4D-Var Method Research Articles

Establishment and analysis of a High-Resolution Assimilation Dataset of the water-energy cycle in China

For better prediction and understanding of land-atmospheric interaction, in-situ observed meteorological data acquired from the China Meteorological Administration (CMA) were assimilated in the Weather Research and Forecasting (WRF) model and the monthly Green Vegetation Coverage (GVF) data, which was calculated using the Normalized Difference Vegetation Index (NDVI) of the Earth Observing System Moderate-Resolution Imaging Spectroradiometer (EOS-MODIS) and Digital Elevation Model (DEM) data of the Shuttle Radar Topography Mission (SRTM) system. Furthermore, the WRF model produced a High-Resolution Assimilation Dataset of the water-energy cycle in China (HRADC). This dataset has a horizontal resolution of 25 km for near surface meteorological data, such as air temperature, humidity, wind vectors and pressure (19 levels); soil temperature and moisture (four levels); surface temperature; downward/upward short/long radiation; 3-h latent heat flux; sensible heat flux; and ground heat flux. In this study, we 1) briefly introduce the cycling 3D-Var assimilation method and 2) compare results of meteorological elements, such as 2 m temperature and precipitation generated by the HRADC with the gridded observation data from CMA, and surface temperature and specific humidity with Global Land Data Assimilation System (GLDAS) output data from the National Aeronautics and Space Administration (NASA). We find that the simulated results of monthly 2 m temperature from HRADC is improved compared with the control simulation and has effectively reproduced the observed patterns. The simulated special distribution of ground surface temperature and specific humidity from HRADC are much closer to GLDAS outputs. The spatial distribution of root mean square errors (RMSE) and bias of 2 m temperature between observations and HRADC is reduced compared with the bias between observations and the control run. The monthly spatial distribution of surface temperature and specific humidity from HRADC is consistent with the GLDAS outputs over China. This study could improve the land surface parameters by utilizing remote sensing data and could further improve atmospheric elements with a data assimilation system. This work provides an effective attempt at combining multi-source data with different spatial and temporal scales into numerical simulations, and the simulated results could be used in further research on the long-term climatic effects and characteristics of the water-energy cycle over China.

AN ERROR SUBSPACE PERSPECTIVE ON DATA ASSIMILATION

Two families of methods are widely used in data assimilation: the four-dimensional variational (4D-Var) approach, and the ensemble Kalman filter (EnKF) approach. The two families have been developed largely through parallel research efforts. Each method has its advantages and disadvantages. It is of interest to develop hybrid data assimilation algorithms that can combine the relative strengths of the two approaches. This paper proposes a subspace approach to investigate the theoretical equivalence between the suboptimal 4D-Var method (where only a small number of optimization iterations are performed) and the practical EnKF method (where only a small number of ensemble members are used) in a linear setting. The analysis motivates a new hybrid algorithm: the optimization directions obtained from a short window 4D-Var run are used to construct the EnKF initial ensemble. The proposed hybrid method is computationally less expensive than a full 4D-Var, as only short assimilation windows are considered. The hybrid method has the potential to perform better than the regular EnKF due to its look-ahead property. Numerical results show that the proposed hybrid ensemble filter method performs better than the regular EnKF method for the test problem considered.

An adjoint sensitivity-based data assimilation method and its comparison with existing variational methods

An adjoint sensitivity-based data assimilation (ASDA) method is proposed and applied to a heavy rainfall case over the Korean Peninsula. The heavy rainfall case, which occurred on 26 July 2006, caused torrential rainfall over the central part of the Korean Peninsula. The mesoscale convective system (MCS) related to the heavy rainfall was classified as training line/adjoining stratiform (TL/AS)-type for the earlier period, and back building (BB)-type for the later period. In the ASDA method, an adjoint model is run backwards with forecast-error gradient as input, and the adjoint sensitivity of the forecast error to the initial condition is scaled by an optimal scaling factor. The optimal scaling factor is determined by minimising the observational cost function of the four-dimensional variational (4D-Var) method, and the scaled sensitivity is added to the original first guess. Finally, the observations at the analysis time are assimilated using a 3D-Var method with the improved first guess. The simulated rainfall distribution is shifted northeastward compared to the observations when no radar data are assimilated or when radar data are assimilated using the 3D-Var method. The rainfall forecasts are improved when radar data are assimilated using the 4D-Var or ASDA method. Simulated atmospheric fields such as horizontal winds, temperature, and water vapour mixing ratio are also improved via the 4D-Var or ASDA method. Due to the improvement in the analysis, subsequent forecasts appropriately simulate the observed features of the TL/AS- and BB-type MCSs and the corresponding heavy rainfall. The computational cost associated with the ASDA method is significantly lower than that of the 4D-Var method.

Variational assimilation of remotely sensed flood extents using a 2-D flood model

Abstract. A variational data assimilation (4D-Var) method is proposed to directly assimilate flood extents into a 2-D dynamic flood model to explore a novel way of utilizing the rich source of remotely sensed data available from satellite imagery for better analyzing or predicting flood routing processes. For this purpose, a new cost function is specially defined to effectively fuse the hydraulic information that is implicitly indicated in flood extents. The potential of using remotely sensed flood extents for improving the analysis of flood routing processes is demonstrated by applying the present new data assimilation approach to both idealized and realistic numerical experiments.

Intercomparison and Coupling of Ensemble and Four-Dimensional Variational Data Assimilation Methods for the Analysis and Forecasting of Hurricane Karl (2010)

AbstractThis study examines the performance of ensemble and variational data assimilation systems for the Weather Research and Forecasting (WRF) Model. These methods include an ensemble Kalman filter (EnKF), an incremental four-dimensional variational data assimilation (4DVar) system, and a hybrid system that uses a two-way coupling between the two approaches (E4DVar). The three methods are applied to assimilate routinely collected data and field observations over a 10-day period that spans the life cycle of Hurricane Karl (2010), including the pregenesis disturbance that preceded its development into a tropical cyclone. In general, forecasts from the E4DVar analyses are found to produce smaller 48–72-h forecast errors than the benchmark EnKF and 4DVar methods for all variables and verification methods tested in this study. The improved representation of low- and midlevel moisture and vorticity in the E4DVar analyses leads to more accurate track and intensity predictions by this system. In particular, E4DVar analyses provide persistently more skillful genesis and rapid intensification forecasts than the EnKF and 4DVar methods during cycling. The data assimilation experiments also expose additional benefits of the hybrid system in terms of physical balance, computational cost, and the treatment of asynoptic observations near the beginning of the assimilation window. These factors make it a practical data assimilation method for mesoscale analysis and forecasting, and for tropical cyclone prediction.

The four dimensional variational data assimilation with multiple regularization parameters as a weak constraint (Tikh-4D-Var) and its preliminary application on typhoon initialization

Traditional variational data assimilation (VDA) with only one regularization parameter constraint cannot produce optimal error tuning for all observations. In this paper, a new data assimilation method of “four dimensional variational data assimilation (4D-Var) with multiple regularization parameters as a weak constraint (Tikh-4D-Var)” is proposed by imposing different regularization parameters for different observations. Meanwhile, a new multiple regularization parameters selection method, which is suitable for actual high-dimensional data assimilation system, is proposed based on the posterior information of 4D-Var system. Compared with the traditional single regularization parameter selection method, computation of the proposed multiple regularization parameters selection method is smaller. Based on WRF3.3.1 4D-Var data assimilation system, initialization and simulation of typhoon Chaba (2010) with the new Tikh-4D-Var method are compared with its counterpart 4D-Var to demonstrate the effectiveness of the new method. Results show that the new Tikh-4D-Var method can accelerate the convergence with less iterations. Moreover, compared with 4D-Var method, the typhoon track, intensity (including center surface pressure and maximum wind speed) and structure prediction are obviously improved with Tikh-4D-Var method for 72-h prediction. In addition, the accuracy of the observation error variances can be reflected by the multiple regularization parameters.

Comparison of the ensemble Kalman filter and 4D-Var assimilation methods using a stratospheric tracer transport model

Abstract. An ensemble Kalman filter (EnKF) assimilation method is applied to the tracer transport using the same stratospheric transport model as in the four-dimensional variational (4D-Var) assimilation system BASCOE (Belgian Assimilation System for Chemical ObsErvations). This EnKF version of BASCOE was built primarily to avoid the large costs associated with the maintenance of an adjoint model. The EnKF developed in BASCOE accounts for two adjustable parameters: a parameter α controlling the model error term and a parameter r controlling the observational error. The EnKF system is shown to be markedly sensitive to these two parameters, which are adjusted based on the monitoring of a χ2 test measuring the misfit between the control variable and the observations. The performance of the EnKF and 4D-Var versions was estimated through the assimilation of Aura-MLS (microwave limb sounder) ozone observations during an 8-month period which includes the formation of the 2008 Antarctic ozone hole. To ensure a proper comparison, despite the fundamental differences between the two assimilation methods, both systems use identical and carefully calibrated input error statistics. We provide the detailed procedure for these calibrations, and compare the two sets of analyses with a focus on the lower and middle stratosphere where the ozone lifetime is much larger than the observational update frequency. Based on the observation-minus-forecast statistics, we show that the analyses provided by the two systems are markedly similar, with biases less than 5% and standard deviation errors less than 10% in most of the stratosphere. Since the biases are markedly similar, they most probably have the same causes: these can be deficiencies in the model and in the observation data set, but not in the assimilation algorithm nor in the error calibration. The remarkably similar performance also shows that in the context of stratospheric transport, the choice of the assimilation method can be based on application-dependent factors, such as CPU cost or the ability to generate an ensemble of forecasts.

The Hybrid Local Ensemble Transform Kalman Filter

Abstract Hybrid data assimilation methods combine elements of ensemble Kalman filters (EnKF) and variational methods. While most approaches have focused on augmenting an operational variational system with dynamic error covariance information from an ensemble, this study takes the opposite perspective of augmenting an operational EnKF with information from a simple 3D variational data assimilation (3D-Var) method. A class of hybrid methods is introduced that combines the gain matrices of the ensemble and variational methods, rather than linearly combining the respective background error covariances. A hybrid local ensemble transform Kalman filter (Hybrid-LETKF) is presented in two forms: 1) a traditionally motivated Hybrid/Covariance-LETKF that combines the background error covariance matrices of LETKF and 3D-Var, and 2) a simple-to-implement algorithm called the Hybrid/Mean-LETKF that falls into the new class of hybrid gain methods. Both forms improve analysis errors when using small ensemble sizes and low observation coverage versus either LETKF or 3D-Var used alone. The results imply that for small ensemble sizes, allowing a solution to be found outside of the space spanned by ensemble members provides robustness in both hybrid methods compared to LETKF alone. Finally, the simplicity of the Hybrid/Mean-LETKF design implies that this algorithm can be applied operationally while requiring only minor modifications to an existing operational 3D-Var system.

A variational data assimilation system for soil–atmosphere flux estimates for the Community Land Model (CLM3.5)

Abstract. This paper presents the development and implementation of a spatio-temporal variational data assimilation system (4D-var) for the soil–vegetation–atmosphere transfer model "Community Land Model" (CLM3.5), along with the development of the adjoint code for the core soil–atmosphere transfer scheme of energy and soil moisture. The purpose of this work is to obtain an improved estimation technique for the energy fluxes (sensible and latent heat fluxes) between the soil and the atmosphere. Optimal assessments of these fluxes are neither available from model simulations nor measurements alone, while a 4D-var data assimilation has the potential to combine both information sources by a Best Linear Unbiased Estimate (BLUE). The 4D-var method requires the development of the adjoint model of the CLM which is established in this work. The new data assimilation algorithm is able to assimilate soil temperature and soil moisture measurements for one-dimensional columns of the model grid. Numerical experiments were first used to test the algorithm under idealised conditions. It was found that the analysis delivers improved results whenever there is a dependence between the initial values and the assimilated quantity. Furthermore, soil temperature and soil moisture from in situ field measurements were assimilated. These calculations demonstrate the improved performance of flux estimates, whenever soil property parameters are available of sufficient quality. Misspecifications could also be identified by the performance of the variational scheme.

Assimilating MTSAT-Derived Humidity in Nowcasting Sea Fog over the Yellow Sea

Abstract An extended three-dimensional variational data assimilation (3DVAR) method based on the Weather Research and Forecasting Model (WRF) is developed to assimilate satellite-derived humidity from sea fog at its initial stage over the Yellow Sea. The sea fog properties, including its horizontal distribution and thickness, are retrieved empirically from the infrared and visible cloud imageries of the Multifunctional Transport Satellite (MTSAT). Assuming a relative humidity of 100% in fog, the MTSAT-derived humidity is assimilated by the extended 3DVAR assimilation method. Two sea fog cases, one spread widely over the Yellow Sea and the other spread narrowly along the coast, are first studied in detail with a suite of experiments. For the widespread-fog case, the assimilation of MTSAT-derived information significantly improves the forecast of the sea fog area, increasing the probability of detection and equitable threat scores by about 20% and 15%, respectively. The improvement is attributed to a more realistic representation of the marine boundary layer (MBL) and better descriptions of moisture and temperature profiles. For the narrowly spread coastal case, the model completely fails to reproduce the sea fog event without the assimilation of MTSAT-derived humidity. The extended 3DVAR assimilation method is then applied to 10 more sea fog cases to further evaluate its effect on the model simulations. The results reveal that the assimilation of MTSAT-derived humidity not only improves sea fog forecasts but also provides better moisture and temperature structure information in the MBL.

Evaluation of a Cloud-Scale Lightning Data Assimilation Technique and a 3DVAR Method for the Analysis and Short-Term Forecast of the 29 June 2012 Derecho Event

Abstract This work evaluates the short-term forecast (≤6 h) of the 29–30 June 2012 derecho event from the Advanced Research core of the Weather Research and Forecasting Model (WRF-ARW) when using two distinct data assimilation techniques at cloud-resolving scales (3-km horizontal grid). The first technique assimilates total lightning data using a smooth nudging function. The second method is a three-dimensional variational technique (3DVAR) that assimilates radar reflectivity and radial velocity data. A suite of sensitivity experiments revealed that the lightning assimilation was better able to capture the placement and intensity of the derecho up to 6 h of the forecast. All the simulations employing 3DVAR, however, best represented the storm’s radar reflectivity structure at the analysis time. Detailed analysis revealed that a small feature in the velocity field from one of the six selected radars in the original 3DVAR experiment led to the development of spurious convection ahead of the parent mesoscale convective system, which significantly degraded the forecast. Thus, the relatively simple nudging scheme using lightning data complements the more complex variational technique. The much lower computational cost of the lightning scheme may permit its use alongside variational techniques in improving severe weather forecasts on days favorable for the development of outflow-dominated mesoscale convective systems.

Radar radial wind data assimilation using the time-incremental 4D-Var method implemented to the WRFDA system

In this study, we selected a heavy rainfall case over the Korean Peninsula, which was characterised by two localised rainfall maxima. Neither of the two maxima is accurately simulated when no radar data are assimilated or when radar data are assimilated using the three-dimensional variational (3D-Var) method of the Weather Research and Forecasting Data Assimilation (WRFDA) system. Using the four-dimensional variational (4D-Var) method included in the WRFDA system improves the rainfall forecast partially. To obtain further improvements in the rainfall forecast, outer loops and the time-incremental 4D-Var method are used. In the time-incremental 4D-Var method, the length of the assimilation window is increased gradually, and the starting point of the current minimisation task comes from the minimiser of the previous minimisation task. The analysis of the experiment using outer loops or the time-incremental 4D-Var method is closer to the observations than that of the experiment using the 4D-Var method. This is because the first guess is improved progressively by using outer loops or the time-incremental 4D-Var method. The gap between nonlinear and linear growth is reduced via outer loops or the time-incremental 4D-Var method compared to the 4D-Var method, because the nonlinearity is accounted for by consistently updating the nonlinear model trajectory. However, the rainfall forecast is improved only in the experiment using the time-incremental 4D-Var method. Analysis increments of the horizontal wind and convective available potential energy (CAPE) result in proper modifications to the analysis, and finally, an improved subsequent forecast. The quasi-static adjustment in the time-incremental 4D-Var method may contribute to finding the global minimum under the high degree of nonlinearity present in the original minimisation problem.

An Adjoint-Based Adaptive Ensemble Kalman Filter

Abstract A new hybrid ensemble Kalman filter/four-dimensional variational data assimilation (EnKF/4D-VAR) approach is introduced to mitigate background covariance limitations in the EnKF. The work is based on the adaptive EnKF (AEnKF) method, which bears a strong resemblance to the hybrid EnKF/three-dimensional variational data assimilation (3D-VAR) method. In the AEnKF, the representativeness of the EnKF ensemble is regularly enhanced with new members generated after back projection of the EnKF analysis residuals to state space using a 3D-VAR [or optimal interpolation (OI)] scheme with a preselected background covariance matrix. The idea here is to reformulate the transformation of the residuals as a 4D-VAR problem, constraining the new member with model dynamics and the previous observations. This should provide more information for the estimation of the new member and reduce dependence of the AEnKF on the assumed stationary background covariance matrix. This is done by integrating the analysis residuals backward in time with the adjoint model. Numerical experiments are performed with the Lorenz-96 model under different scenarios to test the new approach and to evaluate its performance with respect to the EnKF and the hybrid EnKF/3D-VAR. The new method leads to the least root-mean-square estimation errors as long as the linear assumption guaranteeing the stability of the adjoint model holds. It is also found to be less sensitive to choices of the assimilation system inputs and parameters.

Assimilation of T‐TREC‐retrieved wind data with WRF 3DVAR for the short‐term forecasting of typhoon Meranti (2010) near landfall

AbstractAn extended Tracking Radar Echo by Correlation (TREC) technique, called T‐TREC technique, has been developed recently to retrieve horizontal circulations within tropical cyclones (TCs) from single Doppler radar reflectivity (Z) and radial velocity (Vr, when available) data. This study explores, for the first time, the assimilation of T‐TREC‐retrieved winds for a landfalling typhoon, Meranti (2010), into a convection‐resolving model, the WRF (Weather Research and Forecasting). The T‐TREC winds or the original Vr data from a single coastal Doppler radar are assimilated at the single time using the WRF three‐dimensional variational (3DVAR), at 8, 6, 4, and 2 h before the landfall of typhoon Meranti. In general, assimilating T‐TREC winds results in better structure and intensity analysis of Meranti than directly assimilating Vr data. The subsequent forecasts for the track, intensity, structure and precipitation are also better, although the differences becomes smaller as the Vr data coverage improves when the typhoon gets closer to the radar. The ability of the T‐TREC retrieval in capturing more accurate and complete vortex circulations in the inner‐core region of TC is believed to be the primary reason for its superior performance over direct assimilation of Vr data; for the latter, the data coverage is much smaller when the TC is far away and the cross‐beam wind component is difficult to analyze accurately with 3DVAR method.

Analysis of the 3DVAR filter for the partially observed Lorenz'63 model

The problem of effectively combining data with a mathematical model constitutes a major challenge in applied mathematics. It is particular challenging for high-dimensional dynamical systems where data is received sequentially in time and the objective is to estimate the system state in an on-line fashion; this situation arises, for example, in weather forecasting. The sequential particle filter is then impractical and ad hoc filters, which employ some form of Gaussian approximation, are widely used. Prototypical of these ad hoc filters is the 3DVAR method. The goal of this paper is to analyze the 3DVAR method, using the Lorenz '63 model to exemplify the key ideas. The situation where the data is partial and noisy is studied, and both discrete time and continuous time data streams are considered. The theory demonstrates how the widely used technique of variance inflation acts to stabilize the filter, and hence leads to asymptotic accuracy.

Notes and correspondence on ensemble-based three-dimensional variational filters

Several ensemble-based three-dimensional variational (3D-Var) filters are compared. These schemes replace the static background error covariance of the traditional 3D-Var with the ensemble forecast error covariance, but generate analysis ensemble anomalies (perturbations) in different ways. However, it is demonstrated in this paper that they are all theoretically equivalent to the ensemble transformation Kalman filter (ETKF). Furthermore, a new method named EnPSAS is presented. The analysis shows that EnPSAS has a small condition number and can apply covariance localization more easily than other ensemble-based 3D-Var methods.

Impacts of Assimilating Measurements of Different State Variables with a Simulated Supercell Storm and Three-Dimensional Variational Method

Abstract This paper investigates the impacts of assimilating measurements of different state variables, which can be potentially available from various observational platforms, on the cycled analysis and short-range forecast of supercell thunderstorms by performing a set of observing system simulation experiments (OSSEs) using a storm-scale three-dimensional variational data assimilation (3DVAR) method. The control experiments assimilate measurements every 5 min for 90 min. It is found that the assimilation of horizontal wind can reconstruct the storm structure rather accurately. The assimilation of vertical velocity , potential temperature , or water vapor can partially rebuild the thermodynamic and precipitation fields but poorly retrieves the wind fields. The assimilation of rainwater mixing ratio can build up the precipitation fields together with a reasonable cold pool but is unable to properly recover the wind fields. Overall, data have the greatest impact, while have the second largest impact. The impact of is the smallest. The impact of assimilation frequency is examined by comparing results using 1-, 5-, or 10-min assimilation intervals. When is assimilated every 5 or 10 min, the analysis quality can be further improved by the incorporation of additional types of observations. When are assimilated every minute, the benefit from additional types of observations is negligible, except for . It is also found that for , , and measurements, more frequent assimilation leads to more accurate analyses. For and , a 1-min assimilation interval does not produce a better analysis than a 5-min interval.

E3DVar: Coupling an Ensemble Kalman Filter with Three-Dimensional Variational Data Assimilation in a Limited-Area Weather Prediction Model and Comparison to E4DVar

Abstract This study examines the performance of a hybrid ensemble-variational data assimilation system (E3DVar) that couples an ensemble Kalman filter (EnKF) with the three-dimensional variational data assimilation (3DVar) system for the Weather Research and Forecasting (WRF) Model. The performance of E3DVar and the component EnKF and 3DVar systems are compared over the eastern United States for June 2003. Conventional sounding and surface observations as well as data from wind profilers, aircraft and ships, and cloud-tracked winds from satellites, are assimilated every 6 h during the experiments, and forecasts are verified using standard sounding observations. Forecasts with 12- to 72-h lead times are found to have noticeably smaller root-mean-square errors when initialized with the E3DVar system, as opposed to the EnKF, especially for the 12-h wind and moisture fields. The E3DVar system demonstrates similar performance as an EnKF, while using less than half the number of ensemble members, and is less sensitive to the use of a multiphysics ensemble to account for model errors. The E3DVar system is also compared with a similar hybrid method that replaces the 3DVar component with the WRF four-dimensional variational data assimilation (4DVar) method (denoted E4DVar). The E4DVar method demonstrated considerable improvements over E3DVar for nearly all model levels and variables at the shorter forecast lead times (12–48 h), but the forecast accuracies of all three ensemble-based methods (EnKF, E3DVar, and E4DVar) converge to similar results at longer lead times (60–72 h). Nevertheless, all methods that used ensemble information produced considerably better forecasts than the two methods that relied solely on static background error covariance (i.e., 3DVar and 4DVar).

3DVAR versus Traditional Dual-Doppler Wind Retrievals of a Simulated Supercell Thunderstorm

Abstract Use of the three-dimensional variational data assimilation (3DVAR) framework in dual-Doppler wind analysis (DDA) offers several advantages over traditional techniques. Perhaps the most important is that the errors that result from explicit integration of the mass continuity equation in traditional methods are avoided. In this study, observing system simulation experiments (OSSEs) are used to compare supercell thunderstorm wind retrievals from a 3DVAR DDA technique and three traditional DDA methods. The 3DVAR technique produces better wind retrievals near the top of the storm than the traditional methods in the experiments. This is largely attributed to the occurrence of severe errors aloft in the traditional retrievals whether the continuity equation integration proceeds upward (due to vertically accumulating errors), downward (due to severe boundary condition errors arising from uncertainty in the horizontal divergence field aloft), or in both directions. Smaller, but statistically significant, improvement occurs near the ground using the 3DVAR method. When lack of upper-level observations prevents application of a top boundary condition in the traditional DDA framework, the 3DVAR approach produces better analyses at all levels. These results strongly suggest the 3DVAR DDA framework is generally preferable to traditional formulations.

A 20-year reanalysis experiment in the Baltic Sea using three-dimensional variational (3DVAR) method

Abstract. A 20-year retrospective reanalysis of the ocean state in the Baltic Sea is constructed by assimilating available historical temperature and salinity profiles into an operational numerical model with three-dimensional variational (3DVAR) method. To determine the accuracy of the reanalysis, the authors present a series of comparisons to independent observations on a monthly mean basis. In the reanalysis, temperature (T) and salinity (S) fit better with independent measurements than the free run at different depths. Overall, the mean biases of temperature and salinity for the 20 year period are reduced by 0.32 °C and 0.34 psu, respectively. Similarly, the mean root mean square error (RMSE) is decreased by 0.35 °C for temperature and 0.3 psu for salinity compared to the free run. The modeled sea surface temperature, which is mainly controlled by the weather forcing, shows the least improvements due to sparse in situ observations. Deep layers, on the other hand, witness significant and stable model error improvements. In particular, the salinity related to saline water intrusions into the Baltic Proper is largely improved in the reanalysis. The major inflow events such as in 1993 and 2003 are captured more accurately as the model salinity in the bottom layer is increased by 2–3 psu. Compared to independent sea level at 14 tide gauge stations, the correlation between model and observation is increased by 2%–5%, while the RMSE is generally reduced by 10 cm. It is found that the reduction of RMSE comes mainly from the reduction of mean bias. In addition, the changes in density induced by the assimilation of T/S contribute little to the barotropic transport in the shallow Danish Transition zone. The mixed layer depth exhibits strong seasonal variations in the Baltic Sea. The basin-averaged value is about 10 m in summer and 30 m in winter. By comparison, the assimilation induces a change of 20 m to the mixed layer depth in deep waters and wintertime, whereas small changes of about 2 m occur in summer and shallow waters. It is related to the strong heating in summer and the dominant role of the surface forcing in shallow water, which largely offset the effect of the assimilation.