A Forecast Error Correction Method in Numerical Weather Prediction by Using Recent Multiple-time Evolution Data
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摘要
The initial value error and the imperfect numerical model are usually considered as error sources of numerical weather prediction (NWP). By using past multi-time observations and model output, this study proposes a method to estimate imperfect numerical model error. This method can be inversely estimated through expressing the model error as a Lagrange interpolation polynomial, while the coefficients of polynomial are determined by past model performance. However, for practical application in the full NWP model, it is necessary to determine the following criteria: (1) the length of past data sufficient for estimation of the model errors, (2) a proper method of estimating the term "model integration with the exact solution" when solving the inverse problem, and (3) the extent to which this scheme is sensitive to the observational errors. In this study, such issues are resolved using a simple linear model, and an advection-diffusion model is applied to discuss the sensitivity of the method to an artificial error source. The results indicate that the forecast errors can be largely reduced using the proposed method if the proper length of past data is chosen. To address the three problems, it is determined that (1) a few data limited by the order of the corrector can be used, (2) trapezoidal approximation can be employed to estimate the "term" in this study; however, a more accurate method should be explored for an operational NWP model, and (3) the correction is sensitive to observational error.
The initial value error and the imperfect numerical model are usually considered as error sources of numerical weather prediction (NWP). By using past multi-time observations and model output, this study proposes a method to estimate imperfect numerical model error. This method can be inversely estimated through expressing the model error as a Lagrange interpolation polynomial, while the coefficients of polynomial are determined by past model performance. However, for practical application in the full NWP model, it is necessary to determine the following criteria: (1) the length of past data sufficient for estimation of the model errors, (2) a proper method of estimating the term "model integration with the exact solution" when solving the inverse problem, and (3) the extent to which this scheme is sensitive to the observational errors. In this study, such issues are resolved using a simple linear model, and an advection–diffusion model is applied to discuss the sensitivity of the method to an artificial error source. The results indicate that the forecast errors can be largely reduced using the proposed method if the proper length of past data is chosen. To address the three problems, it is determined that (1) a few data limited by the order of the corrector can be used, (2) trapezoidal approximation can be employed to estimate the "term" in this study; however, a more accurate method should be explored for an operational NWP model, and (3) the correction is sensitive to observational error.
The initial value error and the imperfect numerical model are usually considered as error sources of numerical weather prediction (NWP). By using past multi-time observations and model output, this study proposes a method to estimate imperfect numerical model error. This method can be inversely estimated through expressing the model error as a Lagrange interpolation polynomial, while the coefficients of polynomial are determined by past model performance. However, for practical application in the full NWP model, it is necessary to determine the following criteria: (1) the length of past data sufficient for estimation of the model errors, (2) a proper method of estimating the term "model integration with the exact solution" when solving the inverse problem, and (3) the extent to which this scheme is sensitive to the observational errors. In this study, such issues are resolved using a simple linear model, and an advection–diffusion model is applied to discuss the sensitivity of the method to an artificial error source. The results indicate that the forecast errors can be largely reduced using the proposed method if the proper length of past data is chosen. To address the three problems, it is determined that (1) a few data limited by the order of the corrector can be used, (2) trapezoidal approximation can be employed to estimate the "term" in this study; however, a more accurate method should be explored for an operational NWP model, and (3) the correction is sensitive to observational error.
引文
Bao,M.,Y.Q.Ni,and J.F.Chou,2004: The experi-ment of monthly mean circulation prediction usingthe analogy-dynamical model.Chinese Science Bul-letin,49(12),1296–1300.(in Chinese)
Carter,R.G.,J.Dallavalle,and H.Glahn,1989: Statis-tical forecasts based on the National MeteorologicalCenter’s numerical weather prediction system.Wea.Forecasting,4,401–412.
Cao,H.X.,1993: Self-memorization equation in atmo-spheric motion.Science in China (B),36(7),845–855.(in Chinese)
Charney,J.G.,R.Fjortoft,and J.von-Neumann,1950:Numerical integration of the barotropic vorticityequation.Tellus,2,237–254.
Chou,J.F.,1974: A problem of using past data in nu-merical weather forecasting.Scientia Sinica,17(6),814–825.(in Chinese)
Da,C.J.,2011: One scheme which maybe improvethe forecasting ability of the global (regional) as-similation and prediction system.Ph.D.dissertation,School of Atmospheric Sciences,Lanzhou University,100pp.(in Chinese)
Danforth,C.M.,E.Kalnay,and T.Miyoshi,2007: Es-timating and correcting global weather model error.Mon.Wea.Rev.,135,281–299.
Delle Monache,L.,T.Nipen,X.Deng,Y.Zhou,andR.B.Stull,2006: Ozone ensemble forecasts: 2.AKalman-filter predictor bias correction.J.Geophys.Res.,111,D05308,1–15.
Delle Monache,L.,T.Nipen,Y.B.Liu,G.Roux,andR.Stull,2011: Kalman filter and analog schemesto postprocess numerical weather predictions.Mon.Wea.Rev.,139,3554–3570.
DelSole,T.,and A.Y.Hou,1999: Empirical correctionof a dynamical model.Part I: Fundamental issues.Mon.Wea.Rev.,127,2533–2545.
DelSole,T.,M.Zhao,P.A.Dirmeyer,and B.P.Kirt-man,2008: Empirical correction of a coupled land–atmosphere model.Amer.Meteor.Soc.,136,4063–4076.
Eckel,F.A.,and C.F.Mass,2005: Aspects of ef-fective mesoscale,short-range ensemble forecasting.Wea.Forecasting,20,328–350.
Glahn,H.,and D.Lowry,1972: The use of model outputstatistics in objective weather forecasting.J.Appl.Meteor.,11,1203–1211.
Gu,X.Q.,1998: A spectral model based on atmo-spheric self-memorization principle.Chinese ScienceBulletin,43(20),1692–1702.(in Chinese)
Gu,Z.C.,1958: The use of past dat a in numericalweather forecast.Acta Meteorologica Sinica,29(3),176–184.(in Chinese)
Hacker,J.,and D.Rife,2007: A practical approach tosequential estimation of systematic error on near-surface mesoscale grids.Wea.Forecasting,22,1257–1273.
Huang,J.P.,and S.W.Wang,1992: The experimentsof seasonal prediction using the analogy-dynamicalmodel.Acta Meteorologica Sinica (B),35(2),207–216.
Hoke,J.E.,and R.A.Anthes,1976: The initializationof numerical models by a dynamic initialization tech-nique.Mon.Wea.Rev.,104,1551–1556.
Richardson,L.F.,1922: Weather Prediction by Numeri-cal Process.Cambridge University Press,250pp.
Leith,C.E.,1978: Objective methods for weather pre-diction.Annual Review of Fluid Mechanics,10,107–128.
McCollor,D.,and R.Stull,2008: Hydrometeorologicalaccuracy enhancement via post-processing of numer-ical weather forecasts in complex terrain.Wea.Fore-casting,23,131–144.
Qiu,C.J.,and J.F.Chou,1989: An analogue-dynamicalmethod of weather forecasting.Scientia Atmospher-ica Sinica,13(1),22–28.(in Chinese)
Ren,H.L.,and J.F.Chou,2005: Analogue correc-tion method of errors by combining both statisticaland dynamical methods together.Acta MeteorologicaSinica,63(6),988–993.(in Chinese)
Ren,H.L.,and J.F.Chou,2006: Introducing the up-dating of multi-reference states into dynamical ana-logue prediction.Acta Meteorologica Sinica,63(3),315–324.(in Chinese)
Ren,H.L.,and J.F.Chou,2007: Strategy and method-ology of dynamical analogue prediction.Science inChina (D),50(10),1589–1599.
Saha,S.,1992: Response of the NMC MRF model tosystematic error correction within integration.Mon.Wea.Rev.,120,345–360.
Wu,Y.X.,and N.He,2007: The entirey expanding of La-grange’s interpolation formula.Journal of TonghuaTeachers College,28(2),10–12.(in Chinese)
Carter,R.G.,J.Dallavalle,and H.Glahn,1989: Statis-tical forecasts based on the National MeteorologicalCenter’s numerical weather prediction system.Wea.Forecasting,4,401–412.
Cao,H.X.,1993: Self-memorization equation in atmo-spheric motion.Science in China (B),36(7),845–855.(in Chinese)
Charney,J.G.,R.Fjortoft,and J.von-Neumann,1950:Numerical integration of the barotropic vorticityequation.Tellus,2,237–254.
Chou,J.F.,1974: A problem of using past data in nu-merical weather forecasting.Scientia Sinica,17(6),814–825.(in Chinese)
Da,C.J.,2011: One scheme which maybe improvethe forecasting ability of the global (regional) as-similation and prediction system.Ph.D.dissertation,School of Atmospheric Sciences,Lanzhou University,100pp.(in Chinese)
Danforth,C.M.,E.Kalnay,and T.Miyoshi,2007: Es-timating and correcting global weather model error.Mon.Wea.Rev.,135,281–299.
Delle Monache,L.,T.Nipen,X.Deng,Y.Zhou,andR.B.Stull,2006: Ozone ensemble forecasts: 2.AKalman-filter predictor bias correction.J.Geophys.Res.,111,D05308,1–15.
Delle Monache,L.,T.Nipen,Y.B.Liu,G.Roux,andR.Stull,2011: Kalman filter and analog schemesto postprocess numerical weather predictions.Mon.Wea.Rev.,139,3554–3570.
DelSole,T.,and A.Y.Hou,1999: Empirical correctionof a dynamical model.Part I: Fundamental issues.Mon.Wea.Rev.,127,2533–2545.
DelSole,T.,M.Zhao,P.A.Dirmeyer,and B.P.Kirt-man,2008: Empirical correction of a coupled land–atmosphere model.Amer.Meteor.Soc.,136,4063–4076.
Eckel,F.A.,and C.F.Mass,2005: Aspects of ef-fective mesoscale,short-range ensemble forecasting.Wea.Forecasting,20,328–350.
Glahn,H.,and D.Lowry,1972: The use of model outputstatistics in objective weather forecasting.J.Appl.Meteor.,11,1203–1211.
Gu,X.Q.,1998: A spectral model based on atmo-spheric self-memorization principle.Chinese ScienceBulletin,43(20),1692–1702.(in Chinese)
Gu,Z.C.,1958: The use of past dat a in numericalweather forecast.Acta Meteorologica Sinica,29(3),176–184.(in Chinese)
Hacker,J.,and D.Rife,2007: A practical approach tosequential estimation of systematic error on near-surface mesoscale grids.Wea.Forecasting,22,1257–1273.
Huang,J.P.,and S.W.Wang,1992: The experimentsof seasonal prediction using the analogy-dynamicalmodel.Acta Meteorologica Sinica (B),35(2),207–216.
Hoke,J.E.,and R.A.Anthes,1976: The initializationof numerical models by a dynamic initialization tech-nique.Mon.Wea.Rev.,104,1551–1556.
Richardson,L.F.,1922: Weather Prediction by Numeri-cal Process.Cambridge University Press,250pp.
Leith,C.E.,1978: Objective methods for weather pre-diction.Annual Review of Fluid Mechanics,10,107–128.
McCollor,D.,and R.Stull,2008: Hydrometeorologicalaccuracy enhancement via post-processing of numer-ical weather forecasts in complex terrain.Wea.Fore-casting,23,131–144.
Qiu,C.J.,and J.F.Chou,1989: An analogue-dynamicalmethod of weather forecasting.Scientia Atmospher-ica Sinica,13(1),22–28.(in Chinese)
Ren,H.L.,and J.F.Chou,2005: Analogue correc-tion method of errors by combining both statisticaland dynamical methods together.Acta MeteorologicaSinica,63(6),988–993.(in Chinese)
Ren,H.L.,and J.F.Chou,2006: Introducing the up-dating of multi-reference states into dynamical ana-logue prediction.Acta Meteorologica Sinica,63(3),315–324.(in Chinese)
Ren,H.L.,and J.F.Chou,2007: Strategy and method-ology of dynamical analogue prediction.Science inChina (D),50(10),1589–1599.
Saha,S.,1992: Response of the NMC MRF model tosystematic error correction within integration.Mon.Wea.Rev.,120,345–360.
Wu,Y.X.,and N.He,2007: The entirey expanding of La-grange’s interpolation formula.Journal of TonghuaTeachers College,28(2),10–12.(in Chinese)