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United States Department of Agriculture

Agricultural Research Service

Title: Climate Verification Using Running Mann Whitney Z Statistics)

item Mauget, Steven
item Cordero, Eugene
item Brown, Patrick

Submitted to: Journal of Climate
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 8/14/2011
Publication Date: 3/1/2012
Citation: Mauget, S.A., Cordero, E., Brown, P. 2012. Climate Verification Using Running Mann Whitney Z Statistics. Journal of Climate. 25(5): 1570-1586.

Interpretive Summary: Although predictions of future climate change have emphasized mid- or late- 21st century conditions, attention has recently turned to the prediction of upcoming decadal periods. This interest in predicting decadal climate is driven in part by the importance of decadal time scales in human affairs, e.g., the decadal duration of persistent drought and decadal cycles of hurricane activity and fisheries regimes. Generally, the extended duration of typical climate forecasts are inconsistent with the decadal or multi-decadal outlook of managers that make climate-sensitive decisions. However, before decision makers can confidently use decadal climate forecasts the numerical climate models that make those predictions must be tested somehow. Here, a statistical and graphical method used previously to identify decadal climate variation in historical data records was adapted to test three climate model’s abilities to reproduce observed U.S. temperature regimes during 1919-2008. The method samples annual temperature rankings over moving time windows, converts those samples to Mann-Whitney U statistics, and then normalizes the U statistics into Z statistics. The process is repeated using moving windows of varying duration to identify the most significant warm and cool regimes in a data record. By using this statistical-graphical approach to clearly identify where and when a model fails to produce observed IMD climate features, model developers might be better equipped to consider the general questions surrounding decadal climate predictability, identify systematic errors in model results, and trace the source of those errors. Correcting those problems may in turn lead to the ability to forecast decadal climate.

Technical Abstract: A robust method previously used to detect observed intra- to multi-decadal (IMD) climate regimes was adapted to test whether climate models could reproduce IMD variations in U.S. surface temperatures during 1919-2008. This procedure, called the running Mann Whitney Z (MWZ) method, samples data rankings over moving windows of 6-30 years duration, converts those samples to Mann-Whitney U statistics and then normalizes those U statistics into Z statistics. By detecting optimally significant IMD ranking regimes of arbitrary onset and semi-arbitrary duration, this process generates Z series that are a low-passed and normalized transformation of the data record. Principal component analysis of the Z series derived from observed annual temperatures at 92 U.S. grid locations shows two dominant modes: a PC1 mode with cool temperatures before the late 1960s and warm temperatures after the mid-1980s, and a PC2 mode indicating a multi-decadal temperature cycle over the southeastern U.S. Using a graphic analysis of a Z error metric that compares modeled and observed Z series, the three Climate of the 20th Century model simulations tested here are shown to reproduce the PC1 variability but not the PC2 temperature cycle. By providing a way to compare a broad range of grid-level IMD climate response patterns in observed and modeled data, the running MWZ method can play a useful diagnostic role in model development and decadal climate forecasting.

Last Modified: 8/24/2016
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