Errors inevitably exist in numerical weather prediction （NWP） due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the pred...Errors inevitably exist in numerical weather prediction （NWP） due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the prediction equations can be estimated inversely by using the past data, which are presumed to represent the imperfection of the NWP model （model error, denoted as ME）. In this first paper of a two-part series, an iteration method for obtaining the MEs in past intervals is presented, and the results from testing its convergence in idealized experiments are reported. Moreover, two batches of iteration tests were applied in the global forecast system of the Global and Regional Assimilation and Prediction System （GRAPES-GFS） for July-August 2009 and January-February 2010. The datasets associated with the initial conditions and sea surface temperature （SST） were both based on NCEP （National Centers for Environmental Prediction） FNL （final） data. The results showed that 6th h forecast errors were reduced to 10% of their original value after a 20-step iteration. Then, off-line forecast error corrections were estimated linearly based on the 2-month mean MEs and compared with forecast errors. The estimated error corrections agreed well with the forecast errors, but the linear growth rate of the estimation was steeper than the forecast error. The advantage of this iteration method is that the MEs can provide the foundation for online correction. A larger proportion of the forecast errors can be expected to be canceled out by properly introducing the model error correction into GRAPES-GFS.展开更多
An online systematic error correction is presented and examined as a technique to improve the accuracy of real-time numerical weather prediction, based on the dataset of model errors （MEs） in past intervals. Given t...An online systematic error correction is presented and examined as a technique to improve the accuracy of real-time numerical weather prediction, based on the dataset of model errors （MEs） in past intervals. Given the analyses, the ME in each interval （6 h） between two analyses can be iteratively obtained by introducing an unknown tendency term into the prediction equation, shown in Part I of this two-paper series. In this part, after analyzing the 5-year （2001-2005） GRAPES- GFS （Global Forecast System of the Global and Regional Assimilation and Prediction System） error patterns and evolution, a systematic model error correction is given based on the least-squares approach by firstly using the past MEs. To test the correction, we applied the approach in GRAPES-GFS for July 2009 and January 2010. The datasets associated with the initial condition and SST used in this study were based on NCEP （National Centers for Environmental Prediction） FNL （final） data. The results indicated that the Northern Hemispheric systematically underestimated equator-to-pole geopotential gradient and westerly wind of GRAPES-GFS were largely enhanced, and the biases of temperature and wind in the tropics were strongly reduced. Therefore, the correction results in a more skillful forecast with lower mean bias and root-mean-square error and higher anomaly correlation coefficient.展开更多
The concept of cointegration describes an equilibrium relationship among a set of time-varying variables, and the cointegrated relationship can be represented through an error-correction model (ECM). The error-correct...The concept of cointegration describes an equilibrium relationship among a set of time-varying variables, and the cointegrated relationship can be represented through an error-correction model (ECM). The error-correction variable, which represents the short-run discrepancy from the equilibrium state in a cointegrated system, plays an important role in the ECM. It is natural to ask how the error-correction mechanism works, or equivalently, how the short-run discrepancy affects the development of the cointegrated system? This paper examines the effect or local influence on the error-correction variable in an error-correction model. Following the argument of the second-order approach to local influence suggested by reference [5], we develop a diagnostic statistic to examine the local influence on the estimation of the parameter associated with the error-correction variable in an ECM. An empirical example is presented to illustrate the application of the proposed diagnostic. We find that the short-run discre pancy may have strong influence on the estimation of the parameter associated with the error-correction model. It is the error-correction variable that the short-run discrepancies can be incorporated through the error-correction mechanism.展开更多
基金funded by the National Natural Science Foundation Science Fund for Youth (Grant No.41405095)the Key Projects in the National Science and Technology Pillar Program during the Twelfth Fiveyear Plan Period (Grant No.2012BAC22B02)the National Natural Science Foundation Science Fund for Creative Research Groups (Grant No.41221064)
文摘Errors inevitably exist in numerical weather prediction （NWP） due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the prediction equations can be estimated inversely by using the past data, which are presumed to represent the imperfection of the NWP model （model error, denoted as ME）. In this first paper of a two-part series, an iteration method for obtaining the MEs in past intervals is presented, and the results from testing its convergence in idealized experiments are reported. Moreover, two batches of iteration tests were applied in the global forecast system of the Global and Regional Assimilation and Prediction System （GRAPES-GFS） for July-August 2009 and January-February 2010. The datasets associated with the initial conditions and sea surface temperature （SST） were both based on NCEP （National Centers for Environmental Prediction） FNL （final） data. The results showed that 6th h forecast errors were reduced to 10% of their original value after a 20-step iteration. Then, off-line forecast error corrections were estimated linearly based on the 2-month mean MEs and compared with forecast errors. The estimated error corrections agreed well with the forecast errors, but the linear growth rate of the estimation was steeper than the forecast error. The advantage of this iteration method is that the MEs can provide the foundation for online correction. A larger proportion of the forecast errors can be expected to be canceled out by properly introducing the model error correction into GRAPES-GFS.
基金funded by the National Natural Science Foundation Science Fund for Youth (Grant No.41405095)the Key Projects in the National Science and Technology Pillar Program during the Twelfth Fiveyear Plan Period (Grant No.2012BAC22B02)the National Natural Science Foundation Science Fund for Creative Research Groups (Grant No.41221064)
文摘An online systematic error correction is presented and examined as a technique to improve the accuracy of real-time numerical weather prediction, based on the dataset of model errors （MEs） in past intervals. Given the analyses, the ME in each interval （6 h） between two analyses can be iteratively obtained by introducing an unknown tendency term into the prediction equation, shown in Part I of this two-paper series. In this part, after analyzing the 5-year （2001-2005） GRAPES- GFS （Global Forecast System of the Global and Regional Assimilation and Prediction System） error patterns and evolution, a systematic model error correction is given based on the least-squares approach by firstly using the past MEs. To test the correction, we applied the approach in GRAPES-GFS for July 2009 and January 2010. The datasets associated with the initial condition and SST used in this study were based on NCEP （National Centers for Environmental Prediction） FNL （final） data. The results indicated that the Northern Hemispheric systematically underestimated equator-to-pole geopotential gradient and westerly wind of GRAPES-GFS were largely enhanced, and the biases of temperature and wind in the tropics were strongly reduced. Therefore, the correction results in a more skillful forecast with lower mean bias and root-mean-square error and higher anomaly correlation coefficient.
基金This project was supported by the National Natural Science Foundation (No. 79800012 and No. 79400014).
文摘The concept of cointegration describes an equilibrium relationship among a set of time-varying variables, and the cointegrated relationship can be represented through an error-correction model (ECM). The error-correction variable, which represents the short-run discrepancy from the equilibrium state in a cointegrated system, plays an important role in the ECM. It is natural to ask how the error-correction mechanism works, or equivalently, how the short-run discrepancy affects the development of the cointegrated system? This paper examines the effect or local influence on the error-correction variable in an error-correction model. Following the argument of the second-order approach to local influence suggested by reference [5], we develop a diagnostic statistic to examine the local influence on the estimation of the parameter associated with the error-correction variable in an ECM. An empirical example is presented to illustrate the application of the proposed diagnostic. We find that the short-run discre pancy may have strong influence on the estimation of the parameter associated with the error-correction model. It is the error-correction variable that the short-run discrepancies can be incorporated through the error-correction mechanism.
