Nonlinear Bias Correction for Satellite Data Assimilation Using Taylor Series Polynomials

Output from a high-resolution ensemble data assimilation system is used to assess the ability of an innovative nonlinear bias correction (NBC) method that uses a Taylor series polynomial expansion of the observation-minus-background errors to remove both linear and nonlinear conditional biases from all-sky satellite infrared brightness temperatures. Univariate and multivariate NBC experiments were performed in which the satellite zenith angle and variables sensitive to clouds and water vapor were used as the bias correction predictors. The results showed that even though the bias of the entire error distribution is equal to zero regardless of the order of the Taylor series expansion, that there are often large conditional biases that vary as a nonlinear function of the bias correction predictor. The linear 1st order Taylor series term had the largest impact on the entire distribution as measured by reductions in the variance; however, large conditional biases often remained across the distribution when plotted as a function of the predictor. These conditional biases were typically reduced to near zero when the nonlinear 2nd and 3rd order terms were used. The univariate results showed that variables sensitive to the cloud top height are effective NBC predictors especially when higher order Taylor series terms are used. Comparison of statistics for clear-sky and cloudy-sky matched observations revealed that nonlinear bias corrections are more important for cloudy-sky observations as signified by the much larger impact of the 2nd and 3rd order terms on the conditional biases. Together, these results indicate that the NBC method is an effective method to remove the bias from all-sky satellite infrared brightness temperatures.