The summertime West African Sahel has the worldwide highest degree of thunderstorm organisation into long-lived, several hundred-kilometre elongated, fast propagating systems that contribute 90% to the annual rainfall. All current global weather prediction and climate models represent thunderstorms using simplified parameterisation schemes which deteriorates the modelled distribution of rainfall from individual storms and the entire West African monsoon circulation. It is unclear how this misrepresentation of Sahelian convection affects forecasts globally. Our study is the first to demonstrate how a computationally feasible increase of model resolution over West Africa – allowing to avoid convection parameterisation – yields a better representation of organised convection in the Sahel and of moisture within the monsoon system, ultimately improving 5–8-day tropical and mid-latitude weather forecasts. We advocate an operational use of a modelling strategy similar to the one presented here for a cost-effective improvement of global weather prediction and potentially even (sub-)seasonal and climate simulations.