Environmental models have a key role to play in understanding complex environmental phenomena in space and time. Although their inherent uncertainty and non-identifiability are being increasingly recognized with the development and application of various methods, a more holistic analysis of all sources of model uncertainty is warranted. This paper addresses sources of uncertainty from various types of input datasets and model parameters, including those related to model structure assumptions, using a Soil and Water Assessment Tool (SWAT) application for the Minjiang River watershed, China. The holistic uncertainty sources in the SWAT application are summarized, and a sensitivity analysis (SA) is applied to examine the relative importance of the uncertainty sources influencing average streamflow and the load of nitrate. The analysis reveals that uncertainties related to the stream network precision and certain SWAT parameters are the most critical factors. Furthermore, building upon our SA framework to consider uncertainty sources more holistically would provide a good starting point for subsequent SA of spatially distributed environmental models in general.