Quantifying parameter uncertainty in a large-scale glacier evolution model using Bayesian inference: application to High Mountain Asia

Abstract

The response of glaciers to climate change has major implications for sea-level change and water resources around the globe. Large-scale glacier evolution models are used to project glacier runoff and mass loss, but are constrained by limited observations, which result in models being over-parameterized. Recent systematic geodetic mass-balance observations provide an opportunity to improve the calibration of glacier evolution models. In this study, we develop a calibration scheme for a glacier evolution model using a Bayesian inverse model and geodetic mass-balance observations, which enable us to quantify model parameter uncertainty. The Bayesian model is applied to each glacier in High Mountain Asia using Markov chain Monte Carlo methods. After 10,000 steps, the chains generate a sufficient number of independent samples to estimate the properties of the model parameters from the joint posterior distribution. Their spatial distribution shows a clear orographic effect indicating the resolution of climate data is too coarse to resolve temperature and precipitation at high altitudes. Given the glacier evolution model is over-parameterized, particular attention is given to identifiability and the need for future work to integrate additional observations in order to better constrain the plausible sets of model parameters.

Possible biases in scaling-based estimates of glacier change: a case study in the Himalaya

“…This range of β values is comparable to the observed massbalance gradients in the Himalaya (e.g. Wagnon et al, 2013).…”

“…However, the numerical cost of such a computation on a global scale is high, even if simplified approximate descriptions of the ice-flow equations, like shallow-ice approximation (SIA) (Hutter, 1983) or its higher-order variants, were to be used (Egholm et al, 2011;Clarke et al, 2015). One-dimensional SIA-based modelling tools are promising developments in this regard (Maussion et al, 2019;Zekollari et al, 2019;Rounce et al, 2020). The uncertainties associated with various input parameters, e.g.…”

A Systematic, Regional Assessment of High Mountain Asia Glacier Mass Balance

“…While we cannot directly estimate total glacier meltwater runoff contributions from glacierized HMA river basins using our geodetic mass balance estimates, we can estimate the "excess meltwater runoff " (e.g., Radić and Hock, 2014;Brun et al, 2017) or "imbalance component of runoff " (e.g., Pritchard, 2019). This excess glacier meltwater runoff is equal to the glacier mass loss in a given basin (Brun et al, 2017;Pritchard, 2019;Rounce et al, 2020b). In this study, we compute mass loss at multiple scales (individual glaciers, hex cells, basins), and we report excess glacier meltwater runoff for a given basin as the waterequivalent loss from only the glaciers or hex cells with negative mass balance ( M < 0) in that basin.…”

Response to the referee 3comments

“…Comparsion with GlacierMIP2: We are aware of the recent publication in glacier model, GlacierMIP2. It must be noted that some of the models are regionally focussed such as the AND2012, GloGEMflow, KRA2017 and PyGEM, which leaves us to include GLIMB, JULES and OGGM in the comparsion (Anderson et al, 2012;Kraaijenbrink et al, 2017;Maussion et al, 2020;Rounce et al, 2020;Shannon et al, 2019;Zekollari et al, 2019). We will try our best to use the same set of conditions in the model comparsion such as the initial volume, boundary conditions in the revised manuscript.…”