Knowledge of how uncertainty propagates through a hydrological land surface modelling sequence is of crucial importance in the identification and characterisation of system weaknesses in the prediction of droughts and floods at global scale. We evaluated the performance of five state-of-the-art global hydrological and land surface models in the context of modelling extreme conditions (drought and flood). Uncertainty was apportioned between the model used (model skill) and also the satellite-based precipitation products used to drive the simulations (forcing data variability) for extreme values of precipitation, surface runoff and evaporation. We found in general that model simulations acted to augment uncertainty rather than reduce it. In percentage terms, the increase in uncertainty was most often less than the magnitude of the input data uncertainty, but of comparable magnitude in many environments. Uncertainty in predictions of evapotranspiration lows (drought) in dry environments was especially high, indicating that these circumstances are a weak point in current modelling system approaches. We also found that high data and model uncertainty points for both ET lows and runoff lows were disproportionately concentrated in the equatorial and southern tropics. Our results are important for highlighting the relative robustness of satellite products in the context of land surface simulations of extreme events and identifying areas where improvements may be made in the consistency of simulation models.