Optimal Averaging of Meteorological FieldsNational Meteorological Center, 1993 "Although every measurement, including meteorological ones, results in a value averaged to some extent both in space and in time, a majority of measurements, or observations, particularly traditional observations at meteorological stations, are usually referred to, and considered as, giving instantaneous point values. At the same time, it is practically always assumed, explicitly or implicitly, that every result of such measurement is applicable, or representative, not only for the point and time of the measurement, but also for some spatial, particularly horizontal, domain surrounding the observation point, as well as for some interval of time"--Introduction, paragraph 1 |
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analyses applied approximation area-averaged values Area-averaging accuracy area-mean value arithmetic averaging assumed assumption averaged values averaging area averaging method averaging of increments background field CDAS and Reanalysis climate change computations correlation function correlation radius covariance cross-correlation function curves on Fig Data Assimilation decreases density deviations distance equation 16 Error correlation scale estimate forecast first guess global warming grid increase influence integral investigations isotropic larger linear combination matrix meteorological fields meteorological parameter normalized numerical numerical weather prediction objective analysis observed point value Office Note optimal averaging weights optimal interpolation parameter in question particularly problem procedure random observation error relative RMS averaging Renormalized RMS averaging errors RMS error 1000 RMS observation error RO opt Section seen from Fig small areas spatial averaging statistical structure sum and RMS temporal averaging toy example underlying statistics value averaged variability Weight sum WSUM