A statistical approach to modelling permafrost distribution in the European Alps or similar mountain ranges

Estimates of permafrost distribution in mountain regions are important for the assessment of climate change effects on natural and human systems. In order to make permafrost analyses and the establishment of guidelines for e. g. construction or hazard assessment comparable and compatible between regions, one consistent and traceable model for the entire Alpine domain is required. For the calibration of statistical models, the scarcity of suitable and reliable information about the presence or absence of permafrost makes the use of large areas attractive due to the larger data base available. We present a strategy and method for modelling permafrost distribution of entire mountain regions and provide the results of statistical analyses and model calibration for the European Alps. Starting from an integrated model framework, two statistical sub-models are developed, one for debris-covered areas (debris model) and one for steep bedrock (rock model). They are calibrated using rock glacier inventories and rock surface temperatures. To support the later generalization to surface characteristics other than those available for calibration, so-called offset terms have been introduced into the model that allow doing this in a transparent and traceable manner. For the debris model a generalized linear mixed-effect model (GLMM) is used to predict the probability of a rock glacier being intact as opposed to relict. It is based on the explanatory variables mean annual air temperature (MAAT), potential incoming solar radiation (PISR) and the mean annual sum of precipitation (PRECIP), and achieves an excellent discrimination (area under the receiver-operating characteristic, AUROC = 0.91). Surprisingly, the probability of a rock glacier being intact is positively associated with increasing PRECIP for given MAAT and PISR conditions. The rock model is based on a linear regression and was calibrated with mean annual rock surface temperatures (MARST). The explanatory variables are MAAT and PISR. The linear regression achieves a root mean square error (RMSE) of 1.6 degrees C. The final model combines the two sub-models and accounts for the different scales used for model calibration. The modelling approach provides a theoretical basis for estimating mountain permafrost distribution over larger mountain ranges and can be expanded to more surface types and sub-models than considered, here. The analyses performed with the Alpine data set further provide quantitative insight into larger-area patterns as well as the model coefficients for a later spatial application. The transfer into a map-based product, however, requires further steps such as the definition of offset terms that usually contain a degree of subjectivity.