The statistical problem of climate inversion: determination of the relationship between local and large-scale climate

The estimation of the most probable local or mesoscale distribution of a climatic variable, when only the large-scale value is given, may be viewed as a sort of climate inversion problem. As an initial statistical study of this question, the monthly averaged surface temperature and monthly total precipitation for stations in Oregon are analyzed in order to relate their most probable mesoscale distributions to the large-scale monthly anomalies. The first empirical orthogonal mode of the covariance matrix of mesoscale transient departures explains 78.2 and 80.8% of the total variance of temperature and precipitation, respectively. The time structure of the first mode is predominantly seasonal and is in phase with the large-scale anomalies, and the correlation coefficient between this oscillation and the large-scale anomaly is 0.96 for temperature and 0.95 for precipitation. The most probable mesoscale distribution as specified by only the first empirical orthogonal function is predictable, with relative error of