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.
I then updated the transform daily as the snow melted to get the isotropic dynamics.
I compared this to the numerical solution of the dimensionless Snow Partial Differential Equation (tick marks are again the characteristic length)
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.
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.