Accounting for random errors in linear regression: A practical guide

We read with interest Tolman's (1998, hereafter T98) analysis of the effect of observation errors on validation of marine winds. His demonstration of the importance of the correct treatment of the errors in comparative analys is of wind-speed land other types of) data is welcome, as examples of inacc urate comparisons are common, particularly for satellite data validation wh ich is often published in non-refereed reports. Kent et ad. (1998) show tha t apparent trends of the order reported can be directly attributed to error s in both datasets and that the trend appears smaller and in the opposite s ense if the satellite wind speed rather than the ship wind speed is used as the independent variable for plotting. T98 states that 'in special cases, where the ratio of... errors can be esti mated, more advanced regression techniques can be used'. Our aim in this no te is to advocate a simple, established method of data analysis which can l ead to reliable comparisons of pairs of nearly co-located and simultaneous observations from two sources, both containing random errors. This method e nables the use of these advanced regression techniques since the ratio of r andom errors in the datasets to be compared is estimated. The error estimat es can then be verified by using the effects of errors on bin-averaged anal yses highlighted by T98. Following T98 and Kent et al. (1998), we shall dis cuss satellite and in situ wind-speed data comparisons, but again expect th e results to be more widely applicable.