Convective storms in East Africa have severe socio-economic consequences for the region. Lake Victoria is a hotspot for severe weather, which contributes to the estimated 5,000 fatalities on the lake every year, and its reputation as the most dangerous water body in the world. Although East Africa presents its own unique challenges, understanding and predicting tropical convection remains one of the grand challenges of meteorology. Between 2012-2019, the UK Met Office ran a convection-permitting (CP) model over East Africa, aimed at improving forecasts of severe weather, in particular over Lake Victoria. In this thesis, an assessment of the added-value of the CP forecast, relative to the Met Office operational global model, which was convection parametrised, is performed. This is the first evaluation of a CP model in the tropics conducted over an extended period of time (2 years). The evaluation demonstrates the enhanced skill of the CP model for the prediction of sub-daily rainfall, but large uncertainties remain in the predicted location of precipitation, as well as issues with the distribution of rainfall intensities. Poor skill in forecasting over East Africa can also be attributed to an incomplete understanding of the processes responsible for severe weather, which is addressed with modelling and observational studies in this thesis. CP simulations with 1.5 km horizontal grid-spacing highlight the importance of the lake--land breeze circulation, and its interaction with the large-scale prevailing winds, in the formation and propagation of storms. The influence of convection over land on nocturnal storm formation over the lake is also demonstrated. First results from the HyVic pilot flight campaign, using the FAAM aircraft to sample the lake--land breeze circulation over Lake Victoria in unprecedented detail, are presented, and highlight the need for very high-resolution modelling to capture the observed small-scale features of the circulation.