Ocean temperature is an important physical variable in marine ecosystems,and ocean temperature prediction is an important research objective in ocean-related fields.Currently,one of the commonly used methods for ocean...Ocean temperature is an important physical variable in marine ecosystems,and ocean temperature prediction is an important research objective in ocean-related fields.Currently,one of the commonly used methods for ocean temperature prediction is based on data-driven,but research on this method is mostly limited to the sea surface,with few studies on the prediction of internal ocean temperature.Existing graph neural network-based methods usually use predefined graphs or learned static graphs,which cannot capture the dynamic associations among data.In this study,we propose a novel dynamic spatiotemporal graph neural network(DSTGN)to predict threedimensional ocean temperature(3D-OT),which combines static graph learning and dynamic graph learning to automatically mine two unknown dependencies between sequences based on the original 3D-OT data without prior knowledge.Temporal and spatial dependencies in the time series were then captured using temporal and graph convolutions.We also integrated dynamic graph learning,static graph learning,graph convolution,and temporal convolution into an end-to-end framework for 3D-OT prediction using time-series grid data.In this study,we conducted prediction experiments using high-resolution 3D-OT from the Copernicus global ocean physical reanalysis,with data covering the vertical variation of temperature from the sea surface to 1000 m below the sea surface.We compared five mainstream models that are commonly used for ocean temperature prediction,and the results showed that the method achieved the best prediction results at all prediction scales.展开更多
A regional ocean reanalysis system for the coastal waters of China and adjacent seas has been developed by the National Marine Data and Information Service(NMDIS).It produces a dataset package called CORA (China oc...A regional ocean reanalysis system for the coastal waters of China and adjacent seas has been developed by the National Marine Data and Information Service(NMDIS).It produces a dataset package called CORA (China ocean reanalysis).The regional ocean model used is based on the Princeton Ocean Model with a generalized coordinate system(POMgcs).The model is parallelized by NMDIS with the addition of the wave breaking and tidal mixing processes into model parameterizations.Data assimilation is a sequential three-dimensional variational(3D-Var) scheme implemented within a multigrid framework.Observations include satellite remote sensing sea surface temperature(SST),altimetry sea level anomaly(SLA),and temperature/salinity profiles.The reanalysis fields of sea surface height,temperature,salinity,and currents begin with January 1986 and are currently updated every year. Error statistics and error distributions of temperature,salinity and currents are presented as a primary evaluation of the reanalysis fields using sea level data from tidal gauges,temperature profiles,as well as the trajectories of Argo floats.Some case studies offer the opportunity to verify the evolution of certain local circulations.These evaluations show that the reanalysis data produced provide a good representation of the ocean processes and phenomena in the coastal waters of China and adjacent seas.展开更多
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
Large biases exist in real-time ENSO prediction, which can be attributed to uncertainties in initial conditions and model parameters. Previously, a 4D variational (4D-Vat) data assimilation system was developed for ...Large biases exist in real-time ENSO prediction, which can be attributed to uncertainties in initial conditions and model parameters. Previously, a 4D variational (4D-Vat) data assimilation system was developed for an intermediate coupled model (ICM) and used to improve ENSO modeling through optimized initial conditions. In this paper, this system is further applied to optimize model parameters. In the ICM used, one important process for ENSO is related to the anomalous temperature of subsurface water entrained into the mixed layer (Te), which is empirically and explicitly related to sea level (SL) variation. The strength of the thermocline effect on SST (referred to simply as "the thermocline effect") is represented by an introduced parameter, (l'Te. A numerical procedure is developed to optimize this model parameter through the 4D-Var assimilation of SST data in a twin experiment context with an idealized setting. Experiments having their initial condition optimized only, and having their initial condition plus this additional model parameter optimized, are compared. It is shown that ENSO evolution can be more effectively recovered by including the additional optimization of this parameter in ENSO modeling. The demonstrated feasibility of optimizing model parameters and initial conditions together through the 4D-Var method provides a modeling platform for ENSO studies. Further applications of the 4D-Vat data assimilation system implemented in the ICM are also discussed.展开更多
Communication behavior recognition is an issue with increasingly importance in the antiterrorism and national defense area.However,the sensing data obtained in actual environment is often not sufficient to accurately ...Communication behavior recognition is an issue with increasingly importance in the antiterrorism and national defense area.However,the sensing data obtained in actual environment is often not sufficient to accurately analyze the communication behavior.Traditional means can hardly utilize the scarce and crude spectrum sensing data captured in a real scene.Thus,communication behavior recognition using raw sensing data under smallsample condition has become a new challenge.In this paper,a data enhanced communication behavior recognition(DECBR)scheme is proposed to meet this challenge.Firstly,a preprocessing method is designed to make the raw spectrum data suitable for the proposed scheme.Then,an adaptive convolutional neural network structure is exploited to carry out communication behavior recognition.Moreover,DCGAN is applied to support data enhancement,which realize communication behavior recognition under small-sample condition.Finally,the scheme is verified by experiments under different data size.The results show that the DECBR scheme can greatly improve the accuracy and efficiency of behavior recognition under smallsample condition.展开更多
This paper presents an improved approach based on the equivalent-weights particle filter(EWPF)that uses the proposal density to effectively improve the traditional particle filter.The proposed approach uses historical...This paper presents an improved approach based on the equivalent-weights particle filter(EWPF)that uses the proposal density to effectively improve the traditional particle filter.The proposed approach uses historical data to calculate statistical observations instead of the future observations used in the EWPF’s proposal density and draws on the localization scheme used in the localized PF(LPF)to construct the localized EWPF.The new approach is called the statistical observation localized EWPF(LEWPF-Sobs);it uses statistical observations that are better adapted to the requirements of real-time assimilation and the localization function is used to calculate weights to reduce the effect of missing observations on the weights.This approach not only retains the advantages of the EWPF,but also improves the assimilation quality when using sparse observations.Numerical experiments performed with the Lorenz 96 model show that the statistical observation EWPF is better than the EWPF and EAKF when the model uses standard distribution observations.Comparisons of the statistical observation localized EWPF and LPF reveal the advantages of the new method,with fewer particles giving better results.In particular,the new improved filter performs better than the traditional algorithms when the observation network contains densely spaced measurements associated with model state nonlinearities.展开更多
China Ocean ReAnalysis(CORA) version 1.0 products for the period 2009-18 have been developed and validated.The model configuration and assimilation algorithm have both been updated compared to those of the 51-year(195...China Ocean ReAnalysis(CORA) version 1.0 products for the period 2009-18 have been developed and validated.The model configuration and assimilation algorithm have both been updated compared to those of the 51-year(1958-2008) products.The assimilated observations include temperature and salinity field data,satellite remote sensing sea surface temperature,and merged sea surface height(SSH) anomaly data.The validation includes the following three aspects:(1) Temperature,salinity,and SSH anomaly root-mean-square errors(RMSEs) are computed as a primary evaluation of the reanalysis quality.The 0-2000 m domain-averaged RMSEs of temperature and salinity are 0.61℃ and 0.08 psu,respectively.The SSH anomaly RMSE is less than 0.2 m in most regions.(2) The 35°N temperature section is used to evaluate the ability to reproduce the thermocline,mixing layer,and Yellow Sea cold water mass.In summer,the thermocline is reinforced,with the gradient changing from 3℃ in May to 10℃ in August.The mixing-layer depth reproduced by CORA is consistent with that computed from the observed climatology.The Yellow Sea cold water mass forms at a depth of 50 m.(3) The reanalysis current is examined against the tracks of some drifting buoys.The results show that the reanalysis current can capture the mesoscale eddies near the Kuroshio,which are similar to those described by the drifting buoys.Overall,the 2009-18 CORA reanalysis products are capable of reproducing major oceanic phenomena and processes in the coastal waters of China and adjacent seas.展开更多
To further explore enthalpy-based sea-ice assimilation, a one-dimensional (1D) enthalpy sea-ice model is implemented into a simple pycnocline prediction model. The 1D enthalpy sea-ice model includes the physical pro...To further explore enthalpy-based sea-ice assimilation, a one-dimensional (1D) enthalpy sea-ice model is implemented into a simple pycnocline prediction model. The 1D enthalpy sea-ice model includes the physical processes such as brine expulsion, flushing, and salt diffusion. After being coupled with the atmosphere and ocean components, the enthalpy sea-ice model can be integrated stably and serves as an important modulator of model variability. Results from a twin experiment show that the sea-ice data assimilation in the enthalpy space can produce smaller root-mean-square errors of model variables than the traditional scheme that assimilates the observations of ice concentration, especially for slow-varying states. This study provides some insights into the improvement of sea-ice data assimilation in a coupled general circulation model.展开更多
In variational methods,coupled parameter optimization(CPO) often needs a long minimization time window(MTW) to fully incorporate observational information,but the optimal MTW somehow depends on the model nonlinearity....In variational methods,coupled parameter optimization(CPO) often needs a long minimization time window(MTW) to fully incorporate observational information,but the optimal MTW somehow depends on the model nonlinearity.The analytical four-dimensional ensemble-variational(A-4DEnVar) considers model nonlinearity well and avoids adjoint model.It can theoretically be applied to CPO.To verify the feasibility and the ability of the A-4DEnVar in CPO,“twin” experiments based on A-4DEnVar CPO are conducted for the first time with the comparison of four-dimensional variational(4D-Var).Two algorithms use the same background error covariance matrix and optimization algorithm to control variates.The experiments are based on a simple coupled oceanatmosphere model,in which the atmospheric part is the highly nonlinear Lorenz-63 model,and the oceanic part is a slab ocean model.The results show that both A-4DEnVar and 4D-Var can effectively reduce the error of state variables through CPO.Besides,two methods produce almost the same results in most cases when the MTW is less than 560 time steps.The results are similar when the MTW is larger than 560 time steps and less than 880 time steps.The largest MTW of 4 D-Var and A-4DEnVar are 1 200 time steps.Moreover,A-4DEnVar is not sensitive to ensemble size when the MTW is less than 720 time steps.A-4DEnVar obtains satisfactory results in the case of highly nonlinear model and long MTW,suggesting that it has the potential to be widely applied to realistic CPO.展开更多
The calculation of the meridional overturning streamfunction in the southern Indian Ocean is biased by the Indonesian Throughflow.Therefore,this study applies the vertical overturning streamfunction to diagnose the sh...The calculation of the meridional overturning streamfunction in the southern Indian Ocean is biased by the Indonesian Throughflow.Therefore,this study applies the vertical overturning streamfunction to diagnose the shallow overturning circulation in the Indian Ocean.Using the Ocean General Circulation Model for the Earth simulator output,improvements with the vertical overturning streamfunction compared with the meridional overturning streamfunction are explored.The results show that the vertical overturning streamfunction smoothly connects the shallow overturning circulations of the northern Indian Ocean and the southern Indian Ocean with the whole cycle of the subtropical cell and the cross-equatorial cell.The vertical overturning streamfunction shows a much cleaner shallow overturning circulation,which is underestimated by the meridional overturning streamfunction.It shows that the shallow overturning circulation has a magnitude of~13 Sv(1 Sv≡106 m 3 s−1),of which the subtropical cell accounts for~8 Sv.In addition,the vertical overturning streamfunction captures a clockwise overturning cell in the upper 600 m layer between 30°S and 34°S.This cell has a magnitude of about−5 Sv and probably corresponds to the wind-forced subtropical gyre.Therefore,the vertical overturning streamfunction provides a new approach for estimating the shallow overturning circulation in the Indian Ocean.展开更多
基金The National Key R&D Program of China under contract No.2021YFC3101603.
文摘Ocean temperature is an important physical variable in marine ecosystems,and ocean temperature prediction is an important research objective in ocean-related fields.Currently,one of the commonly used methods for ocean temperature prediction is based on data-driven,but research on this method is mostly limited to the sea surface,with few studies on the prediction of internal ocean temperature.Existing graph neural network-based methods usually use predefined graphs or learned static graphs,which cannot capture the dynamic associations among data.In this study,we propose a novel dynamic spatiotemporal graph neural network(DSTGN)to predict threedimensional ocean temperature(3D-OT),which combines static graph learning and dynamic graph learning to automatically mine two unknown dependencies between sequences based on the original 3D-OT data without prior knowledge.Temporal and spatial dependencies in the time series were then captured using temporal and graph convolutions.We also integrated dynamic graph learning,static graph learning,graph convolution,and temporal convolution into an end-to-end framework for 3D-OT prediction using time-series grid data.In this study,we conducted prediction experiments using high-resolution 3D-OT from the Copernicus global ocean physical reanalysis,with data covering the vertical variation of temperature from the sea surface to 1000 m below the sea surface.We compared five mainstream models that are commonly used for ocean temperature prediction,and the results showed that the method achieved the best prediction results at all prediction scales.
文摘A regional ocean reanalysis system for the coastal waters of China and adjacent seas has been developed by the National Marine Data and Information Service(NMDIS).It produces a dataset package called CORA (China ocean reanalysis).The regional ocean model used is based on the Princeton Ocean Model with a generalized coordinate system(POMgcs).The model is parallelized by NMDIS with the addition of the wave breaking and tidal mixing processes into model parameterizations.Data assimilation is a sequential three-dimensional variational(3D-Var) scheme implemented within a multigrid framework.Observations include satellite remote sensing sea surface temperature(SST),altimetry sea level anomaly(SLA),and temperature/salinity profiles.The reanalysis fields of sea surface height,temperature,salinity,and currents begin with January 1986 and are currently updated every year. Error statistics and error distributions of temperature,salinity and currents are presented as a primary evaluation of the reanalysis fields using sea level data from tidal gauges,temperature profiles,as well as the trajectories of Argo floats.Some case studies offer the opportunity to verify the evolution of certain local circulations.These evaluations show that the reanalysis data produced provide a good representation of the ocean processes and phenomena in the coastal waters of China and adjacent seas.
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supported by the National Natural Science Foundation of China (Grant Nos. 41705082, 41475101, 41690122(41690120))a Chinese Academy of Sciences Strategic Priority Project-the Western Pacific Ocean System (Grant Nos. XDA11010105 and XDA11020306)+1 种基金the National Programme on Global Change and Air–Sea Interaction (Grant Nos. GASI-IPOVAI06 and GASI-IPOVAI-01-01)the China Postdoctoral Science Foundation, and a Qingdao Postdoctoral Application Research Project
文摘Large biases exist in real-time ENSO prediction, which can be attributed to uncertainties in initial conditions and model parameters. Previously, a 4D variational (4D-Vat) data assimilation system was developed for an intermediate coupled model (ICM) and used to improve ENSO modeling through optimized initial conditions. In this paper, this system is further applied to optimize model parameters. In the ICM used, one important process for ENSO is related to the anomalous temperature of subsurface water entrained into the mixed layer (Te), which is empirically and explicitly related to sea level (SL) variation. The strength of the thermocline effect on SST (referred to simply as "the thermocline effect") is represented by an introduced parameter, (l'Te. A numerical procedure is developed to optimize this model parameter through the 4D-Var assimilation of SST data in a twin experiment context with an idealized setting. Experiments having their initial condition optimized only, and having their initial condition plus this additional model parameter optimized, are compared. It is shown that ENSO evolution can be more effectively recovered by including the additional optimization of this parameter in ENSO modeling. The demonstrated feasibility of optimizing model parameters and initial conditions together through the 4D-Var method provides a modeling platform for ENSO studies. Further applications of the 4D-Vat data assimilation system implemented in the ICM are also discussed.
基金supported by the National Natural Science Foundation of China(No.61971439 and No.61702543)the Natural Science Foundation of the Jiangsu Province of China(No.BK20191329)+1 种基金the China Postdoctoral Science Foundation Project(No.2019T120987)the Startup Foundation for Introducing Talent of NUIST(No.2020r100).
文摘Communication behavior recognition is an issue with increasingly importance in the antiterrorism and national defense area.However,the sensing data obtained in actual environment is often not sufficient to accurately analyze the communication behavior.Traditional means can hardly utilize the scarce and crude spectrum sensing data captured in a real scene.Thus,communication behavior recognition using raw sensing data under smallsample condition has become a new challenge.In this paper,a data enhanced communication behavior recognition(DECBR)scheme is proposed to meet this challenge.Firstly,a preprocessing method is designed to make the raw spectrum data suitable for the proposed scheme.Then,an adaptive convolutional neural network structure is exploited to carry out communication behavior recognition.Moreover,DCGAN is applied to support data enhancement,which realize communication behavior recognition under small-sample condition.Finally,the scheme is verified by experiments under different data size.The results show that the DECBR scheme can greatly improve the accuracy and efficiency of behavior recognition under smallsample condition.
基金The National Basic Research Program of China under contract Nos 2017YFC1404100,2017YFC1404103 and 2017YFC1404104the National Natural Science Foundation of China under contract No.41676088。
文摘This paper presents an improved approach based on the equivalent-weights particle filter(EWPF)that uses the proposal density to effectively improve the traditional particle filter.The proposed approach uses historical data to calculate statistical observations instead of the future observations used in the EWPF’s proposal density and draws on the localization scheme used in the localized PF(LPF)to construct the localized EWPF.The new approach is called the statistical observation localized EWPF(LEWPF-Sobs);it uses statistical observations that are better adapted to the requirements of real-time assimilation and the localization function is used to calculate weights to reduce the effect of missing observations on the weights.This approach not only retains the advantages of the EWPF,but also improves the assimilation quality when using sparse observations.Numerical experiments performed with the Lorenz 96 model show that the statistical observation EWPF is better than the EWPF and EAKF when the model uses standard distribution observations.Comparisons of the statistical observation localized EWPF and LPF reveal the advantages of the new method,with fewer particles giving better results.In particular,the new improved filter performs better than the traditional algorithms when the observation network contains densely spaced measurements associated with model state nonlinearities.
基金supported by grants from the National Key Research and Development Program of China [grant numbers 2016YFC1401800,2017YFC1404103,2016YFC1401701,and 2019YFC1510000]the National Natural Science Foundation of China [grant number 41976019]the Tianjin Natural Science Foundation [grant number 18JCQNJC01200]。
文摘China Ocean ReAnalysis(CORA) version 1.0 products for the period 2009-18 have been developed and validated.The model configuration and assimilation algorithm have both been updated compared to those of the 51-year(1958-2008) products.The assimilated observations include temperature and salinity field data,satellite remote sensing sea surface temperature,and merged sea surface height(SSH) anomaly data.The validation includes the following three aspects:(1) Temperature,salinity,and SSH anomaly root-mean-square errors(RMSEs) are computed as a primary evaluation of the reanalysis quality.The 0-2000 m domain-averaged RMSEs of temperature and salinity are 0.61℃ and 0.08 psu,respectively.The SSH anomaly RMSE is less than 0.2 m in most regions.(2) The 35°N temperature section is used to evaluate the ability to reproduce the thermocline,mixing layer,and Yellow Sea cold water mass.In summer,the thermocline is reinforced,with the gradient changing from 3℃ in May to 10℃ in August.The mixing-layer depth reproduced by CORA is consistent with that computed from the observed climatology.The Yellow Sea cold water mass forms at a depth of 50 m.(3) The reanalysis current is examined against the tracks of some drifting buoys.The results show that the reanalysis current can capture the mesoscale eddies near the Kuroshio,which are similar to those described by the drifting buoys.Overall,the 2009-18 CORA reanalysis products are capable of reproducing major oceanic phenomena and processes in the coastal waters of China and adjacent seas.
基金co-sponsored by grants from the National Natural Science Foundation (Grant Nos. 41206178, 41306006, 41376015, 41376013 and 41176003)the National Basic Research Program (Grant No. 2013CB430304)+1 种基金the National HighTech R&D Program (Grant No. 2013AA09A505)the Global Change and Air–Sea Interaction Program (Grant No. GASI-01-0112) of China
文摘To further explore enthalpy-based sea-ice assimilation, a one-dimensional (1D) enthalpy sea-ice model is implemented into a simple pycnocline prediction model. The 1D enthalpy sea-ice model includes the physical processes such as brine expulsion, flushing, and salt diffusion. After being coupled with the atmosphere and ocean components, the enthalpy sea-ice model can be integrated stably and serves as an important modulator of model variability. Results from a twin experiment show that the sea-ice data assimilation in the enthalpy space can produce smaller root-mean-square errors of model variables than the traditional scheme that assimilates the observations of ice concentration, especially for slow-varying states. This study provides some insights into the improvement of sea-ice data assimilation in a coupled general circulation model.
基金The National Key Research and Development Program under contract No.2021YFC3101501the National Natural Science Foundation of China under contract No.41876014。
文摘In variational methods,coupled parameter optimization(CPO) often needs a long minimization time window(MTW) to fully incorporate observational information,but the optimal MTW somehow depends on the model nonlinearity.The analytical four-dimensional ensemble-variational(A-4DEnVar) considers model nonlinearity well and avoids adjoint model.It can theoretically be applied to CPO.To verify the feasibility and the ability of the A-4DEnVar in CPO,“twin” experiments based on A-4DEnVar CPO are conducted for the first time with the comparison of four-dimensional variational(4D-Var).Two algorithms use the same background error covariance matrix and optimization algorithm to control variates.The experiments are based on a simple coupled oceanatmosphere model,in which the atmospheric part is the highly nonlinear Lorenz-63 model,and the oceanic part is a slab ocean model.The results show that both A-4DEnVar and 4D-Var can effectively reduce the error of state variables through CPO.Besides,two methods produce almost the same results in most cases when the MTW is less than 560 time steps.The results are similar when the MTW is larger than 560 time steps and less than 880 time steps.The largest MTW of 4 D-Var and A-4DEnVar are 1 200 time steps.Moreover,A-4DEnVar is not sensitive to ensemble size when the MTW is less than 720 time steps.A-4DEnVar obtains satisfactory results in the case of highly nonlinear model and long MTW,suggesting that it has the potential to be widely applied to realistic CPO.
基金supported by the National Key Research and Development Program of China[grant number 2016YFC1401803]the National Natural Science Foundation of China[grant numbers 41976019 and 42076020]+3 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences[grant number XDA20060502]the open project of the State Key Laboratory of Tropical Oceanography,South China Sea Institute of Oceanology,Chinese Academy of Sciences[grant number LTO1910]the Research Program of the Southern Marine Science and Engineering Guangdong Laboratory(Guangzhou)[grant number GML2019ZD0306]the Key Research Program of the Chinese Academy of Sciences[grant number ZDRW-XH-2019-2]。
文摘The calculation of the meridional overturning streamfunction in the southern Indian Ocean is biased by the Indonesian Throughflow.Therefore,this study applies the vertical overturning streamfunction to diagnose the shallow overturning circulation in the Indian Ocean.Using the Ocean General Circulation Model for the Earth simulator output,improvements with the vertical overturning streamfunction compared with the meridional overturning streamfunction are explored.The results show that the vertical overturning streamfunction smoothly connects the shallow overturning circulations of the northern Indian Ocean and the southern Indian Ocean with the whole cycle of the subtropical cell and the cross-equatorial cell.The vertical overturning streamfunction shows a much cleaner shallow overturning circulation,which is underestimated by the meridional overturning streamfunction.It shows that the shallow overturning circulation has a magnitude of~13 Sv(1 Sv≡106 m 3 s−1),of which the subtropical cell accounts for~8 Sv.In addition,the vertical overturning streamfunction captures a clockwise overturning cell in the upper 600 m layer between 30°S and 34°S.This cell has a magnitude of about−5 Sv and probably corresponds to the wind-forced subtropical gyre.Therefore,the vertical overturning streamfunction provides a new approach for estimating the shallow overturning circulation in the Indian Ocean.