Uniform Warming and Snowpack Disappearance in the Western US

Abstract:

Both modeling and observational studies have demonstrated that as the planet continues to warm, mountain snowpack will melt progressively earlier in the year. However, an analysis of nearly 40 years of daily snow water equivalent (SWE) measurements from SNOTEL sites in the Western US shows that this relationship is not uniform. When the effects of precipitation variability are accounted for, in some regions the calendar day when the mountains become snow-free (the “date of disappearance”) recedes by nearly 30 days per degree warming, whereas in others there is almost no change in the date of disappearance under the same amount of warming. In order to understand the source of this heterogeneity in the response of mountain snowpack to increasing temperature, we develop an idealized model of snowpack accumulation and melt, which assumes a sinusoidal annual cycle in daily mean surface air temperature T,

T = T₀ − T₁ sin(ωt)

where T₀ is the annual-mean temperature, T₁ is the amplitude of the annual cycle in temperature, ω is the frequency of the annual cycle, and t is time in days. We analytically solve the model for the date of disappearance ζ, and then take the partial derivative with respect to annual-mean temperature to find the sensitivity of ζ to warming,

∂ζ/∂T₀ = − 1/ω (1+R_a/R_m) (T₁²−T₀²)^—1/2

where R_a and R_m are the rates of snow accumulation and melting, respectively. The magnitude of the solution is large when the difference between T₁ and |T₀| is small, in which case the temperature either spends most of the year above the melting point, or most of the year below the melting point. The mechanism behind the dependence of ∂ζ/∂T₀ on T₀ and T₁ is related to the shape of the seasonal cycle in T. In regions where T₀ > 0 and T₁ is only slightly larger than |T₀|, T crosses zero near the flat trough of the sinusoid, with temperatures below zero occurring only during a brief part of the year. In this case, when T warms there is a large reduction in the number of days when T < 0, leading to a substantially earlier time of complete snowmelt. We validate the proposed theory via comparison with SNOTEL-derived values of ∂ζ/∂T₀, and from simulations performed with the Variable Infiltration Capacity (VIC) hydrologic model, finding that our theory can explain approximately 70% and 100% of the observed and VIC modeled variability in ∂ζ/∂T₀, respectively.