Chi-square goodness-of-fit is used to test the hypothesis that the medium scale of turbulence in the atmospheric surface layer is normally distributed. Coefficients of skewness and excess are computed from the data. If the data are not normal, these coefficients are used in Edgeworth's asymptotic expansion of Gram-Charlier series to determine an alternate probability density function. The observed data are then compared with the modified probability densities and the new chi-square values computed.
Seventy percent of the data analyzed was either normal or approximately normal. The coefficient of skewness g1 has a good correlation with the chi-square values. Events with |g1| < 0.21 were normal to begin with and those with 0.21 < |g1| < 0.43 were approximately normal. Intermittency associated with the formation and breaking of internal gravity waves in surface-based inversions over water is thought to be the reason for the non-normality.