Variational Data Assimilation Framework Research Articles

Impact of Assimilating GK-2A All-Sky Radiance with a New Observation Error for Summer Precipitation Forecasting

In the assimilation of all-sky radiance (ASR), the non-Gaussian behaviour of observation-minus-background (OMB) departures has been the major issue. Treating observation error properly should give the distribution OMB departures closer to Gaussian on which data assimilation systems are based. This study introduces a look-up-table (LUT) observation error inflation (LOEI) for assimilating ASR from three water vapor channels of GEO-KOMPSAT-2A (GK-2A) geostationary satellite based on a three-dimensional variational data assimilation (3DVAR) framework. The impacts are assessed based on summer precipitation cases over South Korea. To confirm all kinds of radiance observations, the ASRs are assimilated without any quality control procedures. The LOEI adopt a pre-estimated radiance error statistics by using the higher order fitting function of cloud amount (CA) and standard deviation (STD) of OMB departures. This LOEI was produced during the summer period from August 1 to 30, 2020, representing the characteristics of the atmosphere condition during the experimental period. The promising impact of LOEI is demonstrated in comparison with the inflated observation error using a simple linier function proposed by Geer and Bauer (GBOEI). Study results revealed the LOEI normalized OMB departures into much more Gaussian form than the GBOEI. Hence, the assimilation of ASR using LOEI (ExpLOEI) produced BT analysis closer to the observation in four cloud phases in contrast with ASR assimilation using GBOEI (ExpGBOEI), which obviously found in the ice phase. The better BT analysis eventually simulated more realistic moisture and temperature variables in the background field. Consequently, the ExpLOEI exhibited more accuracy in precipitation location and intensity compared to the experiment with ExpGBOEI.

A Variational Framework for Coupled Estimation of Evapotranspiration and Recharge Fluxes by Assimilating Land Surface Soil Moisture and Temperature

The evapotranspiration and recharge are the key fluxes that link the land's water and energy cycles. These fluxes have major impacts on agriculture, water supply system, water resources planning, climate, etc. Accurate mapping of these fluxes is limited due to lack of in-situ observation sites and errors in estimation from numerical models. The dynamics of land surface state observations, specifically land surface soil moisture (SM) and temperature (LST), have implicit information on the partitioning of evapotranspiration and recharge fluxes, which provides an opportunity for global mapping of these fluxes across a range of spatial and temporal scales. In this study, a variational data assimilation (VDA) framework is developed for coupled estimation of evapotranspiration and recharge fluxes by assimilating LST and SM observations into a coupled water and energy balance model. We modified LIDA framework (Abdolghafoorian and Farhadi, 2019) to calculate the effective soil hydraulic parameters required for estimating the recharge flux in addition to evaporative flux parameters. Two numerical experiments are conducted using synthetic dataset generated by Hydrus 1-D model to test the accuracy and feasibility of the proposed estimation framework. Second-order information is used to estimate the uncertainty of the estimated parameters and fluxes and guide toward a well-posed optimization problem. Results demonstrate the success of the VDA framework in estimating evaporative and recharge fluxes from implicit information contained in SM and LST data and feasibility test results show promise in extending the framework to large scale using remotely sensed observations.

Comparisons of Hybrid En3DVar with 3DVar and EnKF for Radar Data Assimilation: Tests with the 10 May 2010 Oklahoma Tornado Outbreak

AbstractIn this study, a hybrid En3DVar data assimilation (DA) scheme is compared with 3DVar, EnKF, and pure En3DVar for the assimilation of radar data in a real tornadic storm case. Results using hydrometeor mixing ratios (CVq) or logarithmic mixing ratios (CVlogq) as the control variables are compared in the variational DA framework. To address the lack of radial velocity impact issues when using CVq, a procedure that assimilates reflectivity and radial velocity data in two separate analysis passes is adopted. Comparisons are made in terms of the root-mean-square innovations (RMSIs) as well as the intensity and structure of the analyzed and forecast storms. For pure En3DVar that uses 100% ensemble covariance, CVlogq and CVq have similar RMSIs in the velocity analyses, but errors grow faster during forecasts when using CVlogq. Introducing static background error covariance at 5% in hybrid En3DVar (with CVlogq) significantly reduces the forecast error growth. Pure En3DVar produces more intense reflectivity analyses than EnKF that more closely match the observations. Hybrid En3DVar with 50% outperforms other weights in terms of the RMSIs and forecasts of updraft helicity and is thus used in the final comparison with 3DVar and EnKF. The hybrid En3DVar is found to outperform EnKF in better capturing the intensity and structure of the analyzed and forecast storms and outperform 3DVAR in better capturing the intensity and evolution of the rotating updraft.

Feasibility of Estimating Turbulent Heat Fluxes via Variational Assimilation of Reference-Level Air Temperature and Specific Humidity Observations

This study investigated the feasibility of partitioning the available energy between sensible (H) and latent (LE) heat fluxes via variational assimilation of reference-level air temperature and specific humidity. For this purpose, sequences of reference-level air temperature and specific humidity were assimilated into an atmospheric boundary layer model (ABL) within a variational data assimilation (VDA) framework to estimate H and LE. The VDA approach was tested at six sites (namely, Arou, Audubon, Bondville, Brookings, Desert, and Willow Creek) with contrasting climatic and vegetative conditions. The unknowns of the VDA system were the neutral bulk heat transfer coefficient (CHN) and evaporative fraction (EF). EF estimates were found to agree well with observations in terms of magnitude and day-to-day fluctuations in wet/densely vegetated sites but degraded in dry/sparsely vegetated sites. Similarly, in wet/densely vegetated sites, the variations in the CHN estimates were found to be consistent with those of the leaf area index (LAI) while this consistency deteriorated in dry/sparely vegetated sites. The root mean square errors (RMSEs) of daily H and LE estimates at the Arou site (wet) were 25.43 (Wm−2) and 55.81 (Wm−2), which are respectively 57.6% and 45.4% smaller than those of 60.00 (Wm−2) and 102.21 (Wm−2) at the Desert site (dry). Overall, the results show that the VDA system performs well at wet/densely vegetated sites (e.g., Arou and Willow Creek), but its performance degrades at dry/slightly vegetated sites (e.g., Desert and Audubon). These outcomes show that the sequences of reference-level air temperature and specific humidity have more information on the partitioning of available energy between the sensible and latent heat fluxes in wet/densely vegetated sites than dry/slightly vegetated sites.

A Four Dimensional Variational Data Assimilation Framework for Wind Energy Potential Estimation

In this paper, we propose a Four-Dimensional Variational (4D-Var) data assimilation framework for wind energy potential estimation. The framework is defined as follows: we choose a numerical model which can provide forecasts of wind speeds then, an ensemble of model realizations is employed to build control spaces at observation steps via a modified Cholesky decomposition. These control spaces are utilized to estimate initial analysis increments and to avoid the intrinsic use of adjoint models in the 4D-Var context. The initial analysis increments are mapped back onto the model domain from which we obtain an estimate of the initial analysis ensemble. This ensemble is propagated in time to approximate the optimal analysis trajectory. Wind components are post-processed to get wind speeds and to estimate wind energy capacities. A matrix-free analysis step is derived from avoiding the direct inversion of covariance matrices during assimilation cycles. Numerical simulations are employed to illustrate how our proposed framework can be employed in operational scenarios. A catalogue of twelve Wind Turbine Generators (WTGs) is utilized during the experiments. The results reveal that our proposed framework can properly estimate wind energy potential capacities for all wind turbines within reasonable accuracies (in terms of Root-Mean-Square-Error) and even more, these estimations are better than those of traditional 4D-Var ensemble-based methods. Moreover, large variability (variance of standard deviations) of errors are evidenced in forecasts of wind turbines with the largest rate-capacity while homogeneous variability can be seen in wind turbines with the lowest rate-capacity.

Estimation of Turbulent Heat Fluxes via Assimilation of Air Temperature and Specific Humidity into an Atmospheric Boundary Layer Model

AbstractA number of studies have used time series of air temperature and specific humidity observations to estimate turbulent heat fluxes. These studies require the specification of surface roughness lengths for heat and momentum (that are directly related to the neutral bulk heat transfer coefficientCHN) and/or ground heat flux, which are often unavailable. In this study, sequences of air temperature and specific humidity are assimilated into an atmospheric boundary layer model within a variational data assimilation (VDA) framework to estimateCHN, evaporative fraction (EF), turbulent heat fluxes, and atmospheric boundary layer (ABL) height, potential temperature, and humidity. The developed VDA approach needs neither the surface roughness parameterization (as it is optimized by the VDA approach) nor ground heat flux measurements. The VDA approach is tested over the First International Satellite Land Surface Climatology Project Field Experiment (FIFE) site in the summers of 1987 and 1988. The results indicate that the estimated sensible and latent heat fluxes agree fairly well with the corresponding measurements. For FIFE 1987 (1988), the daily sensible and latent heat fluxes estimates have a root-mean-square error of 25.72 W m−2(27.77 W m−2) and 53.63 W m−2(48.22 W m−2), respectively. In addition, the ABL height, specific humidity, and potential temperature estimates from the VDA system are in good agreement with those inferred from the radiosondes both in terms of magnitude and diurnal trend.

Impact of the variational assimilation of ground-based GNSS zenith total delay into AROME-Morocco model

The impact of assimilating zenith total delay (ZTD) observations from the Moroccan ground-based Global Navigation Satellite System (GNSS) network into the high-resolution operational model AROME-Morocco (2.5 km) is assessed over one month. The objective is to investigate the impact on moisture field and rainy event forecasts in a three-dimensional variational (3D-Var) data assimilation framework with a 3-hour cycling. As a first step, a pre-processing of ZTD observations is performed for quality control and bias correction and it points out that all GNSS stations available in the network can be potentially assimilated. Then, two parallel experiments, with and without assimilation of GNSS ZTD, are performed during February–March 2018, for 48-hour lead times. Compared against other observation systems of humidity (radiosonde and surface network), a small and beneficial improvement is found in the atmospheric moisture short-range forecast, despite the limited number of GNSS stations over Morocco. The impact of assimilating GNSS ZTD data on precipitation forecasts is evaluated both subjectively and objectively. The objective precipitation scores against daily rain gauge observations show that the impact is mixed, positive for larger rainfall accumulations and neutral to negative for smaller rainfall accumulations. A specific evaluation for a case study of a rain event highlights an improvement in terms of intensity and location of precipitating areas when GNSS ZTD observations are assimilated.

The Quest for Model Uncertainty Quantification: A Hybrid Ensemble and Variational Data Assimilation Framework.

This article presents a novel approach to couple a deterministic four‐dimensional variational (4DVAR) assimilation method with the particle filter (PF) ensemble data assimilation system, to produce a robust approach for dual‐state‐parameter estimation. In our proposed method, the Hybrid Ensemble and Variational Data Assimilation framework for Environmental systems (HEAVEN), we characterize the model structural uncertainty in addition to model parameter and input uncertainties. The sequential PF is formulated within the 4DVAR system to design a computationally efficient feedback mechanism throughout the assimilation period. In this framework, the 4DVAR optimization produces the maximum a posteriori estimate of state variables at the beginning of the assimilation window without the need to develop the adjoint of the forecast model. The 4DVAR solution is then perturbed by a newly defined prior error covariance matrix to generate an initial condition ensemble for the PF system to provide more accurate and reliable posterior distributions within the same assimilation window. The prior error covariance matrix is updated from one cycle to another over the main assimilation period to account for model structural uncertainty resulting in an improved estimation of posterior distribution. The premise of the presented approach is that it (1) accounts for all sources of uncertainties involved in hydrologic predictions, (2) uses a small ensemble size, and (3) precludes the particle degeneracy and sample impoverishment. The proposed method is applied on a nonlinear hydrologic model and the effectiveness, robustness, and reliability of the method is demonstrated for several river basins across the United States.

Parameter identification techniques applied to an environmental pollution model

The retrieval of parameters related to an environmental model is explored. We address computational challenges occurring due to a significant numerical difference of up to two orders of magnitude between the two model parameters we aim to retrieve. First, the corresponding optimization problem is poorly scaled, causing minimization algorithms to perform poorly (see Gill et al., practical optimization, AP, 1981,401pp ). This issue is addressed by proper rescaling. Difficulties also arise from the presence of strong nonlinearity and ill-posedness which means that the parameters do not converge to a single deterministic set of values, but rather there exists a range of parameter combinations that produce the same model behavior. We address these computational issues by the addition of a regularization term in the cost function. All these computational approaches are addressed in the framework of variational adjoint data assimilation. The used observational data are derived from numerical simulation results located at only two spatial points. The effect of different initial guess values of parameters on retrieval results is also considered. As indicated by results of numerical experiments, the method presented in this paper achieves a near perfect parameter identification, and overcomes the indefiniteness that may occur in inversion process even in the case of noisy input data.

Optimal sensor placement for variational data assimilation of unsteady flows past a rotationally oscillating cylinder

An optimal sensor placement procedure is proposed within the framework of variational data assimilation (DA) for unsteady flows, with the aim of maximizing the efficiency of the DA procedure. It is dedicated to the a priori design of a sensor network, and relies on a first-order adjoint approach. The proposed methodology first consists in identifying, via optimal control, the locations in the flow that have the greatest sensitivity with respect to a change in the initial condition, boundary conditions or model parameters. In a second step, sensors are placed at these locations for DA purposes. The use of this optimal sensor placement procedure does not require extra development in the case where a variational DA suite is available. The proposed methodology is applied to the reconstruction of unsteady bidimensional flows past a rotationally oscillating cylinder. More precisely, the possibilities of reconstructing the rotational speed of the cylinder and the initial flow, which here encompasses upstream conditions, from various types of observations are investigated via variational DA. Then, the observation optimization procedure is employed to identify optimal locations for placing velocity sensors downstream of the cylinder. Both reduction in the computational cost and improvement in the quality of the reconstructed flow are achieved through optimal sensor placement, encouraging the application of the proposed methodology to more complex and realistic flows.

Characterizing the Effect of Vegetation Dynamics on the Bulk Heat Transfer Coefficient to Improve Variational Estimation of Surface Turbulent Fluxes

Abstract Estimation of turbulent heat fluxes by assimilating sequences of land surface temperature (LST) observations into a variational data assimilation (VDA) framework has been the subject of numerous studies. The VDA approaches are focused on the estimation of two key parameters that regulate the partitioning of available energy between sensible and latent heat fluxes. These parameters are neutral bulk heat transfer coefficient CHN and evaporative fraction (EF). The CHN mainly depends on the roughness of the surface and varies on the time scale of changing vegetation phenology. The existing VDA methods assumed that the variations in vegetation phenology over the period of one month are negligible and took CHN as a monthly constant parameter. However, during the growing season, bare soil may turn into a fully vegetated surface within a few weeks. Thus, assuming a constant CHN may result in a significant error in the estimation of surface fluxes, especially in regions with a high temporal variation in vegetation cover. In this study the VDA approach is advanced by taking CHN as a function of leaf area index (LAI). This allows the characterization of the dynamic effect of vegetation phenology on CHN. The performance of the new VDA model is tested over three sites in the United States and one site in China. The results show that the new model outperforms the previous one and reduces the root-mean-square error (and bias) in sensible and latent heat flux estimates across the four sites on average by 31% (61%) and 21% (37%), respectively.

Using lagged covariances in data assimilation

This paper describes a novel method to incorporate significantly time-lagged data into a sequential variational data assimilation framework. The proposed method can assimilate data that appear many assimilation window lengths in the future, providing a mechanism to gradually dynamically adjust the model towards those data. The method avoids the need for an adjoint model, significantly reducing computational requirements compared to standard four-dimensional variational assimilation. Simulation studies are used to test the assimilation methodology in a variety of situations. The use of lagged covariances is shown to provide robust improvements to the assimilation quality, particularly if data at multiple lags are used to influence the cost function in each window. The methodology developed can be used to improve contemporary global reanalyses by incorporating time-lagged observations that may otherwise not be exploited to their full potential.

Design of the control set in the framework of variational data assimilation

Solving data assimilation problems under uncertainty in basic model parameters and in source terms may require a careful design of the control set. The task is to avoid such combinations of the control variables which may either lead to ill-posedness of the control problem formulation or compromise the robustness of the solution procedure. We suggest a method for quantifying the performance of a control set which is formed as a subset of the full set of uncertainty-bearing model inputs. Based on this quantity one can decide if the chosen ‘safe’ control set is sufficient in terms of the prediction accuracy. Technically, the method presents a certain generalization of the ‘variational’ uncertainty quantification method for observed systems. It is implemented as a matrix-free method, thus allowing high-dimensional applications. Moreover, if the Automatic Differentiation is utilized for computing the tangent linear and adjoint mappings, then it could be applied to any multi-input ‘black-box’ system. As application example we consider the full Saint-Venant hydraulic network model SIC2, which describes the flow dynamics in river and canal networks. The developed methodology seem useful in the context of the future SWOT satellite mission, which will provide observations of river systems the properties of which are known with quite a limited precision.

Uncertainty Quantification in Land Surface Hydrologic Modeling: Toward an Integrated Variational Data Assimilation Framework

Variational data assimilation (VDA) is an effective technique for the estimation of land surface heat fluxes. In this method, sequences of remotely sensed land surface temperature measurements are assimilated into a dynamic surface energy balance model to estimate the key unknown parameters of the turbulent heat fluxes. Despite the advantages of the VDA technique in the retrieval of land surface heat fluxes, it suffers from a key limitation, which is its tendency to be ill posed. Moreover, unlike ensemble-based schemes, the VDA method itself does not provide estimates of the predictive uncertainty of estimated parameters and, thus, retrieved fluxes. This research addresses these shortcomings by proposing an uncertainty quantification (UQ) framework for the VDA technique. The proposed framework utilizes uncertainty analysis and analysis of error covariance approximation as a tool to quantify the uncertainty of estimated parameters and to guide the formulation of a well-posed estimation problem. It provides a calibration-free tool to assess the performance of the VDA technique in retrieving land surface heat fluxes over a range of land surfaces and climatic conditions. The UQ framework suggests that the VDA approach performs poorly over wet and highly vegetated land surface regions and when the difference between land surface and air temperature is low. Moreover, it reveals that characterizing the effect of vegetation dynamics on the bulk heat transfer coefficient reduces the correlation between unknown parameters and, hence, leads to a more robust estimation of parameters.

A framework for variational data assimilation with superparameterization

Abstract. Superparameterization (SP) is a multiscale computational approach wherein a large scale atmosphere or ocean model is coupled to an array of simulations of small scale dynamics on periodic domains embedded into the computational grid of the large scale model. SP has been successfully developed in global atmosphere and climate models, and is a promising approach for new applications, but there is currently no practical data assimilation framework that can be used with these models. The authors develop a 3D-Var variational data assimilation framework for use with SP; the relatively low cost and simplicity of 3D-Var in comparison with ensemble approaches makes it a natural fit for relatively expensive multiscale SP models. To demonstrate the assimilation framework in a simple model, the authors develop a new system of ordinary differential equations similar to the two-scale Lorenz-'96 model. The system has one set of variables denoted {Yi}, with large and small scale parts, and the SP approximation to the system is straightforward. With the new assimilation framework the SP model approximates the large scale dynamics of the true system accurately.

AVALIAÇÃO DA TEMPERATURA DE BRILHO NOS CANAIS SENSÍVEIS À SUPERFÍCIE TERRESTRE NO SISTEMA G3DVAR DO CPTEC/INPE: SÉRIE NOAA

As medidas do AMSU-A para os canais que são sensíveis à superfície terrestre sobre os continentes não tem sido amplamente utilizadas para ajustar a previsão numérica de tempo de curto prazo (PNTs), devido à complexidade das características da superfície terrestre. Nesse sentido, o presente artigo utiliza o Sistema de Assimilação de Dados (G3DVAR) do Centro de Previsão de Tempo e Estudos Climáticos do Instituto Nacional de Pesquisas Espaciais (CPTEC/INPE), que inclui tais medidas de radiâncias feitas pelo sensor que está a bordo dos satélites da série NOAA. A versão operacional do sistema G3DVAR contempla apenas o satélite NOAA-15. Adicionalmente, foram realizados experimentos numéricos que incluíram os satélites NOAA-18 e NOAA-19. É feita uma avaliação sobre a variável temperatura de brilho simulada para os canais sensíveis à superfície terrestre (i), através de uma comparação com observações, e (ii) através da avaliação da equação de transferência radiativa, para os três satélites. Os resultados indicaram que o modelo de transferência radiativa em média superestima a temperatura de brilho nos canais sensíveis à superfície terrestre para os três satélites na região da América do Sul para os meses de verão. Além disso, as observações dos satélites incorporadas no sistema tiveram um aceite superior ao do satélite NOAA-15, de maneira que os satélites NOAA-18 e NOAA-19 podem ser incorporados no modo operacional do Sistema G3DVAR.

Model–data fusion across ecosystems: from multisite optimizations to global simulations

Abstract. This study uses a variational data assimilation framework to simultaneously constrain a global ecosystem model with eddy covariance measurements of daily net ecosystem exchange (NEE) and latent heat (LE) fluxes from a large number of sites grouped in seven plant functional types (PFTs). It is an attempt to bridge the gap between the numerous site-specific parameter optimization works found in the literature and the generic parameterization used by most land surface models within each PFT. The present multisite approach allows deriving PFT-generic sets of optimized parameters enhancing the agreement between measured and simulated fluxes at most of the sites considered, with performances often comparable to those of the corresponding site-specific optimizations. Besides reducing the PFT-averaged model–data root-mean-square difference (RMSD) and the associated daily output uncertainty, the optimization improves the simulated CO2 balance at tropical and temperate forests sites. The major site-level NEE adjustments at the seasonal scale are reduced amplitude in C3 grasslands and boreal forests, increased seasonality in temperate evergreen forests, and better model–data phasing in temperate deciduous broadleaf forests. Conversely, the poorer performances in tropical evergreen broadleaf forests points to deficiencies regarding the modelling of phenology and soil water stress for this PFT. An evaluation with data-oriented estimates of photosynthesis (GPP – gross primary productivity) and ecosystem respiration (Reco) rates indicates distinctively improved simulations of both gross fluxes. The multisite parameter sets are then tested against CO2 concentrations measured at 53 locations around the globe, showing significant adjustments of the modelled seasonality of atmospheric CO2 concentration, whose relevance seems PFT-dependent, along with an improved interannual variability. Lastly, a global-scale evaluation with remote sensing NDVI (normalized difference vegetation index) measurements indicates an improvement of the simulated seasonal variations of the foliar cover for all considered PFTs.

Estimation of surface turbulent heat fluxes via variational assimilation of sequences of land surface temperatures from Geostationary Operational Environmental Satellites

Recently, a number of studies have focused on estimating surface turbulent heat fluxes via assimilation of sequences of land surface temperature (LST) observations into variational data assimilation (VDA) schemes. Using the full heat diffusion equation as a constraint, the surface energy balance equation can be solved via assimilation of sequences of LST within a VDA framework. However, the VDA methods have been tested only in limited field sites that span only a few climate and land use types. Hence, in this study, combined-source (CS) and dual-source (DS) VDA schemes are tested extensively over six FluxNet sites with different vegetation covers (grassland, cropland, and forest) and climate conditions. The CS model groups the soil and canopy together as a single source and does not consider their different contributions to the total turbulent heat fluxes, while the DS model considers them to be different sources. LST data retrieved from the Geostationary Operational Environmental Satellites are assimilated into these two VDA schemes. Sensible and latent heat flux estimates from the CS and DS models are compared with the corresponding measurements from flux tower stations. The results indicate that the performance of both models at dry, lightly vegetated sites is better than that at wet, densely vegetated sites. Additionally, the DS model outperforms the CS model at all sites, implying that the DS scheme is more reliable and can characterize the underlying physics of the problem better.

A GSI-Based Coupled EnSRF–En3DVar Hybrid Data Assimilation System for the Operational Rapid Refresh Model: Tests at a Reduced Resolution

Abstract A coupled ensemble square root filter–three-dimensional ensemble-variational hybrid (EnSRF–En3DVar) data assimilation (DA) system is developed for the operational Rapid Refresh (RAP) forecasting system. The En3DVar hybrid system employs the extended control variable method, and is built on the NCEP operational gridpoint statistical interpolation (GSI) three-dimensional variational data assimilation (3DVar) framework. It is coupled with an EnSRF system for RAP, which provides ensemble perturbations. Recursive filters (RF) are used to localize ensemble covariance in both horizontal and vertical within the En3DVar. The coupled En3DVar hybrid system is evaluated with 3-h cycles over a 9-day period with active convection. All conventional observations used by operational RAP are included. The En3DVar hybrid system is run at ⅓ of the operational RAP horizontal resolution or about 40-km grid spacing, and its performance is compared to parallel GSI 3DVar and EnSRF runs using the same datasets and resolution. Short-term forecasts initialized from the 3-hourly analyses are verified against sounding and surface observations. When using equally weighted static and ensemble background error covariances and 40 ensemble members, the En3DVar hybrid system outperforms the corresponding GSI 3DVar and EnSRF. When the recursive filter coefficients are tuned to achieve a similar height-dependent localization as in the EnSRF, the En3DVar results using pure ensemble covariance are close to EnSRF. Two-way coupling between EnSRF and En3DVar did not produce noticeable improvement over one-way coupling. Downscaled precipitation forecast skill on the 13-km RAP grid from the En3DVar hybrid is better than those from GSI 3DVar analyses.

Variational assimilation of land surface temperature and the estimation of surface energy balance components

Recently, numerous studies have focused on the estimation of surface energy flux components, based on the assimilation of land surface temperature (LST) within a variational data assimilation (VDA) framework. Unlike the previous investigations based on the force-restore equation, in this study, the full heat diffusion equation is employed in the VDA scheme as an adjoint (constraint). In addition, a model error term is added to the surface energy balance (SEB) equation and the VDA scheme to include the model uncertainty. Both VDA schemes (with and without the model uncertainty) are tested over the First International Satellite Land Surface Climatology Project Field Experiment (FIFE) site. The comprehensive comparisons between the present model (with heat diffusion equation) and previous model (with the force-restore equation) demonstrate that the present model will decrease the phase error associated with the ground heat flux diurnal cycle, and improve the evaporative fraction and heat fluxes estimation. The numerical examples also conclude that the errors caused by model structures and noisy data in the SEB equation can be detected and quantified in the present model (with model uncertainty).