## 2 Observations
### Simultaneous Observations of Pulsars and ROT Towards The  
The basic idea of the simultaneous observations of pulsars and ROT is to observe both pulsar and GNSS signals passing the same region of the ionosphere--considering region as an area narrow enough to catch ionospheric irregularities. In order to achieve this, we have tied each observation with a point within the ionosphere. For the ionospheric irregularities analysis, we have applied a single thin layer ionosphere model. This model assumes that all the ionospheric plasma is concentrated within the infinitely thin layer fixed on the certain altitude for the whole Earth. This simplified approach is commonly \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \multirow{2}{*}{**Name**} & \multicolumn{1}{c}{**Right**} & \multirow{2}{*}{**Declination**} & \multirow{2}{*}{**Period**} & \multicolumn{1}{c}{**Dispersion**} & \multirow{2}{*}{**Distance**} & \multirow{2}{*}{**Flux Density 2**} \\  & & [**hms**] & & & & [**pc cm\({}^{-3}\)**]** & & \\ \hline J0332+5434 & 03:32:59.368 & +54:34:43.57 & 0.714519699726 & 26.7641 & 1.18 & -900 \(\pm\) 15\% \\ \hline J1509+5531 & 15:09:25.6298 & +55:31:32.394 & 0.739681922904 & 19.6191 & 2.07 & -800 \(\pm\)15\% \\ \hline \hline \end{tabular}  
* [[http://www.atnf.csiro.au/research/pulsar/psrcat/](http://www.atnf.csiro.au/research/pulsar/psrcat/)]([http://www.atnf.csiro.au/research/pulsar/psrcat/](http://www.atnf.csiro.au/research/pulsar/psrcat/)). 2 Estimated values at 154 MHz based on [31].  
\end{table} 
Table 1: Basic information on J0332+5434 and J1509+5531 adapted from ATNF Pulsar Catalogue 1[47]. used in the ionosphere studies that do not require the information about the 3D plasma distribution, focused only on horizontal plasma distribution. Assuming a single thin layer model of the ionosphere, for each trans-ionospheric line of sight we can find an ionospheric pierce point (IPP). For each collected pulsar observational data set we have calculated sets of corresponding IPPs. In the first step we simply used the radec2 azel function from the Python's [54] library with the pulsar's right ascension and declination as well as the coordinates of the Baldy LOFAR station HBA field center point. After obtaining the full set of horizontal coordinates of subsequent 1-min pulsar observations we recalculated those into IPP latitude and longitude:  
\[ \begin{array}{c}\Psi=\arccos\left(\left(\frac{\mathrm{R_{E}}}{\mathrm{R_{E} +h}}\right),\cos,\mathrm{E}\right)-\mathrm{E}\\ \mathrm{lat_{IPP}}=\mathrm{lon_{0}}+\Psi\cos\mathrm{Az}\\ \mathrm{lon_{IPP}}=\mathrm{lon_{0}}+\frac{\Psi\sin\mathrm{Az}}{\cos\mathrm{lat_ {IPP}}}\end{array}  \tag{5}\]  
where \(\Psi\) is a so-called offset angle, \(\mathrm{R_{E}}\) stands for the Earth's radius, h for the ionospheric layer altitude, E for the elevation angle, and Az for the azimuth. Having the ionospheric pierce points for pulsar observation we searched for the nearby GNSS IPPs. We defined 'nearby' as a zone within 3 degrees of the angular distance from the source--such a scale corresponds with the size of medium scale disturbances. This also corresponds with the scale of observable irregularities with the 30 s GNSS observations, which is from 30 km up to hundreds of kilometers [55]. To find the GNSS close-ups, we have collected the Global Positioning System (GPS) and GLObal NAvigation Satellite System (GLONASS) data from the LAMA permanent station of the International GNSS Service (IGS) network. The station is located \(\sim\)20 km away from the Baldy LOFAR station. However, the ionospheric irregularities can be very small and 20-km range between sensors might cause skipping some of them, in this study we use 30-s averaged data that correspond with larger structures. So long averaging time sets sensitivity threshold on the structure size around few degrees of angular resolution [55].