Water availability and extremes in river discharge associated with floods and droughts are critical determinants of human welfare and ecological function. Modeling the effects of climate scenarios and other social and environmental changes on waterways is thus a key component of effective planning and risk mitigation. Yet, the calibration of multiple-basin models, such as for a national planning framework, can be difficult due to limitations on quality and spatial coverage of available hydrological observations. In this manuscript, we build a process-based whole-country hydrological model for Panama using the Soil and Water Assessment Tool (SWAT). We also extend SWAT by deriving a precipitation interpolation model that incorporates regional climatic variability and spatial autocorrelation of precipitation, and we validate the model using data from 35 hydrological stations. Without calibration, the default application of SWAT reasonably predicted spatiotemporal variability in mean monthly discharge (NSE=0.70), but largely failed to predict variability (NSE=0.26) and maxima (NSE=0.22). However, with our relatively simply precipitation interpolation sub-model, we were able to strengthen predictions of discharge (NSE=0.87), but also able to more than double predictive ability for variance (NSE=0.62) and maxima (NSE=0.53). This moderate modification may allow process-based hydrological models such as SWAT to be much more broadly applied; crucially, even across regions with scarce hydrological data. The resulting precipitation and hydrology layers provide important baseline information for Panama.