 Okay, thank you very much for coming back from the coffee break and This talk is going to be about ensemble generation methods for decadal predictions Before I start I would like to acknowledge the contribution of Camille Marini. She performed all model runs for this study And calculated the singular vector based perturbations This was fast Okay, so a few words why do we have to improve? Existing and sample generation methods. I know there are a lot of things we have to improve in decadal predictions So one more one less does not really matter Okay, so in ensemble predictions by doing them we try to Get a sample of the Evolutions of the climate state and we're aiming to get not just any sample and not just any Evolutions, but we like that this sample to be representative of the uncertainty and So for perfect Ensemble predictions it is expected in other ensemble spread being a representative of their Uncertainty in the forecast So it's expected that the ensemble spread is equal to the error In the ensemble means so this can be evaluated by the spread error ratio So in case this holds a spread equals the mean error then this ratio Should be one in the perfect case in the non-perfect case if the spread is too large or too small We will get the values which are larger than one Well, this are the results for the spread error ratio for sea surface temperature from two Prediction system one me clip based on MPISM model and one from the Met Office. So we see that In the first year or just after the initialization the spread In the initialized timecass seem to be too narrow so under dispersive and Within one year it seems not to grow as fast as the arrow grows while to the end of the prediction Letia 9 for instance the spread gets Over dispersed Well, one of the reasons why do we get the narrow spread just after initialization is maybe because we don't really represent the full range of Uncertainties in initial conditions For instance many decadal prediction studies. They use the assumption of perfect ocean initial condition. So they use different sorts of Atmospheric perturbations to generate an ensemble Well, for instance me clip System uses atmospheric and oceanic leg initialization by but lagging the ocean state by one or two days does not really Make good perturbation to the ocean state. Well, some studies for instance in this column in the middle one The authors by the way, this is Ho and colleagues from 2003 paper, so they use To represent the model uncertainty rather than initial condition uncertainty using the perturbed physics methods and Sometimes the decadal prediction studies the use some sort of the use the sea surface temperature perturbation So as we see I don't really know whether all prediction system Used to be Underspersive at the beginning of the forecast, but I assume those who use atmospheric perturbations. They are So this has been a problem, I guess Assuming Perfect initial conditions While our knowledge about the ocean state is quite uncertain on the other hand and this a good use that ocean The methods of perturbing the ocean state exist and For instance the studies done at all tipamon They showed that perturbing the ocean state affects the variability and thereby this can also influence the Predictability scales Well different ensemble generation method exists and those for instance that aim to represent the fastest growing errors the subred vectors or singular vectors and Ensemble generation methods that they use to indicate the prediction They built a lot on the knowledge and experience of numerical weather prediction community and a seasonal forecasting community The other methods which are not necessarily Account for representing fastest growing errors. They are investigating. They've been investigated now inspects project and the meekly project Well, oceanic singular vector based method was picked for this study and The whole setup was inspired by the study of Molteni And colleagues from 1996 although we had to use some modification of the method because we don't really have the linearized version And the adjoint of the model So the lean model was used the first step was to reduce the degrees of freedom by Applying the Be varied three-dimensional empirical orthogonal function analysis to the temperature and salinity anomalies from the historical run so 28 principle components that picked that to explain 68 percent of variance then assuming that the Evolution of the dynamics of the state vector is linear and driven by the white noise We can Estimates the linear propagator be Based on their covariance matrices of the state vector. This approach was introduced Yesterday, I guess by Matt Newman Well as soon as we have this be Metrics to this mapping We have we can select further them Norma under which we assume the errors will amplify in the system will lead to the maximum growth and the Time of which they should amplify five years in this case and then we can calculate the singular vectors They would represent the eigenvectors of this product here well at this stage with Decided to proceed with the four singular vectors in order to have eight ensemble members for our initialized hindcuffs And just before implementing this perturbations to the forecasts We use the pace space rotation and scaling In order this oceanic perturbations Being representative of the uncertainty in initial conditions. So there should represent the root means fair arrow of the gecko to Ocean synthesis which is used as a source of ocean initial conditions. Yeah Before Performing initialized hindcuffs to their gecko to anomalies were introduced to the NPI SM model by nudging then the initialized hindcuffs were started by from 1991 to 2006 every year so each for each Starting date we have two sets of hindcuffs every set has nine ensemble members eight Pitcher and one unperturbed which is similar in two sets of hindcuffs Well the hindcuffs which are based on atmospheric perturbation. They have different states So this is the atmospheric state which is shifted by one to eight dates from the unperturbed state They use the same ocean initial conditions and their hindcuffs based on oceanic perturbations They have the same atmospheric state and different oceanic states well before starting our hindcuffs we can do a quick check if our initial perturbations they represent The uncertainty in initial conditions so we compare the spread of initial perturbations with respect to the root mean square error of gecko and In principle so this patterns they should correspond and the amplitude should be should correspond But we see it's not always the fact for instance the temperature at 150 meter depths So the spread is much smaller than the arrow Some features are represented in the North Atlantic and something in the equatorial Pacific It's a little bit better for the salinity at 150 meter depths for instance Some features are represented in the Pacific Ocean also a little bit in the Atlantic and Then for the thousand meter depths for temperature. I think the spread is well represented in comparison with 150 meter level and it's quite encouraging that we get a relevant spread in the North Atlantic because we heard today and yesterday that The mechanisms for initialized hindcuffs they are Associated with North Atlantic processes Well, this might not look optimal but we go with this patterns because and we are happy to have them because we use only four singular vectors and this is already amazing that they represent at least some Initial condition uncertainty Then we perform the hindcuffs and we want to know to know if for this singular vector perturbations they Amplify in our system if they grow because this is a non-linear dynamical model and in order to Understand that we calculate the amplification factor. So it's based on the ratio of the norm of Evolved perturbation with respect to the initial perturbation. So this would give us the dashed line the blue one here But say does not tell us anything about how a singular vector based perturbation evolve So this is a total error growth in the hindcuffs in order to see how What is the contribution of oceanic singular vectors? We have to? Project the evolved perturbation on the singular vector space So this is this formula here and then we get this solid blue line the difference between these blue lines is this associated with Atmospheric weather noise and its effect on the air in the ocean the similar Arrow grows was calculated for the atmospheric lacked initialized hunkers. So they are started As human a perfect ocean initial conditions that the air start growing was in the first year very fast They're faster than this the singular vector based perturbations And so what this graph is supposed to show us is that so much in terms of spread so this red Shaded area shows us that so much in terms of spread we can get from using as much atmospheric perturbations And then this blue area shows us How much on top we can gain from using oceanic perturbations? We want to evaluate now our spread and we use for this ensemble spreads This is the same spread error ratio It's just called differently. So this evaluates the reliability of the spread with respect to error and then we use the better score, this is Kind of a summary statistics for the telegram diagram. It shows reliability of the spread with respect to the observer ability The perfect value for the better score is zero for the ensemble spreads for is one and everything Which is below the perfect line? Suggest underestimated spread so we see that in fact using oceanic perturbations also gives us underestimated spread This is for the subsurface ocean temperature Average to over 300 meters and we use the EN3 data as the verification Data set which is not quite usual for the K-doll prediction studies But we use it because our root mean square errors is calculated with respect to this data set I've also looked into the spread score for the sea surface temperature so this is consistent with a Slide that I showed you at the beginning that the spread is underestimated when using atmospheric perturbation The spread is better when using singular vectors. This is suggested by this white areas here. The spread is overestimated in Tropical Atlantic and underestimated slightly in the equatorial Pacific The spread is somehow always overestimated over the poles No matter oceanic perturbations or atmospheric perturbations are used and then to the lead here five I see that Somehow our shening perturbation they kind of overdue a little bit with the spread they produce over dispersive spread Well, this is a very kind of we Found out that using different verification data sets We produce we get different results for the same variable and the same hindcasse and the same lead here. And so the spread error ratio shows us the better Spread for oceanic singular vector based perturbations and this is a very democratic results depending on which Relationship have you built to our singular vectors? You can choose one or another But so I will go with the Reynolds data sets Because it shows the better spread for singular vectors to justify that We took a search Verification data set which is based on satellite microwave radiometer. This I'm the e data set and it shows us that Actually, the hard is esteem might under represent the inter-annual variability and this is shown by this ratio here So it's a biofactor of two sometimes four in the southern ocean in the subtropical gyus while Reynolds SSD seems to be more close to this satellite data while also underestimate inter-annual variability slightly in terms of skill there is Not much difference in the lead year one well oceanic singular vector based hindcasse they slightly do better than Those which use atmospheric perturbations, it's five percent more of errors that get improvement and The difference is seven percent more for the lead year five, but it's when we look on the global picture We can of course zoom into the Atlantic and see that it's actually better for Europe and for the Atlantic surface air temperature using oceanic perturbations So this is one more time just a summary for the North Atlantic surface air temperature skills. So this is This blue line suggests that better skill for starting a little bit for the lead year three than four and five So that's it Thank you for your attention and I will be happy to answer your questions