Towards the Bayesian calibration of a glacier surface energy balance model for unmonitored glaciers

Abstract. Building on Bayesian calibration techniques and leveraging high-resolution climate simulations, we test the current capabilities of calibrating a surface energy balance model for unmonitored glaciers using only globally available satellite observations at Hintereisferner. We developed a multi-objective Bayesian framework for the Coupled Snowpack and Ice surface energy and mass balance model in Python (COSIPY), calibrated with satellite-derived geodetic mass balance, transient snowline altitudes, and mean glacier albedo. The framework is evaluated with in-situ observations and weather station measurements. A Latin Hypercube Sampling ensemble was used to investigate the model's parameter behaviour, establish priors and enable a Markov Chain Monte Carlo calibration helped by a novel and computationally efficient COSIPY emulator. The multi-objective calibration successfully constrains parameter distributions, addressing the equifinality between accumulation and albedo parameters. However, tighter parameter constraints, combined with imperfect climate simulations as forcing, create a model solution that requires a compromise between the three observational targets. Model evaluation shows that the calibrated ensemble reproduces glacier-mean albedos and inter-annual mass-balance variability well, but exhibits a negative bias in mean annual mass balance and a delayed snowline rise. This apparent contradiction arises from both forcing and model limitations. Incoming longwave radiation is overestimated throughout the year, while a warm and humid bias in the meteorological input during the later melt season enhances the positive turbulent fluxes. Early season melt is delayed by underestimated incoming shortwave radiation, and by an overly slow albedo decay caused by too high albedo aging and firn albedo parameters. Such biases in the meteorological forcing data remain a major obstacle to applying surface energy balance models to unmonitored glaciers. The calibration framework presented in this study provides diagnostic tools that help identify shortcomings and compensation effects within the modelling chain, paving the way for correcting forcing biases within a Bayesian framework as more observations become available. The open-source tools developed here have the potential to lower the barrier to studying the atmospheric drivers of glacier change at unmonitored sites with explicit treatment of uncertainty.