The Kernel Density Estimation Technique for Spatio-Temporal Distribution and Mapping of Rain Heights over South Africa: The Effects on Rain-Induced Attenuation

Abstract

The devastating effects of rain-induced attenuation on communication links operating above 10 GHz during rainy events can significantly degrade signal quality, leading to interruptions in service and reduced data throughput. Understanding the spatial and seasonal distribution of rain heights is crucial for predicting these attenuation effects and for network performance optimization. This study utilized ten years of atmospheric temperature and geopotential height data at seven pressure levels (1000, 850, 700, 500, 300, 200, and 100 hPa) obtained from the Copernicus Climate Data Store (CDS) to deduce rain heights across nine stations in South Africa. The kernel density estimation (KDE) method was applied to estimate the temporal variation of rain height. A comparison of the measured and estimated rain heights shows a correlation coefficient of 0.997 with a maximum percentage difference of 5.3%. The results show that rain height ranges from a minimum of 3.5 km during winter in Cape Town to a maximum of about 5.27 km during the summer in Polokwane. The spatial variation shows a location-dependent seasonal trend, with peak rain heights prevailing at the low-latitude stations. The seasonal variability indicates that higher rain heights dominate in the regions (Polokwane, Pretoria, Nelspruit, Mahikeng) where there is frequent occurrence of rainfall during the winter season and vice versa. Contour maps of rain heights over the four seasons (autumn, spring, winter, and summer) were also developed for South Africa. The estimated seasonal rain heights show that rain-induced attenuations were grossly underestimated by the International Telecommunication Union (ITU) recommended rain heights at most of the stations during autumn, spring, and summer but fairly overestimated during winter. Durban had a peak attenuation of 15.9 dB during the summer, while Upington recorded the smallest attenuation of about 7.7 dB during winter at a 0.01% time exceedance. Future system planning and adjustments of existing infrastructure in the study stations could be improved by integrating these localized, seasonal radio propagation data in link budget design.