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Abstract Assimilating polarimetric radar data within a double-moment microphysics scheme requires that both hydrometeor mixing ratios and number concentrations be updated simultaneously to effectively utilize the radar information. This study directly assimilates polarimetric radar data in a fraternal twin observing system simulation experiment (OSSE) using both mixing ratios and number concentrations as analysis variables within a variational approach. A newly developed set of parameterized forward operators for polarimetric radar data, incorporating a new continuous melting model, is employed. To address challenges in minimizing the cost function, a power transformation function is applied to the analysis variables of mixing ratios and number concentrations. This approach alleviates issues arising from the very large dynamic range of number concentrations and the highly nonlinear relationship between the model’s hydrometeors and radar variables. Results from several groups of sensitivity experiments show that updating number concentrations using an appropriate power transformation function together with mixing ratios of hydrometeors reduces the analysis errors of radar variables and improves the analysis of polarimetric radar signatures. Updating number concentrations proves to be quite sensitive when assimilating differential reflectivity, while the additional assimilation of specific differential phase yields smaller analysis errors for reflectivity and mixing ratios of water vapor and rainwater compared to differential reflectivity assimilation alone. Experiments with smaller observation errors provide better analyses of the radar variables but also increase model variable analysis errors. Among the threshold values tested for reflectivity and polarimetric variables, assimilating polarimetric variables at grids where reflectivity exceeds 15 dBZprovides the best qualitative analysis. 

Abstract To cover its large dynamic range, radar reflectivity factors have historically been displayed and used on a logarithmic scale, that is, decibels of reflectivity (dBZ). Logarithmic reflectivity has also been used for data assimilation without being questioned or well validated. However, fundamental limitations exist with directly assimilating logarithmic reflectivity, such as strong nonlinearity of the observation forward operator and the fact that the impacts of small reflectivity values are amplified, leading to exaggerated increments when mapped back into physical space. In this study, we power‐transform both reflectivity and hydrometeor mixing ratios to alleviate the aforementioned issues with using conventional logarithmic reflectivity. Forecast evaluation across eight severe convection events demonstrates that applying the Box‐Cox power transformations to both reflectivity and hydrometeor mixing ratios effectively reduces the nonlinearity between the observations and control variables. This approach significantly improves analyses of model hydrometeor variables and forecasts of composite reflectivity and hourly precipitation. 

Abstract The assimilation of radar reflectivity requires an accurate and efficient forward operator that links the model state variables to radar observations. In this study, newly developed parameterized forward operators (PFO) for radar reflectivity with a new continuous melting model are implemented to assimilate observed radar data. To assess the impact of the novel parameterized reflectivity forward operators on convective storm analysis and forecasting, two distinct sets of cycled assimilation and forecast experiments are conducted. One set of experiments (ExpRFO) uses a conventional Rayleigh‐scattering‐approximation‐based forward operator (RFO) with hydrometeor classification, while the other uses the PFO (ExpPFO_New) for radar reflectivity with a new continuous melting model. Eight high‐impact severe convective weather events from the Hazardous Weather Testbed (HWT) 2019 Spring Experiments are selected for this study. The analysis and forecast results are first examined in detail for a classic tornadic supercell case on 24 May 2019, with the potential benefits provided by the PFO then evaluated for all eight cases. It is demonstrated that ExpPFO_New provides more robust results in terms of improving the short‐term severe weather forecasts. Compared to ExpRFO, ExpPFO_New better reproduces all observed supercells in the analysis field, yields a more continuous and reasonable reflectivity distribution near the melting layer, and improves the strength of the cold pool compared to observations. Overall, ExpPFO_New, initialized from the more accurate analysis fields, produces better forecasts of reflectivity and hourly precipitation with smaller biases, especially at heavy precipitation thresholds. 

Abstract To improve short‐term severe weather forecasts through assimilation of polarimetric radar data (PRD), the use of accurate and efficient forward operators for polarimetric radar variables is required. In this study, a new melting model is proposed to estimate the mixing ratio and number concentration of melting hydrometeor species and incorporated in a set of parameterized polarimetric radar forward operators. The new melting model depends only on the mixing ratio and number concentration of rain and ice species and is characterized by its independence from ambient temperature and its simplicity and ease of linearization. To assess the impact of this newly proposed melting model on the simulated polarimetric radar variables, a real mesoscale convective system is simulated using three double‐moment microphysics schemes. Compared with the output of the original implementation of the parameterized forward operators (PFO_Old) that rely on an “old” melting model which only estimates the mixing ratio of the melting species, the updated implementation with the new melting model (PFO_New) that estimates both the mixing ratio and number concentration of melting species eliminates the very large mass/volume‐weighted mean diameter (D_m) at the bottom of the melting layer and produces more reasonable melting layer signatures for all three double‐moment microphysics schemes that more closely match the corresponding radar observations. This suggests that the new melting model has more reasonable implicit estimates of mixing ratios and number concentrations of melting hydrometeor species than the “old” melting model. 

Abstract This study compares real-time forecasts produced by the Warn-on-Forecast System (WoFS) and a hybrid ensemble and variational data assimilation and prediction system (WoF-Hybrid) for 31 events during 2021. Object-based verification is used to quantify and compare strengths and weaknesses of WoFS ensemble forecasts with 3-km horizontal grid spacing and WoF-Hybrid deterministic forecasts with 1.5-km horizontal grid spacing. The goal of such comparison is to provide evidence as to whether WoF-Hybrid has performance characteristics that complement or improve upon those of WoFS. Results indicate that both systems provide similar accuracy for timing and placement of thunderstorm objects identified using simulated reflectivity. WoF-Hybrid provides more accurate forecasts of updraft helicity tracks. Differences in forecast quality are case dependent; the largest difference in accuracy favoring WoF-Hybrid occurs in eight cases identified as “high-impact” by the quantity of National Weather Service Local Storm Reports, while WoFS performance is favored at short lead times for 10 “moderate-” and 13 “low-impact” events. WoF-Hybrid reflectivity objects are closer in size and location to observed objects. However, a higher thunderstorm overprediction bias is identified in WoF-Hybrid, particularly early in the forecast. Two severe weather events are selected for detailed investigation. In the case of 26 May, both systems had similar skill; however, for 10 December, WoF-Hybrid forecasts significantly outperformed WoFS forecasts. These results show improved performance for WoF-Hybrid over WoFS under certain regimes that warrants further investigation. To understand reasons for these differences will help incorporate higher-resolution modeling into Warn-on-Forecast systems. Significance StatementThe NOAA Warn-on-Forecast (WoF) project uses advanced data assimilation for rapidly updating numerical weather prediction systems to provide forecasts of individual thunderstorms. Forecasts show promise for enabling greater warning lead time for some storms. The flagship Warn-on-Forecast System (WoFS) is a 36-member analysis and 18-member forecast system at 3-km grid spacing. The project also produced a single member system that employs variational analysis and produces a deterministic forecast at 1.5-km grid spacing (WoF-Hybrid). This study seeks to evaluate and compare the performance of WoFS and WoF-Hybrid for 31 severe weather events that occurred during 2021. Results found that WoF-Hybrid predicts storm rotation particularly well compared to WoFS, and several other strengths and limitations of both systems are identified. This research may help us understand the complementary nature of two systems and improve our ability to provide more reliable 0–6-h forecasts in the future. 

Abstract Raindrop size distributions (DSD) and rain rate have been estimated from polarimetric radar data using different approaches with the accuracy depending on the errors both in the radar measurements and the estimation methods. Herein, a deep neural network (DNN) technique was utilized to improve the estimation of the DSD and rain rate by mitigating these errors. The performance of this approach was evaluated using measurements from a two-dimensional video disdrometer (2DVD) at the Kessler Atmospheric and Ecological Field Station in Oklahoma as ground truth with the results compared against conventional estimation methods for the period 2006–17. Physical parameters (mass-/volume-weighted diameter and liquid water content), rain rate, and polarimetric radar variables (including radar reflectivity and differential reflectivity) were obtained from the DSD data. Three methods—physics-based inversion, empirical formula, and DNN—were applied to two different temporal domains (instantaneous and rain-event average) with three diverse error assumptions (fitting, measurement, and model errors). The DSD retrievals and rain estimates from 18 cases were evaluated by calculating the bias and root-mean-squared error (RMSE). DNN produced the best performance for most cases, with up to a 5% reduction in RMSE when model errors existed. DSD and rain estimated from a nearby polarimetric radar using the empirical and DNN methods were well correlated with the disdrometer observations; the rain-rate estimate bias of the DNN was significantly reduced (3.3% in DNN vs 50.1% in empirical). These results suggest that DNN has advantages over the physics-based and empirical methods in retrieving rain microphysics from radar observations. 

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