Empirical eigenmode extraction of thermospheric mass density: MATLAB implementation

This MATLAB function performs principal component analysis (PCA) on a collection of thermospheric density maps, separately for downward (MapD) and upward (MapU) data sets, then projects the density maps onto the extracted eigenmodes to obtain amplitude time series. It further fits regression models to these amplitude time series using geomagnetic and solar indices along with seasonal and local time harmonics. Key steps include: Loading and concatenating density map data from multiple files. Computing the covariance matrix and performing eigen-decomposition to extract spatial eigenmodes (principal components). Projecting individual density maps onto the principal components to obtain amplitude coefficients. Building a regression design matrix using geomagnetic indices (e.g., Fc, Fp, FA, ApA), day-of-year, and local time harmonics. Estimating regression coefficients for the first three principal component amplitude time series, modeling their variation with solar and geomagnetic activity and periodic seasonal/local time effects. Inputs: data_path: A structure array containing the filenames of the density map data to be processed. Outputs: PCs: Structure containing spatial maps of the first seven principal components. Amplitudes: Structure containing the amplitude time series of downward and upward density maps projected onto PCs. Coefficients: Structure containing regression coefficients fitted for the first three principal component amplitudes.