Livina, V. N.; Edwards, N. R.; Goswami, S. and Lenton, T. M.
A wavelet-coefficient score for comparison of two-dimensional climatic-data fields.
Quarterly Journal of the Royal Meteorological Society, 134(633) pp. 941–955.
A single-valued wavelet-coefficient score is proposed for assessing the similarity of two-dimensional climate-data fields (matrices). It is based on the comparison of wavelet-decomposition coefficients by means of a mean-squared-error skill score. Two applications of the score are illustrated: comparison of real and model maps; and comparison of two model maps. The issue of missing data is addressed, and the evaluation is performed both when data are available over continents or oceans only, and when they are available globally, over the whole domain.
The score is tested against the conventional two-dimensional correlation coefficient, which is widely used in evaluating forecast performance. We show that the score eliminates random correlations, which the correlation coefficient incorrectly detects as similarity of fields that are actually dissimilar. The technique is first applied to the case of non-square matrices (spatial fields) of the same dimensions (spatial grids), and then to the most general case of matrices of different dimensions, by applying some necessary interpolations. The technique is tested on data from several runs of different GENIE models. It is then applied to the comparison of climate data (global fields of temperature and specific humidity) from the NCEP and ECMWF reanalyses and from the HadCM3 and GENIE models. To study the time evolution of a given 2D field, we analyse a plot of the score values for consecutive time slices, thus visualizing the temporal dynamics. The technique is particularly useful for automated comparison of large sets of 2D data, where direct visualization is best avoided. The score may be generalized for comparison of data of higher dimensions, in particular 3D ocean fields.
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