Non-Gaussian and Lognormal Characteristics of Temperature and Water Vapor Mixing Ratio

Wednesday, 17 December 2014
Anton Kliewer1, Steven J Fletcher2, John Michael Forsythe1 and Andrew S Jones2, (1)Cooperative Institute for Research in the Atmosphere, Fort Collins, CO, United States, (2)Colorado State University, Cooperative Institute for Research in the Atmosphere, Fort Collins, CO, United States
Many operational data assimilation and retrieval systems assume that the errors and variables come from a Gaussian distribution. This study shows that positive definite variables, specifically water vapor mixing ratio and temperature, can follow a non-Gaussian distribution and moreover a lognormal distribution. The analyzed 1-degree resolution data comes from the National Oceanic and Atmospheric Administration (NOAA) Global Forecast System (GFS) hour zero forecast between January 2, 2005 and December 31, 2005. The data is analyzed spatially and temporally in a seasonal and yearly manner. Results show seasonal shifts in distributions in the Gulf of Mexico and changes when considered over the entire year in the Northern Hemisphere tropical Atlantic. The results are achieved by employing statistical testing procedures which include the Jarque-Bera test, the Shapiro-Wilk test, the Chi-squared goodness-of-fit test, and a composite test which incorporates the results of the former tests. These results indicate the necessity of a Data Assimilation (DA) system to be able to properly use the lognormally-distributed variables in an appropriate Bayesian analysis that does not assume the variables are Gaussian.