Data-driven analysis and mapping of the potential distribution of mountain permafrost

It is commonly accepted that the distribution of mountain permafrost is extremely discontinuous. However, a clear representation on how the phenomenon is spatially distributed in sedimentary deposits is still difficult to obtain. Although physical models are able to efficiently simulate the ground thermal state at a single site (1D, e.g. borehole), they are not adapted to map mountain permafrost distribution (2D), because of the high number and high spatial variability of needed input data. Existing empirico-statistical models are more concerned with the prediction of the permafrost distribution rather than the description of the subsurface thermal state. They usually offer a good overview of the potential distribution at the local and regional scale. However, they are not always able to reproduce the high spatial discontinuity of mountain permafrost at the micro scale (scale of a specific landform; ten to several hundreds of meters) because they are generally thresholding the occurrence of permafrost on the basis of a restricted number of topographical and climatic parameters.

The objective of this research is to find an efficient alternative to both physical and empirico-statistical models. Machine learning (ML) algorithms are able to take into account a higher number of parameters compared to classic approaches, while producing high resolution maps with relative low computational times. With these techniques, the permafrost distribution can be modeled not only using topo-climatic parameters as a proxy, but also by including field permafrost evidences. Therefore, for this study, which deals with the analysis of mountain permafrost in the Western Valais Alps (Switzerland), machine learning algorithms are applied. The input dataset represents a high dimensional variable space (dimension = 20-25, spatial resolution = 10m), which is constructed using a digital elevation model, landcover maps, climate data, etc. Empirical data collected during field campaigns (mainly ERT and SRT profiles, apparent resistivity mapping lines and measured ground (surface) temperatures) and mapped active and inactive rock glaciers serve as training permafrost data. This information is then provided to ML algorithms with the purpose to estimate the class of unseen instances (pixels) using the model trained on known permafrost distribution data (positive and negative permafrost evidences). As we dispose of poor permafrost evidences available for rockwalls, we mainly focus our prediction in loose sediments.

With this approach, functional dependencies between permafrost and its explaining controlling factors are derived directly from data. Conversely to traditional models, these supervised learning techniques have the task of inferring a classification function from labelled training data (pixels of permafrost absence and presence) with the purpose of predicting the permafrost occurrence where the latter is unknown. In addition, ML techniques can be coupled with feature selection algorithms or have an embedded ability to provide measures of the variable importance. This allows the identification of the statistical contribution of each controlling factor and the refinement of the model by excluding non-relevant or redundant predictors (resulting in more robust and less uncertain prediction and reduced computational time). The machine learning algorithms we adopted so far have demonstrated to be efficient for permafrost distribution modelling with consistent results compared to the field reality. For instance, rock glaciers and limits between vegetation and mineral surfaces are correctly recognized and permafrost occurrence in talus slopes is predicted without recurring to altitude thresholds. The high resolution of the input dataset (10 meters) allows also elaborating maps at the micro scale with a modelled permafrost spatial distribution less optimistic than other classic spatial models.