Implementation of Spherical Coordinates in 3DVAR+DIV Model: An Enhancement of Geophysical Data Assimilation.

Accurately estimating three-dimensional wind fields in the mesosphere and lower thermosphere (MLT) is crucial for understanding the dynamics and variability of the middle atmosphere, which exhibits complex behavior driven by a range of atmospheric waves covering spatial scales from kilometers to almost the diameter of the planet and temporal scales reaching from minutes to several days. Vertical winds are of particular interest and determine adiabatic heating/cooling as well as the vertical transport. They are challenging to retrieve due to their relatively weak magnitude compared to the horizontal wind components and instrument limitations. Multistatic meteor radar networks enable sophisticated tomographic wind retrievals, such as the Spherical Volume Velocity Processing (SVVP), or more advanced Bayesian methods like the 3DVAR+DIV algorithm. The current 3DVAR+DIV model is implemented in geographic and Cartesian grid coordinates based on pre-defined grid cells defined by a reference coordinate, which adversely affects the estimation of vertical winds due to the often low statistics and, thus, residual projection errors. The vertical winds are typically an order of magnitude weaker than horizontal winds and highly sensitive to even tiny projection errors.
In this study, we present the 3DVAR+DIV algorithm in spherical coordinates to account for the Earth’s curvature and the latitude-dependent change of the Earth’s radius. This implementation introduces several new unknowns per grid cell and will undergo multiple parameter tests using the Nordic Meteor Radar Cluster (NORDIC). This approach aims to improve the accuracy of wind retrievals, particularly for the vertical wind components. The new algorithm in spherical coordinates will mitigate the residual projection errors caused by the sparsity of the measurements.