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Signals in data are often detected by analyzing anomaly field that is calculated by subtracting the mean value over a time length from the data.  Here we demonstrate that the anomaly calculation removes signals which satisfy that the ratio between the time length of the mean T and signals' period L is an integer (i.e., T/L=n where n is an integer)  and retains other signals if the ratio is not an integer.  In climatic and other studies, the time length of the mean is usually chosen as T=12 months from January to December and the mean is called the monthly climatology.  Anomaly is calculated by subtracting the monthly climatology from data.  This anomaly calculation thus removes the climatic signals with the periods of 12, 6, 4, 3, 2.4, and 2 months which correspond to (12 months)/n with n=1, 2, 3, 4, 5, and 6, respectively, whereas it retains other signals such as those with the periods of 11, 10, 9, 8, 7, and 5 months.  This paper suggests that one should be cautious when an anomaly field is used in research.  The conventional notion is that the monthly anomaly calculation removes the annual cycle.  However, here we show that the anomaly calculation removes all signals as long as the time length of the mean is an integer multiple of signals' period

What Signals Are Removed and Retained by Using an Anomaly Field in Climatic Research?