On the use of Procrustes target analysis for validation of modeled precipitation modes

• Published in: Climate dynamics Vol. 61; no. 11-12; pp. 5065 - 5089
• Main Authors: Ibebuchi, Chibuike Chiedozie, Richman, Michael B.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2023; Springer Nature B.V
• Subjects: Climate change; Climatology; Datasets; Earth and Environmental Science; Earth Sciences; Geophysics/Geodesy; Oceanography; Precipitation; Principal components analysis; Regions; Precipitation; Rotated S-mode PCA; Procrustes target analysis; Reanalysis; Climate models; Africa south of the equator; Model inter-comparisons; Anthropogenic climate change
• ISSN: 0930-7575; 1432-0894
• DOI: 10.1007/s00382-023-06841-4

This study introduces the use of Procrustes target analysis for comparing observed and modeled precipitation patterns obtained from a rotated S-mode principal component analysis. Procrustes target analysis is a manifold alignment method for principal component analysis, requiring that a set of reference principal components are specified, a priori, as the target that the principal components from a second data set are linearly transformed to best fit. The target patterns are selected as they are hypothesized to be more physically realistic, accurate, or reliable, compared to those in the second data set (e.g., using observed or reanalysis data for the target data set and climate model data for the second data set). Using the rotated principal component analysis, we classify the austral summer precipitation in Africa south of the equator into four regions of the domain: the south, east-central, northeast, and northwest. The physical basis for each region is established by examining regional variations in vertical velocity coupled with variations in the patterns of advective moisture fluxes, converging at specific portions in the study region. On this basis, the observed precipitation regions are deemed physically interpretable and serve as the reference patterns to probe the degree of reference pattern consistency with (i) the precipitation patterns from ERA5 and NCEP-NCAR reanalysis, (ii) the precipitation patterns from 2 high-resolution regional climate models driven by ERA-Interim, and by HadGEM2 and (iii) the impact of future climate change on the simulated patterns from the regional climate models. Comparing principal components from different datasets is not straightforward as there are two sources of variability: (i) that arising from non-optimal alignment (misalignment) of the two linear subspaces or manifolds (a manifold is regarded as a vector space) and (ii) that arising from true differences in the modes from the different datasets. The importance of applying Procrustes target analysis is that climate patterns derived from principal component analysis are known to be sensitive to sampling variability. Procrustes target analysis allows for maximal vector alignment, making it possible to disentangle the two sources of variability so that the analyst can assign the dissimilarities to differences in the modes. We document that, after the application of Procrustes target analysis matching, the variability arising from misalignment between the reference set and second set of principal components was reduced, as measured by the improved matching between the vectors from approximately 3.7–41.7% for the various datasets tested. Specifically, for the principal components obtained from reanalysis data, after the removal of the misalignment source of variability, about 3.8–4.9% improvements in the pattern matches were obtained and allowing for the conclusion that the ERA5 outperforms NCEP in capturing the observed austral summer precipitation patterns in the study region. Application of Procrustes target analysis to regional climate models shows that they can replicate a portion of the observed precipitation patterns with spatial mismatches relative to the patterns from observational data with an improvement in the matches from about 6.7–38.6%. The spatial mismatches are dependent on the pattern considered, the specific regional climate models and the data driving the regional climate model. Further, for an anthropogenic climate change scenario, Representative Concentration Pathway 8.5, the simulated future patterns were comparable with the observed patterns. However, relative to the simulated historical patterns, there are spatial shifts in the analyzed future precipitation patterns in regional climate models.