 So, hello and welcome to this special eGee webinar on how to measure the Earth and introduction to geodesy. My name is Simon Clark, I'm the eGee's projects coordination officer. I will surely introduce the speakers, but to begin with, I just want to note that this webinar will last a maximum of one hour, with time dedicated to audience questions and answers at the end. If you have any questions, you can ask them at any time by inputting them into the Q&A box at the bottom of the screen. You can also upvote questions you think are relevant and want the panelists to answer. This webinar will also be recorded, and uploaded to the eGee YouTube channel within a week's time. Our YouTube channel is You Geosciences. So, to introduce our today's speakers, we have Andres Kovar, a postdoc at the Institute of Geodesy and Gras University of Technology in Austria. Rebecca Steffen, a researcher at the Lars Materiat, the Swedish mapping, cholesterol and land registration authority. And Benedict Sodja, assistant professor of space geodesy at BTH Zurich, Switzerland. So, Andres, would you like to begin? Hi, everybody. Thanks for this nice introduction, Simon. And let's start with the technical part of today in this webinar, which we titled How to Measure the Earth and Introduction to Geodesy. Before we start with technical definitions, I want to raise the question, what is geodesy? And we asked this question actually at this year's General Assembly in the Geodesy 101 short course that we held, and we got quite a variety of answers, starting from very technical ones, like coordinate system, satellite observations, gravimetry, but also some more general and a little bit more fun ones, like job security fun, and a lot of applications like faults, tsunami early warning, and so on. And to give this a little bit more rigorous context. Generally, when we talk about geodesy, we mean that it's the geoscience of accurately measuring and understanding Earth's geometric shape, Earth's orientation in space, and Earth's gravity field, and mass change within the Earth system. So we have these three subfields, which in practice are very closely interconnected. And each of these subfields gives us key insights in how our very dynamic planet changes. And it gives us very key insights and what, for example, we can do to mitigate climate change, for example. Starting with the geometric shape of the Earth, when we talk about this, we do not only mean, for example, the topography, so the land area, the land surface, where we, for example, would measure land subsidence as a cause of groundwater collision. So geodesy can measure if land sinks, whether it be inland, or in this other plot that I show here in the coastal areas, so we have coastal subsidence, but we also measure the ocean surface. We now have a very long time series of changes in sea surface height, which obviously reflects the sea level change that we have. The second subfield is Earth's orientation in space, and this essentially is the connection between Earth and space. So the connection between terrestrial applications and space bond applications. So if you in your scientific studies use, for example, the image of a remote sensing satellite, then you have to very accurately know where the satellite was at a given point in time in relation to the point on the Earth surface that you want to investigate. And this is where the orientation in space and Earth rotation comes into play. And finally, we have Earth's gravity field. And as you know, if we have a mass somewhere, this generates a gravitational field. And so by measuring the gravity field, we can essentially weigh things. And in an Earth science context, which things can we weigh. For example, ice sheets or glaciers. So by measuring the gravity field, we can determine how much mass the glaciated area loses over time. And the same thing, we can apply to, for example, large aquifers, so we can essentially look below Earth's surface through the gravity field and see where the groundwater is lost or groundwater aquifer is not recharging anymore. So we can weigh the ocean so we can create a time series of ocean mass change. But also look at solid Earth processes like the cosysmic mass change when we have a large earthquake. So how much mass is actually moved when to plates are displaced by an earthquake, for example. And to make this a little bit more concrete. I look through the general assembly. 2022 geodesiduation abstracts and just compile the bird cloud. And you can see a lot of the stuff that I already mentioned is reflected in these abstracts so we have obviously Earth, because that's more or less always the thing that we want to do. So geodesicization in some way. We have deformation, we have gravity with change. So we are looking at temporary changes obviously. But, and I just blew these words up a little bit. We also have a lot of applications in there. So, geodesy is always involved with quite a lot of other disciplines. So, we look at ice sheet mass change. We have observations, faults, surface deformation, earthquake sense on and with a few geodetic techniques that we have. We have observation time series that reach now 2030 years. So now we can also start looking into effects of climate change that we can see in our measurements. And kind of reverse this process with this word cloud and just look at how many are in all of the abstracts that was submitted to this year's GA mentioned geodetic techniques or core concepts like global navigation systems, or the grace satellite mission, sea level at the Archimetry, we can see that almost all EU divisions kind of interconnected with geodesy and vice versa. So to answer the question geodesy or just partly answer that I would say that geodesy is the Geoscience of accurately measuring and understanding Earth's geometric shape, its orientation in space and gravity field. And it is very densely interconnected with the whole geoscientific field. And with that, I will then hand over to Benedict who will talk about geometry. Thank you very much Andreas for the first part of the talk and some for the introduction. It's now my pleasure to tell you a little bit about geodesy and its role to determine the geometry of the shape of the Earth. Now, why should we do this. As we have seen in the first example shown by Andreas, the Earth is not completely solid and rigid. There's actually a lot going on. And the most important aspect is of course, when humans are affected, for example, in the case of strong earthquakes or earthquakes and geodesy can in this case contribute with measuring the change of deformation. And not only in such extreme examples but also for very long and slow processes, for example, the load due to melting glaciers or related to post-glacial rebound, geodesy can make very important contribution to our understanding of these physical processes. Now, how do we determine the geometry and the changes in the Earth's crust? We have several space genetic techniques that can be used to monitor the Earth and the shape. Maybe most important of these shown here would be the global navigation satellite systems, GNSS, which I will talk about in more detail, but there are also quite a few other suitable techniques such as very long baseline interferometry, which observe extra galactic radio sources, satellite laser ranging, SLR or Doppler orbitography and radio position integrated by satellite, which is the Doris system. Since we are now focusing on GNSS, I will give you a short introduction. GNSS stands for global navigation satellite systems in the sense of global meaning that it's accessible anywhere, anytime on the world, and it's also independent of weather. It can be used for navigation, which maybe most people know about. For example, you can determine your three-dimensional position and the change in position for the velocity and it can also be used for precise timing. And yes, it's a satellite system, which means that all the services are provided by a lot of satellites that orbit the Earth. And yeah, there's an unlimited number of users that can access the signals from the satellites. In the case of GNSS, maybe most people are more familiar with the term GPS, which is just the American system, but nowadays also the Galileo, the European system and the Jonas, the Russian system and the Baidu, the Chinese system are available. So by finding the observations of these different global navigations at light systems, you can get even better accuracy of your determined positions and velocities. And yeah, since we have an unlimited amount of users that can use these techniques simultaneously, it's also possible to put up a lot of geodetic observation stations. And nowadays, there are at least 20,000 geodetic quality GNSS stations available, which means that for these stations, we can determine their positions with an accuracy that is at the low millimeter level. Now, in the next few minutes, I will show you some examples where GNSS can be used in different countries and parts of the world to measure certain geosynthetic phenomenon. For example, if we start in Sweden, and we have a station here called Red Zero, and yeah, our GNSS system is in place to send the signals, which can be then recorded by the station. And we do this over long time spans, you can get a time series of the station positions and how it changes over time. You can get then a three dimensional coordinate time series like in this pot shown, for example, for the east to the north and the up component. And then you can see actually strong movements. First of all, in the horizontal coordinate components, you can strongly see the impact of plate motion. And this can be up to several centimeters per year and will be visible in most GNSS time series that you are dealing with. Quite interesting for the station in Sweden, however, is the strong change in the up component for the vertical. And here, this part is related to the post-racial rebound, which Rebecca told us more about within this webinar. We can also put a station at another place on the earth, for example, in New Zealand, and the time series might look completely different. Here, we have another very striking phenomena, namely a big jump in the time series. This is, in this case, related to a very strong earthquake, which happened in the year 2016. Calipura earthquake, magnitude 7.8, and you can see that the coordinates, primarily the horizontal coordinates have been affected significantly by offsets of more than half a meter. Since we are already speaking of earthquakes, this is, for example, also visible in Japan, where there's a very dense network of GNSS stations available. And this animation shows the deformation due to the Roku-Oki earthquake during the year 2011, which caused an offset of multiple meters actually in the horizontal component. And you can see the ground deformation lasting much longer than during the earthquake. It's also then causing an aftershock here, which can be well observed by GNSS. Maybe a very different example, a completely other part of the world would be here in Hawaii. This is an example of using GNSS to monitor the volcanic volcano and the related deformation of the surface of the earth due to the changing magma within the volcano. And you can see that there are ground deformations away from the center of the volcano, which can be quite interesting when monitoring the characteristics and the state of the volcano and if there would be the potential of future eruptions. Yeah, finally, an example from California where GNSS can be used to monitor seasonal deformations due to the load from snow and water. You can, for example, see that during the winter months, there's a lot of accumulation of snow and then also water while in the spring and summer. All these melts and this load is then removed and as a result, we can see strong uplift in the vertical GNSS components as you can see in this plot. We have uplift of several millimeters up to a centimeter in California due to this changing hydrological conditions. So these were some examples from specific locations all over the world. If we put all these stations together and compute their positions in a joint manner, you can actually determine a global coordinate system, which is very important for jealousy and many different applications. And we refer to this coordinate system as the terrestrial reference frame. In this plot, you can see the changes of these coordinates, the linear changes as in velocities, where you can clearly see the plate motions that drive these very strong motions that you see. The terrestrial reference frame defines this coordinate system in terms of where the origin, the orientation and the scale is based not only actually on GNSS data but in combination with the other techniques that I mentioned earlier, for example, very long line interferometry, the laser range and doors. And overall, it captures very well the long term behavior of stations all over the world. So why do we actually need this terrestrial reference frame, there are quite a few applications, for example positioning to make sure that all these techniques that we are using work that well. These are for love system monitoring, but quite an important application also for climate would be for sea level monitoring. And there the origin of the reference frame is very important since if you would make a change or an error in the sea coordinate of the origin of the coordinate system has been shown that this dramatically affects the sea level that has that would be derived from these machines. And yeah, this would result, for example, this one centimeter change in sea level difference at the millimetre level, which is already the level where we want to determine at which we want to determine this signals. And if you want to find out more about terrestrial reference frames, I can only recommend you to come back next week. We will have to talk by several years on also this seminar series. But yeah, in that context, I should find it also mentioned that the reference frames also supported now and officially recognized by the United Nations has been a resolution on terrestrial reference frame in order to maintain them and improve them into the future. And with that, I will finish the geometry part and over back to Andreas. Now we move from geometry to gravity and mass change. And in the context of jealousy, when we talk about gravity or Earth's gravitational field. We typically talk about the physical shape of our planet. It reflects Earth's mass distribution. So, as you all know from your first physics lectures. If we have an aggregation of mass particles, we do have a unique gravity field that is generate and Earth is nothing different. It's just a very large aggregation of mass particles. And since the gravitational field reflects this mass distribution and changes thereof observing the gravitational field and essentially gives us data of a key quantity for many Earth and space sciences. So we look at the gravity field model. So essentially, once we've gathered all our satellite data, our terrestrial observations and so on, put that through our processing chain, we end up with a gravity field model now as we call it. And these typically do have some static components or a mean field, but also temporal changes that we see. And this particular model, for example, contains a long-term trend. And just by looking at this trend, we can see that our gravity measurements very well reflect geophysical signals. So we can see these large red blobs in Antarctica, Greenland and Alaska. So we see in our gravity measurements essentially the ice mass loss that we have in these large ice sheets. If we go to seasonal changes, so to the middle panel, there we can see the annual amplitude of the seasonal cycle. And this is dominated by terrestrial water storage changes, so by hydrology essentially. We can see, for example, the Amazon basin, or if you look at the bottom plot in Southeast Asia, we can see the Ganges or the Mekong basin where we have these large mass variations that we see in the gravity field. And if you look at the static, so the non-time variable part of the gravity field, we can see quite a lot of topographical features like deep sea trenches, so the Mariana trench, for example, we see island chains like Hawaii, but also see large mountain ranges such as the Himalaya or the Andes. So a static gravity field gives us information or constraints for the structure of the Earth. If we go back to this time variations, the changes that we see in Earth's gravity field are driven by geophysical processes. And in turn, if we continuously measure and monitor gravity field changes, we can get quite a lot of important information about these processes. I've just plotted four examples here. This is obviously not a complete list, but I've already mentioned in the introduction ice sheet mass loss. But we can also look at, for example, hydrologically extreme events like flooding through gravity field, ocean currents, and solid Earth processes like earthquakes or geoshares aesthetic adjustment, which we'll back up and talk about later. We have a few tools on how we can monitor and observe the gravity field and its changes, and two of the most important tools we have for that are the satellite missions grace, which was an orbit from 2002 until 2017, and the successor mission grace for on which was launched in 2018 and is still in orbit and giving us very good data. I've mentioned in the beginning that essentially geometry gravity field and the orientation of the Earth is very much interconnected with integral geodesy. And we can see that here because the primary measurements that we actually use to determine the gravity field geometrical ones. So, in these two missions we use GPS tracking so the position and velocity of the satellites, as well as very precise intersatellite ranging measurements to determine gravitational changes from changes in the satellite motion. But we cannot observe gravity is the gravity field solely from space. We also can put gravimetry gravimeters for example, directly on the ground, which you can see in the left picture, we can mount them on ships and airplanes or helicopters for example in these data. Also widely used for geophysical applications. Why do we have such a variety of different sensors for observing the gravity field. Because one caveat that is present in geometry is that the further essentially go away from a surface, the lower the spatial resolution, I get. So essentially if I move away from this surface, I only see a smooth version of the gravity field. So for extremely localized phenomena, I would use terrestrial geometry, but if I want to look at large spatial scales, I can use satellite geometry. And if I use satellite geometry, this is the advantage that I also get higher spatial coverage. Essentially, grace and grace for long. These two satellite missions I talked about, give us a clover map of gravity field or mass changes every month. And we can essentially put these one after another. And so we get a time series monthly time series of almost 20 years at the moment. And the question is now we have gravity measurements and more most geophysicists interested in mass change because I want to directly see how much ice is melting or how much ground water am I losing. And that's a little bit tricky, because essentially the mass and the gravity field is not unique. So you can have infinitely many mass distributions, which explain the gravity field that we observe. But we kind of if you take the information that we have about the geophysics that are gone in the system, we can essentially restrict our solution space, because we need that. Okay, most of the mass change that we expect happens on a very small, very shallow layer around the surface. And if you think about the geophysical processes that we observe atmosphere mass change, oceanic mass change or the hydrosphere to happen at or around a surface which is very shallow compared to the complete radius of Earth. So we have this direct connection between gravity field and the mass distributions at Earth surface. And with that we can now do very, very cool things. Because one of the advantages that we have with crematory is that we measure the integrated mass change. So we don't have a single geophysical process that we specialize at. We measure everything that goes on. And if our measurements contain everything, then we also can start looking at each individual sub process. And essentially, our measurements are the sum of atmosphere, ocean, hydrosphere, ice sheets and so on. So if we want to look at, for example, water storage changes, so hydrologically applications, we can take our measurements and just subtract everything else, if we have a reasonably good idea what's going on in the other subsystems. For example, if I want to look at solid earth processes, I can do the same approach. Just take the grace mass change, subtract everything else, and I can look at for example, the mass changes that an earthquake has caused. And this very, this versatility that gravimetry or satellite gravimetry gives us is very much reflected in how much this data is used, and how important it is to geoscience. So let's look at some stats from the Grace Telos website hosted by NASA, and grace and grace for on the second most cited NASA satellite mission in the intergovernmental panel for climate change assessment report six, and it contributes to 14 essential samples of Gecos. And another very almost surreal start is that, as of August this year, and there are five over 5000 publications that involve grace or grace and grace for on data, which JPL tracks. So I guess they're much more. And with this very optimistic outlook on how much grace can contribute to geosciences as a whole. I will then think. I will hand over to Rebecca. Yes. Thank you, Andreas and Benedict for giving me a good introduction into the geodesy. So I'm now showing you an application of Geodesy, especially classical as a static adjustment. This adjustment is operated as GIA. And you see in this word cloud of GA. There are many poses as related to GA. We, of course, have class as a static adjustment, but we also have sea level change. We have viscosity we have lotus fears or many poses as from different geoscientific disciplines are affected by GA. But what is GA. So GA is response of the solid earth to ice mass changes. So if you, for example, have an ice sheet here, and if we melt this ice sheet, we get a response of the solid earth in form of an uplifting. And in addition, we get a response of the sea surface because the melting ice or the ice sheet itself is in gravitational attraction to the water. And when we decrease the mass here, we also release some attraction so the water decreases as well, which also in turn means if we get a new sea surface, we also induce subsiding or uplifting beneath the sea surface as well. So now it's the go on and have no ice left in the lower graph. We have an ongoing rebound because the earth is not entirely elastic. It responds in the first part of the years to respond to elastically, but with mantle being whiskers Lee, the other time dependent process involved. So when we have no ice left on the surface, we still have the on rebound ongoing in the area where we had an ice sheet. This also means that we have an additional adjustment of the sea surface. And because we have the mantle, something something has to fill them gap in here where we have uplifting, we have mantle flowing in, which also means that the bulge developed here doing the classification is collapsing. So this is a general concept of GA. And now we can observe this with different disciplines we have geodetic observables, where we have 3d land motion observed by genus s and Inza and satellite technique. This was explained by Benedict already. We have cavity changes found base and satellite data. We have changes in the earth rotation parameters, for example, to polar wonder, polar motion and length of the day. And we have also can see relative sea level changes, for example, from tight gauges and satellite at imagery data. In addition to this we also have parallel observations, more geological observations. Again, relative sea level, where we observe the shoreline deformation, lake limits, tilting and seismicity that we have seen in the past. I don't want to focus on these I want to focus now on the geodetic observers today. So from Benedict's talk we have the 3d motion of the areas where we had or have ice sheets. For example, in northern Europe and Canada where we had large ice sheets, about 20,000 years ago. And also in Greenland where we still have large ice sheet line. We still in all areas we see uplifting. In Finland, Scandinavia, northern Europe we have up to 11 millimeters per year of uplift in a city called, around the city called Umeå and north central Sweden. And it's a bit larger uplift in Canada, it's up to 40 millimeters per year. This is mainly because we had a larger ice sheet here as long ice sheet had a larger area and also larger sickness than the northern European ice sheet. And we also see land uplift in Greenland because Greenland ice sheet was much larger 20,000 years ago than today. So we of course in the time-dependent process of the viscous mantle also in the Greenland observations. In addition to the vertical land uplift we also see a horizontal motion as shown for the northern European data set and the velocities are going out of the uplift maximum. Not only GNSS can contribute to observing land uplift induced by or due to GA, we also see it from INSA where we measure also the change in height and the change in the east-west direction. This is an example for Iceland where we also can clearly identify the uplift happening due to the recent ice mass losses on the Iceland glaciers. As we already saw from Andrea, so we have gravity changes also affecting the solid earth, we can see how solid earth are moving, so we have the satellite data from GRACE, now from Fenuskendia, to the northern Europe and for the northern America and we see a positive signal which is due to the mantle inflow. So it shows us more how the future is going on whereas the GNSS is giving us a more today snapshot of the land uplift. We see a similar signal when we use current data, for example for these data sets absolute gravity data will obtain for several years. So we have here a time series for station Vasa which is about here in Finland and absolute gravity was measured several times over several years, you see a long time span from before 1990 until 2020. And so we see a decrease in the gravity change compared to the GRACE satellite where we had a positive gravity change. We now have a negative gravity change also seen for the entire area using several absolute gravity observations. This is due to that the land is uplifting so the station on the surface is getting further away from the center and so further away from the gravity midpoint. Then we have the changes in the Earth rotation parameters as one of the GA observables we have for example to polar wonder and polar motion. These are observed by several satellite systems so what Bennett already mentioned via API doors and SLR I used to look at look at the Earth rotation parameters and what does it mean why does it change when we have an ice mass changes. We have the rotation axis of the Earth shown by this black line and when we decrease the ice mass the rotation axis moves because the shape of the solid Earth changes and the GA changes. And this is also observed over many years meanwhile and we see a change in the rotation axis wandering around towards the Hudson Bay in Canada. But this observed change in rotation or observed polar motion cannot be explained only by GA. We also need to include other processes and for example geodynamic processes, geodynamic mantle correction models also help us to explain the entire Earth rotation parameter changes. Another parameter is the length of day and again because we distribute water and ice masses, we get a different we get shorter and longer days. For example, when we have built an ice load during a glaciation towards along the poles. This is similar to when a figure skater closes gets the arms closer to the body, it spins faster than when the arms are wide. And opposite happens when we melt the ice sheet, we get water towards a crater. We get a bulge around a crater and it's similar when the figure skater spins the arms outside and then it's slower than having the arms closer. And this was an also observed can be still observe is a change in length of the day. And the last genetic GA observers relative to sea level. This can be observed by tight gauges. Tight gauges exist for several hundred of years in some areas of the world. And why we see here from 1880 to 1889. We had only a few stations and these were increasing remarkably in the last 100 years. But you see that most of these stations are located along the northern hemisphere. Also seen the graph appear most stations are not hemisphere why we only have a few in the southern hemisphere, of course would be better to get a homogeneous data set with stations. All areas in the world. But how does the state get station results look like. So we get a change in water levels tight gauges measuring the change in water level you can exclude some or we can calculate out some. Sickness for example ties. And then you can look at this trend over many years. And this is for Stockholm station in Sweden, one of the oldest station, and you see a clear decrease in water level, which is not really a decrease in water. It's a land uplifting and that's why waters get getting further away from the from the land basically. The line, the trend line shown here is the induced GA or this is a GA uplift. And the deviation from the water level from this line is showing us that we have no additional sea level increase happening in the area. And this can be done for several stations as I told you already, and you see them. This is the GA effect in most of the station and you can correct for this and then you can analyze these data that with respect to other processes. As I already said, we have only a few tight gauge stations available. We would like to have a complete map of how the sea level is changing. So we can also use satellite at imagery a genetic method as well. And then we cover most of the oceanic area and combines them with tight gauges station and GPS data, and get a complete view of sea level change. And this is shown here we have and the sea level change obtained from at imagery. If you now take even the ocean mass change by grace, which is ice melt coming into the ocean. We can then see the straight changes, which of course and isn't a valuable result for ocean aquifers to study the temperature differences and salinity. We can now take all these observations. And now we want to model GA because when we model GA we can say something about the future how Glenn uplift is going on in the areas where we had ice sheet very still have an ice sheet. How does he see a model look like so we have two inputs we have an ice and ocean loading, and we have the earth structure we model entire earth. And then we can run such a GA model and get several outputs which is and compare again to the observations that I showed you before. And we can vary the Earth's parameters there are many variations possible. And in addition is that how the GA or how the solid earth responds to the ice and ocean loading has an effect again on the ice and ocean loading as well so we have to iterate several times to get the realistic result. GA models unfortunately have some uncertainties. If you look at genus s velocities. For today we cannot from these alone we cannot identify if we had a large ice loss or small ice loss depending on what time it was, or if we have a large ice loss and a weak earth versus a small ice loss and strong earth. An observation of genus s data today wouldn't tell us a difference so we also need some logical data to give us modifications. In addition, if you have the one day uplift rate versus a 3d uplift rate this means on me that one day is an homogeneous Earth model with only variations and steps, while a 3d model is lateral heterogeneous Earth model way more realistically including seismological observations. We did see that there is a difference in the uplift rate. And we have to explain our uplift rate that we observe, of course with 3d models 3d Earth models. Another factor is that GA models can have different rheologies and different rheological parameters. And one is the Poisson ratio giving us information about the compressibility of a model. And there are two options and these two options give us can give us complete different results in horizontal velocities. So we have geodynamic parameters as much as the parameters which are important to include in our GA models to explain our observations or genetic observations better. And GA is for some it's what they want to achieve, what they want to look at, for some it's only a noise basically. So what Andreas already showed we can have a graze trend and if you now take a GA model output we can look at the differences. And these differences can be taken into account when we look at the atmosphere changes, ocean changes, hydrological changes, ice sheet changes or solid earth without GA. So you saw that GA involves many disciplines, which EGU divisions deal with GA. Of course it's geodesy that we have observations, but there are many other disciplines in EGU looking at GA as well. So we have genomics because we are doing the modeling, the choir science is because we have the ice sheet we need, ice mass balances and so on. And with this I would like to wrap up our geodesy webinar. So you have seen that geodesy can help you to study mass changes with grace. For example, ice lows, groundwater depletion, earthquakes, GA. And we can also look at position changes with GNSS, similar observations as above but also landslides and other sea levels as well. And geodesy provides a global trusted reference frames for accurate sea level monitoring, which is needed to look also into the future. And of course there's also much more. And with this I already hand over to Simon. Thanks so much for that. We have a short amount of time for questions as a few I can go through the Q&A box. And the first one I want to ask is, which areas are involved in gravity measurements? And how are they handled? I think that's the open question. And I want to jump in on that. Yeah, so I will try to answer that very broadly, because the measurement errors that we have very much depend on the system that we use. If you think about satellite gravimetry, then the measurement error that we have in satellite altitude, then that's a purely geometrical error, because we use in grace and grace for long. We have GPS measurements and these inter-satellite distances that we use. And this propagates then into our gravity fields. The key fact of satellite gravimetry is that this error, the measurement error gets exponentially higher, the smaller spatial scales we look at. This means, essentially, if you look at the gravity field level, we can treat the satellite gravimetry measurement error with a low pass filter. So filtering grace gravity fields with a low pass filter essentially gets rid of most of the observation measurement errors that we have in there. So let's go down to, for example, you have one gravimetry. There, the system is quite complex because you need to track the state, the position, the velocity of the acceleration of the plane that you have, you have to take care of all the vibrations. And I feel that's a very much sensor setup to sensor setup approach and how to deal with the errors that you have there. So I don't, I can't give a concrete answer for that. Thank you. Just speaking of grace, I'll quickly move on to another question of what is the output of grace itself. So there are, there are, in the grace community, we talk about data levels and for the user, the most interesting data levels, the data output levels that we have is level two, which is gravity field. So here you have potential some meter squared per second squared, and then you have level three data, which is already converted into mass change at mass change is typically expressed in equivalent water height. You can think of it as a shallow layer of water around the surface, and you have to increase this layer by one centimeter for the layer and reduce it one centimeter there to explain the gravity field that we measure. So thank you. Moving on from that you mentioned gravity field models. What advice to have someone who wants to carry out an internal accuracy assessment for this models. There is a don't think there is a straight forward answer to that. One advice that I would give is, if you have terrestrial gravity data available. These are a good starting point to evaluate satellite models, for example. That's what we do when we, when we produce such a gravity field model to get a feel of how good it performs. When we talk about the mass change lever, then you have a little bit more options because the data there is a lot more varied. You can use gnss displacements, essentially loading observations, which can be very easily correlated with the mass change that they measure from grace. So these would be the two approaches that I would take. And so much for your answers. I think we have time for just one more question. I was looking at this pops more application focused. Can GIA for example be used to measure sea surface geographies or other such applications. That's too specific. They worry about it. Well, I mean GA itself not GA is just one of the process that if you understand it really well, and are able to model really well using all that advanced methodologies. That's a good correction model for all other disciplines at the end. That's the only way how GA can you contribute in this direction. Excellent. Thanks for that answer. And maybe one final question before I wrap up. Last question here is how do I understand the scale parameter in terms of the threshold reference frame. Yeah, you can imagine like, if this would be the size of the earth and you would change the scale, then you would basically increase the size or increase it. So it's basically a change in the height of all your observation stations. And since the height is quite delicate parameter determine, which is typically the most errors. It's actually quite challenging to determine the scale accurately. So there are techniques that are better suited for that, for example, very long based on the geometry and father techniques like genius as you would need really precise knowledge about the face centers of your antennas. So it's quite important, especially for a sea level change. Because this is also related to the height. But yeah, it's still a lot of effort being put to determine the scale very precisely. Excellent. With that, we're just about to run out of time. So to wrap up this webinar, I want to thank our speakers, Andreas, Rebecca and Benedict for joining today and delivering such information. I thank all the attendees who came today, listened and asked questions.