Quantifying the uncertainty in surface energy fluxes of glacierised environments: How does the lack of information affect estimations of ablation amounts?

Surface-atmosphere energy exchanges control the ablation of snow and ice dominated regions. Although some of the input variables for surface energy balance (SEB) models can be estimated with reasonable accuracy using extrapolated data, remote sensing or meteorological models, estimates of other variables are still difficult, especially across glacierised catchments and at high elevations. Despite the existence of large uncertainties in the forcing variables, ablation amounts are usually simulated by glacio-hydrological models using only deterministic inputs. This is the case for advanced SEB models, which use large amounts of input data, or conceptual models e.g. based on temperature index methods, which rely on the transferability in space and time of empirical parameters.

In this work, we present an approach to explicitly calculate the uncertainty transferred from input variables to energy fluxes and ablation amounts of SEB simulations. For this, we parameterize the probability density functions (pdfs) of the SEB results. We code a point scale SEB model that calculates radiative, turbulent and internal heat fluxes. The model also includes a blowing snow sublimation module to determine mass losses to the atmosphere within the saltation and suspension layers. Using the SEB model, we perform extensive numerical simulations (>2*10⁶ model runs) and obtain results of melt and sublimation within a-priori defined ranges of the input variables. These ranges are relatively wide in order to be representative of highly variable high-elevation conditions. After this, we fit theoretical pdfs to the input and outputs variables of the SEB model and obtain the distribution parameters. Using these results and a Bayesian scheme, we can compute the pdf of each output variable of the SEB as a function of the available (usually limited) information at a particular study site. In order to identify the most relevant information for each output variable, we also show the results of a global sensitivity analysis of the SEB model. The approach is tested using field measurements in the Chilean Andes and the Nepalese Himalaya. The presented method is shown to be effective on the calculation of energy fluxes, and melt and sublimation amounts, explicitly computing their uncertainty using a computationally parsimonious approach.