A New Method for the Comparison of Trend Data with an Application to Water Vapor.

Global total column water vapor trends have been derived from both the Global Ozone Monitoring Experiment (GOME) and the Scanning Imaging Absorption Spectrometer for Atmospheric Chartography (SCIAMACHY) satellite data and from globally distributed radiosonde measurements, archived and quality controlled by the Deutscher Wetterdienst (DWD). The control of atmospheric water vapor amount by the hydrological cycle plays an important role in determining surface temperature and its response to the increase in man-made greenhouse effect. As a result of its strong infrared absorption, water vapor is the most important naturally occurring greenhouse gas. Without water vapor, the earth surface temperature would be about 20 K lower, making the evolution of life, as we know it, impossible. The monitoring of water vapor and its evolution in time is therefore of utmost importance for our understanding of global climate change. Comparisons of trends derived from independent water vapor measurements from satellite and radiosondes facilitate the assessment of the significance of the observed changes in water vapor. In this manuscript, the authors have compared observed water vapor change and trends, derived from independent instruments, and assessed the statistical significance of their differences. This study deals with an example of the Behrens--Fisher problem, namely, the comparison of samples with different means and different standard deviations, applied to trends from time series. Initially the Behrens--Fisher problem for the derivation of the consolidated change and trends is solved using standard ( frequentist) hypothesis testing by performing the Welch test. Second, a Bayesian model selection is applied to solve the Behrens--Fisher problem by integrating the posterior probabilities numerically by using the algorithm Differential Evolution Markov Chain (DEMC). Additionally, an analytical approximative solution of the Bayesian posterior probabilities is derived by means of a quadratic Taylor series expansion applied in a computationally efficient manner to large datasets. The two statistical methods used in the study yield similar results for the comparison of the water vapor changes and trends from the different measurements, yielding a consolidated and consistent behavior. [ABSTRACT FROM AUTHOR]