Abstract Climate models have been improving to better represent the Earth system. They have become common tools for understanding the dynamics of different physical components of the Earth system and providing insights into their future changes. However, a remaining key limitation is persistent biases in model outputs. Existing bias correction methods only rely on model outputs and do not account for the interconnected physical processes within the climate model that are responsible for the biases in simulating the climate variables (e.g., precipitation and temperature). Here we propose a novel machine learning technique using a convolution-based multivariate Gaussian process (MGP) to reduce biases and uncertainties in temperature and precipitation from a climate model in a physically consistent manner. This approach captures the physical interactions driven by surface energy fluxes and incorporates their non-linear relationships with precipitation and temperature, while reducing biases in climate model outputs. Our results indicate that surface energy balance processes act as key physical drivers for quantifying biases and uncertainties in seasonal and regional precipitation and temperature. Consequently, the proposed MGP approach can effectively reduce biases in both temperature and precipitation simultaneously by using their physical relationships to surface energy fluxes.