Data assimilation integrates irregularly distributed observations into model grid points to provide initial values for numerical models. Once a data assimilation system is established on a chosen grid type, it cannot be easily adapted to another grid type. In this paper, we introduce a gridless method for the three-dimensional variation assimilation (3DVar) system. Unlike grid-based methods, the gridless method uses arbitrarily distributed points for calculation and does not require pre-defined grid cells; thus, it can switch to any grid distribution, namely the data assimilation system based on a gridless method can be adapted to most model grid structures without the need to add new codes. In the data assimilation system based on the gridless method presented here, the Cressman analysis technique is adopted as the observation operator and the physical transformation matrix is handled by using the Taylor expansion. Idealized experiments based on the Rankine vortex are conducted to demonstrate the 3DVar system based on the gridless method, and it is validated that the system can handle structured, unstructured, and mixed (structured and unstructured) grids. Furthermore, we demonstrate that the gridless data assimilation method can perform data assimilation on grids of different resolutions and structural types simultaneously using a single cost function.

Doppler radar can provide information of precipitation particles and radial component of atmospheric motion with high spatial and temporal resolutions. The spatial information of precipitation particles, such as reflectivity and dual polarization parameters, are relatively intuitive for application. However, the Doppler radar can only detect radial component of atmospheric motion, which makes it difficult to directly reflect the whole characteristics of atmospheric motion. Thereby it is necessary to develop various retrieval methods for extracting atmospheric motion information, which is useful for the diagnosis, analysis and prediction of meso and microscale systems from radar observations. Doppler weather radar networks have been established in most of the countries in the world. However, wind fields obtained by radars have not been widely used. In this study, the methods for retrieving wind fields from a single Doppler radar or multiple radars are classified and summarized. Some basic derivation formulas are attached in appendix, which makes it convenient for researchers to explore the principles of these retrieval methods. For the single-Doppler radar wind field retrieval, the methods that are based on the spatial continuity assumption and only requires a single radar coverage with convenient application and simple calculation, are analyzed and summarized. However, the accuracy of the single-Doppler retrieval methods based on the assumption of uniform wind field is limited, and the error of such retrieval methods is large for meso and microscale systems. As for the linear variation wind assumption, the retrieval equations are difficult to be fully solved. Therefore, some other extended methods have been derived to improve the accuracy and applicability of the retrieval methods used for single Doppler radar. For the wind retrieval techniques that can be applied to two or more Doppler radars, the principles and characteristics of these methods are summarized. The multi-Doppler radar retrieval method can yield accurate information of three-dimensional wind field with high resolution, but the applicability of those methods depends on spatiotemporal synchronization of observations. With the development of radar network and phased array radar, the applicability of the multi-Doppler radar retrieval method has been improved and attracted more and more attention. Finally, the future direction of the development of Doppler radar wind field retrieval technique are discussed.

This study examined the rainfall characteristics and related synoptic processes of two extreme rainfall events that affected North China during 29 July–1 August 2023 (“23·7” rainstorm) and 3–5 August 1996 (“96·8” rainstorm), respectively. A stable dual-typhoon circulation pattern was observed in both rainstorm events. The surviving vortex of a landed typhoon, slowly approaching the rainstorm region, was blocked by a high-pressure system as it moved northwestward. Meanwhile, the second typhoon over the western Pacific Ocean facilitated remote northward transport of moisture. The low-level jet between the surviving vortex and the western Pacific subtropical high relayed moist warm air from the area of the South China Sea and western Pacific into the rainstorm region. Although the circulation patterns are similar, the stratification conditions, driving factors, and moisture budget of the two rainstorms differed during the main period of rainfall. The “23·7” rainstorm was categorized as warm-sector rainfall, as a result of the lifting of warm moist air over the eastern foothills of Taihang Mountains. In comparison with the situation of the “96·8” rainstorm, the surviving vortex of the “23·7” rainstorm traveled further northeastward and directly impacted the occurrence and progression of the rainfall, leading to relative northward displacement of the rainfall center, while the stronger net inward moisture flux caused greater regional average rainfall. The “96·8” rainstorm was broadly analogous to precipitation of a cold front, and the rainfall center was observed in the convergence area of warm and cold air masses before the mountains; the surviving vortex did not exert direct impact on the rainfall; and the more unstable stratification led to stronger hourly rainfall. The results derived through comparison of the two rainstorms could serve as valuable scientific reference for operational forecasting of heavy rainfall under similar environmental conditions over North China.

North China experienced devastating rainfall from 29 July to 1 August 2023, which caused substantial flooding and damage. This study analyzed observations from surface rain gauges and S-band dual-polarization radars to reveal the following unique features of the precipitation evolution from the plain to the mountains during this event. (1) The total rainfall was found concentrated along the Taihang Mountains at elevations generally > 200 m, and its spatiotemporal evolution was closely associated with northward-moving low-level jets. (2) Storms propagated northwestward with southeasterly steering winds, producing continuous rainfall along the eastern slopes of the Taihang Mountains owing to mountain blocking, which resulted in the formation of local centers of precipitation maxima. However, most rainfall episodes with an extreme hourly rainfall rate (HRR), corresponding to large horizontal wind shear at low levels, actively occurred in the plain area to the east of the Taihang Mountains. (3) The western portion of the extreme heavy rain belt in the north was mainly caused by long-lasting cumulus–stratus mixed precipitation with HRR < 20 mm h⁻¹; the eastern portion was dominated by short-duration convective precipitation with HRR > 20 mm h⁻¹. The contributions of convective precipitation and cumulus–stratus mixed precipitation to the total rainfall of the southern and middle rain belts were broadly equivalent. (4) The local HRR maxima located at the transition zone from the plain to the mountains were induced by moderate storm-scale convective cells with active warm-rain processes and large number of small-sized rain droplets. (5) During the devastating rainfall event, it was observed that the rainfall peaked at around 1800 local time (LT) every day over the upstream plain area (no diurnal cycle of rainfall was observed in relation to the accumulated rainfall centers over mountain areas). This was attributable to convective activities along the storm propagation path, which was a result of the more unstable stratification with a suitable steering mechanism that was related to afternoon solar heating and enhanced water vapor. The findings of this study improve our understanding and knowledge of the extreme precipitation that can develop from the plain to the mountains in North China.