Approximation of Scattered Data for Meteorological Applications

Abstract

In meteorology the process of approximating a (usually) multidimensional function (or field) from estimates (with error) of its value at some points is called objective analysis. The problem occurs in a number of contexts, but perhaps the most common is the following. At a given time, some measurements of meteorological variables are taken at points which are scattered in space. Usually there is also some variation in time, but in this paper I will ignore that, as well as the fact that when measurements are taken by weather balloon the latitude and longitude vary somewhat with the height because the balloon drifts. Previously computed values from a Numerical Weather Prediction (NWP) model are also available, usually on a grid. The problem is to use the data to determine as accurately as possible the values of the meteorological variables at the grid points. Rephrased, the problem is that of determining from both observations and prediction the state of the atmosphere at the given time. The values derived from the objective analysis, called the analyzed values, are then used as initial values for the next NWP prediction cycle, but in an application of lesser importance may be used to construct weather maps such as appear in the daily newspaper.