Glacier and snow melt are the primary sources of water for streams, and rivers in upper Indus region of the western Himalaya. However, the magnitude of runoff from this glacierized basin is expected to vary with the available energy in the catchment. Here, we used a physically based energy balance model to estimate the surface energy and surface mass balance (SMB) of the upper Chandra Basin glaciers for 7 hydrological years from 2015 to 2022. A strong seasonality is observed, with net radiation being the dominant energy flux in the summer, while latent and sensible heat flux dominated in the winter. The estimated mean annual SMB of the upper Chandra Basin glaciers is −0.51 ± 0.28 m w.e. a−1, with a cumulative SMB of −3.54 m w.e during 7 years from 2015 to 2022. We find that the geographical factors like aspect, slope, size and elevation of the glacier contribute towards the spatial variability of SMB within the study region. The findings reveal that a 42% increase in precipitation is necessary to counteract the additional mass loss resulting from a 1°C increase in air temperature for the upper Chandra Basin glaciers.

The propagation of elastic-flexural–gravity waves through an ice shelf is modeled using full three-dimensional elastic models that are coupled with a treatment of under-shelf sea-water flux: (i) finite-difference model (Model 1), (ii) finite-volume model (Model 2) and (iii) depth-integrated finite-difference model (Model 3). The sea-water flow under the ice shelf is described by a wave equation involving the pressure (the sea-water flow is treated as a “potential flow”). Numerical experiments were undertaken for an ice shelf with ‘rolling’ surface morphology, which implies a periodic structure of the ice shelf. The propagation of ocean waves through an ice shelf with rolling surface morphology is accompanied by Bragg scattering (also called Floquet band insulation). The numerical experiments reveal that band gaps resulting from this scattering occur in the dispersion spectra in frequency bands that are consistent with the Bragg’s law. Band gaps render the medium opaque to wave, that is, essentially, the abatement of the incident ocean wave by ice shelf with rolling surface morphology is observed in the models. This abatement explains the ability of preserving of ice shelves like the Ward Hunt Ice Shelf, Ellesmere Island, Canadian Arctic, from the possible resonant-like destroying impact of ocean swell.

Jostedalsbreen in western Norway is the mainland Europe's largest ice cap and a complex system of more than 80 glaciers. While observational records indicate a significant sensitivity to climate fluctuations, knowledge about ice-cap wide spatiotemporal mass changes and their drivers remain sparse. Here, we quantify the surface mass balance (SMB) of Jostedalsbreen from 1960 to 2020 using a temperature-index model within a Bayesian framework. We assimilate seasonal glaciological SMB to constrain accumulation and ablation, and geodetic mass balance to adjust model parameters for each glacier individually. Overall, we find that Jostedalsbreen has experienced a small mass loss of −0.07 m w.e. a−1 (−0.21 to +0.08 m w.e. a−1), but with substantial spatiotemporal variability. Our results suggest that winter SMB variations were the main control on annual SMB between 1960 and 2000, while increasingly negative summer SMB is responsible for substantial mass losses after 2000. Spatial variations in SMB between glaciers or regions of the ice cap are likely associated with local topography and its effect on orographic precipitation. We advocate for models to leverage the growing availability of observational resources to improve SMB predictions. We demonstrate an approach that incorporates complementary datasets, while addressing their inherent uncertainties, to constrain models and provide robust estimates of spatiotemporal SMB and associated uncertainties.