Ensemble Kalman Filter Analyses Research Articles

Assimilation of satellite swaths versus daily means of sea ice concentration in a regional coupled ocean–sea ice model

Abstract. Operational forecasting systems routinely assimilate daily means of sea ice concentration (SIC) from microwave radiometers in order to improve the accuracy of the forecasts. However, the temporal and spatial averaging of the individual satellite swaths into daily means of SIC entails two main drawbacks: (i) the spatial resolution of the original product is blurred (especially critical in periods with strong sub-daily sea ice movement), and (ii) the sub-daily frequency of passive microwave observations in the Arctic are not used, providing less temporal resolution in the data assimilation (DA) analysis and, therefore, in the forecast. Within the SIRANO (Sea Ice Retrievals and data Assimilation in NOrway) project, we investigate how challenges (i) and (ii) can be avoided by assimilating individual satellite swaths (level 3 uncollated) instead of daily means (level 3) of SIC. To do so, we use a regional configuration of the Barents Sea (2.5 km grid) based on the Regional Ocean Modeling System (ROMS) and the Los Alamos Sea Ice Model (CICE) together with the ensemble Kalman filter (EnKF) as the DA system. The assimilation of individual swaths significantly improves the EnKF analysis of SIC compared to the assimilation of daily means; the mean absolute difference (MAD) shows a 10 % improvement at the end of the assimilation period and a 7 % improvement at the end of the 7 d forecast period. This improvement is caused by better exploitation of the information provided by the SIC swath data, in terms of both spatial and temporal variance, compared to the case when the swaths are combined to form a daily mean before assimilation.

Reconstructing tephra fall deposits via ensemble-based data assimilation techniques

Abstract. In recent years, there has been a growing interest in ensemble approaches for modelling the atmospheric transport of volcanic aerosol, ash, and lapilli (tephra). The development of such techniques enables the exploration of novel methods for incorporating real observations into tephra dispersal models. However, traditional data assimilation algorithms, including ensemble Kalman filter (EnKF) methods, can yield suboptimal state estimates for positive-definite variables such as those related to volcanic aerosols and tephra deposits. This study proposes two new ensemble-based data assimilation techniques for semi-positive-definite variables with highly skewed uncertainty distributions, including aerosol concentrations and tephra deposit mass loading: the Gaussian with non-negative constraints (GNC) and gamma inverse-gamma (GIG) methods. The proposed methods are applied to reconstruct the tephra fallout deposit resulting from the 2015 Calbuco eruption using an ensemble of 256 runs performed with the FALL3D dispersal model. An assessment of the methodologies is conducted considering two independent datasets of deposit thickness measurements: an assimilation dataset and a validation dataset. Different evaluation metrics (e.g. RMSE, MBE, and SMAPE) are computed for the validation dataset, and the results are compared to two references: the ensemble prior mean and the EnKF analysis. Results show that the assimilation leads to a significant improvement over the first-guess results obtained from the simple ensemble forecast. The evidence from this study suggests that the GNC method was the most skilful approach and represents a promising alternative for assimilation of volcanic fallout data. The spatial distributions of the tephra fallout deposit thickness and volume according to the GNC analysis are in good agreement with estimations based on field measurements and isopach maps reported in previous studies. On the other hand, although it is an interesting approach, the GIG method failed to improve the EnKF analysis.

EAKF-Based Parameter Optimization Using a Hybrid Adaptive Method

Abstract To effectively reduce model bias and improve assimilation quality, we adopt a hybrid adaptive approach of ensemble adjustment Kalman filter (EAKF) and multigrid analysis (MGA), called EAKF-MGA, to implement parameter optimization as follows. For each assimilation cycle, observations are used to adjust the prior ensembles of both state variables and parameters using the EAKF without inflation. Then, the MGA is adaptively triggered to extract multiscale information from the observational residual to innovate the ensemble mean of the state once again. Results of biased twin experiments consisting of a barotropic spectral model and idealized observation systems show that the proposed EAKF-MGA is insensitive to state variance inflation and localization during the parameter optimization process, compared with the EAKF with adaptive inflation. We also find that computational efficiency is another important advantage of the EAKF-MGA for both state estimation and parameter estimation since extremely small ensemble size is allowed, while the EAKF with adaptive inflation does not work anymore. In essence, the EAKF-MGA is designed to estimate and correct systematic errors jointly with model’s state variables. Through alleviating biases, including the model bias caused by the biased parameter and the analysis bias resulting from the sampling noise given the limited ensemble size, it can be guaranteed that the analysis in the EAKF-MGA will be proceeded onward with the standard assumption of the unbiased model background field in modern data assimilation theory to be met.

Short-Term Convection-Allowing Ensemble Precipitation Forecast Sensitivity to Resolution of Initial Condition Perturbations and Central Initial States

Abstract Nine sets of 36-h, 10-member, convection-allowing ensemble (CAE) forecasts with 3-km horizontal grid spacing were produced over the conterminous United States for a 4-week period. These CAEs had identical configurations except for their initial conditions (ICs), which were constructed to isolate CAE forecast sensitivity to resolution of IC perturbations and central initial states about which IC perturbations were centered. The IC perturbations and central initial states were provided by limited-area ensemble Kalman filter (EnKF) analyses with both 15- and 3-km horizontal grid spacings, as well as from NCEP’s Global Forecast System (GFS) and Global Ensemble Forecast System. Given fixed-resolution IC perturbations, reducing horizontal grid spacing of central initial states improved ∼1–12-h precipitation forecasts. Conversely, for constant-resolution central initial states, reducing horizontal grid spacing of IC perturbations led to comparatively smaller short-term forecast improvements or none at all. Overall, all CAEs initially centered on 3-km EnKF mean analyses produced objectively better ∼1–12-h precipitation forecasts than CAEs initially centered on GFS or 15-km EnKF mean analyses regardless of IC perturbation resolution, strongly suggesting it is more important for central initial states to possess fine-scale structures than IC perturbations for short-term CAE forecasting applications, although fine-scale perturbations could potentially be critical for data assimilation purposes. These findings have important implications for future operational CAE forecast systems and suggest CAE IC development efforts focus on producing the best possible high-resolution deterministic analyses that can serve as central initial states for CAEs. Significance Statement Ensembles of weather model forecasts are composed of different “members” that, when combined, can produce probabilities that specific weather events will occur. Ensemble forecasts begin from specified atmospheric states, called initial conditions. For ensembles where initial conditions differ across members, the initial conditions can be viewed as a set of small perturbations added to a central state provided by a single model field. Our study suggests it is more important to increase horizontal resolution of the central state than resolution of the perturbations when initializing ensemble forecasts with 3-km horizontal grid spacing. These findings suggest a potential for computational savings and a streamlined process for improving high-resolution ensemble initial conditions.

Object-Based Verification of GSI EnKF and Hybrid En3DVar Radar Data Assimilation and Convection-Allowing Forecasts within a Warn-on-Forecast Framework

Abstract The Center for Analysis and Prediction of Storms has recently developed capabilities to directly assimilate radar reflectivity and radial velocity data within the GSI-based ensemble Kalman filter (EnKF) and hybrid ensemble three-dimensional variational (En3DVar) system for initializing convective-scale forecasts. To assess the performance of EnKF and hybrid En3DVar with different hybrid weights (with 100%, 20%, and 0% of static background error covariance corresponding to pure 3DVar, hybrid En3DVar, and pure En3DVar) for assimilating radar data in a Warn-on-Forecast framework, a set of data assimilation and forecast experiments using the WRF Model are conducted for six convective storm cases of May 2017. Using an object-based verification approach, forecast objects of composite reflectivity and 30-min updraft helicity swaths are verified against reflectivity and rotation track objects in Multi-Radar Multi-Sensor data on space and time scales typical of National Weather Service warnings. Forecasts initialized by En3DVar or the best performing EnKF ensemble member produce the highest object-based verification scores, while forecasts from 3DVar and the worst EnKF member produce the lowest scores. Averaged across six cases, hybrid En3DVar using 20% static background error covariance does not improve forecasts over pure En3DVar, although improvements are seen in some individual cases. The false alarm ratios of EnKF members for both composite reflectivity and updraft helicity at the initial time are lower than those from variational methods, suggesting that EnKF analysis reduces spurious reflectivity and mesocyclone objects more effectively.

Dynamics and Predictability of Tropical Cyclone Rapid Intensification in Ensemble Simulations of Hurricane Patricia (2015).

Hurricane Patricia (2015) over the eastern Pacific was a record‐breaking tropical cyclone (TC) under a very favorable environment during its rapid intensification (RI) period, which makes it an optimal real case for studying RI dynamics and predictability. In this study, we performed ensemble Kalman filter analyses at Patricia's early development stage using both traditional observations and the Office of Naval Research Tropical Cyclone Intensity (TCI) field campaign data. It is shown that assimilating the inner‐core TCI observations produces a stronger initial vortex and significantly improves the prediction of RI. Analysis of observation sensitivity experiments shows that the deep‐layer dropsonde observations have high impact on both the primary and secondary circulations for the entire troposphere while the radar observations have the most impact on the primary circulations near aircraft flight level. A wide range of intensification scenarios are obtained through two sets of ensemble forecasts initialized with and without assimilating the TCI data prior to the RI onset. Verification of the ensemble forecasts against the TCI observations during the RI period shows that forecast errors toward later stages can originate from two different error sources at early stages of the vortex structure: One is a timing error from a delayed vortex development such that the TC evolution is the same but shifted in time; the other is due to a totally different storm such that there is no moment in time the simulated storm can obtain a correct TC structure.

Comparing Partial and Continuously Cycling Ensemble Kalman Filter Data Assimilation Systems for Convection-Allowing Ensemble Forecast Initialization

Abstract Several limited-area 80-member ensemble Kalman filter (EnKF) data assimilation systems with 15-km horizontal grid spacing were run over a computational domain spanning the conterminous United States (CONUS) for a 4-week period. One EnKF employed continuous cycling, where the prior ensemble was always the 1-h forecast initialized from the previous cycle’s analysis. In contrast, the other EnKFs used a partial cycling procedure, where limited-area states were discarded after 12 or 18 h of self-contained hourly cycles and reinitialized the next day from global model fields. “Blended” states were also constructed by combining large scales from global ensemble initial conditions (ICs) with small scales from limited-area continuously cycling EnKF analyses using a low-pass filter. Both the blended states and EnKF analysis ensembles initialized 36-h, 10-member ensemble forecasts with 3-km horizontal grid spacing. Continuously cycling EnKF analyses initialized ∼1–18-h precipitation forecasts that were comparable to or somewhat better than those with partial cycling EnKF ICs. Conversely, ∼18–36-h forecasts with partial cycling EnKF ICs were comparable to or better than those with unblended continuously cycling EnKF ICs. However, blended ICs yielded ∼18–36-h forecasts that were statistically indistinguishable from those with partial cycling ICs. ICs that more closely resembled global analysis spectral characteristics at wavelengths > 200 km, like partial cycling and blended ICs, were associated with relatively good ∼18–36-h forecasts. Ultimately, findings suggest that EnKFs employing a combination of continuous cycling and blending can potentially replace the partial cycling assimilation systems that currently initialize operational limited-area models over the CONUS without sacrificing forecast quality. SIGNIFICANCE STATEMENT Numerical weather prediction models (i.e., weather models) are initialized through a process called data assimilation, which combines real atmospheric observations with a previous short-term weather model forecast using statistical techniques. The overarching data assimilation strategy currently used to initialize operational regional weather models over the United States has several disadvantages that ultimately limit progress toward improving weather model forecasts. Thus, we suggest an alternative data assimilation strategy be adopted to initialize a next-generation, high-resolution (∼3 km) probabilistic forecast system currently being developed. This alternative approach preserves forecast quality while fostering a framework that can accelerate weather model improvements, which in turn will lead to better weather forecasts.

Evaluation of soil state representation in the NCAR ensemble analysis system

Accurate characterization of soil state is imperative for weather and climate research, hydrological modeling, agriculture, water resources management, and drought monitoring. Limited-area data assimilation (DA) systems can provide high-resolution real-time soil state analyses. However, soil state representations from regional continuously cycling DA systems have not been examined. This study evaluates soil moisture and temperature estimates and spread characteristics from a real-time, limited-area, continuously-cycling ensemble Kalman filter (EnKF) data assimilation (DA) system run at the National Center for Atmospheric Research (NCAR) for 2.7 years over the conterminous United States (CONUS). Soil moisture and temperature data from both the EnKF and operational Global Forecast System (GFS) analysis are compared against the North American Land Data Assimilation System (NLDAS-2) soil state estimates. Results demonstrate the continuously-cycling EnKF was generally able to represent the spatial and temporal characteristics of soil moisture and temperature across the CONUS, demonstrating the feasibility of using limited-area continuously cycling EnKFs as a method to improve simulations of soil moisture and temperature. Soil state estimates from the NCAR ensemble exhibited lower Bias and RMSE compared to GFS analyses over west and southeast CONUS. Additionally, the ensemble spread characteristics suggest that future limited-area continuously cycling EnKF systems could successfully assimilate both in situ and remotely-sensed soil moisture and temperature observations to further improve soil state analyses.

Nonlinear Forecast Error Growth of Rapidly Intensifying Hurricane Harvey (2017) Examined through Convection-Permitting Ensemble Assimilation of GOES-16 All-Sky Radiances

AbstractThe dynamics and predictability of the rapid intensification (RI) of Hurricane Harvey (2017) were examined using convection-permitting initialization, analysis, and prediction from a cycling ensemble Kalman filter (EnKF) that assimilated all-sky infrared radiances from the Advanced Baseline Imager on GOES-16. The EnKF analyses were able to evolve the various scales of the radiance fields associated with Harvey close to those observed, including those associated with scattered individual convective cells before the onset of rapid intensification (RI) and the organized vortex-scale convective system during and after RI. This was true for more than 3 days of a continuous assimilation cycling. Deterministic forecasts initialized from the EnKF analyses captured the rapidly deepening intensity of Harvey more than 24 h prior to its onset. To explore the predictability of Harvey’s intensity during RI, ensemble probabilistic forecasts and sensitivity analyses were conducted. It was found that significant ensemble spread growth was induced by initial perturbations individually in either the wind or moisture fields. The nonlinear interactions between wind and moisture perturbations further limited the predictability of the intensification process of Harvey by increasing the uncertainty in the simulated wind and moisture distributions and modifying the convective activity and its feedback on vortex flow. This study highlights both the importance of better initializing the dynamic and moisture state variables simultaneously and the potential contribution of satellite all-sky radiance assimilation on constraining them and their associated convective activity that impacts RI of tropical cyclones.

Toward Unifying Short-Term and Next-Day Convection-Allowing Ensemble Forecast Systems with a Continuously Cycling 3-km Ensemble Kalman Filter over the Entire Conterminous United States

AbstractUsing the Weather Research and Forecasting Model, 80-member ensemble Kalman filter (EnKF) analyses with 3-km horizontal grid spacing were produced over the entire conterminous United States (CONUS) for 4 weeks using 1-h continuous cycling. For comparison, similarly configured EnKF analyses with 15-km horizontal grid spacing were also produced. At 0000 UTC, 15- and 3-km EnKF analyses initialized 36-h, 3-km, 10-member ensemble forecasts that were verified with a focus on precipitation. Additionally, forecasts were initialized from operational Global Ensemble Forecast System (GEFS) initial conditions (ICs) and experimental “blended” ICs produced by combining large scales from GEFS ICs with small scales from EnKF analyses using a low-pass filter. The EnKFs had stable climates with generally small biases, and precipitation forecasts initialized from 3-km EnKF analyses were more skillful and reliable than those initialized from downscaled GEFS and 15-km EnKF ICs through 12–18 and 6–12 h, respectively. Conversely, after 18 h, GEFS-initialized precipitation forecasts were better than EnKF-initialized precipitation forecasts. Blended 3-km ICs reflected the respective strengths of both GEFS and high-resolution EnKF ICs and yielded the best performance considering all times: blended 3-km ICs led to short-term forecasts with similar or better skill and reliability than those initialized from unblended 3-km EnKF analyses and ~18–36-h forecasts possessing comparable quality as GEFS-initialized forecasts. This work likely represents the first time a convection-allowing EnKF has been continuously cycled over a region as large as the entire CONUS, and results suggest blending high-resolution EnKF analyses with low-resolution global fields can potentially unify short-term and next-day convection-allowing ensemble forecast systems under a common framework.

Enhancing ensemble data assimilation into one‐way‐coupled models with one‐step‐ahead smoothing

AbstractThis study investigates the filtering problem with one‐way coupled (OWC) state‐space systems, for which the joint ensemble Kalman filter (EnKF) is the standard solution. In this approach, the states of the two coupled sub‐systems are jointly updated with all incoming observations. This enables transfer of the information across the sub‐systems, which should provide coupled‐state estimates in better agreement with the observations. The state estimates of the joint EnKF highly depend on the relevance of the joint ensembles' cross‐covariances between the sub‐systems' variables. In this work, we propose a new joint EnKF scheme based on the One‐Step‐Ahead (OSA) smoothing formulation of the filtering problem for efficient assimilation into OWC systems. The scheme introduces an extra smoothing step for both states' sub‐systems with the future observations, followed by an analysis step for each sub‐system state using only its own observation, all within a Bayesian‐consistent framework. The extra OSA smoothing step enables us to more efficiently exploit the observations, to enhance the representativeness of the EnKF covariances, and to mitigate for reported inconsistencies in the joint EnKF analysis step. We demonstrate the relevance of the proposed approach by presenting and analyzing results of various numerical experiments conducted with a OWC Lorenz‐96 model.

Evaluating Ensemble Kalman Filter Analyses of Severe Hailstorms on 8 May 2017 in Colorado: Effects of State Variable Updating and Multimoment Microphysics Schemes on State Variable Cross Covariances

Abstract Ensemble Kalman filter (EnKF) analyses of the storms associated with the 8 May 2017 Colorado severe hail event using either the Milbrandt and Yau (MY) or the NSSL double-moment bulk microphysics scheme in the forecast model are evaluated. With each scheme, two experiments are conducted in which the reflectivity (Z) observations update in addition to dynamic and thermodynamic variables: 1) only the hydrometeor mixing ratios or 2) all microphysical variables. With fewer microphysical variables directly constrained by the Z observations, only updating hydrometeor mixing ratios causes the forecast error covariance structure to become unreliable, and results in larger errors in the analysis. Experiments that update all microphysical variables produce analyses with the lowest Z root-mean-square innovations; however, comparing the estimated hail size against hydrometeor classification algorithm output suggests that further constraint from observations is needed to more accurately estimate surface hail size. Ensemble correlation analyses are performed to determine the impact of hail growth assumptions in the MY and NSSL schemes on the forecast error covariance between microphysical and thermodynamic variables. In the MY scheme, Z is negatively correlated with updraft intensity because the strong updrafts produce abundant small hail aloft. The NSSL scheme predicts the growth of large hail aloft; consequently, Z is positively correlated with storm updraft intensity and hail state variables. Hail production processes are also shown to alter the background error covariance for liquid and frozen hydrometeor species. Results in this study suggest that EnKF analyses are sensitive to the choice of MP scheme (e.g., the treatment of hail growth processes).

Simultaneous Assimilation of Radar and All-Sky Satellite Infrared Radiance Observations for Convection-Allowing Ensemble Analysis and Prediction of Severe Thunderstorms

Abstract This study explores the benefits of assimilating infrared (IR) brightness temperature (BT) observations from geostationary satellites jointly with radial velocity (Vr) and reflectivity (Z) observations from Doppler weather radars within an ensemble Kalman filter (EnKF) data assimilation system to the convection-allowing ensemble analysis and prediction of a tornadic supercell thunderstorm event on 12 June 2017 across Wyoming and Nebraska. While radar observations sample the three-dimensional storm structures with high fidelity, BT observations provide information about clouds prior to the formation of precipitation particles when in-storm radar observations are not yet available and also provide information on the environment outside the thunderstorms. To better understand the strengths and limitations of each observation type, the satellite and Doppler radar observations are assimilated separately and jointly, and the ensemble analyses and forecasts are compared with available observations. Results show that assimilating BT observations has the potential to increase the forecast and warning lead times of severe weather events compared with radar observations and may also potentially complement the sparse surface observations in some regions as revealed by the probabilistic prediction of mesocyclone tracks initialized from EnKF analyses as various times. Additionally, the assimilation of both BT and Vr observations yields the best ensemble forecasts, providing higher confidence, improved accuracy, and longer lead times on the probabilistic prediction of midlevel mesocyclones.

The Impact of Satellite Radiance Data Assimilation within a Frequently Updated Regional Forecast System Using a GSI-based Ensemble Kalman Filter

A regional ensemble Kalman filter (EnKF) data assimilation (DA) and forecast system was recently established based on the Gridpoint Statistical Interpolation (GSI) analysis system. The EnKF DA system was tested with continuous three-hourly updated cycles followed by 18-h deterministic forecasts from every three-hourly ensemble mean analysis. Initial tests showed negative to neutral impacts of assimilating satellite radiance data due to the improper bias correction procedure. In this study, two bias correction schemes within the established EnKF DA system are investigated and the impact of assimilating additional polar-orbiting satellite radiance is also investigated. Two group experiments are conducted. The purpose of the first group is to evaluate the bias correction procedure. Two online bias correction methods based on GSI 3DVar and EnKF algorithms are used to assimilate AMSU-A radiance data. Results show that both variational and EnKF-based bias correction procedures effectively reduce the observation and background radiance differences, achieving positive impacts on forecasts. With proper bias correction, we assimilate full radiance observations including AMSU-A, AMSU-B, AIRS, HIRS3/4, and MHS in the second group. The relative percentage improvements (RPIs) for all forecast variables compared to those without radiance data assimilation are mostly positive, with the RPI of upper-air relative humidity being the largest. Additionally, precipitation forecasts on a downscaled 13-km grid from 40-km EnKF analyses are also improved by radiance assimilation for almost all forecast hours.

Combining ensemble Kalman filter and multiresolution analysis for efficient assimilation into adaptive mesh models

A new approach is developed for data assimilation into adaptive mesh models with the ensemble Kalman filter (EnKF). The EnKF is combined with a wavelet-based multiresolution analysis (MRA) scheme to enable robust and efficient assimilation in the context of reduced-complexity adaptive spatial discretization. The wavelet representation of the solution enables the use of different meshes that are individually adapted to the corresponding members of the EnKF ensemble. The analysis step of the EnKF is then performed by involving coarsening, refinement, and projection operations on its ensemble members. Depending on the choice of these operations, five variants of the MRA-EnKF are introduced, and tested on the one-dimensional Burgers equation with periodic boundary condition. The numerical results suggest that, given an appropriate tolerance value for the coarsening operation, four out of the five proposed schemes significantly reduce the computational complexity of the assimilation system, with marginal accuracy loss compared to the reference, full resolution, and EnKF solution. Overall, the proposed framework offers the possibility of capitalizing on the advantages of adaptive mesh techniques, and the flexibility of choosing suitable context-oriented criteria for efficient data assimilation.

Data assimilation using adaptive, non-conservative, moving mesh models

Abstract. Numerical models solved on adaptive moving meshes have become increasingly prevalent in recent years. Motivating problems include the study of fluids in a Lagrangian frame and the presence of highly localized structures such as shock waves or interfaces. In the former case, Lagrangian solvers move the nodes of the mesh with the dynamical flow; in the latter, mesh resolution is increased in the proximity of the localized structure. Mesh adaptation can include remeshing, a procedure that adds or removes mesh nodes according to specific rules reflecting constraints in the numerical solver. In this case, the number of mesh nodes will change during the integration and, as a result, the dimension of the model's state vector will not be conserved. This work presents a novel approach to the formulation of ensemble data assimilation (DA) for models with this underlying computational structure. The challenge lies in the fact that remeshing entails a different state space dimension across members of the ensemble, thus impeding the usual computation of consistent ensemble-based statistics. Our methodology adds one forward and one backward mapping step before and after the ensemble Kalman filter (EnKF) analysis, respectively. This mapping takes all the ensemble members onto a fixed, uniform reference mesh where the EnKF analysis can be performed. We consider a high-resolution (HR) and a low-resolution (LR) fixed uniform reference mesh, whose resolutions are determined by the remeshing tolerances. This way the reference meshes embed the model numerical constraints and are also upper and lower uniform meshes bounding the resolutions of the individual ensemble meshes. Numerical experiments are carried out using 1-D prototypical models: Burgers and Kuramoto–Sivashinsky equations and both Eulerian and Lagrangian synthetic observations. While the HR strategy generally outperforms that of LR, their skill difference can be reduced substantially by an optimal tuning of the data assimilation parameters. The LR case is appealing in high dimensions because of its lower computational burden. Lagrangian observations are shown to be very effective in that fewer of them are able to keep the analysis error at a level comparable to the more numerous observers for the Eulerian case. This study is motivated by the development of suitable EnKF strategies for 2-D models of the sea ice that are numerically solved on a Lagrangian mesh with remeshing.

Ensemble Kalman Filter Assimilation of Polarimetric Radar Observations for the 20 May 2013 Oklahoma Tornadic Supercell Case

Abstract Real polarimetric radar observations are directly assimilated for the first time using the ensemble Kalman filter (EnKF) for a supercell case from 20 May 2013 in Oklahoma. A double-moment microphysics scheme and advanced polarimetric radar observation operators are used together to estimate the model states. Lookup tables for the observation operators are developed based on T-matrix scattering amplitudes for all hydrometeor categories, which improve upon previous curved-fitted approximations of T-matrix scattering amplitudes or the Rayleigh approximation. Two experiments are conducted: one assimilates reflectivity (Z) and radial velocity (Vr) (EXPZ), and one assimilates in addition differential reflectivity (ZDR) below the observed melting level at ~2-km height (EXPZZDR). In the EnKF analyses, EXPZZDR exhibits a ZDR arc that better matches observations than EXPZ. EXPZZDR also has higher ZDR above 2 km, consistent with the observed ZDR column. Additionally, EXPZZDR has an improved estimate of the model microphysical states. Specifically, the rain mean mass diameter (Dnr) in EXPZZDR is higher in the ZDR arc region and the total rain number concentration (Ntr) is lower downshear in the forward flank than EXPZ when compared to values retrieved from the polarimetric observations. Finally, a negative gradient of hail mean mass diameter (Dnh) is found in the right-forward flank of the EXPZZDR analysis, which supports previous findings indicating that size sorting of hail, as opposed to rain, has a more significant impact on low-level polarimetric signatures. This paper represents a proof-of-concept study demonstrating the value of assimilating polarimetric radar data in improving the analysis of features and states related to microphysics in supercell storms.

Using the hybrid gain algorithm to sample data assimilation uncertainty

At the Canadian Meteorological Centre (CMC), an ensemble variational (EnVar) data assimilation system is used for the global deterministic prediction system and an ensemble Kalman filter (EnKF) is used for the global ensemble prediction system. These two systems are co‐developed and co‐evolving at the CMC and in this study we explore how to maximize the impact of having two algorithms.Following earlier work at the European Centre for Medium‐Range Weather Forecasts (ECMWF), we perform experiments with a pure EnKF and an EnKF system that is recentered on the EnVar solution, as well as with a hybrid gain configuration, in which the EnKF system is recentered on the mean of the EnKF and EnVar analyses. Encouraged by the results of the hybrid gain algorithm, we modify it to leave half of the members unchanged and to recenter the other half on the EnVar analysis. With this multi‐analysis approach, we sample the different design decisions made for the EnKF and EnVar and see corresponding improvements, notably for the stratospheric analysis.An evaluation using humidity‐sensitive radiance channels shows more mixed results of the hybrid gain and multi‐analysis approaches. An investigation of the spread–skill relation showed that the background ensembles were overdispersive for humidity and this issue was resolved by a reduction of the additive error for humidity. This highlights the fact that diagnostic information from two analysis systems can be used to identify where those systems have room for improvement. Finally, for various aspects of data assimilation systems, we weigh the benefits of algorithmic diversity against the corresponding additional development cost.

Assimilation of All-Sky Infrared Radiances from Himawari-8 and Impacts of Moisture and Hydrometer Initialization on Convection-Permitting Tropical Cyclone Prediction

Abstract This study explores the impacts of assimilating all-sky infrared satellite radiances from Himawari-8, a new-generation geostationary satellite that shares similar remote sensing technology with the U.S. geostationary satellite GOES-16, for convection-permitting initialization and prediction of tropical cyclones with an ensemble Kalman filter (EnKF). This case studies the rapid intensification stages of Supertyphoon Soudelor (2015), one of the most intense tropical cyclones ever observed by Himawari-8. It is found that hourly cycling assimilation of the infrared radiance improves not only the estimate of the initial intensity, but also the spatial distribution of essential convective activity associated with the incipient tropical cyclone vortex. Deterministic convection-permitting forecasts initialized from the EnKF analyses are capable of simulating the early development of Soudelor, which demonstrates encouraging prospects for future improvement in tropical cyclone prediction through assimilating all-sky radiances from geostationary satellites such as Himawari-8 and GOES-16. A series of forecast sensitivity experiments are designed to systematically explore the impacts of moisture updates in the data assimilation cycles on the development and prediction of Soudelor. It is found that the assimilation of the brightness temperatures contributes not only to better constraining moist convection within the inner-core region, but also to developing a more resilient initial vortex, both of which are necessary to properly capture the rapid intensification process of tropical cyclones.

A two-stage ensemble Kalman filter based on multiscale model reduction for inverse problems in time fractional diffusion-wave equations

Ensemble Kalman filter (EnKF) has been widely used in state estimation and parameter estimation for the dynamic system where observational data is obtained sequentially in time. Very burdened simulations for the forward problem are needed to update a large number of EnKF ensemble samples. This will slow down the analysis efficiency of the EnKF for large-scale and high dimensional models. To reduce uncertainty and accelerate posterior inference, a two-stage ensemble Kalman filter is presented to improve the sequential analysis of EnKF. It is known that the final posterior ensemble may be concentrated in a small portion of the entire support of the initial prior ensemble. It will be much more efficient if we first build a new prior by some partial observations, and construct a surrogate only over the significant region of the new prior. To this end, we construct a very coarse model using generalized multiscale finite element method (GMsFEM) and generate a new prior ensemble in the first stage. GMsFEM provides a set of hierarchical multiscale basis functions supported in coarse blocks. This gives flexibility and adaptivity to choosing degree of freedoms to construct a reduce model. In the second stage, we build an initial surrogate model based on the new prior by using GMsFEM and sparse generalized polynomial chaos (gPC)-based stochastic collocation methods. To improve the initial surrogate model, we dynamically update the surrogate model, which is adapted to the sequential availability of data and the updated analysis. The two-stage EnKF can achieve a better estimation than standard EnKF, and significantly improve the efficiency to update the ensemble analysis (posterior exploration). To enhance the applicability and flexibility in Bayesian inverse problems, we extend the two-stage EnKF to non-Gaussian models and hierarchical models. In the paper, we focus on the time fractional diffusion-wave models in porous media and investigate their Bayesian inverse problems using the proposed two-stage EnKF. A few numerical examples are carried out to demonstrate the performance of the two-stage EnKF method by taking account of parameter and structure inversion in permeability fields and source functions.