Background error covariance (BEC) is a crucial component of variational data assimilation frameworks. Constructing a BEC that more accurately represents reality is essential for enhancing the assimilation and forecasting capabilities of numerical prediction systems. Based on the CMA-MESO kilometer-scale regional numerical prediction system, diurnal variations of BEC parameters are analyzed, and the variational parameters are applied in actual assimilation and forecasting experiments to assess their impacts. The ensemble method is used to calculate background error samples, and BEC parameters are statistically analyzed at eight times of a day with a 3 h interval (00: 00—21: 00 UTC) to investigate their diurnal variations. The results show that the standard deviation (STD) of background error and spatial correlation scale of the background error for various variables exhibit clear diurnal variation features in the lower and middle troposphere. The STD of background error of wind and humidity fields are generally larger at night than during the day, with the maximum values occurring at 12: 00 UTC. For temperature, the STD is larger at 06: 00 and 09: 00 UTC with more pronounced variations below 850 hPa. Regarding horizontal correlation, larger correlation scales are observed during 18: 00—03: 00 UTC, while smaller correlation scales are found during 06: 00—15: 00 UTC when vertical convective mixing is stronger. As for vertical correlation coefficient of the background error, the diurnal variation is most prominent at 06: 00 UTC, with smaller differences at other times. The idealized experiment results demonstrate that the newly estimated diurnal variation parameters can adjust the influence weights and propagation distances of observational information at different times, ensuring that the assimilation analysis matches the diurnal variation characteristics of BEC. Month-long assimilation and forecasting cycle experiments show that using the diurnal variation BEC parameters reduces assimilation analysis errors in wind and temperature fields, improves precipitation forecasts-particularly for heavy rain and thunderstorms and also reduces 2 m air temperature forecast errors.

In order to improve the analysis capability of micro- and meso-scale flows and provide a kilometer-scale applicable assimilation scheme for the China Meteorological Administration (CMA) operational regional numerical weather prediction system CMA-MESO, a new formulation of the minimization control variables in the GRAPES (Global/Regional Assimilation and Prediction System) variational assimilation system has been developed. The new scheme uses eastward velocity u and northward velocity v to replace the original stream function and velocity potential as the new momentum control variables, and uses temperature and surface pressure (T, p_s) to replace the original unbalanced dimensionless pressure as the new mass field control variable. In addition, the new scheme no longer introduces quasi-geostrophic balance constraint but uses a weak mass continuity constraint to ensure analysis balance. Results of background error statistics and numerical experiments show that the adoption of the reformulated control variables results in a more local propagation of observational information and a more reasonable analysis, avoiding the spurious correlation problem of the original scheme when applied at micro- and meso-scale analysis. The introduction of the weak mass continuity constraint suppresses unrealistic convergence and divergence in the analysis, making the new analysis more balanced. Results of one-month assimilation cycles and forecasts show that the new scheme can reduce analysis errors in wind and mass fields, which in turn significantly improves precipitation and 10 m wind field forecast scores of the CMA-MESO system.

For numerical weather prediction (NWP), data assimilation (DA) combines short-term forecasts and various atmospheric observations to achieve optimal initial conditions, based on which subsequent forecasts are launched. With the rapid advancements in numerical models and observing systems, DA has been significantly evolved. Modern methods now can account for uncertainties of state variables across various spatiotemporal scales, incorporate multiscale observation error statistics, and enforce dynamical constrains and model balances. Meanwhile, observations from various platforms, such as ground-based, aircraft, and satellite, have been assimilated. These include data from polar-orbiting and geostationary satellites, radar-derived radial winds and reflectivity, Global Navigation Satellite System (GNSS) radio occultations, etc. To further utilize the advanced observing systems and DA techniques for high-impact weather predictions, target observation strategies have been developed to identify areas where additional observations can yield the greatest predict improvements. Based on the advancements of DA theories and methods, China’s operational systems have made significant progress, establishing advanced operational DA systems. Over the past decade, the forecast skill of 5-day global weather prediction has improved by approximately 15%. The article reviews a century of development in DA, and discusses future directions, including the advanced DA methods, operational frameworks, integration of novel observations, and the synergy between DA and artificial intelligence.