i.e., x denotes the position along the compression axis in the initial configuration (thus the x interval occupied by the sample in the graphs does not shorten during compression). The colour contrast demonstrates the strongly localized nature of deformation. A moving deformation front appears on the space-time plot as an inclined zone of high strain rate. The inclination slope defines the front velocity in the Lagrangian frame. The first front nucleates at the top of the sample and moves at constant (Lagrangian) speed downwards. Once it reaches the bottom of the sample, a new front nucleates there and moves upwards across the sample until it reaches the top. Repetition of this process leads to a bouncing motion of the locus of deformation. Oscillatory features are also manifest on the force vs. time curves as band nucleation is associated with an up-down oscillation of the driving force (see the dashed lines in Fig. 2 which illustrate the correspondence). Occasionally the bouncing pattern is interrupted as seen in Fig. 2(c) where the first band gets stuck in the middle of the sample and deformation is taken over by a second band nucleating at the bottom and moving upwards until it merges with the first, whereafter a new band nucleates at the top and the bouncing pattern is resumed. The observations are similar for both investigated deformation rates. 

## 4.2 Simulation results 

In our simulations we use the following model parameters (for discussion, see the Supplementary Material): Initial elastic modulus E$_{0}$ = 10 MPa, volumetric change parameter α = 0 . 499 , friction coefficient at container surface µ = 0 . 5 , mean initial (homogeneous) strength of snow Σ$_{0}$ = 8 × 10 4 Pa, exponent of density dependence of elastic modulus c = 3 , exponent of density dependence of strength a = 8 , softening strain ε$_{S}$ = 0 . 05 , residual strength Σ$_{R}$ = 0 . 05Σ$_{0}$ , characteristic time for rapid sintering τ = 10 s. The internal length is taken to be ξ = 0 . 2 mm, which we also use as spacing of our computational grid. To mimic microstructural heterogeneity, the initial strength at the different grid points is assumed to be Weibull distributed with mean Σ$_{0}$ and Weibull exponent β = 5 . Finally, to mimick the effect of near-surface heterogeneities and stress concentrations due to uneven loading at the specimen ends, structural strength is assumed to decrease towards zero across two surface layers of width 1 mm (5 grid points) and 0.4mm (2 grid points), located at the top and bottom of the specimen, respectively. 

Simulations were carried out at imposed strain rates ˙ e$_{ext}$ = 5 . 7 × 10 − $^{3}$s − 1 and ˙ e$_{ext}$ = 2 . 5 × 10 − $^{2}$s − 1 , matching the experimental data shown in Fig. 2. The two runs shown for the higher strain rate differ only with respect to the initial random distribution of local strength. 

It is seen that, similar to the experiment, the nucleation of new bands is associated with oscillations in the force vs. time/strain curves, though these are less pronounced than in the experimental counterparts. In the absence of strength fluctuations we consistently observe a bouncing band pattern similar to Fig. 2(a). 

