Correction of Variance for Extraneous Contribution of Gradient - Winger, Carsten M. (The International Hydrographic Review, 2018)
The drawing of isolines of standard deviation for a function (temperature, for example) necessitates having a sufficient number of stationary points, sufficiently close together, for which the frequency distributions of the function are known. Over ocean areas, however{ this necessity is not met, and will not be met, presumably, for a very long time. T h e best that can be done at present is to deal with the observations for a finite area over a finite period of time, combining them as elements of a single frequency distribution for some point near the center of the area in question. This procedure introduces extraneous spatial deviations, giving the variance of our function too large a value. The magnitude of this error increases with the size of the area and with the numerical value of the gradient, and also varies to some extent with the latitude and the orientation of the isolines of the function. This report proposes a formula for the correction of this error.