On the advantage of stochastic methods in the modeling of ionospheric total electron content: Southeast Asia case study

This article describes an implementation of precise point positioning (PPP) and the least-squares collocation (LSC) method in the modeling of total electron content (TEC) in Southeast Asia, which is characterized by relatively homogeneous Global Navigation Satellite Systems (GNSS) data from International GNSS Service (IGS) stations and the occurrence of the highest TEC anomalies. A homogeneous coverage of the data in this region provides an opportunity for the testing of different spatial modeling methods applied to TEC data. The spherical harmonic expansion (SHE) and spherical splines (SS) have been the most popular mathematical tools for the interpolation of TEC in the ionosphere over the last decades. The developed stochastic model (PPPLSC) is compared with the well-known stochastic global UQRG model, which is interpolated by the ordinary kriging (OK) and CODG global TEC model based on spherical harmonics (SH), and also the IGSG model, which is a combination of several models developed by the IGS Ionosphere Associate Analysis Centers. These four models derived from different approaches are assessed together using self-consistency analysis based on a geometry-free combination of carrier-phase observations, and also using external validation employing dual-frequency altimeter TEC from three low-Earth-orbit satellites. The study implements the LSC modeling technique, which is quite new for TEC and is a valuable step towards increasing the accuracy and resolution of ionosphere models. LSC, similarly to OK, is a stochastic parametric technique, applying the covariance based on data properties. Therefore LSC restores the fullest possible signal in the interpolated model in terms of spatial resolution. Leave-one-out (LOO) validation of the covariance parameters assures optimal interpolation results in the least-squares sense. The covariance matrices of LSC parametrized by LOO validation enable estimation with reliable internal precision for the model. The self-consistency analysis of TEC models with the use of carrier-phase observations proves a better consistency of stochastic models in relation to TEC models based on SHE. The set of statistical values of external comparisons with three altimetry-derived trajectories of TEC observations additionally confirms the advantage of stochastic PPPLSC and UQRG models. The validation results all together indicate a better quality of stochastic models in relation to those based on the summation of spherical functions. The factor that is suspected to decrease the accuracy of the latter models is the loss of the higher frequency signal due to the spectral limitation coming from the low order of SHE applied in IGSG and CODG.