Observation-Based Initialization for Inverse Modeling of Atmospheric Temperature with Rossby-Constrained Transport

We consider a finite-dimensional inverse problem for atmospheric temperature transport from sparse satellite observations. A spectral stream function with Rossby dispersion defines the horizontal velocity, and a convection--diffusion equation maps its parameters to temperature measurements. The main methodological component is a regularized construction of the initial temperature and compatible latitudinal boundary values from the preceding day's observations. A bounded latitude coordinate, a low-order background, and two longitudinal harmonics provide a smooth periodic initial field without using the assimilation day's temperatures. Continuous piecewise-linear finite elements, implicit Euler stepping, and streamline upwind/Petrov--Galerkin stabilization solve the forward problem. An adaptive artificial bee colony algorithm identifies 28 flow parameters under a shared perturbation-speed constraint. For 105 nighttime Aura Microwave Limb Sounder measurements on 6 March 2011, the fine-mesh root-mean-square discrepancy is 5.129 K and the Pearson correlation is 0.660. The corresponding linear-initialization experiment gives 6.127 K and 0.373, respectively. The root-mean-square discrepancy therefore decreases by 16.3\%. A static evaluation of the new initial field gives a correlation of 0.549, providing a reference for assessing the additional improvement obtained with optimized transport. The results support observation-based initialization for temperature reconstruction within the considered model and motivate further evaluation of predictive performance and flow identifiability.