Local Ensemble Kalman Filter Research Articles

Assimilation of ground-based GNSS data using a local ensemble Kalman filter

Tropical cyclones become increasingly nonlinear and dynamically unstable in high-resolution models. The initial conditions are typically sub-optimal, leaving scope to improve the accuracy of forecasts with improved data assimilation. Simultaneously, the lack of real ground-based GNSS observations over the ocean poses significant challenges when evaluating the assimilation results in oceanic regions. In this study, an Observation System Simulation Experiment is carried out based on a tropical cyclone case. Assimilation experiments using the WRF-PDAF framework are conducted. Conventional and GNSS observation operators are implemented. A diverse array of synthetic observations, encompassing temperature (T), wind components (U and V), precipitable water (PW), and zenith total delay (ZTD), are assimilated utilizing the Local Error-Subspace Transform Kalman filter (LESTKF). The findings highlight the improvement in forecast accuracy achieved through the assimilation process over the ocean. Multiple observation types further improve the forecast accuracy. The study underscores the crucial role of GNSS data assimilation techniques. The assimilation of GNSS data presents potential for advancing weather forecasting capabilities. Thus, the construction of ground-based GNSS observation stations over the ocean is promising.

Dust storm forecasting through coupling LOTOS-EUROS with localized ensemble Kalman filter

Super dust storms re-occurred over East Asia in 2021 spring and casted great health damages and property losses. It is essential to achieve an accurate dust forecast to reduce the damage for early warning. The forecasting system fundamentally relies on a numerical model which can forecast the full evolution of dust storms. However, large uncertainties exist in model forecasts. Meanwhile, various near-real-time observations are available that contain valuable dust information. A dust storm forecasting system is here developed through coupling a chemical transport model, LOTOS-EUROS, and Localized EnKF (LEnKF) assimilation approach. The assimilations are carried out via an interface of our self-designed assimilation toolbox, PyFilter v1.0. Ground-based PM10 measurements from air quality monitoring network are assimilated. Sequential assimilation tests are carried out over the 2021 spring super dust storms. The results show that the assimilation-based forecasting system produces a promising dust forecast than model-only forecast, and the improvements is also validated through comparing to the independent MODIS aerosol optical depth (AOD). Superior performance is obtained when LEnKF is implemented, as the localization helps EnKF in resolving the PM10 measurements that have a large spatial variability with limited ensemble members. In addition, sensitivity experiments are conducted to exploit the distance-dependent localization for the LEnKF. Considering both cases, the optimal choice of the distance is tested to be around 500 km: the larger distance is less effective in removing the spurious correction, while the smaller one easily falls into the local optimum and the model would become divergent rapidly.

Localized ensemble Kalman inversion

Ensemble Kalman inversion (EKI) is an adaption of the ensemble Kalman filter (EnKF) for the numerical solution of inverse problems. Both EKI and EnKF suffer from the ‘subspace property’, i.e. the EKI and EnKF solutions are linear combinations of the initial ensembles. The subspace property implies that the ensemble size should be larger than the problem dimension to ensure EKI’s convergence to the correct solution. This scaling of ensemble size is impractical and prevents the use of EKI in high-dimensional problems. ‘Localization’ has been used for many years in EnKF to break the subspace property in a way that a localized EnKF can solve high-dimensional problems with a modest ensemble size, independently of the number of unknowns. Here, we study localization of the EKI and demonstrate how a localized EKI (LEKI) can solve high-dimensional inverse problems with a modest ensemble size. Our analysis is mathematically rigorous and applies to the continuous time limit of the EKI. Specifically, we can prove an intended ensemble collapse and convergence guarantees with an ensemble size that is less than the number of unknowns, which sets this work apart from the current state-of-the-art. We illustrate our theory with numerical experiments where some of our mathematical assumptions may only be approximately valid.

Water table depth assimilation in integrated terrestrial system models at the larger catchment scale

As an important source of water for human beings, groundwater plays a significant role in human production and life. However, different sources of uncertainty may lead to unsatisfactory simulations of groundwater hydrodynamics with hydrological models. The goal of this study is to investigate the impact of assimilating groundwater data into the Terrestrial System Modeling Platform (TSMP) for improving hydrological modeling in a real-world case. Daily groundwater table depth (WTD) measurements from the year 2018 for the Rur catchment in Germany were assimilated by the Localized Ensemble Kalman Filter (LEnKF) into TSMP. The LEnKF is used with a localization radius so that the assimilated measurements only update model states in a limited radius around the measurements, in order to avoid unphysical updates related to spurious correlations. Due to the mismatch between groundwater measurements and the coarse model resolution (500 m), the measurements need careful screening before data assimilation (DA). Based on the spatial autocorrelation of the WTD deduced from the measurements, three different filter localization radii (2.5, 5, and 10 km) were evaluated for assimilation. The bias in the simulated water table and the root mean square error (RMSE) are reduced after DA, compared with runs without DA [i.e., open loop (OL) runs]. The best results at the assimilated locations are obtained for a localization radius of 10 km, with an 81% reduction of RMSE at the measurement locations, and slightly smaller RMSE reductions for the 5 and 2.5 km radius. The validation with independent WTD data showed the best results for a localization radius of 10 km, but groundwater table characterization could only be improved for sites <2.5 km from measurement locations. In case of a localization radius of 10 km the RMSE-reduction was 30% for those nearby sites. Simulated soil moisture was validated against soil moisture measured by cosmic-ray neutron sensors (CRNS), but no RMSE reduction was observed for DA-runs compared to OL-run. However, in both cases, the correlation between measured and simulated soil moisture content was high (between 0.70 and 0.89, except for the Wuestebach site).

Ionospheric Assimilation of GNSS TEC into IRI Model Using a Local Ensemble Kalman Filter

Ionospheric total electron content (TEC) is important data for ionospheric morphology, and also an important parameter for ionospheric correction in Global Navigation Satellite System (GNSS) precise positioning, navigation, and radio science. In this study, we present a data assimilation model for regional ionosphere based on a local ensemble Kalman filter (LEnKF) with the International Reference Ionosphere 2016 (IRI-2016) model as the background, to assimilate ionospheric TEC observations from GNSS. To demonstrate the results, the TEC estimates from the Crustal Movement Observation Network of China (CMONOC), which is about 260 stations in China, are applied as observation. The assessments are performed against the TEC estimates from BeiDou Navigation Satellite System (BDS) geostationary earth orbit (GEO) and against the final products from the Center for Orbit Determination in Europe (CODE). The assimilation results are in good agreement with BDS GEO TEC and the CODE TEC on a quiet or disturbed day. The correlation coefficient after assimilation is increased by about 17% compared with that before assimilation, and the RMSE after assimilation is decreased by about 42% compared with that before assimilation. Furthermore, the assimilated method is also evaluated in the single-frequency precise point positioning (PPP). The experimental results indicate that the PPP/Assimilated method can improve the GNSS positioning accuracy more effectively in comparison to the PPP/CODE. These results reveal that the LEnKF method can be considered as a useful tool for ionospheric assimilation.

State, global, and local parameter estimation using local ensemble Kalman filters: Applications to online machine learning of chaotic dynamics

AbstractIn a recent methodological article, we showed how to learn chaotic dynamics along with the state trajectory from sequentially acquired observations, using local ensemble Kalman filters. Here, we investigate more systematically the possibility of using a local ensemble Kalman filter with either covariance localisation or local domains, in order to retrieve the state and a mix of key global and local parameters. Global parameters are meant to represent the surrogate dynamical core, for instance through a neural network, which is reminiscent of data‐driven machine learning of dynamics, while the local parameters typically stand for the forcings of the model. Aiming at joint state and parameter estimation, a family of algorithms for covariance and local domain localisation is proposed. In particular, we show how to update global parameters rigorously using a local‐domain ensemble Kalman filter (EnKF) such as the local ensemble transform Kalman filter (LETKF), an inherently local method. The approach is tested with success on the 40‐variable Lorenz model using several of the local EnKF flavors. A two‐dimensional illustration based on a multilayer Lorenz model is finally provided. It uses radiance‐like nonlocal observations. It features both local domains and covariance localisation, in order to learn the chaotic dynamics and the local forcings. This article addresses more generally the key question of online estimation of both global and local model parameters.

Online learning of both state and dynamics using ensemble Kalman filters

<p style='text-indent:20px;'>The reconstruction of the dynamics of an observed physical system as a surrogate model has been brought to the fore by recent advances in machine learning. To deal with partial and noisy observations in that endeavor, machine learning representations of the surrogate model can be used within a Bayesian data assimilation framework. However, these approaches require to consider long time series of observational data, meant to be assimilated all together. This paper investigates the possibility to learn both the dynamics and the state online, i.e. to update their estimates at any time, in particular when new observations are acquired. The estimation is based on the ensemble Kalman filter (EnKF) family of algorithms using a rather simple representation for the surrogate model and state augmentation. We consider the implication of learning dynamics online through (ⅰ) a global EnKF, (ⅰ) a local EnKF and (ⅲ) an iterative EnKF and we discuss in each case issues and algorithmic solutions. We then demonstrate numerically the efficiency and assess the accuracy of these methods using one-dimensional, one-scale and two-scale chaotic Lorenz models.</p>

An algorithm for estimating greenhouse gas fluxes using satellite data for a global transport and diffusion model

The task of estimating the greenhouse gas fluxes in the atmosphere from satellite data is relevant. This problem is solved based on a data assimilation system using a model of transport and diffusion of an impurity in the atmosphere. The paper discusses an approach to solving the problem of estimating the greenhouse gas fluxes based on the use of the ensemble Kalman filter for the global model of transport and diffusion. The paper proposes a numerical algorithm based on the decomposition of the model domain. The originality of this work is the application of the local ensemble Kalman filter algorithm. The case of this study when the greenhouse gas fluxes are considered as a variable is discussed. Here are the results of the simulated numerical experiments on the implementation of the step of analyzing the data assimilation algorithm in the case of the global model of transfer and diffusion.

Saturation-based localization within EnKF approach for history matching in SAGD processes

The history matching method with the ensemble Kalman filter (EnKF) technique has been successfully applied in the steam-assisted gravity drainage (SAGD) processes. In the application of the EnKF method, usually, large ensemble size is required to eliminate spurious correlations, which also increases the computation cost. In this paper, a newly defined saturation-based localized EnKF approach is proposed and proved to be much more efficient than the standard EnKF method. This approach is able to use a small ensemble to obtain the desired history match and prediction results. Therefore, the computation cost can be reduced. Simulation results from a large ensemble (1000 ensembles) size are used to conduct cross-covariance analysis to determine the regions of the localization function. Based on the positive covariance regions, the localization regions are defined. Oil saturation is used as localization scale to define the saturation-based localization function. Good history match results and prediction results are obtained by adopting saturation-based localized EnKF approach. A small ensemble (10 ensembles) size is employed to test the efficiency of the newly defined localization function. Without localization, the ensemble variability collapses quickly when using small ensembles which will have no data assimilation ability. The saturation-based localized EnKF approach with small ensembles (10 ensembles) can avoid ensemble variability collapse and obtain desired history matching results.

Global Assimilation of Ocean‐Color Data of Phytoplankton Functional Types: Impact of Different Data Sets

AbstractPhytoplankton functional‐type (PFT) data are assimilated into the global coupled ocean‐ecosystem model MITgcm‐REcoM2 for two years using a local ensemble Kalman filter. The ecosystem model has two PFTs: small phytoplankton (SP) and diatoms. Three different sets of satellite PFT data are assimilated: Ocean‐Color‐Phytoplankton Functional Type (OC‐PFT), Phytoplankton Differential Optical Absorption Spectroscopy (PhytoDOAS), and SYNergistic exploitation of hyper‐ and multi‐spectral precursor SENtinel measurements to determine Phytoplankton Functional Types (SynSenPFT), which is a synergistic product combining the independent PFT products OC‐PFT and PhytoDOAS. The effect of assimilating PFT data is compared with the assimilation of total chlorophyll data (TChla), which constrains both PFTs through multivariate assimilation. While the assimilation of TChla already improves both PFTs, the assimilation of PFT data further improves the representation of the phytoplankton community. The effect is particularly large for diatoms where, compared to the assimilation of TChla, the SynSenPFT assimilation results in 57% and 67% reduction of root‐mean‐square error and bias, respectively, while the correlation is increased from 0.45 to 0.54. For SP the assimilation of SynSenPFT data reduces the root‐mean‐square error and bias by 14% each and increases the correlation by 30%. The separate assimilation of the PFT data products OC‐PFT, SynSenPFT, and joint assimilation of OC‐PFT and PhytoDOAS data leads to similar results while the assimilation of PhytoDOAS data alone leads to deteriorated SP but improved diatoms. When both OC‐PFT and PhytoDOAS data are jointly assimilated, the representation of diatoms is improved compared to the assimilation of only OC‐PFT. The results show slightly lower errors than when the synergistic SynSenPFT data are assimilated, which shows that the assimilation successfully combines the separate data sources.

Hourly Aerosol Assimilation of Himawari‐8 AOT Using the Four‐Dimensional Local Ensemble Transform Kalman Filter

AbstractThe next‐generation geostationary satellite Himawari‐8 has a much higher observation frequency of the aerosol field than polar‐orbiting satellites. Aerosol analyses with a geostationary satellite can advance our understanding of the rapid spatiotemporal evolution of aerosols, which is especially critical for studies of air pollution and its mechanisms. We present a one‐monthlong hourly aerosol analysis using an aerosol data assimilation based on the local ensemble Kalman filter (LETKF), Himawari‐8‐retrieved hourly aerosol optical thicknesses (AOTs), and a global model named Non‐hydrostatic Icosahedral Atmospheric Model coupled with an aerosol model named Spectral Radiation Transport Model for Aerosol Species (NICAM‐SPRINTARS). To assimilate asynchronous observations and avoid frequent switching between the assimilation and ensemble aerosol forecasts, the LETKF is also extended to the four‐dimensional LETKF (4D‐LETKF). The hourly aerosol analyses are evaluated with both the assimilated Himawari‐8 AOTs and independent Moderate Resolution Imaging Spectroradiometer (MODIS)‐ and AErosol RObotic NETwork (AERONET)‐retrieved AOTs. All evaluations show that the assimilations positively affect the model performances and produce simulated AOTs that are closer to the observations. The analyses correctly reduce the significantly positive biases and root‐mean‐square errors of the control experiment, especially over East China and Australia. Our results also show that hourly aerosol analyses with more frequent Himawari‐8 observations are superior to those using the polar satellite MODIS observations. The performances among the LETKF and 4D‐LETKF experiments are generally not so different, but the computational load of the 4D‐LETKF is much lighter than that of the LETKF.

On the consistency of the local ensemble square root Kalman filter perturbation update

We examine the perturbation update step of the ensemble Kalman filters which rely on covariance localisation, and hence have the ability to assimilate non-local observations in geophysical models. We show that the updated perturbations of these ensemble filters are not to be identified with the main empirical orthogonal functions of the analysis covariance matrix, in contrast with the updated perturbations of the local ensemble transform Kalman filter (LETKF). Building on that evidence, we propose a new scheme to update the perturbations of a local ensemble square root Kalman filter (LEnSRF) with the goal to minimise the discrepancy between the analysis covariances and the sample covariances regularised by covariance localisation. The scheme has the potential to be more consistent and to generate updated members closer to the model’s attractor (showing fewer imbalances). We show how to solve the corresponding optimisation problem and discuss its numerical complexity. The qualitative properties of the perturbations generated from this new scheme are illustrated using a simple one-dimensional covariance model. Moreover, we demonstrate on the discrete Lorenz–96 and continuous Kuramoto–Sivashinsky one-dimensional low-order models that the new scheme requires significantly less, and possibly none, multiplicative inflation needed to counteract imbalance, compared to the LETKF and the LEnSRF without the new scheme. Finally, we notice a gain in accuracy of the new LEnSRF as measured by the analysis and forecast root mean square errors, despite using well-tuned configurations where such gain is very difficult to obtain.

Parameter and state estimation with ensemble Kalman filter based algorithms for convective‐scale applications

Representation of clouds in convection‐permitting models is sensitive to numerical weather prediction (NWP) model parameters that are often very crudely known (for example roughness length). Our goal is to allow for uncertainty in these parameters and estimate them from data using the ensemble Kalman filter (EnKF) approach. However, to deal with difficulties associated with convective‐scale applications, such as non‐Gaussianity and constraints on state and parameter values, modifications to classical EnKF are necessary. In this article, we evaluate and extend several recently developed EnKF‐based algorithms that either incorporate constraints such as mass conservation and positivity of precipitation explicitly or introduce higher order moments on the joint state and parameter estimation problem. We compare their results with the localized EnKF for a common idealized test case. The test case uses perfect model experiments with the one‐dimensional modified shallow‐water model, which was designed to mimic important properties of convection. We use a stochastic dynamical model for parameters, in order to prevent underdispersion in parameter space. To deal with localization for estimation of parameters, we introduce a method called global updating, which is a computationally cheap modification of spatial updating and was proven successful in this context. The sensitivity of the results to the number of ensemble members and localization, as well as observation coverage and frequency, is shown. Although all algorithms are capable of reducing the initial state and parameter errors, it is concluded that mass conservation is important when the localization radius is small and/or the observations are sparse. In addition, accounting for higher order moments in the joint space and parameter estimation problem is beneficial when the ensemble size is large enough or when applied to parameter estimation only.

Performance Analysis of Local Ensemble Kalman Filter

Ensemble Kalman filter (EnKF) is an important data assimilation method for high dimensional geophysical systems. Efficient implementation of EnKF in practice often involves the localization technique, which updates each component using only information within a local radius. This paper rigorously analyzes the local EnKF (LEnKF) for linear systems, and shows that the filter error can be dominated by the ensemble covariance, as long as 1) the sample size exceeds the logarithmic of state dimension and a constant that depends only on the local radius; 2) the forecast covariance matrix admits a stable localized structure. In particular, this indicates that with small system and observation noises, the filter error will be accurate in long time even if the initialization is not. The analysis also reveals an intrinsic inconsistency caused by the localization technique, and a stable localized structure is necessary to control this inconsistency. While this structure is usually taken for granted for the operation of LEnKF, it can also be rigorously proved for linear systems with sparse local observations and weak local interactions. These theoretical results are also validated by numerical implementation of LEnKF on a simple stochastic turbulence in two dynamical regimes.

Assimilation of Ocean‐Color Plankton Functional Types to Improve Marine Ecosystem Simulations

AbstractWe assimilated phytoplankton functional types (PFTs) derived from ocean color into a marine ecosystem model, to improve the simulation of biogeochemical indicators and emerging properties in a shelf sea. Error‐characterized chlorophyll concentrations of four PFTs (diatoms, dinoflagellates, nanoplankton, and picoplankton), as well as total chlorophyll for comparison, were assimilated into a physical‐biogeochemical model of the North East Atlantic, applying a localized Ensemble Kalman filter. The reanalysis simulations spanned the years 1998–2003. The skill of the reference and reanalysis simulations in estimating ocean color and in situ biogeochemical data were compared by using robust statistics. The reanalysis outperformed both the reference and the assimilation of total chlorophyll in estimating the ocean‐color PFTs (except nanoplankton), as well as the not‐assimilated total chlorophyll, leading the model to simulate better the plankton community structure. Crucially, the reanalysis improved the estimates of not‐assimilated in situ data of PFTs, as well as of phosphate and pCO2, impacting the simulation of the air‐sea carbon flux. However, the reanalysis increased further the model overestimation of nitrate, in spite of increases in plankton nitrate uptake. The method proposed here is easily adaptable for use with other ecosystem models that simulate PFTs, for, e.g., reanalysis of carbon fluxes in the global ocean and for operational forecasts of biogeochemical indicators in shelf‐sea ecosystems.

Performance of AMSR_E soil moisture data assimilation in CLM4.5 model for monitoring hydrologic fluxes at global scale

In this study, we evaluated the performance of community land surface model (CLM4.5) to simulate the hydrologic fluxes, such as, soil moisture (SM), evapotranspiration (ET) and runoff with (without) remote sensing data assimilation. The Advanced Microwave Scanning Radiometer-Earth Observing System (AMSR_E) daily SM (both ascending and descending) are incorporated into the CLM4.5 model using data assimilation (DA) technique. The GLDAS data is used to validate the AMSR_E SM data and evaluate the performance of CLM4.5 simulations. The AMSR_E SM data are rescaled to meet the resolution of CLM4.5 model. By assimilating the AMSR_E SM data into the CLM4.5 model can improve the SM simulations, especially over the climate transition zones in Africa, East Australia, South South America, Southeast Asia, and East North America in summer season. The Local Ensemble Kalman Filter (LEnKF) technique improves the performance of CLM4.5 model compared to the directly substituted method. The improvement in ET and surface runoff simulations from CLM4.5 model assimilated with AMSR_E SM data shares similar spatial patterns with SM.

Localizing the Ensemble Kalman Particle Filter

Ensemble methods such as the Ensemble Kalman Filter (EnKF) are widely used for data assimilation in large-scale geophysical applications, as for example in numerical weather prediction. There is a growing interest for physical models with higher and higher resolution, which brings new challenges for data assimilation techniques because of the presence of non-linear and non-Gaussian features that are not adequately treated by the EnKF. We propose two new localized algorithms based on the Ensemble Kalman Particle Filter, a hybrid method combining the EnKF and the Particle Filter (PF) in a way that maintains scalability and sample diversity. Localization is a key element of the success of EnKF in practice, but it is much more challenging to apply to PFs. The algorithms that we introduce in the present paper provide a compromise between the EnKF and the PF while avoiding some of the problems of localization for pure PFs. Numerical experiments with a simplified model of cumulus convection based on a modified shallow water equation show that the proposed algorithms perform better than the local EnKF. In particular, the PF nature of the method allows to capture non-Gaussian characteristics of the estimated fields such as the location of wet and dry areas.

Decadal reanalysis of biogeochemical indicators and fluxes in the North West European shelf‐sea ecosystem

AbstractThis paper presents the first decadal reanalysis simulation of the biogeochemistry of the North West European shelf, along with a full evaluation of its skill, confidence, and value. An error‐characterized satellite product for chlorophyll was assimilated into a physical‐biogeochemical model of the North East Atlantic, applying a localized Ensemble Kalman filter. The results showed that the reanalysis improved the model simulation of assimilated chlorophyll in 60% of the study region. Model validation metrics showed that the reanalysis had skill in matching a large data set of in situ observations for 10 ecosystem variables. Spearman rank correlations were significant and higher than 0.7 for physical‐chemical variables (temperature, salinity, and oxygen), ∼0.6 for chlorophyll and nutrients (phosphate, nitrate, and silicate), and significant, though lower in value, for partial pressure of dissolved carbon dioxide (∼0.4). The reanalysis captured the magnitude of pH and ammonia observations, but not their variability. The value of the reanalysis for assessing environmental status and variability has been exemplified in two case studies. The first shows that between 325,000 and 365,000 km2 of shelf bottom waters were vulnerable to oxygen deficiency potentially threatening bottom fishes and benthos. The second application confirmed that the shelf is a net sink of atmospheric carbon dioxide, but the total amount of uptake varies between 36 and 46 Tg C yr−1 at a 90% confidence level. These results indicate that the reanalysis output data set can inform the management of the North West European shelf ecosystem, in relation to eutrophication, fishery, and variability of the carbon cycle.

Assimilation and correction of radiosonde humidity observations in the data assimilation system based on the local ensemble Kalman filter

Implemented is the procedure of assimilation of humidity observations in the data assimilation system based on the local ensemble Kalman filter. Applied is the correction of the time lag and solar heating in the process of humidity radiosonde observations. Presented are the results of the assimilation of humidity radiosonde observations and the results of their correction as compared with assimilation without humidity data. It is demonstrated that the use of the correction of humidity observations enables error reduction at the assimilation in the cycle.

Global carbon assimilation system using a local ensemble Kalman filter with multiple ecosystem models

AbstractIn this paper, a global carbon assimilation system (GCAS) is developed for optimizing the global land surface carbon flux at 1° resolution using multiple ecosystem models. In GCAS, three ecosystem models, Boreal Ecosystem Productivity Simulator, Carnegie‐Ames‐Stanford Approach, and Community Atmosphere Biosphere Land Exchange, produce the prior fluxes, and an atmospheric transport model, Model for OZone And Related chemical Tracers, is used to calculate atmospheric CO2 concentrations resulting from these prior fluxes. A local ensemble Kalman filter is developed to assimilate atmospheric CO2 data observed at 92 stations to optimize the carbon flux for six land regions, and the Bayesian model averaging method is implemented in GCAS to calculate the weighted average of the optimized fluxes based on individual ecosystem models. The weights for the models are found according to the closeness of their forecasted CO2 concentration to observation. Results of this study show that the model weights vary in time and space, allowing for an optimum utilization of different strengths of different ecosystem models. It is also demonstrated that spatial localization is an effective technique to avoid spurious optimization results for regions that are not well constrained by the atmospheric data. Based on the multimodel optimized flux from GCAS, we found that the average global terrestrial carbon sink over the 2002–2008 period is 2.97 ± 1.1 PgC yr−1, and the sinks are 0.88 ± 0.52, 0.27 ± 0.33, 0.67 ± 0.39, 0.90 ± 0.68, 0.21 ± 0.31, and 0.04 ± 0.08 PgC yr−1 for the North America, South America, Africa, Eurasia, Tropical Asia, and Australia, respectively. This multimodel GCAS can be used to improve global carbon cycle estimation.