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Radar rainfall forecasting is of major importance to predict flows in the sewer system to enhance early flood warning systems in urban areas. In this context, reducing radar rainfall estimation uncertainties can improve rainfall forecasts. This study utilises an ensemble generator that assesses radar rainfall uncertainties based on historical rain gauge data as ground truth. The ensemble generator is used to produce probabilistic radar rainfall forecasts (radar ensembles). The radar rainfall forecast ensembles are compared against a stochastic ensemble generator. The rainfall forecasts are used to predict sewer flows in a small urban area in the north of England using an Infoworks CS model. Uncertainties in radar rainfall forecasts are assessed using relative operating characteristic (ROC) curves, and the results showed that the radar ensembles overperform the stochastic ensemble generator in the first hour of the forecasts. The forecast predictability is however rapidly lost after 30 min lead-time. This implies that knowledge of the statistical properties of the radar rainfall errors can help to produce more meaningful radar rainfall forecast ensembles.

Sophisticated strategies are required for flood warning in urban areas regarding convective heavy rainfall events. An approach is presented to improve short-term precipitation forecasts by combining ensembles of radar nowcasts with the high-resolution numerical weather predictions COSMO-DE-EPS of the German Weather Service. The combined ensemble forecasts are evaluated and compared to deterministic precipitation forecasts of COSMO-DE. The results show a significantly improved quality of the short-term precipitation forecasts and great potential to improve flood warnings for urban catchments. The combined ensemble forecasts are produced operationally every 5 min. Applications involve the Flood Warning Service Hamburg (WaBiHa) and real-time hydrological simulations with the model KalypsoHydrology.

This study describes a real-time implementation of valid time shifting (VTS) within the Gridpoint Statistical Interpolation–based ensemble-variational (EnVar) data assimilation system, developed at the Multi-Scale Data Assimilation and Predictability Laboratory. This system, featuring data assimilation of mesoscale conventional observations and storm-scale radar reflectivity observations and interfaced with the next-generation Finite Volume Cubed Sphere Dynamical Core limited-area model (FV3-LAM), was run in real-time during the 2021 Hazardous Weather Testbed Spring Forecast Experiment. The VTS method efficiently increases ensemble size by incorporating ensemble forecast output before and after the central analysis. Two configurations were examined to systematically evaluate VTS: a baseline 36-member system with hourly data assimilation (NOVTS), and an experiment testing VTS for the radar analysis step. Verification across 22 cases shows statistically significant benefits of VTS to increase ensemble spread and better fit first guesses to observations. Control member forecasts launched at 0000 UTC have consistently higher skill, lower bias, and higher reliability in VTS than in NOVTS throughout the 18-h forecast evaluation period, especially from severe cases often featuring upscale growth into mesoscale convective systems. Verification of updraft helicity-based ensemble surrogate severe probabilistic forecasts against observed storm reports shows higher skill of VTS when verifying on finer scales, with benefits to constraining higher probabilities over report locations and reducing probabilities over no-report locations. This study is a first step toward the next-generation Rapid Refresh Forecast System (RRFS), demonstrating the feasibility of such a real-time system and the potential benefits of VTS implementation.

This paper reviews the development of the ensemble Kalman filter (EnKF) for atmospheric data assimilation. Particular attention is devoted to recent advances and current challenges. The distinguishing properties of three well-established variations of the EnKF algorithm are first discussed. Given the limited size of the ensemble and the unavoidable existence of errors whose origin is unknown (i.e., system error), various approaches to localizing the impact of observations and to accounting for these errors have been proposed. However, challenges remain; for example, with regard to localization of multiscale phenomena (both in time and space). For the EnKF in general, but higher-resolution applications in particular, it is desirable to use a short assimilation window. This motivates a focus on approaches for maintaining balance during the EnKF update. Also discussed are limited-area EnKF systems, in particular with regard to the assimilation of radar data and applications to tracking severe storms and tropical cyclones. It seems that relatively less attention has been paid to optimizing EnKF assimilation of satellite radiance observations, the growing volume of which has been instrumental in improving global weather predictions. There is also a tendency at various centers to investigate and implement hybrid systems that take advantage of both the ensemble and the variational data assimilation approaches; this poses additional challenges and it is not clear how it will evolve. It is concluded that, despite more than 10 years of operational experience, there are still many unresolved issues that could benefit from further research. Contents Introduction ...4490 Popular flavors of the EnKF algorithm ...4491 General description...4491 Stochastic and deterministic filters...4492 The stochastic filter...4492 The deterministic filter...4492 Sequential or local filters...4493 Sequential ensemble Kalman filters...4493 The local ensemble transform Kalman filter...4494 Extended state vector...4494 Issues for the development of algorithms...4495 Use of small ensembles ...4495 Monte Carlo methods...4495 Validation of reliability...4497 Use of group filters with no inbreeding...4498 Sampling error due to limited ensemble size: The rank problem...4498 Covariance localization...4499 Localization in the sequential filter...4499 Localization in the LETKF...4499 Issues with localization...4500 Summary...4501 Methods to increase ensemble spread ...4501 Covariance inflation...4501 Additive inflation...4501 Multiplicative inflation...4502 Relaxation to prior ensemble information...4502 Issues with inflation...4503 Diffusion and truncation...4503 Error in physical parameterizations...4504 Physical tendency perturbations...4504 Multimodel, multiphysics, and multiparameter approaches...4505 Future directions...4505 Realism of error sources...4506 Balance and length of the assimilation window ...4506 The need for balancing methods...4506 Time-filtering methods...4506 Toward shorter assimilation windows...4507 Reduction of sources of imbalance...4507 Regional data assimilation ...4508 Boundary conditions and consistency across multiple domains...4509 Initialization of the starting ensemble...4510 Preprocessing steps for radar observations...4510 Use of radar observations for convective-scale analyses...4511 Use of radar observations for tropical cyclone analyses...4511 Other issues with respect to LAM data assimilation...4511 The assimilation of satellite observations ...4512 Covariance localization...4512 Data density...4513 Bias-correction procedures...4513 Impact of covariance cycling...4514 Assumptions regarding observational error...4514 Recommendations regarding satellite observations...4515 Computational aspects ...4515 Parameters with an impact on quality...4515 Overview of current parallel algorithms...4516 Evolution of computer architecture...4516 Practical issues...4517 Approaching the gray zone...4518 Summary...4518 Hybrids with variational and EnKF components ...4519 Hybrid background error covariances...4519 E4DVar with the α control variable...4519 Not using linearized models with 4DEnVar...4520 The hybrid gain algorithm...4521 Open issues and recommendations...4521 Summary and discussion ...4521 Stochastic or deterministic filters...4522 The nature of system error...4522 Going beyond the synoptic scales...4522 Satellite observations...4523 Hybrid systems...4523 Future of the EnKF...4523 APPENDIX A ...4524 Types of Filter Divergence ...4524 Classical filter divergence...4524 Catastrophic filter divergence...4524 APPENDIX B ...4524 Systems Available for Download ...4524 References ...4525

In the ensemble Kalman filter (EnKF), the covariance localization radius is usually small when assimilating radar observations because of high density of the radar observations. This makes the region away from precipitation difficult to correct using only radar data stating “no echo” if no other observations are available, as there is no reason to correct the background. To correct errors away from innovating radar observations, a multiscale localization (MLoc) method adapted to dense observations like those from radar is proposed. In this method, different scales are corrected successively by using the same reflectivity observations, but with a different degree of smoothing and localization radius at each step. In the context of observing system simulation experiments, single and multiple assimilation experiments are conducted with the MLoc method. Results show that the MLoc assimilation updates areas that are away from the innovative observations and improves on average the analysis and forecast quality in single cycle and cycling assimilation experiments. The forecast gains are maintained until the end of the forecast period, illustrating the benefits of correcting different scales.

The success of the National Severe Storms Laboratory’s (NSSL) experimental Warn-on-Forecast System (WoFS) to provide useful probabilistic guidance of severe and hazardous weather is mostly due to the frequent assimilation of observations, especially radar observations. Phased-array radar (PAR) technology, which is a potential candidate to replace the current U.S. operational radar network, would allow for even more rapid assimilation of radar observations by providing full-volumetric scans of the atmosphere every ∼1 min. Based on previous studies, more frequent PAR data assimilation can lead to improved forecasts, but it can also lead to ensemble underdispersion and suboptimal observation assimilation. The use of stochastic and perturbed parameter methods to increase ensemble spread is a potential solution to this problem. In this study, four stochastic and perturbed parameter methods are assessed using a 1-km-scale version of the WoFS and include the stochastic kinetic energy backscatter (SKEB) scheme, the physically based stochastic perturbation (PSP) scheme, a fixed perturbed parameters (FPP) method, and a novel surface-model scheme blending (SMSB) method. Using NSSL PAR observations from the 9 May 2016 tornado outbreak, experiments are conducted to assess the impact of the methods individually, in different combinations, and with different cycling intervals. The results from these experiments reveal the potential benefits of stochastic and perturbed parameter methods for future versions of the WoFS. Stochastic and perturbed parameter methods can lead to more skillful forecasts during periods of storm development. Moreover, a combination of multiple methods can result in more skillful forecasts than using a single method.

The current study explores the use of an ensemble Kalman filter (EnKF) based on the Weather Research and Forecasting (WRF) Model to continuously assimilate high-resolution Doppler radar data during the peak-intensity stage of Tropical Cyclone (TC) Vicente (2012) before landfall. The WRF-EnKF analyses and forecasts along with the ensembles initialized from the EnKF analyses at different times were used to examine the subsequent evolution, three-dimensional (3D) structure, predictability, and dynamics of the storm. Vicente was an intense western North Pacific tropical cyclone that made landfall around 2000 UTC 23 July 2012 near the Pearl River Delta region of Guangdong Province, China, with a peak 10-m wind speed around 44 m s−1 along with considerable inland flooding after a rapid intensification process. With vortex- and dynamics-dependent background error covariance estimated by the short-term ensemble forecasts, it was found that the WRF-EnKF could efficiently assimilate the high temporal and spatial resolution 3D radar radial velocity to improve the depiction of the TC inner-core structure of Vicente, which in turn improved the forecasts of the track and intensity along with the associated heavy precipitation inland. The ensemble forecasts and sensitivity analyses were further used to explore the leading dynamics that controlled the prediction and predictability of track, intensity, and rainfall during and after its landfall. Results showed that TC Vicente’s intensity and precipitation forecasts were largely dependent on the initial relationship between TC intensity and location and the initial steering flow.

Ensemble-based probabilistic forecasts are performed for a mesoscale convective system (MCS) that occurred over Oklahoma on 8–9 May 2007, initialized from ensemble Kalman filter analyses using multinetwork radar data and different microphysics schemes. Two experiments are conducted, using either a single-moment or double-moment microphysics scheme during the 1-h-long assimilation period and in subsequent 3-h ensemble forecasts. Qualitative and quantitative verifications are performed on the ensemble forecasts, including probabilistic skill scores. The predicted dual-polarization (dual-pol) radar variables and their probabilistic forecasts are also evaluated against available dual-pol radar observations, and discussed in relation to predicted microphysical states and structures. Evaluation of predicted reflectivity (Z) fields shows that the double-moment ensemble predicts the precipitation coverage of the leading convective line and stratiform precipitation regions of the MCS with higher probabilities throughout the forecast period compared to the single-moment ensemble. In terms of the simulated differential reflectivity (ZDR) and specific differential phase (KDP) fields, the double-moment ensemble compares more realistically to the observations and better distinguishes the stratiform and convective precipitation regions. The ZDR from individual ensemble members indicates better raindrop size sorting along the leading convective line in the double-moment ensemble. Various commonly used ensemble forecast verification methods are examined for the prediction of dual-pol variables. The results demonstrate the challenges associated with verifying predicted dual-pol fields that can vary significantly in value over small distances. Several microphysics biases are noted with the help of simulated dual-pol variables, such as substantial overprediction of KDP values in the single-moment ensemble.

We present Multi-Source Weighted-Ensemble Precipitation, version 2 (MSWEP V2), a gridded precipitation P dataset spanning 1979–2017. MSWEP V2 is unique in several aspects: i) full global coverage (all land and oceans); ii) high spatial (0.1°) and temporal (3 hourly) resolution; iii) optimal merging of P estimates based on gauges [WorldClim, Global Historical Climatology Network-Daily (GHCN-D), Global Summary of the Day (GSOD), Global Precipitation Climatology Centre (GPCC), and others], satellites [Climate Prediction Center morphing technique (CMORPH), Gridded Satellite (GridSat), Global Satellite Mapping of Precipitation (GSMaP), and Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis (TMPA) 3B42RT)], and reanalyses [European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-Interim) and Japanese 55-year Reanalysis (JRA-55)]; iv) distributional bias corrections, mainly to improve the P frequency; v) correction of systematic terrestrial P biases using river discharge Q observations from 13,762 stations across the globe; vi) incorporation of daily observations from 76,747 gauges worldwide; and vii) correction for regional differences in gauge reporting times. MSWEP V2 compares substantially better with Stage IV gauge–radar P data than other state-of-the-art P datasets for the United States, demonstrating the effectiveness of the MSWEP V2 methodology. Global comparisons suggest that MSWEP V2 exhibits more realistic spatial patterns in mean, magnitude, and frequency. Long-term mean P estimates for the global, land, and ocean domains based on MSWEP V2 are 955, 781, and 1,025 mm yr−1, respectively. Other P datasets consistently underestimate P amounts in mountainous regions. Using MSWEP V2, P was estimated to occur 15.5%, 12.3%, and 16.9% of the time on average for the global, land, and ocean domains, respectively. MSWEP V2 provides unique opportunities to explore spatiotemporal variations in P, improve our understanding of hydrological processes and their parameterization, and enhance hydrological model performance.

A combined mesoscale and storm-scale ensemble data-assimilation and prediction system is developed using the Advanced Research core of the Weather Research and Forecasting Model (WRF-ARW) and the ensemble adjustment Kalman filter (EAKF) from the Data Assimilation Research Testbed (DART) software package for a short-range ensemble forecast of an 8 May 2003 Oklahoma City, Oklahoma, tornadic supercell storm. Traditional atmospheric observations are assimilated into a 45-member mesoscale ensemble over a continental U.S. domain starting 3 days prior to the event. A one-way-nested 45-member storm-scale ensemble is initialized centered on the tornadic event at 2100 UTC on the day of the event. Three radar observation assimilation and forecast experiments are conducted at storm scale using a single-moment, a semi-double-moment, and a full double-moment bulk microphysics scheme. Results indicate that the EAKF initializes the supercell storm into the model with good accuracy after a 1-h-long radar observation assimilation window. The ensemble forecasts capture the movement of the main supercell storm that matches reasonably well with radar observations. The reflectivity structure of the supercell storm using a double-moment microphysics scheme appears to compare better to the observations than that using a single-moment scheme. In addition, the ensemble system predicts the probability of a strong low-level vorticity track of the tornadic supercell that correlates well with the observed rotation track. The rapid 3-min update cycle of the storm-scale ensemble from the radar observations seems to enhance the skill of the ensemble and the confidence of an imminent tornado threat. The encouraging results obtained from this study show promise for a short-range probabilistic storm-scale forecast of supercell thunderstorms, which is the main goal of NOAA's Warn-on-Forecast initiative.