# On the Feasibility of Interhemispheric Patch Detection Using Ground-Based GNSS Measurements
## 2 Methodology and Data Set  
As previous studies showed, the time series of \(L_{4}\) measurements and relative STEC values can be successfully used for the detection of ionospheric disturbances [38; 39; 40; 41]. Considering the polar patches, such approach was applied for particular arcs only [9; 14]. In this paper, we provided an algorithm aimed at the combined processing of network-derived observations in order to extend GNSS-based analyses of a high-latitude ionosphere. The computation of relative STEC values is realized in two steps. The first one is the detection and repair of phase cycle-slips, which frequently occur at high latitudes [5; 42]. Initially, we implemented the modified algorithm proposed in [43], which assumes searching and repairing phase cycle-slips using the difference between real and approximated rates of TEC values. However, the preliminary analysis for the southern hemisphere data indicated that the real change of STEC (without cycle-slip) can reach even 15 TECu/min (see Figure 1), and setting up such a high threshold limit led to the unstable work of the algorithm. Hence, we decided to perform a cleaning of the \(L_{4}\) data using their leveling with code one, according to the equation:  
\[\widetilde{L}_{4(k)}=L_{4(k)}-\text{median}(L_{4(k)}+P_{4(k)})_{arc} \tag{1}\]  
where \(\widetilde{L}_{4(k)}\), \(L_{4(k)}\), and \(P_{4(k)}\) correspond to the shifted phase, phase, and code data at epoch \(k\), respectively. Due to the opposite sign of the ionospheric effect in both types of observations, the factor in brackets contains the constant term (differences of ambiguities and hardware delays on both frequencies) and the median of noise. Figure 1: Background slant total electron content (STEC) estimation using iterative polynomial fitting. The levelling and cleaning of phase data is performed as follows. At first, the large cycle-slips are detected using temporal differences of \(L_{4}\) with the threshold limit set to 20 TECu/min. Then, each clean part of an arc longer than 15 min is leveled according to Equation (1). In the case of the shorter periods, which are characterized by corrupted phase data, they are replaced with a five-epoch moving average of \(-P_{4(k)}\). This process slightly smooths the pattern of structure in the time domain, but the values that are derived in such way can be still a good approximation of ionospheric variations. According to our tests, the standard deviation of differences between the applied moving average and raw phase data is at the level of 2 TECu, while the periods of frequent cycle-slips are mostly related to STEC enhancement exceeding 20 TECu. Finally, due to the high threshold limit, we examine the leveled phase measurements using the median of differences between them and the five-epoch averaged code data in 15-min periods. If the absolute values of this indicator are higher than six TECu, what corresponds to three \(\sigma\), the phase data are shifted accordingly. The next step of the algorithm is the extraction of patch signatures from clean arcs of \(L_{4}\) data. According to our preliminary results given in [37], this can be effectively performed with an iterative fitting of a fourth-order polynomial in a three-step procedure. The starting point involves a shift of the \(L_{4}\) time series to set their minimal values to 0.2. Subsequently, the initial fitting with unit weights is performed. If the maximal difference between the \(L_{4}\) values and fitted polynomial does not exceed three TECu, the background STEC assessment process is terminated. In the opposite case, the polynomial coefficients are estimated in a two-step iterative mode, removing epochs with differences higher than 1.5 TECu. These repetitions are performed with weights equal to \(1/L_{4}\). The first step is related to iterative fitting only, and enables the application of appropriate weights.