Background Error Covariance Matrix Research Articles

Characterization of the Ionospheric Vertical Error Correlation Lengths Based on Global Ionosonde Observations

AbstractData assimilation is one of the most important approaches to monitoring the variations of ionospheric electron densities. The construction of the background error covariance matrix is an important component of ionospheric data assimilations. To construct the background error covariance matrix, the information about the spatial ionospheric correlations is required. We present a statistical analysis on the ionospheric vertical error correlation length (VCL) based on a global network of ionosondes and the Neustrelitz Electron Density Model. We show that the locally derived VCL is well‐defined and the VCL does not show a considerable dependency on the geographical seasons while local time dependencies of the VCL are shown to be present. A novel VCL model is also established based on the ionospheric scale heights. We show that the ionospheric VCL can be characterized by the variance ratio between the ionosphere model and ionospheric measurements. The altitudinal variations of VCLs are controlled by the interactions between the inherent VCLs of the ionosphere model and the measurements. Two experiments are conducted at two different latitudes based on the proposed model. The results show that the proposed model is stable and well‐correlated with the observed VCLs, which implies a potential to be generalized for a global correlation model. The proposed model can be used in the temporal evolution of error covariance matrices in the ionospheric 4D‐Variational (4D‐Var) assimilations, which may overcome the main drawbacks of the static error covariance specifications in the ionospheric 4D‐Var assimilations.

A Space-Time Variational Method for Retrieving Upper-Level Vortex Winds from GOES-16 Rapid Scans over Hurricanes

A space-time variational method is developed for retrieving upper-level vortex winds from geostationary satellite rapid infrared scans over hurricanes. In this method, new vortex-flow-dependent correlation functions are formulated for the radial and tangential components of the vortex wind. These correlation functions are used to construct the background error covariance matrix and its square root matrix. The resulting square root matrix is then employed to precondition the cost function, constrained by an advection equation formulated for rapidly scanned infrared image movements. This newly formulated and preconditioned cost function is more suitable for deriving upper-level vortex winds from GOES-16 rapid infrared scans over hurricanes than the cost function in the recently adopted optical flow technique. The new method was applied to band-13 (10.3 µm) brightness temperature images scanned every min from GOES-16 over Hurricanes Laura on 27 August 2020 and Hurricanes Ida on 29 August 2021. The retrieved vortex winds were shown to not only be much denser than operationally produced atmospheric motion vectors (AMVs) but also more rotational and better organized around the eyewall than the super-high-resolution AMVs derived from optical-flow technique. By comparing their component velocities (projected along radar beams) with limited radar velocity observations available near the cloud top, the vortex winds retrieved using the new method were also shown to be more accurate than the super-high-resolution AMVs derived from the optical-flow technique. The new method is computationally efficient for real-time applications and potentially useful for hurricane wind nowcasts. Furthermore, the combined use of VF-dependent covariance functions and imagery advection equation is not only novel but was also found to be critically important for the improved performance of the method. This finding implies that similar combined approaches can be developed with improved performance for retrieving vortex flows rapidly scanned using other types of remote sensing on different scales, such as tornadic mesocyclones rapidly scanned by phased-array radars.

Impact of correlated observation errors on the conditioning of variational data assimilation problems

SummaryAn important class of nonlinear weighted least‐squares problems arises from the assimilation of observations in atmospheric and ocean models. In variational data assimilation, inverse error covariance matrices define the weighting matrices of the least‐squares problem. For observation errors, a diagonal matrix (i.e., uncorrelated errors) is often assumed for simplicity even when observation errors are suspected to be correlated. While accounting for observation‐error correlations should improve the quality of the solution, it also affects the convergence rate of the minimization algorithms used to iterate to the solution. If the minimization process is stopped before reaching full convergence, which is usually the case in operational applications, the solution may be degraded even if the observation‐error correlations are correctly accounted for. In this article, we explore the influence of the observation‐error correlation matrix () on the convergence rate of a preconditioned conjugate gradient (PCG) algorithm applied to a one‐dimensional variational data assimilation (1D‐Var) problem. We design the idealized 1D‐Var system to include two key features used in more complex systems: we use the background error covariance matrix () as a preconditioner (B‐PCG); and we use a diffusion operator to model spatial correlations in and . Analytical and numerical results with the 1D‐Var system show a strong sensitivity of the convergence rate of B‐PCG to the parameters of the diffusion‐based correlation models. Depending on the parameter choices, correlated observation errors can either speed up or slow down the convergence. In practice, a compromise may be required in the parameter specifications of and between staying close to the best available estimates on the one hand and ensuring an adequate convergence rate of the minimization algorithm on the other.

Anisotropic diffusion filters for flow-dependent variational data assimilation of sea surface temperature

It is well known that the background error covariance matrix in the data assimilation is anisotropic and varied with the flow field, that is, flow-dependent. However, it is generally assumed to be isotropic and static for ease of implementation. Therefore, to enhance the quality of the background error covariance, two easy-to-implement, flow-dependent three-dimensional variational analysis (3DVar) schemes, the advection–diffusion filter (ADF) and the Smagorinsky diffusion filter (SDF), are tentatively proposed. These serve as alternative schemes for the traditional methods that are based on the isotropic assumption. First, a correctness test of the gradient for the ADF is performed to verify the validity of the adjoint code. Then, the response analysis for the 1D advection–diffusion​ equation is investigated to validate the anisotropic characteristic of the ADF with various flow velocities. Second, the two flow-dependent 3DVar schemes are verified via single-observation assimilation experiments. Compared to the existing diffusion filter with a static diffusion coefficient, both new schemes show a flow-dependent capability in the assimilation experiment because they successfully spread the observational information anisotropically. Finally, a retroactive real-time forecast experiment framework based on a 3D baroclinic primitive equation ocean model is used to investigate the effects of the ADF/SDF on the analysis and forecast accuracy of sea surface temperature (SST). While the traditional variational assimilation method with an isotropic diffusion filter generally reduces initial field errors, both the ADF and SDF can further enhance the accuracy of the initial fields in strong current areas. In addition, better forecast skills can be obtained with the two flow-dependent schemes in the East China Sea.

Deep learning-enhanced ensemble-based data assimilation for high-dimensional nonlinear dynamical systems

Data assimilation (DA) is a key component of many forecasting models in science and engineering. DA allows one to estimate better initial conditions using an imperfect dynamical model of the system and noisy/sparse observations available from the system. Ensemble Kalman filter (EnKF) is a DA algorithm that is widely used in applications involving high-dimensional nonlinear dynamical systems. However, EnKF requires evolving large ensembles of forecasts using the dynamical model of the system. This often becomes computationally intractable, especially when the number of states of the system is very large, e.g., for weather prediction. With small ensembles, the estimated background error covariance matrix in the EnKF algorithm suffers from sampling error, leading to an erroneous estimate of the analysis state (initial condition for the next forecast cycle). In this work, we propose hybrid ensemble Kalman filter (H-EnKF), which is applied to a two-layer quasi-geostrophic turbulent flow as a test case. This framework utilizes a pre-trained deep learning-based data-driven surrogate that inexpensively generates and evolves a large data-driven ensemble of the states to accurately compute the background error covariance matrix with smaller sampling errors. The H-EnKF framework outperforms EnKF with only dynamical model or only the data-driven surrogate, and estimates a better initial condition without the need for any ad-hoc localization strategies. H-EnKF can be extended to any ensemble-based DA algorithm, e.g., particle filters, which are currently too expensive to use for high-dimensional systems.

A Multivariate Additive Inflation Approach to Improve Storm‐Scale Ensemble‐Based Data Assimilation and Forecasts: Methodology and Experiment With a Tornadic Supercell

AbstractEnsemble‐based convective‐scale radar data assimilation commonly suffers from an underdispersive background ensemble. This study introduces a multivariate additive‐inflation method to address such deficiency. The multivariate additive inflation (AI) approach generates coherent random perturbations drawn from a newly constructed convective‐scale static background error covariance matrix for all state variables including hydrometeors and vertical velocity. This method is compared with a previously proposed univariate AI approach, which perturbs each variable individually without cross‐variable coherency. Comparisons are performed on the analyses and forecasts of the 8 May 2003 Oklahoma City tornadic supercell. Within assimilation cycles, the multivariate approach is more efficient in increasing reflectivity spread and thus has a reduced spinup time than the univariate approach; the additional inclusion of hydrometeors and vertical velocity results in more background spread for both reflectivity and radial velocity. Significant differences among AI experiments also exist in the subsequent forecasts and are more pronounced for the forecasts initialized from the earlier assimilation cycles. The multivariate approach yields better forecasts of low‐level rotation, reflectivity distributions, and storm maintenance for most lead times. The additional inclusion of hydrometeor and vertical velocity in the multivariate method is beneficial in forecasts. Conversely, the additional inclusion of hydrometeor and vertical velocity in the univariate method poses negative impacts for the majority of forecast lead times.

Modifying Covariance Localization to Mitigate Sampling Errors from the Ensemble Data Assimilation

The ensemble-based Kalman filter requires at least a considerable ensemble (e.g., 10,000 members) to identify relevant error covariance at great distances for multidimensional geophysical systems. However, increasing numerous ensemble sizes will enlarge sampling errors. This study proposes a modified Cholesky decomposition based on the covariance localization (CL) scheme, namely a covariance localization scheme with modified Cholesky decomposition (CL-MC). Our main idea utilizes a modified Cholesky (MC) decomposition technique for estimating the background error covariance matrix; meanwhile, we employ the tunable singular value decomposition method on the background error covariance to improve the ensemble increment and avoid the imbalance of the system. To verify if the proposed method can effectively mitigate the sampling errors, numerical experiments are conducted on the Lorenz-96 model and large-scale model (SPEEDY model). The results show that the CL-MC method outperforms the CL method for different data assimilation parameters (ensemble sizes and localizations). Furthermore, by performing one year of assimilation experiments on the SPEEDY model, it is found that the 1-day forecast RMSEs obtained by the CL are approximately equal to the 5-day forecast RMSEs of CL-MC. So, the CL-MC method has potential advantages for long-term forecasting. Maybe the proposed CL-MC method achieves good prospects for widespread application in atmospheric general circulation models.

Impact of Feature-Dependent Static Background Error Covariances for Satellite-Derived Humidity Assimilation on Analyses and Forecasts of Multiple Sea Fog Cases over the Yellow Sea

Assimilation of satellite-derived humidity with a homogenous static background error covariance (B) matrix computed over the entire computational domain (Full-B) tends to overpredict sea fog coverage. A feature-dependent B (Fog-B) is proposed to address this issue. In Fog-B, the static error statistics for clear air and foggy areas are calculated separately using a feature-dependent binning method. The resultant error statistics are used simultaneously at appropriate locations guided by the satellite-derived sea fog. Diagnostics show that Full-B generally has broader horizontal and vertical length scales and larger error variances than Fog-B below ~300 m except for the vertical length scale near the surface. Experiments on three sea fog cases over the Yellow Sea are conducted to understand and examine the impact of Fog-B on sea fog analyses and forecasts. Results show that using Full-B produces greater and broader water vapor mixing ratio increments and thus predicts larger sea fog coverage than using Fog-B. Further evaluations suggest that using Fog-B has greater forecast skills in sea fog coverage and more accurate moisture conditions than using Full-B.

Developing 4D-Var for Strongly Coupled Data Assimilation Using a Coupled Atmosphere–Ocean Quasigeostrophic Model

Abstract Four-dimensional variational (4D-Var) data assimilation (DA) is developed for a coupled atmosphere–ocean quasigeostrophic application. Complications arise in coupled data assimilation (CDA) systems due to the presence of multiple spatiotemporal scales. Various formulations of the background error covariance matrix (), using different localization strategies, are explored to evaluate their impact on 4D-Var performance in a CDA setting. 4D-Var requires access to tangent linear and adjoint models (TLM/AM) to propagate information about the misfit between the forecast and observations within an optimization window. In practice, particularly for coupled models, the TLM and adjoint are often difficult to produce, and for some models are nonexistent in analytic form. Accordingly, a statistical data-driven alternative is also employed and evaluated to determine its feasibility for a 4D-Var CDA system. Using experiments conducted with a coupled atmosphere–ocean quasigeostrophic model, it is found that ensemble generation of flow-dependent error covariance statistics can increase the accuracy of 4D-Var CDA. When observing all variables, the hybrid climatological/flow-dependent constructions outperform either independently. The use of a hybrid matrix combined with a rapid updating ensemble transform Kalman filter (RU-ETKF) using either strongly or weakly CDA resulted in lower overall RMSE. The ocean component achieved its lowest RMSE when using a fully flow-dependent matrix generated using 4D-ETKF and using weakly CDA. These results show the importance of time scales and analysis update frequencies. The use of a statistically derived TLM/AM generated from the ETKF ensemble perturbations produces results similar to cases using the analytical coupled TLM/AM in 4D-Var.

Hybrid ensemble-variational data assimilation in ABC-DA within a tropical framework

Abstract. Hybrid ensemble-variational data assimilation (DA) methods have gained significant traction in recent years. These methods aim to alleviate the limitations and maximise the advantages offered by ensemble or variational methods. Most existing hybrid applications focus on the mid-latitudinal context; almost none have explored its benefits in the tropical context. In this article, hybrid ensemble-variational DA is introduced to a tropical configuration of a simplified non-hydrostatic convective-scale fluid dynamics model (the ABC model, named after its three key parameters: the pure gravity wave frequency A, the controller of the acoustic wave speed B, and the constant of proportionality between pressure and density perturbations C), and its existing variational framework, the ABC-DA system. The hybrid ensemble-variational DA algorithm is developed based on the alpha control variable approach, often used in numerical weather prediction. Aspects of the algorithm such as localisation (used to mitigate sampling error caused by finite ensemble sizes) and weighting parameters (used to weight the ensemble and climatological contributions to the background error covariance matrix) are implemented. To produce the flow-dependent error modes (ensemble perturbations) for the ensemble-variational DA algorithm, an ensemble system is also designed for the ABC model which is run alongside the hybrid DA system. A random field perturbations method is used to generate an initial ensemble which is then propagated using the ensemble bred vectors method. This setup allows the ensemble to be centred on the hybrid control analysis. Visualisation software has been developed to focus on the diagnosis of the ensemble system. To demonstrate the hybrid ensemble-variational DA in the ABC-DA system, sensitivity tests using observing system simulation experiments are conducted within a tropical framework. A 30-member ensemble was used to generate the error modes for the experiments. In general, the best performing configuration (with respect to the “truth”) for the hybrid ensemble-variational DA system used an 80%/20% weighting on the ensemble-derived/climatological background error covariance matrix contributions. For the horizontal wind variables though, full weight on the ensemble-derived background error covariance matrix (100%/0%) resulted in the smallest cycle-averaged analysis root mean square errors, mainly due to large errors in the meridional wind field when contributions from the climatological background error covariance matrix were involved, possibly related to a sub-optimal background error covariance model. The ensemble bred vectors method propagated a healthy-looking DA-centred ensemble without bimodalities or evidence of filter collapse. The ensemble was under-dispersive for some variables but for others, the ensemble spread approximately matched the corresponding root mean square errors. Reducing the number of ensemble members led to slightly larger errors across all variables due to the introduction of larger sampling errors into the system.

An Improved 1D-VAR Retrieval Algorithm of Temperature Profiles from an Ocean-Based Microwave Radiometer

In this study, a one-dimensional variational algorithm that combines brightness temperatures (BTs), measured by ocean-based microwave radiometers (MWR), with reanalysis data was developed to generate high accuracy temperature profiles. A forward radiative transfer model was used to simulate the BTs. For the V band (50–70 GHz), there is a good agreement between observations and simulations, but for K band (20–30 GHz), which is more affected by water vapor, large errors are observed. To reduce the errors, a combined temperature and water vapor background error covariance matrix is applied to the 1D-Var algorithm. In addition, a correction factor is added to the 1D-Var iterative equation to improve retrieval accuracy. The results of the improved 1D-Var method have been compared with the MWR built-in neural network (NN) method, original 1D-Var method, and radiosonde data, which shows that the retrievals of the combined 1D-Var method showed significant improvements between 0 to 10 km. The statistical results show that the maximum mean absolute error of the combined 1D-Var method is less than 2 K in clear sky and cloudy conditions. This paper demonstrates that the proposed combined 1D-Var method has better performance than many known retrieval methods.

3‐D Regional Ionosphere Imaging and SED Reconstruction With a New TEC‐Based Ionospheric Data Assimilation System (TIDAS)

AbstractA new TEC‐based ionospheric data assimilation system (TIDAS) over the continental US and adjacent area (20°–60°N, 60°–130°W, and 100–600 km) has been developed through assimilating heterogeneous ionospheric data, including dense ground‐based Global Navigation Satellite System (GNSS) Total Electron Content (TEC) from 2,000+ receivers, Constellation Observing System for Meteorology, Ionosphere, and Climate radio occultation data, JASON satellite altimeter TEC, and Millstone Hill incoherent scatter radar measurements. A hybrid Ensemble‐Variational scheme is utilized to reconstruct the regional 3‐D electron density distribution: a more realistic and location‐dependent background error covariance matrix is calculated from an ensemble of corrected NeQuick outputs, and a three‐dimensional variational (3DVAR) method is adopted for measurement updates to obtain an optimal state estimation. The spatial‐temporal resolution of the reanalyzed 3‐D electron density product is as high as 1° × 1° in latitude and longitude, 20 km in altitude, and 5 min in universal time, which is sufficient to reproduce ionospheric fine structure and storm‐time disturbances. The accuracy and reliability of data assimilation results are validated using ionosonde and other measurements. TIDAS reanalyzed electron density is able to successfully reconstruct the 3‐D morphology and dynamic evolution of the storm‐enhanced density (SED) plume observed during the St. Patrick's day geomagnetic storm on 17 March 2013 with high fidelity. Using TIDAS, we found that the 3‐D SED plume manifests as a ridge‐like high‐density channel that predominantly occurred between 300 and 500 km during 19:00–21:00 UT for this event, with the F2 region peak height being raised by 40–60 km and peak density enhancement of 30%–50%.

Influences of 1DVAR Background Covariances and Observation Operators on Retrieving Tropical Cyclone Thermal Structures

Spaceborne passive microwave sounding instruments are important for monitoring tropical cyclones (TCs) over oceans. However, previous studies have found large retrieval errors at TCs’ inner region at the lower troposphere where heavy precipitation occurs. In this study, the background error covariance matrix used in the variational retrieval algorithm is designed to vary with atmospheric conditions. It is found that the errors of retrieved temperature and humidity profiles are significantly reduced under the TC conditions, when they are compared with those from using a static covariance matrix. The retrieval errors of temperature and humidity are about 1.5 K and 10–20%, respectively, in the troposphere. Moreover, the influence of different observation operators on the retrievals are also investigated. It is shown that ARMS (Advanced Radiative Transfer Modeling System) used as an observation operator can produce a higher retrieval accuracy, compared to CRTM (Community Radiative Transfer Model). For the relative humidity profile, the error can be reduced by up to 5% from ARMS. The reason may be attributed to the more comprehensive handling of the scattering from various hydrometeors in ARMS, which results in a higher retrieval accuracy under cloudy conditions.

Geostationary Hyperspectral Infrared Sounder Channel Selection for Capturing Fast-Changing Atmospheric Information

Various methodologies have been developed for selecting a subset of channels from a hyperspectral infrared (IR) sounder for assimilation. The information entropy iterative method was considered optimal for channel selection. However, this method only considers the decrease in uncertainty in the atmospheric state caused by measurements at a single time, without considering the dynamic effect of measurements over a period of time; therefore, it might not be optimal for hyperspectral IR sounders onboard geosynchronous satellites that mainly aim to observe rapidly changing weather events. An alternative channel selection method is developed by adding an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> index, which reflects the Jacobian variance over time; the adjusted algorithm is ideal for the Geosynchronous Interferometric Infrared Sounder (GIIRS), which is the first high-spectral-resolution advanced IR sounder onboard a geostationary weather satellite. Comparisons between the conventional algorithm (information entropy iterative method) and the adjusted algorithm show that the channels selected from GIIRS by the adjusted algorithm will have larger brightness temperature diurnal variations and better information content than the conventional algorithm, based on the same background error covariance matrix, the observational error covariance matrix, and the channel blacklist. The adjusted algorithm is able to select the channels for monitoring atmospheric temporal variation while retaining the information content from the conventional method. The 1-D variational (1Dvar) retrieval experiment also verifies the superiority of this adjusted algorithm; it indicates that using the channel selected by the adjusted algorithm could enhance the water vapor profile retrieval accuracy, especially for the lower and middle troposphere atmosphere.

Impacts of uncertainties in emissions on aerosol data assimilation and short-term PM2.5 predictions over Northeast Asia

To improve PM2.5 predictions in Northeast Asia, we estimated a new background error covariance matrix (BEC) for aerosol data assimilation using surface PM2.5 observations. In contrast to the conventional method of BEC estimation that uses perturbations in meteorological data, this method additionally considered the perturbations using two different emission inventories. By taking the emission uncertainty into account, we found that the standard deviations in the BEC were significantly increased. The standard deviations became around three times larger than those in the conventional method at the surface. The impacts of the new BEC were then tested for the prediction of surface PM2.5 over Northeast Asia using the Community Multiscale Air Quality (CMAQ) model initialized by three-dimensional variational method (3D-VAR). The surface PM2.5 data measured at 154 sites in South Korea and 1535 sites in China were assimilated every 6 h during the campaign period of the Korea-United States Air Quality Study (KORUS-AQ) (1 May–14 June 2016). The data assimilation with the new BEC showed better agreement with the surface PM2.5 observations than with the BEC from the conventional method. Our method was also more consistent with the observations in 24-h PM2.5 predictions than the conventional method (specifically, with a ∼44% reduction of negative biases). We concluded that increased standard deviations, together with updated horizontal and vertical length scales in the new BEC, improved the data assimilation and short-term predictions of the surface PM2.5. This paper also suggests several research efforts to further improve the BEC for better short-term PM2.5 predictions in Northeast Asia.

Multivariate localization functions for strongly coupled data assimilation in the bivariate Lorenz 96 system

Abstract. Localization is widely used in data assimilation schemes to mitigate the impact of sampling errors on ensemble-derived background error covariance matrices. Strongly coupled data assimilation allows observations in one component of a coupled model to directly impact another component through the inclusion of cross-domain terms in the background error covariance matrix. When different components have disparate dominant spatial scales, localization between model domains must properly account for the multiple length scales at play. In this work, we develop two new multivariate localization functions, one of which is a multivariate extension of the fifth-order piecewise rational Gaspari–Cohn localization function; the within-component localization functions are standard Gaspari–Cohn with different localization radii, while the cross-localization function is newly constructed. The functions produce positive semidefinite localization matrices which are suitable for use in both Kalman filters and variational data assimilation schemes. We compare the performance of our two new multivariate localization functions to two other multivariate localization functions and to the univariate and weakly coupled analogs of all four functions in a simple experiment with the bivariate Lorenz 96 system. In our experiments, the multivariate Gaspari–Cohn function leads to better performance than any of the other multivariate localization functions.

Impact of assimilating lidar water vapour and temperature profiles with a hybrid ensemble transform Kalman filter: Three‐dimensional variational analysis on the convection‐permitting scale

AbstractWe discuss the analysis impact of the ensemble‐based assimilation of differential absorption lidar observed water vapour and Raman lidar observed temperature profiles into the Weather Research and Forecasting model at convection‐permitting scale. The impact of flow‐dependent background error covariance in the data assimilation (DA) system that uses the hybrid three‐dimensional variational (3DVAR) ensemble transform Kalman filter (ETKF) was compared to 3DVAR DA. The 3DVAR‐ETKF experiment resulted in a 50% lower temperature and water vapour RMSE than the 3DVAR experiment when taking the assimilated lidar data as reference and 26% (38%) lower water vapour (temperature) RMSE when comparing against independent radiosonde observations collocated with the lidar site. The planetary boundary‐layer height of the analyses compared to independent ceilometer data provided additional evidence of improvement. The 3DVAR analysis RMSE showed 140 m, whereas 3DVAR‐ETKF showed 60 m. Although limited to a single case study, we attribute these improvements to the flow‐dependent background error covariance matrix in the 3DVAR‐ETKF approach. The vertical profile measured from a single stationary lidar system established a spatial impact with a 100 km radius. This seems to indicate future assimilation of water vapour and temperature data from an operational lidar network. The assimilation impact persisted 7 hr into the forecast time compared with the ceilometer data and 4 hr with GPS observations.

Development of Convective-Scale Static Background Error Covariance within GSI-Based Hybrid EnVar System for Direct Radar Reflectivity Data Assimilation

AbstractA convective-scale static background-error covariance (BEC) matrix is further developed to include the capability of direct reflectivity assimilation and evaluated within the GSI-based three-dimensional variational (3DVar) and hybrid ensemble–variational (EnVar) methods. Specific developments are summarized as follows: 1) Control variables (CVs) are extended to include reflectivity, vertical velocity, and all hydrometeor types. Various horizontal momentum and moisture CV options are included. 2) Cross correlations between all CVs are established. 3) A storm intensity-dependent binning method is adopted to separately calculate static error matrices for clear-air and storms with varying intensities. The resultant static BEC matrices are simultaneously applied at proper locations guided by the observed reflectivity. 4) The EnVar is extended to adaptively incorporate static BECs based on the quality of ensemble covariances. Evaluation and examination of the new static BECs are first performed on the 8 May 2003 Oklahoma City supercell. Detailed diagnostics and 3DVar examinations suggest zonal/meridional winds and pseudo–relative humidity are selected as horizontal momentum and moisture CVs for direct reflectivity assimilation, respectively; inclusion of cross correlations favors spin up and maintains the analyzed storms; application of binning improves characteristics and persistence of the simulated storm. Relative to an experiment using the full ensemble BECs (Exp-PureEnVar), incorporating static BECs in hybrid EnVar reduces spinup time and better analyzes reflectivity distributions while the background ensemble is deficient in sampling errors. Compared to both pure 3DVar and Exp-PureEnVar, hybrid EnVar better predicts reflectivity distributions and better maintains a strong mesocyclone. Further examination through the 20 May 2013 Oklahoma supercells confirms these results and additionally demonstrates the effectiveness of adaptive hybridization.

Intercomparison of the impact of INSAT-3D atmospheric motion vectors in 3DVAR and hybrid ensemble-3DVAR data assimilation systems during Indian summer monsoon

The impact of observations in a data assimilation (DA) may depend on various factors, and one aspect that can affect the impact is the specification of the background error covariance matrix. The present study compares the impact of INSAT-3D atmospheric motion vector (AMV) observations in traditional three-dimensional variational (3DVAR) DA system and hybrid ensemble transform Kalman filter (ETKF)-3DVAR DA system (HYBRID) available in Weather Research and Forecast (WRF) modeling system. The objective of the study is to understand how the impact of INSAT-3D AMV observations differ when assimilated using 3DVAR and HYBRID DA systems. The DA experiments are conducted over a ~4-week period of Indian summer monsoon rainfall of July 2016. Four sets of experiments are performed with and without INSAT-3D AMV in both the DA systems. The domain-wide verification with respect to radiosonde observations reveals that forecasts in HYBRID experiments are more accurate than 3DVAR experiments, in general. Geographical distribution depicts the positive impacts of INSAT-3D AMV observations across the domain in both 3DVAR and HYBRID DA systems. The AMV observations show a larger relative impact in HYBRID than in 3DVAR. The relative improvement in HYBRID with AMV DA compared to 3DVAR is 77% and 71% for wind and tropical temperature. The skill scores for quantitative evaluation of precipitation forecast indicate a modest improvement in rainfall for HYBRID run, and incorporating the AMV observation does not considerably enhance the skill of 24-h and 48-h rainfall forecast.

An updated global atmospheric paleo-reanalysis covering the last 400 years.

Data assimilation techniques are becoming increasingly popular for climate reconstruction. They benefit from estimating past climate states from both observation information and from model simulations. The first monthly global paleo‐reanalysis (EKF400) was generated over the 1600 and 2005 time period, and it provides estimates of several atmospheric fields. Here we present a new, considerably improved version of EKF400 (EKF400v2). EKF400v2 uses atmospheric‐only general circulation model simulations with a greatly extended observational network of early instrumental temperature and pressure data, documentary evidences and tree‐ring width and density proxy records. Furthermore, new observation types such as monthly precipitation amounts, number of wet days and coral proxy records were also included in the assimilation. In the version 2 system, the assimilation process has undergone methodological improvements such as the background‐error covariance matrix is estimated with a blending technique of a time‐dependent and a climatological covariance matrices. In general, the applied modifications resulted in enhanced reconstruction skill compared to version 1, especially in precipitation, sea‐level pressure and other variables beside the mostly assimilated temperature data, which already had high quality in the previous version. Additionally, two case studies are presented to demonstrate the applicability of EKF400v2 to analyse past climate variations and extreme events, as well as to investigate large‐scale climate dynamics.