09:01:43 Well how we do have a lot of speakers today so so how about we get started.
09:01:54 I'm going to just begin with a quick overview before we go to our speakers.
09:02:01 This is where we're at this is the climate applications Working Group. Oh, and I'm in edit mode I don't want to do that.
09:02:11 Oh boy, hopefully this works great. So we've had three working group meetings so far this is the last one. This is the last week of the entire workshop, and today we're going to do a brainstorming session on how to incorporate the large scale influence
09:02:25 of oceanic staircases into general circulation models.
09:02:30 This is a sort of a accrued list of some of the outstanding problems to be considered in this regard.
09:02:38 One question, do the ocean staircases have a significant impact on the ocean AMS is this even worth considering.
09:02:46 If so, then how do they influence the transport and mixing mixing.
09:02:50 And then there's all these other factors such as sheer internal waves Eddie's How do they influence the staircases evolution. And I guess vice versa how to staircases affect the evolution of Eddie's journal ways and so on.
09:03:03 So, if we agree that this is something that is important for ocean climates and ultimately the Earth's climate.
09:03:11 Can we parameters these processes. And really I guess the goal in the end is can we take what's resolved by large scale GCM and put in the subscript separate scale dynamics.
09:03:24 So, how to make progress I mean there's the standard tools observation simulations experiments in theory but to my mind anyways what's driving this right now or observations were getting a wealth of observations coming in, I'll say, roughly in the last
09:03:39 We're getting a wealth of observations coming in, I'll say, roughly in the last 20 years, more than that if you want to look at the staircases in the tropics.
09:03:45 But, and what we're finding is depending where you're looking to transport properties properties can change depending on their manifestation where they are and how they occur.
09:03:55 And then something that Erica brought up in the discussion just before last week's meeting.
09:03:59 Even where they do not occur is information, and something that we should be considered.
09:04:04 So what we're going to be doing today is using the skills of the people we have in the working group to touch on some of these problems. So the issue of observations of the recurrence evolution transport properties, some of that will be touched on by
09:04:20 Fe fine.
09:04:21 They'll be impacts of delta fusion on on the global ocean circulation by Corinne observations and experiments, examine the creation of or not obscure cases that will be by Erica.
09:04:34 And then finally, we'll touch on what is known for parameter ization of things like internal waves in ocean general circulation models and ask if we can adapt those ideas to the two staircase in the ocean.
09:04:48 I want to point out by the way today is International Women's Day and I can't think of a better way to mark this day.
09:04:54 Then with these excellent speakers we have before us. So with that, I'm going to pass it on to Sonia, who will introduce our speakers,
09:05:04 if I can.
09:05:05 Okay, thank you very much. Bruce. So, we have five speakers, including myself and I will be just giving a short review at the very end.
09:05:15 So first up we have Erica Fishel from Western Washington University talking about a glimpse into mixing over sloping boundaries, from blab and ocean studies, a glimpse into mixing setting boundaries from lab and motion studies may leave us with more questions
09:05:34 than answers. Over to Erica, you can share your screen.
09:05:38 See.
09:05:50 Okay.
09:05:52 Get some of these little things out a way.
09:05:57 No, don't do it.
09:05:58 Alright, so I want to thank you all for being here first of all this morning and thanks Sonia for inviting me to speak today and I'm going to be presenting some laboratory experiments from a really long time ago I did these over 20 years ago for my PhD,
09:06:16 and as well as some more recent field studies. I want to thank collaborators from both of those the laboratory work and field work.
09:06:25 And this little picture down here.
09:06:28 I want to get you all tuned a little bit before we get started that I. This work is kind of about the idea of vertical flexes points the flux is that are temporal, and then they lose their energy to lateral flux is that you translate to kinetic energy
09:06:47 is a horizontal little bit different from some of the stuff that we've talked about.
09:06:53 So let me get started. Oh my goodness that's not working.
09:06:56 Okay, move to the other screen.
09:06:59 Sonia and I were talking about, I have a new operating system and I go I just everything. Okay, got that figured out. Okay, so the goals of the research or to look at lateral transport costs by mixing.
09:07:11 And this is about boundary interior exchange, this is what I've been focused on while thinking about these things, motivations for thinking about the ocean and climate, really are things that we've been talking about before, in terms of climate it's ocean
09:07:25 heat budget question. The main ocean thermal Klein dominates the transport of heat and cold between the bottom and the surface of the ocean, and we've often been paying a ton of attention to boundary mixing and start to be higher at boundaries.
09:07:41 So you see this little picture I have over Ridge, we've thought about that already in our sessions and talks carbon transport from the edges and margins out into the ocean interiors also a reason that we would care about lateral exchange from boundaries
09:07:57 into the interior.
09:08:03 Here are some of the papers that I am signing in this talk. When the slides are up, you can go back and get these references.
09:08:13 So, some of the laboratory experiments. I'm showing a picture here, a one breaking wave against a sloping boundary. I cannot give you a lot of detail about these experiments because this is supposed to be a short talk but I was using a tank that was about
09:08:30 a meter and a half long 40 ish centimeters Hi. Sorry, 15 centimeters high and 40 can't remember how wide it was, had a bobber on one side to make waves they were somewhat in a beam structure and they provided kind of a run up scenario against the boundary
09:08:50 and I want to emphasize that this was not a two layer bore kind of situation which is a much more familiar internal wave tank experiment that people are used to seeing running the ways that different energies, and with slopes and different energies you
09:09:07 can vary the wave around the critical condition for internal wave reflection, was a linear salt stratification which will get our minds to the fact that this was not a double the Feasts of experiment.
09:09:19 So here you see this beautiful internal wave breaking scenario you can kind of imagine surfing on it right there. And here I have a bunch of sort of very simplified snapshots in time of 2d and visit models.
09:09:35 These aren't that realistic but the reason that I'm showing them to you is it that I want to emphasize that we can see how overturns scales.
09:09:51 May be set for turbulence, without actually having to model turbulence and that you can see. Link scales and potentially timescales because of these are oscillating systems that set the largest scales for turbulence.
09:10:04 Right and shadow graph images normally what we're looking for.
09:10:08 The larger structures of the ups and downs of internal waves and if you blow your eyes you can sort of see one structure of an internal wave here, but what popped out where these laminate.
09:10:22 So why am I in the staircase session in the first place. Well, probably because I was doing this work, and showed these little layers these beautiful laminate that popped out for mixing at the near boundary and of course they're really beautiful we were
09:10:40 captured by their beauty.
09:10:42 Again, I want to emphasize that these were not what I was studying I was interested in the mixing and offshore dispersal of mixed fluid, but in the next slides, I'm going to be showing you some things that I want to make the points about what I'm going
09:10:56 to be showing you dying spreading along these little laminate.
09:11:01 They seem to point out that that we're alternating bands of convergent and divergent flux is to make the sky spread out that the die, that these little laminated criminalists little highways for lateral transport.
09:11:13 So let me go through
09:11:17 these pictures. So before I show you I'm just going to go flipping through a few almost like a little movie out of a few pictures.
09:11:25 There's boundary along. Sorry dialogue the boundary, it's spread out along these laminate which you can see in the foreground of these pictures. It's actually being worked by the overturn of the internal wave.
09:11:38 And in the background you see the shadow graph image you see both the shadow graph which shows those fine density discontinuity, as well as a picture of the DI can going to flip through them.
09:11:52 1234, and go backwards, 4321, and they're just so beautiful. We can't help looking at them a few times and you see them mean distorted by the internal way feel but you see how they hold their structure.
09:12:14 Okay so
09:12:18 findings about these laminate themselves, is that it seems that first that they are kind of curiosity, they weren't that related to the goal of the general experiments, but that it didn't find that they had a separation scale, their with their vertical
09:12:34 extent scale so awesome enough scale.
09:12:39 And again, they themselves were sort of offshore transport highways.
09:12:44 So an obvious question might be worth it wasn't necessary to have these laminate to get offshore transport in the answer to that question is no.
09:12:52 You could see them often but not always in the beginning of an experiment. But as stuff progressed and moved offshore you would they would fall apart and in high energy cases they weren't often observed at all.
09:13:06 So really what we were looking for was was evidence of lateral transport and that tended that was related to the energy, Richard flux Richardson number times the divergence of the internal wave energy flocks.
09:13:25 And so I guess what I want to emphasize that these layers, were there, they were super cool but they were not necessarily for the slider and transport but they clearly were related in some way to the energy and to the, to the buoyancy flux that we observed
09:13:41 in these tank experiments.
09:13:52 When we move on to the field experiments and I want to emphasize that I'm trying to get across a very small tip of an iceberg, relative to a lot more that could be said to the some short talk.
09:14:06 So, this is a Monterey summer in California canyon in Central California. And do you want to go and study a place that has internal tides, you might as well go to a place that's like the ultimate place look at internal waves This is somewhat of a funnel
09:14:22 or like a beach for incident low mode semi diurnal internal tides we know what they're doing. For models and from measurement studies but it was really well known that this was a place where internal tides come in to dissipate and get trapped.
09:14:38 And in the study that I did with James curtain and Eric Kinsey. We did more studies to demonstrate that and as well did very very detailed studies of the internal wave field as well as microstructure measurements of the dissipation within this region
09:14:58 and found this area that we call now mixing hotspot. So not only did we figure out that there was a flux convergence of incoming wave energy but we've measured the dissipation throughout this range.
09:15:14 So, thinking back to those lab experiments, let me show you a few things about this situation. First, since I've had some questions from folks about internal waves, people who weren't familiar with the ocean I want to give you a little bit of a sense
09:15:31 of what this looks like here are two stations.
09:15:36 Go back to the last slide and give you a sense of where they are stations 22 and 45. The first one is here.
09:15:44 And the other one is out here.
09:15:50 And what we're looking at our contour so we go from 200 meters steps down to 1200 meters. The time covers about 12 hours, and we're looking at contours lines are density, and the colors in the background are a proxy for spine suspended sediments.
09:16:09 And it does not settle over those 12 hours. So, what we're seeing here are the up and down heaving of the internal ties.
09:16:20 And what you see at this station, five kilometers offshore that station you see this boundary layer stuff the sediment has been moved offshore into this thin layer, about five kilometers away at the other station, thinking back to the lab experiments
09:16:36 I showed you, if you remember that stuff moving off of the boundary. This is the analogy for that in the ocean if slid offshore from the high energy mixing zone and was pushing office and intrusion.
09:16:48 So that's we're demonstrating that we're demonstrating that the mixing hotspot is a place of convergence buoyancy flux, and moving offshore. The other thing to point out is our measurements showed that in the bottom couple of hundred meters, the turbulent
09:17:03 kinetic energy dissipation was 10 times higher than it was in the interior water column above that. So these are really important findings and they're spread across a couple different papers, trying to show it all in one fell swoop.
09:17:17 The next slide shows more evidence of that trans fertile of mixed water from the hotspot that mixing hotspot within that center part of the canyon moving offshore without getting into too much detail I just want to draw your eyes to these two panels.
09:17:36 This is in that range that depth range of the squishing offshore.
09:17:44 Of those, that tracer of the suspended settlements. And then this is another tracer that we've discovered more recently, which is an oxygen anomaly. and both of them show these transitions stations reading offshore from that hotspot moving out to the
09:18:00 outer Canyon, where you no longer have that tracer.
09:18:06 And they get thinner as you go off shore. So, and this one. I think I'll leave this out for now but if you have questions and we have time we can come back to it's an oxygen profile and it helps shows mixing throughout the mixing hotspot and helps understand
09:18:26 these tracers that are squishing and moving the stuff away from that region.
09:18:33 So coming back to the question of layers.
09:18:36 I will admit to you that this is work I did and just the last week, inspired by some of the talks that I've seen within this conference. I'm really trying to think about, well, is there any evidence of the kind of things going on that people have presented
09:18:49 and either the Arctic or Alexa says presentations and stratified transition zone between the surface mix layer, and the more stratified water column below, because we have this really miss interesting place where there's quite elevated turbulence but
09:19:05 a constant replenishment of water that they apply that keeps it stratified. And so I've done some work looking for structures. We only have 12 profiles at a time throughout the summer period.
09:19:21 And I think the answer is just well maybe you do see some things that look kind of cool flattening out of the density, but I will leave that as a maybe one thing you can do is come in here and say well if you know what epsilon it and is, it's easy to
09:19:37 calculate awesome dos scales, and they should be about one meter in the upper part of the water column and about 10 meters in the deeper part of the water column close to the bottom.
09:19:49 That gives you thought scales that are about the same order magnitude and so, these aren't surprising because you so you can estimate epsilon from Thorpe scale so that's a little tautological but it does give you something you can compare to.
09:20:02 And so I did that and calculated looked at these for a bunch of different places and have made some histograms, and they do work out and they show you some pretty neat things.
09:20:13 So, most of these around one and so I've cut that off to make the histograms more interesting. These are up in the middle of the water column, but down in the deeper part closer to the sea floor here we see evidence of a lot of overturned scales and sort
09:20:26 of 10, all the way up to 20 and more rain, Erica, can we wrap up soon. Absolutely, thank you because I didn't want to tell you that I have no way to see the time on here so thank you very much and this is my pretty much my last slide.
09:20:39 So I do want to tell you that. Yeah. What we can do is ask questions about this with structure, we have large overturns, and that is what I think is the most interesting here.
09:20:49 And I'm hoping that that will give us something that you all can think about helping with looking at this kind of data analysis and stratified boundary layer so here are some questions to leave you all with that I think are the interesting places to go,
09:21:06 we don't understand.
09:21:08 So, the renewal of water to maintain stratification in these mixing constantly mixing layers as the big question.
09:21:19 I'm curious about the fact that we have sloping boundaries in the ocean and whether or not they may have some analogy to those old fashioned stirring road experiments in the ocean.
09:21:31 And again to bring back to the idea of time.
09:21:35 It's not steady state mixing internal waves have this at least the tides do this thing where they happen every 12 hours and how long does the mixing last.
09:30:14 Okay, great, thanks so let's move on to define who's going to talk about heat from the deep Arctic staircases and I should say if he is a postdoc at so what's hot oceanographic.
09:30:25 If you do want to show your screen.
09:30:32 Yeah that's such very nice.
09:30:36 So thanks very much Sonia.
09:30:38 So he said I'm a postdoc at the whitfill Oceanographic Institution.
09:30:43 And I'll be giving a very brief overview of staircases on the Arctic Ocean kind of want to acknowledge that there have been a lot of really good talks on this topic of the last week starting with Mary Louise give a full length talk on surfaces in the
09:30:56 Arctic and then the last two discussion sections and also had a lot of really good talks about these so please refer back to those if it seems like I'm brushing over things quickly.
09:31:05 So it's going to just kind of be to drag everyone's memory and get us on the same page with the discussion.
09:31:10 So the Arctic Ocean is a Mediterranean Sea, and it has influenced current from both the Atlantic and the Pacific.
09:31:18 And these currents carry a relatively warm water into the Arctic, and it's also because it's Mediterranean Sea, a watershed for your Asia and North America so it has a lot of fresh water river input and precipitation as well.
09:31:32 And because the Arctic is purely cold and has all these different interesting freshwater inputs salinity largely controls density in the Arctic Ocean.
09:31:42 And that means that we have can have persistent temperature maximums subsurface that exists due to the that warm and flowing water.
09:31:51 So here I have temperature and salinity from a Jackson at all paper, and the deckchairs logarithmic so it really blows up the structure here the surface.
09:32:00 And what we see working up from the bottom as you have relatively warm water from the Atlantic, which was beneath cooler winter modified Pacific water, because the Atlantic is saltier than the Pacific.
09:32:12 And then there's a warmer layer of Pacific summer water which is more intermittent throughout the western Arctic not found on the east, and then then it's usually cooler water above that and sometimes another temperature match them to the surface.
09:32:26 And what we know is that these conditions are unstable to double diffusion and particularly diffuse of convection because we have salinity that increases with stops and then wherever we have this warm layer players, there's cold and fresh water both warm
09:32:41 and salty water and so that can result in staircases.
09:32:47 And in particular, they're persistent staircases above the Atlantic water and this has been observed for many years. Both of these figures come from okay perfect my list tournament's all.
09:32:59 And so here we have a temperature and salinity profile showing the staircases. And the way that they show up in a profile is bc layers where temperature and salinity are just about constant and up because they're homogenized.
09:33:14 And then those are separated by interfaces over which both temperature and salinity change quite rapidly. So these layers are on the order of few meters tall and the interfaces themselves are more like a few centimeters tall.
09:33:30 And what's very, very striking about these is that they're coherent on very large lateral skills. So this was from that same paper, and the dots in this TS diagram or measurements from ITP data that spanned believe 800 kilometers.
09:33:45 And so it says the temperature inside a very and this plot, but there's this characteristic clustering, and these clusters have a little bit of a slope, but they're, they're coherent.
09:33:55 So each of these clusters corresponds to one of these layers where temperature and salinity are pretty constant. And you can see how well all these profiles line up even though they cover huge spatial range.
09:34:09 More recent work by Nicole Shibly shows where we find staircases, so the blue hair is it profiles that have staircases and the yellow is profiles that do not.
09:34:20 And you can see the staircases are most common in the western and central Arctic, and they tend to finish here that there shouldn't boundaries and let's thought to be possibly do to increase background turbulence that disrupts them are those boundaries.
09:34:33 Nicole also calculated vertical heat boxes to the staircases using four thirds Fox was.
09:34:40 And these are pretty small there on the order of point one wants from meter squared, although they do various facially.
09:34:49 In comparison, the ocean is foxes, that the surface are on the order of one to 10 watts per meter squared.
09:34:56 So one of the interesting things about the staircases is the lateral persistence of them, and recent work by yada yada.
09:35:05 So just let me staircases might form from boundary currents of the edges of the base and so the edges of the base center have that relatively warm water from the Atlantic coming in, and where we get a lateral prompt between warm and salty water and cold
09:35:20 and fresh Arctic water, you can get through my alien intrusions where the warm water, kind of comes out of that current and fingers that have the double the scientific use of convection instability above them and assault fingering instability below.
09:35:35 As those spread laterally into the basin. Eventually, the salt fingering and stability and and face of competitive instabilities are so efficient, that these winds down into staircases so instead of being alternating warm and cold and warm or cold it
09:35:51 just gets warmer and warmer going down.
09:35:55 And this part from your newspaper shows the link scale that we had expected. These intrusions to survive as intrusions as opposed to staircases as a function of book depth and the diffuse 72 to salt fingering since that's what really drives the winding
09:36:13 down process. as we see us depending on the depth. These intrusions can persistent to the basin, hundreds or even thousands of kilometers.
09:36:22 So that pretty much sums up a summary of the Atlantic water staircases and the other thing I mentioned briefly, as I've been a couple observations of staircases above Pacific water as well.
09:36:33 So here I have work represented actually last week for my thesis looking at staircases about 4am Pacific summer water Eddie's and there been other observations including that color good yet all paper of ideas with a strong diffuse of convective instability
09:36:49 on top. These might be associated with a significantly higher heat flux of order one watt per meter squared.
09:36:55 But of course they also occur, it over these small discrete areas and not for the whole quarter.
09:37:03 So in terms of the climate impacts of this. I think you can kind of break this down into a couple of considerations that maybe will be interesting for discussion.
09:37:12 So, the first and most obvious one is the vertical heat flux.
09:37:16 The Atlantic water has a pretty modest heat flux but it's very widespread and it's very persistent.
09:37:22 So if you think about the surface foxes and the Arctic.
09:37:27 A lot of the oceanic flux comes seasonally there's installation little ocean surface warms up and then that gets released to ice. And so even though the Atlantic water flux is much lower.
09:37:39 It's kind of different from that picture because it's not just an exchange between you know that is an ocean of the atmosphere slipping back into each other it's a team that's really come from a different place, and the Pacific water is a larger flux,
09:37:53 but also very highly localized and not persistent in that same sense, but it couldn't be important in the same way.
09:38:01 kind of as Caitlin was describing if we have occasional features of really high hip flexors that might matter for climate, even if, on average, they have very little impact.
09:38:13 The internal leaf field is potentially has some relationships with staircases and this could go both directions the staircases might modify the internal a field impact, which would affect sort of background, mixing rates, and also the internal ID field
09:38:28 may modify staircases.
09:38:31 That might be the staircases don't persist in areas where they internally feel strong and I think the question is about sort of what wins out, and what what he has come out of interactions between a tournament is a circus those are open questions plans.
09:38:47 And then finally, that this work by IANA really suggests that understanding, not just the this stable staircases but also the diffuse of connective and salt fingering instabilities that are creating them along this there my Ellen institutions might be
09:39:07 to understand the lateral circulation on the Arctic. If these are. If the staircase features are really what sets that circulation.
09:39:13 Seems like it also might be important for that.
09:39:24 And to wrap things up, I just want to mention it, it's difficult to talk about climate and the Arctic without considering climate change in the Arctic. Of course the Arctic sea ice has declined in recent years, and a number of other things are changing the Arctic right now putting some other questions that might be
09:39:33 some other questions that might be interesting for the group or kind of how are they circus is likely to be affected by warming surface waters as both the Atlantic and Pacific and coming water heats changes and stratification including more freshwater
09:39:48 input and then decrease the ice, which could result and changes to the wind input for both federal grants and the internal a field. So I will leave things there and take any discussion now or later.
09:40:00 Thank you Effie.
09:40:02 And I see that we have a hand up. Brian do you want to ask your question.
09:40:07 Yes. If he can you. I often think of the Arctic Ocean is being quiescent.
09:40:16 And I sell them think about what its tides are.
09:40:20 And I'm wondering if, when you talk about an excitation of an eternal Wakefield.
09:40:24 Are you talking about the tides happening in the Arctic Ocean and the topography, sending off.
09:40:32 Internal waves into the interior assess what's being discussed.
09:40:36 That's a really good question. So the tides on the architect are generally week and a lot of the articles about the critical attitude and so they're confined to typography.
09:40:46 So, local. They look like places where that is important and that could be part of why maybe I don't, I don't want to say this too strongly because I am not sure but I think that might play into why maybe we don't see staircases near typography if that's
09:41:01 actually where we see more internal there's two times what I'm thinking about more over the basin is the wind driven component of the internal way field which is also very weak in the Arctic, but could potentially changes the exchanges.
09:41:19 Okay, any more quick questions. Otherwise, we'll move on to our final talk before my summary and that is Karen, I apologize because I didn't check with you in advance how to pronounce your name, and so Karen fundable is going to us about the contribution
09:41:40 of double diffuse of mixing to the global ocean situation.
09:41:44 So thank you for having me and I think you pronounced it gets trapped. Oh, That was accidental.
09:41:53 I will share my screen.
09:41:59 Yes.
09:42:03 So, so I'm, I'm clean from the world, and I'm a graduate student from your green is not sharing anymore.
09:42:13 And it's gone resume share do seed now know, and it was a visible before, and then something happened.
09:42:24 No. And it was a visible before, and then something happened. We'll try again.
09:42:30 Okay, it's good now. Yes. Okay, perfect.
09:42:34 So together with my supervisor suite estimated the global impact of double diffuse mixing. And as you can see by the third two I'm hope my.
09:42:45 So, that, that we estimated that double diffuse mixing makes a small contribution to the global ocean circulation.
09:42:54 And in the next few slides I want to explain to you how we came to this conclusion.
09:43:02 And let's see, yeah. And I think a nice way of starting is with the flow chart for brunch and Ferrari for the energy bucket of the ocean and you see the energy input on the top row in the blue boxes, the energy reservoirs in the gray boxes and the dissipation
09:43:20 in the white boxes and actually a large part of participation is done by mixing over turbulent mixing and that is necessary for the maintenance of the base of stratification.
09:43:33 But as wish, wish and Ferrari also mentioned in their discussion is that they miss double diffuse of mixing in this process and that's actually the contribution we will have I will estimate here.
09:43:53 And we will do that by using staircases because the staircase are much larger vertical and scales.
09:44:01 And then the micro structure of the double diffused mixing itself.
09:44:05 So they can be observed with our beer floats and I stated profilers.
09:44:10 So that brings up the question.
09:44:12 Can we use Terminator staircases to estimate the impact of global diffusion.
09:44:17 And our answer is quite simple. Yes, why not.
09:44:22 But we need a few things for that. So first of all, we need a global overview of thermo Hayden staircases.
09:44:29 And we need to estimate the, the effect of the facilities, using the staircases.
09:44:37 So yes, let's go to the global overview and to get that overview we build a staircase detection algorithm.
09:44:50 And this algorithm consist five steps. And I will briefly talk prudent. So the first step is to look for the mix layers, so the subsurface mix layers which are indicated by the green dots in the schematic on the road.
09:45:04 Then we go to the interfaces and we check whether the weather the temperature, salinity and that's the difference in the interface or larger in the detected mixed layers.
09:45:15 We compare the height of the interfaces to the height of the mix layers.
09:45:21 And then we determine whether we have salt fingering interface or diffuse of conductive interfaces. And we determine that by seeing whether whether the salinity and temperature both increase or decrease with that.
09:45:36 And then afterwards we look for sequences of interfaces.
09:45:43 And then, this is what we get.
09:45:47 So here you see a few example profiles of salt finger dominated staircase is that the algorithm detected. You see, temperature on the x axis, and we shouldn't we shifted the profile so it's more clear and more visible and the mix layers are old shown
09:46:02 in red, that the algorithm found.
09:46:05 And this actually works. it looks quite, quite reasonable.
09:46:12 So we applied this algorithm to over 400,000 floats of profile sorry from Argo floats and I stated profilers.
09:46:23 And this is what we got in red.
09:46:41 And I have to say that we plotted the highest numbers on top so that's why most of the ocean, lights up.
09:47:03 But in total we have approximately 6.4% of all profiles have diffuse of convective staircases and 8.1 of salt fingering staircases
09:47:02 yes or no, we can go to the computation, or to our estimate for the dissipation by for the dispatch by double the future mixing.
09:47:13 And we use the equation for monk for monk, and once for that, that they used to estimate the discussion in open ocean.
09:47:22 And that's on the left hand side and on the right hand side we have the mixing efficiency, the effective diversity of density, the gravitational acceleration area of the ocean and density difference over the interface.
09:47:37 And as I said, we have not all profile show staircases, so we multiply this equation by the staircase appearance, which is indicated by the end.
09:47:49 And we use the same number for the gravity area and density difference.
09:47:57 As Mark and lunch, and the mixing efficiency of staircase approaches minus one and it's both for a diffuser convective staircases indicated by this, DC, and assault Ring Ring staircase indicated by SF.
09:48:12 And now we need to calculate the effective diversity of density.
09:48:16 And we do that for every interface of the staircase that we start guessed it D we detected.
09:48:22 And we used the flux loss for the diffusion of conductive staircases, and an empirical estimate for the salt fingering staircases.
09:48:32 And what you see in the back is again, included the fugitive convective staircases, you see the average over the, over each profile and assault fingering Oregon shown you read.
09:48:45 And we got some very similar numbers for both cases so we got minus 1.5 times, 10 to the power minus five
09:49:03 square meter per second for the effective diversity diversity in both cases, we can fill in the staircase occurence, and then multiply everything to obtain the dissipation and the total dissipation for the salt fingering staircases it's 4.2 gigawatts
09:49:19 a diffuse of convective staircases its frequent free gigawatts. And that's leads to if we add those two numbers up that leads to less than 0.01 terabytes.
09:49:38 And we can go back then, to a figure from the introduction which showed all the numbers for the other types of mixing, and we see that we seen a double diffuse of mixing has a much lower contribution to the maintenance of the stratification, then, then,
09:49:47 then, then, for example, the boundaries tournaments, but there are a few side notes that I want to mention very briefly, is that this estimate is an upper limit, because now we looked at profiles that contain staircases, but the staircase are only found
09:50:04 in a part of the water column.
09:50:06 We also estimated the temperature step of the diffuse of competitive interfaces so probably are effectively facilities too high, and the mixing efficiency of turbulence and double diffuse of mixing is different.
09:50:21 And so what that means is that
09:50:26 it's a double diffuse of mixing recertified the water column, and if you have a certain energy dissipates you might enter an energy input breath.
09:50:39 And we need five times more turbulent mixing to the stratified it, or to mix it again.
09:50:42 And of course their regional variations, as what we saw.
09:50:47 By the global overview and it shows that they're probably staircase mixing all sports which have most of the, which which have to bulk of the number I just showed you.
09:51:00 And I think I will leave it with that.
09:51:04 And these are the references that are used.
09:51:10 Thank you very much, Karen, and I see a hand up.
09:51:16 Brian, do you want to ask you a question. Yes.
09:51:19 I, my I was drawn to this maximum in the staircase convection that went right across the Pacific Ocean, is if it had to do with beta upwelling or something, can you give a physical understanding for by that you may need some Yeah, exactly.
09:51:40 Yeah, so we don't actually know but they're also much more measurements there.
09:51:46 And they also don't know exactly why they're much more arco friends, near the equator. That also means that if there's accidentally something happening but not sure, but they're never strong staircase so it could also be something like upwelling.
09:52:09 Yeah. Okay, I'm actually not really sure you tend to ask your question.
09:52:08 Yeah, I'm so high I have a clarification question, which is related with the permission scheme that you use, where you're activating flexes.
09:52:21 Yeah, it's, yeah this one. Yeah, so I have a question for the South finger in parts, which you claim now you use the formula for radical estimates in 2012, like based on my understanding this work.
09:52:42 The salting were in flux is estimated from this work is based purely on the homogeneous of England fields, instead of the soft staircases so I just want to like, ask her how, how did you use this estimation, or this, or how did you use this
09:53:00 formula to make the estimation in reflexes.
09:53:04 Yes.
09:53:06 Yes. So that's a good point. So, in the flux last you use the temperature difference across interfaces and this empirical estimate doesn't.
09:53:18 So what we actually do and what the inputs, I'm not exactly sure what goes into that we use the background stratification so we think it's.
09:53:28 It has the density ratio as an input so we calculate those from the staircase profiles near every interface. So that's how we implement.
09:53:40 So yeah, I guess my question is, like, because it's really describing the homogeneous viewed and homogeneous flubs these are usually, you know, smaller than the interface of fluxes if you formed a syrupy so I guess there might be a chance that you can
09:53:55 have an underestimation of success by using this formula. Yeah, this is just like my gas.
09:54:05 And that could be in.
09:54:07 Okay, thank you.
09:54:08 Okay, so I think Mikhail was next. And then I think we'll hold the rest of the questions till the discussion session so we call it, ask your question.
09:54:17 Thank you.
09:54:19 I just want to say the map that you have of the locations of all the staircases is amazing.
09:54:26 And I just wanted to know, because I'm curious about your algorithm for figuring out whether there's a staircase are not have you compare that to any other studies that have looked first.
09:54:40 Um, yes.
09:54:41 So actually, we, we published an algorithm in our system science data and there. There's.
09:54:51 There will also compared it to other studies in some regions where we know where we for example noticed archives appearance in the steps across interfaces and that sort of things.
09:55:04 Okay. Did you find that you're finding services are on the same places that other people.
09:55:25 that's one one of the findings. Yeah.
09:55:29 Thank you so much.
09:55:30 You're welcome.
09:55:32 Okay so and then in the interest of time, I think we should move on and I'm next and Bruce you're going to manage the questions and stuff for me right, we'll do.
09:55:44 Okay, so I need to figure out how to share my screen.
09:55:51 Can you see my PowerPoint, everyone. Yes again.
09:55:55 Okay, great. So I'm going to give a very quick overview of what we're doing at the moment for prioritizing mixing, and most of this is not my own work, and I want to acknowledge that some of it comes from the climate process team on internal waver from
09:56:10 mixing that was led by john McKinnon and is described in the band's article in 2017 and Caitlin also mentioned that. And then I also use examples from the GFDLOM for which is that the latest version of the ocean model at GFDL.
09:56:27 And those, the members of that team are my, my co co workers at GFDL so I'm drawing on their expertise and. So first, certainly a very rough sketch.
09:56:41 So I'm having trouble finding my buttons Okay, here's a very rough sketch of the different types of mixing processes that we tried to prioritize in ocean models.
09:56:51 So we've heard about many of these during the last few weeks, we have mixing under the ice, that can live give rise to layering. We have the most important layer in the ocean the surface surface mix layer.
09:57:07 And we have a region of stable stratification in the interior of the ocean where we can have mixing driven by double diffuse the processes, and by internal wave breaking.
09:57:16 And we also have bottom boundary layer turbulence, that as Erica shows can give rise to intrusions in there.
09:57:29 So I'm going to very briefly just describe how we try and prioritize some of these, but first just to kind of orientate you in terms of climate models and climate model resolutions are typically for horizontal resolutions, one to two degree horizontal
09:57:44 grid spacing so below that grid size you have many different processes going on and they all need to be privatized if they have some impact on the large scale fields, the vertical grid spacing can be quite fine near the surface but as you go deeper it
09:57:58 becomes quite course. And so, that not only are we not pro rep explicitly simulating the processes that can give rise to last, but we wouldn't even be able to resolve the layers tool.
09:58:10 So we have to think about what's the impact of the layers on the large scale circulation and are we prioritizing that small scale mixing processes in climate models are usually represented in terms of an add facility with a corresponding Eddie discussed
09:58:25 it as well. And then that Eddie the facility has to depend on the resolve parameters so we have some sort of Formula relating Eddie different activity, the turbulent Eddie the facility to the mean flow field and the mean density and their gradients and
09:58:41 so on, and so we also need our privatizations to be cheap in climate models, you can have multiple additional equations which increase the cost of the climate model integration by too much because then you might as well just run your funding model at
09:58:55 higher resolution.
09:58:58 And then finally we, We want to promise realizations that are constrained by physical understanding and which allowed the facility to vary both spatially and temporarily, because we want to be able to run our climate models in a different climate.
09:59:14 So we want to be able to calculate the facilities and the way that they change as the climate changes.
09:59:19 And so just some examples of current problems rotations. If we have shared driven mixing the old standard for climate for course resolution models was to represent the turbulent festivity in terms of some background the facility which was a arbitrary
09:59:33 dimensional constant multiplied by some non dimensional function of the Richardson number.
09:59:41 And the idea here is that lower to the numbers you would have large the facility. That's a large rich the numbers you have small the facility. And so you're trying to capture the impact for example of Calvin Helmholtz instability on mixing.
09:59:56 And so because this has this dimensional constant, it's not very easy to tune foot with lab experiments and so on. So, right now in the GFDL ocean model we're using this formula here, and where we have the facility represented in terms of the large scale
10:00:12 shear and the non dimensional function of riches number. And so this avoids dimensional constants and, but it still depends on the results share, not on sheer which is smoke, so find scale that we can't resolve it.
10:00:26 And it's the resolve share also that goes into this Richardson number estimate.
10:00:31 And in the surface Mick slur we have a long history of prioritization, and the key here is that surface mixed
10:00:40 and then given the surface flexes as well. What do we think the turbulence is doing inside that next layer. And so a parameter ization that's used in a lot of climate models is this k profile parameter ization where you have the vertical fluxes of some
10:01:02 quantity at a distance d from surface, being given by the turbulence diffuse 70 here times the large scale great into that quantity. And then there's this counter gradient flux term, which is intended to represent the effects of buoyancy driven convection.
10:01:16 And everything is represented in terms of these.
10:01:27 These non dimensional shape functions gdH, and then some dimensional vertical velocity and the height of the mix there. And so, this is a very tried and tested parameter ization, but it doesn't include any energetic constraints and so GFDL we've moved
10:01:40 recently to an editor facility that again depends on some non dimensional parameter, C, and a dimensional velocity and length scale, but uses energetic constraints, given a well mixed boundary layer and the surface fluxes that are taking place to calculate
10:01:58 what this turbulence velocity and turbulent length scale should be.
10:02:03 So theme I'm trying to get up, is it's good to have energetic constraints for parameter ization and double diffusion driven mixing is not an area that I know very much about and I know many of you are much more experts and I am, what I want to emphasize
10:02:17 here so I cut and pasted the formula from the larger till 1994 paper. And what I want to emphasize is that we have not made much progress in climate models, and we're still using these formula or some variation of these formulas for double diffuse have
10:02:35 driven mixing, and then I should say that, to my surprise I discovered that GFDLOM for actually has no prep translation of double diffusion different mixing, they decided there was enough mixing and so they just left it out.
10:02:49 So there's a lot we can do to improve the double diffusion driven mixing given all the advances and understanding have taken place, I think, um, so what I do know a little bit more about is internal wave driven mixing, and it's the key thing here is that
10:03:06 we can't think of it just in the vertical. It's a non local global problem so we generate internal waves in one place, they propagate around the ocean they break and they cause mixing somewhere else.
10:03:18 And we've been trying to represent the different activity in terms of the dissipation multiplied by some mixing efficiency, this divided by the local stratification.
10:03:31 And in most of our climate model implementations. We've been using a constant mixing efficiency and we know that's incorrect and we should be using something variable.
10:03:38 So that's something to think about if we're thinking about the role of nonlinear mixing efficiencies in terms of generating staircases and stratified turbulence, for example, and we have a parameter ization for the local internal type driven mixing, which
10:03:54 were the dissipation at any local points in three in three dimensions, depends on the horizontal rate at which energy is converted from the bar traffic to the bar clinic tied, and that the standard formula for that just given here.
10:04:08 So depends on the rms velocity of the tides, the topographic height. Some wave number k which comes from the physics of internal tides, but actually is often used as a tuning parameter in climate models.
10:04:24 the bottom stratification and B, and the density, and then we say from this energy that goes into the bar clinic tired how much of it gets used for mixing locally.
10:04:33 So we have a fraction q that's used for mixing locally and originally it's set to one third in the original implementation by Saint Laurent at all. And then we have a vertical structure function.
10:04:44 And that's in the original implementation is an exponential decay, with a, an arbitrary vertical length scale for that.
10:04:53 That decay, and that same like scale being used all over the globe. So we know that these are kind of placeholders, and there's a lot we can do to improve it.
10:05:01 And that's what the climate process team focused on. And so we know now that we have this local title dissipation. Which, where the energy conversion depends on many different parameters title velocities the Coriolis need the frequency of the tides, were
10:05:17 they talking about empty tides or other types, the bottom stratification, and also topographic parameters, the height, the length and also the relative steepness of the topography so very steep topography has a different conversion rates then more shallow
10:05:31 topography, and the local dissipation fraction, and the way it's distributed in the vertical depend on what processes are responsible for the way breaking.
10:05:43 So you can have way wave interactions or the direct breaking of nonlinear ways for example, at the topography, and they all give rise to different vertical distributions of this dissipation.
10:05:55 and then the remainder of the internal wave energy is going to propagate around the globe, and where it dissipates is going to depend on firstly where that wave energy has gone, and then what way breaking process leads to the dissipation that will determine
10:06:12 determine where in the water column that energy gets deposited. So to just give an idea of the kind of state of the arts currently. And this is what which I should say Caitlyn is also a co author on this work and I am not.
10:06:22 This is an end to end model for the title driven components of internal wave mixing, and by Kazmir deliver and several co authors including Caitlyn Waylon.
10:06:34 And the idea here is that we have models for the generation of internal tides, we can determine what fraction of the energy goes into different vertical length scales.
10:06:45 And the very small length scales are assumed to break locally, while the large length scales the low mood waves propagates around the ocean. They have an energy tracker to determine where this energy goes around the ocean, and then several different modules
10:06:58 for how those waves will break through interaction with topography critical slopes like Erica was talking about, and showing in shallow typography wave wave interactions and again more scattering bias or hills and based on this model you can come up with
10:07:16 with global three dimensional maps of the title internal tide dissipation. And that's what's shown here that if you servitude you to these internal tides.
10:07:26 And so you can see the spatial variability. This is a depth, this is somewhat higher in the water column. This should be very reminiscent of one of the maps that Caitlyn showed us from other derived data, and then this is a zone or average here, I should
10:07:40 say this is not yet included in the GFDLRM for and I think it's being implemented right now and MIMO so it's making its way into climate models. And so that's the state of the art, and the thing I want to bring out here is how it's been split into lots
10:07:55 of different pieces. We were trying to constrain everything energetically, but think about the energy in how it goes and different, different processes.
10:08:06 So some guidance for staircase privatizations we want to constrain from transitions energetically, we want to avoid arbitrary dimensional constants we want to be able to tune everything against the bar experiments high resolution simulations and so on.
10:08:19 We want to avoid extra prognostic equations because they lead to high costs which climate models cancer can't cope with, and we want to break down the entire process into components steps if possible.
10:08:32 And so I'm thinking particularly of these lateral intrusions, that we may want to break from translations down into vertical and lateral processes and tie them together in a way that they're energetic consistent.
10:08:45 Ok I will stop there.
10:08:48 Thank you very much Sonia, um, how about we if there's a quick question we can ask. And then I think what we're going to do is have a bit of a break and then we're going to enter a discussion based on all the topics that we've seen.
10:09:03 I think people want to break right now.
10:09:07 So we're going to take, I'll say a six minute break we'll be back at quarter past the hour, and then we'll begin our discussion going back to the original question, how important is this and if so how do we do it.
10:09:21 So, Sonia really set the stage wonderfully for us there. See you in just about five six minutes. Thanks Bruce.
10:09:31 Thank you. Great talk.