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Correction to “Sensitivity of distributions of climate system properties to the surface temperature data set”
Author(s) -
Libardoni Alex G.,
Forest Chris E.
Publication year - 2013
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1002/grl.50480
Subject(s) - statistics , probability density function , data set , goodness of fit , observational study , mathematics , climatology , series (stratigraphy) , meteorology , environmental science , geography , geology , paleontology
[1] In the paper “Sensitivity of distributions of climate system properties to the surface temperature data set” by A. G. Libardoni and C. E. Forest (Geophys. Res. Lett., 38, L22705, doi:10.1029/2011GL049431), two errors were made. First, there was an offset of 1 month when comparing model data to observational data. Second, the likelihood function that was used to relate model goodness-of-fit statistics to a probability distribution, while derived from basic understanding of probability distributions, is not acceptable as a likelihood function to statisticians. [2] In this correction, we fix the mismatch that existed between model and observational annual averages. When calculating annual averages from model output, seasonal means were averaged, resulting in a given year being the average from December through November. When calculating annual averages from observational data, monthly means were averaged, resulting in a given year being the average from January through December. To correct for this 1 month mismatch, all annual mean temperatures derived from observations are calculated as December to November means, subject to the threshold criterion described in Libardoni and Forest [2011]. Because decadal mean temperatures are used for the surface temperature diagnostic, the 1 month shift in the averaging window has minimal impact on the resulting observational time series. Across all five decades and four zonal bands, the temperature differences due to the 1 month shift are at most 0.05C. The revised time series are not shown. [3] We also present revised results that implement a likelihood function proposed in Lewis [2013] that is more statistically sound as applied to the Bayesian methodology used in Libardoni and Forest [2011]. It will be shown below that the updated likelihood function alters the posterior distributions. The changes to the likelihood function involve changing the shape of the distributions used in statistical tests, changing the test statistic, and taking into account the necessary volumetric correction when making a change of variable. In total, the following changes were made to account for the likelihood estimate from Lewis [2013]: