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Spatial and temporal support of meteorological observations and predictions

TitleSpatial and temporal support of meteorological observations and predictions
Publication TypeConference Paper
Year of Publication2014
AuthorsPebesma E
Conference NameDailyMeteo.org/2014
Date Published06/2014
PublisherFaculty of Civil Engineering, University of Belgrade
Conference LocationBelgrade
Abstract

Support refers to the physical size of the area, volume, and/or temporal duration of a measured or predicted data value. Support of measurements is often related to the physical constraints: we cannot directly observe the temperature of a square kilometre, not even of an area of 100 m2; rainfall measurements also usually refer to devices with a catchment area of less than 1 m2. By choosing measurement sites carefully, we hope, by the idea of representativity, that measured values carry more information about their surroundings than when they were not chosen with the same care. Representativity could reflect the notion that we would like to be able to measure average values over larger areas, as local extreme conditions are typically avoided. Nevertheless, measured value and local or regional averages will differ. Geostatistical theory allows for predicting linearly aggregated (mean) values by regularizing (averaging) semivariances, and by predicting nonlinearly aggregated values by simulation. The type of aggregation (function), the aggregation predicate (target support), and the variability of the predictant all play a role here. Aggregation is the process of deriving a single number from a collection of numbers. The aggregation function may be simple such as in the case of mean or max, it may also be complex, e.g. computing catchment discharge from spatially distributed precipitation values. The aggregation predicate is the spatial area and/or temporal period over which aggregation takes place. Aggregation may be useful to (i) match data that is collected at a coarser support (ii) increase accuracy of predictions, and (iii) smooth out local, or short-term variability. When we want to aggregate over a continuous area but do not have exhaustive (continuous) measurement data available for this area, a model for the observation data is required to fill the area with missing data in with predictions. Typical models are stationary covariance models, as used in geostatistics. When, in these models, we assume the mean function to depend on external variables with a different support (e.g. derived from satellite imagery, or elevation data), we introduce a bias that depends on the difference of the external variable at the support we have it and that, at the support that would match that of the primary observation data. We will discuss where this bias comes from, and how it may be dealt with.

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