Abstract
Abstract. Simulation approaches to firn densification often rely on the assumption that grain boundary sliding is the leading process driving the first stage of densification. Alley (1987) first developed a process-based material model of firn that describes this process. However, often so-called semi-empirical models are favored over the physical description of grain boundary sliding owing to their simplicity and the uncertainties regarding model parameters. In this study, we assessed the applicability of the grain boundary sliding model of Alley (1987) to firn using a numeric firn densification model and an optimization approach, for which we formulated variants of the constitutive relation of Alley (1987). An efficient model implementation based on an updated Lagrangian numerical scheme enabled us to perform a large number of simulations to test different model parameters and identify the simulation results that best reproduced 159 firn density profiles from Greenland and Antarctica. For most of the investigated locations, the simulated and measured firn density profiles were in good agreement. This result implies that the constitutive relation of Alley (1987) characterizes the first stage of firn densification well when suitable model parameters are used. An analysis of the parameters that result in the best agreement revealed a dependence on the mean surface mass balance. This finding may indicate that the load is insufficiently described, as the lateral components of the stress tensor are usually neglected in one-dimensional models of the firn column.
Highlights
Firn densification models fall into two basic categories
We aim to evaluate (i) whether the description of grain boundary sliding given by Alley (1987) is suitable for the simulation of firn densification at low density, (ii) how a modification of the constitutive relation introduced by Bréant et al (2017) affects simulation results, (iii) whether hidden or additional dependencies on climatic or other conditions can be identified in the constitutive relation, and (iv) how the constitutive relation of Alley (1987) might be improved
Note that our study aims to assess the constitutive relation for grain boundary sliding proposed by Alley (1987)
Summary
Firn densification models fall into two basic categories. Models in the first category, which includes most existing models, follow the so-called semi-empirical approach of Herron and Langway (1980), which itself is based on Sorge’s law (Bader, 1954) and the Robin hypothesis (Robin, 1958). In the second category of firn densification models, an attempt is made to quantify the physical processes related to firn densification These processes include various types of creep and diffusion. Micromechanical models are used for small-scale investigations (Johnson and Hopkins, 2005; Theile et al, 2011; Fourtenau et al, 2020), whereas models based on continuum mechanics can be used for large-scale simulations. Examples of the latter are the models of Arthern and Wingham (1998), Arnaud et al (2000), and Goujon et al (2003)
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