Long-term climatic variations and trends often have seasonal and diurnal cycles, which have not been studied systematically due to the lack of an adequate technique and computational resources. Here we discuss a recently developed statistical technique for describing climatic processes with seasonal and diurnal cycles in statistical moments and trends. It has proven to be extremely efficient for analyzing climatic records with arbitrary observation times. By using adequate approximations of non-stationary cyclic components in expected values of climatic variables, we are able to compute time series of residuals which may be considered as stationary random processes for which lag and cross-correlations can be studied without any danger of false results. This technique also provides new opportunities to analyze long term changes in climate variability.

I will discuss the latest improvements in inter-satellite calibration along with application of this new statistical technique to determine the diurnal and seasonal cycles and climatic trends of the 1978-2004 tropospheric temperature using Microwave Sounding Unit measurements. The latitudinal distribution of temperature trends from the surface and troposphere with each other and with model simulations during the past 26 years will be compared. We found that warming trends in observations at the surface and troposphere are consistent with climate model simulations. At mid- and high latitudes in the Northern Hemisphere, the zonally averaged temperature at the surface increased faster than in the troposphere while at low latitudes of both hemispheres the temperature increased more slowly at the surface than in the troposphere. The resulting global averaged tropospheric trend is +0.20 K/10 yr, with a standard error of 0.05 K/10 yr, which compares very well with the trend obtained from surface reports.

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