For variational data assimilation, the background error covariance matrix plays a crucial role because it is strongly linked with the local meteorological features, and is especially dominated by error correlations between different analysis variables. Multivariate background error (MBE) statistics have been generated for two regions, namely the Tropics (covering Indonesia and its neighborhood) and the Arctic (covering high latitudes). Detailed investigation has been carried out for these MBE statistics to understand the physical processes leading to the balance (defined by the forecasts error correlations) characteristics between mass and wind fields for the low and high latitudes represented by these two regions. It is found that in tropical regions, the unbalanced (full balanced) part of the velocity potential (divergent part of wind) contributes more to the balanced part of the temperature, relative humidity, and surface pressure fields as compared with the stream function (rotational part of wind). However, the exact opposite happens in the Arctic. For both regions, the unbalanced part of the temperature field is the main contributor to the balanced part of the relative humidity field. Results of single observation tests and six-hourly data assimilation cycling experiments are consistent with the respective balance part contributions of different fields in the two regions. This study provides an understanding of the contrasting dynamical balance relationship that exists between the mass and wind fields in high-and low-latitude regions. The study also examines the impact of MBE on Weather Research and Forecasting model forecasts for the two regions.

Himawari‐8 is the first launched and operational new‐generation geostationary meteorological satellite. The Advanced Himawari Imager (AHI) on board Himawari‐8 provides continuous high‐resolution observations of severe weather phenomena in space and time. In this study, the capability to assimilate AHI radiances has been developed within the Weather Research and Forecasting (WRF) model's data assimilation system. As the first attempt to assimilate AHI using WRF data assimilation at convective scales, the added value of hourly AHI clear‐sky radiances from three water vapor channels on convection‐permitting (3 km) analyses and forecasts of the “7.19” severe rainstorm that occurred over north China during 18–21 July 2016 was investigated. Analyses were produced hourly, and 24 h forecasts were produced every 6 h. The results showed that improved wind and humidity fields were obtained in analyses and forecasts verified against conventional observations after assimilating AHI water vapor radiances when compared to the control experiment which assimilated only conventional observations. It was also found that the assimilation of AHI water vapor radiances had a clearly positive impact on the rainfall forecast for the first 6 h lead time, especially for heavy rainfall exceeding 100 mm when verified against the observed rainfall. Furthermore, the horizontal and vertical distribution of features in the moisture fields were improved after assimilating AHI water vapor radiances, eventually contributing to a better forecast of the severe rainstorm.

Analysis of the cloud components in numerical weather prediction models using advanced data assimilation techniques has been a prime topic in recent years. In this research, the variational data assimilation (DA) system for the Weather Research and Forecasting (WRF) Model (WRFDA) is further developed to assimilate satellite cloud products that will produce the cloud liquid water and ice water analysis. Observation operators for the cloud liquid water path and cloud ice water path are developed and incorporated into the WRFDA system. The updated system is tested by assimilating cloud liquid water path and cloud ice water path observations from Global Geostationary Gridded Cloud Products at NASA. To assess the impact of cloud liquid/ice water path data assimilation on short-term regional numerical weather prediction (NWP), 3-hourly cycling data assimilation and forecast experiments with and without the use of the cloud liquid/ice water paths are conducted. It is shown that assimilating cloud liquid/ice water paths increases the accuracy of temperature, humidity, and wind analyses at model levels between 300 and 150 hPa after 5 cycles (15 h). It is also shown that assimilating cloud liquid/ice water paths significantly reduces forecast errors in temperature and wind at model levels between 300 and 150 hPa. The precipitation forecast skills are improved as well. One reason that leads to the improved analysis and forecast is that the 3-hourly rapid update cycle carries over the impact of cloud information from the previous cycles spun up by the WRF Model.

As powerful and deep tropical low-pressure systems, hurricane formation is always associated with cloud systems and precipitation, which is of large uncertainties caused by models' inability to correctly represent complex physical processes (Errico et al., 2007;Li et al., 2016). Therefore, hurricane forecast relies not only on a well-defined analysis of the environmental field in the clear sky area but also on providing an accurate initial field in the cloudy sky area. In addition to conventional observations, non-conventional observations

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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.

In this paper, the theoretical model of Rossby waves in two-layer fluids is studied. A single quasi-geostrophic vortex equation is used to derive various models of Rossby waves in a one-layer fluid in previous research. In order to explore the propagation and interaction of Rossby waves in two-layer fluids, from the classical quasi-geodesic vortex equations, by employing the multi-scale analysis and turbulence method, we derived a new (2+1)-dimensional coupled equations set, namely the generalized Zakharov-Kuznetsov(gZK) equations set. The gZK equations set is an extension of a single ZK equation; they can describe two kinds of weakly nonlinear waves interaction by multiple coupling terms. Then, for the first time, based on the semi-inverse method and the variational method, a new fractional-order model which is the time-space fractional coupled gZK equations set is derived successfully, which is greatly different from the single fractional equation. Finally, group solutions of the time-space fractional coupled gZK equations set are obtained with the help of the improved ( G ′ / G ) -expansion method.

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.