Depth of Liquid Water Infiltration in Greenland Firn Based on L-Band Radiometry, a Snow Physics Model, and Machine Learning

As melting of the firn layer across the Greenland Ice Sheet increases, determining the fate of infiltrating meltwater is crucial for assessing the evolution of the firn and its potential to buffer runoff. While L-band satellite radiometry can estimate the vertically integrated liquid water amount (LWA), using such retrievals in firn studies is challenging because resolving vertical LWA profiles requires complex inversions or physically tuned models. In this study, we developed and tested a decoder consisting of long short-term memory (LSTM) and convolutional neural network (CNN) layers that assigns a vertical profile to the liquid water measured by L-band radiometry. We trained the decoder on an ensemble of time series generated by the SLF-SNOWPACK model to generate a latent representation of the depth distribution of LWA as determined by model physics. The decoder reproduced the relationship between LWA time series and the modeled liquid mass per cell, maximum depth of infiltration, and duration of wetting with mean errors of 29%, 15%, and 6%, respectively. We then applied the decoder to the L-band retrieved LWA time series for a low and high-melt-intensity year and assessed time/space trends in the refreezing amount and maximum depth of infiltration. The patterns are consistent with expectations from observations, lending confidence to the predictions. The method thus utilizes observational constraints from L-band time series to create vertical profiles of water and refreezing in firn, which can be incorporated into firn models and serve as validation targets for regional climate models.