An altimeter operated from a satellite is a radar that's sends a vertical pulse and records the echo once the signal goes back to the antenna. So with the detailed analysis of the form and the time when this pulse has been received, the radar is able to determine the very high precision. What's the distance between the satellite and the ocean surface? This is a general scheme of what happens here. The altimeter is measuring this distance from the satellite to the ocean surface, but what we are, in fact, interested with is the shape of the surface with respect to some kind of reference. So we use what is called a reference surface, in this case, the ellipsoid that describes the shape of the earth. Then we have to know very accurately what's the position of the satellite with respect to this reference to be able to subtract the measured made by the satellite. This way, we have what's the surface of the sea? To do these, it's very important first to have a very accurate measurement of the satellite position, of the orbit. This is something that has been evolving from the first altimeters that we're operating in the late '70s that had the precision of the order of one meter until the last altimeters that can be able to determine the orbit of the satellite. We seen very few centimeters. In fact, this is not the altimeter what is determining the orbit. There are other measurements that are providing the orbit of the satellite. With such precise orbit and considering also other effects, like that propagation through the atmosphere, et cetera, that modifying the propagation of the signal, this is how we are able to determine a measurement of the altimeter and as a consequence, the sea surface height with an accuracy of a very, very few centimeters. What is the surface height that an altimeter is measuring? So what is this distance from the reference to the top of the ocean? The signals that are included here are first of all the geoid. The geoid is a surface on the Earth that is shaped depending on the differences on gravity. The ocean surface is also following the bottom of the ocean because of the distribution of the different masses, the rock masses on the bottom. So what do we have here is the geoid. The geoid is something that has a variability of the order of 100 meters. On top of the geoid, we have variations of the oceans surface that are due to the dynamical processes, for example, currents, eddies, effects of wind, etc. This is something that is of the order of two meters and has two components. One steady component is something that is constant along the time, for example, the effect of big currents and also variable components. These variable components can be due to the effect of wind, to the moving currents, etc. Then on top of this, we have to consider also that the surface of the ocean is affected by tides. The tides have an oscillation of the order of few meters depending on the location. Even on top of this, the ocean surface is affected by the atmospheric pressure. Where we have higher pressure, the surface is depressed. This is what is called the inverse barometer effect. Then we have geoid that is the one that produces the higher deviation with respect to the reference. Then we have the rest of the effects that include what we consider, the dynamic information we're interested with for the ocean, and then what somehow can we called noise, due to the tides and the effect of the atmospheric pressure that we would like to remove from models or from additional information to have that oceanographic information we are looking for. This is a map that one could guess it's a map of the bottom of the ocean. No, this is not this. This is a map of the ocean surface without correcting for the geoid. This indicates that the main component in the ocean surface is due to the geoid. So the geoid is reflecting the ocean bottom just on the surface. So when we analyze altimeter signal, what we have is something like this. This big differences are due to the geoid. If we are able to remove the information on the geoid, what we will have is the information that is related to ocean conditions. In this case, we have a range of four meters in this portion of the signal. The problem is that, in general, it's very difficult to have a good description of the geoid. So if we want to have a very precise information, we cannot remove from the signal, something that we don't know precisely. So the solution, let say the trick that has been used, is to remove not the geoid that we don't know but to remove the mean signal after a long time of recording altimeter data. This is what we call the mean sea level. We remove the mean sea level and what remains is the sea level anomaly, the differences with respect to this mean, the problem is that if we are in a region of the ocean where the steady part of the dynamic topography is important, when we remove the mean, we also remove this steady part. So we just obtain information on variability with respect to the main current. In this case here, we have removed the mean sea level. So then the variability that was of the order of four meters now is the order of 30 or 40 centimeters. This is the signal, the blue part that we are interested with and that after some smoothing we get this red curve. Recently, there have been a couple of satellite missions dedicated to measure the gravity of the Earth. That is, to obtain the required information on the geoid. One of these missions was GOCE, a European satellite that was launched in 2009, and during four years, it was measuring that geoid everywhere to building maps like this one where the different colors indicate different takes of the geoid. This is with a resolution of one to two centimeters if we are looking at scales of just 100 kilometers. But if we look at scales of 1,000 kilometers, the accuracy is of the order of 0.1 centimeter. This way, we start now having precise information from the geoid that we can remove from the altimeter signal and then obtaining the full dynamic topography. The main application of altimetry in oceanography is the capability of deriving the geostrophic circulation. If you remember from the previous module of this course, geostrophic equilibrium is reached when the Coriolis force balances the pressure force. This way, we can have an ocean surface that is not flat, and that intensity of the current if will look from above is something that can be computed in a way that we have in one side light water that usually corresponds to warm and fresh, and on the other side, we'll have dense water that is cold and saline. This way, if we have information on the inclination of the ocean surface, we can infer the velocity of the geostrophic current close to the surface. That is in the upper ocean layer, and this is illustrated here. We have here the shape of the ocean's surface in one case of an anticyclonic gyre. If we cross, that means if a radar altimeter is crossing these structure along this line, the shape that is measuring is something like this, let's say, a bump like this one, while if the altimeter is crossing these structure, not by the center but to one of its sides, the signal is much less. Sorry. The signal is here. In one case, and in the other case, from the information of the ocean surface, that is of the ocean topography, we can derive the geostrophic current. In this case, as it can be seen in these arrows here, the current is going in this direction in this side to the other direction the other side when crossed by the altimeter line and same for the other one but with much less intensity. Until now we have seen that with an altimeter track, we can compute the velocity at the surface but perpendicular to these track. When we have several altimeter tracks like in this image here, we can compute for sure the velocity in one direction or in the other direction, perpendicular to each one of these tracks. Then through an analysis, in fact, some kind of procedure that mix these information from all the tracks, we can build two-dimensional maps. So from measurements along straight lines, we can derive maps of the structures in the ocean surface that are directly related to ocean currents. This is a representation of the surface velocity field. For sure, depending on the position of the tracks, we'll have better representation of the velocity field. Close to that tracks, the information will be very good. Far from the tracks, we are extrapolating and the information will not be so good. But for this, an important aspect is that when we have more than one altimeter, if we have several satellites with altimeters operating simultaneously, we can have a much better coverage. In this case, this is the Mediterranean Sea, and this was in 2004. But at that time, we are lucky of having four different altimeters working in parallel. So here in the image, we see with different colors that tracks of all these altimeters. As much altimeters we have, we have a more dense coverage of the area, and the velocity maps that we are able to derive from here are more accurate. See this example here. This is a map derived from Jason-1. This is an altimeter that had a repeat cycle of 10 days, which means that every 10 days, the satellite was repeating the same track, and at the equator, the separation between tracks was of 315 kilometers. On the other side, we have Envisat, another altimeter, where the repeat cycle was longer, but that means that the different orbits were separating more slowly one from the other. That means that at the equator, the separation was only of 80 kilometers. These will provide better temporal resolution, this will provide better spatial resolution. This is for the area of the Kuroshio near Japan in the Pacific Ocean. When we integrate both sources of data, we will obtain a map like this one. Where the description of the mesoscale structures associated to the Kuroshio is better that the two maps originally created from the two different altimeters. This is an example of another information that can be extracted from altimetry. This is not to compute ocean currents, this is to compute the sea surface height. With an adequate analysis of the signal, we can obtain the variability at much higher frequency. This is the case of two different altimeters in the North Atlantic. Along these tracks, we can obtain the significant wave height. Here we compare what has been produced by the satellite with information coming from models, and we can see the degree of accuracy that we can work in this case.
