A Nonlinear Statistical Model for Extracting a Climatic Signal From Glacier Mass Balance Measurements

Abstract

Understanding changes in glacier mass balances is essential for investigating climate changes.However, glacier-wide mass balances determined from geodetic observations do not provide a relevant climatic signal as they depend on the dynamic response of the glaciers. In situ point mass balance measurements provide a direct signal but show a strong spatial variability that is difficult to assess from heterogeneous in situ measurements over several decades. To address this issue, we propose a nonlinear statistical model that takes into account the spatial and temporal changes in point mass balances. To test this model, we selected four glaciers in different climatic regimes (France, Bolivia, India, and Norway) for which detailed point annual mass balance measurements were available over a large elevation range. The model extracted a robust and consistent signal for each glacier. We obtained explained variances of 87.5, 90.2, 91.3, and 75.5% on Argentière, Zongo, Chhota Shigri, and Nigardsbreen glaciers, respectively. The standard deviations of the model residuals are close to measurement uncertainties. The model can also be used to detect measurement errors. Combined with geodetic data, this method can provide a consistent glacier-wide annual mass balance series from a heterogeneous network. This model, available to the whole community, can be used to assess the impact of climate change in different regions of the world from long-term mass balance series.Numerous studies have investigated the spatial-temporal mass balance distribution at glacier-wide scale (e.g.

Reanalysing the 2007–19 glaciological mass-balance series of Mera Glacier, Nepal, Central Himalaya, using geodetic mass balance

“… = 0.34 m w.e. and the residuals of the nonlinear model of Vincent and others (2018) weighted over the total area of the glacier (see section S3 of supplementary information for the details of the calculations). Inside the 2012–18 calibration period, is equal to 0.16 m w.e.…”

“…The supplementary text (section S3) presents an alternative method to estimate the annual glacier-wide mass balance from point measurements using the nonlinear model of Vincent and others (2018). This model is applied not only for comparison purposes but above all to carry out a rigorous evaluation of uncertainties (see Section 4.3. and supplementary section S3.2).…”

A Review of the Current State and Recent Changes of the Andean Cryosphere

“…Tropical glaciers are characterized by large vertical mass balance gradients in the ablation area (e.g., Kaser et al, 1996;Favier et al, 2004;Soruco et al, 2009;Vincent et al, 2018), implying a significant contribution of the lowest areas of the glacier to total ablation. For example, for the Zongo glacier in Bolivia, the ablation area (one third of the glacier surface at the low elevation ranges) contributes with 80% to the yearly specific mass balance of the glacier (Soruco et al, 2009).…”

On the Imbalance and Response Time of Glaciers in the European Alps

“…Glaciers have globally been losing mass at an accelerated pace over the past few decades (Wouters et al, 2019;Zemp et al, 2019). This is also the case in the European Alps Dehecq et al, 2016;Fischer et al, 2015), where glaciers have been subject to strongly negative mass balances (e.g., Charalampidis et al, 2018;Thibert et al, 2018;Vincent et al, 2018;Zekollari & Huybrechts, 2018). By retreating, glaciers lose ice at their lower elevations, which has a stabilizing feedback on their mass balance, hence reducing the imbalance between glacier geometry and the climatic conditions (hereafter referred to as "glacier-climate imbalance").…”