Synthesizing tropical analysis perturbations for use with the Naval Operational Global Atmospheric Prediction System (NOGAPS)

One of the main objectives of ensemble prediction is to adequately describe the forecast error variance associated with analysis uncertainty. This objective has proven difficult to achieve, particularly in the case of ensemble forecasts for tropical regions. In these regions the variance of a single-model ensemble is generally smaller than the observed forecast error variance. Part of the problem owes to existing methods of analysis perturbation. For instance, global perturbations derived from correlated random noise tend to rapidly decay in the tropics, while dynamically conditioned global perturbations derived using the singular vector method or the bred-mode cycling method tend to strongly favor the growth of extratropical, baroclinic features. Recent work at the Naval Research Laboratory (NRL) suggests that the ensemble transform (ET) cycling method also is unable to induce sufficient forecast variance in the tropics. The ET method generates analysis perturbations by rotating and scaling a set of ensemble-derived forecast errors under a global constraint defined by estimates of analysis error variance. Work shows that the ensemble forecasts are so exceedingly sub-variant in the tropics that despite the global constraint the resulting analysis perturbations are themselves substantially sub-variant in the tropics. These perturbations engender sub-variant forecasts that introduce the tropical variance deficit into the next ensemble-generation cycle. Since all current analysis perturbation schemes are inadequate for tropical purposes, further work on the analysis perturbation problem has the opportunity to improve the utility of tropical ensemble forecasts.

Presented here is a modification to the standard ET method that is intended to compensate for global ensembles' tropical variance deficit. The main element of the modification is the synthesis of a set of perturbations whose variance closely replicates the standard ET analysis perturbations' missing variance in the tropics. The modification proceeds as follows. First, a random sample of perturbation fields is derived from an archive comprised of analyses, observed forecast errors, or ensemble-derived forecast errors. The random sample fills the role of a mathematical basis for the vector space defined by the model grid. Second, the random fields are linearly transformed so that their variance is globally consistent with the standard ET perturbations' missing variance. Third, the transformed perturbations are input into a constrained optimization that serves to focus their variance in the tropics while maintaining its global consistency with the standard ET perturbations' missing variance. At the completion of this step the new perturbations have a prescribed level of variance in the tropics as well as realistic correlations and a certain level of dynamical balance. The correlations and balance inherent in the perturbations owes to their adaptation from perturbations that were present in either model integrations or analyses. The last step is to add the new tropical perturbations to the standard ET perturbations and perform one more transformation to maximize the consistency between the combined perturbations' variance and the analysis error variance. The combined perturbations' improved consistency with analysis error variance and their well-correlated and balanced nature in the tropics should result in improved growth rates and more representative tropical forecast error variance. In the best-case scenario the improved forecast error variance would be sensed by the standard ET algorithm during the next ensemble-generation cycle, resulting in better perturbations from the standard ET algorithm and diminished need for inclusion of the tropical perturbations. Over a number of cycles the need for the tropical perturbations may even be obviated.

The efficacy of the above modification is gauged by applying it to an ET scheme implemented for the Naval Operational Global Atmospheric Prediction System (NOGAPS). The implementation employs flow-dependent analysis error estimates provided via the NRL Atmospheric Variational Data Assimilation System (NAVDAS). A month's worth of distinct ensembles are generated using both the unmodified and modified ET schemes. Each ensemble is comprised of 32 members integrated for 120h at spectral resolution T119 and with 30 vertical levels. The ability of the modified ET scheme to produce analysis perturbations with variance that better matches the benchmark NAVDAS analysis error variance is assessed. The evolved perturbations from the modified ET scheme are assessed in terms of their growth rates, and in terms of whether their forecast variance is a better predictor of error in the control forecast. Probabilistic forecasts derived from the modified ET ensemble are evaluated using the Brier Score and Relative Operating Characteristic (ROC) to see how any improvement in the tropical ensemble variance is reflected in these forecasts. Finally, the sensitivity of the modified ET perturbations' character to the size and composition of the random sample used in constructing the tropical perturbations is examined. Recommendations are made for further refinement of the tropical perturbations and their use with the ET scheme.