An iterative inverse method to estimate basal topography and initialize ice flow models

Abstract

Abstract.We evaluate an inverse approach to reconstruct distributed bedrock topography and simultaneously initialize an ice flow model. The inverse method involves an iterative procedure in which an ice dynamical model (PISM) is run multiple times over a prescribed period, while being forced with space-and time-dependent climate input. After every iteration bed heights are adjusted using information of the remaining misfit between observed and modeled surface topography. The inverse method is first applied in synthetic experiments with a constant climate forcing to verify convergence and robustness of the approach in three dimensions. In a next step, the inverse approach is applied to Nordenskiöldbreen, Svalbard, forced with height-and timedependent climate input since 1300 AD. An L-curve stopping criterion is used to prevent overfitting. Validation against radar data reveals a high correlation (up to R = 0.89) between modeled and observed thicknesses. Remaining uncertainties can mainly be ascribed to inaccurate model physics, in particular, uncertainty in the description of sliding. Results demonstrate the applicability of this inverse method to reconstruct the ice thickness distribution of glaciers and ice caps. In addition to reconstructing bedrock topography, the method provides a direct tool to initialize ice flow models for forecasting experiments.

Estimating the volume of glaciers in the Himalayan–Karakoram region using different methods

“…A1 and A2), representing approximately the range given in the literature (cf. Svensson, 1959;Graf, 1970;Pattyn and Decleir, 1995). It needs to be kept in mind that real glacier cross sections can vary much more, depending on a variety of factors including e.g., geological properties and characteristics of present or past glaciations.…”

“…We calibrate GlabTop2 against idealized valley cross sections derived from fitting a power law to measured cross sections in formerly glaciated terrain (e.g., Svensson, 1959;Graf, 1970). By calibrating GlabTop2 against idealized shapes we avoid using the few ice thickness measurements in the HK regions for the purpose of model calibration.…”

“…The so-called form-ratio F R (Graf, 1970) was calculated according to F R = h f /W . Idealized glacier cross sections are finally calculated using a power law of the form y = a x b (Svensson, 1959), where y is the elevation of the valley side and x the horizontal distance (always measured positive) from the valley center. The factor a is used to scale the cross sections to their respective F R .…”

“…Various approaches to estimate glacier volumes have been proposed, such as volume-area (V-A) relations (e.g., Chen and Ohmura, 1990;Bahr et al, 1997), slope-dependent icethickness estimations (Haeberli and Hoelzle, 1995), and more recently, a variety of spatially distributed ice-thickness models (e.g., Farinotti et al, 2009;Linsbauer et al, 2009;Huss and Farinotti, 2012;Li et al, 2012;Clarke et al, 2013;McNabb et al, 2012;van Pelt et al, 2013).…”

Understanding Dynamics of Himalayan Glaciers: Scope and Challenges of Remote Sensing

“…Estimations of ice volumes in the Himalayas are highly uncertain and range from ~2300 km 3 to ~6500 km 3 (Bolch et al, 2012).Various approaches have been proposed to estimate glacier volumes for the HKH region, such as volume-area (V-A) relations (e.g., Chen and Ohmura, 1990;Bahr et al, 1997), slope-dependent ice thickness estimations (Haeberli and Hoelzle, 1995), and more recently, a variety of spatially distributed ice-thickness models (e.g., Clarke et al, 2009;Farinotti et al, 2009;Linsbauer et al, 2009;Huss and Farinotti, 2012;Li et al, 2012;McNabb et al, 2012;Van Pelt et al, 2013). The total volume estimates from area-related relations are larger than those from other approaches (Frey et al, 2013).…”