# Statistical & Diagnostic Methods Overview

The following is by Dennis Shea (NCAR)

By definition, climate is the statistics of weather over an arbitrarily defined time span. The methods used to derive the statistical estimates can be simple or very complex. The most common statistic is the average of some variable (eg., temperature). However, soley focusing on the average can be misleading. For example, the average temperature may be consistent with previous time spans but the variance may have changed in some 'significant' way. The gradual change of some variable over time is defined as a trend. Extreme value analysis (EVA) is used to assess the likelihood of events at the tails of a variable's distribution. Classical statistical methods use the assumption of stationarity which implies that a variable's distribution (e.g., mean, variance, no trend, etc.) does not vary with time. Obviously, the stationarity assumption is violated under a climate changing (eg., warming) scenario. However, there are preprocessing approaches such as detrending which allow the resulting data to be treated as 'approximately' stationary.

In addition to conventional statistics, there are 'diagnostics' which are used to assess the nature of climate variations on differing time scales. Some commonly used diagnostic methods are discussed in the menu links below.

The German Climate Service Center provides a downloadable brochure entitled Statistical methods for the analysis of simulated and observed climate data which provides a concise overview of statistical methods commonly used in climate research.

The following is by David Schneider (NCAR):

Professor Dennis Hartmann of the University of Washington teaches a classic course in applied data analysis. The class notes provide concise overviews of these topics, illustrated with many examples.