Random Errors

Individual observation
Wind Sea Swell Significant Wave Height Wind Sea Period Swell Period Dominant Period

Monthly mean errors
Wind Sea Swell Significant Wave Height Wind Sea
Swell Period Dominant Period

    In order to estimate random observational errors of wave variables, we used semi-variagram approach. This    technique was earlier used by Kent et al. [1999] for the estimation of random observational errors in basic    meteorological variables and by Lindau [1995] for the development of equivalent Beufort scale. It was adopted by    Gulev and Hasse [1999] for the wave observations in the North Atlantic. This method is based on the consideration    of differences between simultaneous observations for the certain classes of ship-to-ship distances. It is assumed, that when the distance is equal to zero, natural variability does not contribute to the total variance, and the latter should represent only the error variance sig02/2 , which has to be divided by two to get the squared measurement error em2 = sig02/2 (Lindau 1995). To arrive to the sig02/2 estimate the polynomial extrapolation has to be used, although Kent et al. [1999] used finite linear functions for the approximation. We estimated ship-to ship differences  in different wave parameters for 20 by 20 degree boxes for the World Ocean for different months of the year. Spatial resolution of 20 degrees allows to get large number of pairs for further statistical processing. However, for some poorly sampled regions in the South Ocean, even 20-degree boxes do not provide the possibility to get enough number of pairs for all classes. Analysis was performed for 50-km classes of ship-to-ship distances in the range of 325 km. For the approximation of the dependence of the squared error on the ship-to-ship distance and its extrapolation we used polynomial functions.

    Estimation of the random observational errors in individual visual observations allows to derive random observational uncertainties of monthly means. According to Taylor [1982] for the case of normally distributed random error he overall random uncertainty of mean taken from the collection of measurements will be reduced by n1/2, where n is the number of observations. Since, the individual random observational errors were estimated for 20°*20° boxes, and we are interested in estimation of random uncertainties for 2°*2° cells, we assumed that the estimate derived for 20°*20° box is valid for all 2° cells within 20°*20° box. Then we scaled the estimates of random errors with the square root of the average number of samples for each 2°*2° box per individual month. Thus, our estimates of random errors are given for individual monthly means.

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