Nonlinear Bias Correction for Satellite Data Assimilation Using Taylor Series Polynomials

Abstract

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