Ice-Dynamic Constraints on Glacier Climatic Mass Balance using Inverse Technique

The performance of models for surface mass balance (SMB) builds on reliable atmospheric information as input as well as on in-situ stake measurements for calibration. Both data should best show appropriate quality and spatial coverage. In remote and high mountain regions, in-situ information is often impractical to obtain due to logistical and ressource limitations. Consequently, modellers can often only rely on climate reanalysis data and remotely sensed mass balance observations. As ground-truthing is limited in many mountain regions, this step introduces substantial uncertainties in transient simulations. Given the importance of glaciers as climate indicators and water resources, accurately simulating their evolution is crucial, but cannot be achieved with large uncertainties in forcing and calibration data. This study presents a proof-of-concept to overcome the limitation when estimating glacier-wide mass balance fields by combining mass conservation and stress balance with remotely sensed observations. Target quantity is the 2D SMB field, in particular first-order quantities such as vertical gradients and the equilibrium line altitude (ELA). The flux divergence is calculated using a built-in inversion within the Instructed Glacier Model (IGM).  The model relies on a deep-learning informed surrogate model to simulate ice flow. A sensitivity analysis of this inverse data assimilation was performed to assess the influence of uncertainties of observational input. This analysis emphasises the critical role of ice-thickness measurements. Together with surface velocites, ice thickness controls the spatial pattern and magnitudes in the flux divergence – a key field to infer the unknown SMB. Our approach was further validated in real-world application to Rhône Glacier, Aletsch Glacier and Kanderfirn, demonstrating SMB results largely consistent with available observational records. We extended the application to other glaciers with available SMB measurements and show sound transferability. We are therefore convinced that the resulting SMB fields can be employed to improve the calibration step of melt models of various complexity. As the method exclusively relies on remotely sensed observations it is readily transferible to glacierised regions worldwide. Moreover, the SMB field can provide new insights into poorly constrained precipitation magnitudes over mountainous regions. This is potentially relevant as additional constraints on reanalysis datasets. In summary, this method can seamlessly be integrated into glacier evolution modelling, is readily transferible and adaptable to the specific needs and we are convinced that it will in the future be a valid procedure for melt-model calibration.