The four-dimensional variational assimilation(4D-Var)has been widely used in meteorological and oceanographic data assimilation.This method is usually implemented in the model space,known as primal approach(P4D-Var).A...The four-dimensional variational assimilation(4D-Var)has been widely used in meteorological and oceanographic data assimilation.This method is usually implemented in the model space,known as primal approach(P4D-Var).Alternatively,physical space analysis system(4D-PSAS)is proposed to reduce the computation cost,in which the 4D-Var problem is solved in physical space(i.e.,observation space).In this study,the conjugate gradient(CG)algorithm,implemented in the 4D-PSAS system is evaluated and it is found that the non-monotonic change of the gradient norm of 4D-PSAS cost function causes artificial oscillations of cost function in the iteration process.The reason of non-monotonic variation of gradient norm in 4D-PSAS is then analyzed.In order to overcome the non-monotonic variation of gradient norm,a new algorithm,Minimum Residual(MINRES)algorithm,is implemented in the process of assimilation iteration in this study.Our experimental results show that the improved 4D-PSAS with the MINRES algorithm guarantees the monotonic reduction of gradient norm of cost function,greatly improves the convergence properties of 4D-PSAS as well,and significantly restrains the numerical noises associated with the traditional 4D-PSAS system.展开更多
The impact of diabatic processes on 4-dimensional variational data assimilation (4D-Var) was studied using the 1995 version of NCEP's global spectral model with and without full physics.The adjoint was coded manua...The impact of diabatic processes on 4-dimensional variational data assimilation (4D-Var) was studied using the 1995 version of NCEP's global spectral model with and without full physics.The adjoint was coded manually.A cost function measuring spectral errors of 6-hour forecasts to 'observation' (the NCEP reanalysis data) was minimized using the L-BFGS (the limited memory quasi-Newton algorithm developed by Broyden,Fletcher,Goldfard and Shanno) for optimizing parameters and initial conditions.Minimization of the cost function constrained by an adiabatic version of the NCEP global model converged to a minimum with a significant amount of decrease in the value of the cost function.Minimization of the cost function using the diabatic model, however,failed after a few iterations due to discontinuities introduced by physical parameterizations.Examination of the convergence of the cost function in different spectral domains reveals that the large-scale flow is adjusted during the first 10 iterations,in which discontinuous diabatic parameterizations play very little role.The adjustment produced by the minimization gradually moves to relatively smaller scales between 10-20th iterations.During this transition period,discontinuities in the cost function produced by 'on-off' switches in the physical parameterizations caused the cost function to stay in a shallow local minimum instead of continuously decreasing toward a deeper minimum. Next,a mixed 4D-Var scheme is tested in which large-scale flows are first adiabatically adjusted to a sufficient level,followed by a diabatic adjustment introduced after 10 to 20 iterations. The mixed 4D-Var produced a closer fit of analysis to observations,with 38% and 41% more decrease in the values of the cost function and the norm of gradient,respectively,than the standard diabatic 4D-Var,while the CPU time is reduced by 21%.The resulting optimal initial conditions improve the short-range forecast skills of 48-hour statistics.The detrimental effect of parameterization discontinuities on minimization was also reduced.展开更多
The key mathematics and applications of various modern atmospheric/oceanicdata assimilation methods including Optimal Interpolation (OI), 4-dimensional variational approach(4D-Var) and filters were systematically revi...The key mathematics and applications of various modern atmospheric/oceanicdata assimilation methods including Optimal Interpolation (OI), 4-dimensional variational approach(4D-Var) and filters were systematically reviewed and classified. Based on the data assimilationphilosophy, i. e. , using model dynamics to extract the observational information, the commoncharacter of the problem, such as the probabilistic nature of the evolution of theatmospheric/oceanic system, noisy and irregularly spaced observations, and the advantages anddisadvantages of these data assimilation algorithms, were discussed. In the filtering framework, allmodern data assimilation algorithms were unified: OI/3D-Var is a stationary filter, 4D-Var is alinear (Kalman) filter and an ensemble of Kalman filters is able to construct a nonlinear filter.The nonlinear filter such as the Ensemble Kalman Filter (EN-KF), Ensemble Adjustment Kalman Filter(EAKF) and Ensemble Transformation Kalman Filter (ETKF) can, to some extent, account for thenon-Gaussian information of the prior distribution from the model. The flow-dependent covarianceestimated by an ensemble filter may be introduced to OI and 4D-Var to improve these traditionalalgorithms. In practice, the performance of algorithms may depend on the specific numerical modeland the choice of algorithm may depend on the specific problem. However, the unification ofalgorithms allows us to establish a unified test system to evaluate these algorithms, which providesmore insights into data assimilation philosophies and helps improve data assimilation techniques.展开更多
基金The National Key Research and Development Program of China under contract Nos 2017YFC1501803 and2018YFC1506903the National Natural Science Foundation of China under contract Nos 91730304,41475021 and 41575026
文摘The four-dimensional variational assimilation(4D-Var)has been widely used in meteorological and oceanographic data assimilation.This method is usually implemented in the model space,known as primal approach(P4D-Var).Alternatively,physical space analysis system(4D-PSAS)is proposed to reduce the computation cost,in which the 4D-Var problem is solved in physical space(i.e.,observation space).In this study,the conjugate gradient(CG)algorithm,implemented in the 4D-PSAS system is evaluated and it is found that the non-monotonic change of the gradient norm of 4D-PSAS cost function causes artificial oscillations of cost function in the iteration process.The reason of non-monotonic variation of gradient norm in 4D-PSAS is then analyzed.In order to overcome the non-monotonic variation of gradient norm,a new algorithm,Minimum Residual(MINRES)algorithm,is implemented in the process of assimilation iteration in this study.Our experimental results show that the improved 4D-PSAS with the MINRES algorithm guarantees the monotonic reduction of gradient norm of cost function,greatly improves the convergence properties of 4D-PSAS as well,and significantly restrains the numerical noises associated with the traditional 4D-PSAS system.
基金NSF grant ATM-9812729NOAA grant NA77WA0571Qiao is also supported by the Chinese National Key Basic Research Project under Contract G1999043809
文摘The impact of diabatic processes on 4-dimensional variational data assimilation (4D-Var) was studied using the 1995 version of NCEP's global spectral model with and without full physics.The adjoint was coded manually.A cost function measuring spectral errors of 6-hour forecasts to 'observation' (the NCEP reanalysis data) was minimized using the L-BFGS (the limited memory quasi-Newton algorithm developed by Broyden,Fletcher,Goldfard and Shanno) for optimizing parameters and initial conditions.Minimization of the cost function constrained by an adiabatic version of the NCEP global model converged to a minimum with a significant amount of decrease in the value of the cost function.Minimization of the cost function using the diabatic model, however,failed after a few iterations due to discontinuities introduced by physical parameterizations.Examination of the convergence of the cost function in different spectral domains reveals that the large-scale flow is adjusted during the first 10 iterations,in which discontinuous diabatic parameterizations play very little role.The adjustment produced by the minimization gradually moves to relatively smaller scales between 10-20th iterations.During this transition period,discontinuities in the cost function produced by 'on-off' switches in the physical parameterizations caused the cost function to stay in a shallow local minimum instead of continuously decreasing toward a deeper minimum. Next,a mixed 4D-Var scheme is tested in which large-scale flows are first adiabatically adjusted to a sufficient level,followed by a diabatic adjustment introduced after 10 to 20 iterations. The mixed 4D-Var produced a closer fit of analysis to observations,with 38% and 41% more decrease in the values of the cost function and the norm of gradient,respectively,than the standard diabatic 4D-Var,while the CPU time is reduced by 21%.The resulting optimal initial conditions improve the short-range forecast skills of 48-hour statistics.The detrimental effect of parameterization discontinuities on minimization was also reduced.
文摘The key mathematics and applications of various modern atmospheric/oceanicdata assimilation methods including Optimal Interpolation (OI), 4-dimensional variational approach(4D-Var) and filters were systematically reviewed and classified. Based on the data assimilationphilosophy, i. e. , using model dynamics to extract the observational information, the commoncharacter of the problem, such as the probabilistic nature of the evolution of theatmospheric/oceanic system, noisy and irregularly spaced observations, and the advantages anddisadvantages of these data assimilation algorithms, were discussed. In the filtering framework, allmodern data assimilation algorithms were unified: OI/3D-Var is a stationary filter, 4D-Var is alinear (Kalman) filter and an ensemble of Kalman filters is able to construct a nonlinear filter.The nonlinear filter such as the Ensemble Kalman Filter (EN-KF), Ensemble Adjustment Kalman Filter(EAKF) and Ensemble Transformation Kalman Filter (ETKF) can, to some extent, account for thenon-Gaussian information of the prior distribution from the model. The flow-dependent covarianceestimated by an ensemble filter may be introduced to OI and 4D-Var to improve these traditionalalgorithms. In practice, the performance of algorithms may depend on the specific numerical modeland the choice of algorithm may depend on the specific problem. However, the unification ofalgorithms allows us to establish a unified test system to evaluate these algorithms, which providesmore insights into data assimilation philosophies and helps improve data assimilation techniques.
