 Welcome to the Distinguished Lecture today. Just a little bit of background. Professor Anthacabi is one of five distinguished scientists, researchers, engineers who were selected as part of the Neil Armstrong Distinguished Visiting Fellowship. This was a program that was put together for the Purdue 150th anniversary celebration activities. And again, the intent is to bring distinguished researchers from around the world to work with Purdue faculty over a three-year period. I'm very happy that Dara was selected for this. And my goal in this collaboration is that we can build a kind of a stronger connection between the engineering side at Purdue and the science side and the agriculture side in applications of Earth remote sensing. So with that in mind, I'd like to turn this over to Dara, who is a named professor at the MIT School of Civil and Environmental Engineering and project scientist for the Soil Moisture Active Passive or SMAT mission from NASA. All right, so I'll turn it over to Dara. OK. Thanks again for everyone for coming. So what I'm going to talk about is the Soil Moisture Active Passive Mission, which was launched in 2015. So it's four years of data right now. And the question is, what have we learned from the data and what we promised to learn from the data? And this is really a presentation of the work of some of my students on postdocs. Some of them have moved on. That have one way or another worked on this particular project over the last few years. And to begin, let's just look at what is in the contract between NASA and the implementation agencies, institutions, JPL, Goddard, and several others. So there's a contract with NASA headquarters on what this mission will deliver. And the five questions that you see up here are five areas or the areas that are specific promises to NASA that the data that this mission collects is going to be used for and is going to have a return on their investment. So this is directly out of that several page requirements letter. They fall into two groups. One of them is basic earth system science. And it has to do with understanding processes that link the water, energy, and carbon cycles. And I get to what we mean by that in a second and why those three cycles in a second. But the link between those cycles, not just the cycles themselves. And the second grouping of returns, which was unique for this class of NASA missions, is that there's actually, we promised, several applications returns. So data from NASA mission going to operational agencies like NOAA, USGS, Environmental Protection Agency, and so forth. And NASA is an exploration agency. It's a technology agency. So it has no mandate to have applications returns. But obviously, since it's funded with taxpayer dollars, they have to convince Congress to fund NASA missions. If that aspect exists, it's a major plus for NASA. So there was no mandate. But we promised it with this particular measurement. So as the name suggests, the mission is about soil moisture. And this was the first NASA mission dedicated to anything in the land surface hydrology. And soil moisture is something that we do have in C2 measurements, but they're so sparse that they don't produce fields or maps. So this would be the first mapping of this variable as best as we can with the existing technology. So based upon years of trial and with airborne measurements and theory and ground-based measurements, it was clear that the way to make these measurements is to see right through the atmosphere and see as much as possible through canopy, because that's where the interesting soil moisture is. You just don't want to look at bare grounds in deserts. You know what the soil moisture is. So you want to go through the atmosphere, not have atmospheric vapor and temperature or clouds or raindrops affect you, because you want to see the surface and go through vegetation. And also as much as possible, sense a good chunk of the surface soil. That means that you want to be at very low frequencies in microwaves. So L band is around 21 centimeter wavelength. And that has those desirable properties. Now this is something in lower orbit. So it's an antenna that would focus on the surface. So in order to map effectively, you have to not only go around the earth, but rotate around yourself to have a swat, a wide swat of measurements. So that means that the antenna has to be rotated at some speed, in this case 14 RPM, to give a global coverage every two to three days. So what we have is a very low frequency microwave radiometer and radar at the time. That means you have to have a large antenna to focus on the surface. So this is a six meter dish antenna. So in order to launch it, it has to collapse like an umbrella and open up. So it's made out of a mesh, metal mesh. And it opens up and stiffens and is basically a solid surface at 21 centimeter. And it has to rotate. So you're rotating a large offset mass at 14 RPM. So the mechanics of keeping this thing stable was one of the risks that we had to overcome through simulation studies and such. And that's what took so long, because no one would believe you could have a stable spacecraft with such a large mass rotating at 14 RPM. So these are what we promised, again, link between the water, energy, and carbon cycles and applications, specifically in weather forecast, drought, and flood prediction. A little more about the instruments. The system has a feed that was shared by two instruments, a L-band radar and a L-band radiometer. And the radar was supposed to give us low sensitivity but good resolution. The radiometer is low resolution but high sensitivity. That was the primary instrument. The radar, we unexpectedly failed very early in the mission. It failed after two months, which is very unusual. You either fail within the first few minutes because you're not supposed to be there, pull the design, or you fail after years of just wear and tear. So failing after two months was rather unexpected. But the main instrument, the radiometer, has now over four and a half years of data. And we were forced to look at the radiometer data much more carefully in order to maximize its use. We were kind of relying on the radar a lot. So now we have to do it all with the radiometer. So actually, we learned a lot about sampling and over sampling. Conical scan at a constant incidence angle so you don't have the confounding influence of incidence angle on interpreting the data. 6 a.m., 6 p.m., it's on synchronous orbit. At 6 a.m., the temperature profile between the soil, vegetation, and air is isothermal, which is advantageous. Launched in 2015. We have this map handbook that says all about the system and how the design was done. It's online. So back to these, again, five science questions. And let's just see what we have learned after four and a half years. So I want to focus on three basic questions today. And from a NASA mission point of view, these are historical loaded questions. The first one is, did we deliver on our primary science promise? So did we actually, with the data, deliver on what we promised the data would say? So that's the first question. The second question is that this is just one satellite mission. And it's mapping the world in every two to three days. How much of the water cycle do we actually see? The sort of the loaded question here from NASA perspective is that, is this a science mission or a tech demonstration mission? So a lot of NASA missions, as the agency mandate says, are technology demonstration and exploration. But are they, if this is a science mission, is this also serving that role as well? And the last one is that we experimented, including societal benefits explicitly in our project from the very beginning that we delivered on those promises. The research to operation R2O transition is in notoriously difficult effort in general. So what have we done with that? So going back to the first of those questions, what have we exactly learned about the coupling between the water and engine and carbon cycles? And the way I'd like to sort of make a visual of this is that these three cycles, water, engine, carbon, are the three main metabolic cycles of the Earth system. The main metabolism of the climate system is a result of these three cycles. And they are very strongly coupled together. And the way they're linked means how anomalies or perturbations in one translate to another. So if you have a perturbation in the energy cycle, how it reflects in the water cycle and how it reflects in the carbon cycle are the result of what is the rate of linking between these or what is the diameter of the gears and the size of the cogs. And all Earth system models, from new macro weather prediction to climate projections, decadal climate projections for global change, these are all Earth system models. And all Earth system models include at least these three cycles. And it includes the closure relationship between them, the link between them. But there is no protocol or accepted database for how these linkages should behave. Every modeling center, there's about dozen, dozen and a half modeling centers around the world that can run these very expensive numerical models. Each one has developed the linkage between these three main metabolic cycles on their own of what they believe was the right thing. There's no standard protocol. As a result, there's wide variations in how they do it. And as a result, they get different results when they force the same perturbations on their Earth systems. That's a major source of uncertainty. Enhanced reliability of Earth climate change projections, which is a major problem, as you can imagine. So how are these cycles linked? What metrics can we use to see how they're linked? It would be nice if we could have metrics that are non-dimensional, because then they're transferable among models, and we don't have to worry about units. So how the water and energy, two of those gears are coupled is we call it evaporative fraction, which is the amount of energy used in vaporizing water out of the total available energy. What fraction of the total available energy is used to vaporize water, evaporate it, versus conduct it as heat into the atmosphere? So that's a nice non-dimensional measure between 0 and 1. The second one is so-called water use efficiency. Water use efficiency is related to plant transpiration. Photosynthesis is taking carbon dioxide from the gas from the atmosphere, and liquid water from the soil. And in the process of photosynthesis, with solar energy, creating sugars and releasing water vapor. So what use efficiency is the rate of that process, is the amount of biomass produced per unit transpiration. So it's the exchange of carbon dioxide and water vapor. Also, now, air system models are usually thousands of, tens of thousands of lines of code. But as far as these three cycles, for the sake of just conceptualization, let's boil it down to three equations. Every air system model has these, but spread through thousands of lines of code to deal with all sorts of exceptions, and frozen ground, and different vegetation types, and inundation, and so forth. But bottom line, this is what's the engine of the air system models as far as these three cycles goes. The first one is water balance. It says the change in storage of water usually denoted by volumetric soil water content theta over some depth is precipitation in, so P in minus evaporation out. So evaporation out is the amount of available energy times evaporative fraction, in order to make it vapor flux. The second equation is heat balance. It's change in storage of heat. On the left-hand side, in the second equation is available energy minus the total conduction of heat away from the surface, turbulent heat, either through conduction or through vaporization. So evapative fraction comes in there as well, because the vaporization is involved. The third one is the change in biomass equals to how much evaporation is taking place, how much transpiration is taking place, so the term above, times the water use efficiency. What does it mean in terms of carbon? Minus some senescence. So these three equations clearly are linked to evapative fraction and water use efficiency, those two non-dimensional closure relationships. And again, Earth system models have this over thousands of lines of code, but bottom line, this is what's happening and this is how they're coupled at the heart of it. And how these closure relationships depend on the main state variables like soil moisture is determined by each modeling group according to their own intuition, knowledge, base, or experience, but there's no standing. So if these relationships are different in each climate model, it's no surprise that the projections are gonna be very different as well. So this is the motivation. Again, just to state the problem, here is evapative fraction versus soil moisture. Okay, that we can get from five or six different Earth system models, the acronyms don't matter because there's a dozen of them and this is just six of them that had data for the period that we're interested in. And this is how the relationship between them is for different models. Again, this is linking the water and the energy cycle over land, those two main cycles of the climate system. And the variations among models is a lot, more than what anyone should be comfortable with. That's the statement of the problem, is that we don't have a standard way of doing this. If you look at the carbon flux in terms of gross primary productivity versus, they sometimes even have opposite signs, little long variations. So this is the state of the art and this is the statement of the problem. So in order to fix this issue, we need independent data sets observed, not models. If you put models, you get models back. Independent true observations of soil moisture and dependent observations of the y-axis. So this is what we tried to do with a combination of satellite data and surface weather station data. So the soil moisture X-axis is coming from SMAP. The carbon flux is coming from solar induced fluorescence measurements, which is a narrow band measurement in the optical thermal infrared instruments have sometimes have them from two satellites. So it's a measurement that measures fluorescence during photosynthesis, so we can call it carbon exchange. And then for the surface energy fluxes, sensible heat, latent heat, we use the weather stations around the US, which is good coverage. So after all that, this is the one deliverable that we have, which is evaporative fraction observed versus soil moisture observed for different regions of the US. So Great Plains, Midwest, and so forth. This is just a summary plot. There's a lot more detail obviously out there. And we see a behavior that is intuitively what we expected. There is a region of soil moisture when it's quite wet that the evaporation is energy limited, not water limited. There's plenty of water, but not enough energy. So there's no sensitivity to soil moisture. But then there's a region where it keeps going down as one would expect, as the soil becomes dry and dry, evaporation comes less and less. Okay, so this is a relationship which any farmer or gardener could have told you. So that's why it's intuitive. But where those transitions happen and the slope of that is the rate of linkage between the water and energy cycle. So yes, it's intuitively what we expect, but we need this quantitatively, not just in work. And then if you do solar induced fluorescence as a measure of photosynthesis versus soil moisture, again, all satellite measurements, you get the same behavior, but now it's different for breakpoint for different vegetation types. Again, this is just a summary high level plot. And they plateau at different levels because these are again different vegetation types. They just have different photosynthetic processes and also different densities of photosynthetic surface area. And then if you translate this, summarize them into what use efficiency. Sorry, the label got cut off. So that's what use efficiency and the Y and soil moisture from SMAP on the X axis. They're hyperbolic relationships. The inset is just the blow up of the larger range inset. If I said that right, it's just the same plot, just squeeze. And it's a very hyperbolic relationship and distributed for different vegetation types. This relationship has actually been measured and gets measured all the time in laboratories and greenhouses. And they published them in journals like Plants. It's just an example, measured inside the chamber in a laboratory. So it has, you see the same hyperbolic relationship as you would do from, but now from space. So we can map this and track this over time. It's not just a bench top experiment. Now, so that's the coupling of the water, energy and carbon cycles. Now I wanna go to what we learned about hydrology, the discipline I work in. The, you know, in some agency like NASA, the success of a science mission really should be measured as did it sort of compel the community to rewrite their textbooks? Did it have that level of effect? Okay, and there's precedent for that. And when we look at older oceanography textbooks, the ones that I had in my classes, figure one, chapter one, was the thermal hairline circulation or the conveyor belt, the slow sinking of waters in the North Atlantic and then coming up around the southern continents and going back up. And that was the conceptualization of what is it to study oceanography? This is what oceanography is. After Topos Poseidon, which is one of the early NASA altimeters, follow up with Jason one, Jason two, these are oceanography missions measuring the fields of ocean height over time and space. And once they started looking at that data, they sort of realized that much of the transport is actually happening through turbulent eddies. There's eddy motion that is large part of the transport and the mean motion is, yes, it's there, but it's not the only thing in town. Okay, and that totally transformed the way they think about their core discipline oceanography. Same thing in atmospheric science. When, you know, we had these figures in textbooks, figure one of many meteorology textbooks called the general circulation of the atmosphere. You had these cells, tree cell structure of the atmosphere, symmetric with longitude. You had the Hadley cell in the tropics, the Federal cell in the mid-latitudes and the Porter cells in the higher latitudes, is symmetric in Northern Summon Hemisphere. This was equivalent to the conveyor belt, a mean motion, but with the age of satellite measurements, especially geostationary ones, they see how turbulent this fluid is and that sort of the general circulation is an incomplete picture for their textbooks. Now, we're now having space-time fields of the state variable of surface hydrology, so we ought to see how that will allow us to question some of our basic assumptions. So, after that long-winded introduction to this, now, soil moisture itself as a variable does not really have a scientific value. It's what it indicates in terms of dominant hydrologic processes and hydrologic regimes and transition between them. That's important. In other words, it's a state variable that makes the surface hydrologic processes transition from one regime to another, okay? So, we know these regimes exist. We've mentioned one already. Water evaporation is either water limited or energy limited. Those are two regimes. What makes you transition from one to another? When does it happen? Under what conditions? Quantitatively, not just in terms of general understanding. Same thing with drainage, you know? So, those are that kind of questions. Now, how can you have identified hydrologic regimes from just measuring soil moisture from space? Okay, that's the state variable. At face value, you can't. Okay, it's just measuring, measuring temperature. It doesn't necessarily tell you anything about processes. It's just a temperature, a state variable. So, here's the typical measurements of soil moisture over location in Oklahoma, I believe this is. The purple dots, it goes up and down. Every time it rains, it jumps up and then exponentially it goes down and up and down and stationary. Now, what if you take the derivative of this? Okay, so the inset is the derivative of soil moisture between overpasses. So, every time there's a positive increment, the red, it jumps up, right? And then, these are very pointed events. It rains one day and this thing jumps up and it doesn't rain for a few days and it jumps up again. The blues are the dry downs. They are higher right after a rainstorm and they exponentially go down, okay? The rate of soil moisture becomes lost, becomes slower and slower and slower as the dry down continues. But the red after a rain is very fast, okay? So, that, we know, or we can see. Is there a signature of hydrologic regimes in here, deeply hidden in this data? Again, you're not using models. If you use models, you get models back. You wanna use just data. So, if this is a stationary process, statistically stationary process, which it is, you don't indefinitely accumulate or lose water. It goes back. So, if it's statistically stationary, the mean of these two distributions, the blue and the red, should be identical. But it doesn't mean the rest of the distribution is identical. So, here's the PDF of the blue and the red. The red line is the mean. They're identical. It's a statistically stationary process. You go back to where you started every year, or every once in a while. But the distribution around that is very different, okay? Is there a signature of hydrologic processes in here? Can we tease it out without models? So, let's look at how possibly we can do that. So, this is a time series that you saw before, or piece of it at least. And the precipitation is marked there from surface station data just to show that the jumps are coincident with precipitation. We don't need it in this analysis. So, let's identify dry younds. Those are periods where you consistently, so much is going down, as evident in the time series record at any location. Those are the red. You just put some criteria. Every day you go down, you don't go up more than a certain amount. And let's isolate one of those. So, one of those red dry downs, let's bring it down here. Right after a storm, the rate of dry down is very fast. And after each of these dots is separated by two to three days, then the rate of dry down becomes slower and slower and slower. There's a signature of hydrologic processes in there. At the very beginning, the dry down is very fast. And it goes from whatever the post storm level was to this thing called theta FC, field capacity. Again, that's a term from agronomy and agriculture. Field capacity is the water content of the soil that has completed gravity drainage. So, gravity force has removed all the water in the larger pores and all the other water remaining in the soil is through capillary tension and surface tension and gravity is not enough force to remove it. It's a technical term and it's also an agricultural term. So, up to that point, the drainage is very fast. So now, drainage stops. Evaporation now is the dominant loss rate. Right after field capacity, soil is very wet. So, the evaporation is energy limited, likely, for a while. So, then the evaporation is equal to its potential rate or the energy rate. So, the rate of loss is linear. So, the soil moisture drawdown is linear. And after a certain time when you reach a certain critical soil moisture, it becomes transitions to water-limited regime and now along the dry down is no longer linear but it's some sort of a hyperbolic. So, there's three regimes in here and it's all the signature is in soil moisture rate of dry downs. Again, no models. So, if I plot the rate of loss during each of these regimes, the loss rate looks like this. At the very beginning, the loss rate is very large. That's drainage. Then it becomes constant. This evaporation, potential evaporation or stage one evaporation. And then it's below that doesn't necessarily have to be linear which is stage two or water-limited evaporation. So, this is the loss rate versus soil moisture. What is the loss? It's the negative increment over the period lapsed. It's being plotted as a function of soil moisture. So, it's conditions on soil moisture and you have a lot of data. So, you take an ensemble conditional average and that reproduces for you the loss function that you were after. And once you have the loss function, you know the three regimes. So, you can construct which regime is the dominant process by looking at the increments and soil moisture itself condition statistically processed. So, this is what the map of the US looks like. We look at percentage of time in each of those regimes. In the water-limited regime, different percentages mostly out west. In the energy-limited regime, mostly further east and drainage dominated some percentage of time. Over the US as shown here. Now, this is a purely observation-derived map of which regime should be dominant where what percentage of time and what time. Do hydrologic models reproduce this? Is this a benchmark data set for the performance of hydrologic models? This is the way that we can rethink some of our models is by having benchmark data sets that are purely based upon observations but have the transitions between regimes that we want. Now, the drainage dominated, a lot of it looks like according to the data to occur where there's a lot of agricultural tiles. But that's pure speculation. I'm just speculating if that's coincident or not. Yeah. Is the management role of vegetation coming to play in terms of the less functions and the maps? The biggest slide as well. Yeah, that's the goal in the short-term and long-term. We've done some of that, there's a lot more to do. Is to see what is the soil type and the vegetation type. So all the papers that we've done on this we divided by soil percentage of sand and clay and also vegetation type. I'm trying to see what is the role of these two. Some of them, actually I have some examples I can show. So now the second question, we have three questions. Second question is, is this a science mission or just a technology demonstration of a large antenna or both? It would be nice if it's both because technology demonstration and science go hand in hand, they're just different sizes at the same point. So how much of the water cycle do we see? Is two to three days sampling of soil moisture really that is adequate? And the way to measure that is to see how much of the water cycle is actually routed through soil moisture and how much of the dynamics of soil moisture represent the water cycle. The rate of the global water cycle is say precipitation or evaporation globally. They must balance obviously, so either one. Precipitation we measure a lot better. So that's the rate of the water cycle. Now what fraction of that is evident in the dynamics of soil moisture? And the way you can measure that very easily is to look at the change in storage of this one variable you're measuring, top soil, soil moisture, divided by the rate of the water cycle. What percentage of the water cycle is evident in the ups and downs of this one variable? And the kind of numbers you get are surprisingly large. It's this inset fraction is the PDF of the fractions. So anywhere from a few percent to 20, 30% of the water cycle is evident in this tiny little measurement every two to three days. Okay, and the reason for that is that soil moisture is sort of sitting at the gate between the surface and the subsurface, two main stores of the water cycle. And any drop of water has to go through that gate. So if you're sitting at that gate, you're gonna see a lot of people going back and forth. So if you look at the budget of the global water cycle, soil moisture is a tiny fraction, tiny, tiny fraction. Less than 1,000th of a percent, but it captures about 20% of the water motion. So that's how much of, you know, and one answer to this question, how much of the water cycle do we see? Another one is this issue that you're only looking at the top few centimeters. Is that adequate? Something like five centimeter plus or minus. And the answer to that is to sort of try to think of this variable in a new light rather than a discrete measurement over a certain depth. The sensing depth itself is not a fixed five centimeters. Depending on the soil moisture level, it can be one or two centimeters or it can be a meter depending on how wet or dry it is. So even that number is not a fixed number. The same way, why not think of the hydrologic scale as also a variable and not a fixed number. So neither of them are a fixed number. Does that sort of get us out of this conundrum? They're, none of them are fixed, but they're linked. And the way we can show their length is by looking at real observation data. This is a depth zero to 20 centimeter measurement at a location in Oregon over time. And this is the heat map of the soil moisture volumetric water content. And what do you see here? Every time it drains, there's an infiltration front and then it goes away, drains and evaporates and then there's another one. Sometimes if the rain is isolated and small, the penetration depth is very small. Sometimes if there's a cluster of rain events, the soil is very wet, very conductive. Water goes right through the front, goes very deep. What if instead of looking at soil moisture at five centimeter, 10 centimeter, 15 centimeter, we look at the volume of stuff that is light yellow or green. We look at the magnetic convex hull of this diagram. So we do a water balance on water in the landscape, not at a point. And to do that, let's begin with the basic equations. Change in soil moisture over some depth, characteristic length scale is precipitation minus evaporation minus drainage. I can rewrite that as the change in moisture is precipitation over that depth minus the loss function. And the loss function is what that conditional expectation I showed before. So we have three terms in the water balance for this landscape. And remarkably you can get it all from space. From global precipitation mission, we get the precipitation. From SMAP, we get the conditional expectations on the right hand side and the change in soil moisture dynamic over time. So you can estimate this landscape, landscape globally with no models, all data and global because it's satellites and no knowledge of soil type or vegetation type. Now you can slice and dice it to see what is the effect of soil and vegetation on things. And it closes the water balance. This is a water balance closure from space without models. And this length scale, for instance, just focusing on the US, it's on the order of several hundred millimeters. And it's PDF it's shown here and the red line is the five centimeter nominal sensing depth. So obviously you're tracking water a lot more than five centimeters, okay? Now I wanna go back in the time remaining. So far we have been looking at the total loss function, L. But we know that L has got two components, evaporation and drainage. Can we separate the flux into those two? So now we can look at the dynamics and dependence of each of these individual fluxes rather than some total on the state variable. So we don't wanna impose a model to estimate those, but we need to parameterize each of those functions as a functional form. We need to give it some functional form. So for drainage, the functional form is a hyperbolic function choice, sort of inspired by the gravity drainage in the soil. This is the sort of soil hydraulic model that's various forms of it exists. It's always some sort of a hyperbolic function. It's pretty standard in soil physics and agronomy that it should have some dependence like this, but we don't know what these parameters are. Let them be totally free. No imposition with prior. And that function can go left and right. You can go anywhere in this space. With evaporation, we have two regimes. We have the flat part, energy limited stage one and the curved dipping part, which is stage two or the water limited regime. Let's give it a functional form. Again, not a model, just a functional form that is a sigmoid like that. And the parameters A and B can make it go anywhere in that space, okay? So four parameters, right? That one of them, the red is drainage, hyperbolic, the black line is evapotranspiration, two regimes, and their sum is the blue. That's the total loss function. So we have four parameters. So, and a very flexible function for these things. So let's estimate them using a variational approach where you invert the instrument measurements, brightness, temperature. We always do that to retrieve soil moisture, but we do it inside this whole machinery. And we adjoin using a Lagrange variable over the entire period of record. The water balance with the Lagrange variable. And this thing's very efficient to run. So you fit the black dots, which is map observations with the blue line, which is this model. And you get the fluxes out with precipitation input, obviously. The green is drainage. So it only occurs when there's a lot of rain, right? You don't get gravity drainage. And then the red is the evaporation. So during periods when there's no drainage, it's basically all of the losses. But when there's drainage, it caps at the potential evaporation, the energy limited. And the parameters A, B, and C, and D look like this, but this is not what we were after. We're not building a model. What we want is the fluxes. So you can put them inside the relationships and get the fluxes, evaporator transpiration, and drainage out, okay? And this is not from a flux tower, but from a satellite to satellite data, GPM and SMAP. And no models except for those two regime and conceptual functions. How does this compare with what we measure? This is, over the US, we have several flux net sites. These are towers that measure evaporation flux. So over the three years record, about 70% explained variance. And if you look at USGS drainage over these basins, it's about 70% explained variance. So it's sort of getting these fluxes from space. One last thing I wanna talk about is what can we say about climate change with four years of record? Again, these are the loss functions. This is the soil moisture record, which has that marginal PDF. If you think of it, it's that PDF turned on the side the conditional expectation, or the expectation of each of these functions with that PDF is the flux. That's how we calculated the flux in the previous. So this is the PDF of soil moisture. This is how the losses depend on soil moisture. So this PDF and those functions give you the expected value. Now, the water balance equation is change in storage is precipitation minus potential evaporation on some loss function and drainage. Climate change, if you have more energy trapped in the atmosphere and made available, that would increase the available energy at the surface. That would increase PET. So that would be a negative in storage increment. But precipitation also goes up. There's more evaporation, more coming going up, more coming down. Which one wins in shifting this PDF to the left or the right is an unknown. They're being pulled in two different directions. If it was pulled in one direction, I would say, okay, with some certainty, I can say the flux is gonna go down or up, but I don't know how much. But I can't even tell for the surface flux is on the global warming, whether it's gonna go left and right because there's two competing factors. Now, that's the same graph over there. You have the PDF, marginal distribution. And what if I go to basic thermodynamics and scale precipitation and potential evaporation using the Clausius-Clapeyron thermodynamic relationship? That's the rate of the increase of saturation, vapor pressure with temperature. The known thermodynamic relationship, there's no questions about that. And they definitely are one of the major factors for why precipitation or potential evaporation would go down. So if I increase potential evaporation by 20%, the PDF goes down, the purple goes below the nominal black line. If I increase precipitation by 20%, it goes up. The question is in different regions with different loss functions, which wins? Well, since I'm applying the Clausius-Clapeyron, I apply it to one degree Celsius, two degrees Celsius, three degrees Celsius to both potential evaporation and precipitation and look at which one wins by how much over the US example here. So even with three years of data, four years of data, and without using any substantial models, there is stuff we can say about even global change. Let me very quickly say something about global ecology. In Witt's map, we not only derive soil moisture, but we derive how much attenuation occurs through plants, which is proportional to their water content. And the time series looks like this. Soil moisture goes up and down in blue. The green is the vegetation water content, simultaneous retrievals. And again, we look at dry down the red ones. And if I look at a few dry down events, sometimes soil moisture is always going down. But sometimes the moisture water content goes up, sometimes goes down, doesn't seem like there's any rhyme or reason to it. If you plot the phase space, meaning plot soil moisture versus vegetation water content, time is taken out of this picture. Soil moisture when it's wet, it goes in this direction, and the vegetation water content it doesn't seem like there's much relationship. What if I plot it instead of just one pixel, there's only so many dry downs in one pixel, I plot it for regions with similar climate and vegetation. So over Africa, these regions. Now there's a lot of overlapping dry downs. Again, it's very difficult to see anything in there. So let's, this is a phase space. So we can map the phase trajectories. So we just look at regions in this phase space and where this trajectory originating from that point goes. Now we see something about the vegetation in there. The soil, when the soil is wet right after a storm, the vegetation is picking up water. So the slope is positive. And sorry, negative. So it's picking up water. But as the dry down continues, there is a point in this particular vegetation type when the plant starts losing water, it wilts, which is a property of the plant itself. And then it crashes. So what we do now is look at different vegetation types, trying to see what is the rate of water uptake and what is the collapse point. And the rate of water uptake is that slope. So we map that and look at different vegetation types. I'm going fast here. The point at which it wilts is where that it's change in sign occurs. That's the PDF in megapascals. Earth system models right now mostly use 1.5 megapascals as a fixed number for all vegetation types globally. So this is a way of looking that number and seeing how it varies around the globe. So two minutes on the final thing. Again, the third question was, has the mission delivered on your societal benefits promises, weather prediction, droughts and floods. And again, research to operations is a very difficult thing. People who work in operations have their hands full. They're putting out fires all the time. They don't have time to play around with new data sets. And there is liability in introducing a new data set. What if the weather forecast becomes worse? Who's to blame? So you can't just say, here's great data, use it. They have to have parallel systems for a long time before they make that transition. And they just have, you know, every agency is under financial and personnel headcount stress. So no one has really had time to play around with new data. So how do we make this happen in that environment? So here's a sort of the kind of approaches we've taken. For instance, in the case of droughts, the drought monitor is a multi-agency, USDA, EPA, Department of Interior and so forth. Out of Lincoln, Nebraska, that creates a weekly drought monitor report. Okay, so that's the map you see up there. Puts out weekly, this was 2017. And it has droughts in the standard drought levels, D0 to D4, D4 being the worst drought. That's sort of in the community of practitioners, this is fairly normal, I went on this too. So the way we kind of try to show, and this is based upon soil moisture deficit, but modeled soil moisture deficit, not observed. So the way we try to say, okay, maybe the data that we're producing can be of use to you. You just don't throw it at the data at them or throw it over the fence. What you gotta do is create maps that they're used to seeing every day in the same units and the same color code. This is what we can do, and this is how it matches your current operations. And try to convert them that way. So this is the same color map and the same flash drought of 2017 in Montana. You know, this is the sort of the steps you need to take to make the transition. Another one, which was a surprise to us, is this thing called the crop progress report from the National Agricultural Statistics Service. It's based upon human observers, and it's reported as percentage area of each state or each county. And it puts soil moisture in four categories. So very short, short, adequate, or surplus. So four categories of soil moisture and by human observers in counties. And we took that data and matched it by looking at this PDF with map observations and remarkably they're consistent. So the human observers are actually quite accurate. But the difference is that instead of counties or states, now we can do it at every pixel that you observe. So you can map the same four categories, surplus to very short to not cultivate it, and show them this map saying this is the same table you have, but now at every granular and updated every three days. The last example is weather forecast. And this is out of Environment Canada. This is the impact of initializing weather forecasts on predicting precipitation. And in fact, they picked a case, which to my credit, that is most difficult case. They took all of North America during July and August, so middle of the summer, at late evening, 30 hour ahead prediction. That's the thunderstorm sort of max of the year. And what's plotted here is probability of detection. So probability of good forecast in number between zero and one, the higher the better. As a function of the intensity of the storms, as the storm becomes more intense, it's more or more difficult to predict. We kind of know that. And the difference with and without SMAP data is the blue line and the red line. So SMAP is above the blue line, which is good, but it doesn't look like much improvement, okay? But in this community, the way they measure improvement is by how much should I shift the red line and the blue line in time? So they measure forecast lead. And it's half a day, that's a lot. So a forecast that was good at two and a half days, now is just as good in three days. Half a day is a lot in this process. So in summary, four years of seasonal cycle data, which is a lot that's still possible to do with it. Our main promise was the linkage between water energy and carbon cycle. So using only observed data, no models, can we show at least some benchmark relationships. Landscape hydrologic fluxes, drainage and evaporation, and the regime transitions between them. One example I showed, again, it can be done with only SMAP and GPM data. So it's global. Tracking water in the soil vegetation continuum, different plants, uptaking water and wilting, for which type of plant, when and where that happens. And even looking at the issue of climate change from a short-term record, it is possible. Okay, just have to, and then research and transition operations, the approach is to match the current products and then show the incremental benefits. Okay, thanks a lot. Right, so how do we work toward a unifying theory of the water, carbon and energy cycle linkages? Like you mentioned that the bigger system models out there don't agree either how they're implemented in the model or how the output looks. So how do we work on getting a unifying theory? Well, not unifying theory, but unified approach, maybe is the better. It would be good if we have benchmark tests and data sets that all modeling centers use as they do that, for instance, it would wins and things like that by looking at radiosounds that is shared among everyone. We need to do the same thing for some of the things that are parameterized in the models, like the water, energy and carbon cycles. There's no agreement on what are the benchmark data sets. We have a lot of efforts in model intercomparison studies. Okay, there's a lot of CMIF climate model intercomparison, there's a lot of M with different initials at the beginning. But it's not comparing models is a first step, but maybe we need to go take one step further, define the metrics and define the benchmark data that are not model dependent. Okay. I'm sure those organizations are thinking or have been thinking about this for a long time, but as of yet, there's no evidence that we have made much progress. That was very, very clever. I mean, I've seen your papers, but you're explaining it as outstanding how you came up with the thinking. So two questions, how do we detect the human influence on the water cycle with this kind of data, especially in terms of, say, management decisions like irrigation or dams or even urban areas which one have, that's one. And the second one would be, when you have a data which is from soil data for a grid and you have observations which are point or your models which are being run in different, what is your suggested strategy for doing intercomparison between SMAP fields with models or data sets so that people don't abuse. Yeah. The, your first question is that humans are everywhere dominant on the landscape. I mean, it's hard to come across a location where there's no imprint. And they're part of the system and what the satellite sees is what's there. But I think if I understand correctly what you're driving is that what is the changes that we have made? What is the impact of those? And like the class we were discussing this yesterday, the design class in an AeroAstro. The global change has two components. There's the atmospheric composition and radiative greenhouse additions that come into play. But also there's a global change that's already occurred on which is land use change. And for hydrologists who deal with runoff, stream flow and evaporation, we have changed those fluxes by factor of two, three, not 5%, 2%. And the challenge for us is to look at how we have changed that and how further changes will affect. And with satellite data, you trade space for time. We can't go back in time. We can't have a satellite for 50 years. But there's a lot of different parts of the world that are in different stages of that transition and can we relate them that way? And in terms of your second question, in terms of a satellite sees 40 kilometers in case of SMAP, what does that have to do with the real conditions? Again, any farmer or gardener can tell you in the same plot of land, the same garden, you can put your feet in a mud puddle and you can kick up dust. Okay, so what does 40 kilometer mean if it's that heterogeneous? I'm not sure what we see and experience with our hands and feet and eyes scales to what the satellite sees. The satellite is seeing climate. It's not seeing the puddle. It's not seeing where the vegetation patterns and rain patterns have occurred. It's a different phenomenon. It's like measuring turbulence, which can go in any direction, any second versus wind from west to east. Both of them exist. It's just you can't compare them. It's just a vantage point. Is there any hope for doing something like this in tropical forests or what happens with tropical forests? Just one, the big issue for us is that even at L-Bands, if the vegetation becomes too dense, then it's difficult to see. The signal gets attenuated so that it's within the instrument's precision and then you can't do anything. We had estimated that that level is around five kilograms per meter squared, which in sort of plain terms, it means everything except tropical broadleaf forests and boreal vegetation. After some time, we're suspecting that it's, that was too conservative. That you can actually see much more. But the exact level is, but there is definitely a level beyond which the vegetation is just too dense to see anything. But what that is, is a little more than what we think now, but not 100%. It's, to answer that, we are planning airborne experiments specifically focused on that for next year. If you want to volunteer, do. And we're doing a lot of modeling. We're asking exactly that question. What is that exact number? That's way over. All right, so thank you very much. Thank you everyone. Thanks everyone for attending. Very interesting discussions.