A four-dimensional variational （4D-Var） data assimilation method is implemented in an improved intermediate coupled model （ICM） of the tropical Pacific. A twin experiment is designed to evaluate the impact of the ...A four-dimensional variational （4D-Var） data assimilation method is implemented in an improved intermediate coupled model （ICM） of the tropical Pacific. A twin experiment is designed to evaluate the impact of the 4D-Var data assimilation algorithm on ENSO analysis and prediction based on the ICM. The model error is assumed to arise only from the parameter uncertainty. The ＂observation＂ of the SST anomaly, which is sampled from a ＂truth＂ model simulation that takes default parameter values and has Gaussian noise added, is directly assimilated into the assimilation model with its parameters set erroneously. Results show that 4D-Var effectively reduces the error of ENSO analysis and therefore improves the prediction skill of ENSO events compared with the non-assimilation case. These results provide a promising way for the ICM to achieve better real-time ENSO prediction.展开更多
A new data assimilation method called the explicit four-dimensional variational (4DVAR) method is proposed. In this method, the singular value decomposition (SVD) is used to construct the orthogonal basis vectors from...A new data assimilation method called the explicit four-dimensional variational (4DVAR) method is proposed. In this method, the singular value decomposition (SVD) is used to construct the orthogonal basis vectors from a forecast ensemble in a 4D space. The basis vectors represent not only the spatial structure of the analysis variables but also the temporal evolution. After the analysis variables are ex-pressed by a truncated expansion of the basis vectors in the 4D space, the control variables in the cost function appear explicitly, so that the adjoint model, which is used to derive the gradient of cost func-tion with respect to the control variables, is no longer needed. The new technique significantly simpli-fies the data assimilation process. The advantage of the proposed method is demonstrated by several experiments using a shallow water numerical model and the results are compared with those of the conventional 4DVAR. It is shown that when the observation points are very dense, the conventional 4DVAR is better than the proposed method. However, when the observation points are sparse, the proposed method performs better. The sensitivity of the proposed method with respect to errors in the observations and the numerical model is lower than that of the conventional method.展开更多
A method has been presented to improve ensemble forecast by utilizing these initial members generated by four-dimensional variational data assimilation (4-D VDA), to conquer limitation of those initial members generat...A method has been presented to improve ensemble forecast by utilizing these initial members generated by four-dimensional variational data assimilation (4-D VDA), to conquer limitation of those initial members generated by Monte Carlo forecast (MCF) or lagged average forecast (LAF). This method possesses significant statistical characteristic of MCF, and by virtue of LAF that contains multi-time information and its initial members are harmonic with展开更多
This study examines the performance of coupling the deterministic four-dimensional variational assimilation system （4DVAR） with an ensemble Kalman filter （EnKF） to produce a superior hybrid approach for data assim...This study examines the performance of coupling the deterministic four-dimensional variational assimilation system （4DVAR） with an ensemble Kalman filter （EnKF） to produce a superior hybrid approach for data assimilation. The coupled assimilation scheme （E4DVAR） benefits from using the state-dependent uncertainty provided by EnKF while taking advantage of 4DVAR in preventing filter divergence： the 4DVAR analysis produces posterior maximum likelihood solutions through minimization of a cost function about which the ensemble perturbations are transformed, and the resulting ensemble analysis can be propagated forward both for the next assimilation cycle and as a basis for ensemble forecasting. The feasibility and effectiveness of this coupled approach are demonstrated in an idealized model with simulated observations. It is found that the E4DVAR is capable of outperforming both 4DVAR and the EnKF under both perfect- and imperfect-model scenarios. The performance of the coupled scheme is also less sensitive to either the ensemble size or the assimilation window length than those for standard EnKF or 4DVAR implementations.展开更多
Accurate forecast of rainstorms associated with the mei-yu front has been an important issue for the Chinese economy and society. In July 1998 a heavy rainstorm hit the Yangzi River valley and received widespread atte...Accurate forecast of rainstorms associated with the mei-yu front has been an important issue for the Chinese economy and society. In July 1998 a heavy rainstorm hit the Yangzi River valley and received widespread attention from the public because it caused catastrophic damage in China. Several numerical studies have shown that many forecast models, including Pennsylvania State University National Center for Atmospheric Research’s fifth-generation mesoscale model （MM5）, failed to simulate the heavy precipitation over the Yangzi River valley. This study demonstrates that with the optimal initial conditions from the dimension-reduced projection four-dimensional variational data assimilation （DRP-4DVar） system, MM5 can successfully reproduce these observed rainfall amounts and can capture many important mesoscale features, including the southwestward shear line and the low-level jet stream. The study also indicates that the failure of previous forecasts can be mainly attributed to the lack of mesoscale details in the initial conditions of the models.展开更多
The generalized variational data assimilation for non-differential dynamical systems is studied.There is no tangent linear model for non-differential systems and thus the general adjoint model can not be derived in th...The generalized variational data assimilation for non-differential dynamical systems is studied.There is no tangent linear model for non-differential systems and thus the general adjoint model can not be derived in the traditional way.The weak form of the original system was introduced, and then the generalized adjoint model was derived. The generalized variational data assimilation methods were developed for non-differential low dimensional system and non-differential high dimensional system with global and local observations. Furthermore, ideas in inverse problems are introduced to 4DVAR (Four-dimensional variational) of non-differential partial differential system with local observations.展开更多
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
An investigation is carried out on the problem involved in 4D variational data assimilation (VDA) with constraint conditions based on a finite-element shallow-water equation model. In the investigation, the adjoint te...An investigation is carried out on the problem involved in 4D variational data assimilation (VDA) with constraint conditions based on a finite-element shallow-water equation model. In the investigation, the adjoint technology, penalty method and augmented Lagrangian method are used in constraint optimization field to minimize the defined constraint objective functions. The results of the numerical experiments show that the optimal solutions are obtained if the functions reach the minima. VDA with constraint conditions controlling the growth of gravity oscillations is efficient to eliminate perturbation and produces optimal initial field. It seems that this method can also be applied to the problem in numerical weather prediction. Key words Variational data assimilation - Constraint conditions - Penalty methods - finite-element model This research is supported by National Natural Science Foundation of China (Grant No. 49575269) and by National Key Basic Research on the Formation Mechanism and Prediction Theory of Severe Synoptic Disasters (Grant No. G1998040910).展开更多
Theoretical aspects of variational data assimilation （VDA） for a simple model with both global and local observational data are discussed. For the VDA problems with global observational data, the initial conditions ...Theoretical aspects of variational data assimilation （VDA） for a simple model with both global and local observational data are discussed. For the VDA problems with global observational data, the initial conditions and parameters for the model are revisited and the model itself is modified. The estimates of both error and convergence rate are theoretically made and the vahdity of the method is proved. For VDA problem with local observation data, the conventional VDA method are out of use due to the ill-posedness of the problem. In order to overcome the difficulties caused by the ill-posedness, the initial conditions and parameters of the model are modified by using the improved VDA method, and the estimates of both error and convergence rate are also made. Finally, the validity of the improved VDA method is proved through theoretical analysis and illustrated with an example, and a theoretical criterion of the regularization parameters is proposed.展开更多
It is not reasonable that one can only use the adjoint of model in data assimilation. The simulated numerical experiment shows that for the tidal model, the result of the adjoint of equation is almost the same as that...It is not reasonable that one can only use the adjoint of model in data assimilation. The simulated numerical experiment shows that for the tidal model, the result of the adjoint of equation is almost the same as that of the adjoint of model: the averaged absolute difference of the amplitude between observations and simulation is less than 5.0 cm and that of the phase-lag is less than 5.0°. The results are both in good agreement with the observed M2 tide in the Bohai Sea and the Yellow Sea. For comparison, the traditional methods also have been used to simulate M2 tide in the Bohai Sea and the Yellow Sea. The initial guess values of the boundary conditions are given first, and then are adjusted to acquire the simulated results that are as close as possible to the observations. As the boundary conditions contain 72 values, which should be adjusted and how to adjust them can only be partially solved by adjusting them many times. The satisfied results are hard to acquire even gigantic efforts are done. Here, the automation of the treatment of the open boundary conditions is realized. The method is unique and superior to the traditional methods. It is emphasized that if the adjoint of equation is used, tedious and complicated mathematical deduction can be avoided. Therefore the adjoint of equation should attract much attention.展开更多
It is not reasonable that one can only use the adjoint of model in data assimilation. The simulated numerical experiment shows that for the tidal model, the result of the adjoint of equation is almost the same as that...It is not reasonable that one can only use the adjoint of model in data assimilation. The simulated numerical experiment shows that for the tidal model, the result of the adjoint of equation is almost the same as that of the adjoint of model: the averaged absolute difference of the amplitude between observations and simulation is less than 5.0 cm and that of the phase-lag is less than 5.0°. The results are both in good agreement with the observed M2 tide in the Bohai Sea and the Yellow Sea. For comparison, the traditional methods also have been used to simulate M2 tide in the Bohai Sea and the Yellow Sea. The initial guess values of the boundary conditions are given first, and then are adjusted to acquire the simulated results that are as close as possible to the observations. As the boundary conditions contain 72 values, which should be adjusted and how to adjust them can only be partially solved by adjusting them many times. The satisfied results are hard to acquire even gigantic efforts are done. Here, the automation of the treatment of the open boundary conditions is realized. The method is unique and superior to the traditional methods. It is emphasized that if the adjoint of equation is used, tedious and complicated mathematical deduction can be avoided. Therefore the adjoint of equation should attract much attention.展开更多
Seasonal and interannual changes in the Earth's gravity field are mainly due to mass exchange among the atmosphere,ocean,and continental water sources.The terrestrial water storage changes,detected as gravity chan...Seasonal and interannual changes in the Earth's gravity field are mainly due to mass exchange among the atmosphere,ocean,and continental water sources.The terrestrial water storage changes,detected as gravity changes by the Gravity Recovery and Climate Experiment(GRACE) satellites,are mainly caused by precipitation,evapotranspiration,river transportation and downward infiltration processes.In this study,a land data assimilation system LDAS-G was developed to assimilate the GRACE terrestrial water storage(TWS) data into the Community Land Model(CLM3.5) using the POD-based ensemble four-dimensional variational assimilation method PODEn4 DVar,disaggregating the GRACE large-scale terrestrial water storage changes vertically and in time,and placing constraints on the simulation of vertical hydrological variables to improve land surface hydrological simulations.The ideal experiments conducted at a single point and assimilation experiments carried out over China by the LDAS-G data assimilation system showed that the system developed in this study improved the simulation of land surface hydrological variables,indicating the potential of GRACE data assimilation in large-scale land surface hydrological research and applications.展开更多
Accurate estimation of the background error covariance matrix denoted as B remains a critical challenge in numerical weather prediction(NWP),directly influencing data assimilation(DA)performance and forecast accuracy....Accurate estimation of the background error covariance matrix denoted as B remains a critical challenge in numerical weather prediction(NWP),directly influencing data assimilation(DA)performance and forecast accuracy.Although hybrid ensemble–variational(En Var)methods combine static and flow-dependent matrices to improve assimilation,their effectiveness is constrained by empirically fixed weights.To address this limitation,we propose DRL-En Var,an adaptive hybrid En Var DA method enhanced with deep reinforcement learning.DRL-En Var integrates deep learning(DL)components,including a novel cyclic convolution module to extract abstract features from data,and employs reinforcement learning(RL)to dynamically optimize hybrid weighting strategies.The system adaptively combines multiple ensemble-based flow-dependent matrices with one or more static matrices to construct a time-varying hybrid matrix B that better reflects real-time background errors.Experimental results demonstrate that DRL-En Var performs better than the traditional ensemble Kalman filter(En KF)and hybrid covariance DA(HCDA)methods,especially under sparse observations or transitional changes in state variables.It achieves competitive or superior assimilation accuracy with lower computational cost,and can be flexibly integrated into both three-dimensional variational assimilation(3DVar)and four-dimensional variational assimilation(4DVar)frameworks.Overall,DRL-En Var offers a novel and efficient approach to adaptive DA,particularly valuable for improving forecast skill during transitional weather regimes.展开更多
An adaptive variational data assimilation method is proposed by Zhu and Kamachi[1]. This method can adaptively adjust the model state without knowing explicitly the model error covariance matrix. The method enables ve...An adaptive variational data assimilation method is proposed by Zhu and Kamachi[1]. This method can adaptively adjust the model state without knowing explicitly the model error covariance matrix. The method enables very flexible ways to form some reduced order problems. A proper reduced order problem not only reduces computational burden but also leads to corrections that are more consistent with the model dynamics that trends to produce better forecast. These features make the adaptive variational method a good candidate for SST data assimilation because the model error of an ocean model is usually difficult to estimate. We applied this method to an SST data assimilation problem using the LOTUS data sets and an ocean mixed layer model (Mellor-Yamada level 2.5). Results of assimilation experiments showed good skill of improvement subsurface temperatures by assimilating surface observation alone.展开更多
A large number of observational analyses have shown that lightning data can be used to indicate areas of deep convection. It is important to assimilate observed lightning data into numerical models, so that more small...A large number of observational analyses have shown that lightning data can be used to indicate areas of deep convection. It is important to assimilate observed lightning data into numerical models, so that more small-scale information can be incorporated to improve the quality of the initial condition and the subsequent forecasts. In this study, the empirical relationship between flash rate, water vapor mixing ratio, and graupel mixing ratio was used to adjust the model relative humidity, which was then assimilated by using the three-dimensional variational data assimilation system of the Weather Research and Forecasting model in cycling mode at 10-min intervals. To find the appropriate assimilation time-window length that yielded significant improvement in both the initial conditions and subsequent forecasts, four experiments with different assimilation time-window lengths were conducted for a squall line case that occurred on 10 July 2007 in North China. It was found that 60 min was the appropriate assimilation time-window length for this case, and longer assimilation window length was unnecessary since no further improvement was present. Forecasts of 1-h accumulated precipitation during the assimilation period and the subsequent 3-h accumulated precipitation were significantly improved compared with the control experiment without lightning data assimilation. The simulated reflectivity was optimal after 30 min of the forecast, it remained optimal during the following 42 min, and the positive effect from lightning data assimilation began to diminish after 72 min of the forecast. Overall,the improvement from lightning data assimilation can be maintained for about 3 h.展开更多
Variational method is capable of dealing with observations that have a complicated nonlinear relation with model variables representative of the atmospheric state, and so make it possible to directly assimilate such m...Variational method is capable of dealing with observations that have a complicated nonlinear relation with model variables representative of the atmospheric state, and so make it possible to directly assimilate such measured variables as satellite radiance, which have a nonlinear relation with the model variables. Assimilation of any type of observations requires a corresponding observation operator, which establishes a specific mapping from the space of the model state to the space of observation. This paper presents in detail how the direct assimilation of real satellite radiance data is implemented in the GRAPES-3DVar analysis system. It focuses on all the components of the observation operator for direct assimilation of real satellite radiance data, including a spatial interpolation operator that transforms variables from model grid points to observation locations, a physical transformation from model variables to observed elements with different choices of model variables, and a data quality control. Assimilation experiments, using satellite radiances such as NOAA17 AMSU-A and AMSU-B (Advanced Microwave Sounding Unit), are carried out with two different schemes. The results from these experiments can be physically understood and clearly reflect a rational effect of direct assimilation of satellite radiance data in GRAPES-3DVar analysis system.展开更多
The variational method of data assimilation is used to solve an inverse problem in the transport of sediment in river, which plays an important role in the change of natural environment. The cost function is defined t...The variational method of data assimilation is used to solve an inverse problem in the transport of sediment in river, which plays an important role in the change of natural environment. The cost function is defined to measure the error between model predictions and field observations. The adjoint model of IAP river sedimentation model is created to obtain the gradient of the cost function with respect to control variables. The initial conditions are taken as the control variables; their optimal values can be retrieved by minimizing the cost function with limited memory quasi Newton method (LMQN). The results show that the adjoint method approach can successfully make the model prediction well fit the simulated observations. And it is expected to use this method to solve other inverse problems of river sedimentation. But some numerical problems need to be discussed before applying to real river data.展开更多
This study introduces a novel sequential data assimilation method that uses conditional denoising score matching(CDSM).The CDSM leverages iterative refinement of noisy samples guided by conditional score functions to ...This study introduces a novel sequential data assimilation method that uses conditional denoising score matching(CDSM).The CDSM leverages iterative refinement of noisy samples guided by conditional score functions to achieve real-time state estimation by incorporating observational constraints at each time step.Unlike traditional methods,such as variational assimilation and Kalman filtering,which rely on Gaussian assumptions and can be computationally expensive because of iterations or ensembles,CDSM is based on stochastic differential equations(SDEs).展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.41490644,41475101 and 41421005)the CAS Strategic Priority Project(the Western Pacific Ocean System+2 种基金Project Nos.XDA11010105,XDA11020306 and XDA11010301)the NSFC-Shandong Joint Fund for Marine Science Research Centers(Grant No.U1406401)the NSFC Innovative Group Grant(Project No.41421005)
文摘A four-dimensional variational （4D-Var） data assimilation method is implemented in an improved intermediate coupled model （ICM） of the tropical Pacific. A twin experiment is designed to evaluate the impact of the 4D-Var data assimilation algorithm on ENSO analysis and prediction based on the ICM. The model error is assumed to arise only from the parameter uncertainty. The ＂observation＂ of the SST anomaly, which is sampled from a ＂truth＂ model simulation that takes default parameter values and has Gaussian noise added, is directly assimilated into the assimilation model with its parameters set erroneously. Results show that 4D-Var effectively reduces the error of ENSO analysis and therefore improves the prediction skill of ENSO events compared with the non-assimilation case. These results provide a promising way for the ICM to achieve better real-time ENSO prediction.
基金the 973 Program (Grant No. 2004CB418305)the National Natural Science Foundation of China (Grant No. 40575049)
文摘A new data assimilation method called the explicit four-dimensional variational (4DVAR) method is proposed. In this method, the singular value decomposition (SVD) is used to construct the orthogonal basis vectors from a forecast ensemble in a 4D space. The basis vectors represent not only the spatial structure of the analysis variables but also the temporal evolution. After the analysis variables are ex-pressed by a truncated expansion of the basis vectors in the 4D space, the control variables in the cost function appear explicitly, so that the adjoint model, which is used to derive the gradient of cost func-tion with respect to the control variables, is no longer needed. The new technique significantly simpli-fies the data assimilation process. The advantage of the proposed method is demonstrated by several experiments using a shallow water numerical model and the results are compared with those of the conventional 4DVAR. It is shown that when the observation points are very dense, the conventional 4DVAR is better than the proposed method. However, when the observation points are sparse, the proposed method performs better. The sensitivity of the proposed method with respect to errors in the observations and the numerical model is lower than that of the conventional method.
文摘A method has been presented to improve ensemble forecast by utilizing these initial members generated by four-dimensional variational data assimilation (4-D VDA), to conquer limitation of those initial members generated by Monte Carlo forecast (MCF) or lagged average forecast (LAF). This method possesses significant statistical characteristic of MCF, and by virtue of LAF that contains multi-time information and its initial members are harmonic with
基金sponsored by the U.S. National Science Foundation (Grant No.ATM0205599)the U.S. Offce of Navy Research under Grant N000140410471Dr. James A. Hansen was partially supported by US Offce of Naval Research (Grant No. N00014-06-1-0500)
文摘This study examines the performance of coupling the deterministic four-dimensional variational assimilation system （4DVAR） with an ensemble Kalman filter （EnKF） to produce a superior hybrid approach for data assimilation. The coupled assimilation scheme （E4DVAR） benefits from using the state-dependent uncertainty provided by EnKF while taking advantage of 4DVAR in preventing filter divergence： the 4DVAR analysis produces posterior maximum likelihood solutions through minimization of a cost function about which the ensemble perturbations are transformed, and the resulting ensemble analysis can be propagated forward both for the next assimilation cycle and as a basis for ensemble forecasting. The feasibility and effectiveness of this coupled approach are demonstrated in an idealized model with simulated observations. It is found that the E4DVAR is capable of outperforming both 4DVAR and the EnKF under both perfect- and imperfect-model scenarios. The performance of the coupled scheme is also less sensitive to either the ensemble size or the assimilation window length than those for standard EnKF or 4DVAR implementations.
基金the National Basic Research Program (973 Program) (No.2010CB 951604)the China Meteorological Administration for the R&D Special Fund for Public Welfare Industry (meteorology) [Grant No. GYHY(QX)200906009]+1 种基金the National High Technology Research and Development Program of China (863 Program) (No. 2010AA012304)the LASG free exploration fund
文摘Accurate forecast of rainstorms associated with the mei-yu front has been an important issue for the Chinese economy and society. In July 1998 a heavy rainstorm hit the Yangzi River valley and received widespread attention from the public because it caused catastrophic damage in China. Several numerical studies have shown that many forecast models, including Pennsylvania State University National Center for Atmospheric Research’s fifth-generation mesoscale model （MM5）, failed to simulate the heavy precipitation over the Yangzi River valley. This study demonstrates that with the optimal initial conditions from the dimension-reduced projection four-dimensional variational data assimilation （DRP-4DVar） system, MM5 can successfully reproduce these observed rainfall amounts and can capture many important mesoscale features, including the southwestward shear line and the low-level jet stream. The study also indicates that the failure of previous forecasts can be mainly attributed to the lack of mesoscale details in the initial conditions of the models.
文摘The generalized variational data assimilation for non-differential dynamical systems is studied.There is no tangent linear model for non-differential systems and thus the general adjoint model can not be derived in the traditional way.The weak form of the original system was introduced, and then the generalized adjoint model was derived. The generalized variational data assimilation methods were developed for non-differential low dimensional system and non-differential high dimensional system with global and local observations. Furthermore, ideas in inverse problems are introduced to 4DVAR (Four-dimensional variational) of non-differential partial differential system with local observations.
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National Natural Science Foundation of China (Grant No. 49575269) National Key Basic Research on the Formation Mechanism and
文摘An investigation is carried out on the problem involved in 4D variational data assimilation (VDA) with constraint conditions based on a finite-element shallow-water equation model. In the investigation, the adjoint technology, penalty method and augmented Lagrangian method are used in constraint optimization field to minimize the defined constraint objective functions. The results of the numerical experiments show that the optimal solutions are obtained if the functions reach the minima. VDA with constraint conditions controlling the growth of gravity oscillations is efficient to eliminate perturbation and produces optimal initial field. It seems that this method can also be applied to the problem in numerical weather prediction. Key words Variational data assimilation - Constraint conditions - Penalty methods - finite-element model This research is supported by National Natural Science Foundation of China (Grant No. 49575269) and by National Key Basic Research on the Formation Mechanism and Prediction Theory of Severe Synoptic Disasters (Grant No. G1998040910).
基金Project supported by the National Natural Science Foundation of China(Nos.40675020, 50505005)
文摘Theoretical aspects of variational data assimilation （VDA） for a simple model with both global and local observational data are discussed. For the VDA problems with global observational data, the initial conditions and parameters for the model are revisited and the model itself is modified. The estimates of both error and convergence rate are theoretically made and the vahdity of the method is proved. For VDA problem with local observation data, the conventional VDA method are out of use due to the ill-posedness of the problem. In order to overcome the difficulties caused by the ill-posedness, the initial conditions and parameters of the model are modified by using the improved VDA method, and the estimates of both error and convergence rate are also made. Finally, the validity of the improved VDA method is proved through theoretical analysis and illustrated with an example, and a theoretical criterion of the regularization parameters is proposed.
文摘It is not reasonable that one can only use the adjoint of model in data assimilation. The simulated numerical experiment shows that for the tidal model, the result of the adjoint of equation is almost the same as that of the adjoint of model: the averaged absolute difference of the amplitude between observations and simulation is less than 5.0 cm and that of the phase-lag is less than 5.0°. The results are both in good agreement with the observed M2 tide in the Bohai Sea and the Yellow Sea. For comparison, the traditional methods also have been used to simulate M2 tide in the Bohai Sea and the Yellow Sea. The initial guess values of the boundary conditions are given first, and then are adjusted to acquire the simulated results that are as close as possible to the observations. As the boundary conditions contain 72 values, which should be adjusted and how to adjust them can only be partially solved by adjusting them many times. The satisfied results are hard to acquire even gigantic efforts are done. Here, the automation of the treatment of the open boundary conditions is realized. The method is unique and superior to the traditional methods. It is emphasized that if the adjoint of equation is used, tedious and complicated mathematical deduction can be avoided. Therefore the adjoint of equation should attract much attention.
文摘It is not reasonable that one can only use the adjoint of model in data assimilation. The simulated numerical experiment shows that for the tidal model, the result of the adjoint of equation is almost the same as that of the adjoint of model: the averaged absolute difference of the amplitude between observations and simulation is less than 5.0 cm and that of the phase-lag is less than 5.0°. The results are both in good agreement with the observed M2 tide in the Bohai Sea and the Yellow Sea. For comparison, the traditional methods also have been used to simulate M2 tide in the Bohai Sea and the Yellow Sea. The initial guess values of the boundary conditions are given first, and then are adjusted to acquire the simulated results that are as close as possible to the observations. As the boundary conditions contain 72 values, which should be adjusted and how to adjust them can only be partially solved by adjusting them many times. The satisfied results are hard to acquire even gigantic efforts are done. Here, the automation of the treatment of the open boundary conditions is realized. The method is unique and superior to the traditional methods. It is emphasized that if the adjoint of equation is used, tedious and complicated mathematical deduction can be avoided. Therefore the adjoint of equation should attract much attention.
基金supported by the National Natural Science Foundation of China(Grant Nos.41075062,91125016)the National Basic Research Program of China(Grants Nos.2010CB951001,2010CB428403)
文摘Seasonal and interannual changes in the Earth's gravity field are mainly due to mass exchange among the atmosphere,ocean,and continental water sources.The terrestrial water storage changes,detected as gravity changes by the Gravity Recovery and Climate Experiment(GRACE) satellites,are mainly caused by precipitation,evapotranspiration,river transportation and downward infiltration processes.In this study,a land data assimilation system LDAS-G was developed to assimilate the GRACE terrestrial water storage(TWS) data into the Community Land Model(CLM3.5) using the POD-based ensemble four-dimensional variational assimilation method PODEn4 DVar,disaggregating the GRACE large-scale terrestrial water storage changes vertically and in time,and placing constraints on the simulation of vertical hydrological variables to improve land surface hydrological simulations.The ideal experiments conducted at a single point and assimilation experiments carried out over China by the LDAS-G data assimilation system showed that the system developed in this study improved the simulation of land surface hydrological variables,indicating the potential of GRACE data assimilation in large-scale land surface hydrological research and applications.
基金Project supported by the National Key R&D Program of China(No.2022YFB3207304)the National Natural Science Foundation of China(No.42205161)the Natural Science Foundation of Hunan Province,China(No.2023JJ30630)。
文摘Accurate estimation of the background error covariance matrix denoted as B remains a critical challenge in numerical weather prediction(NWP),directly influencing data assimilation(DA)performance and forecast accuracy.Although hybrid ensemble–variational(En Var)methods combine static and flow-dependent matrices to improve assimilation,their effectiveness is constrained by empirically fixed weights.To address this limitation,we propose DRL-En Var,an adaptive hybrid En Var DA method enhanced with deep reinforcement learning.DRL-En Var integrates deep learning(DL)components,including a novel cyclic convolution module to extract abstract features from data,and employs reinforcement learning(RL)to dynamically optimize hybrid weighting strategies.The system adaptively combines multiple ensemble-based flow-dependent matrices with one or more static matrices to construct a time-varying hybrid matrix B that better reflects real-time background errors.Experimental results demonstrate that DRL-En Var performs better than the traditional ensemble Kalman filter(En KF)and hybrid covariance DA(HCDA)methods,especially under sparse observations or transitional changes in state variables.It achieves competitive or superior assimilation accuracy with lower computational cost,and can be flexibly integrated into both three-dimensional variational assimilation(3DVar)and four-dimensional variational assimilation(4DVar)frameworks.Overall,DRL-En Var offers a novel and efficient approach to adaptive DA,particularly valuable for improving forecast skill during transitional weather regimes.
基金This work was supported by the National Key Basic Research Development Programme (Grant No. G1998040901-5)the National Natural Science Foundation of China (Grant No. 40176009) the Hundred Talents Project of the Chinese Academy of Sciences.
文摘An adaptive variational data assimilation method is proposed by Zhu and Kamachi[1]. This method can adaptively adjust the model state without knowing explicitly the model error covariance matrix. The method enables very flexible ways to form some reduced order problems. A proper reduced order problem not only reduces computational burden but also leads to corrections that are more consistent with the model dynamics that trends to produce better forecast. These features make the adaptive variational method a good candidate for SST data assimilation because the model error of an ocean model is usually difficult to estimate. We applied this method to an SST data assimilation problem using the LOTUS data sets and an ocean mixed layer model (Mellor-Yamada level 2.5). Results of assimilation experiments showed good skill of improvement subsurface temperatures by assimilating surface observation alone.
基金National Key Basic Research and Development(973)Program of China(2014CB441406)National Natural Science Foundation of China(91537209 and 41675001)Basic Research Fund of Chinese Academy of Meteorological Sciences(2016Z002and 2016Y008)
文摘A large number of observational analyses have shown that lightning data can be used to indicate areas of deep convection. It is important to assimilate observed lightning data into numerical models, so that more small-scale information can be incorporated to improve the quality of the initial condition and the subsequent forecasts. In this study, the empirical relationship between flash rate, water vapor mixing ratio, and graupel mixing ratio was used to adjust the model relative humidity, which was then assimilated by using the three-dimensional variational data assimilation system of the Weather Research and Forecasting model in cycling mode at 10-min intervals. To find the appropriate assimilation time-window length that yielded significant improvement in both the initial conditions and subsequent forecasts, four experiments with different assimilation time-window lengths were conducted for a squall line case that occurred on 10 July 2007 in North China. It was found that 60 min was the appropriate assimilation time-window length for this case, and longer assimilation window length was unnecessary since no further improvement was present. Forecasts of 1-h accumulated precipitation during the assimilation period and the subsequent 3-h accumulated precipitation were significantly improved compared with the control experiment without lightning data assimilation. The simulated reflectivity was optimal after 30 min of the forecast, it remained optimal during the following 42 min, and the positive effect from lightning data assimilation began to diminish after 72 min of the forecast. Overall,the improvement from lightning data assimilation can be maintained for about 3 h.
基金Key Technologies Research and Development Program (Grant No. 2001BA607B02)National Natural Science Foundation of China (Grant No. 40475042)
文摘Variational method is capable of dealing with observations that have a complicated nonlinear relation with model variables representative of the atmospheric state, and so make it possible to directly assimilate such measured variables as satellite radiance, which have a nonlinear relation with the model variables. Assimilation of any type of observations requires a corresponding observation operator, which establishes a specific mapping from the space of the model state to the space of observation. This paper presents in detail how the direct assimilation of real satellite radiance data is implemented in the GRAPES-3DVar analysis system. It focuses on all the components of the observation operator for direct assimilation of real satellite radiance data, including a spatial interpolation operator that transforms variables from model grid points to observation locations, a physical transformation from model variables to observed elements with different choices of model variables, and a data quality control. Assimilation experiments, using satellite radiances such as NOAA17 AMSU-A and AMSU-B (Advanced Microwave Sounding Unit), are carried out with two different schemes. The results from these experiments can be physically understood and clearly reflect a rational effect of direct assimilation of satellite radiance data in GRAPES-3DVar analysis system.
基金Project partially supported by the State Key Laboratory of Numerical Modelling for Atmospheric Sciences and Geoplysical Fluid Dynmics,Institute of Atmosphenic Physics,Chinese Academy of Sciences.
文摘The variational method of data assimilation is used to solve an inverse problem in the transport of sediment in river, which plays an important role in the change of natural environment. The cost function is defined to measure the error between model predictions and field observations. The adjoint model of IAP river sedimentation model is created to obtain the gradient of the cost function with respect to control variables. The initial conditions are taken as the control variables; their optimal values can be retrieved by minimizing the cost function with limited memory quasi Newton method (LMQN). The results show that the adjoint method approach can successfully make the model prediction well fit the simulated observations. And it is expected to use this method to solve other inverse problems of river sedimentation. But some numerical problems need to be discussed before applying to real river data.
基金supported by the National Natural Science Foundation of China(grant number 42450178).
文摘This study introduces a novel sequential data assimilation method that uses conditional denoising score matching(CDSM).The CDSM leverages iterative refinement of noisy samples guided by conditional score functions to achieve real-time state estimation by incorporating observational constraints at each time step.Unlike traditional methods,such as variational assimilation and Kalman filtering,which rely on Gaussian assumptions and can be computationally expensive because of iterations or ensembles,CDSM is based on stochastic differential equations(SDEs).
