Multi-objective environmental model evaluation by means of multidimensional kernel density estimators: Efficient and multi-core implementations

Abstract

a b s t r a c tWe propose an extension to multiple dimensions of the univariate index of agreement between Probability Density Functions (PDFs) used in climate studies. We also provide a set of high-performance programs targeted both to single and multi-core processors. They compute multivariate PDFs by means of kernels, the optimal bandwidth using smoothed bootstrap and the index of agreement between multidimensional PDFs. Their use is illustrated with two case-studies. The first one assesses the ability of seven global climate models to reproduce the seasonal cycle of zonally averaged temperature. The second case study analyzes the ability of an oceanic reanalysis to reproduce global Sea Surface Temperature and Sea Surface Height. Results show that the proposed methodology is robust to variations in the optimal bandwidth used. The technique is able to process multivariate datasets corresponding to different physical dimensions. The methodology is very sensitive to the existence of a bias in the model with respect to observations.

Identifying the urban-rural fringe using wavelet transform and kernel density estimation: A case study in Beijing City, China

“…In quantitative spatial analysis, KDE has been widely used in density surface mapping and "hotspot" detection by converting spatial sample points to a raster map of density surface (Bornmann and Waltman, 2011;Lopez-Novoa et al, 2015). This method was originally applied in studies on crime mapping and public health, especially the source of infections (Brunsdon, 1995;Han et al, 2005).…”

MIDAS: A Benchmarking Multi-Criteria Method for the Identification of Defective Anemometers in Wind Farms

“…The climate models cannot be expected to reproduce the daily atmospheric states, but they can be expected to generate a similar probability density function [29,30]. Recently, some of the authors of this study proposed an extension of the previous evaluation strategy to multiple dimensions [28].…”

“…The multidimensional probability density function (MPDF) technique is a general-purpose method implemented by the authors [28] that makes it possible to compare two multidimensional probability density functions (PDFs) that were estimated by a kernel-based multivariate approach. This method provides a score between 0 (completely different PDFs) and 1 (perfect match) for multidimensional data distributions by computing the common volume under both PDFs.…”

“…The practical implementation of this MPDF technique as described in [28] was carried out in three steps:…”

“…The software was written in ANSI-C and is freely available as indicated in [28] (https://github. com/isg-ehu/unai.lopez/tree/master/density-parallel), where more specific mathematical details on every step can be found.…”