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Effects of observation errors in linear regression and bin‐average analyses

Effects of observation errors in linear regression and bin‐averaged (BA) validation techniques are investigated using the example of marine wind speeds. It is shown that a conventional linear regression systematically underestimates the slope of the regression line, and systematically overestimates the random model error. A BA analysis systematically understimates extreme wind speeds, incorporates spurious nonlinearity, and overestimates random model errors. Correction techniques are suggested for studies in which the observation error can be estimated. Using synthetic data the potential of the correction techniques in illustrated, and it is shown that the above errors are generally not negligible for wind speed validation studies. Practical examplies consider the random errors of anemometers and wind speed estimates from satellites. These examples highlight the importance of the error corrections, and illustrate the difficulty of estimating observation errors. Finally, it is argued that the well‐known symmetric slope regression should not be used for the validation of forecast systems. Although the present study deals with marine wind speeds, its results are expected to be valid for a wide range of validation studies.