Optimal averaging of incomplete climatological data

We present a multivariate statistical interpolation method for optimal aver aging of incomplete climatological data. This objective analysis is based o n a linear regression of the data under the constraints of unbiasedness and minimized analysis error variance. One of the important features of the pr esented interpolation is the efficient, exchange of common information betw een the analysed variables. This exchange is controlled by the covariances and leads to a remarkable reduction of the analysis error variance compared with the univariate optimal interpolation. The second moment statistics ar e estimated exclusively on the basis of the given data using empirical orth ogonal functions (EOFs). Another important feature of the analysis is the partition of the entire an alysis area into subregions. The estimation of the covariances and the calc ulation of the EOFs are carried out in each of these subregions separately. This results in a robust covariance estimation, and the regional dynamical characteristics are taken into account as well. The analysis is applied to the monthly horizontal wind data of the Comprehensive Ocean-Atmosphere Dat a Set (COADS). Uni-, bi-, and trivariate analyses of the vector wind and th e scalar wind velocity are performed for the Januaries 1951-1993 restricted to the Atlantic Ocean. The results show a remarkable decrease of the analy sis error when the number of simultaneously analysed variables is increased .