Sun, D-Z., and A. H. Oort, 1995: Humidity-temperature relationships in the tropical troposphere. Journal of Climate, 8(8), 1974-1987.

Abstract: Based on the observed interannual variations of water vapor and temperature over the past 26 years the authors have examined the relationship between the variations of water vapor and temperature in the tropical troposphere. The authors find that in both the lower and upper troposphere, tropical mean specific humidity increases with temperature. The rate of fractional increase of specific humidity with temperature at 500 mb is as large as that in the surface boundary layer. However, the rate of fractional increase of specific humidity with temperature is significantly smaller than that given by a model with a fixed relative humidity, particularly in the region immediately above the tropical convective boundary layer. The variations of tropical mean relative humidity show consistently a negative correlation with the temperature variations.
The authors have further compared the spatial structure of the specific humidity variations with that of the temperature variations. Though the vertical structure of tropical mean specific humidity has more variability than that of the tropical mean temperature, the leading EOF for the normalized specific humidity variations is almost exactly the same as the leading EOF for the normalized temperature variations. The characteristic horizontal structure of the specific humidity variations at levels in the free troposphere, however, is very different from that of the temperature variations. The leading EOF for the normalized specific humidity variations at levels in the free troposphere is characterized by regions with alternating positive and negative signs, while the leading EOF for the corresponding temperature variations has a single sign throughout the Tropics. When the variations are averaged zonally, the leading EOF for the normalized specific humidity variations still differs significantly from that of the normalized temperature variations, but the leading EOF has the same sign from the deep Tropics to the subtropics.