 So, I think it's a bit more than nine o'clock. So, let's start. So, we talked today about S2S model initialization and ensemble generation. So, that's a topic that has already been quite discussed in previous talks. We have some things on those earth. So, there will be a bit of a repeat, but I think sometimes it's not bad to see several times the same concept. So, we start, first of all, with a model initialization. And so, this slide here represents the end-to-end forecasting system, like the one of the S2S models, like the same way for handset and others. So, the first stage is observation, is to collect observation for the atmosphere, for the ocean. I will go a bit more in detail later on. The second stage is to transform those observations into initial conditions. There are two sort of projects, those observations into the model space, so that those initial conditions are at the same resolution than the model we will run. Then, we integrate ensemble forecasts where we use the ocean-atmosphere-couple system. And, this is a Taylor forecast product at the end. So, this is an example from the CMDF seasonal forecast system, system four. We have anomalies of SSTs. You can have a tropical cyclone predictions, or you have an anion prediction. So, which information do we use to initialize the atmosphere? We use quite a lot of different type of instruments. We use satellites, use stationary satellites. We use polar orbiting satellites. We also use GPS satellites. We use also aircraft. We have also drop zones. We have also radars. And, we have also seen-up data from land. And, we also ship. We have also buoys drifting mode. So, we have quite a large number of instruments now. And, there has been a really very strong increase. I will show that later in the number of observations coming from satellites. Actually, that's been quite a big revolution over the recent years. So, to give you an order of magnitude, we receive about 150 million observations. 99% from satellites are received daily. The current system, data transmission system, CMDF, uses only 15 million observations. So, 10%, 96% from satellites, which are used every 12 hours. So, the coverage of satellites is usually very good. You look over the most of the areas. For land observations, it's a bit which are crucial for really high-quality initial conditions. Yes? Yes, exactly, 10 years ago. I will show a slide later on showing this. Yeah, yeah. Yes. Yeah, Sirain Tehrim is about 1.5 million. Yes. So, the land observations over land are very in-emergency news. You get areas which are extremely well covered, very well covered, and some areas where you have very few observations. And, there is much more observation over land than over ocean. So, over land is still a very strong in-emergency. And, from the ocean initiation for ocean observations, we initialize the ocean by running an ocean model. For that, we need observation of SST, and we need subsurface ocean information. So, the observations from the ocean have a very strong big revolution over the recent years. So, before 1982, the only ocean observations we had were HBT's, which were measurement from ships. Those were scientific vessels or could be ships of opportunities, like commercial ships, which were doing some measurements. So, you can see here, for example, the tracks of those measurements. And, it was mostly at the surface of the ocean. You didn't measure the deep ocean. From 1982, it was the introduction of a satellite observation for the ocean. But, the electromagnetic radiation from the satellite don't penetrate inside the ocean. So, the information you get from satellites for the ocean are only for SST and the ocean level. And, from 1993, okay, during the 1980s, there were two very strong El Nino events. There was a 1982, 1982, 1983, 1986, 1987, which generated a lot of interest for El Nino. And, the scientific community realized that there was very little observations to really be able to produce very good forecasts of those El Nino. So, there has been a project called Togacor, which led to the installation of moorings, the Tau and Triton moorings in the Pacific, in the equatorial Pacific, which was extended to the Pirata in the Atlantic and later on to Mara in the Indian Ocean. So, this is all an array of buoys which are anchored to the bottom of the ocean. And, they are extremely useful. And, they started in 1993 to produce a time series of temperatures, salinity currents, for example, from 1983 to now. The problem of those buoys, that's an example here, is that they are very vacuously to maintain. There has been a vessel, actually a scientific vessel from the U.S., which is really used full-time to maintain the buoys in the tropical Pacific. There is a lot of problem of some of them shutting down for particular reasons, a lot of vandalism. Some are stolen because they contain some quite expensive piece of equipment. And, recently, actually, this vessel was a rougher beach and only 20 or 30% of those buoys are still active. So, there has been some talk recently to suppress them or to replace them to something else. So, there is still no conclusion about that. Because since 2001, and that has been a really big revolution for the use of argo floats, which were then really operational, fully operational in 2005. So, those floats start at the surface. They are not anchored to the bottom of the ocean. They are just floating. They go down to about 2,000 meters, give measurements of temperature, salinity. Those give very good profile of the ocean subsurface. And then, they go up, transmit the information to the satellite. We give it to the operational centers, and then go down again and again. So, they are not always located at the same location. They can drift. But, there are so many of those buoys that, actually, it covers very well the whole ocean, all the oceans. So, as we can see here. So, this plot here shows the coverage, an example for June 1982. So, there are only observations, as I said, at that time, where HBT is. So, from ships. So, you can see the ship tracks. So, you can see that area where you have a lot of commercial ships are somewhat covered. You have some bizarre trajectory like this one, which is actually a scientific vessel, probably, which was observing the East Pacific. And, this is a coverage. But, you can see that entire area, for example, here, the South Pacific and Antarctic regions are completely devoid of any observations. The South Indian Ocean was very poorly observed. Today, this is an observation from November 2005. There is even more now. So, we can see still the ships being used, HBT observation in black. The red is the Tau Tracton Array, pirata in the Atlantic, Mara here, a few more ins in the Indian Ocean. So, they are all along, they are in it, all along the tropical ocean. And, all the blue represents one of those Argo floats. So, we have quite a nice coverage about it. So, as you can see, the problem for reanalysis is that we have a very strong inconsistency in the observing system from between a period from one period to another. And, for the ocean analysis, it can be quite a problem. It means that we have, I would say, a correct observation of the ocean only since November 2005. And, this is from the atmosphere, too. We have the same problem of inconsistency in time. This is the number of observations used at this MWF. Similar plot that Adrian showed the other day, a bit more recent. And, we can see there has been really a revolution in the huge increase in the number of satellites used. So, for a high interior at that time, we have much, much more observations now. And, once again, for reanalysis, this is quite a challenging because it means that there will be some inconsistency before 2000 and after more recent periods. OK. So, once you get the observation, you have to go to the next step, which is data simulation. So, the idea here is to use those observations to produce the best estimate as possible of the initial conditions and to project them into the model world. So, what is done usually at the MWF is to use a 4D bar data simulation where you run from the previous analysis a forecast, a simple forecast, which is called the first model and you compare it with new observations at the time, the recent time, and then you change the trajectory. OK. So, once again, we have over 50 million observations estimated to correct 100 million variables that define the model's virtual atmosphere. And, the assimilation relies only on the quality of the model. So, the quality of the initial condition is due to the quality of the observations themselves, but also the quality of the model, which is the same as the first to produce a forecast. One thing I want to point out is this data simulation is extremely costly. I mean, the MWF data simulation is done with a 4D bar at 16 kilometers, which is the same resolution as the high resolution model. And, it's about five times more costly to run the data simulation than to run a forecast. So, this is really the big part, which is of the cost of forecasting a system. So, this is an example from 4D bar. So, we start from analysis. We run what we call a virtual forecast, the first guess. And, then we modify slightly the initial condition. Those are the trajectory that fits the best with the observations. And, then we start the forecast. OK. So, the simulation is very important for the, particularly for the ocean, because models have their own drift, they have their own climate. And, if you don't use these observations, then you can get, you can get a relatively long mislay of this. And, this is mentioned, it's partly important to correct the slope on the mean depth of the equatorial thermo-cline. So, in a free model, for instance, we get an equatorial thermo-cline like this. After a data simulation, we tend to get usually much more realistic data simulation. So, it's a very important process for the forecast. So, once you have done this, you will start your forecast. And, one issue you have with the forecast is, as was discussed two days ago, is the initialization shock, which is an accelerated development of model errors at the beginning of the forecast, which can be due to several things. One, there is an inconsistency between the model atmospheric initial conditions and the model physics. That's why people try to use the same model for data simulation on model integrations, which can reduce this problem. But, when you do a re-forecast, you start usually from a re-analysis which has been produced from, sometimes, no different operational centers. For example, you use ERA, Interim. That's the case, for example, Bureau of Meteorology, where they are using ERA Interim. And, they start with the atmospheric model is completely different. And, this created a shock. Problem, too, is that usually, the atmosphere and ocean are initialized separately. You have a data simulation for the evaporation of the atmosphere. For example, three divas for the ocean, and they may not be in close balance at the start of the model integration. We also perturb differently the atmosphere with the ocean. So, there is a bit of inconsistency between the two. So, there are several solutions. Some people do the nudging techniques, which consist of running the model over the past several years. This will ensure that the initial condition to be more consistent with the model physics. That's been an example from Bureau of Meteorology. As I said, the re-forecast started with ERA Interim. They had a big shock at the beginning. So, what they did is to run their own model and relax the UVT to ERA Interim and then start the initial condition from that. And, this gave much, much better results, actually. And, the other trend is to go to couple data simulation, which can reduce the initialization shock since the atmosphere on the ocean will be closer balanced at the start of the integration. So, regarding full couple data simulation, the advantage is that you have a more balanced ocean atmosphere and perturbation, the important for tropical convection. This is also a framework to treat model erode, initialization and forecast, and consistency across certain scales. So, current approach is to go for weak couple data simulation, which means that you run the first guess with a couple model, but you produce a separate data simulation for ocean atmosphere. That's the example is done at NCEP, with CFASR, ECMWF, with the ESA-SERA project. So, our next analysis, for instance, ERA 5 will be produced with a weak couple data simulation. Strong couple data simulation is much more difficult because the atmosphere on the ocean has very different time scales. And, the data simulation uses a much longer windows in that ocean than in the atmosphere. So, usually, people take me to use UJ's sensible command filter. OK? So, now we have initial conditions. We can run your model. And, as I mentioned previously, for subsinular forecast, we need to run reforecast. We run real-time forecast, for example, we send away 51 members of the model, and then we calibrate with a five-member ensemble at that time from 1984 to 2003-13. Now, what is very important is to, though this reforecast or handcast is used to estimate the climate of the model, what is what important is the initialization of this reforecast to be as consistent as possible with the initialization of the real-time forecast. So, for example, at this end wave, the initial conditions from the reforecast are used in Iran and Tehran because we don't have the same analysis as for the real-time forecast. We use the ocean reanalysis, solar analysis, and perturbation. We use it quite to mimic exactly the same type of perturbation we do for the real-time forecast using the Lola vectors. And, simple data simulation for recent years because we don't have them in the past, we don't have the same basket of schemes on the total physics. Now, this is, we say, quite a very difficult, very big challenge for seasonal predictions is to get this right. I mean, here I will show you an example of a forecast which was issued quite some time ago. I mean, this was issued on the 11th of May 2006. It shows the probability of two meter temperature to be in the lowest air size. So, red means you have warm conditions, blue means cold conditions. So, can someone spot something weird about this forecast? Sorry? The point here, exactly, yeah. So, this looks a bit weird to have in the middle of sort of, this was a period of heat wave, just a few points which tells you that actually the temperature will be much colder than normal. So, we actually, when we issue this forecast, we got a phone call from Meteo Suisse wondering what was going on. They say, what tell you exactly what they say? So, what can cause this? I mean, what do you think was the reason for this problem? Does anybody have any idea what can cause that? Adrian? Partially. I mean, that's our region. It's two of a high geography. And for those of you who are not very familiar with the Europe geographies, this is Switzerland. You have the Alps, the very high geography. And the operational analysis is a much higher resolution than the era in Tehrim. At that time, actually, we were using era 40, which was at E159. So, that was part of the problem. That was not all of it. The main reason, when we look at it, was actually to look at the surface, initial conditions. And in May, here we are in May. And we will look at the snow analysis. So, this plot here shows you the volume of snow from the ESEM-DOF analysis from 1994 to 2006 over a blob here. So, what it shows is that from 1994 to 2003, there is virtually no snow in the ESEM-DOF analysis over Switzerland. And, suddenly, after 2004 to 2006, the analysis tells you there should be about 10 cm of snow on average over this area. And, if we look at observations over Switzerland, we can see that there should always be snow, and there is nothing special from 2004 onward. Now, what happened is that in 2004, we started to use an SD satellite, which gave a much better observation of snow. The data simulation scheme changed, although the snow scheme in the land, which means that this increase is, of course, completely artificial. So, in era 14, there is also two in era 13, there is virtually no snow in Switzerland at this time of the year. Whereas, in the ESEM-DOF analysis, you have quite a lot of snow. So, what happens here is that the real-time forecast starts with snow, those very cold conditions. And you calibrate with the forecast, which has no snow. That's why you get a sort of permanent cold spot over Switzerland. And this cold spot can last 30 days because the snow takes a long time to melt. And you could see all along the spring period and over all the monthly forecast from 2005 to 2006, 2004 to 2005 to 2006. So, that was really a big problem of inconsistency between real-time and re-forecast. And this is the reason, since that we do not use the soil initial condition for Meraintérym because it's a completely obsolete scheme. It's also true for snow. It's also true for soil moisture. It uses a TESOL scheme, not a HTSOL. We can do a sort of recalibration, but it's not as good. It's still the cause problem. That's why we are using a Sol Reanalysis, which consists in running the HTSOL model, which is a soil analysis model, forced by ERA Interim and also corrected by GPCP because the precipitation from ERA Interim are not that good. And simply so do 20, 30 years reanalysis. And it's very, very cheap because it's not really a data simulation. We don't estimate observations. And it takes about two days to run 20 years of re-forecast. And the advantage of it is that we can run it at the same resolution as the real-time forecast, as the first 10 days forecast at 32 km. So, we don't need after that to interpolate to get the right model resolution, which can sometimes be a cause of problems. So, to give you an idea, this is an example of the snow. This is a total snow cover in January, something that's January 17, 9. This was in ERA Interim. And that's with a new scheme, with a new model. And this model is not perfectly consistent with the one we use in real-time forecast. So, we ensure, at least, much more consistency. And you can see quite some difference. First of all, in ERA Interim, it's a much, much more smoother field. This one has much better, and all much better, topography. And you can see some very big difference over Canada. Here we have much more snow in ERA Interim than you get in this new solar re-analysis. So, if you do the difference between the new climates, new snow cover from the new solar analysis minus ERA Interim, that's surface temperature, you can find differences of the order of more than 4 to 8 degrees in the high altitudes, not so much across in the tropics. And this can generate very different forecast. So, here is an example of a forecast from 1st of January 2011. We are looking at day five to 11. And this is, the real-time forecast is the same. But in this left panel, we calibrate, we produce an anomaly relative to a re-forecast initialized from ERA Interim. So, it tells you there will be cold anomaly over the other one anomaly here. On the right is a forecast, so with the same real-time forecast once again, but this time calibrated from re-forecast initialized from this new soil initial conditions. And you can get the almost exact opposite signal. Here it tells you it's warm and it will be cold over near the legs. And if we compare within obdata, we find this one is much more consistent within obdata anomalies than with all one. So, once again, this is something that is consistent between real-time and re-forecast. And that's the problem for people who are using, for example, ERA Interim to initialize a re-forecast on their own analysis for real-time forecast. You can generate very unrealistic signals. Okay, Ansible generation. It was a bit covered over the last days, but it would be a bit of a repeat. So, as I said, there is a lot of different strategies to initialize to generate the Ansible members. So, first of all, why do we need Ansible? Because the models are not perfect. The model can fail for several reasons. The initial conditions are not accurate enough. They are due to poor coverage and observation error in the assimilation. That's the initial uncertainty. So, for example, we have a poor coverage of Atlantic, which can generate model errors. And the model used to assimilate the data to make a forecast described are not perfect. They describe only an approximate way of the true atmospheric phenomena. So, the addition of them means that forecast may go to the wrong direction. So, we need to sample those errors. And the Ansible prediction, the goal is to estimate the probability density function of forecast taking into account all possible sources of forecast error. So, we start from a PDF of the initial conditions to measure the uncertainty in the initial conditions. Then, we will propagate the forecast to obtain a PDF at the end. So, this is quite an important process because it gives very important information to the user of how confident it can be. As an example, here is predictability for tropical cyclones. So, here we have tropical cyclones. So, the black line represents the high-gradation of deterministic forecast. And the colors represent the probability distribution. So, it shows here that most of the old Ansible member basically predicts that the storm will recurve and go in this direction. So, the spreading is relatively small, showing that people can really trust the forecaster, and really have more trust in this forecast. You have other cases where you can see the Ansible going in all directions, which can tell the forecaster that, well, for this case, we may not know what is going to happen. And that's an information you cannot get with a single deterministic forecast. So, that's something really important for the users. So, OK, they tell you for each Ansible member, so you have 51 of them, what is the intensity of the tropical cyclone for day one up to day ten? So, if it's orange, it tells you it's a tropical storm. So, green is a depression, and orange means it's a hurricane. So, it gives you a bit more idea of the distribution. Ansible member will go here more than seven days, or some stop at day seven. So, it's a way to see what is going to happen. So, to create initial prediction, a simple method is a lag approach. That's why we did a C&UF for seasonal forecast system one. It simply will run the model one Ansible member every day. And the difference from day to day is a measure for uncertainty, basically. And to see to create an Ansible forecast for seasonal forecast, we are taking simply all the seasonal forecast starting for the 15 of a month to the 15 of the following months, which give you a result. And that was the way to create the model. Some model in S2S, like a Met Office, although are running their model once a day, but with four Ansible members. There is a bit still the same ID. And the other technique is to do burst initial conditions like at C&UF. Here we run 51 Ansible member from 15 perturbed initial conditions versus the lag Ansible where you can run several Ansible member once a day. So, as discussed already, I mean, I won't go too much into this. There is an advantage to each. One thing I want to say is that the burst approach, the advantage is the freshest initial conditions. And you have more control on the Ansible generation. The other one is a bit hard dock. You initialize the model from one day apart and you expect that it will give you the white Ansible spread. Whereas with the burst approach you can really calibrate well your Ansible spread so that the AMS error matches the spread. The disadvantage of the burst approach is that, first of all, it is too costly to run daily, at least for substantial forecast. For maybe your money, we run it twice a day. But for substantial forecast, we run it currently twice a week. And there are some things that really forecast their absolutely head is what I call the flip-flop forecast. So, you have a forecast in one day which tells you, well, next Sunday it will be very rainy over three years. Be very careful. There will be very, very difficult conditions. On the following forecast, which is issue 12 hours later, tells you actually it will be very sunny. On the forecast, 12 hours later, come back to very wet conditions. On the one after, come back again to sunny conditions. And that's something which happens sometimes, which is called the flip-flop. And once again, sometimes the forecaster prefers the model to be totally worn, consistently worn than to have these sort of jumps. Yes? No, we haven't done that. And that's something we plan to do in S2S, actually. And the S2S database will be quite useful for that. I mean, that's one big question actually for the S2S database to understand what is the best approach. I'll say we don't know yet what has been, or they really compare. Yes? Because the lag approach, you average over seven days. OK? So you sample much more forecast. The forecast are evolving much slowly from day to day. OK? So if your forecast suddenly becomes different, you still have six forecasts. We are the same before. And then you see the variation is really looking much more slowly. And that's what people prefer sometimes. You have a much smoother evolution of forecast. Although the forecast can be less skillful for one event time than the best approach. And the longer actually you take your windows to average, the smoother actually you are. And the less dramatic change you have. Yeah? Yes, but the problem if you do that, then your sample becomes to be very small. So that's a trade-off. And that's, again, an important question we plan to address. For example, NCEP has a 16-member ensemble every day. So what is the best strategy? Just to issue us like a 16-member birth ensemble and do all your forecast priority on those 16-member? Or is it more skillful to combine with the day before to get a 32-member ensemble on day greats like your initial condition? Or to go three days behind that you have a bigger ensemble can do maybe a more accurate prediction of extreme events on the one? So that's an important question we need to address. But the response to this may depend on the time range because for short-range forecast, there is really a huge disadvantage to use a lag approach because the quality of the initial condition will have a dramatic effect. For a longer, for a single time range, it may probably not matter because we are long enough to lose this memory. OK, so there is, for the birth sample, there is two different approaches, the Monte Carlo approach which is to sample all sources of forecast error and to perturb it on any model parameter that is not perfectly known. So it's taking into question as many sources as possible of forecast error and then perturb them randomly. Or there is a reduced sampling which is mostly used in operational centers, is to try to target specific source of forecast error and pre-authorize, so optimize the sampling. And for that, what is used as I said, PCMWF is to try to detect the growing components which will dominate the forecast error growth because we have a big constraint, although it is a limited process. So all initial conditions will be defined. We have to find in which directions the error grows as we have a maximum growth. So we have two different techniques. I won't go into details. Don't worry, I am going into the equations. But one is a singular vectors technique at PCMWF. The goal is to find, we built a linear version of our model. And we look at which direction of the largest growth after 48 hours. And then that was the way we defined our 50-member ensemble. EnSEP as a slightly different technique which is the brilliant vector. Here they are based on perturbation of going faster in the analysis cycles. And then adding a random perturbation, evolving and rescaling, and then repeat. But since I thought evolving quickly. And then we have also a new technique starting this ensemble data simulation. So here the philosophy is a bit the same as for the forecast. Initially, the medium range forecast were issued with only one single model, hard resolution model. In the 1990s, we went to the ensemble models trying to quantify the uncertainty after the forecast. And for the data simulation, the same. For a very long time, we had just one single data simulation at very high resolution, 16 kilometers. And now as with forecast, we have an ensemble of data simulations for using for diva but a much lower resolution, which are used to perturb the main analysis. So we don't start actually exactly from the each ensemble data simulation member. What we do is to compute the difference between the two ensemble member of the data simulation and add it to the hard resolution analysis because we find that the hard resolution analysis will give you an advantage in the short medium range forecast. So the way it works is that we know of an ensemble of data simulations and that's where we start to run our model. If those data simulation were perfect, we should adjust that should be enough to calculate the ensemble. The problem is that the spread with the ensemble data simulation alone is not large enough. So we still need to combine those ensemble data simulation with the breathing vector or cellular vectors to generate our ensemble. For the ocean, the ocean lacks a bit behind the atmosphere in terms of technique for ensemble generation. What we are doing at ISMDUF is a very hard rock way to perturb the ocean. We do an ensemble of data simulation, a five-ocean. We produce five-ocean analysis or analysis by perturbing randomly surface winds used to force the ocean model. And in addition to that, we add a random SSD perturbation added at step zero. So those random perturbations are calculated but taking the difference between different SSD products that give us a sort of idea of what are all certain things, the SSDs, and we apply them randomly to a step zero. And we give them a 3D structure today to 60 meters. And the plan is to use weekly couple data simulations in the future to initialize both atmosphere and ocean. This one is the first guess. Before, really, use the data simulation. And then after, you compare with observations, you modify slightly the trajectory so that they fit the observations. So that's really where your initial condition will be. And then you start your first EPS. So this one, the red one, is the first guess, the first run. You start your analysis. You run your model for 6,000 and that. And then you do corrections. And that's the second which gives you the other tracks. And then you start. Exactly after the 12 hours. Yes. The 12 hour window. Yes, the 12 hour window. Yes, sorry. And then you start at 21, then the forecast. OK. So you have seen that. What is important is the reliability of the ensemble. Normally the reliable ensemble spread is a predictor of the ensemble error. So you expect your error to be generally inside the ensemble distribution, as was explained in the previous talks. The problem if your model is under dispersive, it means that the error is often outside your error. So your model is overconfident. So we have seen this previously. So the problem is that if you just perturb your ensemble, you just perturb your initial condition the way I explained, you usually end up with a quite an under dispersive spread, just traditionally too small. Because you have not taken into account another important source of errors, which is a model error. So the physics, as you can see, the processes we try to simulate in our model are very complex. We use, as Adrian explained, the parameterizations, which are not perfect. And we need to estimate or to add this uncertainty in the model physics into our model integrations. So, particularly the atmosphere exhibit and upscale propagation of kinetic energy at all timescale. So the grid are relatively large. So there are a lot of processes which are not resolved by your grid because your mesh of your model is way too large. Even 60 kilometers is too large to really represent correctly the upscale propagation of kinetic energy, for instance. So to represent model errors, there are several techniques. One is to use a different physics parameterization for each ensemble member. It's not something we like to do for synopsis and forecast because it means that each ensemble member will have a completely different physics, a different climatology. One other way is to do multimodal ensemble, but it's the same problem as this one. You have different models with completely different parameters. Or you have to also perturb explicitly the model with the structural schemes. For example, ICMWF, we use two schemes. I will go briefly into that. I don't want to go into details. We have a SPPT scheme on the back scatter scheme. So the SPPT scheme was initially implemented in 1998, was revised in 2009. The idea is to simulate model uncertainty due to physical parameterization. And it's done in two steps by taking the net parameterized physics of u, v, t, q, coming from radiation, gravity wave drag, that is from mixing convection cloud physics, and add it a noise to it. And we had a coefficient also to go zero near the surface on the stratosphere. The original idea was there was only one pattern of random perturbations. In the more recent physics, we had different patterns to target different time scales. This is a time scale of six hours, three days. And then for 30 days, we have a scale of more than 2,000 kilometers. And this is, for example, here's the evolution of this random parameter. We can see for the six hours, which can go from minus one to one. And then we have the one at three days time scale, which is much slower, much slower evolution, under one for 30 days, which is more important for seasonal forecasting. Yeah? Yes? It's evolving with time, yes, yes. It's computed at each time set, yes. Yes, it's evolved during the model integration. On the second one is a basket scheme. I don't want to go into details. Just to say the main goal is to attempt to see the process of the absent from the model, which is a sketch transfer of energy from subgrid scales. If you are interested, you can find some literature about it. I mean, it would take quite a while to go into this. But the point I want to make is those stochastic physics schemes, they have a strong impact on the spread of the ensembles. They allow the model to be more reliable. But they also have some impact on the model climate, actually. And one impact, for example, is on the MGO, where we find where in general the green line represents the number of days on MGO in system four. System four is in phase one to phase eight. So, you can see on black is the verification from erintherin. So, you can see that in general in system four, the model has much weaker MGO, much less active phase of the MGO. So, here we are looking only at the cases where the amplitude of the MGO is larger than one. On the red is when we use the stochastic. So, green is without stochastic physics. On the red is with stochastic physics. So, here we see quite a slack improvement. It's still far from observation, from the reanalysis, but there is quite some improvement. For that is because the impact is not completely linear. So, you don't, and you get a better representation slightly of a convection. Once again, with the subscale, you get a much better representation of energy, cascade of energy from small scale. You have better interaction from small to large scale, the cascade of energy from one to another. So, he has a green one, yes, without stochastic physics, yes. Black one is verification. Sorry, if you combine them, you mean? So, the green one is a seasonal forecast without any stochastic visit, without SPPT on basket scatter scheme. So, you just perturb the initial conditions. On the red is if you add this stochastic physics. On the black one is a verification. So, you see a slack improvement when you have suggested physics. Both schemes, yes, with both schemes. We did also test with each scheme separately. And, in this case, it was a SPPT scheme, which was actually more important. And, here is another way to see this. This is a distribution of, that's one today, an impact of both schemes together, to see the distribution of the amplitude. The number of days with an MGO has a function of the amplitude of the MGO. And, that's from an error in Terim. Those are the verifications. That's from with stochastic physics of. So, just a perturbing initial condition with the system for with stochastic physics. So, it's difficult to see here by height the difference. You have a feeling that there's more days with a higher MGO amplitude in this case and this one. And, this plot shows the difference between this one and this one with stochastic physics and without stochastic physics, showing that when you have stochastic physics off, you tend to get more days with a weak MGO, without MGO, and less days with a strong MGO. So, this goes to the same direction as with Erang Terim. So, this one is more realistic, closer to Erang Terim than this one. So, once again, it makes the point that with stochastic physics, you tend to generate also the difference. So, in a reliable ensemble, as was mentioned, we expect the reliability and stable spread to cover the MSO. Another way to see it is if your model is really well calibrated, then you should get a more reliable forecast. So, you expect that when the model predicts a 0% chance to happen, and even if it should happen 0%, you should be along the diagonal. And this is generally what we get in the medium range forecast. The problem is that for models like SMWF, where the system forecasts are an extension of the medium range forecast, most of those techniques to perturb the ensemble are usually more designed and targeting really the short medium range. For example, the singular vectors are targeting a maximum growth of 48 hours, which is not necessarily what is important for long range prediction. So, if we look, for example, at the MGO, this is a skill score. This represents the IMS error from the SMWF model, which goes from day 0 to day 45. Green is climatology, so we reach climatology around day 25 or around day 30. But the blue line represents the unstable spread, which shows that the unstable spread is much smaller than the IMS error, which means that the model is overconfident. Normally, those two curves, if the model was perfectly calibrated, then the unstable spread should be on top of the IMS error, which means that there is still some work to be done that we may need to target specifically some events like MGO in no perturbations. I've done some work at NASA, for example, to define singular vectors targeting specifically the MGO. But things have gone a bit better recently with ensemble data simulation because before the singular vectors were applied only in the extra tropics, tropics were usually before not perturbed in the initial conditions, whereas no ensemble data simulation allowed to perturb the whole globe. So, conclusions. So, we have no very large number of observations used to initialize the atmosphere on the ocean. The initial shock is an important issue when starting a forecast. The couple of data simulation and urgent techniques may help to reduce the initial shocks. Reforecasts on real-time fork initial conditions need to be as consistent as possible. And that's, I would say, a big challenge for operational centers. There are various strategies for ensemble generation, right ensemble, not clear which one is optimal. And ensemble generation includes perturbations in the initial conditions, perturbations in the model physics. It's optimized for medium-range forecast usually, but not necessarily for extended range on the signal forecast.