 So as I mentioned, at this point, I walk you through how we do the inverse problem to go from the level one satellite data to the level two, sort of composition information. Now we can take this level two information and do the inverse problem again to go after the surface emissions, which is what we're interested in from their quality perspective or in terms of estimating carbon sources and sinks. So the problem is similar but slightly different now. Our problem is that we're starting off with some set of emissions which in our atmospheric model represents a set of parameters P. And these emissions are being used as essential boundary conditions in a model to produce atmospheric concentrations of CO or CO2 or methane depending on the emissions of interest. And for the inverse problem we are interested in in looking at the discrepancies between our model simulation of say carbon monoxide and the market observations to use this discrepancy to try to optimize the emissions to bring our model into agreement with the observations given the uncertainty we have on the observations and our prior uncertainty on the emissions, assuming we take a Bayesian approach. So in this case, the expression for the analysis looks pretty much the same as I showed you before with the difference being that for the inverse problem we're estimating the atmospheric state the CO concentrations in the atmosphere. But now we're interested in estimating the model parameters P, which are the emissions, the surface emissions. So, and in this case would be our atmospheric model that takes the state at some time, I plus the emissions and propagates that forward in time to I plus one. When we construct the, the, the innovation in the analysis, our observation operator has to account for not only the any interpolation in space and time that's needed to go from our model to our observation. And so that spatial interpolation is indicated here by the subscript J. But it also has has to account for the smoothing influence of the satellite retrieval, so that we can properly map our model into the satellite space. And so the observation operator here now has to account for the average in kernel in the case of, in the case of the Mopit CO, the after-console I showed you before. As well as the prior information that went into the Mopit retrieval to produce the level two data that we're assimilating. The observation operator may not necessarily be linear. This retrieval could actually be nonlinear. And in that case, you know, we would linearize it to produce the tangent linear model. So it's just the derivative of this observation operator with respect to the model parameters. And that's what's used here in this analytical expression for the analysis. And before we had B for the background information, but now B sub p represents the a priori covariance for the emissions as opposed to the covariance for the state that we talked about before when we went from the satellite radians to the state. So it's very much the same approach, same equations. The big difference here is the change in the observation operator and the change in the control vector going from the state previously to the emissions in this case. So, you know, rather than going through the technical details of this, I'm going to show you some applications of this approach and talk about the implications of the inversion approach that's chosen and the observations that are being used. So one very nice example is from 2006. This is an example of the type of early inversions that were done using MAPA data shortly after the data became available. The analysis expression is shown here. Many of these early inversion analyses starting from the late 1980s through the early 2000s. And for computational reasons used a fairly low resolution to grid for the inversion so the emissions P were discretized into very large geographical regions to form the control vector. And the reason for this is that to construct the H matrix. So for each of these regions, we perturbed separately the emissions in each of the individual regions here. And then propagated those perturbations in the missions through the atmospheric model to construct the columns of the H matrix. So for each of these regions you perturb the emissions, you run it through the model sampled of the observation locations and time and in doing so you construct the column of the H matrix. So for computational reasons, you know, starting from as I said the late 1980s through until about 2015 years or so, though, it was computationally expensive to run these inversions with more than, you know, 10 to 50 elements in the state vector in the control So in this inversion, they broke up the surface emissions of carbon monoxide into these large geographic regions and constructed the H matrix as I said by running these perturbations through the model as a function of time to get monthly mean estimates of carbon emission carbon dioxide carbon monoxide emissions to run from each of these large regions. You know on a monthly basis. So monthly mean emissions stepping through the year to give you a sense as to how well this works and it works reasonably well considering where we were at that time. So this is showing the difference between the observations the map data and the prior model simulation so with the a priori estimates of the emissions, and you can see there are large discrepancies between the model and the model and the observations with the model being by a slow in the winter hemisphere. So here in in April in the northern hemisphere and then here in in September in the southern hemisphere. Once the emissions are optimized, you can pass those optimize emissions through the model again and generate a set of posterior CO2 fields and look at the residual differences between the observations and the optimized model, and you see that these biases are much smaller now than what we started with before. So this is paper by Ave Aralano as part of he did this is part of his PhD thesis, and you can see in the middle here, the emissions, the monthly mean emissions function time, the emissions here in teragrams of carbon monoxide per year for each of the different regions that are plotted to some of the different regions are plotted here. So we need to focus on the details here there to their two aspects here that I want you to look at. One is that compare the red line which is the posterior emissions to the black line. And if you look at Southern Africa you see the prior emissions had a peak here in early summer boreal summer, and a secondary peak here in late summer, and the posterior emissions suggested a shift in the phasing. That peak in late summer which is much more consistent with what we now know about these emissions from Southern Africa. And the other thing is to look at the red line which is the posterior emissions with this green line this green line is from a prior study that was published a year or two before this study that use market observations to also estimate monthly mean emissions in a time dependent matter. And in the case of Southern Africa the emissions are fairly consistent there's some differences but they're fairly consistent. For Europe and Asia you can see there's a big difference between the posterior results from this study, and the posterior results from the previous study shown here in green. And I'll try to come back to that a little bit later on toward the end of the talk and if I don't explain why they're so different, someone could remind me in the chat with your choice. So clearly the sort of the state of the arts, about 15 years ago, these big region inversions, which we had to do for computational reasons. The problem with this is that there's a passive assumption being made that we know what the sub grid scale variability in the region are for each of these regions. If you have an error in these in the sub grid structure of the emissions, that will introduce an aggregation error in the inversion that will bias the inversion. Because implicitly what we're doing here is we're, we're coming up with one correction factor for all of the emissions within this entire large region. It's a spatial structure is wrong and the observations aren't dense enough to allow us to capture that we can produce an aggregation error and that can be quite large in some cases. So, ultimately, you know we really want to construct the inversion, carry out the inversion at the highest spatial resolution possible preferably at the resolution of the model itself. And you can, based on the smoothing aspects of the inversion decide what are the spatial scales to which you should aggregate your estimates given where you have information from the observations and where you dealt. But by assuming these large grid boxes, if you know you're, you're, you're setting yourself up to incur an aggregation error. But for computational reasons, this was the way things were done for this type of analytical inversion at the time. So over the last 10 years as a result of computing power, it's now possible to do these inversion analytical inversions, but with very high spatial resolution. This is a paper looking at the inversion of methane data from the GoSat satellite to estimate global methane emissions by Brian Massikers from Harvard that was published in 2019 and here it's a grid based inversion with 2025 elements in the control vector. And here they're perturbing each of these elements to construct that H matrix. And they can do this because we now have access to massively parallel computing systems. And also many of the matrices are sparse matrices so you can take advantage of a lot of the space sparse matrix, matrix tools and the parallel computing capabilities that we have to do this inversion in an analytical framework at high spatial resolution. And it works beautifully. It really is a very nice example of, you know, the value of some of the computing tools that we have today. So on the left here we have the prior methane emissions that went into their inversion on the bottom left are the posterior so what they estimated from the analysis. They're showing the ratio of the posterior to prior emissions are showing the change as a result of the inversion. But because you have all of these matrices and you can take advantage of the fact that there's sparse matrices, you can also easily construct the average in kernel for this inversion to isolate where you have sensitivity to methane surface emissions. This plot on the top right are showing the grid boxes where there is sensitivity to the emissions where the estimate of the emissions has sensitivity to the actual true emissions so similar quantity to what I showed you for the satellite retrieval can be derived for the emission inverse problem. The size of the state vector, as I said is 2025 elements, but the degrees of freedom for signals only 128. So, we are able to constrain, and as you'll see, emissions from some of the major source regions, but they're still significant smoothing they're still large parts of the globe where we don't have a strong signal. So it's an observing system that we have to estimate these emissions alive. One of the things that this study was addressing is this, you know, ongoing puzzle, this outstanding puzzle regarding the increase in methane in the atmosphere. This is showing methane measurements as a function of time so monthly mean methane global average globally average from the 1980s to the present. In the mid 90s starting in the late 19 in the early 1990s we saw that the growth rate started leveling off and essentially methane flattened in the atmosphere. The growth rate just flattened. For about a decade, the methane stopped increasing and then around 2005 it started increasing again. And so this analysis was interested in the study was interested in using those that data to try to understand this increase in emissions that we saw after this. And they attributed a lot of this to tropical wetlands. They're arguing that the tropical wetlands are contributing large fraction to a large fraction of this trend is global trend about 43% of the trend here is coming from wetlands, mostly in the tropics, some in Asia as well, and that oil and gas accounted for about 11% of the trend and livestock, about 16% of the trend. There are still limitations with the satellite observations, as you can see from the total degrees of freedom for signal the number of independent pieces of information that we can get from the data, but the data are good enough to start allowing us to answer some really important questions like, you know, how is an oil and gas contributing to global trends in methane, you know we can start to try to tease out what's driving some of the signals that we're seeing here. So the point of this slide was to show how we can do this grid based inversion, as a result of the computing power that we now have compared to say 20 years ago. However, 20 years ago, we could, we were able to do grid based inversions using adjoint approaches. So the adjoint approach or 40 bar approach, Colin talked about on Tuesday, as well. This is a way of taking advantage of the adjoint to which would give us a sensitivity of the model state to the model parameters very efficiently. And so it's a nice way to do a grid based inversion, without having to take this brute force approach to perturb every element in the control of course the drawback is you need to develop the adjoint of the model and that's computation that's very expensive to do, even with automatic differentiation software. And often those software can sometimes provide code that's not optimal and requires a lot of manual treatment. So it is an expensive thing to do but if you can do so develop the adjoint model. It's a very nice tool that you would then have at your disposal. So the 40 bar approach as discussed briefly yesterday and on Tuesday is a smoother that tries to assimilate observations over a time window over the simulation. And the way to think about it the way I should say the way 40 bars typically used in the atmospheric sciences community is we try to optimize the initial model state at the beginning of some time period assimilation window. So that we can construct a model trajectory over that time period to best match up all of the observations that are available over that interval. So if you have a model forecast that takes a trajectory that's a that's this form here. We want to use all of the observations distributed over this time interval to optimize the initial state so that we get a better trajectory to match the observations over that interval. And we use the model adjoint to project this information from the observations back onto our initial state to optimize our initial state to get the trajectory that better matches the observations. So the model trajectory over that time period is providing a very strong constraint on the optimization we're assuming that when we estimate our initial state and try to project that forward in time, or take the information of and project them back in time for the adjoint that is being done without any errors and being introduced so the model is assumed to be perfect in terms of how we use the information distributed over the simulation window. So it's a strong constraint on the optimization and this initial state optimization is called strong constraint 40 bar. So this is how it's typically used in the certainly in the numerical prediction community. For the inverse modeling community. It is slightly different in formulation. So in terms of estimating emissions with 40 bar. There are two different approaches. You can estimate the initial state, as well as the model parameters. So this is the same cost function. I didn't go into details of the cost function in the interest of time. It's very similar to what you saw on Tuesday. But now instead of having only this background term as a constraint in the optimization you also have this term for the emissions as well the parameters in the optimization. Another course is that we don't really have a dynamic model for the emissions. So the 40 bar and this is why I put 40 bar in quotes here, the 40 component isn't doesn't strictly hold for the emission estimation. This goes back to the discussion that we had that on Tuesday after Collins talk about how you need to modify each of these different schemes for your particular application in the case of the emission estimation, we don't have a dynamic model for the emissions and we don't have surface fluxes, but we are using the model dynamics to propagate that information forward in time to take advantage of the smoothing aspects of 40 bar so that we can use observations from the future to inform the fluxes in the past emissions in the past so it is it is a 40 bar system. The 40 component is there, but we're not evolving the emissions using a dynamic model. So there's a fundamental difference there that's important to be aware of. The other approach that's often used is one in which we just optimize only the emissions and not even the initial state. It usually requires some other means of optimizing the initial state and then from that optimized initial state, you then construct the, you then do the inversion to get the emission estimates. So I'll show you an example of how that's done. So here is an analysis in which we use this 40 bar scheme to quantify CO2 fluxes using data from the go set satellite. In this case, we were interested in looking at the differences, the constraints that we get from observations over land versus observations, versus combining the observations of the land with ocean data. And the motivation here is that if you look at the green colors here these are land data, you see that there are regions where there are significant gaps in the observational coverage. These are regions where you have persistent cloud cover and the satellite cannot see through clouds of course and so we don't have data in those regions. But if we have ocean data, we can capture the outflow from these continental regions and use that information over the ocean to try to inform our estimates of the fluxes over the continental regions. And in this analysis we assume that 12 month simulation window to estimate monthly mean fluxes so we're taking advantage of the fact that 40 bar is a smoother. And we can use observations from you know if we're estimating fluxes in January for example you can use observations from February, March, April, May with the adjoint to project that information back on to the the January fluxes. So we want to do this, we want to use as much data as possible. Because of the nature of the observations that we have, if the observations don't provide really dense sampling over your domain, you may not be able to use an assimilation window of only a day to estimate daily fluxes. In the case of the orbiting carbon observatory the repeat cycle for the orbit is 16 days. So you really want to use a long window to get as much information as possible from the observations to inform your fluxes. Another issue is the strength of the signal in the observations. Many of these fluxes don't have a very strong signal on the on the in the observations and so you want to use as much data as possible to get more robust flux estimates. So in our case, we ran with these 12 month of simulation windows and use only the first six months of each year to estimate our prior fluxes. The idea being we want to ensure that every month has at least six months worth of observations informing the flux estimate that we that we provide. So we stepped through time at these 12 month intervals, taking only the first 12 months, six months of data, and then starting the next assimilation cycle shifted six months ahead and run and ran that forward for 12 months. So an example of the type of fluxes that we estimate are shown here for 2010 2011 and 2012, the red colors indicate emissions of CO2 to the atmosphere the blue colors represents uptake of CO2. And, you know, if you look, it's very nice actually if you look at 2010 over South America versus 2011 versus 2012, you can see a significant change in the emissions and this is because 2011 was a linear year we're seeing the impact of precipitation changes in Brazil, acting on the fluxes here during the linear conditions compared to the linear conditions that we had in 2010. So this is one approach using the adjoint to estimate fluxes at the grid box scale, and it's a very computationally efficient way of doing so, when you have a large number of a large state space as opposed to the brute force approach that I talked about. Another way of doing so is using an ensemble common filter, and carbon tracker system at NOAA is a very beautiful example of the use of an ensemble common filter for CO2 flux estimation. This is using an atmospheric model called TM5. Globally, they run a core spatial resolution, but over North America they run at a higher resolution of one by one degree, since this is really focused on providing North American fluxes but they do provide global fluxes as well. Operation a carbon tracker fluxes that are available are typically similar surface data, ship based data, aircraft observations using a square root ensemble common filter scheme, and they estimate weekly fluxes in predefined echo regions. So with the common filter you can very efficiently can estimate fluxes at the grid base grid box scale. But for a carbon tracker they realize that the observations aren't able to provide constraints on the fluxes at those scales, but they also know that as I said you don't really want to do the inversion of very core scales and introduce an aggregation error. And so the compromise they chose is a very nice one in which they start off with these course regions that were developed for historical, for independent comparison projects starting in the late 1990s. So in each of these large geographic domain, they then further divided the region into 19 different echo zones, based on the vegetation types that are present. So the inversion is done on these echo zones, rather than at the grid box scale. And you know the idea is that by optimizing the individual echo zones you are less likely to current aggregation errors result of this incorrect subgrid scale estimate of the fluxes. So in their case they are running with 150 ensemble members, perturbing these echo zones to construct the H matrix, which as part of their ensemble analysis. And the analysis produces fluxes that look like this on the echo, these echo regions, which they can then interpolate onto a one by one degree grid which is what's reported when you download the data from their website. So this relies on a terrestrial bias model to help guide this, this activation here, or interpolation I should say. So, you know, just to be clear, for this region here this boreal region in North America, these are the echo zones that are optimized and for the temperate American region here. These are the echo zones that are being optimized. So where we are today in the communities, you know, most of the inversions are using either a 40 bar scheme or sometimes an ensemble common filtering scheme to optimize these fluxes at the grid based grid box scale or close to it. And we now have in support of some of the satellite missions, you know, a very large active international community focused on producing fluxes. As an example, we have the OCO to orbiting carbon observatory model into comparison projects. This is an ongoing activity to take advantage of the OCO to data as well as go set data to try to provide flux estimates that can be used by the international community for carbon cycle studies. We have there are nine different 10 different groups involved in this that are listed here the models and the different institutions are group is one of the groups involved here. And, you know, there's three different models that are participating in the analysis. And unfortunately, most of us are using the 40 bar scheme. There's a carbon tracker that's using the ENTF scheme. And there's one project that CSU that's using an analytical Bayesian inversion approach. So there's some variety but not enough diversity across all of the different groups here to give us a true spread of how the different models and inversion frameworks might impact the fluxes. I'm showing you here example of the fluxes that we get from the analysis this is showing the ensemble means or the mean of the 10 different fluxes that are the 10 different fluxes that we get from the various groups when we assimilate only the surface data or different flavors of the satellite observations. I think the key thing that I want to point out here is that if you assimilate, you know, one set of satellite data versus a different set of satellite data you do you do see some differences in the fluxes. But what's emerged over the last five years is that there's some really coherent signatures that we are picking up that is telling us something about the carbon cycle, and it's actually quite exciting. That's one example of what we're seeing right now and a beautiful example of that is this paper that was published by Palmer at all. In a nature communications two years ago and this, in this analysis, they were three different models, some of them participated in this model into comparison project that I mentioned before. And they looked at using its surface mark measurements, situ data versus two different satellite data OCO two and go sat and found that across the tropics. There is a strong emission signature carbon and in particular the tropical African biosphere seems to be a very large provide a very large source of carbon to the atmosphere. We are seeing that tropical Africa provides about 1.4, 1.5 to 1.65 petergrams of carbon to the atmosphere and this is quite unexpected. And there are two centers of emission that they've identified one over Western Ethiopia, one over Western tropical Africa. This is not something this is a large source of carbon much larger than expected and it did the results seem to be robust it was a beautiful study that came out of this this Edinburgh group. And you know it's it's it's a bit of a surprise and this is generating a lot of interest a lot of new research activity in the community at the OCO two science team meeting recently we learned from part of both Leicester in the UK that they're now working on producing this set up a site in Uganda, near Lake Victoria where they're trying to make ground based measurements that would provide some complimentary constraints on the African carbon budget to help us understand, you know what we're seeing here from the satellites are the results that we're getting from the inversions using satellite data that suggests this very large source of carbon realistic is this are the results, you know they're robust across the models, but are they real. And unfortunately we just don't have a lot of data across Africa to help us understand what's going on there and so this is as I said, generated a lot of interest and spurred new research focusing on the asset and carbon balance. So here I've talked a fair bit about how we got the foxes and in the grid based context versus this big region context. You know there's work using 40 bar schemes using ENTF schemes and implicit in many of these analysis is that our models are unbiased we don't really have a way of dealing with systematic errors in the models. That is becoming a critical issue for the carbon inverse model and community and we're starting to see and push now to try to better characterize systematic errors in our atmospheric models just the way they satellite teams that do these retrievals this inversion analysis to produce the level to data focus a lot on how to characterize in biases and their inversions and mitigating those biases, we now are trying to do the same in our atmospheric models to provide more robust flux estimates. And one approach for doing that that you know my group has been looking at is using a reconstruct 40 bar approach. As I mentioned a few slides before in the 40 bar case, you optimize the initial condition and use the model to project that initial condition that over your simulation, simulation window, assuming that the model does so perfectly. And so, as I said it's called strong constraint 40 bar because you're using the model trajectory as a strong constraint in the optimization. In the 40 bar, we recognize that there may be errors introduced in the propagation of the state forward in time, and those errors are represented by Ada here. So we can modify the we constrained approach and optimize not only the initial condition, which is being projected forward in time by our model, but also these data terms these model error terms and every time step over the simulation window. The cross function for the 40 bar looks very similar but now we have an additional term that's added to it, because we've taken these error terms, and we've incorporated them into the control vector. And of course we need to come up with an error covariance for these model errors so there's this queue here so model error covariance, but otherwise the optimization looks very much the same. So there's a lot of flexibility in terms of how you deal with this data, you can imagine for example, if you just had a constant Ada or the entire simulation window, this data, you can think of as just a large scale bias, in which you're scaling the trajectory up or down, you can optimize Ada at the same time step as the model so as written here, where Ada varies from time step one to end, or you can choose to optimize Ada at a different time and a different temporal resolution than the rest of the model and that's what we've been exploring in our analysis. This we constrained approach, you know, really was nicely described in an early paper by Derber in 1989, called a variational continuous assimilation technique. Here he says just going through the abstract. Because in this variational continuous simulation approach the model equations do not have to be satisfied exactly. Some of the effects of systematic model errors can be removed from the simulation. Thus, the variational continuous simulation technique was able to consistently fit the data better than the adjoint technique. And what's really nice from our perspective is as he notes here, as a byproduct of this technique and empirical correction for the model systematic error is produced. And we were interested in, in this aspect of it in trying to use this week constraint as a way of trying to characterize the potential systematic errors in our atmospheric model. There was work that was done independently suggesting that of course resolution. There were vertical transport errors in the model the vertical transport was too sluggish in the model and so we were curious as to whether with this week constraint approach we can characterize that and hopefully mitigated in the context of our inversion work. The, some of the results from using this week constraint approach was published recently in this paper by Stanowich et al. So we're done by former student Ilja Stanowich. And here we assimilated goes that methane data into our model at two different resolutions of course four by five resolution, and a slightly higher two by two and a half degree resolution. So this analysis we focused just on the February through May time period to look at the, these data terms try to characterize data terms to see if they can tell us something about the vertical transport errors within the model to see if they're systematic transport errors in the model to see if the data terms can point to the presence of the systematic errors that we think were present in the model. So just to give you a sense as to how this works on the left here are monthly mean differences between the model with the prior methane emissions and the go side observations for March, April and May. And, you know, I want you to focus on these three regions here East Asia, Central Africa, and South America so here in Central Africa and East Asia the model is biased high relative to the go side data, and in northern South America the model is biased high relative to the data. When we use the reconstruction approach to optimize the model states we optimize the initial methane distribution as well as these eight terms over the simulation window. With a moving window over this time period from February through May 2010. We end up with residual differences that look like this. So you can see these biases in the model relative to data are significantly reduced, we match the data fairly well. So what do the data terms look like this these corrections that are being added to the model states. Over the simulation window. The top panels are plotted the mean data terms. Average for March through May. The top panel shows the latitude, longitude distribution of these mean data terms in the upper troposphere at around eight kilometers. This is at the surface. And if we focus just on the surface one to begin with you can see that over Central Africa we have this downward correction of the methane, which is consistent with the fact that the model is biased high. Similarly over East Asia we have a downward correction of the methane because of the high bias, and over northern South America, we see this upward correction of the methane due to this low bias. Warm colors here, yellow to red represent a positive increase in methane, and the blue color represents a negative change in methane in the model, and it's really just these data terms that are being that are being added to the model. And you can see there's very nice structure that emerges if you look in the upper troposphere over East Asia, you see these negative corrections persisting throughout the column, the atmosphere column. Right off shore over the continent, you see the change in sign so you go from negative corrections, the positive corrections downwind. We can now take a slice through the atmosphere at 34 degrees north and look at the vertical structure of these corrections so this is showing altitude versus longitude along this red line here. And over East Asia, we see this negative correction in the surface that propagates up through the column, all the way in altitude up through the upper troposphere. But then we see this change in sign downwind. And this nice dipole pattern off the coast of Asia is consistent with our prior belief that the vertical transport in the model is too sluggish and so not enough of the methane was being exported from the continent. And that's over the North Pacific. So too much of it was being trapped, contributing to this overestimate that we see here with the state optimization using this weak constraint approach, we're able to correct for this overestimate over the continent because of this trapping, and also produce more add more methane downwind where you'd expect to see more of methane from the outflow. The same thing applies for Africa. If we now look at along the equator here, where we have these negative corrections you see these negative corrections here, but then you see increase export off the coast of off the coast of Africa over the Atlantic towards South America. So this really shows the beauty of using this mean this this week constraint approach to try to diagnose the systematic errors in the model transport and we're now applying this for our carbon dioxide assimilation as well to try to mitigate some of the export of the biases that we know are present in the model when we run course resolution to hopefully get more reliable estimates of the CO2 fluxes, but then what we've been able to do in the past. I'm going to change gears a little bit. Much of what I've been talking about so far has focused on using observations of a single trace gas to estimate emissions of that particular trace gas. So this is here, we're using methane observations to say something about methane fluxes in the atmosphere or CO2 observations to say something about CO2 fluxes to the atmosphere. But there is growing realization in the community that we need to assimilate multiple trace constituents to better constrain the potential chemistry biases that are present in our atmospheric models, because biases in the chemistry can impact the flux estimates and we, until recently have ignored those biases. A beautiful example of how we can do that is by looking at carbon monoxide. So going back to this carbon inversion problem. This is a paper by Bo Zhang, looking at the atmospheric budget of carbon monoxide over this 18 year period from 2000 to 2017. And the key thing here is to realize that when we talk about carbon monoxide, it's not only produced from combustion fuel from fuel combustion or wildfires by mass burning. CO is also produced from the oxidation of methane and other non methane hydrocarbons those all produce CO. It's removed in the atmosphere by reaction with the hydroxyl radical OH. So if you are using a model to infer emissions of CO because you're interested in getting at the fuel combustion emissions and how they're changing in time. If you have a bias in methane or a bias in the OH in your model that will produce a bias in those biases will get projected onto the estimated emissions. So it's really critical to try to characterize these, these, these biases. And that study that I showed you before where there were differences. In the Muppet study where there were differences between the two different studies, a large part of that is due to discrepancies in the OH in the models. So in this paper, they took advantage of observations of methane to provide a constraint on the methane source for CO oxide, which is a byproduct of the oxidation of hydrocarbons to provide a constraint on the hydrocarbon source of CO. And they also took advantage of measurements of metachloroform which is a CFC that reacts with OH to provide a constraint on the OH in the atmosphere. And in doing so they can now constrain the chemistry much better mitigate a lot of possible chemistry errors in the model and get more robust signals estimates of the CO fluxes. So when I'm focused on just on this picture here, this is showing the linear trend in the CO sources that they inferred, and you can see reductions in CO emissions or some negative trends across Eastern North America, Europe, and parts of East Asia. And this is really consistent with what we see in the Muppet data. Over the last 20 years, CO concentrations have been going down, driven largely by the reduction in emissions from these regions. The signals are now fairly robust. In the tropics for this particular inversion they showed some positive trends over Africa that they associated with anthropogenic emissions, but the signal is not as robust in different sensitivity experiments that they ran in the study. There were some differences that showed up in the tropics. So, you know, these signals are much more robust than the signals were seen in the tropics. The example that I have is this is one of a multi constituent assimilation and that integrates a fairly broad suite of observations to provide a consistent description of the chemical evolution of the atmosphere over a given time period. This is an analysis from Kazumi Izaki, a JPL, using an ensemble common filter assimilation scheme to assimilate a broad range of chemical constituents from 2005 to 2018 to constrain various aspects of the chemistry. This schematic here shows the really messy world of tropospheric chemistry that is embedded in our atmospheric models and discrepancies in the chemistry here will impact the emissions that we estimate when we use these models in an inverse modeling context. But the good news is that we have satellite observations and the situational observations as well of a large number of these constituents and so we can combine those data together in a multi constituent assimilation to provide a fairly strong constraint on, I shouldn't use that word, a good constraint on the chemistry and thereby get better estimates of the fluxes but also start to use these reanalysis because this is a reanalysis to try to understand the chemical evolution of the atmosphere as a result of anthropogenic emissions as a result of pollution emissions over time. And there's some very nice work that's coming out of JPL doing that. I'll show you quickly on the next slide, some examples of just how nice this system behaves. So the first example is showing vertical profiles of ozone in the troposphere in the lower part of the atmosphere. The blue line is the control model without any assimilation. The black line are balloon measurements, ozone sound measurements of ozone in the atmosphere, and the red line are the reanalysis. So these are the ozone coming out of the assimilation system. Bind and latitudinal bins from the southern hemisphere to the northern hemisphere. And on the bottom, this is the percent bias. And you can see if you focus here, the control run is clearly has some fairly large biases which are significantly reduced in the reanalysis. The bottom line is just showing the root mean squared errors and you're seeing significant error reduction as well as a result of bringing together this large sweep of observations. If you look at the change in surface nox emissions, this is showing the trend in the nox emissions. As I mentioned earlier, nox is a precursor gas that leads to ozone production. And you can see across North America, Europe and parts of Asia, there are clear negative trends, strong negative trends. I talked about this early at the beginning of the lecture. In South Asia, we're seeing an increase in nox emissions over this time period. These are the trends in carbon monoxide. Here are the negative, this robust signature that I talked about before on the previous slide, showing the negative trend in CO over North America, Europe and Asia as well. The OH radical, which reacts with carbon monoxide, changed dramatically in the analysis. This is showing the total carbon monoxide, the carbon monoxide is a function of latitude and time. So it's a half molar plot. And you can see, if we just focus on this one here, just the seasonal variation in OH, there's a strong seasonal cycle because it's driven by sunlight reacting with ozone and water vapor. However, when you do the analysis, we see a significant increase in OH. So this would suggest that if you use the control model to estimate carbon monoxide emissions, this OH is biased quite, is biased, which would then introduce a bias in the flux estimates that you would get for CO. So with the multi-constitutional approach, we now have a really nice way of constraining more of the chemistry to provide this consistent description of the chemical evolution of the state. And there's work being done now to look at using these reanalysis to better understand trends and use them for air quality studies and looking at health impacts and so on. So the suite of satellite observations that we now have really are allowing us finally in a data simulation context to start bringing together many different types of satellite observations to constrain the atmospheric state as well as the surface fluxes. I was hoping to spend a little bit of time talking about a new project that we are just writing up in our group in which we're using machine learning as a way to combine this information that we get from these chemical reanalysis with in situ observations and that sort of transfer learning, but I will skip this in the interest of time so that we have time for discussions. And just jump forward to the conclusions. The main point that I would like to leave you with today is that over the last few decades, there's been significant effort to take advantage of this wealth of atmospheric composition measurements that are now available so that we can quantify the emissions of environmentally important trace gases for air quality and carbon cycle studies in my particular case, but this applies for a range of other applications. And what's key is that the observing system as well as the data simulation tools that we have have reached a point where we can now provide information on surface sources and sinks of key trace constituents on policy relevant scales. And a very nice example of that that I want to draw your attention to is the fact that the community on earth, these observations satellites see us. That's an organization of space agencies have an activity to use observations of atmospheric CO2 and methane to provide surface atmospheric fluxes of these gases for the UNFCCC global stock take which is part of which is a component of their Paris agreement. So this is a very nice example where we're reached point where we can now start to use these data in an interesting policy relevant play. As we look to the future, we're going to need to see a continued expand expansion of the observing system both ground based as well as space based to provide constraints at greater spatial and temporal resolution. As we look to the future, you know one exciting development that's coming down the pipeline are geostationary observations for air quality. We have gems, which is a Korean satellite to geostationary satellite that was launched last year. Next year we'll see the launch of tempo, which is a NASA geostationary air quality satellite, followed by the Sentinel for which is a European geostationary satellite. And there's a geostationary carbon cycle satellite geocarb that's scheduled for launch probably in late 2023 early 2024 and combining these geostationary measurements that will give us tremendous temporal resolution with some of the low Earth orbiting polar satellites will allow us to constrain what's happening on the continents as well as to capture this intervent of continental transport of pollution very nicely. To do that, we're going to need to continue to develop new data simulation approaches so that we can integrate these data effectively across a wide range of spatial and temporal scales, because the chemistry covers a broad range of the temporal scales. The OH radical has a lifetime of seconds, carbon monoxide has a lifetime of a month or a few months, and methane has a lifetime of a decade. So as a broad range of time scales that you have to deal with in your assimilation, when you try to integrate these these data and so we're going to need to come with much more computationally effective and innovative data simulation approaches to deal with this growing wealth of observations. So without that and take any questions that you have. Thank you very much. Thank you very much. I agree with also with time scales which are really makes a big issue in the assimilation of data and so on because it's important so resolution. But anyway, it's I think you're very much for the wonderful survey which you today give us survey through the atmospheric modeling chemical modeling and how it's particularly connected with the photo bar and the techniques and so on it's used in this modeling. So this is some time for questions, answers and as I mentioned there are a few questions in the chat box. I can read them.