to cope with the predictability problems of weather and climate, which are superior to the corresponding linear theory. A possible mechanism for the ＂spring predictability barrier＂ phenomenon for the E1 Nifio-Southern Oscillation （ENSO） was provided based on a theoretical model. To improve the forecast skill of an intermediate coupled ENSO model, a new initialization scheme was developed, and its applicability was illustrated by hindcast experiments. Using the reconstruction phase space theory and the spatio-temporal series predictive method, Chinese scientists also proposed a new approach to improve dynamical extended range （monthly） prediction and successfully applied it to the monthly-scale predictability of short-term climate variations. In statistical forecasts, it was found that the effects of sea surface temperature on precipitation in China have obvious spatial and temporal distribution features, and that summer precipitation patterns over east China are closely related to the northern atmospheric circulation. For ensemble forecasts, a new initial perturbation method was used to forecast heavy rain in Guangdong and Fujian Provinces on 8 June 1998. Additionally, the ensemble forecast approach was also used for the prediction of a tropical typhoons. A new downscaling model consisting of dynamical and statistical methods was provided to improve the prediction of the monthly mean precipitation. This new downscaling model showed a relatively higher score than the issued operational forecast.展开更多
Linear singular vector and linear singular value can only describe the evolution of sufficiently small perturbations during the period in which the tangent linear model is valid. With this in mind,the applications of ...Linear singular vector and linear singular value can only describe the evolution of sufficiently small perturbations during the period in which the tangent linear model is valid. With this in mind,the applications of nonlinear optimization methods to the atmospheric and oceanic sciences are introduced, which include nonlinear singular vector (NSV) and nonlinear singular value (NSVA), conditional nonlinear optimal perturbation (CNOP), and their applications to the studies of predictability in numerical weather and climate prediction. The results suggest that the nonlinear characteristics of the motions of atmosphere and oceans can be explored by NSV and CNOP. Also attentions are paid to the introduction of the classification of predictability problems, which are related to the maximum predictable time, the maximum prediction error, and the maximum allowing error of initial value and the parameters. All the information has the background of application to the evaluation of products of numerical weather and climate prediction. Furthermore the nonlinear optimization methods of the sensitivity analysis with numerical model are also introduced, which can give a quantitative assessment whether a numerical model is able to simulate the observations and find the initial field that yield the optimal simulation. Finally, the difficulties in the lack of ripe algorithms are also discussed, which leave future work to both computational mathematics and scientists in geophysics.展开更多
文摘Considering the limitation of the linear theory of singular vector （SV）, the authors and their collabora- tors proposed conditional nonlinear optimal perturbation （CNOP） and then applied it in the predictability study and the sensitivity analysis of weather and climate system. To celebrate the 20th anniversary of Chinese National Committee for World Climate Research Programme （WCRP）, this paper is devoted to reviewing the main results of these studies. First, CNOP represents the initial perturbation that has largest nonlinear evolution at prediction time, which is different from linear singular vector （LSV） for the large magnitude of initial perturbation or/and the long optimization time interval. Second, CNOP, rather than linear singular vector （LSV）, represents the initial anomaly that evolves into ENSO events most probably. It is also the CNOP that induces the most prominent seasonal variation of error growth for ENSO predictability; furthermore, CNOP was applied to investigate the decadal variability of ENSO asymmetry. It is demonstrated that the changing nonlinearity causes the change of ENSO asymmetry. Third, in the studies of the sensitivity and stability of ocean＇s thermohaline circulation （THC）, the nonlinear asymmetric response of THC to finite amplitude of initial perturbations was revealed by CNOP. Through this approach the passive mechanism of decadal variation of THC was demonstrated; Also the authors studies the instability and sensitivity analysis of grassland ecosystem by using CNOP and show the mechanism of the transitions between the grassland and desert states. Finally, a detailed discussion on the results obtained by CNOP suggests the applicability of CNOP in predictability studies and sensitivity analysis.
基金the National Key Basic Research Project Research on the Formation Mechanism and Prediction Theory of Severe Synoptic Disasters i
文摘The uncertainties caused by the errors of the initial states and the parameters in the numerical model are investigated. Three problems of predictability in numerical weather and climate prediction are proposed, which are related to the maximum predictable time, the maximum prediction error, and the maximum admissible errors of the initial values and the parameters in the model respectively. The three problems are then formulated into nonlinear optimization problems. Effective approaches to deal with these nonlinear optimization problems are provided. The Lorenz’ model is employed to demonstrate how to use these ideas in dealing with these three problems.
基金supported by the Chinese Academy of Sciences(No.KZCX2-208)the National Natural Scientific Foundation of China(Nos.40233029,40075015,and 40221503).
文摘Since the last International Union of Geodesy and Geophysics (IUGG) General Assembly (1999), the predictability studies in China have made further progress during the period of 1999-2002. Firstly, three predictability sub-problems in numerical weather and climate prediction are classified, which are concerned with the maximum predictability time, the maximum prediction error, and the maximum allowable initial error, and then they are reduced into three nonlinear optimization problems. Secondly, the concepts of the nonlinear singular vector (NSV) and conditional nonlinear optimal perturbation (CNOP) are proposed, which have been utilized to study the predictability of numerical weather and climate prediction. The results suggest that the nonlinear characteristics of the motions of atmosphere and oceans can be revealed by NSV and CNOP. Thirdly, attention has also been paid to the relations between the predictability and spatial-temporal scale, and between the modei predictability and the machine precision, of which the investigations disclose the importance of the spatial-temporal scale and machine precision in the study of predictability. Also the cell-to-cell mapping is adopted to analyze globally the predictability of climate, which could provide a new subject to the research workers. Furthermore, the predictability of the summer rainfall in China is investigated by using the method of correlation coefficients. The results demonstrate that the predictability of summer rainfall is different in different areas of China. Analysis of variance, which is one of the statistical methods applicable to the study of predictability, is also used to study the potential predictability of monthly mean temperature in China, of which the conclusion is that the monthly mean temperature over China is potentially predictable at a statistical significance Ievel of 0.10. In addition, in the analysis of the predictability of the T106 objective analysis/forecasting field, the variance and the correlation coemcient are calculated to explore the distribution characteristics of the mean-square errors. Finally, the predictability of short-term climate prediction is investigated by using statistical methods or numerical simulation methods. It is demonstrated that the predictability of short-terrn climate in China depends not only on the region of China being investigated, but also on the time scale and the atmospheric internai dynamical process.
文摘Since the last International Union of Geodesy and Geophysics General Assembly （2003）, predictability studies in China have made significant progress. For dynamic forecasts, two novel approaches of conditional nonlinear optimal perturbation and nonlinear local Lyapunov exponents were proposed to cope with the predictability problems of weather and climate, which are superior to the corresponding linear theory. A possible mechanism for the ＂spring predictability barrier＂ phenomenon for the E1 Nifio-Southern Oscillation （ENSO） was provided based on a theoretical model. To improve the forecast skill of an intermediate coupled ENSO model, a new initialization scheme was developed, and its applicability was illustrated by hindcast experiments. Using the reconstruction phase space theory and the spatio-temporal series predictive method, Chinese scientists also proposed a new approach to improve dynamical extended range （monthly） prediction and successfully applied it to the monthly-scale predictability of short-term climate variations. In statistical forecasts, it was found that the effects of sea surface temperature on precipitation in China have obvious spatial and temporal distribution features, and that summer precipitation patterns over east China are closely related to the northern atmospheric circulation. For ensemble forecasts, a new initial perturbation method was used to forecast heavy rain in Guangdong and Fujian Provinces on 8 June 1998. Additionally, the ensemble forecast approach was also used for the prediction of a tropical typhoons. A new downscaling model consisting of dynamical and statistical methods was provided to improve the prediction of the monthly mean precipitation. This new downscaling model showed a relatively higher score than the issued operational forecast.
文摘Linear singular vector and linear singular value can only describe the evolution of sufficiently small perturbations during the period in which the tangent linear model is valid. With this in mind,the applications of nonlinear optimization methods to the atmospheric and oceanic sciences are introduced, which include nonlinear singular vector (NSV) and nonlinear singular value (NSVA), conditional nonlinear optimal perturbation (CNOP), and their applications to the studies of predictability in numerical weather and climate prediction. The results suggest that the nonlinear characteristics of the motions of atmosphere and oceans can be explored by NSV and CNOP. Also attentions are paid to the introduction of the classification of predictability problems, which are related to the maximum predictable time, the maximum prediction error, and the maximum allowing error of initial value and the parameters. All the information has the background of application to the evaluation of products of numerical weather and climate prediction. Furthermore the nonlinear optimization methods of the sensitivity analysis with numerical model are also introduced, which can give a quantitative assessment whether a numerical model is able to simulate the observations and find the initial field that yield the optimal simulation. Finally, the difficulties in the lack of ripe algorithms are also discussed, which leave future work to both computational mathematics and scientists in geophysics.
