# TEC and ROTI Measurements from a New GPS Receiver at BOWEN University, Nigeria
## 3 Methodology
To compute the VTEC, herein called TEC, the STEC will be multiplied by the mapping function S(E), as shown in the equation below:  
\[\text{VTEC}=\text{ STEC }\times\text{ S(E)} \tag{1}\]  
References [17; 18] defined S(E) as the obliquity factor with zenith angle, Z, at the ionospheric pierce point (IPP) and is represented by  
\[\text{S(E)}=\frac{1}{\text{COS(Z)}}=\left(\frac{1-\text{R}_{\text{E}}\times \text{ cos(E)}^{2}}{\text{R}_{\text{E}}+\text{h}_{\text{s}}}\right)^{-0.5} \tag{2}\]  
where R\({}_{\text{E}}\) is the mean radius of the Earth measured in km and h\({}_{\text{s}}\) is the height of the ionosphere from the surface of the Earth at \(\sim\)350 km. These equations are implemented into the GOPI software [19]. In this investigation, we used the Rate of the TEC index (ROTI), as one of the most common indices to characterize ionospheric activity [20]. Ionospheric irregularities are strongly related to scintillation because they can be used to characterize small-scale and/or rapid variations in TEC [3; 4; 5; 5; 9]. The calculation of the ROTI is based on the measurement from a normal GNSS receiver which is far more common than the scintillation receiver, thus making it more advantageous over the scintillation indices [21]. These discoveries have continued to encourage more investigations on the response of fluctuations in the ionosphere using ROTI, especially around the geomagnetic equator and low latitude in the African region. Figure 3: The data processing chart. However, ROTI is derived from the time derivative of TEC (i.e., rate of change of TEC (ROT)), as given in the equations below. ROTI is calculated as the standard deviation of ROT over a 5 min period [4; 16]. These are expressed mathematically as follows:  
\[\text{ROT}=\frac{\text{dTEC}}{\text{dt}} \tag{3}\]  
\[\text{ROTI}=\sqrt{<\text{ROT}^{2}>--<\text{ROT}>^{2}} \tag{4}\]  
Reference [22] calculated the average ROTI (ROTIave) using the expression in Equation (5). As the average of ROTI is over 30 min for a satellite and then the average across all satellites in view, ROTIave is a suitable proxy to indicate the 30 min phase fluctuation level over an area. The average level of anomalies (phase fluctuation) for a half-hour over the station is provided by this result:  
\[\text{ROTI}_{\text{ave}}(0.5\text{h})=\frac{1}{\text{nsat}(0.5\text{h})}\sum _{i=1}^{\text{nsat}}\sum_{i}^{\text{k}}\sum_{i}^{\text{k}}\frac{\text{ROTI}( \text{n},\ 0.5\text{h},\text{i})}{\text{k}} \tag{5}\]  
where n is the number of satellites, h is the half hour, i is a 5 min section within the half hour (i = 1, 2, 3, 4, 5, and 6), nSat (0.5 h) is the number of satellites observed within the half hour, and k is the number of ROTI values available within the half hour for a particular satellite. This ROTI (0.5 h) finds the occurrence of significant electron density anomalies on scales ranging from meters to kilometers. Over the ROTI and ROT index, it offers the advantage of eliminating errors caused by noise spikes. [12] previously classified the values of ROTIave into three categories: ROTIave < 0.4 to denote the absence of phase fluctuation activity, ROTIave < 0.8 to denote the presence of phase fluctuation activity, and ROTIave > 0.8 to denote severe phase fluctuation activity. Figure 4 showed the results from our analysis concerning ROTI, which is calculated from the time variation in TEC (rate of change of TEC, ROT).