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Chaotic Pattern Dynamics in Sun-melted Snow

MSc Slides

In my masters, I studied the patterns, called suncups that form spontaneously in the surface of melting snow. Using an ip camera near the summit of Whistler Mountain, I observed the trajectory of individual suncups.

Raw Snowcam Image

Snowcam

Isotropic Snowcam Image

Isotropic Snowcam

First however, I had to invert the perspective transformation implied by imaging the surface from an oblique angle to get an isotropic surface image. The grid spacing and tick marks indicate the characteristic length of the surface pattern.

Suncup Dynamics

I then updated the transform daily as the snow melted to get the isotropic dynamics.

Numerical Simulation

I compared this to the numerical solution of the dimensionless Snow Partial Differential Equation (tick marks are again the characteristic length)

Snow Equation

Using independent measurements of the height of the suncups as they formed from a flattened snow surface, the only free parameter remaining to fit to the observed dynamics was β/α, which governs how quickly the suncups diffuse.

Numerical and Experimental RMS Suncup Displacement

RMS Displacement

From this I, fit β/α = 1.1 ± 0.3. This has interesting implications because the |∇h|2 term accelerates the surface melt rate, while the ∇2|∇h|2 does not. Therefore, its relative size given by β/α gives information about how the pattern affects the melt rate.