## 1. Introduction

[2] The ionosphere affects the operation of various systems such as high frequency (HF), satellite communication, and navigation systems. The performance of these systems can be improved by adjusting the system parameters or correcting the ionospheric error with respect to the varying nature of the ionosphere. Monitoring the ionospheric variability that constitutes an important component of space weather is a complicated task due to the coupling of solar, geomagnetic, and seismic activity. The ionosphere is a temporally and spatially varying medium that is characterized by its electron density distribution. Total electron content (TEC), defined as the total number of free electrons in a tube with cross-sectional area of 1 m^{2} centered along a raypath, is one of the important parameters used to investigate ionospheric variability. TEC is measured in terms of TECU (1 TECU = 10^{16} el/m^{2}). TEC can be obtained from the worldwide network of dual frequency global positioning system (GPS) receivers [*Manucci et al.*, 1993; *Wilson and Mannucci*, 1994; *Komjathy*, 1997; *Komjathy et al.*, 1998; *Manucci et al.*, 1998; *Hernández-Pajares et al.*, 1999; *Schaer*, 1999; *Arikan et al.*, 2003, 2004; *Nayir et al.*, 2007]. Owing to sparse and irregular distribution of these receivers, TEC cannot be directly obtained everywhere on the ionosphere. Accurate and robust interpolation methods can be used to estimate TEC for every desired location in a given region [*Hernández-Pajares et al.*, 2002; *Opperman et al.*, 2007; *Foster and Evans*, 2008; *Sayin*, 2008; *Sayin et al.*, 2008b; *Yilmaz et al.*, 2009; *Arikan et al.*, 2009]. To better visualize the spatial ionospheric variation, TEC maps can be produced by estimating TEC values on a dense grid.

[3] The temporal update period (TUP) of consecutive TEC maps (time between consecutive TEC maps) is an important parameter in regional and global monitoring of ionospheric variability. The optimum TUP should be sufficiently small to capture the significant variations in the underlying physics of the ionosphere; however, it should be sufficiently large to allocate computational and storage resources efficiently [*Erol and Arikan*, 2005; *Akdogan et al.*, 2007; *Sayin et al.*, 2009]. Typically, TEC maps are produced at time intervals that do not necessarily capture the variability of regional ionospheres. For example, the global ionospheric maps (GIM) are produced with a time resolution of 2 hours and a spatial resolution of 2.5° in latitude and 5° in longitude by the analysis centers of the International GNSS Service (IGS), available at ftp://cddisa.gsfc.nasa.gov/gps/products/ionex. Although these maps indicate the general temporal and spatial trends of the ionosphere, regional variations in both time and space cannot be observed with a desired level of sensitivity and accuracy. Furthermore, the Jet Propulsion Laboratory (JPL), http://iono.jpl.nasa.gov, provides GIMs updated every 5 minutes; the Space Weather Application Center-Ionosphere (SWACI), http://swaciweb.dlr.de/, provides TEC maps over Europe for every 5 minutes; the National Oceanic and Atmospheric Administration (NOAA)/Space Weather Prediction Center (SWPC) in the USA, http://www.swpc.noaa.gov, provides TEC maps over the USA for every 15 minutes; and MIT Haystack Observatory, http://madrigal.haystack.mit.edu/madrigal/, provides TEC values over global landmass where GPS receivers are operational for every 5 minutes. Also, there are satellite-based augmentation systems (SBAS) such as the Wide Area Augmentation System (WAAS), http://www.nstb.tc.faa.gov and European Geostationary Navigation Overlay Service (EGNOS), http://www.egnos-pro.esa.int, that provide real-time ionospheric corrections to their users. In the literature, there is no study discussing the optimum temporal update periods or how these 5 minute, 15 minute, or 2 hour temporal update periods are chosen. In this study, we propose a novel technique to choose the optimum TUP adaptively for regional ionosphere monitoring. Owing to the time-varying nature of the ionosphere, standard statistical methods do not provide reliable information. Therefore, the TUP should be estimated by using statistical analysis methods with a regional random field model [*Sayin et al.*, 2008a; *Sayin*, 2008].

[4] Investigation of a regional wide sense stationarity (WSS) period can be considered a practical solution in optimizing the TUP [*Akdogan et al.*, 2007; *Sayin et al.*, 2009]. In a WSS period, first- and second-order moments that correspond to the mean and variance are constants [*Papoulis and Pillai*, 2002]. The regional WSS period of a stochastic process is the time interval in which the mean and variance of the process can be considered as constants. If the WSS period is chosen as the TUP, then significant variations of the regional ionosphere can be captured. In the work of *Arikan and Erol* [1998], an efficient tool is developed to obtain the statistical characterization of the time variability of HF channel response. The method employs sliding window statistical analysis to estimate the time-varying mean and variance to capture the temporal variability. In the work of *Erol and Arikan* [2005], the method is applied to the TEC data computed from GPS observables, and the WSS periods of individual GPS stations are estimated manually for both quiet and disturbed days of the ionosphere. In the work of *Akdogan et al.* [2007], the method is further developed to obtain the WSS periods automatically.

[5] In this study, the WSS period is proposed to be used as the optimum TUP of the regional TEC maps. For this purpose, GPS-TEC is obtained for a wide selection of European IGS stations for quiet and disturbed days of the ionosphere. The WSS period of TEC for individual IGS stations is estimated for each hour of the chosen days. Also, TEC maps are produced by the ordinary Kriging interpolation algorithm for every 2.5 minute time interval. To quantify the variation from one map to the other, we have employed four different techniques: namely, symmetric Kullback-Leibler Distance (KLD), *K*; pointwise maximum of the KLD, *k*_{m}; sum of the absolute value of the pointwise differences, *A*; and the maximum of absolute value of the pointwise differences, *A*_{m}. The differences between the TEC maps during a day are obtained using all of these methods from 0000 UT to 2400 UT with a step size of 2.5 minutes. The difference levels between maps are compared with the WSS periods of the regional TEC maps. It is observed that WSS periods of TEC for individual GPS stations are a promising and cost-efficient indicator of ionospheric temporal variability for the regional TEC maps for both quiet and disturbed days.