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Interpolation of temperature in a mountainous region using nonlinear profiles and non-Euclidean distances



In mountain regions, the distribution of surface air temperature happens to show marked horizontal gradients and nonlinear variations with topographic height. These pose a major challenge for the construction of area-wide temperature datasets on a regular grid. This study introduces a new deterministic method's for the spatial interpolation of daily temperature from station measurements. Building on a scale-separation concept, the methods main features are (1) a nonlinear parametric function to model nonlinearities in the vertical thermal profile at the scale of major basins, and (2) a distance weighting scheme with a non-Euclidean metric that accounts for terrain effects on the spatial representativity of measurements. The method is configured for the territory of Switzerland (European Alps) and is applied for the construction of a km-scale grid dataset from 70-100 stations over all days from 1961 to 2010. Several illustrative cases attest the method's potential, also under challenging conditions. Temperature patterns from basin-scale inversions and surface heated/cooled boundary layers are realistically reproduced. In situations with valley-scale cold-air pools and foehn, the method is less prone to artificial upslope/downslope extrapolation often observed with other techniques. With a network of 100 stations in Switzerland, typical interpolation errors (mean absolute error MAE, cross-validation) range from 0.5 °C over flat and hilly terrain in summer to 1.5 °C in the Alps in winter. Larger and partly systematic errors (MAE ≥ 3 °C) must be expected in un-sampled valleys in winter due to the missing out of local-scale cold pools. Interpolation accuracy was found to vary with the change in station density over time, demonstrating improvements in the overall representativity of the measurement network. But this also compromises the long-term homogeneity of the grid dataset, despite it being based on homogeneous records. The presented method may be applicable in other mountain regions after some configuration.