The Indus watershed is a highly populated region that contains parts of India, Pakistan, China, and Afghanistan. Changes in precipitation patterns and rates of glacial melt have significantly impacted the region in recent years, and climate change is projected to result in further serious human and environmental consequences. To understand the climate dynamics of the Indus watershed and surrounding regions, reanalysis and satellite data from products such as APHRODITE-2, TRMM, ERA5, and MERRA-2 are often used, yet these products are not always in agreement regarding critical variables such as precipitation. Here we objectively evaluate the level of agreement between precipitation from these four products. Because these data are on different spatial scales, we propose a low-rank spatio-temporal dynamic linear model for precipitation that integrates information from each of the above climate products. Specifically, we model each data source as the combination of a modified shared process, a discrepancy process, and Gaussian noise. We define the shared process at a high spatial resolution that can be upscaled according to the resolution of the observed data. Our proposed model's shared process provides a cohesive picture of monthly precipitation in the Indus watershed from 2000 to 2009, while the product-specific discrepancies provide insight into how and where the products differ from one another.