## 1 Introduction

[2] Ionosphere is a key player in monitoring Space Weather (SW). The major observable feature of ionosphere is total electron content (TEC), which is defined as the line integral of electron density distribution on given ray path. The variability of TEC directly reflects the variability in electron density profile, which is a complicated function of position, height, and time. In recent decades, the worldwide, dual-frequency GPS receivers provide a cost-effective means in estimating TEC [*Coster et al.*, 1992; *Komjathy*, 1997; *Hajj et al.*, 2000; *Nayir et al.*, 2007]. GPS receivers can be used in Continuously Operating Reference Station (CORS) networks to increase the accuracy and reliability for positioning and surveying applications. CORS network receivers are generally distributed to a large region, and they can be placed at remote locations [*Steigenberger et al.*, 2006]. Due to various physical or operational disturbances, such as temporary antenna obstructions, power cuts, remote login problems, and geophysical or geomagnetic disturbances, GPS-TEC can be disrupted for a certain period during the day or the GPS receiver may cease to operate for a certain number of days. Services in navigation, positioning, surveying, and monitoring of SW require continuous operation of GPS receivers and uninterrupted TEC estimation for 24 h. The continuous data sets are used in modeling of ionosphere, TEC mapping, computerized ionospheric tomography (CIT), within-the-hour statistical analysis, ionospheric earthquake precursor studies, and prediction of SW events such as those provided in *Erturk et al*. [2009]; *Karatay et al*. [2010]; *Turel and Arikan*, [2010]; and *Foster and Evans* [2008]. Thus, it is an important task to interpolate the missing TEC values within a day or for a whole day. Ionosphere is a magnetoplasma; an anisotropic, inhomogeneous, time and space variable, and time and space dispersive channel. Therefore, spatial and temporal correlation structure of ionosphere has to be utilized in any interpolation scheme. As shown in previous studies such as [*Sayin et al.*, 2010], the temporal wide-sense stationarity (WSS) period of ionosphere is about 7.5–15 min for a quiet day. WSS reduces to 5 min for ionospheric conditions including geomagnetic storms and sunrise/sunset periods. Typical spatial correlation distances roughly correspond to 80 km to 150 km in midlatitude regions [*Komjathy*, 1997; *Karatay et al.*, 2010; *Foster and Evans*, 2008]. In order to complete the TEC data gaps, both the geophysical structure and the space-time correlation of ionosphere have to be taken into account [*Orús et al*., 2005; *Hernández-Pajares et al*., 2006].

[3] Another important problem is the prediction of spatio-temporal variability in TEC. It may be necessary to estimate the TEC of a GPS station from its neighbors for 1 day and then compare it to the station's own data to observe the spatial differences. Such a study is very useful to predict local disturbances that affect only a few stations in a dense grid. The temporal variability over a station can be observed by comparing the station's own data with the predictions from the previous days of the same station in a less dense grid. In this study, two different interpolation algorithms that join spatial and temporal properties of ionosphere are introduced. Both algorithms can be used for both filling in the TEC data gaps and prediction of spatio-temporal variability of TEC over a station. The two algorithms make use of optimization by least squares fit to available data. Spatio-temporal interpolation can be applied for data gaps as short as a few minutes to 24 h. The algorithms are applied to interpolate in the missing GPS-TEC values for Turkish National Permanent GPS CORS Network (TNPGN) for the years of 2001 to 2011 with great success. In section 2, the two novel spatio-temporal interpolation algorithms are provided. In section 3, the results are presented.