In this paper, we have extended the Cooray‐Rubinstein (C‐R) approximate formula into the fractal rough ground surface and then validate its accuracy by using three‐dimensional (3‐D) finite‐difference time‐domain (FDTD) method at distances of 50 m and 100 m from the lightning channel. The results show that the extended C‐R formula has an accepted accuracy for predicting the lightning‐radiated horizontal electric field above the fractal rough and conducting ground, and its accuracy increases a little better with the higher of the earth conductivity. For instance, when the conductivity of the rough ground is 0.1 S/m, the error of the peak value predicted by the extended C‐R formula is less than about 2.3%, while its error is less than about 6.7% for the conductivity of 0.01 S/m. The rough ground has much effect on the lightning horizontal field, and the initial peak value of the horizontal field obviously decreases with the increase of the root‐mean‐square height of the rough ground at early times (within several microseconds of the beginning of return stroke).

The equivalent propagation method adopts a variable propagation velocity in lightning location, minimizing the location error caused by various factors in the long-range lightning location network. To verify the feasibility of this method, we establish a long-range lightning location network in China. A new method is used to extract the ground wave peak points of the lightning sferics and is combined with the equivalent propagation velocity method for lightning location. By comparing with the lightning data detected by the lightning locating system called advanced direction and time-of-arrival detecting (ADTD) that has been widely used for tens of years in China, the feasibility of this method is initially verified. Additionally, it is found that the relative detection efficiency of our long-range lightning location network can reach 53%, the average location error is 9.17 km, and the detection range can reach more than 3000 km. The equivalent propagation method can improve the average location accuracy by ~1.16 km, compared with the assumed light speed of lightning-radiated sferic from the lightning stroke point to the observation station. The 50th percentile of the equal propagation velocity is 0.998c, which may be used in the long-range lightning location networks.

Very low frequency (VLF) electromagnetic waves distort along the long propagation path, and that causes the arrival time of the signals measured by the long-range lightning system to be delayed. In this paper, based on the propagation correction method by compensating the peak time delay of the ground wave, the location accuracy of the long-range lightning detection network in China is greatly improved. The improvement of the relative location accuracy and location offsets are evaluated by comparing with the Advanced Direction Time Lightning Detection System (ADTD) datasets. It shows that the mean relative accuracy is improved from 7.74 km to 4.32 km, and the median relative accuracy is improved from 7.28 km to 2.46 km. The mean westwards offset of the total lightning location data drops from 2.05 km to 0.93 km, and the mean southwards offset drops from 1.19 km to 0.63 km. In addition, it is found that the location accuracy will be greatly improved if the observation site affected by the terrain is removed. The mean relative location accuracy is further improved to 4.11 km and the median to 2.32 km.

In this study, the effect of day/night factor on the detection performance of the FY4A lightning mapping imager (LMI) is evaluated using the Bayesian theorem, and by comparing it to the measurements made by a ground-based low-frequency magnetic field lightning location system. Both the datasets were collected in the summers of 2019–2020 in Hainan, China. The results show that for the observed summer thunderstorms in Hainan, the daytime detection efficiencies of LMI (DE_LMI) were 20.41~35.53% lower than the nighttime DE_LMI. Compared to other space-based lightning sensors (lightning imaging sensors/optical transient detectors (LIS/OTD) and geostationary lightning mapper (GLM)), the detection performance of LMI is more significantly influenced by the day/night factor. The DE_LMI rapidly dropped within about four hours after sunrise while it increased before sunset. For the storms that formed at night and lasted for an entire day, the DE_LMI remained relatively low during the daytime, even as the thunderstorms intensified. The poor detection performance of LMI during daytime is probably because of the sunlight reflection by clouds and atmosphere, which results in larger background radiative energy density (RED) than that at night. During night, LMI captured the lightning signals well with low RED (8.38~10.63 μJ sr⁻¹ m⁻² nm⁻¹). However, during daytime, signals with RED less than 77.12 μJ sr⁻¹ m⁻² nm⁻¹ were filtered, thus lightning groups could rarely be identified by LMI, except those with extremely high RED. Due to the limitations of the Bayesian theorem, the obtained DE in this study was “relative” DE rather than “absolute” DE. To obtain the absolute DE of LMI, the total lightning density is necessary but can hardly be measured. Nonetheless, the results shown here clearly indicate the strong impact of day/night factor on the detection performance of LMI, and can be used to improve the design and post-processing method of LMI.

The effect of the number and configuration of participating stations on lightning location outside the network is herein studied by evaluating the deviation distance between the reference location and the locations determined by the ToA technique, using recorded data from the location network in Fujian. It was found that the deviation distance decreases with the increase of number of stations, changing from 0.07 to 424.7 km with an average of 35 km for five stations while being 0.03~21.6 km and 2.2 km, respectively, for eight stations. The spatial distribution of those locations outside the network seems to be on a straight line. When the number of stations was five, the station linear configuration led to a narrow and long intersection region, resulting in a large deviation distance. The more dispersed distribution of stations leads to the minimum deviation distance. The percentage of deviation distance less than specific location accuracy (LA) can provide references on network design. 7 stations are sufficient to locate the lightning near and inside the network. 8–9 stations are necessary for an LA of 1 km when the lightning is 200 to 300 km away from the center of the network. The network is not suitable for locating the lightning from each station more than 400 km on average.

The Fengyun-4A (FY-4A) geostationary satellite carries the Lightning Mapping Imager that measures total lightning rate of convective systems from space at high spatial and temporal resolutions. In this study, the performance of FY-4A lightning data assimilation (LDA) on the forecast of non-typhoon oceanic mesoscale convective systems (MCSs) is investigated by using an LDA method implemented in the Weather Research and Forecasting-Four Dimensional Data Assimilation (WRF-FDDA). With the LDA scheme, three-dimensional graupel mixing ratio fields retrieved from the FY-4A lightning data and the corresponding latent heating rates are assimilated into the Weather Research and Forecasting model via nudging terms. Two oceanic MCS cases over the South China Sea were selected to perform the study. The subjective evaluation results demonstrate that most of the oceanic convective cells missed by the control experiments are recovered in the analysis period by assimilating FY-4A lightning data, due to the promoted updrafts by latent-heat nudging, the more accurate and faster simulations of the cold pools, and the associated gust-fronts at the observed lightning locations. The cold pools and gust-fronts generated during the analysis period helped to maintain the development of the MCSs, and reduced the morphology and displacement errors of the simulations in the short-term forecast periods. The quantitative evaluation indicates that the most effective periods of the LDA for simulation enhancement were at the analysis time and the nowcasting (0–2 h forecast) periods.