Approximation of Atmospheric Temperature Data Using Rossby Harmonics and a Two-Strategy Adaptive Artificial Bee Colony Algorithm

Keywords: Rossby waves, bee colony method, satellite data, Aura (MLS)

This report presents a methodology for approximating atmospheric temperature data using Rossby harmonics based on an adaptive two-strategy artificial bee colony algorithm (TSaABC) with hard thresholding. The algorithm is designed to solve complex optimization problems related to nonlinear space-time models that describe the dynamics of large-scale wave processes. The proposed approach efficiently selects significant components from a large dictionary of possible harmonics, ensuring both high accuracy in data reconstruction and sparsity.

The Rossby waves considered in this study play a key role in atmospheric dynamics, as they are the primary mechanism for transferring energy and momentum between different layers of the atmosphere. These waves are especially important in the winter stratosphere, where they contribute to the development of sudden stratospheric warmings and participate in the formation of meridional circulation. For the analysis of these processes, satellite data from the EOS MLS instrument aboard the Aura spacecraft were used, providing high vertical and temporal resolution. Temperature data within the latitude range of 58°–68°N at an altitude of approximately 80 km were selected, corresponding to the region of maximum wave activity.

The research methodology involves formulating an inverse problem, where the objective functional consists of two parts: the misfit between the model and observational data (in terms of L2-norm), and a penalty for the number of harmonics used (in terms of L1-norm). This allows identifying a minimal set of significant harmonics that accurately describe the observed temperature structure. To solve this problem, a two-strategy adaptive TSaABC algorithm was employed, combining mechanisms of deep exploitation and broad exploration of the solution space. An important enhancement to the algorithm was the inclusion of hard thresholding, which enables the elimination of less significant harmonics during optimization and reduces the dimensionality of the problem.

Numerical experiments demonstrated that the proposed method achieves a relative error level of about 12%, which is acceptable given the presence of shortwave disturbances such as internal gravity waves. It was also found that the algorithm converges rapidly due to the combination of two search strategies and the adaptive selection of the most effective optimization directions. The resulting approximating functions allowed visualization of the spatial and temporal distribution of temperature anomalies caused by Rossby waves.

The presented methodology can be applied to improve forecasting of climate and weather phenomena, as well as for analyzing wave dynamics in the atmospheres of other planets. A promising direction for future research includes extending the model to three dimensions and integrating additional atmospheric parameters, such as wind and pressure, for a more comprehensive description of dynamic processes.