Assimilating near real-time mass balance observations into a model ensemble using a particle filter

Abstract. Glaciers fulfil important short-term functions like drinking water supply and they are important indicators of climate change. This is why the interest in near real-time mass balance nowcasting is high. Here, we address this interest and provide an evaluation of seven continuous observations of point mass balance based on on-line cameras transmitting images every 20 minutes on three Swiss glaciers during summer 2019. Like this, we read 352 near real-time daily point mass balances in total from the camera images, revealing melt rates of up to 0.12 meter water equivalent per day (m w.e. d⁻¹) and the biggest total melt on the tongue of Findelgletscher with more than 5 m w.e. in 81 days. These observations are assimilated into an ensemble of three temperature index (TI) and one simplified energy balance mass balance models using an augmented particle filter with a custom resampling method. The state augmentation allows estimating model parameters over time. The custom resampling ensures that temporarily poorly performing models are kept in the ensemble instead of being removed during the resampling step of the particle filter. We analyse model performance over the observation period, and find that the model probability within the ensemble is highest on average with 58 % for an enhanced TI model, a simple TI model reaches about 19 %, while models incorporating additional energy fluxes have probabilities between 8 % and 15 %. When compared to reference forecasts produced with both mean model parameters and parameters tuned on single mass balance observations, the mass balances produced with the particle filter performs about equally well on the daily scale, but outperforms predictions of cumulative mass balance. The particle filter improves the performance scores of the reference forecasts by 91–97 % in these cases. A leave-one-out cross-validation on the individual glaciers shows that the particle filter is able to reproduce point observations at locations on the glacier where it was not calibrated, as the filtered mass balances do not deviate more than 8 % from the cumulative observations at the test locations. A comparison with glacier-wide annual mass balance by Glacier Monitoring Switzerland (GLAMOS) involving additional measurements distributed over the entire glacier, mostly show good agreement, but also deviations of up to 0.41 m w.e. for one instance.