 Thank you everybody and welcome to this seminar organized by the science, technology and innovation unit of the international center for theoretical physics. Today, we will speak about ionospheric modeling and the speaker will be Dr. Alessio Piñandeli. Nationality Geophysical and Volcanology. He's talking there. Sorry. The only person you know is Alicella. Please, move the microphones for the audience online please. There are 22 participants. One, two, three, four, five, one, two, three, four, thirty-three. Sorry, please. For the participants online if you could move your microphone please. Thank you. So the speaker is Dr. Alessio Piñandeli from the Institute of Nationality Geophysical Volcanology in Rome who is visiting us here at the CTB. And he will give the presentation, modeling the top side ionosphere, improving the quick through radiocultation data. So Alessio please, the floor is yours. Thank you Bruno. Thank you for the last presentation. Thank you for inviting me to take you to this seminar here at the CTB and to the CTB all for guesting me for this four weeks period. The presentations about modeling of the top side ionosphere with particular focus on the quick top side model which are trying to improve through radiocultation measurements. This presentation will summarize the results of the last three years of work and some of new applications in the very recent results. This is the beginning of the seminar. Sorry, I'm not here to go online. That's it. I will briefly introduce the terrestrial ionosphere. What's your name? People are focused on the top side of the ionosphere. I will speak about how we can model the ionosphere. And then we need to remain topics of the presentation. I don't want to be seen. Sorry online. I know the people I know. Gladio is not there. Humberto is not there. No, no, we are the ones coming. We are there. We are the ones. Can you mute the microphone please? Thank you. Okay, the presentation, the main topics of the presentation is how we use top side ions for electron density observation recorded by radiocultation satellites to calculate the effective values. And then how the effective scale values are used to improve the description of the top side parameters. Then I will show you how these parameters behave in different conditions and how it can be used for improve the top side modeling by the peak. What we call the ionosphere is that portion of the upper atmosphere where free electrons and diodes exist under the control of the gravity and magnetic field. And in this region they are present in a point that is sufficient to affect the reflection index of the atmosphere. And so to affect the propagation of electromagnetic wave in the atmosphere above all ready waves. You can see a sketch of the ionosphere with its electron density profile starting from about 50 km up to about 1000 km then shedding in the upper plasma sphere. In the ionosphere is most of the lower torbis satellites and also the plasma sphere in the genesis satellites. The ionosphere is a plasma, specifically a weakly ionized plasma because only a small portion of the neutral density is affected with the ionized by solar radiation or by muscular radiation by sun. The very important point is that being a plasma is strongly coupled with the geomagnetic field. So most of the transport effects in the ionosphere are driven by the geomagnetic field lines configuration. And of course, because we have electron density in the ionosphere, this changes the reflection index. And this is the way we are more commonly discovered in the ionosphere and we use the ionosphere to propagate signals which between two stations distance about 3000 km away that was not possible with ground wave but this communication is possible through the sky wave. And because of the existence of the ionosphere. So the most important parameter for the description of the ionosphere is the electron density vertical profile. On the left you can see modern values of the electron density in black with a color attached lines, the presence of different ions at different levels at different altitudes. The ionosphere is characterized by an absolute maximum at the F2 layer region which is always present in the ionosphere and can ideally divide the ionosphere into different regions. The bottom side from the ground to the F2 layer peak which is subdivided in other different regions with a relative maximum because of the presence of different ions at different altitudes that are produced by the solar input radiation, specifically the extreme UP and the X-ray radiation. This is the region that was first brought by ground based facilities like ionosomes which are particular high frequency weather. And this is the region we know better with this kind of measurements. While in the top side, which is the region from the peak so from HL2 which is the altitude of the peak to the line plasma sphere is characterized by a monotonic decrease of the electron density. And compared to the bottom side is dominated by the diffusion of plasma along the geomagnetic lines. By the bottom side, the production of ions is the principle. Compared to the bottom side, the top side is also a region difficult to probe because it cannot be solved by ground based ionosomes. So we have to use more expensive and sophisticated instruments like instrumentation or satellites or increase cathodeuradas from ground. The data set we are going to use is the electron density profiles recorded by radiation and we will spend some words later in the presentation about radiation. So the quick model is an ion-spheric electron-density model that was developed here at ICTP in Trieste in collaboration with the University of Graz in Austria. And as the name says, it's a quick-run empirical model of the ionosphere that which a main aim is to reproduce the median behavior of the ionosphere. So to represent the main spatial, the original sequence or to the variations. It allowed to calculate the electron density in the entire ion-spheric altitude range from the ground to GSS altitudes and also the total electron content by integration of the electron density. Compared to other empirical models of the ionosphere, we cast a great advantage to calculate the electron density. And so the TEC also post-land path. Because this is an empirical model, it takes advantage of the data sets underlying the model and the fact that this is a very great advantage for us. Because when new data sets from new instruments or new other missions, for example, are provided, we can use this new data set to further improve the model. And this is what we are trying to do by using the radiation observation to improve the top-side representation by the empirical model. The quick was also recommended by ITUR as the recommended model for a total electron content estimation. Its top-side formulation was also adopted as one of the top-side options by the International Reference Ionosphere, which is the reference empirical model for the ionospheric community. And also a specific version of the quick. The quick G was implemented by the European Space Agency as the single frequency ionospheric correction algorithm for the Galileo-Genesis constellation. And finally the quick was also included by ESA in the Space Environment Information System. So let's spend some words on the quick formulation, which is based on six semi-examination layers. The semi-examination layers mathematical formulation is represented here. It is a combination of exponential function. And these six layers are anchored to the three main regions of the ionosphere. One in the F2 region. We have six semi-examination layers because the layer thickness parameter be here represented in the green. This parameter is different from the bottom to the top of each layer. So let's take a simple position, time and solar flux, the F10.7 daily solar flux, and give us out the electron density in the entire ionospheric activity range and also the electron content by numerical integration. Concerning the top-side formulation by the quick. Again, it is formulated as a semi-examination layer anchored to the F2 layer peak. And the layer thickness parameter, which here is called H, because it plays the role of an effective skeleton. Effective skeleton, and not plasma skeleton because effective skeleton values are those derived directly from electron density measurements, while plasma skeleton values are derived from the theory by the knowledge of the distribution of ions in the ionosphere and also plasma temperature. The quick model of the defective skeleton in this way, where it depends on three top-side parameters, H0, red, RNG parameter in the green and blue. So if we study the skeleton behavior in the top-side and specifically the skeleton near the F2 layer peak by expanding the initial series, the quick formulation of the skeleton, we find that the skeleton near the peak has a linear behavior where H0, which is the intercept here, represents the value assumed by the skeleton at the peak. YG is the vertical gradient of the skeleton and it has a lot of implication in the description of the shape of the top-side electron density profile. While if we study the skeleton at infinity, I think with infinity here I mean very distant from the peak. So GNSS altitudes at 20,000 km can be considered infinity compared to the F2 layer peak altitude, which is at about 300 km. So in this limit, the skeleton is equal to H0 times 1 plus R. So the R parameter is the parameter that was introduced to control the asymptotic behavior of the skeleton very distant from the peak. In the quick model, gender parameters are constant, G equal to 0.125 and R equal to 100. While H0 in the quick is derived from bottom-side GNSS parameters with a correction factor which was calculated based on top-side soundness data. So the benchmark here is that H0 in the quick is compared from bottom-side parameters, while we know that there are some cases where the bottom side, the top-side skeleton, behave in a very different way. So our goal is to improve the description of this three top-side parameter by using radio-pultation suspensions. Radio-pultation is a remote sensing measurement technique which makes use of radio waves and electromagnetic signals sent by GNSS satellites. We sketch on the net using GPS satellites at about 20,000 km altitude that are recorded by lower torbids satellites, in this case cosmic, in a radio-pultation geometry. Specifically, since the ion sphere is a refractive medium, the radio waves from GNSS to radio satellites propagate across the ion sphere and then experience a phase delay which is dependent on the total electron content in the path. In the radio-pultation geometry, it is possible to, from the total electron content between the GPS and the radio satellites to calculate in a spherical approximation to calculate the electron density in the tangent point of the radio-pultation. And because the satellites move, different altitudes can be scanned to obtain a quasi-vertical electron density profile. It was vertical because of course satellites move, so the tangent points are not in the same location, but in most of the cases these profiles can be considered as quasi-vertical. Our dataset is composed by cosmic forms of three radio-pultation electron density profiles from the beginning of the mission in 2006 to the 2018. Specifically, satellites have a 72 degree of inclination, so can cover most of the latitudes, only the very high latitudes are not covered by this dataset, and at about 800 km altitude. So, how we calculate the effective scale height? To do so, we developed a straightforward mathematical methodology, which starting from the Nebriks semi-active formulation allows to mathematically incorporate the effective scale height. So, we can mathematically by some mathematical steps, with a change of variables defined in the T as a function of the scale height and the alpha as the ratio between the electron density in the top side and the electron density at the peak. If we change, if we make this change of variables, the Nebriks semi-active layer become a second degree equation in the variable T, which is dependent on the scale height. So, the question has two analytical solutions. T1 and T2 that can be obtained by electron density measurements in the top side. And then from the T, parameter we can obtain H by making the inverse of this change of variables. Both two solutions are mathematically acceptable, because when we put them in the scale height, they produce the same electron density profile, but T1 produces positive values of the scale height in the top side, while T2 gives negative values of the scale height in the top side. So, we consider the physical, the physical we write the solution of one with T1. So, if we put T1 in this formulation of the scale height, we obtain what we call the Epstein scale height, which is the effective scale height that is mathematically deduced by the semi-epstein. So, as you can see, to calculate the Epstein scale height, we only need information on the F2 layer peak. It's half to the HLF2 and the absolute maximum absolute values of the electron density at the peak and MF2. And we need to know the top side electron density profile. With this information, we can obtain information on the effective scale height in all the top side profile. And fortunately, the reputation by cosmic give us this information. So we observe electron density values in the top side, we can calculate the Epstein scale height. And then, we make a non-linear fit of the Neuquic top side scale height over this calculated effective values. I will show you in the next slide an example based on a specific radiation profile. The results of this non-linear fit gives us output three optimised values of the three top side parameters. In fact, in the fit, it's 0, R, NG are three parameters that we optimise to reduce, to minimise the residuals between modulate and measure in top side scale height values. In the fit, if it will obtain the optimised values of the three top side parameters, that can be used to calculate new values of the Neuquic top side scale height and then new values of the electron density in the top side. So let's have a look at an example. On the left, on the plot on the left, you have top side electron density values, while on the right, top side scale height values. Our starting point is the electron density measured by cosmic, which is represented by the blue points in the left plot. On this electron density values, we calculate the effective scale height with this formulation, I've just shown in the next slide, to obtain the vertical profile of the effective scale height, which is represented by the blue points in the right plot. So in these blue points, we fit the Neuquic top side scale height, represented here, by leaving three H0, R, and G parameters. And so the results of the fit give us the optimised values of the three top side parameters, which is in this case H0 of optimised values equal to 34.11 km, R is equal to 8.68 and G equals to 0.236. So you can see that these values are different from the ones commonly used by the Neuquic model. So the results of the fit is the red line of the right plot, which keeps the vertical variation of this scale height, and then by putting this scale height in the top side formulation of the Neuquic, we obtain updated values of the electron density by Neuquic, which is, which are represented by the red line on the left plot. And as you can see then, exactly match the values measured by cosmic. So we applied this methodology to the entire cosmic data set, specifically about 1.8 millions of profiles recorded from 2006 to 2018. And first of all, we made a validation to test the ability of our methodology in reproducing the cosmic top side data set. So from the only measured and moderate profiles, we calculated some statistical metrics. In the middle of the slide, we have the percentage residuals, electron density percentage residuals between values of the model by Neuquic with optimised top side parameters and electron density values reported by cosmic. And the profiles are normalised to the peak. So here at zero kilometres, the altitude from the peak, from the peak in the top side. Well, it is quite visible that residuals lie for all the altitude in a range between plus and minus 5%. We consider the top side of the total electron content by integrating the electron density profile from the peak to the cosmic altitude. And by calculating the residuals between mesh and moderate values, we can see that the residuals are very peak at around zero with very small dispersion. So this test tells us that our methodology is able, with our methodology, we can reproduce the cosmic top side profiles by using Neuquic with optimised top side parameters. And now see how this parameter behaves in different conditions. These are the residuals for H0. So we have a large data set of values, 1.10 million of values, so we can study the behaviour of the parameter as a function of spatial time, noon, seasonal and also sort of a magnetic activity variations. The ones represented here on the left are the median values of HG0 as a function of geographical coordinates, while on the right, median H0 values as a function of the quasi-temporal magnetic latitude on y-axis and time on the x-axis for the entire data set. For most of these plots, we use a magnetic latitude because looking at the plots in geographical coordinates, we can see that H0 show variations which are strongly connected with the geomagnetic fit lines configuration. In fact, it maximise around the geomagnetic equator and also in the overall region. And it also exhibit time variation, seasonal and also sort of activity variation with maximum values during years of high solar activity. These are the corresponding results for the G parameter. I remind you that G in the region earthquake is a constant, equal to 0.125, while from our results we see that G is not constant, it's not constant spatially and even in time, and it also lies in a range between 0.1 and 0.3. So the values by the earthquake is quite reliable just at the real latitudes, while at the middle and high latitudes it represents an underestimation of the G value that we can obtain from radio-portation measurements. And also these results tell us that we need to relax the constancy of the G parameters and also we need to model it as a function at least of spatial time variables. These are the results for the R parameter. Again, R parameter is constant to 100 in a week, while from our results we see that R shows spatial time variations in a range between 0 and 20, so much lower than those used by the original week. And I want to draw your attention to this question behavior of the R parameter at very low latitudes, where we can see a sudden drop of the R parameter for a range of latitudes between plus, minus, 30 degrees and generally low latitudes. This is, we wondered if this is a physical feature of the ion sphere of this R parameter or it is in some way connected to the methodology or the data set we used to it with the R parameter. To investigate this we looked at a specific topside profiles recorded at low latitudes and we came out with the conclusion that this behavior is due to too many reasons. This one is when we have, we have topside profiles with a limited altimeter extension. Like in this case where we have a change of about 370 kilometer and the upper point in the topside is at about 200 kilometer above the peak. So keep in mind that R parameter described the asymptotic behavior of the scale, so very distant from the peak. It is understandable that with a very limited extension the topside profile we cannot reliably construct this parameter and in fact in this case R is equal to about one. Another, another, another concept is not very low latitudes so far is represented here in the second plot where we have enough topside profile in this case the upper point is at about 800 kilometer. But in this case we have a topside scale height represented there on the bottom, which is perfectly linear in the topside. In this case we can reliably calculate the zero and G parameter, but we obtain not the meaningful R parameter parts, which is this case very high. And why this happens? Well, if we consider the mathematical formulation in the topside scale height and make the limit for R parameter which tend to infinity, we can easily demonstrate that in this limit the scale height is again linear. So this means that when we have topside profiles whose scale height is exactly linear, we cannot estimate the R parameter, which describe the nonlinear behavior of the scale height very distant from the peak. So from very linear profiles we cannot estimate the nonlinear part of the scale height which is given by the R parameter. So we are working on this issue by also using the different measurements other than the radiation to constrain the R parameter behavior at very low latitudes. So let's have a look at the original seasonal variation of the three topside parameters, the original top plots, so function of local time, while the bottom plot the seasonal variation as a function of the day of the year for the three parameters. Well, about age zero, you probably recognize most of the features that were also found by other authors by using the different topside formulation or different datasets, while the results from G and R are quite original. Again, for the R parameter, you can see that for most of the local time, we cannot estimate the R parameter at very low latitudes, but for specific local times at around the sunrise, you can see that we can also estimate the R parameter also at very low latitudes. This is because at these local times at very low latitudes, the ions is very compressed, so HM2 is very low. So considering that the cosmic satellite is a fixed altitude, when we have HM2 very low, it means that we have more data in the topside. So, in such cases, we have enough topside profile to estimate also the R parameter, but this is not possible for other local times where the HM2 is higher than at around sunrise. These are the results about solar magnetic activity variations. Age zero is positively correlated with the solar activity as a function of the 81 day aluminum of the F10.7, while G doesn't show a very high, very high activity variation on the very high latitudes. And again, our families have shown this strange behavior we are trying to solve. About magnetic activity, we have to say that for very disturbed conditions, that's very limited. And so this is a working progress. But we are mainly interested to the spatial, the urinal systems of the variation because they are the variation that are described by the big model, why the magnetic activity currently is not included in the big model. So, to conclude, I will show you a first application of our calculated optimized topside parameters by replicating a test made by Bilica in 2009. And specifically, Bilica in this paper used the three topside options, one of them is the big one. To study the electron behavior in the topside, along for different geometry latitudes at 16 local time for the northern summer season and medium solar activity levels. We are mainly interested in the electron density variation, the topside of the very low latitudes because measurements that last at the edge at the F2 layer peak altitude. We have the double crest of the quadrilateral normally, while the topside, the two crests should merge in a single layer above the geomagnetic orbital. And the big does not reproduce this behavior because the original week, the skeleton is calculated from bottom side parameters. So, so it tends to keep the double crest also at higher altitudes in the topside. So let's have a look at if we don't recognize why we can reproduce the desired behavior in the topside. So, our grades of a calculated effective in topside parameters is still gender. We consider the local time at 16 by Bilica. And then you obtain this latitudinal profiles, geomagnetic latitudes coordinates for the three parameters, where you can see how the issue we have in there are parameter which is sudden drop values around zero. So if you use this three topside parameters in the quick topside formulation, you obtain this latitudinal section of the topside profiles. Of course, when we have this very low our values at low latitudes, it means that for these cases, we have a very low. The topside is the light and this means that the electron density in these cases fall to rapidly. And then we have this whole in the ion sphere at low latitudes. And this is why we have to solve this problem of the parameter because it keeps not physical features. But if we focus on the shape of these lines, we can see that we have a single maximum, which is, which is the behavior we want to reproduce. So we made some funny tests. This one, we consider only a zero and G from the core from cosmic so optimized values from cosmic input are equal to 100, which is the values, the values by the quick up posteriori. When we put another value up posteriori. The resources. Because in the quick topside formulation, RG parameter, are meaning to each other. So we cannot fix one bar and Jeep are bar meter, why G is calculated from other machines. Doesn't work. If we put R equal to zero. This means that the skylight in all the topside is equal to the skylight at the peak. Of course, this is a pool of values of the skylight, which, which reproduces are too fast, the reason of the electron dance in the topside, but with the only the zero parameter, we can reproduce. So this tells us that the zero parameters can effectively describe the natural behavior of the skylight. This is why from cosmic we considered only G to optimize values and put G both G and R equal to the ones just by the quick. In this case, we see that we are almost able to reproduce the single peak, the merging of the two crests in a single place about the German and gentlemen, with just a slight. Last test. This is zero from cosmic and G equal to 0.188, which is the average values by considering optimizing values of six at 16 local time. So the, the, all the values of different levels for such local times are every two, and we obtain this value, while are equal to 15. So we can, in our first approximation, they do from the knowledge of the plasma skylight by considering in a very close approximation that the plasma skylight doesn't change, doesn't change. In this case, the variation the skylight plasma skylight is only due to the change of mass from the peak to the infinity, where at the peak we have only, almost only a plus items. So the mass 16 at infinity, we have only H plus items must equal to one. So the skylight from the peak to the infinity scale by a factor of 16. And this behavior has to be equal to 15. So if we use this value for our, we obtain, we obtain such good results with single quest about the general meeting whether and vertical gradients of the skylight, which are very similar to those expected So we wanted our approach by using zero electron density observation by several neo satellites from champ, which is near to death to make a pick up about 385 kilometer, then going up to raise will be icon in the SPF 15, which is the highest one of about 850 kilometers. Measurements are in way with dispersion and while the color of the groups are the water advice. I want to draw your attention mainly on the quick results for the MP attitudes. What are what are the plot. You can see that the quick original week in blue. And this article described the double quest of the weather. Normally, when that I show a series of this. And using of the miles and miles of the top five parameters, we obtain the blue, the black curve here, which is able to better describe both the latitudinal behavior of the electricity and also with values, which are more in agreement with the ones measured by the sunlight. But this is just this validation of the approach. But of course, these results are only based on the use of optimized HCO values from cosmic. Because here we put G and R constant but different from the original one. While our final goal is to obtain our model for all the three top side parameters. In addition, we developed a normal methodology to calculate the effective scan item at the top side ionosphere by using electron density measurements by radiation of cosmic satellites. And with this methodology, we obtain optimized values of the three week top side parameters, and we also show that this parameter special temporal variations. The main emphasis that G and R parameter, which are kept constant by originally weaker, actually are not constant. And then we need to model this parameter as a function of different times. Among the three parameters, the most important one for the description of the top side specifically for the description of the latitudinal variation of the electron density in the top side. So, we are working on the improvement of the description of the R parameter at low latitudes because at the current stage. We calculated R values at low latitudes and to do so we are using some other electron density measurements other than radiation to constrain the R behavior at low latitudes. After solving this problem, we will be ready to global model the three top side parameters and then include them in the quick top side formulation and finally find the new top side model based on different data sources. So this concludes my presentation and personal welcome. Thank you. Presentation presentation. And of course if there are questions. Unless you will be so kind to answer stuff from the audience here if not we can go in the chat maybe. Yes, you can read the question from here. If you can unmute yourself and ask the question we should be able to hear you. Hello. Yes, can you hear me. Yeah, thanks a lesson very interesting presentation so I have a couple of questions for you if you can go back to your slide number 14. No 13. Yeah, apologize. One. Yeah. Yeah, this one. So I have a question regarding your right plot. I see some sort of fluctuations in a in the value of age zero along the magnetic equator from year 2006 to 2018 you seek like quasi periodic fluctuations up and down. So, do you have any idea why it may happen is, could it be because a quasi dipole magnetic field is not actually representing the reality or maybe some other physical processes behind that fluctuation. Okay. So, I think that they are probably due to the fact that, of course, the maximum is above the genetic equator, but the equatorial organization of my quest also show a latitudinal dependence for as a function of the season. So, there is also a control geographic latitudinal control in the water organization normally that of course cannot be described by using the magnetic. It seems to be that you have also a solar activity level dependence in that location. Right. Like towards the solar maximum 2014 1214 you have a displacement of the maximum towards northern latitudes, right towards North Pole. Okay, you mean that this fluctuation is symmetric around the geometry. I mean, yeah, I mean, if you if you look at the at the zero line, you have a displacement of the of the peak around years of high solar activity level 2012 14, and it looks like it is displaced towards like 510 is tennis show in latitude, or maybe I'm just very good point. To invest in the future. I don't have extra I don't have a balance for this. Yeah, because one of the things we used to when I used to work with neck week is is this quasi dipole latitude or magnetic field description or more deep. It actually doesn't include that the changes in the magnetic field with time right so my first idea was, it couldn't be because of that reason or maybe something else but yeah. Thanks. It's it's really interesting to me and I have a one more technical question so talking about age zero again. If you you said you you are able to find an optimal or let's say age zero that is better represent in the reality. My question is how you made sure that your transition from bottom side to top side because bottom side you have an age zero that is produced by other means and a top site age zero you say you found it in from your experimental data. My question is, how would you ensure the transition from bottom side smooth transition from bottom side to top side. Because, as you perfectly know, in the quick, the two. Skelite values, the bottom side and the top side are related by a key parameter. So, to use this age zero values to put them in the modern. If we, if we believe that age zero values from the top side are the right one. So, we will have to to to recover the bottom size scale I starting from the top and not calculate the top size scale I started from the bottom side, as is done, but it is done by the current week. So, inclusion of this model of this model in the in the week is not simple, because if we want to keep the philosophy of the week of connected the bottom side of the top size to light. We have to also recalculate the bottom size to light starting from the top. Okay. Yeah. Yeah, I understand that. Yeah, it's not easy. That's why I was curious how you. Next step. Yeah, thank you Alessio. That's all from my side. There is a question in the chat. Okay, there is a question in the chat by Sasha Pustov. How often do you have situations with huge R values. Well, looking, looking at these plots, you see that that very low latitudes. The huge values are huge are values are very common. And in fact, to obtain these plots. At the first step, I excluded all the values higher than 1000 because using such a high value. It means that the scale of this type of the big is too high. And then the total electron content values would be too high. So these plots are, are obtained with by excluding a very high values. And if we include very high values, we, we have only the cases where the are parameters very low, which is this first case here, as I said before because for most of the local time hours at low latitudes. We don't have enough top side profile to constrain the parameter behavior. But of course, we have also had many cases. I don't know the percentage of this case, but they are very high percentage of cases where the skeleton is very, very linear. And of course, we cannot solve this problem by using only ready potential measurements because also, if you will use other really potential satellites, the cosmic one is the highest one. So it doesn't exist as a satellite. So we, we need to, we need to use a different kind of measurements. I have a question. If I were to, you were mentioning in this slide game. This is not that we are seeing for our needs. So the data set you're using is a limitation of record. Yeah. Well, we are trying to include the information given by a tri electron content, because we know that from the reputation we can let the company is zero and G parameter. So the point is that we can modify the parameter to match the total electron content from, which come from different measurements. So we are trying to apply this by using the precise of the determination to the electron for the values, but by the same cosmic satellite. So we are trying to match the product. By the pd. We are trying to obtain an optimized value of the art. So the energy aspect equal to the ones given by the radiation. And then we start from the other value given by radiation change it to match the total electron content by getting at the same location at the same time. And we, we are investigating that if we can, if we can calculate the parameters also for these cases where we cannot calculate it from only from radiation profiles. It's a working process. I think the question, the question was not, are you writing okay, because there is something that is in line with this question I think by Fabrizio, if I understand correctly. Well, did you try to use the old machine was derived by the topside sounder. Yes, this is one of the test. I use a lot of nice is topside sounders by using the same methodology developed here for writing quotation, but unfortunately, also the topside sounders, but topside values are not higher enough. And also we don't have enough topside sounder profile to correctly describe the RBA also different latitudes different local times and so. So, the best is that yes we try but they are not enough to solve our problem. There is another question. So, I'm not in the field. Sorry, please could you come here if not maybe you cannot be here by the colleagues. Well, I know this, this is very empirical, but do you know it efforts to make a framework and what do you, this H4 equals 10 thermal force divided by gravity force come from. Okay. To answer this question, I have some backup slides. I want to show you the link between the theoretical skeleton, which is my from plasma before the diffusion theory and the effective skeleton which is an empirical parameter that is from electronic measurements. Well, in a paper in 2020 we demonstrated that they are related each other. And then from the equation for motion for the ions and electrons in the plasma and the polar diffusion theory. We can calculate the, what is called the vertical skeleton, which gives the rate of change of the electron density in this plasma state. And then the vertical skeleton as this from theory as this mathematical formulation, where KB, the piece, the parameter temperature KB was more constant and it's the reduce mass of the ions gives the gravity if we consider only the balance between the pressure gradient. And we obtain what is called the plasma skeleton, which is KB Dp over mg. But including also the effect of the gradient of plasma skeleton and the collision with new drugs, we obtain this vertical skeleton. So this is the skeleton. Well, starting from the way top side formulation, we can obtain the same quantity. That was the light for the big liquid, which has this formulation as a function of the effective skeleton. Well, the question here is that these two vertical skeleton are linked each other. So mathematically, yes, but if you calculate the limit for the altitude of the infinity, the ratio of this quantity is 0 to 1. So the effective skeleton should tend to the curative or vertical skeleton at infinity. And the same the vertical gradients. Of course, they would be the same at infinity, but we are interested if they are the same near the peak in the top side ions. Well, by applying these two top side radiation profile, specific results coming from a cosmic profile on the left, we have the top side skeleton on the right. We have the vertical gradient of the skeleton. The points are the ones coming from the measurements, where there's a linear field of measurements and the green line is the vertical skeleton from the theory. Well, we can see that the green line approach to the effective values. And also the skeleton gradient is the last that, okay, they are equal to the infinity, but they are also very similar, just some hundreds of kilometers above the epic. So this is the last that effective skeleton values should tell us something about the theoretical values that can be done from the plasma. Just an example. On the left, we have the skeleton gradient calculated from cosmic, which is equal to the GPAR meter in the vehicle, vertical scratch gradient. On the right, the electron temperature from the satellites at about 500 kilometers. The top plot are the journal variability or different. This is not a beauty. Well, we see that on the left we have a purely empirical parameter, which is deduced from the next to the measurements, while on the right we have a left and temperature which is a proxy of the plasma temperature. We know that the skeleton is strongly driven by the plasma temperature we have in the top side. Well, these two quantities and people are theoretical behavior in a very similar way for the on the system variation. Of course, this is on the premise us, but it allows that the empirical parameters has a very strong connection with theoretical with physical parameters that can be used in the theory. And so we are trying to find link between empirical and theoretical parameters. If there are other questions. No. Okay. If you have any questions, we can conclude the seminar we think again Alexio, the audience online and here in prison. And thank you very much. Thank you. Thank you.