An improved temperature index model for alpine glaciers using derived degree-day factors from climatic inputs

Glacier melt rates are strongly affected by minor perturbations in climatic systems. Quantifying changes in glacier melt rates is therefore important, particularly in areas where melt-water contributes to hydroelectric power generation, irrigation, or flood risks. Several methods currently exist for modeling glacier melt rates, but one widely used method is temperature index modeling, also called positive degree-day modeling. This model is often applied due to its simplicity and small number of input variables, but it still depends on an empirically-measured scaling constant (the degree-day factor). These degree-day factors can vary by a factor of five from one glacier to the next, complicating the applicability of the approach to new regions, or to different time periods. Previous work suggests the degree-day factor may be a function of the surface albedo, solar radiation, and near-surface air temperature. Thus, it is possible the degree-day factor itself is predictable. In this study we present a method to derive these melt factors directly from easily obtained climatic variables, thus allowing for the ready application of temperature index modeling to a much wider suite of glaciers with greater accuracy. We used a full energy-balance model to calculate possible degree-day factors over the full range of climate conditions commonly encountered with alpine glaciers. We then constructed a statistical emulator (a linear model which considers numerous interactions and polynomial effects) using select climate variables (insolation, positive degree-days, and albedo) as inputs. The statistical model is tuned using the energy-balance output as training data. The model skill will be tested against a suite of empirically-derived degree-day factors. These results would allow for the application of more accurate glacier melt models with quantified uncertainties to under-sampled glacial regions and paleoclimate reconstructions.