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This software takes samples of an image (known as patches) and searches for them in subsequent images, thus producing a displacement vector for each patch. The software is capable of locating a patch with sub-pixel accuracy. When this software was used to track small translations of an undeformed specimen, the mean error was found to be sig- nificantly less than 40 µ m. The images were analyzed sequentially, using a grid of 64x64 pixel patches spaced at 4.5 mm and with the patch positions reset to this grid for each image. Local strain tensors were then calculated from the displacement fields by taking the tensorial displacement gradient which was evaluated using the ParaView package [3], and strain rate tensors were evaluated from strain tensors pertaining to sequential images in terms of finite differences. 

## 2 Application of the constitutive model to the com- pression experiments 

The general constitutive framework has been defined in the main paper. When applying this framework to the compression experiments, we make the simplifying assumptions that α = 1 / 2 and ν = 0. These assumptions are tantamout to assuming that, under uniaxial compression, the material exhibits neither elastic nor plastic expansion in the lateral direction. In other words, in this approximation the snow does not interact with the container side walls and the confined snow behaves exactly as a free standing column where we are dealing with a purely uniaxial stress and strain state. The accuracy of these assumptions will be demonstrated in the section on model parameters below. 

With α = 1 / 2 the equivalent stress is given by 

The plastic strain rate as derived from the associated flow rule is 

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Identifying the compression direction with the x axis direction of a Cartesian coordinate system and using ν ≈ 0, the stress, elastic and plastic strain tensors then have the simple structure 

Owing to the parameter choices α = 1 / 2 and ν = 0 there is no lateral expansion or contraction of the sample and hence no interaction with the confining walls. The measured data for the axial compaction forces and lateral forces allow us to assess the quality of this approximation: At the end of each deformation experiment we find typical axial forces of 250 N which, given the sample geometry, translates into a typical axial stress σ$_{xx}$ = 5 × 10 4 Pa. With an end height of the sample of L ′ ≈ 140 mm, the typical lateral force of 45 N translates into a typical lateral stress of σ$_{zz}$ = 12 × 10 $^{2}$Pa = 0 . 025 σ$_{xx}$ . Thus, lateral stresses can be neglected to a very good approximation: the elastic state of the sample is almost fully characterized by the scalar axial stress s . 

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