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The impact of spatial correlation and incommensurability on model evaluation
Authors:Jenise L Swall  Kristen M Foley
Institution:1. National Astronomical Observatories /Yunnan Observatory, Academica Sinica, Kunming 650011, PR China;2. National Astronomical Observatories, Chinese Academy of Science, Beijing 100012, PR China;3. Seismological Bureau of Yunnan Province, Kunming 650224, PR China;1. UNIS, The University Centre in Svalbard, Postboks 156, 9171 Longyearbyen, Norway;2. Department of Geosciences, The University of Oslo, Sem Sælands Vei 1, 0371 Oslo, Norway;1. Université Lille, Nord de France, CRIL, CNRS UMR 8188, Artois, F-62307 Lens, France;2. Université Paris Descartes, LIPADE, France;1. Department of Oral and Maxillofacial Surgery, Meenakshi Ammal Dental College and Hospital, Chennai, India;2. Craniomaxillofacial Surgery, Amrita Institute of Medical Sciences, Kochi, India;3. Department of Oral and Maxillofacial Surgery, Saveetha Dental College and Hospital, Chennai, India;1. Department of Hydrology and Water Resources, The University of Arizona, Tucson, AZ, USA;2. Departamento del Agua, Centro Universitario Región Litoral Norte, Universidad de la República Uruguay, Salto, Uruguay;3. GHS UPC-CSIC, Institute of Environmental Assessment and Water Research (IDAEA), CSIC, Barcelona, Spain;1. Department of Mathematics, Vidyasagar University, Midnapore, Paschim-Medinipur, West Bengal 721102, India;2. Department of Mathematics, Mahishadal Raj College, Mahishadal, Purba-Medinipur, West Bengal 721628, India
Abstract:Standard evaluations of air quality models rely heavily on a direct comparison of monitoring data matched with the model output for the grid cell containing the monitor's location. While such techniques may be adequate for some applications, conclusions are limited by such factors as the sparseness of the available observations (limiting the number of grid cells at which the model can be evaluated) and the incommensurability between volume-averages and pointwise observations. We examine several sets of simulations to illustrate the effect of incommensurability in a variety of cases distinguished by the type and extent of spatial correlation present. Block kriging, a statistical method which can be used to address the issue, is then demonstrated using the simulations. Lastly, we apply this method to actual data and discuss the practical importance of understanding the impact of spatial correlation structure and incommensurability.
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