Panama faces seasonal floods and droughts as well as rising freshwater demands ranging from domestic consumption to hydro-power and the operation of the Panama Canal. A process-based hydrological model of the country is a desirable scenario planning tool to complement the existing national water security plan. In Panama as in much of the Global South, sufficient observed data do not exist for all watersheds to calibrate complex hydrological models. Understanding and improving the performance of uncalibrated hydrological models could greatly expand their utility in such regions. In this study, we build and validate an uncalibrated Soil and Water Assessment Tool (SWAT) model for Panama. We extend the default precipitation submodel and demonstrate the importance of sufficiently accounting for for spatial autocorrelation patterns in precipitation inputs: we found large improvements over the default model, not only for monthly means (NSE = 0.88, from NSE= 0.69 for default SWAT), but especially for standard deviations (NSE = 0.59, from 0.27) and maxima (NSE = 0.51, from 0.21) of discharge across locations and months. We found a strong seasonal trend and regional differences in the spatial autocorrelation of rainfall, suggesting that this phenomenon should not be modeled statically. The resulting precipitation and hydrology models provide important baseline information for Panama, especially on variability and extremes, and could serve as a template for other regions with limited data.