The impact of sampling errors on the perceived response of a climate model to a sea surface temperature anomaly

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Abstract
When neighbouring points in a field of climatic data are correlated with each other, local univariate tests of statistical significance are inadequate measures of large‐scale climatic change, since the data samples cannot be regarded as statistically independent. The problem of assessing the presence of significant climatic change in atmospheric models is further complicated when, as is typically the case for general circulation simulations, relatively few samples of model climate are available for statistical diagnosis. In the present study the effect of limited sample size on the perceived climatic sensitivity of the Held‐Suarez model to a sea surface temperature anomaly is empirically investigated by means of a bootstrap sampling procedure. The bootstrap method entails the random selection of different, but equal‐sized, subsets of the available realizations of anomalous climate of the model, and the calculation of a sample mean for each such selection. The variability of these mean climatic fields is a graphic indication of the size and location of the errors associated with the limited number of samples of the model's anomalous climate. It is found that the sampling errors in the fields of anomalous mean climate can be large enough to lead to a serious misinterpretation of the actual climatic change in the model, but the severity of this problem is a function of the meteorological variable that is chosen as a measure of climatic change. It is shown that the utility of a meteorological variable as an accurate indicator of climatic change is related to the degree of correlation of neighbouring points in its field or, equivalently, to the number of effectively independent samples of the variable that are available. These results are consistent with previous theoretical analyses of the deficiencies of local univariate significance tests when applied to climate sensitivity experiments.

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