## 4 Technique Validation and Discussion
### Spatial Gradients. Accuracy of Determining TEC at a Growing Distance from a Station  
Figure 9 presents the TEC latitude and longitude gradients for IRKJ, NTUS, and THU2. The data were obtained as a result of simulation based on the IRI-2012. The initial measurements are the same, as those for Figure 6. The parameters presented in the figure are a solution for a consistent set of Equations (7). The black dotted line marks the results of the TuRBOTEC operation; the red line shows the vertical TEC data and gradients from IRI-2012 model.  
Absolute gradients differ from \(<\)0.1 TECU/deg. for longitude gradients in the high-latitude regions to 2.5 TECU/deg. for latitude gradients in the equatorial regions during the equatorial anomaly evolution.  
The IRI-2012 gradients and their TuRBOTEC estimates are qualitatively similar. However, as compared with the vertical TEC recovery accuracy, the accuracy of determining the spatial gradients is substantially lower. Notably, for equatorial stations, the divergence in the latitude gradient may reach 1 TECU/deg. during the equatorial anomaly evolution. This is related to that model (3) involves \(S\) function that converts the slant TEC into the vertical TEC. In the equatorial anomaly region, such an approximation works worst of all, and, whereas the vertical TEC estimate is quite reasonable (see Figure 6), the spatial gradient estimate may not be satisfactory.  
When estimating the vertical TEC at a growing distance from a station, this leads to an error. In Figure 10, we present the value of this error at different UT for various distances from a station. The figure presents the simulation data for the mid-latitude IRKJ station. Panel (a) shows the error when moving away from the station along the latitude; panel (b) does the same when moving away from the station along the longitude. The arrowlets mark the local midday and the solar terminator time at 200 km: SR is the morning (sunrise) terminator, SS being the night (sunset) one. On panel (b), the time of local midday and the terminator is marked for the longitude extremities: for 124.3\({}^{\circ}\) E (arrowlets at the plot top) and for 84.3\({}^{\circ}\) E (arrowlets at the plot bottom).  
Figure 9: Simulation for the TEC latitude (**a–c**) and longitude (**d–f**) gradients recovery for IRKJ (**a,d**), NTUS (**b,e**), and THU2 (**c,f**). The black dotted line presents the results of the TuRBOTEC operation; the red line exhibits the IRI-2012 TEC gradient data, and the blue line shows the difference between the results of the TuRBOTEC operation and those from the IRI-2012 model. The green line shows the similar differences, but for the IRI-plas simulation. The axis for the blue and green lines are on the right, for the red and black lines on the left.  
One can see that the latitude errors grow more than when moving at a similar distance by longitude. This may be determined by that the \(S\) mapping function has an essential latitude dependence. Therefore, at a significant deviation, the vertical TEC value converted from the slant TEC is not precisely determined. Hence, the gradients are not precisely determined, either. It is worth noting that, in this case, this error would grow almost linearly. From Figure 10, one can see that this is not absolutely so. The real and the model latitude gradients have a dramatically spatially inhomogeneous character as one moves away from the station, and, at distances more than 10\({}^{\circ}\)-15\({}^{\circ}\), the estimates start to surpass 10 TECU.