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This study presents a multiscale four-dimensional variational data assimilation (MS-4DVar) scheme that aims to assimilate multiscale information from conventional and radar observations. The MS-4DVar scheme separately assimilates conventional and radar data in different outer loop iterations of an incremental 4DVar with varied resolutions in the tangent linear and adjoint models (TLM/ADM) and time window lengths in the 4DVar. The MS-4DVar scheme was evaluated through a series of single observation tests and several cycled assimilation and forecasting experiments for a real squall line case. Our results indicated that different TLM/ADM resolutions and time window lengths applied to the conventional and radar observations improved the multiscale analysis. In addition, the MS-4DVar scheme was more efficient than the common 4DVar because of the low-resolution TLM/ADM used for conventional data and the shortened time window length for radar data. Verification of the squall line forecasts suggested that the MS-4DVar scheme improved the hourly accumulated precipitation and radar reflectivity forecast skills and reduced the forecast errors of both largescale environmental and convective-scale states. Further diagnosis revealed that the improvement of precipitation forecast skill was attributable to the stronger cold pool, deeper saturated water vapor layer, and stronger updraft of the simulated squall line system, as well as a more favorable convective environment.

The two types of wind observations, profiler and radar radial velocity, have been successfully assimilated into numerical weather prediction (NWP) systems. However, the added value of profiler data, especially from a densely deployed profiler network, is unknown when assimilated together with Doppler radar radial velocity. In this article, two combined assimilation strategies of profilers along with radar radial winds are compared within a convective-scale data assimilation (DA) framework. In strategy I, the profiler data are assimilated with conventional observations to generate an intermediate analysis that acts as a prior for radar data assimilation. In strategy II, both profiler and radar data are considered as storm-scale and assimilated within the same pass. Single- and dual-observation assimilation experiments indicate that for strategy I, the profiler DA improvement can be partly canceled by the potentially negative impact of the assimilation of single-radar radial velocity afterward, particularly when the radial wind is nearly orthogonal to the prevailing wind. For strategy II, important complements are provided when profilers are assimilated within the same pass along with radial winds. The diagnostics for a low-level jet case demonstrate that both strategies facilitate improved analyses and forecasts. But strategy II may bring more moderate analysis increments, which indicate mutual constraints of the profiler and radial winds when assimilated within the same pass. The results obtained in 1-month, retrospective cycling experiments also show that the strategy II outperforms the strategy I with slightly better wind and precipitation forecasts. Significance Statement Due to the high spatial–temporal wind information provided by profiler and radar radial velocity measurements, their combined assimilation would be expected to improve wind analysis. To fully utilize dense profiler data and radar radial wind in future operational applications, this study proposes a suitable assimilation strategy. If the profilers are defined as synoptic-scale observations, the profiler and Doppler radar data must be assimilated in different passes to adopt different length and variance scales. Whereas it is more reasonable to use a small background correlation length consistent with the radial velocity and, therefore, assimilate in the same pass if the profiler data are considered to better sample storm-scale features. Single- and dual-observation experiments indicate that profiler data provide important complements, while the assimilation of single-radar radial wind may yield analyzed wind results that do not depict the ground truth. A low-level jet case and a 1-month impact study further show that the combined assimilation strategy of assimilating both profiler and Doppler radar using smaller background correlation lengths enhances the analysis and forecasting of wind, resulting in more accurate accumulated precipitation forecasts.

Use of data assimilation to initialize hydrometeors plays a vital role in numerical weather prediction (NWP). To directly analyze hydrometeors in data assimilation systems from cloud-sensitive observations, hydrometeor control variables are necessary. Common data assimilation systems theoretically require that the probability density functions (PDFs) of analysis, background, and observation errors should satisfy the Gaussian unbiased assumptions. In this study, a Gaussian transform method is proposed to transform hydrometeors to more Gaussian variables, which is modified from the Softmax function and renamed as Quasi-Softmax transform. The Quasi-Softmax transform method then is compared to the original hydrometeor mixing ratios and their logarithmic transform and Softmax transform. The spatial distribution, the non-Gaussian nature of the background errors, and the characteristics of the background errors of hydrometeors in each method are studied. Compared to the logarithmic and Softmax transform, the Quasi-Softmax method keeps the vertical distribution of the original hydrometeor mixing ratios to the greatest extent. The results of the D’Agostino test show that the hydrometeors transformed by the Quasi-Softmax method are more Gaussian when compared to the other methods. The Gaussian transform has been added to the control variable transform to estimate the background error covariances. Results show that the characteristics of the hydrometeor background errors are reasonable for the Quasi-Softmax method. The transformed hydrometeors using the Quasi-Softmax transform meet the Gaussian unbiased assumptions of the data assimilation system, and are promising control variables for data assimilation systems.

The high observation efficiency, scanning speed and observation frequency of the Fengyun-4A (FY-4A) satellite indicates the progress of Chinese geostationary meteorological satellites. The characteristics of FY-4A atmospheric motion vectors (AMVs) derived from the high-level water vapor (WV-High) channel, mid-level water vapor (WV-Mid) channel, and infrared (IR) channel of FY-4A are analyzed, and their corresponding observation errors estimated. Then, the impacts of single-channel and multi-channel FY-4A AMVs on RMAPS-ST (the Rapid-refresh Multi-scale Analysis and Prediction System—Short Term) are evaluated based on one-month data assimilation cycling and forecasting experiments. Results show that the observation errors of FY-4A AMVs from the three channels have an explicit vertical structure. Results from the cycling experiments indicate that the assimilation of AMVs from WV-High produces more apparent improvement of the wind in the upper layer, while a more positive effect in the lower layer is achieved by the assimilation of AMVs from IR. Furthermore, the assimilation of AMVs from IR is more skillful for medium and moderate precipitation than from other channels owing to the good quality of data in the lower layer in the AMVs from IR. Assimilation of FY-4A AMVs from the three channels could combine the advantages of assimilation from each individual channel to improve the wind in the upper, middle and lower layers simultaneously.

Accurate and long leading time flood forecasting is very important for flood disaster mitigation. It is an effective method to couple the Quantitative Precipitation Forecast (QPF) products provided by Numerical Weather Prediction (NWP) models to a distributed hydrological model with the goal of extending the leading time for flood forecasting. However, the QPF products contain a certain degree of uncertainty and would affect the accuracy of flood forecasting, especially in the mountainous regions. Radar data assimilation plays an important role in improving the quality of QPF and further improves flood forecasting. In this paper, radar data assimilation was applied in order to construct a high-resolution atmospheric-hydrological coupling model based on the WRF and WRF-Hydro models. Four experiments with conventional observational and radar data assimilation were conducted to evaluate the flood forecasting capability of this coupled model in a small-medium sized basin based on eight typical flood events. The results show that the flood forecast skills are highly QPF-dependent. The QPF from the WRF model is improved by assimilating radar data and further increasing the accuracy of flood forecasting, although both precipitation and flood are slightly over-forecasted. However, the improvements by assimilating conventional observational data are not obvious. In general, radar data assimilation can improve flood forecasting effectively in a small-medium sized basin based on the atmospheric-hydrological coupling model.

The background error covariance (B) behaves differently and needs to be carefully defined in cloudy areas due to larger uncertainties caused by models’ inability to correctly represent complex physical processes. This study proposes a new cloud-dependent B strategy by adaptively adjusting the hydrometeor-included B in the cloudy areas according to the cloud index (CI) derived from the satellite-based cloud products. The adjustment coefficient is determined by comparing the error statistics of B for the clear and cloudy areas based on the two-dimensional geographical masks. The comparison highlights the larger forecast errors and manifests the necessity of using appropriate B in cloudy areas. The cloud-dependent B is then evaluated by a series of single observation tests and three-week cycling assimilation and forecasting experiments. The single observation experiments confirm that the cloud-dependent B allows cloud dependency for the multivariate analysis increments and alleviates the discontinuities at the cloud mask borders by treating the CI as an exponent. The impact study on regional numerical weather prediction (NWP) demonstrates that the application of the cloud-dependent B reduces analyses and forecasts bias and increases precipitation forecast skills. Diagnostics of a heavy rainfall case indicate that the application of the cloud-dependent B enhances the moisture, wind, and hydrometeors analyses and forecasts, resulting in more accurate forecasts of accumulated precipitation. The cloud-dependent piecewise analysis scheme proposed herein is extensible, and a more precise definition of CI can improve the analysis, which deserves future investigation.

Geostationary meteorological satellites can provide continuous observations of high-impact weather events with a high temporal and spatial resolution. Sounding the atmosphere using a microwave instrument onboard a geostationary satellite has aroused great study interests for years, as it would increase the observational efficiency as well as provide a new perspective in the microwave spectrum to the measuring capability for the current observational system. In this study, the capability of assimilating future geostationary microwave sounder (GEOMS) radiances was developed in the Weather Research and Forecasting (WRF) model’s data assimilation (WRFDA) system. To investigate if these frequently updated and widely distributed microwave radiances would be beneficial for typhoon prediction, observational system simulation experiments (OSSEs) using synthetic microwave radiances were conducted using the mesoscale numerical model WRF and the advanced hybrid ensemble–variational data assimilation method for the Lekima typhoon that occurred in early August 2019. The results show that general positive forecast impacts were achieved in the OSSEs due to the assimilation of GEOMS radiances: errors of analyses and forecasts in terms of wind, humidity, and temperature were both reduced after assimilating GEOMS radiances when verified against ERA-5 data. The track and intensity predictions of Lekima were also improved before 68 h compared to the best track data in this study. In addition, rainfall forecast improvements were also found due to the assimilation impact of GEOMS radiances. In general, microwave observations from geostationary satellites provide the possibility of frequently assimilating wide-ranging microwave information into a regional model in a finer resolution, which can potentially help improve numerical weather prediction (NWP).

As the first Geostationary Satellite with the LMI (Lightning Mapping Imager) instrument aboard running over the eastern hemisphere, FY-4A (Feng-Yun-4A) can better indicate severe convection and compensate for the limitations of radar observation in temporal and spatial resolution. In order to realize the application of FY-4A lightning data in numerical weather prediction (NWP) models, a logarithmic relationship between FY-4A lightning density and maximum radar reflectivity is presented to convert FY-4A lightning data into maximum FY-4A proxy reflectivity. Then, according to the profiles of radar reflectivity, the maximum FY-4A proxy reflectivity is extended to 3D FY-4A proxy reflectivity. Finally, the 3D FY-4A proxy reflectivity is assimilated in RMAPS-ST (Rapid-refresh Multi-scale Analysis and Prediction System—Short Term) to compare with radar assimilation. Four groups of continuous cycling data assimilation and forecasting experiments are carried out for a severe rainfall case. The results demonstrate that cycling assimilation of 3D FY-4A proxy reflectivity can adjust the moisture condition effectively, and indirectly affects the temperature and wind fields, then makes the thermal and dynamic analysis more reasonable. The Fractions Skill Scores (FSSs) show that the rainfall forecasts are improved significantly within 6 h by assimilating 3D FY-4A proxy reflectivity, which is similar to the parallel experiments in assimilating radar reflectivity. In addition, other cycling data assimilation experiments are carried out in mountainous areas without radar data. The improvement of precipitation forecasts in mountainous areas further proves that the application of assimilating 3D FY-4A proxy reflectivity can be considered a useful substitute where observed radar data are missing. Through the two severe rainfall cases, this method could be framed as an example of how to use lightning for data assimilation.

Besides the traditional hybrid covariance data assimilation (referred to as “HCDA” in this paper) method, the hybrid gain data assimilation (referred to as “HGDA”) has been proposed recently to combine the ensemble Kalman filter and variational methods, showing potential advantages in global models. To evaluate the impact of HGDA on regional and meso-scale numerical weather prediction using WRF model over east China, both single observation tests and full cycling experiments for 3-weeks in July 2013 were conducted using the 3DVar, EnKF, HCDA and HGDA methods. The results of single observation tests showed that the analysis increments of HGDA retained more characteristics of the EnKF than HCDA because of utilizing the EnKF analysis ensemble mean in the re-center step. Both the hybrid data assimilation methods showed superiority over the pure EnKF and 3DVar in full cycling experiments. The average RMSE of HGDA was slightly smaller than the HCDA. It was also found that the HGDA method showed its advantage over HCDA at shorter leading time and yielded the highest precipitation score. For rainfall field, the HGDA had the best results in terms of intensity and coverage. Furthermore, the HGDA showed better results for supplying sufficient moisture conditions over rainfall area, such as precipitable water and water vapor flux. The uplift vertical velocity that contributed to the improvement of precipitation simulation was also strengthened. In general, both of the hybrid data assimilation methods showed better results than EnKF and 3DVar. Especially, the HGDA method showed advantage benefiting from the utilization of optimal EnKF analysis mean and 3DVar analysis which equals to the linearly combination of the gain matrix, considering the total error variance.

The research of algebraic gravity solitary waves is an advanced field which has important practical and theoretical value in physical, oceanography, aerology and etc. By calculation condition and theoretical method limit, previous researches mainly focused on the ( 1 + 1 ) dimensional models, and ( 2 + 1 ) dimensional models were few considered. In this paper, from the non-static equilibrium equation, a new ZK-ILW equation is derived by using multi-scale analysis and perturbation method in finite depth stratified atmosphere, which is the first time obtained. The model can reduce to ZK-BO model ( h → ∞ ) , and ZK model ( h → 0 ) and is the generalization of the above two models. In order to further understand the nature of algebraic gravity solitary waves, we get the analytical solution of ZK-ILW equation by using the trial function method and discuss the conservation laws. Furthermore, the fission process of algebraic gravity solitary waves is studied, and we can judge that one of the possible formation mechanism of squall lines is the fission of algebraic gravity solitary waves.

The gravity solitary waves are a kind of waves which are caused by the disturbance of static equilibrium. The nonlinearity concentration of the gravity solitary waves makes the energy assemble together and forms disastrous weather phenomena, such as squall lines. By the calculation condition and theoretical method limit, previous studies tried hard to reduce the variable numbers and discussed the gravity solitary waves in barotropic atmosphere, but the baroclinic problem of atmosphere is inevitable topic. In this paper, from the basic kinetic equations in baroclinic non-static equilibrium atmosphere, by using multi-scale analysis and perturbation method, a new model is derived to describe the algebraic gravity solitary waves, we call it Boussinesq-BO equation. Comparing with the former models, the Boussinesq-BO model can describe the propagation process of waves in two directions and is more suitable for the real atmosphere condition. With the help of the trial function method, an exact solution of Boussinesq-BO equation is obtained and the fission property of algebraic gravity solitary waves is discussed. Finally, we can find that the fission of algebraic gravity solitary waves is also a possible formation mechanism of squall lines.

Background error covariance (BEC) plays a key role in variational data assimilation systems. The National Meteorological Center (NMC) method has been used widely to generate forecast error samples for BEC estimation. At present, most variational-based rapid update and cycling (RUC) data assimilation and forecasting systems use a fixed BEC without consideration of diurnal variation. In this study, diurnal variation BECs were estimated using three month forecast error samples (0000 UTC 01 June to 2100 UTC 31 August 2019), which came from the Rapid-refresh Multi-scale Analysis and Prediction System-Short Term (RMAPS-ST). Series of single observation tests and one-month partial cycling data assimilation and forecasting experiments with diurnal variation BECs were carried out based on the system. The results showed the following: 1) Diurnal variation is found in the standard deviation of forecast error samples, with the minimum value of standard deviation appearing at nightfall (0900 UTC, 1700 BJT), and the maximum value appearing at the early morning (2100 UTC, 0500 BJT). The eigenvalues also show similar diurnal variation features, indicating the diurnal variation characteristics of background error are consistent in the physical space and the EOF space. 2) The diurnal variation of BEC is further verified by single observation tests, and the analysis increments well response to the BEC diurnal variation. 3) The results of one-month cycling experiments show that diurnal variation BECs could improve the assimilation and forecasting performance of RMAPS-ST.

This study evaluates the performance of three-dimensional variational (3DVar) and a hybrid data assimilation system using time-lagged ensembles in a heavy rainfall event. The time-lagged ensembles are constructed by sampling from a moving time window of 3 h along a model trajectory, which is economical and easy to implement. The proposed hybrid data assimilation system introduces flow-dependent error covariance derived from time-lagged ensemble into variational cost function without significantly increasing computational cost. Single observation tests are performed to document characteristic of the hybrid system. The sensitivity of precipitation forecasts to ensemble covariance weight and localization scale is investigated. Additionally, the TLEn-Var is evaluated and compared to the ETKF(ensemble transformed Kalman filter)-based hybrid assimilation within a continuously cycling framework, through which new hybrid analyses are produced every 3 h over 10 days. The 24 h accumulated precipitation, moisture, wind are analyzed between 3DVar and the hybrid assimilation using time-lagged ensembles. Results show that model states and precipitation forecast skill are improved by the hybrid assimilation using time-lagged ensembles compared with 3DVar. Simulation of the precipitable water and structure of the wind are also improved. Cyclonic wind increments are generated near the rainfall center, leading to an improved precipitation forecast. This study indicates that the hybrid data assimilation using time-lagged ensembles seems like a viable alternative or supplement in the complex models for some weather service agencies that have limited computing resources to conduct large size of ensembles.

Hydrometeor variables (cloud water and cloud ice mixing ratios) are added into the WRF three-dimensional variational assimilation system as additional control variables to directly analyze hydrometeors by assimilating cloud observations. In addition, the background error covariance matrix of hydrometeors is modeled through a control variable transform, and its characteristics discussed in detail. A suite of experiments using four microphysics schemes (LIN, SBU-YLIN, WDM6 and WSM6) are performed with and without assimilating satellite cloud liquid/ice water path. We find analysis of hydrometeors with cloud assimilation to be significantly improved, and the increment and distribution of hydrometeors are consistent with the characteristics of background error covariance. Diagnostic results suggest that the forecast with cloud assimilation represents a significant improvement, especially the ability to forecast precipitation in the first seven hours. It is also found that the largest improvement occurs in the experiment using the WDM6 scheme, since the assimilated cloud information can sustain for longer in this scheme. The least improvement, meanwhile, appears in the experiment using the SBU-YLIN scheme.

Atmospheric moisture content or humidity is an important analysis variable of any meteorological data assimilation system. The humidity analysis can be univariate, using humidity background (normally short-range numerical forecasts) and humidity observations. However, more and more data assimilation systems are multivariate, analyzing humidity together with wind, temperature and pressure. Background error covariances, with unbalanced velocity potential and humidity in the multivariate formulation, are generated from weather research and forecasting model forecasts, collected over a summer rainy season and a winter dry season. The unbalanced velocity potential and humidity related correlations are shown to be significantly larger, indicating more important roles unbalanced velocity potential and humidity play, in the rainy season than that in the dry season. Three cycling data assimilation experiments of two rainfall events in the middle and lower reaches of the Yangtze River are carried out. The experiments differ in the formulation of the background error covariances. Results indicate that only including unbalanced velocity potential in the multivariate background error covariance improves wind analyses, but has little impact on temperature and humidity analyses. In contrast, further including humidity in the multivariate background error covariance although has a slight negative effect on wind analyses and a neutral effect on temperature analyses, but significantly improves humidity analyses, leading to precipitation forecasts more consistent with China Hourly Merged Precipitation Analysis.

A resampling method that selects historical forecasting samples as supplementary samples is proposed for the hybrid ensemble-variational data assimilation system to alleviate the computational burden of ensemble forecasting samples. To select reasonable samples from all historical forecasting samples, the first modes of absolute vorticity are abstracted by the empirical orthogonal function (EOF) as indicators of atmospheric dynamic features from the background and each of historical forecasting sample, then they are matched at the analysis time. A series of single observation tests and 19-day cycling data assimilation and forecasting experiments for a Mei-yu period are carried out to evaluate the impact of the selected historical forecasting samples. The single observation tests indicate that the use of selected historical forecasting samples is able to provide reasonable flow-dependent background error covariance for the data assimilation system. The cycling data assimilation and forecasting experiments demonstrate that the analyses and forecasts as well as precipitation forecast skills are improved by using the combination of selected historical forecasting samples and ensemble forecasting samples. The sample-combined experiment performs close to the experiment with full-size ensemble forecasting samples, but it spends fewer computational resources. The diagnosis of a heavy rainfall case is presented to further illustrate the role of the selected historical forecasting samples. It is found that the simulation of vertical velocity and relative humidity are improved for the case in the experiment of the combined samples, leading to better intensity and position forecasts of the precipitation.

Two momentum control variable schemes are typically used in most data assimilation systems: stream function and unbalanced velocity potential (ψ/χu scheme) and eastward and northward velocity (U/V scheme). The wind profiler radar (profiler) plays an important role in the expansion of meteorological observations networks. In this study, the impacts of two momentum control variable schemes on assimilating a dense wind profiler network are discussed based on the single profiler station observation tests and six convective rainfall events cycling experiments. Single profiler station observation tests indicate that profiler data assimilation is sensitive to control variables. The dynamical increments using U/V scheme contain more elaborate structure, which contributes to valuing the straightforward effects of profiler observations objectively. By contrast, unrealistic increments occur around the observation station in the experiment using ψ/χu scheme. Six continuous cycling experiments further demonstrate that, for convective rainfall events, experiment using U/V scheme leads to more skillful quantitative precipitation forecasts of convective rainfall. Diagnostic analysis results show that analysis using ψ/χu scheme prevents a good fitting to the profiler data, and accurate dynamical analysis containing abundant small-scale disturbances are the main reason for improving precipitation prediction of convective rainfall when U/V scheme is adopted.

An efficient regional hybrid ensemble-variational (EnVar) data assimilation method using the global-ensemble-model-augmented error covariance is proposed and preliminarily tested in this study. This method uses the global ensemble error covariance as the complementary low-resolution regional ensemble error covariance. The high-resolution dynamic ensemble mean is used as the first guess in hybrid EnVar and then re-centered to the updated high-resolution dynamic ensemble perturbations after minimization analysis. In this study, the proposed method is implemented into the Weather Research and Forecasting Model&rsquo, s (WRF) data assimilation system coupled with the ensemble transform Kalman filter (ETKF) and preliminarily tested for numerical weather prediction during the Mei-Yu season over eastern China. It is found that the experiment containing fewer regional dynamic ensemble members but augmented with global ensemble error covariance obtains similar results to the experiment containing many more regional dynamic ensemble members. However, the former experiment only takes up one third of the latter experiment&rsquo, s computational cost. The method proposed in this study also outperforms the 3DVar, hybrid EnVar using the pure global ensemble error covariance, as well as the hybrid EnVar using regional ETKF ensemble with a smaller size. The method proposed in this paper effectively combines the contributions of the ensemble error covariance from both the global and the regional models to produce better initial conditions for the regional WRF data assimilation system.