 So this is a work of a lot of people that are all listed here, if I can, all right. So this is, I'm just here basically as kind of one of the authors of a large group of people. We've basically tried to write a kind of a reassessment, revisitation as it were of the Pacific Decadal Oscillation, kind of summarizing a little more understanding that we have of this statistical mode that's been kind of gained over the last 10 or 15 years. The paper is currently in review in Journal of Climate. So I'll just start with kind of the conclusions. It's probably a good place to start on this talk, which is going to go by very fast. The key point here is that the PDO is not a physical mode. It's really a statistical mode. And as such, it really represents the sum of several different physical processes, stochastic forcing, essentially kind of a random fast forcing by weather noise, and also forcing by ENSO via a mechanism called the atmospheric bridge, which also changes pollution, low variability, obviously more. And seasonal timescales, that drives changes in SST in the North Pacific. That's integrated by the ocean. So you actually redden the effect of the forcing, and the reddening is strengthened by the fact that you have a reemergence process that actually brings anomalies back from winner to winner. But then in addition, there are strictly internal North Pacific dynamics, particularly variations in the Oishio Extension region in the western North Pacific. So that combination means that some aspects of the PDO, that SST anomaly, might act to force an atmospheric response. But quite a bit of the PDO is forced by the atmosphere, and therefore we need to distinguish PDO-correlated and PDO-forced signals in the climate system. Models capture some of this, but in particular they have a very definite deficiency in capturing the tropical forcing of the North Pacific. And as such, one needs to kind of keep in mind that you're trying to measure this multivariate system with one number, with one index, and that has inherent limitations, which I'll try to discuss a little. All right, so this is what the PDO looks like. This is the definition of it. It's defined as the leading EOF of SST where the monthly global mean SST is removed. That's important to keep in mind, so it's an attempt to detrend the data in that respect. And you see the very typical pattern of kind of cooling in the central Pacific, which is called the PDO-positive phase. Now that's defined in the North Pacific, but in reality it's got worldwide connections. So this is a regression of SST on the PDO index, and as you can see it's not localized just to the North Pacific. There's a very obvious ENSO component, and there are anomalies in the South Pacific, Indian Ocean, and in the Atlantic. So it's really kind of representing a global pattern. And as Clara noted on Monday, a lot of these patterns tend to look similar. If I do a regression off of ENSO, I'm also going to get a very, very similar looking pattern just with different amplitudes. The time series of the PDO however, as opposed to ENSO, seems to have somewhat more of this decadal characteristic. There's this tendency for it to seem to stay in one sign for some period of time, as you can see here, and then seem to switch sign fairly rapidly and stay in the other sign for some period of time. It's pretty robust. These time series are not too different depending on which data set you use, even as far back as about 1920. And similarly, the patterns from the different data sets are also quite robust. And of course, the PDO is associated not just with ocean changes, but with worldwide climate changes, ecosystem changes, water resource changes. And so people have tried to correlate various things to the PDO and tried to understand could the PDO be forcing these sorts of things. And again, what we'd like to do is develop more of a process understanding of the PDO so that we could better understand these prediction and application issues. Now you can get essentially a PDO pattern fairly simply here. For example, one can run an AGCM coupled to a slab mix layer model. So the leading EOF of sea level pressure anomalies. The dominant pattern is basically an allusion low variability. And that will, turns out, drive SST anomalies that look something like the PDO. Pretty close to the PDO. So this is a model. In fact, there's no ENSO. There's no currents. This is just only atmospheric coupling. And so just weather noise variations alone will drive a PDO pattern. And that's basically happening because as you're changing the winds at the surface, you're changing surface fluxes. So typically you strengthen the winds. If you strengthen westerly winds, you'll get additional latent heat fluxes, additional sensible heat fluxes, more cooling. Also drive Ekman drift, which also turns out to drive cooling as well. Now, observationally, this is very easy to see. On the right, I'm showing a cross correlation between the NPI, which is basically a measure of the allusion low. And essentially that always leads the PDO. Because something one sees very easily in observations, that atmospheric anomalies will precede the PDO. And that's pretty clear here. Pretty much every month of the year. So this kind of, this is just basically stratifying this cross correlation by season. And similarly, you can see a pattern, a PDO-like pattern, if you look at, say, the allusion low regressed or correlated with SST three months later. But we can also see that just in terms of ENSO. And so again, if we do the same sort of calculation, but with an ENSO index, ENSO also leads the PDO throughout the year. And again, there's this pattern of ENSO correlated, leading the SST in the North Pacific. So basically what's happening here is you have an ENSO anomaly here. And typically a couple months later, you're seeing the PDO response as ENSO drives changes in convection, drives changes into the exotropics, and then hence drives changes in the surface winds in the North Pacific. Think until I skip a slide, I can't. All right, but like I said, in addition, there are ocean processes, which are actually driving enhanced integration. So although the mix layers acting to integrate the forcing, that would only give you a time scale on the order of months. But in reality, the time scale is really more on the order of years, and that's because of this reemergence process, which you can see here computed from aura data in three different locations. So we basically correlated PDO to the ocean temperatures. So we're looking at wintertime PDO and just seeing how the ocean temperatures evolve. So if you look in the central, the center picture, basically what you see is the PDO, the forcing is driving a deep mix layer anomaly in the winter. And then as you go into the summer, you get the shoaling of the mix layer. So the anomaly stays below the surface, but it's basically decoupled from above. And then as a result, the following winter, when the mix layer deepens again, that anomaly comes back up through what's called reemergence, basically a remixing of the water. And so the anomaly comes back after a year. And in fact, you can see here in observations that this process occurs for a second year. So this reemergence is tending to bring back that anomaly for a couple of years. And that obviously means the ocean is doing a substantial amount of integration of forcing on it by the atmosphere either through weather noise or through ENSO. And if you look at the PDO autocorrelation, you actually can kind of see this in observations as well. There's this tendency to have these kind of ridges in the autocorrelation, essentially whenever you are correlating with a succeeding spring. So correlations are typically high from a particular PDO looking forward to springs. So the correlation will be a maximum from spring to spring, but if you go, say, from a particular time into summer or fall, the correlation basically drops to zero. So it's very definitely tied to the seasonal cycle, and that's a result of this reemergence process. In addition, we can also have just an internal variability where base and wide wind systems are acting to drive oceanic Rossby waves that propagate westward. And these take a couple of years to propagate to the western boundary, which can be seen in this figure here. These are essentially sea surface height. So you're seeing this propagation occurring on a couple of year timescales, and it's associated with SST anomalies in the western Pacific. And these patterns are not the same as a PDO pattern, but they project on the PDO pattern. And in fact, that's true for all these processes. They're all producing SST patterns that are similar to but not identical to the PDO EOF. They all project on it. Now, in atmospheric models, it's always been a question of whether the atmosphere might respond to these SST anomalies and basically driving shifts in the Oishio current here in the western Pacific. And it may well be that this is a resolution issue. We've done some runs where when we increase the resolution of the atmospheric model to a quarter degree, we get a much different response to these SST anomalies because the synoptic eddies storm track actually is now resolved well enough that changes in heat fluxes appear to be captured. So it's possible that there is some atmospheric response to this part of the SST anomaly. So again, that's something to keep in mind. The PDO, although it's largely forced by the atmosphere, it's not only a response. It could act as some forcing. But the question is how and how much? All right, so we're going to try to put all of this together. And the way we're using here is a statistical model basically called a linear inverse model. And it's essentially just a multivariate extension of an AR1 model. So rather than thinking of a univariate time series with a single number here, this X now represents an entire map. So the entire SST map and maybe heat content map and wins essentially the state vector of the climate system in some truncated form. Here it's very truncated because I'm only using SST. But when one does this, one can get this operator from the observations, the lag co-variability in just the same way you would do a univariate analysis. But the difference is that this operator now, the eigenmodes of this operator represent different dynamical patterns with different dynamical time scales. So you can kind of see that here. I'm not going to go into all the details of how this is done. But these are, apart from kind of a trend-like pattern, these are the leading, in terms of the least damped, the slowest-evolving patterns. And you can see you get a, you get on the top, you get a pattern which looks somewhat like this North Pacific structure that I was talking about earlier. And you can see that has a very slow evolution. And then there are different components that are essentially like a Central Pacific and so Eastern Pacific and so it's really the combination of these different and so eigenmodes which give kind of the full and so diversity that we observe. And you can see the time scales, the time series associated with each of these in terms of the projection of the PDO on these patterns. So now if you just take these three, in reality there are obviously there are more modes in the system but I'm just going to try to simplify it into just these three. And if you add these together you can get kind of a PDO reconstruction these little vertical green lines by the way are times that people talk about as regime shifts of the PDO. And we can compare that to the observed PDO and the correlation is basically about 0.8. So here what we're getting then is we are taking a number of different patterns where the patterns are similar, they're not orthogonal, they're not orthogonal, but they have very different time evolution. So you can think of each pattern as representing a different univariate red noise process and we're just summing these up to make a multivariate kind of red noise system. But as you add univariate red noises together you can generate processes that will get fairly rapid regime shifts. So in fact this is a fairly well-known result I guess in econometrics that you get 1 over f noise in a system with certain interesting nonlinear processes or if you just add up a very large number of univariate red noises with different decorrelation time scales. And that seems to be at least a plausible explanation for PDO regime shifts here. So we can take a look at the well-known 76 regime shift. So I've got the PDO index down there again and you can see the 76 regime shift we're just going to look at what the pattern looked like. So we take the 20 years before 76, subtracted from the 20 years after 76 and the SST pattern is shown there. It's kind of the classic, it's the well-known PDO regime shift pattern. So was that a coherent North Pacific regime shift? Well, if you remember one of the Eigen modes that evolved very slowly it actually had a transition more around 68, 69 so I'm doing the exact same calculation but just centering on 69 and now I get a very different pattern and in fact in the North Pacific I'm getting a larger amplitude and in fact it seems to be more related to the Atlantic. So it's clear again that it's hard to talk about 76, 77 and it's some sort of global climate regime shift based on looking at one tropically based index changing sign. It's clear that different things are going on at different times, in other words we're adding these different processes which have different evolutions and they can line up for a particular index at a particular time and give a fairly rapid shift but that's partly an artifact of choosing an index and as opposed to say looking at the global pattern. Now obviously if ENSO is a large contributor to the PDO you might expect that what PDO skill you have is going to either come from ENSO or be limited by ENSO and in fact I would argue that it's mostly limited by ENSO so here what I'm showing is the hindcast skill of a number of the different Seaman 5 hindcast models compared in the bottom left to a similar hindcast again from this kind of statistical model now this is a global one and you can see with those yellow circles that the one place where there's low skill whether you're looking at a full GCM or this empirical model is in this tropical northeast Pacific area and of course one of the problems here is you're trying to predict ENSO on a two to five or six to nine year timescale ENSO is not predictable on these timescales to that extent ENSO then acts as noise not just in the tropical Pacific but then again in the northeast Pacific so it'll be difficult then to make PDO kind of forecast alright so I'll try to do this real quickly because I don't have too much time so this is the summary of what I'm going to show basically I'm just going to talk a little bit about how the PDO looks in climate models and paleo reconstructions and the key points here is that while most Seaman 5 models have a recognizable PDO pattern they tend to underestimate the connection to the tropics and they're somewhat overestimating the north Pacific internal variability and paleo reconstructions also have a similar sort of problem so here's a Taylor diagram comparing the PDO pattern in all the Seaman 3 and Seaman 5 20th century runs and also in comparison these little black dots if I can show them here are essentially recomputing the PDO from the data set but just doing 50 year sub-samples kind of a bootstrapping and the little triangles are the PDO from the other 3SST data since I'd shown earlier so they're all kind of within the sampling uncertainty but basically the models are all well outside of it so essentially no model is really reproducing the PDO EOF they have PDO-like patterns I think it's probably a better way to put it and that may be at least in part because of this issue of the connection to the tropics so we can do a kind of a simpler AR-1 model shown on the top here where we're doing a regression on a tropical EOF-1 and then EOF-2 which is more this east-west kind of ENSO pattern and having an autocorrelation R for the time series and the observations are in the red on the right so if you look particularly on this second plot here you can see that almost all the models with one or two exceptions and they have their own interesting behavior and variability but almost all the models the correlation to ENSO is too low so models typically underestimate the tropical relationship to the North Pacific so that can tend to give kind of a false impression sometimes if you use a model to try to investigate the PDO you may think that you've got something which has got more internal dynamics or dynamics that's unrelated to the tropics but in reality that's because the models are not able to recapture this kind of behavior and we can also take a look at the spectra so again we can use this multivariate AR-1 model now for the null hypothesis in just the same way that a univariate red noise is typically used as a null hypothesis so in all three of these I'm putting the observed spectra on it's the black line here there's four black lines they're all obviously very close together right in the center there and then these kind of this gray shaded region with the thinner black line boundary is essentially this multivariate AR-1 null hypothesis and you can see how all the models kind of lie within it the reconstructions typically are too weak and again you see this kind of spectral slope behavior of the PDO you're not seeing so much significant peaks really in the observations as a slope in the spectrum again that's characteristic of this kind of 1 over f this 1 over f noise process which again could be a result of the summation of different processes with different time scales so I think I'll just end on this bottom panel so we can then look at the paleo reconstructions and say well how do they do compared to each other and essentially there's almost no agreement prior to the instrumental records they all agree very well obviously after about 1950 but prior to 1950 there's very little agreement the gray shading is kind of indicating a kind of a percent common variance explained and in the bottom panel I'm showing a 20 year smoother so it's even more obvious that all these reconstructions basically can have opposite signs for potentially big PDO events so you can use these PDO reconstructions to say pretty much whatever you want depending upon the reconstruction you pick so there are a number of possible reasons for why this could be why they could disagree so substantially having to do with various sorts of processes in terms of tree room reconstruction and so forth but I would suggest that there may be a more fundamental problem here because these are all coming these reconstructions are based on sites in different locations and these different locations may be sensitive essentially to different parts of these PDO processes so they're not really seeing the same PDO pattern so they're getting trained on a PDO index but one location may be essentially sensitive to tropical forcing which is simultaneously forcing a response say in the west coast to North America and the North Pacific and another site might be in a place where maybe it's more sensitive primarily to weather noise and another may be sensitive to a place which actually is responding to some forced SSC response coming from the Curacao and that mix may make these reconstructions very difficult to make consistent so long as they're being trained on a single index so I'll just kind of conclude there essentially this is sort of a summary side as it were of these various mechanisms and this just leaves us with a couple of implications in terms of how do you use something like the PDO I would argue that this is probably true for other areas maybe this is true for the Atlantic as well trying to differentiate between the forced response in a location if you're interested not just in predicting the ocean but in predicting ocean effects on land you'd like to differentiate between those effects that are forced by the ocean and those effects that are simultaneously forced by some atmospheric variability also forced in the ocean separating that out I think is a much harder problem than maybe has been people have been willing to deal with so far and a lot of this is coming about because we're used to trying to treat these much more complicated systems with a single index with one number and that has inherent limitations which can also give rise to some behavior such as regime shifts which may be more an artifact of using one index than a true representation of the climate system so I'll stop there