Vertical correlation functions for temperature and relative humidity errors

Abstract

This article gives the details and results of an investigation into the properties of the temperature and relative humidity errors from the Navy Operational Global Atmospheric Prediction System for a 4-month period from March to June 1998. The spatial covariance data for temperature errors and for relative humidity errors were fit using eight different approximation functions/weighting methods. From these, two were chosen as giving good estimates of the parameters and variances of the prediction and observation errors and were used in further investigations. The vertical correlation between temperature errors at different levels and relative humidity errors at different levels was approximated using a combination of functional fitting and transformation of the pressure levels. The cross covariance between temperature and relative humidity errors at various pressure levels were approximated in two ways: 1) by directly computing and approximating the cross-covariance data, and 2) by approximating variance of the difference of normalized data. The latter led to more consistent results. Figures illustrating the results are included.