Optimal Geostatistical Methods for Interpolation of the Ionosphere: A Case Study on the St Patrick's Day Storm of 2015.

Geostatistical Analyst is a set of advanced tools for analysing spatial data and generating surface models using statistical and deterministic methods available in ESRI ArcMap software. It enables interpolation models to be created on the basis of data measured at chosen points. The software also provides tools that enable analyses of the data variability, setting data limits and checking global trends, as well as creating forecast maps, estimating standard error and probability, making various surface visualisations, and analysing spatial autocorrelation and correlation between multiple data sets. The data can be interpolated using deterministic methods providing surface continuity, and also by stochastic techniques like kriging, based on a statistical model considering data autocorrelation and providing expected interpolation errors. These properties of Geostatistical Analyst make it a valuable tool for modelling and analysing the Earth's ionosphere. Our research aims to test its applicability for studying the ionosphere, and ionospheric disturbances in particular. As raw source data, we use Global Navigation Satellite Systems (GNSS)-derived ionospheric total electron content. This paper compares ionosphere models (maps) developed using various interpolation methods available in Geostatistical Analyst. The comparison is based on several indicators that can provide the statistical characteristics of an interpolation error. In this contribution, we use our own method, the parametric assessment of the quality of estimation (MPQE). Here, we present analyses and a discussion of the modelling results for various states of the ionosphere: On the disturbed day of the St Patrick's Day geomagnetic storm of 2015, one quiet day before the storm and one day after its occurrence, reflecting the ionosphere recovery phase. Finally, the optimal interpolation method is selected and presented.