 And then, okay, and then you're ready to share your screen. And thank you. Okay. Well, thank you, Judith and Anish, for inviting me. And sorry I got a little confused about the schedule. I'll talk today about the work that we have done with my colleagues at Naval Recessional Laboratory. And it was sponsored by O&R that provided us the capability to run the three large simulation experiments. Now, I'll talk today about ensemble forecast in the context of ocean measure scale models. And this work is published in the paper led by Prasad Tapil. Okay, so what are ocean measure scales? So this is a picture of Corosio current. And you can see this swirls. It's very similar to Gulfstream. I'm pretty sure that everybody in this room knows about ocean measure scales. But to the summarize, there's these features in about 100 kilometers across, no scale, about hundreds of kilometers. But the essential for, the essential dominate energetics of the ocean, modified mass, heat and fresh water transport, primary production and gas exchange in the upper ocean. Joe Metsger looked at predictability of these features in deterministic models. And he find that the predictability is about two weeks. So for example, on the right, he has this die off curves for anomaly correlation for Corosio SSH or the same view using SSH RMS. And you could see that the reach point six anomaly correlation about two weeks or they reach the climatological RMS at about the same two weeks. However, some case studies suggest that sometimes edit dynamics can be predicted out to order of 100 days. There is no systematic study of ocean middle scale predictability like we saw from Judith Falco earlier today. So we don't have a more theoretical upper limit like we have for mid-latitude weather. So classical view of how we're gonna get better ocean forecast is to just essentially write the Moore's law. And here we have this graph from Baylor Fox camper that looks at how IPCC model ocean resolution increases as a Moore's law increases. And there is a study by Cheseney and others. There are many very similar studies that shows that as you increase model resolution you can better represent the climate of Western boundary currents. To note, naval models were always about an order of magnitude better resolved than IPCC models and they've been resolved in middle scale for about two decades now. So with this latest project on coupled forecasting that we had at the Navy called Navy ESPC we had a unique ability to test the hypothesis that improved resolution and improved physics can lead to improved ocean middle scale prediction. So we had two models that we developed a deterministic short-term model which was zero to 16 days at 19 kilometer atmosphere in about four and a half kilometer ocean in mid-latitudes. And we had a probabilistic forecast to zero to 45 days, 16 members, little bit coarser atmosphere and about nine kilometer mid-latitude resolution for the ocean. Deterministic model also had tides as part of the formulation. So these two model configuration allow us to test the following experiments. Hypothesis, does increased resolution help for ocean weather scale prediction? Does better physics help such as coupling and tides and do ensembles help? So a quick look here on the left is the original picture from Metzger and a very similar picture from our experiments. So one of the first things you would notice that our climatology got better. So if before the RMSE of climatology was about 14 centimeters, now it's an order of 11 centimeters and this new climatology is computed I think using a dynamical model. So the second thing you would notice that both high-res and low-res, you know, 112 is not considered by low-res by most people but the 112 degree model have the same deterministic skill for a cessation normally. So doubling the resolution and including tides did not really improve a bulk measure like RMSE of mid-latitude ocean weather. But doing ensemble predictions almost tripled the score. If you look at other metrics in mid-latitudes such as the Institute of SST, temperature from upper ocean temperature, from profiles, mixed layer depths and surface heat flux, you can see that ensemble forecasting helps in every single case. One thing you would notice is the error bars on the subsurface properties is much higher because we have fewer measurements. And you also notice the surface heat flux is very short, you know, we're talking about less than 10 days' skill. And I think it's because surface heat flux is highly dependent on what the atmosphere is doing. And as we know, the atmospheric predictability is under two weeks. So this next set of questions to ask, why is ensemble mean forecast better? Is it because ensemble mean is smoother? And are we penalizing the high-res forecast by using RMSE scores? And a lot of this work has been already done in an atmospheric weather forecasting. So it's not new, but all of this work was new to the ocean domain. So that's the novelty of this work. And we're kind of right in, in the wake of atmospheric research here. So the way we're gonna do it, we're gonna explore this along track SSH altimetry. So you can see the pictures of this SSH tracks on the top figure. And we're gonna decompose it in a spectral domain. So we'll look along the track. So it's a 1D measurement. And we're gonna decompose it. We can look at the power spectrum density of the altimeter measurement itself, which is a black curve here. Let me switch to a pointer. We can decompose the signal of the model and we can decompose the error of the model minus altimeter minus model. But our skill metric will be the R-square skill metric. So we'll take the ratio of power spectrum of error divided by the power spectrum of the signal. And the way you interpret it, if your R-square is above one, it means that your errors are higher than your signal. So you have no skill, your errors are higher. And if your observation error is low and the variance of your model is comparable to the variance of the signal, that the maximum R-square is two, which means that you have your perfectly off phase in your observations and in your model. So if you perfectly off phase, the R-square is two. However, if your R-square is less than one, it means you do have skill, your errors are smaller than your signal. And we determine it as a skillful model. An important note here is that altimeter does not provide useful information for under 150 kilometers. So for average over multiple ensemble realizations, we can look at a one day forecast as a proxy for initial condition in a 10 day forecast. And we can see that in both deterministic models, they lack skill under 300 kilometers. So it's a kind of lack skill in this important metascale regime, but ensemble does. And the same picture stands for 10 day forecast. So our suggestion is that this happens through the snow linear filtering of scales, of uncertain scales. So we can see that in a deterministic sense, initial condition is not constrained for scales under 300 kilometers. So let's look closely at this filtering of scales. So look at it from two perspectives. So the most intuitive one, I can look at the ratio and I can plot the location of fronts between cold and warm water. So in this case, it's an SSH front. And you could see that if I plot individual forecasts in the ensemble, that the gray lines, there is a very high uncertainty in location of very small edges. But the large fronts are much better constrained. And what happens that when you average over this multiple realizations of ensemble, you come up with some consensus of where the large fronts are located and where the potential is a small edge is allocated. And that's what I mean by filtering of scales. Another way to look at it, you can initialize a low resolution deterministic forecast from ensemble mean. And as you do your forecast, initially you're tracking the error of ensemble mean, but after a while, because it's a deterministic forecast, your skill converges to that of a traditional deterministic forecast. And it's because you have a specific front realization that will always be erroneous, losing the ability to filter scales through averaging. So now the criticism was always like, well, you know, ensemble mean is smoother. So what if you just smooth a high resolution simulation where you get a more skillful result? So we did smooth our high resolution simulation. So here on the left, we're looking at R square again. And indeed a smooth solution is skillful, but there is a gap in skill between ensemble mean and Gaussian smoothing. And to demonstrate it, we can look at the splots on the left where we have high rest resolution, high rest simulation, low rest simulation. Ensemble mean, smoothed high rest and smoothed low rest. And there are a few things you will notice. First, once you smooth, you lose the variance of the single signal. That's one thing that happens, but you also lose a lot of information about the sharp gradients. You could see that ensemble mean preserves quite a bit more information about where these edits are located and we know it's a skillful information. While the smoothing just, it's a blunt tool. But the benefit is that, when you smooth a high rest simulation, it's a much cheaper computation and you know, you inherit the low biases of high resolution model. My final slide. So not all ensembles are born the same. So here I'm looking at the spread of our eddy resolving ensemble versus the spread of one degree ensemble. And the spread of high resolution ensemble is about 20 centimeters in the boundary currents. And eddy parameterized ensemble, the spread is about one centimeter. So it's about an order of magnitude less. If we run a quarter degree model, maybe we can compensate for the deficit by running stochastic physics, but that's an open question. So to summarize, first increase in ocean model resolution beyond one-twelfth degree, in addition, improved physics at least little skill to the deterministic ocean forecast. Eddy resolving the ocean ensemble considerably increased the skill of the ocean weather scale forecast and the superior skill of ensembles achieved through no linear filtering of poorly constrained ocean weather scales, which is similar to the results we had in the atmosphere. To really improve the ocean weather scale forecast, we need more observations. So there are a couple of observation missions that are currently planned, one's called vacuum, the other one's called SWOT, that can really beat down that initial condition uncertainty. And that's my end of my talk and I'm happy to take any questions. Yeah, thank you, thank you very much. That was quite interesting and I'm not an ocean person, so it was new for me too, but what it reminded me of is when I worked on an ensemble system that was very at the time lacking spread in the tropics, you could do anything, anything, any stochastic optimization and the skill would go up and the reason was that you had these unpredictable scales that were represented in all ensemble members and all you had to do is noise them up a little bit and then the skill would go up dramatically because all these scales were the same but they were all uncertain and so there was too much correlation in the unpredictable system. That's sort of what this talk reminded me of but as the system improved, it became much and much harder to have the same effect in this case with stochastic criminalizations because the ensemble members had more diversity and so a lot of the things you talked about sort of interpreted sort of from that experience. So thank you, are there any questions? Cickel, I want to add on your comment, Judith. So the difference here is that the initial condition is unconstrained. I think that the main problem we don't have because we can't simulate all scales. I mean, this is 300 kilometers and our model has a four kilometer resolution so we can definitely, if we have a better initial condition, we can't carry these fronts very well. So it's a little bit different than tropics in the atmosphere. I appreciate that remark. Thanks so much, Anish. Thanks, Durit. Thanks, Agay, it was really interesting and I guess my question is somewhat related to the initialization problem that you just mentioned. So we have trouble observing these scales as well in the real ocean, right? With the satellite, you would observe the surface. We would SWAT and Wacom, we would get close to these scales but with the subsurface, we don't have observations that would capture this unless you have like really high resolution gliders in like very specific regions. So in terms of initializing either global models or regional forecasting models, are there plans to observe these in the subsurface or do you think like just observing the surface and then using some kind of SQG or other theories to extrapolate to what the subsurface mezzo and submesoscales would look like to initialize them, would that suffice? I mean, you could see if I go back. So on this slide, I'm showing the middle panels is a subsurface temperature. It's not as well constrained to the surface temperature. So adding more and like mixed-layer depths, even worse constrained. So if you're interested in the subsurface, I think you just have to have subsurface measurements. So should that be just in the upper ocean like the mixed layer and? It depends on your application, right? I mean, if you're thinking about weather forecast, right? Yeah. SST is a key and if anything, SST is all observed right now. Yeah. We have as many SST measurements per day as all atmospheric measurements together. But I mean, especially in the tropics, it's not just the SST, right? Like the mixed layer. Yeah, so you want to know what the thermocline is doing, right? And you want to know the depth of the mixed layer, so you know how fast the ocean can respond to your atmospheric perturbations. And you have to observe it. I mean, there is no, I mean, Yeah. You can't, you know, you don't know the SSH can only tell you the displacement of the thermocline that can not tell you where the thermocline is located. Yeah. And there's nothing on the surface. Well, there's a few measurements on the surface that can tell you in fairer the depth of the mixed layer. I'm saying some optical measurements for shallow mixed layers, but you know, that's... Right. That's not going to help, I mean. Right. Yeah. I mean, the other question I had, if I can't do it, I don't see it. So the other observations that currently we don't have at these scales is the surface fluxes, right? SST is one component of it, but we don't observe the planetary boundary layer and its impact on the surface fluxes, which also is really key for the coupling problem at these scales, mesoscales. And especially in the mid latitudes, there's been studies that show that the mesoscale air-sea interaction does matter for atmospheric weather evolution. So, yeah, would you have a comment on observing the surface fluxes and assimilating them as well? So, especially in this western boundary currents, you know, the ocean atmosphere is highly coupled. Yeah. And it is easier to observe high resolution flux at a high repeat ratio than to observe SSH with the same resolution. And there are plans to do just that, you know, the butterfly walk on missions that will allow you to observe fluxes over these areas. And I think the challenge for the data assimilation communities to be able to invert these fluxes into location of edges. And I think that that will dramatically improve our ability to constrain the initial condition for the ocean. Great, thanks. Thanks very much. So, next we're going to go to Gatotown. Thank you so much for posting the link, Anish. And we can look at the posters and just network in the different areas, both private and public. And then you will return after the networking and a break at 11 a.m. And our next speaker will be Sam Stevenson. So, see you over in Gatotown and then for sure you are at 11, Sam's top. Thank you. Thanks to all speakers today. It was great.