Estimation of Errors in Seasonal Cycles

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Abstract
A formula is first given for the error in a 2-harmonic seasonal curve of best fit through a set of N oceanographic data points, assuming the departures from the true mean are independent random numbers. Departures of actual oceanographic measurements from the mean seasonal cycle are in fact correlated with one another, owing to long-period nonseasonal variability: hence the error estimate from the formula will generally be too small. If the data set can be split into two sets that are statistically independent, a method is given for estimating (in an averaged sense) the factor by which the formula should be multiplied, to account for the effect of correlations on the error estimate. Results from four ways of splitting the data into two sets for steric height data off Western Australia suggest that the results are reasonably independent of the method of splitting. Abstract A formula is first given for the error in a 2-harmonic seasonal curve of best fit through a set of N oceanographic data points, assuming the departures from the true mean are independent random numbers. Departures of actual oceanographic measurements from the mean seasonal cycle are in fact correlated with one another, owing to long-period nonseasonal variability: hence the error estimate from the formula will generally be too small. If the data set can be split into two sets that are statistically independent, a method is given for estimating (in an averaged sense) the factor by which the formula should be multiplied, to account for the effect of correlations on the error estimate. Results from four ways of splitting the data into two sets for steric height data off Western Australia suggest that the results are reasonably independent of the method of splitting.

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