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WRIT seasonal correlation mapping page: interpretation and caveats

A correlation is a measure of the linear fit of two time-series. In the calculation on this page, the time mean is removed and the correlation is calculated using a sample population. There are a number of caveats when interpreting maps of correlations with index time series.

• Correlation is not causation!!!! Time-series may be related by chance, because they are related to a third factor, or the relationship may not be linear. Users are encouraged to further explore relationships using scatter plots and examining values in other ways.
• Statistical Significance at a grid: Users can consult tables on the statistical significance of correlation at a point. Note that the degrees of freedom may be less than the number of years if there either the variable of the index time-series has a non-zero autocorrelation (like SST).
• Statistical Significance for map: When calculating the significance at a number N of grid points, there are N times the chances of getting a significant value. So for a large area, there will likely be higher correlations merely by chance. Spatial points are often correlated with each other which complicates things. Researchers try to determine 'field significance' using techniques like Monte Carlo analysis.
• How the index was generated may matter a lot, especially for types of patterns that move seasonally.
• Datasets matter: spatial resolutions, temporal selection (4x daily vs 2x daily values will give different monthly values). Datasets may assimilate different observations or assimilate the same observations differently. They handle missing values differently.
• Time Range matters. There are both real and spurious trends in atmospheric data. There may also be trends in the data assimilated (for example, adding satellite data or having SST measured in a new way). There are different amounts of missing data over time and there may be seasonal differences as well.
• Relationships may not be linear and so correlations may underestimate relationships. In fact, if the 2 variables are in quadrature, the correlation may be zero yet one variable can be exactly calculated from the other. Relationships may be linear for certain ranges only. Examine timeseries in different areas to see how they co-vary.
• Seasonal vs monthly correlations may differ depending on how anomalies are calculated.
• Missing values matter, especially if not distributed evenly in time.