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Application of a Nonlinear Transformation Function to the Variational Analysis of Visibility and Ceiling Height
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    In order to meet the growing requirements from general aviation services and helicopter emergency rescue, the Real-Time Mesoscale Analysis (RTMA) system provides analyses of surface visibility and cloud ceiling height since 2013 and 2016 respectively. Its analysis component uses NCEP’s Grid-point Statistical Interpolation (GSI) configured to run in the two-dimensional surface mode. The fundamental assumption justifying the existence of an optimal analysis solution is that the innovation follows a Gaussian distribution. However, visibility and ceiling height fields are characterized by high degrees of discontinuity in both spatial and temporal dimensions and their conditional error statistics vary with states. Directly using these fields in a variational analysis system often undermines the relatively accurate observations in circumstances dominated by severe weather systems, where the first guess is likely to depart far from the observations. Many efforts have been made to transform non-Gaussian variables to have a Gaussian distribution, or close to it. Among the methods, a logarithmic transformation is often used. The logarithmic transformation in visibility and ceiling height improves the convergence in minimizing the cost function and uses more observation data, particularly in the areas occupied by stormy weather systems. However, this method often generates spuriously large analysis increments over the areas of clear weather. In this study, a nonlinear transformation function (NLTF) is applied to visibility and ceiling height analysis in the RTMA. In this method, a function is derived to map the visibility and ceiling height into a space tending to a more uniform variance. Modulated by a varying parameter in the range of [0-1], the function family includes linear and logarithmic functions at the respective ends of the parameter range. A subjective approach, based on evaluating histograms of the variables, is used to determine the optimal value of the parameter. The statistical errors were estimated based on the statistics of innovation and then adjusted based on the statistics from single observation test and months-long analysis run. An experimental RTMA with the NLTF was conducted for eight months and compared to the control run that uses the previous analysis algorithm. The assessment and evaluation are carried out using a complete set of measures appropriate to categorized visibility and ceiling height according to FAA flight category definitions. The results showed that NLTF improves the visibility and ceiling height analysis consistently. Therefore, NLTF was implemented into the operational RTMA system on 5th December 2018.
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