A scale‐space approach for detecting significant differences between models and observations using global albedo distributions

[1] This paper describes how a statistical scale-space technique can be used for evaluating climate models. A difference image between model and validation data is used as input. Hypothesis testing is performed at each difference pixel for a broad range of image resolutions (or scales). This approach circumvents some of the classical problems of hypothesis testing. An area, at a particular scale, is claimed to be significant if it is sufficiently different from zero in the difference image. such differences are called features. As the scale gradually increases from fine to coarse, features are created, they grow and merge and may finally annihilate. The scale-space algorithm produces maps for statistical inference and the degree of significance at different locations. The adapted scale-space technique was applied for validation of ECHAM5 Global Circulation Model surface albedo against a remote sensing surface albedo climatology. Overall, the largest discrepancies were detected over snow and ice-covered areas, and ECHAM5 was found to overestimate the albedo compared to the albedo climatology for all scales in March. Successively coarser spatial scales resulted in more and larger significant areas in the difference image. At the finest scales (280 km) very few areas of significant albedo differences were detected because of relatively high interannual variability for the areas of largest difference. At 1100 km, significant albedo differences were found in the southern part of the Arctic Ocean adjacent to the ice edge, probably because of the different positions of the ice edge in the two data sets. A scale of 2500 km was found to be reasonable for validating albedo as the statistical significance agrees well with differences meaningful from a climatologist's point of view. At this scale most of the snow covered regions in Northern Eurasia with high positive differences and relatively low interannual variability were found to be significant.

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