Improving the estimate of the secular variation of Greenland ice mass in the recent decades by incorporating a stochastic process

Bao Zhang, Lin Liu, Yibin Yao*, Tonie van Dam, Shfaqat Abbas Khan

*Corresponding author for this work

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The irregular interannual variations observed in the Greenland ice sheet (GrIS) mass balance can be interpreted as stochastic. These variations often have large amplitudes, and, if not accounted for correctly in the mass change model parameterization, could have profound impacts on the estimate of the secular trend and acceleration. Here we propose a new mass trajectory model that includes both the conventional deterministic components and a stochastic component. This new model simultaneously estimates the secular rate and acceleration, seasonal components, and the stochastic component of mass changes. Simulations show that this new model improves estimates of model parameters, especially accelerations, over the conventional model without stochastic component. Using this new model, we estimate an acceleration of −1.6 ± 1.3 Gt/yr2 in mass change (minus means mass loss) for 2003-2017 using the Gravity Recovery and Climate Experiment (GRACE) data and an acceleration of −1.1 ± 1.3 Gt/yr2 using the modeled surface mass balance plus observed ice discharge. The corresponding rates are estimated to be −288.2 ± 12.7 Gt/yr and −274.9 ± 13.0 Gt/yr. The greatest discrepancies between the new and the conventional model parameter determinations are found in the acceleration estimates, −1.6 Gt/yr2 vs. −7.5 Gt/yr2 from the GRACE data. The estimated accelerations using the new method are apparently smaller than those estimated by other studies in terms of mass loss. Our quantitative analysis elucidates that the acceleration estimate using the conventional method is the lower bound (i.e., −7.5 Gt/yr2 for 2003–2017) while the acceleration estimated by the new method lies in the middle of the possible ranges. It is also found that these discrepancies between the new and the conventional methods diminish with sufficiently long (>20 yr) observation records.
Original languageEnglish
Article number116518
JournalEarth and Planetary Science Letters
Number of pages7
Publication statusPublished - 2020

Bibliographical note

This is an open access article under the CC BY license (


  • Greenland
  • Secular mass changes
  • Interannual variations
  • Stochastic process

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