Variational Data Assimilation Experiments Research Articles

Block-Circulant Approximation of the Precision Matrix for Assimilating SWOT Altimetry Data

The recently deployed Surface Water and Ocean Topography (SWOT) mission for the first time has observed the ocean surface at a spatial resolution of 1 km, thus giving an opportunity to directly monitor submesoscale sea surface height (SSH) variations that have a typical magnitude of a few centimeters. This progress comes at the expense of the necessity to take into account numerous uncertainties in calibration of the quality-controlled altimeter data. Of particular importance is the proper filtering of spatially correlated errors caused by the uncertainties in geometry and orientation of the on-board interferometer. These “systematic” errors dominate the SWOT error budget and are likely to have a notable signature in the SSH products available to the oceanographic community. In this study, we explore the utility of the block-circulant (BC) approximation of the SWOT precision matrix developed by the Jet Propulsion Laboratory for assessment of a mission’s accuracy, including the possible impact of the systematic errors on the assimilation of the wide-swath altimeter data into numerical models. It is found that BC approximation of the precision matrix has sufficient (90–99%) accuracy for a wide range of significant wave heights of the ocean surface, and, therefore, could potentially serve as an efficient preconditioner for data assimilation problems involving altimetry observations by space-borne interferometers. An extensive set of variational data assimilation (DA) experiments demonstrates that BC approximation provides more accurate SSH retrievals compared to approximations, assuming a spatially uncorrelated observation error field as is currently adopted in operational DA systems.

Test of Power Transformation Function to Hydrometeor and Water Vapor Mixing Ratios for Direct Variational Assimilation of Radar Reflectivity Data

Abstract Assimilating radar reflectivity into convective-scale NWP models remains a challenging topic in radar data assimilation. A primary reason is that the reflectivity forward observation operator is highly nonlinear. To address this challenge, a power transformation function is applied to the WRF Model’s hydrometeor and water vapor mixing ratio variables in this study. Three 3D variational data assimilation experiments are performed and compared for five high-impact weather events that occurred in 2019: (i) a control experiment that assimilates reflectivity using the original hydrometeor mixing ratios as control variables, (ii) an experiment that assimilates reflectivity using power-transformed hydrometeor mixing ratios as control variables, and (iii) an experiment that assimilates reflectivity and retrieved pseudo–water vapor observations using power-transformed hydrometeor and water vapor mixing ratios (qυ) as control variables. Both qualitative and quantitative evaluations are performed for 0–3-h forecasts from the five cases. The analysis and forecast performance in the two experiments with power-transformed mixing ratios is better than the control experiment. Notably, the assimilation of pseudo–water vapor with power-transformed qυ as an additional control variable is found to improve the performance of the analysis and short-term forecasts for all cases. In addition, the convergence rate of the cost function minimization for the two experiments that use the power transformation is faster than that of the control experiments. Significance Statement The effective use of radar reflectivity observations in any data assimilation scheme remains an important research topic because reflectivity observations explicitly include information about hydrometeors and also implicitly include information about the distribution of moisture within storms. However, it is difficult to assimilate reflectivity because the reflectivity forward observation operator is highly nonlinear. This study seeks to identify a more effective way to assimilate reflectivity into a convective-scale NWP model to improve the accuracy of predictions of high-impact weather events.

Reconstruction of the Rheological Parameters in a Sea Ice Model with Viscoplastic Rheology

Abstract We analyzed the feasibility of the reconstruction of the spatially varying rheological parameters through the four-dimensional variational data assimilation of the sea ice velocity, thickness, and concentration into the viscoplastic (VP) sea ice model. The feasibility is assessed via idealized variational data assimilation experiments with synthetic observations configured for a 1-day data assimilation window in a 50 × 40 rectangular basin forced by the open boundaries, winds, and ocean currents and should be viewed as a first step in the developing the similar algorithms which can be applied for the more advanced sea ice models. It is found that “true” spatial variability (∼5.8 kN m−2) of the internal maximum ice strength parameter can be retrieved from observations with reasonable accuracy of 2.3–5.3 kN m−2, when an observation of the sea ice state is available daily in each grid point. Similar relative accuracy was achieved for the reconstruction of the compactness strength parameter α. The yield curve eccentricity e is found to be controlled by the data with less efficiency, but the spatial mean value of e could be still reconstructed with a similar degree of confidence. The accuracy of , α, and e retrievals is found to increase in regions of stronger ice velocity convergence, providing prospects for better processing of the observations collected during the recent MOSAiC experiment. The accuracy of the retrievals strongly depends on the number of the control variables characterizing the rheological parameter fields.

Retrieval and Application of Rapid-Scan Atmospheric Motion Vectors Using an Infrared Channel of the INSAT-3DR Satellite

The advanced Indian meteorological satellite INSAT-3DR was configured in rapid-scan mode during the formation of tropical cyclone ‘Fani’ over the North Indian Ocean. This study is carried out to explore the possibility of further enhancement in atmospheric motion vectors (AMVs) to understand the extreme weather event using rapid-scan observations. A novel experiment has been performed to retrieve rapid-scan AMVs (RS-AMVs) with different tracer sizes at two different temporal scales (10 and 15 min) using the Thermal Infrared (TIR)-1 channel of the INSAT-3DR satellite. The RS-AMVs are able to capture small-scale variations of winds in rapid-scan mode, compared to AMVs retrieved by the operational INSAT-3D satellite available at 30-min intervals. Initial quality assessment of retrieved RS-AMVs is performed using winds from NCEP final analysis, ERA-5 reanalysis, and radiosonde observations. The number of wind vectors are enhanced significantly in RS-AMVs against operational AMVs from INSAT-3DR. An improvement of about 12% in RS-AMVs relative to operational 30-min INSAT-3D-retrieved AMVs has been achieved. Moreover, a sensitivity study has been performed using four-dimensional variational data assimilation experiments to understand the impact of newly retrieved RS-AMVs against operational INSAT-3D-retrieved AMVs for tropical cyclone Fani. Results suggest noteworthy improvements in track prediction when RS-AMVs are used for assimilation as compared to operational AMVs. The model-simulated surface wind structures are also compared with satellite observations for the radius of the maximum winds $$(R_{\max } )$$ and the maximum radial extent of surface winds.

Parameter optimization in sea ice models with elastic–viscoplastic rheology

Abstract. The modern sea ice models include multiple parameters which strongly affect model solution. As an example, in the CICE6 community model, rheology and landfast grounding/arching effects are simulated by functions of the sea ice thickness and concentration with a set of fixed parameters empirically adjusted to optimize the model performance. In this study, we consider the extension of a two-dimensional elastic–viscoplastic (EVP) sea ice model using a spatially variable representation of these parameters. The feasibility of optimization of the landfast sea ice parameters and rheological parameters is assessed via idealized variational data assimilation experiments with synthetic observations of ice concentration, thickness and velocity. The experiments are configured for a 3 d data assimilation window in a rectangular basin with variable wind forcing. The tangent linear and adjoint models featuring EVP rheology are found to be unstable but can be stabilized by adding a Newtonian damping term into the adjoint equations. A set of observation system simulation experiments shows that landfast parameter distributions can be reconstructed after 5–10 iterations of the minimization procedure. Optimization of sea ice initial conditions and spatially varying parameters in the stress tensor equation requires more computation but provides a better hindcast of the sea ice state and the internal stress tensor. Analysis of inaccuracy in the wind forcing and errors in sea ice thickness observations show reasonable robustness of the variational DA approach and the feasibility of its application to available and incoming observations.

Using multi-platform 4D-Var data assimilation to improve modeling of Adriatic Sea dynamics

A year-long Four-Dimensional Variational (4D-Var) data assimilation experiment, formulated on the physical-space statistical analysis system (PSAS) algorithm, has been applied to the Adriatic Sea for the very first time. High-resolution multi-platform observations were assimilated into the Regional Ocean Modeling System (ROMS) forced by mesoscale atmospheric model ALADIN/HR (Aire Limitée Adaptation dynamique Développement InterNational), including important freshwater river inflows and realistic open boundary conditions for the period between October 2014 and September 2015. The observations included sea surface temperature (SST) measured by satellites, in situ temperature and salinity data measured by various moving (Argo profiling floats, shipborne CTDs, sea glider, towed CTD profiler) and moored platforms, ocean current profiles measured by moored Acoustic Doppler Current Profilers (ADCPs), and 30-minute de-tided surface currents from high-frequency (HF) radars. Three model simulations were integrated: (1) a non-assimilative simulation over a year-long period — baseline simulation; (2) a non-assimilative simulation initiated by the previous assimilation 4-day cycle — background simulation, and (3) a fully assimilative simulation that used all available observations during the 4-day assimilation cycle — analysis simulation. The assimilation significantly improved the modeling system performance, especially in SST, with time average rmse equaling 0.9, 0.7 and 0.5 °C and bias equaling 0.39, 0.15, 0.01 °C for the baseline, background and analysis simulations, respectively. These reductions were mostly achieved during the wintertime outbreaks of a cold and dry bora wind, caused by an underestimation of heat and momentum fluxes by the atmospheric model. Such fine adjustments in the northern and middle Adriatic may be responsible for improved reproduction of dense water generation and the associated Adriatic thermohaline circulation.

Predicting extreme rainfall events over Jeddah, Saudi Arabia: impact of data assimilation with conventional and satellite observations

The impact of variational data assimilation for predicting two heavy rainfall events that caused devastating floods in Jeddah, Saudi Arabia is studied using the Weather Research and Forecasting (WRF) model. On 25 November 2009 and 26 January 2011, the city was deluged with more than double the annual rainfall amount, caused by convective storms. We used a high‐resolution, two‐way nested domain WRF model to simulate the two rainfall episodes. Simulations include control runs initialized with National Centers for Environmental Prediction (NCEP) Global Forecasting System (GFS) data and three‐dimensional variational (3D‐Var) data assimilation experiments conducted by assimilating NCEP PREPBUFR and radiance observations. Observations from Automatic Weather Stations (AWSs), synoptic charts, radar reflectivity and satellite pictures from the Presidency of Meteorology and Environment (PME), Jeddah are used to assess the forecasting results. To evaluate the impact of the different assimilated observational datasets on the simulation of the major flooding event of 2009, we conducted 3D‐Var experiments assimilating individual sources and a combination of all datasets. Results suggest that while the control run had a tendency to predict the storm earlier than observed, the assimilation of profile observations greatly improved the model's thermodynamic structure and led to better representation of simulated rainfall both in timing and amount. The experiment with assimilation of all available observations compared best with observed rainfall in terms of timing of the storm and rainfall distribution, demonstrating the importance of assimilating different types of observations. Retrospective experiments with and without data assimilation, for three different model lead times (48, 72 and 96 h), were performed to examine the skill of the WRF model to predict the heavy rainfall events. Quantitative rainfall analysis of these simulations suggests that 48 h lead time runs with assimilation of all observational data provide the best statistical scores.

Effect of Data Assimilation Using WRF-3DVAR for Heavy Rain Prediction on the Northeastern Edge of the Tibetan Plateau

The numerical weather prediction (NWP) is gaining more attention in providing high-resolution rainfall forecasts in the arid and semiarid region. However, the modeling accuracy is negatively affected by errors in the initial conditions. Here we investigate the potential of data assimilation in improving the NWP rainfall forecasts in the northeastern Tibetan Plateau. Three of three-dimensional variational (3DVar) data assimilation experiments were designed on running the advanced research weather research forecast (WRF) model. Two heavy rain events selected with different rainfall distribution in space and time are utilized to examine the improvement for rainfall forecast after data assimilation. For the spatial distribution, the improvement of rainfall accumulation and area is obvious for the both two events. But for the temporal variation, the improvement is more obvious for the event with even rainfall distribution in time, while the effect of data assimilation is not ideal for the rainfall event with uneven distribution in space and time. It is noteworthy that, for both the spatial and temporal distribution of rainfall, satellite radiances have greater effect on rainfall forecasts than surface and upper-air meteorological observations in this high-altitude region. Moreover, the data assimilation experiments provide more detail information to the initial fields.

Three-Dimensional Variational Data Assimilation Experiments for a Heavy Rainfall Case in the Downstream Yangtze River Valley Using Automatic Weather Station and Global Positioning System Data in Southeastern Tibetan Plateau

Three-Dimensional Variational Data Assimilation Experiments for a Heavy Rainfall Case in the Downstream Yangtze River Valley Using Automatic Weather Station and Global Positioning System Data in Southeastern Tibetan Plateau

Improved state estimations of lower trophic ecosystems in the global ocean based on a Green’s function approach

A lower trophic ecosystem model, which was originally developed for describing the variability in plankton distribution in the western North Pacific, is applied to the global ocean. A realistic time series of dynamically self-consistent circulation fields obtained by a 4-dimensional variational ocean data assimilation experiment is used for the environmental fields in the ecosystem model. An optimization of the bio-ecological parameter values in 40 provinces by a Green’s function approach enables the ecosystem model to represent the observed variabilities of nutrients and surface chlorophyll concentration with a relatively small number (11) of compartments. In addition, artificial trends of the ecosystem variables due to model errors are generally suppressed by the optimization. The obtained parameter values and ecosystem fields are generally consistent with observations in terms of assimilated and non-assimilated metrics. The integrated lower-trophic ecosystem and physical fields in the global ocean offer important information on the mechanisms (such as El Niños) responsible for the seasonal–interannual variability in the lower trophic ecosystem. Our results demonstrate that, with adequate parameter sets capable of modifying indirectly the model and significance of each pathway to reflect the characteristics of local species, a simple ecosystem model can be applied in quantitative analyses to enhance our understanding of the influence of climate variations on the ocean ecosystem.

On variational downscaling, fusion, and assimilation of hydrometeorological states: A unified framework via regularization

[1] Improved estimation of hydrometeorological states from down-sampled observations and background model forecasts in a noisy environment has been a subject of growing research in the past decades. Here we introduce a unified variational framework that ties together the problems of downscaling, data fusion, and data assimilation as ill-posed inverse problems. This framework seeks solutions beyond the classic least squares estimation paradigms by imposing a proper regularization, expressed as a constraint consistent with the degree of smoothness and/or probabilistic structure of the underlying state. We review relevant smoothing norm regularization methods in derivative space and extend classic formulations of the aforementioned problems with particular emphasis on land surface hydrometeorological applications. Our results demonstrate that proper regularization of downscaling, data fusion, and data assimilation problems can lead to more accurate and stable recovery of the underlying non-Gaussian state of interest with improved performance in capturing isolated and jump singularities. In particular, we show that the Huber regularization in the derivative space offers advantages, compared to the classic solution and the Tikhonov regularization, for spatial downscaling and fusion of non-Gaussian multisensor precipitation data. Furthermore, we explore the use of Huber regularization in a variational data assimilation experiment while the initial state of interest exhibits jump discontinuities and non-Gaussian probabilistic structure. To this end, we focus on the heat equation motivated by its fundamental application in the study of land surface heat and mass fluxes.

Experimental 4D-Var Assimilation of SYNOP Rain Gauge Data at ECMWF

Abstract Four-dimensional variational data assimilation (4D-Var) experiments with 6-hourly rain gauge accumulations observed at synoptic stations (SYNOP) around the globe have been run over several months, both at high resolution in an ECMWF operations-like framework and at lower resolution with the reference observational coverage reduced to surface pressure data only, as would be expected in early twentieth-century periods. The key aspects of the technical implementation of rain gauge data assimilation in 4D-Var are described, which include the specification of observation errors, bias correction procedures, screening, and quality control. Results from experiments indicate that the positive impact of rain gauges on forecast scores remains limited in the operations-like context because of their competition with all other observations already available. In contrast, when only synoptic station surface pressure observations are assimilated in the data-poor control experiment, the additional assimilation of rain gauge measurements substantially improves not only surface precipitation scores, but also analysis and forecast scores of temperature, geopotential, wind, and humidity at most atmospheric levels and for forecast ranges up to 10 days. The verification against Meteosat infrared imagery also shows a slight improvement in the spatial distribution of clouds. This suggests that assimilating rain gauge data available during data-sparse periods of the past might help to improve the quality of future reanalyses and subsequent forecasts.

Experiments of the WRF three-/four-dimensional variational (3/4DVAR) data assimilation in the forecasting of Antarctic cyclones

The three-/four-dimensional variational data assimilation systems (3/4DVAR) of the Weather Research and Forecasting (WRF) model were explored in the forecasting of two Antarctic synoptic cyclones, which had large influence on the Ross Sea/Ross Ice Shelf region in October 2007. A suite of variational data assimilation experiments, including regular 3DVAR, high-resolution 3DVAR, and 4DVAR experiments, were designed to evaluate their performances in weather analysis and forecasting in Antarctica. In general, both 4DVAR and high-resolution 3DVAR experiments showed better forecasting skill than regular 3DVAR experiments. High-resolution 3DVAR experiments were the most efficient in reducing the analysis errors of surface winds and temperature, and had the best performance during the first 24 h of forecasting. However, during the following forecast period, 4DVAR experiments showed either better or about comparable performance to high-resolution 3DVAR experiments. These results indicate that increasing the spatial resolution during 3DVAR is an economical approach to improving the weather analysis and forecasting over Antarctica. At the same time, the 4DVAR approach had a longer impact on forecasting than the high-resolution 3DVAR approach. Understandably, both of the variational assimilation approaches are promising techniques toward improving the regional analysis and forecasting over Antarctica.

Analysis of four‐dimensional variational state estimation of the Hawaiian waters

In this study, we evaluate results from an incremental strong constraint four‐dimensional variational data assimilation (IS4D‐Var) experiment applied to the circulation around the Hawaiian Islands using the Regional Ocean Modeling System (ROMS). Assimilated observations include (1) satellite‐derived high‐resolution swath radiometer sea surface temperatures (SST) and along‐track altimetric sea surface heights (SSH) and (2) in situ temperature and salinity profiles from Argo floats, autonomous Seagliders, and shipboard conductivity‐temperature‐depth. Two assimilation configurations are compared: adjusting initial conditions versus adjusting both initial conditions along with atmospheric forcing. In the latter case, we compare two separate forcing products. For all experiments, we investigate how the assimilation alters the tidal, inertial, and mesoscale variability. Significant improvements in the observation‐model fit are found for SST and salinity regardless of assimilation configuration or atmospheric forcing; however, significant change to the subsurface temperature is made when adjusting only initial conditions. Baroclinic tides are altered during the assimilation because of changes in the density field in regions of strong internal tide generation. Spurious inertial oscillations are found in assimilation circulations that are associated with the IS4D‐Var increment when using either SST or SSH observations; however, this increase in the inertial energy had minimal effect on the mesoscale variability.

Evaluation of a Spatial/Spectral Covariance Localization Approach for Atmospheric Data Assimilation

In this study, several approaches for estimating background-error covariances from an ensemble of error realizations are examined, including a new spatial/spectral localization approach. The new approach shares aspects of both the spatial localization and wavelet-diagonal approaches. This approach also enables the use of different spatial localization functions for the covariances associated with each of a set of overlapping horizontal wavenumber bands. The use of such scale-dependent spatial localization (more severe localization for small horizontal scales) is shown to reduce the error in spatial correlation estimates. A comparison of spatial localization, spatial/spectral localization, and wavelet-diagonal approaches shows that the approach resulting in the lowest estimation error depends on the ensemble size. For a relatively large ensemble (48 members), the spatial/spectral localization approach produces the lowest error. When using a much smaller ensemble (12 members), the wavelet-diagonal approach results in the lowest error. Qualitatively, the horizontal correlation functions resulting from spatial/spectral localization appear smoother and less noisy than those from spatial localization, but preserve more of the heterogeneous and anisotropic nature of the raw sample correlations than the wavelet-diagonal approach. The new spatial/spectral localization approach is compared with spatial localization in a set of 1-month three-dimensional variational data assimilation (3D-Var) experiments using a full set of real atmospheric observations. Preliminary results show that spatial/spectral localization provides a nearly similar forecast quality, and in some regions improved forecast quality, as spatial localization while using an ensemble of half the size (48 vs 96 members).

An effective genetic algorithm to VDA with discontinuous “on-off” switches

With more and more improvements of atmosphere or ocean models, a growing number of physical processes in the form of parameterization are incorporated into the models, which, on the one hand, makes the models capable of describing the atmospheric or oceanic movement more precisely, and on the other hand, introduces non-smoothness in the form of “on-off” switches into the models. “On-off” switches enhance the nonlinearity of the models and finally result in the loss of the effectiveness of variational data assimilation (VDA) based on the conventional adjoint method (ADJ). This study, in virtue of the optimization ability of a genetic algorithm (GA) for non-smooth problems, presents a new GA (referred to as GA NEW) to solve the problems of the VDA with discontinuous “on-off” processes. In the GA-NEW, adaptive selection and mutation operators blend crossover operator, and elitist strategy are combined in application. In order to verify the effectiveness and feasibility of the GA NEW in VDA, an idealized model of partial differential equation with discontinuous “on-off” switches in the forcing term is adopted as the governing equation. By comparison with the ADJ, it is shown that the GA NEW in VDA is more effective and can yield better assimilation retrievals. In addition, VDA experiments demonstrate that the performance of a GA is greatly related to the configuration of genetic operators (selection, crossover and mutation operators) and much better results may be attained with more proper genetic operations. Furthermore, the robustness of the GA NEW to observational noise, model errors and observation density is investigated, and the results show that the GA NEW has stronger robustness than the ADJ with respect to all the three observation noises, model errors, and sparse observation.

Mesoscale Data Assimilation of Myanmar Cyclone Nargis Part II: Assimilation of GPS-Derived Precipitable Water Vapor

Four-dimensional variational (4D-Var) data assimilation (DA) experiments using Global Positioning System (GPS)-derived precipitable water vapor (PWV) were conducted for the tropical cyclone (TC) Nargis in 2008. In order to analyze the initial field at 1200 UTC 30 April 2008, 12, 24, 36, and 48 h sequential DA experiments with 3 h assimilation windows were performed. The initial fields made by these DA experiments were applied to subsequent forecast experiments using a nonhydrostatic model (NHM) with a horizontal resolution of 10 km. NHM predictions using initial fields produced by DA experiments that used only ordinary observational data (without GPS PWV) exhibited a large variation of predicted maximum TC intensity (958 to 983 hPa) for each experiment. In these experiments, a longer assimilation period did not necessarily result in better prediction. The DA of GPS PWV yielded a smaller variation of predicted maximum TC intensity (964 to 974 hPa), and a longer assimilation period tended to bring deeper depression of TC central pressure. Overall, TC intensities determined by DA experiments with GPS data were closer to the best track produced by the Regional Specialized Meteorological Centre (RSMC) New Delhi than the DA experiments without GPS data. The 48 h DA without GPS PWV resulted in the weakest prediction of TC development with the deepest TC central pressure of 983 hPa, while 48 h DA with GPS PWV successfully predicted rapid TC development with the deepest pressure of 967 hPa. One cause of the incomplete development of Nargis in the 48 h DA experiment without GPS PWV was insufficient observations in the Bay of Bengal, especially in the first 12 h. Underestimation of precipitation was conspicuous in the first 12 h of the DA. Implementation of GPS PWV into the DA contributed to increasing the precipitation and changed the fields of pressure and wind in the bay. In the first several hours, modifications of the fields of pressure and wind around the Andaman Islands were conspicuous. These affected areas extended with time and created a more favorable environment for TC development.

Interannual variability of North Pacific eastern subtropical mode water formation in the 1990s derived from a 4-dimensional variational ocean data assimilation experiment

Abstract The interannual variability of eastern subtropical mode water (ESTMW) formation in the North Pacific is examined using a new ocean dataset constructed by a 4-dimensional variational data assimilation experiment covering the decade of the 1990s. The volume of newly formed ESTMW varies due to interannual variability in the following three physical processes taking place in the surface layer: (1) convergence in the transport of surface saline water induced by Ekman flow in the vicinity of the formation region, (2) thermal stratification in the preconditioning phase in association with the insolation anomaly induced largely by low-level cloud coverage, and (3) wintertime surface cooling in the eastern subtropics. We find that, in addition to the surface forcing, the properties of both the ESTMW and the upper mixed-layer water are broadly controlled by the volume of the new ESTMW component, and that the variations in the upper mixed-layer water affect the properties of ESTMW formed in the following winter. Due to the combined effect of these processes, the ESTMW subducts down to subsurface layers with a wide range of σ θ values lying between 24.8 and 25.4 and with significant interannual variation in water mass formation.

Intercomparison of Variational Data Assimilation and the Ensemble Kalman Filter for Global Deterministic NWP. Part I: Description and Single-Observation Experiments

Abstract An intercomparison of the Environment Canada variational and ensemble Kalman filter (EnKF) data assimilation systems is presented in the context of global deterministic NWP. In an EnKF experiment having the same spatial resolution as the inner loop in the four-dimensional variational data assimilation system (4D-Var), the mean of each analysis ensemble is used to initialize the higher-resolution deterministic forecasts. Five different variational data assimilation experiments are also conducted. These include both 4D-Var and 3D-Var (with first guess at appropriate time) experiments using either (i) prescribed background-error covariances similar to those used operationally, which are static in time and include horizontally homogeneous and isotropic correlations; or (ii) flow-dependent covariances computed from the EnKF background ensembles with spatial covariance localization applied. The fifth variational data assimilation experiment is a new approach called the Ensemble-4D-Var (En-4D-Var). This approach uses 4D flow-dependent background-error covariances estimated from EnKF ensembles to produce a 4D analysis without the need for tangent-linear or adjoint versions of the forecast model. In this first part of a two-part paper, results from a series of idealized assimilation experiments are presented. In these experiments, only a single observation or vertical profile of observations is assimilated to explore the impact of various fundamental differences among the EnKF and the various variational data assimilation approaches considered. In particular, differences in the application of covariance localization in the EnKF and variational approaches are shown to have a significant impact on the assimilation of satellite radiance observations. The results also demonstrate that 4D-Var and the EnKF can both produce similar 4D background-error covariances within a 6-h assimilation window. In the second part, results from medium-range deterministic forecasts for the study period of February 2007 are presented for the EnKF and the five variational data assimilation approaches considered.

Assimilation of satellite‐derived soil moisture from ASCAT in a limited‐area NWP model

AbstractA simplified Extended Kalman Filter is developed for the assimilation of satellite‐derived surface soil moisture from the Advanced Scatterometer (ASCAT) instrument (on board the polar‐orbiting satellite METOP) in a limited‐area NWP model where soil water vertical transfers are described by a force–restore method. An analytic formulation of the land surface scheme Jacobians is derived to simplify the coupling between land surface and atmospheric data assimilation systems. Various steps necessary before the assimilation of ASCAT products are defined: projection of satellite data on the model grid, screening based on various criteria, bias correction using a CDF matching technique, and specification of model and observation errors. Three‐dimensional variational data assimilation experiments are then performed during a four‐week period in May 2009 over western Europe. A control assimilation is also run where the soil moisture evolves freely. Forecasts from these analyses show that the assimilation of ASCAT data slightly reduces the daytime low‐level relative humidity positive bias of the control run. Forecast skill scores with respect to other variables are rather neutral. A comparison of the control run with the operational system where soil moisture is corrected from short‐range forecast errors of screen‐level observations show similar improvements but are more pronounced. These differences come from the fact that the number of screen‐level observations from the surface network over Europe is significantly larger than those provided by a polar‐orbiting satellite. These results are consistent with those obtained at ECMWF using soil moisture products derived from other satellite instruments (X‐band radiometer TMI and C‐band scatterometer ERS). Several avenues for improving this preliminary methodology are proposed. Copyright © 2010 Royal Meteorological Society