 So, hello everybody to the next talk here at Stage Clark. The next talk will be held in English and here is a quick announcement in German for the translation. Der nächste Vortrag wird in Englisch sein und wir haben eine deutsche Übersetzung unter streaming.c3lingo.org und wir haben das auch auf einer Folie und es wird auch eine französische Übersetzung geben für diesen Vortrag. Der wird auch eine französische Translation und eine deutsche Translation für den nächsten Talk. Und ihr könnt alles finden unter streaming.c3lingo.org und ich hoffe, dass es hinter mir ist. Der nächste Talk ist called Watching the Changing Earth. Satellite Daten und die Veränderung in der Gravitational-Field der Erde kann uns viel erzählen. Es ist besonders, wenn es so viele öffentliche Domain-Satellite Daten kommen, von verschiedenen Projekten oder vielleicht CCBi-Satellite Daten. Und wie das neue Knowledge-Finding aus diesem großen Heap von Daten gemacht wird. Das wird erklärt von Manuel in dem Talk. Er drückt Dinge an, um zu sehen, ob die Gravitational-Fields-Fields-Satellite noch funktioniert. Oder in Fancy-Words, er macht Grave-Metric, Methods und Sensoren in Geodisi. Ist das das genutzt, oder? Ich bin nicht sicher. Aber geile Scheiße, oh, das war der Sound. Hallo und willkommen zu meiner Präsentation auf den Watching the Changing Earth. Dieses Jahr habe ich die Papers für den Kongress geöffnet, um meine Arbeit und die Gravitational-Fields-Satellite zu sprechen. Der Kongress ist unter unerstaunlichem Fonds der Natur. In den nächsten wenigen Minuten will ich über Gravitational-Fields-Satellite sprechen. Ich bin über die Grave-Satellite-Mission, die die Earth-Gravity-Fields-Fields-Fonds mapen. Ich bin über die Gravitational-Fields-Fonds und ich werde gute Resulte zeigen. Dann werden wir uns dann in die Zukunft fangen. Das ist schön. Es ist eigentlich geodisi. Ich gebe Ihnen eine kurze Interdiktion auf Geodisi. Friedrich Robert Helmut defined it in 1880 as the science of mapping and measuring the Earth on its surface. And this still holds up today. It depends on your methods and applications, but he was correct. The most known profession is probably land surveying. People with colorful instruments and traffic cones. You find them on construction sites, on the side of the road. But we actually have a lot of applications, not only in geodisi, but in related fields like geophysics, fundamental physics. If you want to build an autonomous car, you need geodisists, metrology. This talk is specifically about physical geodisi, which is the mapping of the gravitational field of the Earth. And in this case specifically with satellites. So I drop stuff on the Earth, which is terrestrial gravimetry. This talk is about satellite gravimetry. Now gravity and gravitation, we usually talk about gravitational potential. This is a scalar field. Gravitational acceleration is the gradient of the gravitational potential. And when we talk about gravity and geodisi, it's usually the combination of attraction of the masses, gravitation and the centrifugal acceleration. But here we talk most about gravitation. And the potential can easily be calculated, at least according to this very short equation. We have capital G, which is the gravitational constant of the Earth, or other planets if you want to do. We have an ugly triple integral about the whole Earth. And this is basically what breaks the neck. We have to integrate about the whole mass of the Earth. We divide up into small parts and we need to know the density of these parts. So density times small volume, we have the mass of the Earth if you integrate over it. So what the density of the whole Earth is not known. So if you want to calculate the potential sufficiently, you would need the density of a penguin on the other side of the world. We don't know that. So what do you do if you cannot calculate a quantity? You write a proposal and get all the funding. This is what happened about, let's say, 20 years ago. And the result was the gravity recovery and climate experiment, or GRACE for short. In this talk we will only cover gravity recovery, so gravity field of the Earth. As we can see, these are two satellites. They are flying in the same orbit. And the main instrument is the distance measurement between these two satellites. Here we see these two satellites prior to its launch in 2002. And the scaleband microwave-ranging, which is the instrument, gives us a high-resolution gravity field of the Earth. This is a spatial resolution of around 200 km. Okay, you might think 200 km is not really a high resolution, but we have it for the whole planet and not, let's say, for Germany. And also we get the temporal variations. So for 15 years now we have each month with only a few exceptions, a picture of the gravitational field of the Earth. The satellites fly in a height of about 450 km, 220 km apart. And we see here the orbits of a single day, so 15 orbits per day. And we take one month of data to generate one gravity field. The working principle is quite simple. The distance between the two satellites is affected by gravity. So we measure the distance and then we calculate gravity. In a homogeneous gravity field, this is quite simple. Let's say we take a spherical Earth, it has only a single density. The satellites fly along and the distance between the two satellites does not change. There's nothing to pull one or another. They just move along, not changing the distance. Now we introduce a mass, let's say a mountain. This can be any mass change, a density change, somewhere inside the Earth. And the leading satellite experiences a gravitational pull by this mass. And as gravitation falls off with distance, it is stronger than the pull experienced by the trailing satellite. So the distance between the two satellites increases. Now the trailing, the leading satellite has passed the mass. And it is still in its gravitational pull, but now it's being decelerated because the mass is behind. And the trailing satellite is still being accelerated towards the mass. This means the distance between the satellite decreases. And finally, the second satellite passes the mass and it now also feels the gravitational pull decelerating the satellite. The leading satellite is feeding less and less gravitational pull and once both satellites left the gravitational influence of this mass, we will have the same distance as prior to encountering the mass. So the gravitational acceleration is a zero sum at this point. So, of course, the Earth is a little more complex than a single mountain or a single density anomaly in the ground. But this is the basic concept. Now, how do we come from these measurements to the actual potential? The formula is basically the same as a couple of slides earlier. We are still calculating the potential. It looks more complicated, but we don't have triple integrals anymore. And all these quantities in here are basically easily calculated. We start with the gravitational constant at the mass of the Earth, which we can get from a physics book, if you'd like. Then we have a couple of geometric quantities. A and R are basically the size of my Earth's ellipsoid, the major axis, and R is the distance from my calculating point. Let's say this podium, for which I want to know the potential value to the center of the ellipsoid. And then we have lambda and tetra at the end. These are the geographical coordinates of this podium. Capital P is short for the associated legende functions, also depending solely on geometry, not on the mass of the Earth, depending on the software where you want to implement this formula, it probably has already a function to calculate this. And if not, it's easily done by yourself. The formulas look very long, but they are quite simple. The interesting part are the two parameters C and S. These are spherical harmonic coefficients. They include all the information about the mass of the Earth as measured by the satellites. So we have the satellites in space, and the user gets just the C and S coefficients, which are a couple of thousand for the gravity field, implements this formula and has the potential value. So these spherical harmonic coefficients are calculated from the GRACE Level 1 B products. These are the actual measurements done by the satellite. This is the ranging information, the distance between the satellites, satellite orbits, star camera data, and so on. You add a couple of additional models for Earth's gravity, which you do not want to include in your satellite gravity field, and then you do your processing. This is done by a couple of different groups, JPL, GFZ, which is the German Research Center for Geosciences, CSR is the Center for Space Research at the University of Austin. These three institutes also provide these GRACE Level 1 B data. So they take the raw satellite data, process it to the GRACE Level 1 B products, which are accessible for all users, and then calculate further these coefficients C and S. But there are also additional groups who provide gravity fields, who calculate these coefficients. For example, Institute for Geodesy of the University of Graz, or the Astronomical Institute of the University of Bern. They all have slightly different approaches to the topic and come to more or less the same conclusions. There are countless papers comparing these different gravity fields with each other. But the user usually starts with the coefficients C and S. And then it takes a formula like the one on top of this slide and calculates your gravity value, or whatever you want. Now, I'm talking about potential, I'm talking about acceleration. These are not really useful quantities in day-to-day life. If someone told to you in Greenland, gravity decreased by 50 microgall, you have two choices, you can say, wow, awesome, or you can say, oh, no, we are all going to die. So 50-50 chance, you'd say the correct thing. So we are looking for a more useful representation of the gravity changes in the gravity field. Now, gravity field reflects mass redistributions. And the most dynamic redistribution we have is water storage. Summer, winter, more snow, more rain, less water in summer. So we express our gravity change in a unit called equivalent water height. This is the layer of water on the surface with a thickness equivalent to the mass change measured with the satellites. This is also easily calculated. This is my last equation, I promise. But this looks familiar. The last, the second half of this equation is basically the same we saw one slide prior. And the pyrometers in front of the sum is the average density of Earth, which is around 5,500 kg per cubic meter. We need the density of water, let's say it's 1,000 kg per cubic meter. And in this fraction in the middle we need the parameter k, which are the so-called Lauff numbers. Now, this is not a numerical representation of mutual attraction, but was put forward by, I think, Albert Lauff in 1911. And they are parameters concerning the elastic response of the Earth to forces. So if you put a lot of weight on a part of the Earth, the Earth deforms, and these parameters describe the elastic response of the Earth to such loading. Now we have calculated our equivalent water height, let's say for two months, in May 2002, und 15 Jahre später in May 2017, und wir just substrackt these two gravity fields, these two equivalent water heights from these two epochs. Then what we have left is the change in gravity between these two epochs, 15 years apart, expressed in a water layer equivalent to the change in gravity measured. And we can see a couple of features here. There should not be any seasonal variations because it's the same month, just 15 years apart. So we see long-term gravity change between these two epochs. And what we see is, for example, mass loss in the northern and southern ice shields, and we see two red blobs, one in northern Canada and one in northern Europe, which are geophysical processes. So this is glacial isostatic adjustment. During the last Ice Age, the ice shields deformed the Earth downward. The material in the mantle had to flow aside. And now the ice is gone, the land is uplifting and the material in the mantle is flowing back. So it's flowing back and the Earth is uplifting. This process has been going on for 10,000 years and will probably a couple of years longer. Now, how do you get your data? Everyone can get the GRACE Level 1B data, which are the observations by the satellite, like, again, ranging information between the satellite, orbits, accelerometer data, star-camera data and so on. And you can get them without hurdles at the ISDC, which is the information system and data center at the geoforschungszentrum Potsdam oder at the Physical Oceanography Distributed Active Archive Center run by JPL. And if you would like, you can calculate your own spherical harmonic coefficients for gravity fields. Or you can compare, for example, satellite orbits. They give you, with one, you integrate it yourself using your own gravity field to see if they fit together or not. You can get gravity field models, if you'd like. A large collection is at the International Center for Global Earth Models. They have recent and historic gravity models all in the same data format, so you only need to implement your software once from the 1970s to today. They also have the proper references, the papers. You want to read to work with them. These are so-called Level 2 products. So you can take a gravity field from there, use the equation I showed you earlier and calculate your equivalent water height, if you'd like. If you don't want to do this, there's someone to help you. A service called Tell Us, which is a play on words I don't want to go into detail about. They offer equivalent water heights calculated for each monthly solution from the gray satellites. This tells us a lot about the earth, if you look closer into it. In der following, I will use the monthly solutions from the ITSG GRACE 2016, provided by Institute for Geodesy at University of Graz. The previous graph I showed you was also created with that gravity model. I will not go into detail about further processing, like filtering and gravity reductions done to this, not enough time. So, here are some results. Let's start with the most obvious one, the green and ice shield, which has, as we saw earlier, the greatest loss of mass according to the gravity field. And we see here a water layer on the whole land mass, describing the loss of mass expressed as a water layer of a certain thickness. So, let's say, in the southern tip, you have one meter water layer. This would be equivalent in gravity to the actual mass lost in Greenland. But we also see that the signal is not very localized. So, it's not bound to the land mass, it's also in the ocean. This effect is called leakage. If you do signal processing, you will know this. There are methods to reduce leakage. My next slide will show such a result, but I have done no reduction to this. So, if you use my formula, I showed you, you will pretty much get a result like this. This gives you a trend of around 280 gigatonnes per year in mass loss over the whole land mass of Greenland. And our gigatonnes is also not very useful in expression. One cubic meter of water has a weight of 1,000 kilos, one ton. One gigaton is 10 to the power of nine tons. If you are familiar with ball sports, a soccer field, one soccer field with 140 kilometer high water column has a weight of one ton, one gigaton. Or if you are not a fan of sportsball, if you are more of a playing guy, the A380-800 has a maximum take-off weight of 575 tons. So, you need 1.7 million of these airplanes for one gigaton. So, this is a more beautiful representation of the process in Greenland. Done by NASA JPL. If you go to the website of the GRACE Project, they have a couple of these illustrations. They obviously worked hard on the leakage. You can see localized where most of the gravity, most of the mass is lost on the left. And on the right you see accumulated over time the mass, which is lost and which trend it gives you. Also, if you look closely in the center of Greenland, you see black lines. These are the ice flow, as determined by radar interferometry. So, we now pretty much know where ice is lost, where mass is lost. This goes into the ocean. And this would be a good idea to check our GRACE results. The mass we find missing on Earth, so the melted ice. And the additional mass in the ocean. Does this agree with other methods who determine the sea level rise? One of these methods is satellite radar altimetry. It started in the 1970s. But since 1991 we have lots of dedicated satellite missions, which only job is basically mapping the global sea surface. So, they send down a radar pulse, which is reflected at the sea surface. They measure the run time and then they have a geometric representation of the global sea surface. Now, if you compare this with the mass, we calculated, or we got from the GRACE result, calculate a sea level rise from this additional mass in the ocean. And these two systems would not add up. The geometric sea level rise is higher than just the additional mass. So, there's a second process, which is thermal expansion of the water. If water gets warm, it needs more space. In 2000, the deployment of so-called agro-floats started. These are free floating devices in the ocean. Currently, there are over 3,000. And they measure temperature and salinity between sea surface and depth of 2,000 meters. These are globally distributed. So, we have, at least for the upper layer of the ocean, how much thermal expansion there is. And what we want to see is, do these components of additional mass in the ocean, as determined by GRACE, and thermal expansion of the upper ocean layer come to the same result as the geometrical measurements done by satellite altimetry. On the left, we see an image taken from the last IPCC report on climate change from 2013. In green, we see the sea level rise as measured with the satellite altimetry in the time span 2005 to 2012. And in orange, we see the combination of additional mass as measured by GRACE and thermal expansion as determined with agro-floats inside the ocean. And these two follow each other quite, so these two graphs follow each other quite well. On the right, we see a recent publication by Chen Wilson and Tapley, the latter one being one of the PIs of the GRACE mission, who accumulated the data from 2005 to 2011, who basically come to the same conclusion. So, now, if you really don't want to do the math, there are online services who make the graphs for you. One of those is Axiom, European Gravity Service for Improved Emergency Control. If we can measure how much water is stored in a certain area, we know that this amount of water has sooner or later to be removed from this area. This can be a flood, for example, and with a mission like GRACE, we can determine how much mass, how much water is there, and are the rivers large enough to allow for this water to be flowing away. This was the intention behind this service. Oops, no, this is not the future. So, I wanted to do the live demo, but yeah, live demo did not work as expected. So, you will be greeted with this graphic. You can plot for all areas in the world. Now, the first thing you have to do is you change your gravity function. We want water heights. This is what I talked about in this talk. Then you want to look at the data set and at the bottom you see a large list of GRACE Gravity Fields. These are different groups, I mentioned, providing these monthly solutions. And so, we choose one of these groups. Then we choose an area, which we are interested in. You can freely choose one area like here, Phenoskandia, or you can use predetermined areas, for example, the Amazon River Basin or Elbe River or something like that. These areas are all over the world and you can see the gravity change in these areas. So, let's look here at Phenoskandia. And then you are greeted with a plot like this. This is equivalent water height. Even though this is a geophysical process, so we see here the layer of water, which would have been added to the region as selected. And we see a clear trend upward. Again, this is a geophysical process. This is not additional ice or water or anything. Can I return to mine? No, I cannot. So, yeah, life didn't work. So, if you want to do this yourself, I have uploaded to the FAR plan all my resources, all my links, and the Xeam page also includes the description of what is done in the back end and where the data comes from and what you can see in the various fields. Now, I want to give a last impression on the future because unfortunately, while I was preparing my abstract for this conference, one of the gray satellite was turned off due to age. It was launched in 2002, planned for a five-mission year. It survived 15 years, which is quite good. But now we have no more ranging information between these satellites. We had ranging information and micrometer accuracy, a couple of micrometer, and now we cannot rely on these information anymore. This means no more gravity fields with high spatial resolution and I'm not sure about the temporal resolution. So, the current walk, which is done, is taking all satellites, which are in low enough orbits and calculate the gravity field from their positions because everything, which is in low Earth orbit, is affected by the Earth's gravity field. So, if I take the satellite orbits, look how does this orbit change and the reason is gravity, so I can calculate the gravity field. Unfortunately, not in this high resolution we are used to. But fortunately, there already is next generation gravity field mission on its way. It arrived last week in the US, where it will be launched in late March, early April by SpaceX. You might look at this image and think, I just saw this earlier and you are quite correct. The mission called Grace Follow On is a copy of Grace, which improved components, of course, und now with lasers. We see not only the microwave ranging between the two satellites, but additionally a laser interferometer. So, from micrometer accuracy in the distance measurements, we go to, yeah, nanometer accuracy, hopefully. But the main instrument will be the microwave ranging. So, in conclusion, I hope I showed you that the gravity field can show mass transport on the surface and inside the Earth. So, this offers in combination with other methods new insights and also some kind of mutual verification if several different types of observations come to the same conclusion. None of them can be awfully wrong. And that the access to these methods are relatively easy. The data is available. All the methods are described in geodesy textbooks and the technical documentation. And there are other applications, other than, let's say, climate change. You can look into draft and flood prediction, the end-in-deusisern observation, oscillation you can predict from grace gravity field data. So, lots of work to do. So, this would be the end for my talk. I thank you for your interest in the topic. Thank you, Manu, for the talk. And I think we have time for one or two, maybe two very short questions. Please be seated during the Q&A session. Is there some questions? Okay, microphone three, please. Yeah, hi. Hello, do you hear me? Okay, hey. So, my question is regarding acceleration. What's the influence of Earth, atmosphere and other planetary bodies like the moon? And does it need to be accounted for? So, the external gravity needs to be accounted for. So, the tidal effects of sun and moon would be one of those additional models. You put into the processing of the satellite data. The Earth's atmosphere has an effect on the satellites themselves, which is measured on board by accelerometers and then reduced. And the gravitational effect of the atmosphere part of this is averaged out because we take a month of time series and the rest are also provided as extra products, at least by the Institute for Geodesy in Graz. So, the atmosphere, the mass of the atmosphere has to be accounted for, yes. Okay, microphone two has vanished. All of a sudden, then microphone one, please. Is it possible to measure changes in the temperature of the oceans or in the ocean's streams? Like, can you see if El Nino is active by just measuring the gravity, changing gravity fields? As a precursor to El Nino, as I understand it, certain regions of the oceans get warmer, its density change. And of course, this would be measured as part of Argo and it's also in the grey gravity field. There are probably papers on it. So, the extent of the last El Nino was predicted by Graz. I don't know to what extent this was correct, but... Okay, then... Good, then that's all the time we have. A big round of applause for Manuel and his talk, please.