Local Ensemble Transform Kalman Filter Research Articles

The Local Unscented Transform Kalman Filter for the Weather Research and Forecasting Model

In this study, the local unscented transform Kalman filter (LUTKF) proposed in the previous study estimates the state of the Weather Research and Forecasting (WRF) model through local analysis. Real observations are assimilated to investigate the analysis performance of the WRF-LUTKF system. The WRF model as a regional numerical weather prediction (NWP) model is widely used to explain the atmospheric state for mesoscale meteorological fields, such as operational forecasting and atmospheric research applications. For the LUTKF based on the sigma-point Kalman filter (SPKF), the state of the nonlinear system is estimated by propagating ensemble members through the unscented transformation (UT) without making any linearization assumptions for nonlinear models. The main objective of this study is to examine the feasibility of mesoscale data assimilations for the LUTKF algorithm using the WRF model and real observations. Similar to the local ensemble transform Kalman filter (LETKF), by suppressing the impact of distant observations on model state variables through localization schemes, the LUTKF can eliminate spurious long-distance correlations in the background covariance, which are induced by the sampling error due to the finite ensemble size; therefore, the LUTKF used in the WRF-LUTKF system can efficiently execute the data assimilation with a small ensemble size. Data assimilation test results demonstrate that the LUTKF can provide reliable analysis performance in estimating the WRF model state with real observations. Experiments with various ensemble size show that the LETKF can provide better estimation results with a larger ensemble size, while the LUTKF can achieve accurate and reliable assimilation results even with a smaller ensemble size.

Implementation and Testing of Radar Data Assimilation Capabilities Within the Joint Effort for Data Assimilation Integration Framework With Ensemble Transformation Kalman Filter Coupled With FV3‐LAM Model

AbstractCapabilities to directly assimilate radar data are implemented within the local ensemble transform Kalman filter (LETKF) and the gain‐form LETKF (LGETKF) algorithms of the Joint Effort for Data assimilation Integration (JEDI) system. The capabilities are evaluated for the analysis and forecast of a severe convection case of 20 May 2019 in the Southern Great Plains using the limited area model version of the FV3 dynamical core (FV3‐LAM) from a recent release for Short‐Range Weather Application (SRW App). The LETKF and LGETKF implementations are shown to produce analyses and short‐range forecasts comparable to those using the ensemble square‐root Kalman Filter (EnSRF) within the Gridpoint Statistical Interpolation (GSI) framework used by current NCEP operational models. In addition, LGETKF retaining only 60% variances for model‐space vertical localization performs similarly to LGETKF retaining 99% of variance and LETKF using observation error‐based vertical localization. JEDI LETKF shows better parallel scalability than LGETKF and GSI EnSRF.

Estimation of AMSU-A Radiance Observation Impacts in an LETKF-Based Atmospheric Global Data Assimilation System: Comparison with EFSO and Observing System Experiments

Abstract This work assesses the contribution of assimilating AMSU-A satellite-based radiance measurements to a global data assimilation system based on an atmospheric general circulation model and the local ensemble transform Kalman filter (LETKF). The radiance measurements were from three channels that are sensitive to the upper troposphere and lower stratosphere. The contribution of these measurements, or AMSU-A observation impact, was estimated both through ensemble-based forecast sensitivity to observations (EFSO) and observing system experiments (OSEs). Two streams of data-denial experiments for the AMSU-A observations were performed for about one month during winter in each hemisphere. The OSEs quantified the accumulated observation impact by cycling (repeating) data denials: including AMSU-A observations reduced the total observation impact for all observations of each data assimilation cycle. In contrast, EFSO estimated AMSU-A to increase the total observation impact. The opposing effects were attributed to the accumulated observation impact in the OSEs; the accumulation could stabilize the data assimilation cycles. In both experiments, the accumulated observation impact of AMSU-A was strongest in the upper troposphere, particularly in the austral midlatitudes where westerly jets exist and observations of other types are sparse. EFSO also assessed AMSU-A to have the most beneficial observation impact in similar locations. The AMSU-A observation impact tended to accumulate just downstream of where EFSO estimated the beneficial observation impact signals. The accumulated AMSU-A observation impact was tied to dynamic processes in the upper-tropospheric and general stratospheric circulation. Therefore, EFSO helps estimate the beneficial distributions of AMSU-A accumulated observation impact by considering their dynamical propagation. Significance Statement The Advanced Microwave Sounding Unit-A (AMSU-A) satellite radiance assimilation technique was successfully integrated into the Atmospheric General Circulation Model for the Earth Simulator (AFES)–LETKF data assimilation system. We conducted OSEs and used EFSO to assess the AMSU-A observation impact. The two estimation methods identified opposite observation impacts due to the cycling (repeating) OSEs of the AMSU-A observations. We interpreted the causes of the opposite estimations. However, even for the cycling OSEs, EFSO appeared to help estimate distributions of the accumulated observation impact. It is important to consider the dynamical propagation of accumulated observation impact in general circulation.

Ensemble-based data assimilation of significant wave height from Sofar Spotters and satellite altimeters with a global operational wave model

An ensemble-based method for wave data assimilation is implemented using significant wave height observations from the globally distributed network of Sofar Spotter buoys and satellite altimeters. The Local Ensemble Transform Kalman Filter (LETKF) method generates skillful analysis fields resulting in reduced forecast errors out to 2.5 days when used as initial conditions in a cycled wave data assimilation system. The LETKF method provides more physically realistic model state updates that better reflect the underlying sea state dynamics and uncertainty compared to methods such as optimal interpolation. Skill assessment far from any included observations and inspection of specific storm events highlight the advantages of LETKF over an optimal interpolation method for data assimilation. This advancement has immediate value in improving predictions of the sea state and, more broadly, enabling future coupled data assimilation and utilization of global surface observations across domains (atmosphere-wave-ocean).

Assimilation of radar‐derived refractivity and radar data in the context of ensemble Kalman filter: Cases study of the Southwest Monsoon Experiment

AbstractRadar‐derived refractivity provides moisture information near the surface, which plays a crucial role in convective initiation and of heavy rain. In this study, the high‐resolution Weather Research and Forecasting local ensemble transform Kalman filter data assimilation system was employed for two cases in the Southwest Monsoon Experiment to conduct two experimental sets. The first set was applied in both cases to investigate the effects of assimilating radar‐retrieved refractivity along with reflectivity and radial wind. The second set was conducted in the second case to examine the benefit of increasing the frequency of refractivity assimilation and investigate the optimal strategy to assimilate refractivity. Results of the two cases revealed that assimilating reflectivity and radial velocity modified near‐surface humidity on the basis of the flow‐dependent error correlation estimated by the ensemble, but the spatial distribution may not be fully accurate, causing underestimation of rainfall. With further refractivity assimilation, stronger convergence and more accurate low‐level moisture, temperature, and wind field corrections were obtained, leading to superior forecasts for both light and heavy rainfall during six hours. The results of the second set indicated that increasing the assimilation interval of refractivity enabled capturing the dramatic moisture variation and enhancing wind convergence, resulting in short‐term forecast improvement. The strategy that solely assimilated refractivity before the appearance of the convection system optimized the correction of environmental moisture, then accurately represented the humidity and strengthened the wind convergence when precipitation occurred. Consequently, the achieved improvement of the short‐term forecast was most noteworthy, particularly for heavy rain.

Estimation of CH4emission based on an advanced 4D-LETKF assimilation system

Abstract. Methane (CH4) is the second major greenhouse gas after carbon dioxide (CO2) which has substantially increased during recent decades in the atmosphere, raising serious sustainability and climate change issues. Here, we develop a data assimilation system for in situ and column-averaged concentrations using a local ensemble transform Kalman filter (LETKF) to estimate surface emissions of CH4. The data assimilation performance is tested and optimized based on idealized settings using observation system simulation experiments (OSSEs), where a known surface emission distribution (the truth) is retrieved from synthetic observations. We tested three covariance inflation methods to avoid covariance underestimation in the emission estimates, namely fixed multiplicative (FM), relaxation-to-prior spread (RTPS), and adaptive multiplicative. First, we assimilate the synthetic observations at every grid point at the surface level. In such a case of dense observational data, the normalized root mean square error (RMSE) in the analyses over global land regions is smaller by 10 %–15 % in the case of RTPS covariance inflation method compared to FM. We have shown that integrated estimated flux seasonal cycles over 15 regions using RTPS inflation are in reasonable agreement between true and estimated flux, with 0.04 global normalized annual mean bias. We then assimilated the column-averaged CH4 concentration by sampling the model simulations at Greenhouse Gases Observing Satellite (GOSAT) observation locations and time for another OSSE. Similar to the case of dense observational data, the RTPS covariance inflation method performs better than FM for GOSAT synthetic observation in terms of normalized RMSE (2 %–3 %) and integrated flux estimation comparison with the true flux. The annual mean averaged normalized RMSE (normalized mean bias) in LETKF CH4 flux estimation in the case of RTPS and FM covariance inflation is found to be 0.59 (0.18) and 0.61 (0.23), respectively. The χ2 test performed for GOSAT synthetic observations assimilation suggests high underestimation of background error covariance in both RTPS and FM covariance inflation methods; however, the underestimation is much higher (>100 % always) for FM compared to RTPS covariance inflation method.

LORA: a local ensemble transform Kalman filter-based ocean research analysis

We have produced an eddy-resolving local ensemble transform Kalman filter (LETKF)-based ocean research analysis (LORA) for the western North Pacific (WNP) and Maritime Continent (MC) regions (LORA-WNP and LORA-MC, respectively). This paper describes the system configuration and validation comparisons with Japan Coastal Ocean Predictability Experiment 2M (JCOPE2M) reanalysis and Archiving, Validation, and Interpretation of Satellite Oceanographic Data (AVISO) observational datasets. The results show that the surface horizontal velocity in the LORA-WNP is closer to independent drifter buoy observations in the mid-latitude region, especially along the Kuroshio Extension (KE), and is less close in the subtropical region than the JCOPE2M, although the AVISO is the closest over the whole domain. The sea surface temperatures (SSTs) in the LORA-WNP correspond better to assimilated satellite observations than the JCOPE2M over most of the domain except for coastal regions. The results using an independent buoy south of the KE indicate that better fit of temperature in the LORA-WNP may be limited to the upper 300 m depth, probably because of the prescribed vertical localization cutoff length of 370 m. In the MC region, the surface velocity in the LORA-MC is closer to the independent drifter buoys in the equatorial coastal region and is less close in the offshore region than the AVISO. The SSTs in the LORA-MC correspond better to the assimilated satellite observations in the offshore region than the nearshore region. Therefore, the LORA-WNP and LORA-MC have sufficient accuracy for geoscience research applications as well as for fisheries, marine transport, and environment consultants.

Performance of a Hybrid Gain Ensemble Data Assimilation Scheme in Tropical Cyclone Forecasting with the GRAPES Model

Hybrid data assimilation (DA) methods have received extensive attention in the field of numerical weather prediction. In this study, a hybrid gain data assimilation (HGDA) method that combined the gain matrices of ensemble and variational methods was first applied in the mesoscale version of the Global/Regional Assimilation and Prediction System (GRAPES_Meso). To evaluate the performance of the HGDA method in the GRAPES_Meso model, different DA schemes, including the three-dimensional variational (3DVAR), local ensemble transform Kalman filter (LETKF), and HGDA schemes, were compared across eight tropical cyclone (TC) cases, and FY-4A atmospheric motion vectors were assimilated. The results indicated that the HYBRID scheme outperformed the 3DVAR and LETKF schemes in TC position forecasting, and with ensemble forecasting techniques, the HYBRID scheme promoted the accuracy of the prediction TC intensity. The threat score (TS) values for the light and medium precipitation forecasts obtained in the HYBRID experiment were higher than those for the forecasts obtained in the 3DVAR and LETKF experiments, which may be attributed to the forecasting accuracy for the TC position. Regarding heavy and extreme rainfall, the HYBRID scheme achieved a more stable effect than those of the 3DVAR and LETKF schemes. The results demonstrated the superiority of the HGDA scheme in TC prediction with the GRAPES_Meso model.

Ensemble‐Based Data Assimilation of GPM DPR Reflectivity: Cloud Microphysics Parameter Estimation With the Nonhydrostatic Icosahedral Atmospheric Model (NICAM)

AbstractDirect assimilation of Dual‐frequency Precipitation Radar (DPR) data of the Global Precipitation Measurement (GPM) core satellite is challenging mainly due to its long revisiting intervals relative to the time scale of precipitation, and precipitation location errors. This study explores a method for improving precipitation forecasts using GPM DPR through model parameter estimation. We developed a 28 km mesh global atmospheric data assimilation system that integrates the Nonhydrostatic ICosahedral Atmospheric Model (NICAM) and Local Ensemble Transform Kalman Filter (LETKF) coupled with a satellite radar simulator. Using the NICAM‐LETKF and GPM DPR observations, this study estimates a model cloud physics parameter corresponding to snowfall terminal velocity. To overcome the difficulties of long revisiting intervals and precipitation location errors, we propose a parameter estimation method based on a two‐dimensional histogram known as the contoured frequency by temperature diagram (CFTD). Parameter estimation effectively mitigated the gap between simulated and observed CFTD, resulting in improved 6 hr precipitation forecasts.

УЧЕТ СКОРРЕЛИРОВАННОСТИ ОШИБОК СПУТНИКОВЫХ ДАННЫХ НАБЛЮДЕНИЙ AMV В АНСАМБЛЕВОЙ СИСТЕМЕ УСВОЕНИЯ ДАННЫХ

The effect of considering correlated errors in AMV (Atmospheric Motion Vectors) satellite observations of wind in the local ensemble transform Kalman filter data assimilation system is studied. It is customary to use a diagonal covariance matrix of errors in observations taking part in assimilation. When assimilating satellite data with correlated errors, the data are thinned, and the values of diagonal elements of the error covariance matrix are often overestimated. This is accompanied by the loss of useful information about the correlation between the errors. The present study uses a different method: the elements of the error covariance matrix for AMV satellite observations are simulated using a second-order autoregressive function. It is shown that such approach reduces the root-mean-square error in initial data for a numerical weather prediction model, in particular on small scales, and improves the forecast quality. It is found that the application of the non-diagonal AMV observation error covariance matrix increases the accuracy of analysis and forecast fields.

Retrieving Soil Physical Properties by Assimilating SMAP Brightness Temperature Observations into the Community Land Model.

This paper coupled a unified passive and active microwave observation operator-namely, an enhanced, physically-based, discrete emission-scattering model-with the community land model (CLM) in a data assimilation (DA) system. By implementing the system default local ensemble transform Kalman filter (LETKF) algorithm, the Soil Moisture Active and Passive (SMAP) brightness temperature TBp (p = Horizontal or Vertical polarization) assimilations for only soil property retrieval and both soil properties and soil moisture estimates were investigated with the aid of in situ observations at the Maqu site. The results indicate improved estimates of soil properties of the topmost layer in comparison to measurements, as well as of the profile. Specifically, both assimilations of TBH lead to over a 48% reduction in root mean square errors (RMSEs) for the retrieved clay fraction from the background compared to the top layer measurements. Both assimilations of TBV reduce RMSEs by 36% for the sand fraction and by 28% for the clay fraction. However, the DA estimated soil moisture and land surface fluxes still exhibit discrepancies when compared to the measurements. The retrieved accurate soil properties alone are inadequate to improve those estimates. The discussed uncertainties (e.g., fixed PTF structures) in the CLM model structures should be mitigated.

A Method for Imaging Energetic Particle Precipitation With Subionospheric VLF Signals

AbstractEnergetic particle precipitation (EPP) is a key loss mechanism for radiation belt particles. Quantification of the precipitation loss rate feeds into the electron lifetimes used by radiation belt models and is needed to improve understanding of radiation belt dynamics. EPP deposits most of its energy in the D‐region ionosphere, a layer so weakly ionized that it is not observed using standard ionosphere measurement techniques. However, very low frequency (VLF) radio signals propagate great distances because of the naturally occurring waveguide formed by Earth’s surface and the D‐region. If the ground conductivity is known along the propagation path to a receiver, then the amplitude and phase of a VLF transmitter signal can be used to infer the average conductivity of the D‐region ionosphere. This article simulates the propagation of narrowband VLF signals through realistic ionosphere profiles enhanced by EPP. By using a distributed array of VLF receivers, the observations can be simultaneously inverted to estimate the spatial extent of a precipitation patch. These images of the ionosphere are generated using the local ensemble transform Kalman filter. We demonstrate this method with several simulated observation experiments, including four EPP events. Precipitation patches are identified in daytime, but accurate estimation of nighttime ionospheres remains a challenge.

A local data assimilation method (Local DA v1.0) and its application in a simulated typhoon case

Abstract. Integrating the hybrid and multiscale analyses and the parallel computation is necessary for current data assimilation schemes. A local data assimilation method, Local DA, is designed to fulfill these needs. This algorithm follows the grid-independent framework of the local ensemble transform Kalman filter (LETKF) and is more flexible in hybrid analysis than the LETKF. Local DA employs an explicitly computed background error correlation matrix of model variables mapped to observed grid points/columns. This matrix allows Local DA to calculate static covariance with a preset correlation function. It also allows the conjugate gradient (CG) method to be used to solve the cost function and allows localization to be performed in model space, observation space, or both spaces (double-space localization). The Local DA performance is evaluated with a simulated multiscale observation network that includes sounding, wind profiler, precipitable water vapor, and radar observations. In the presence of a small-size time-lagged ensemble, Local DA can produce a small analysis error by combining multiscale hybrid covariance and double-space localization. The multiscale covariance is computed using error samples decomposed into several scales and independently assigning the localization radius for each scale. Multiscale covariance is conducive to error reduction, especially at a small scale. The results further indicate that applying the CG method for each local analysis does not result in a discontinuity issue. The wall clock time of Local DA implemented in parallel is halved as the number of cores doubles, indicating a reasonable parallel computational efficiency of Local DA.

A local particle filter and its Gaussian mixture extension implemented with minor modifications to the LETKF

Abstract. A particle filter (PF) is an ensemble data assimilation method that does not assume Gaussian error distributions. Recent studies proposed local PFs (LPFs), which use localization, as in the ensemble Kalman filter, to apply the PF efficiently for high-dimensional dynamics. Among others, Penny and Miyoshi (2016) developed an LPF in the form of the ensemble transform matrix of the local ensemble transform Kalman filter (LETKF). The LETKF has been widely accepted for various geophysical systems, including numerical weather prediction (NWP) models. Therefore, implementing the LPF consistently with an existing LETKF code is useful. This study develops a software platform for the LPF and its Gaussian mixture extension (LPFGM) by making slight modifications to the LETKF code with a simplified global climate model known as Simplified Parameterizations, Primitive Equation Dynamics (SPEEDY). A series of idealized twin experiments were accomplished under the ideal-model assumption. With large inflation by the relaxation to prior spread, the LPF showed stable filter performance with dense observations but became unstable with sparse observations. The LPFGM showed a more accurate and stable performance than the LPF with both dense and sparse observations. In addition to the relaxation parameter, regulating the resampling frequency and the amplitude of Gaussian kernels was important for the LPFGM. With a spatially inhomogeneous observing network, the LPFGM was superior to the LETKF in sparsely observed regions, where the background ensemble spread and non-Gaussianity were larger. The SPEEDY-based LETKF, LPF, and LPFGM systems are available as open-source software on GitHub (https://github.com/skotsuki/speedy-lpf, last access: 16 November 2022) and can be adapted to various models relatively easily, as in the case of the LETKF.

An ensemble Kalman filter system with the Stony Brook Parallel Ocean Model v1.0

Abstract. This study develops an ensemble Kalman filter (EnKF)-based regional ocean data assimilation system in which the local ensemble transform Kalman filter (LETKF) is implemented with version 1.0 of the Stony Brook Parallel Ocean Model (sbPOM) to assimilate satellite and in situ observations at a daily frequency. A series of sensitivity experiments are performed with various settings of the incremental analysis update (IAU) and covariance inflation methods, for which the relaxation-to-prior perturbations and spread (RTPP and RTPS, respectively) and multiplicative inflation (MULT) are considered. We evaluate the geostrophic balance and the analysis accuracy compared with the control experiment in which the IAU and covariance inflation are not applied. The results show that the IAU improves the geostrophic balance, degrades the accuracy, and reduces the ensemble spread, and that the RTPP and RTPS have the opposite effect. The experiment using a combination of the IAU and RTPP results in a significant improvement for both balance and analysis accuracy when the RTPP parameter is 0.8–0.9. The combination of the IAU and RTPS improves the balance when the RTPS parameter is ≤0.8 and increases the analysis accuracy for parameter values between 1.0 and 1.1, but the balance and analysis accuracy are not improved significantly at the same time. The experiments with MULT inflating the forecast ensemble spread by 5 % do not demonstrate sufficient skill in maintaining the balance and reproducing the surface flow field regardless of whether the IAU is applied or not. The 11 d ensemble forecast experiments show consistent results. Therefore, the combination of the IAU and RTPP with a parameter value of 0.8–0.9 is found to be the best setting for the EnKF-based ocean data assimilation system.

Applying prior correlations for ensemble-based spatial localization

Abstract. Localization is an essential technique for ensemble-based data assimilations (DAs) to reduce sampling errors due to limited ensembles. Unlike traditional distance-dependent localization, the correlation cutoff method (Yoshida and Kalnay, 2018; Yoshida, 2019) tends to localize the observation impacts based on their background error correlations. This method was initially proposed as a variable localization strategy for coupled systems, but it can also can be utilized extensively as a spatial localization. This study introduced and examined the feasibility of the correlation cutoff method as an alternative spatial localization with the local ensemble transform Kalman filter (LETKF) preliminary on the Lorenz (1996) model. We compared the accuracy of the distance-dependent and correlation-dependent localizations and extensively explored the potential of the hybrid localization strategies. Our results suggest that the correlation cutoff method can deliver comparable analysis to the traditional localization more efficiently and with a faster DA spin-up. These benefits would become even more pronounced under a more complicated model, especially when the ensemble and observation sizes are reduced.

Global and regional carbon budget for 2015–2020 inferred from OCO-2 based on an ensemble Kalman filter coupled with GEOS-Chem

Abstract. Understanding carbon sources and sinks across the Earth's surface is fundamental in climate science and policy; thus, these topics have been extensively studied but have yet to be fully resolved and are associated with massive debate regarding the sign and magnitude of the carbon budget from global to regional scales. Developing new models and estimates based on state-of-the-art algorithms and data constraints can provide valuable knowledge and contribute to a final ensemble model in which various optimal carbon budget estimates are integrated, such as the annual global carbon budget paper. Here, we develop a new atmospheric inversion system based on the 4D local ensemble transform Kalman filter (4D-LETKF) coupled with the GEOS-Chem global transport model to infer surface-to-atmosphere net carbon fluxes from Orbiting Carbon Observatory-2 (OCO-2) V10r XCO2 retrievals. The 4D-LETKF algorithm is adapted to an OCO-2-based global carbon inversion system for the first time in this work. On average, the mean annual terrestrial and oceanic fluxes between 2015 and 2020 are estimated as − 2.02 and − 2.34 GtC yr−1, respectively, compensating for 21 % and 24 %, respectively, of global fossil carbon dioxide (CO2) emissions (9.80 GtC yr−1). Our inversion results agree with the CO2 atmospheric growth rates reported by the National Oceanic and Atmospheric Administration (NOAA) and reduce the modeled CO2 concentration biases relative to the prior fluxes against surface and aircraft measurements. Our inversion-based carbon fluxes are broadly consistent with those provided by other global atmospheric inversion models, although discrepancies still occur in the land–ocean flux partitioning schemes and seasonal flux amplitudes over boreal and tropical regions, possibly due to the sparse observational constraints of the OCO-2 satellite and the divergent prior fluxes used in different inversion models. Four sensitivity experiments are performed herein to vary the prior fluxes and uncertainties in our inversion system, suggesting that regions that lack OCO-2 coverage are sensitive to the priors, especially over the tropics and high latitudes. In the further development of our inversion system, we will optimize the data-assimilation configuration to fully utilize current observations and increase the spatial and seasonal representativeness of the prior fluxes over regions that lack observations.

Impact of the Ensemble Kalman Filter Based Coupled Data Assimilation System on Seasonal Prediction of Indian Summer Monsoon Rainfall

AbstractThe sensitivity of seasonal prediction (June to September) of Indian monsoon to initial state from two variants of coupled data assimilation (CDA) products, viz. the Climate Forecast System (CFS) Reanalysis (CFSR) and Indian Institute of Tropical Meteorology, University of Maryland‐ Weakly Coupled Analysis (IWCA) is explored in this study. The IWCA implements the local ensemble transform Kalman filter, and incorporates theoretically advanced features of flow‐dependency and ensemble‐based analysis compared to CFSR. The CFS version‐2 predictions using IWCA simulate the large‐scale monsoon features, and convection centers well, and improve prediction skills compared to CFSR predictions. The enhanced analysis quality and Ocean‐Atmospheric cross‐domain equilibrium in IWCA reduce initial shocks in springtime predictions. Further, the sustained ensemble consistency aided to simulate the variability better and improved the seasonal predictions. The study strongly advocates the adaptation of advanced CDA methods for seasonal monsoon and probable seamless predictions.

Improving the joint estimation of CO2 and surface carbon fluxes using a constrained ensemble Kalman filter in COLA (v1.0)

Abstract. Atmospheric inversion of carbon dioxide (CO2) measurements to better understand carbon sources and sinks has made great progress over the last 2 decades. However, most of the studies, including a four-dimensional variational ensemble Kalman filter and Bayesian synthesis approaches, directly obtain only fluxes, while CO2 concentration is derived with the forward model as part of a post-analysis. Kang et al. (2012) used the local ensemble transform Kalman filter (LETKF), which updates the CO2, surface carbon flux (SCF), and meteorology fields simultaneously. Following this track, a system with a short assimilation window and a long observation window was developed (Liu et al., 2019). However, this data assimilation system faces the challenge of maintaining carbon mass conservation. To overcome this shortcoming, here we apply a constrained ensemble Kalman filter (CEnKF) approach to ensure the conservation of global CO2 mass. After a standard LETKF procedure, an additional assimilation is used to adjust CO2 at each model grid point and to ensure the consistency between the analysis and the first guess of the global CO2 mass. Compared to an observing system simulation experiment without mass conservation, the CEnKF significantly reduces the annual global SCF bias from ∼ 0.2 to less than 0.06 Gt and slightly improves the seasonal and annual performance over tropical and southern extratropical regions. We show that this system can accurately track the spatial distribution of annual mean SCF. And the system reduces the seasonal flux root mean square error from a priori to analysis by 48 %–90 %, depending on the continental region. Moreover, the 2015–2016 El Niño impact is well captured with anomalies mainly in the tropics.

Estimation of Flow Field in Natural Convection with Density Stratification by Local Ensemble Transform Kalman Filter

For estimating thermal flow in a nuclear reactor during an accident accurately, it is important to improve the accuracy of computational fluid dynamics simulations. The temperature and flow velocity are not homogeneous and have large variations in a reactor containment vessel because of its very large volume. In addition, Kelm’s work pointed out that the influence of variations of initial and boundary conditions was important. Therefore, it is necessary to set the initial and boundary conditions taking into account the variations of these physical quantities. However, it is a difficult subject to set such complicated initial and boundary conditions. Then, we can obtain realistic initial and boundary conditions and an accurate flow field by data assimilation, and we can improve the accuracy of the simulation result. In this study, we applied data assimilation by a local ensemble transform Kalman filter to a simulation of natural convection behavior in density stratification, and we performed a twin model experiment. We succeeded in estimating the flow fields and improving the simulation accuracy by the data assimilation, even if we applied the boundary condition with error for the true condition.