A flow-dependent estimate for the sampling error

Abstract

A pragmatic method is presented for obtaining a flow-dependent estimate of the sampling error which arises when comparing line measurements (whose horizontal extent is quasi one-dimensional (1-D)) with model grid box averages (whose horizontal extent is 2-D). The errors are computed from synthetic data which share important statistical properties with the observed field and which can be generated from the information obtained from the 1-D measurements. Flow dependency is obtained through a statistical measure (or "score") which is linked to the sampling error through a quasi-empirical relationship that is obtained from the synthetic data. The success of the method particularly depends on how well the employed score differentiates situations with different error magnitudes. A score is proposed which is based on local estimates of the structure function maximum (i.e., the maximum over neighborhoods of different spatial extent) and therefore exploits information from different space scales. Since the proposed method is heuristic (in the sense that the adequacy of the synthetic data cannot be inferred from first principles), a large part of this paper is devoted to demonstrating the robustness of this method in the context of data from scanning satellite instruments for which 1-D estimates can be compared directly with the corresponding 2-D averages. © 2010 by the American Geophysical Union.