Is cloud dynamics impossibly complex or fundamentally simple?

00:14 - It’s my great pleasure and honor to introduce Professor Tim Garrett from the University of Utah.

00:20 - Tim got his bachelor’s in physics from the University of Waterloo back in the ‘90s, and then went to the University of Washington to do his PhD with Peter Hobbs.

00:32 - I think maybe the mid ‘90s, late ‘90s, you defended- 2000.

00:37 - 2000. So, some of us get advice from our advisors to kind of stick with what you do best and stick with one thing and you’ll have a successful career.

00:48 - Tim didn’t take that advice, his breadth of research is really quite impressive.

00:55 - So Tim can build things, he can actually build instruments and has built successful instruments to measure snowflakes.

01:03 - He’s been involved with field campaigns, he has interests spanning theoretical problems and applications.

01:12 - He’s interested in climate problems and weather problems from the poles to the tropics, from the smallest turbulence scales to global scales, he’s even dabbled in economic theory and energy flows, but I think according to him, his proudest moment was the discovery of a new cloud type called mammatocumulus lucullus.

01:36 - And apparently, lucullus is a delicacy in the North of France, which is a layer of foie gras and smoked beef tongue and it sounds really good, clouds look like that apparently.

01:48 - But the WMO didn’t like the name so it took a long time to get that to be official.

01:55 - So without further ado Tim please, the floor is yours.

02:05 - Thanks Brian and thanks everyone for coming out here.

02:07 - I know it’s a poster day and you’re probably all very busy and have other things to do after the poster session, but I think I should start off first by acknowledging Brian.

02:15 - I saw a presentation remotely where Brian was present along with Graham Stevens and Kate Marvel and they gave us a wonderful presentation about the work that’s done on clouds and climate here, how you can diagnose clouds with various wavelengths and look at their properties and also look at long term trends, fascinating work.

02:34 - But I think the most interesting thing was in the question period where there was a question from the audience, looking for some expertise on chem trails.

02:45 - And I think the main thing that stood out for me was Kate Marvel and Graham Stevens immediately pointed at Brian, as being the JPL expert on this conspiracy theory phenomenon.

02:59 - So anyway, he did very well I thought. So I’m going to talk about some ideas I’ve been playing with about cloud dynamics in the tropics, just start off and just provide some historical context.

03:15 - This is a bit stimulated by some conversations with Joel, but it got me thinking about where weather modeling, numerical modeling came from.

03:25 - And then really some of the origins that came from, both Bjerknes and Lewis Fry Richardson in his underappreciated work at that time in 1922, weather prediction by numerical processes.

03:41 - Where he imagined creating a grid and having measurements in a grid, from weather stations, and then doing computations to make a forecast for the future that would be able to be done faster than the weather would actually arrive.

04:00 - And this is his part of his vision this, it was something called the weather forecast factory he where he imagined that he would take about 64,000 people in this weather forecast factory to make a prediction that fast.

04:14 - And in fact, that was probably an underestimate, it may have been closer to a million people would be necessary.

04:19 - Remember, this is before the age of computing, but nonetheless, he made his own attempt and he came up with a six hour forecast for the pressure tendency of 146 millibars so he wasn’t able to do this very successfully.

04:35 - But nonetheless, he had this dream and this was a very important dream of course and the dream was that perhaps someday in the dim future it will be possible to advance the computations faster than weather advances and it would cost less than the savings to mankind due to the information gained.

04:50 - But that is a dream, and of course that dream has been successfully, realized weather forecasts now are tremendously good many days in advance and they happen very quickly.

05:00 - Now when we think about climate, well, let’s take the most basic climate parameter, which is climate sensitivity, which is the equilibrium global temperature response to a doubling of CO2 concentrations.

05:13 - And there I think maybe the history is a little less positive.

05:17 - I mean, we have the Charney Report in 1979 which predicts a climate sensitivity of 1. 5 degrees Celsius to 4. 5 degrees Celsius and as we go through the various IPCC reports, well, really, that prediction has not changed.

05:32 - I mean, that’s a factor of three difference in that range, and then there are more extreme values that are considered as well.

05:40 - And of course since 1979, climate has changed so I’m not sure that we are realizing this.

05:47 - I mean, this is perhaps being a bit provocative, but I’m saying perhaps someday in the dim future it will be possible to advance the computations faster than climate advances, and at a cost less than the saving to mankind due to the information gained.

06:01 - But that is a dream. So I mean, of course why is this so hard? And I think the reason is, is that the cloud feedbacks are difficult to constrain.

06:14 - If we look at the various feedbacks in the climate system, the water vapor long the lapse rate feedback is well constraining, the albedo is relatively small, but then the cloud feedbacks, even expressed as a somewhat canceling long wave cloud feedback and short wave cloud feedback they are a bit all over the map.

06:34 - And they are the primary thing that contributes to the equilibrium climate sensitivity shown on the right.

06:42 - So this is the target that we want to focus on, but of course, the challenge is that if we look at something like this, we are faced with phenomenal complexity.

06:58 - This isn’t like a clear sky, water vapor field that might vary over synoptic scales, here we have tremendous variability over scales of well even down to millimeters.

07:10 - Or even if you look at ice crystals at the mesoscopic scale, the roughness of an ice crystal has important impacts on climate.

07:20 - So we have this extraordinary level of detail that makes this problem hard.

07:25 - And of course, this is where the parametrizations come in, we want to try to parametrize this sort of detail suitably so that it can be used in the GCM in a way that can improve the forecast.

07:39 - And we have been doing that and this is the thing, is that even though we have been doing that and we’ve had tremendous advances in computational skill and physical understanding, the climate sensitivity is not narrowing.

07:51 - So that’s a bit curious, but the approach we use is to do detailed numerical simulations.

07:58 - So this is the Giga-LES, which was a simulation done about 10 years ago.

08:03 - It’s a billion grid points calculated every two seconds, over 24 hours, has about 12 hour spin up and then 12 hour quasi equilibrium simulation time.

08:18 - And to here we’re just looking at a cloud field just for a small fraction of this time period.

08:26 - And the Giga-LES is a great tool for developing some sort of intuitive understanding of how complex tropical cloud fields evolve.

08:36 - This is where we took… Ian Glen was actually a part of radiative transfer class I was teaching, the class project he did was he passed the Giga-LES through SHDOM to create a 3D radiative transfer simulation of what the clouds would look like.

08:53 - And you can see here that the Giga-LES, produces something that looks astonishingly realistic.

09:01 - So we might have some reason to believe that this is a useful tool for trying to understand what clouds are actually doing.

09:11 - And in fact, we can even go a step further and actually say well, we have got particular kinds of ice crystals in the model and then do the SHDOM realization at really quite fine angles with many streams and get such things as halos.

09:28 - In fact, there’s a 46 degree halo in this too which well, you can just see a little bit of color down there.

09:35 - So you might look at this and think okay, so this models doing pretty well and so if we want to use this as a tool for developing parametrizations, then maybe this is useful.

09:48 - But of course, the sacrifice is that this comes at tremendous computational expense.

09:54 - We have well lots of equations that go into each one of those billion cells, and we have to run it every two seconds and it’s complicated.

10:09 - Of course, this is a large computational expense to do this sort of thing.

10:15 - But then I want to come back to something basic, which is that if we look at a tropical cloud field you know that’s a tropical cloud field in a moment.

10:26 - You don’t have to do any analysis to know that’s a tropical cloud field, your brain is doing something to recognize that this is a tropical cloud field.

10:38 - So well, what is your brain doing? And I think one part of this is well, you see maybe one big cloud, that’s a cirrus anvil in this scene and lots of little small clouds.

10:52 - And that might be different like if you were looking at a mid latitude, at a stratus cloud field you might see something that’s a different pattern and that would immediately tell you that this was a stratus cloud field, but your brain would do that instantly.

11:03 - And one could look at a different picture, this is a different case, but again you know instantly this is somewhat similar.

11:14 - So I think this brings up the question is Richardson’s approach really the best one to be approaching the cloud climate problem? Do we want to model clouds in a deterministic fashion? It does not appear to be working out particularly well, for us.

11:42 - Is there perhaps a statistical approach that may be better? And this was a question when Joel came to the University of Utah, he raised this question, he goes really is the best way to model clouds for climate models deterministically like weather models? Why do we model climate deterministically like Richardson dreamed of? So I think maybe an analogue here is to say, well, so [inaudible 00:12:08] I’m not very artistic, but let’s say you imagine you have two kids on a seesaw and the kids weigh the same, and it’s just a regular seesaw and they’re going up and down.

12:20 - And you can imagine modeling this deterministically, and with ever successive scales of complexity you might do not adjust the dynamics of the seesaw itself, but include maybe the tendons and the legs and muscular movements, maybe even some kids psychology and try to parametrize that and you would ultimately get some representation of the up and down moment, up and down movements.

12:49 - And then you say, okay, now I want some climatological mean, and you’d average over all those up and down movements.

12:55 - And you’d get, of course, the answer that you could just arrive at the equilibrium state very quickly by just saying, well, the kids are of equal weight and have length and that’s equal on both sides so therefore we should get the average.

13:09 - So that’s sort of the approach that I want to take here suggesting as being a possible alternative.

13:16 - This is a paper that came out in JGR last year with my co-authors Ian Glenn and Steve Krueger, I will also be showing some work with Nicola Ferlay, he’s at the University of Lille, he was my co-author also for the mammatocumulus lucullus.

13:35 - But Ian Glenn is now in NOA in Boulder and Steve Kruger is a professor at the University of Utah.

13:41 - So just to give some ideas for the flavor of how I want to approach this problem and know there is only one paper that I’ve done on this work, so I’d very much appreciate your feedback on whether or not you think I’m totally out to lunch on this because perhaps I am.

13:59 - But I would like to start first by quoting the famous cloud physicist, John Donne who said something similar, “No cloud is an island entire of itself; every cloud is a piece of a cloud field, a part of the troposphere. ” So I think this is one key thing, is that these clouds are interacting and we may want to represent how these clouds are interacting rather than treating, let’s say, a single cloud as some sort of isolated system.

14:28 - There are large scale constraints. And then another thing is well, we may want to choose our appropriate coordinate system.

14:38 - And, of course, I’m not going to assume a spherical cloud because clouds aren’t spherical, but the point here is just simply that if one were to represent a sphere in a coordinate system, you wouldn’t choose a cartesian coordinate system displaced from the center of the sphere and choose a spherical coordinate.

14:56 - So I mean, the choice of coordinate system matters, now typically of course if we’re doing numerical modeling, the coordinate system is 3D spatial coordinates and time.

15:09 - And then we have all the fields for energy and matter that get moved around within that system.

15:17 - So I’m going to suggest that there’s a different coordinate system that dramatically simplifies the problem of looking at clouds in a way that’s almost perhaps a bit astonishing.

15:27 - Which is that we want to look at clouds statistically, removing time, look at PDS, so a number distribution of clouds, and that the two variables that reduce this problem to something more simple are as the energy coordinate, the saturated static energy evaluated at cloud edge and for the material coordinate the perimeter at cloud edge.

15:57 - Now, this may seem rather unorthodox because it’s not space and time, but I hope that I can satisfactorily explain why this might make some sense.

16:14 - So first off, the saturate static energy it’s like the moist static energy, but evaluated at the point of saturation.

16:23 - So the moist static energy, which is this thing up here, the saturated static energy * represents saturation.

16:32 - It’s just simply the summation of the sensible heat, the geopotential and the latent heat at saturation.

16:41 - And then the cloud perimeter, well, that’s just some line around the cloud perimeter, evaluated along some surface of constant saturated energy, which actually maps pretty well in the tropics to height, which was convenient.

16:57 - If you’re not familiar with moist static energy and prefer equivalent potential temperature, that’s fine.

17:04 - I like energy rather than equivalent potential temperature, but there’s often a difference between the meteorological background and physics background.

17:12 - But either ones fine, it’s just there’s a simple transformation that goes between the two for equivalent potential temperature.

17:21 - And so the reason to think about these variables is that while the saturate static energy can be related to stability in a way that’s very simple, and I’ll express this.

17:34 - So if we had |?h/?z|, then that’s a measure of stability, if your prefer usually in like Wells and Hobbs say it’d be |?e/?c| as a simple measure of the stability of the environment.

17:47 - And then why perimeter? Well, the thing about perimeters perimeter is…

17:51 - I can’t think of another, is the only property that is shared between clouds and clear skies.

17:56 - I mean, if you think clear skies, you actually have a perimeter, and that’s the same perimeter as the clouds have.

18:05 - So if we want to the goal here is to relate cloud properties to something more simple, which is the bulk tropospheric values of some thermodynamic quantity, particular the stability.

18:17 - And the perimeter is important because that is the point at which there are exchanges between the clouds and surrounding clear skies.

18:27 - The magnitude of the exchanges is just going to be related to the magnitude of this length.

18:33 - And of course, we have perimeters down here and lots of little perimeters, we have a whole bunch of perimeters.

18:39 - So rather than focusing on area which is the typical thing, we will focus on perimeter and we will focus on stability.

18:45 - Now the reason for doing this is that of course here we have a vertical motion, this is the moist Brunt-Vaisala frequency, the buoyancy frequency of the atmosphere.

18:54 - The answer is always jiggling up and down vertically and has a frequency that’s related to the stability.

19:00 - For exchanges going laterally, well then you have fixed diffusion laws go there and those have their own timescales for exchanges going this way.

19:09 - And then we can try to connect those two because ultimately, we have the continuity and we’ve circulations around cloud edge so that this time scale has to be similar to this time scale.

19:23 - And then we start to think about having a link between cloud perimeter and bulk tropospheric stability.

19:31 - So the question I want to raise here is, is there a simple link between a bulk thermodynamic property for the troposphere as a whole and geometry? Yes.

19:41 - Speaker 3: [inaudible 00:19:42]. No all clouds, any cloud.

19:46 - Speaker 3: Any cloud. Any cloud could have a perimeter.

19:50 - Speaker 3: But like this kind of cloud, I mean the larger area that you can see [inaudible 00:20:00].

20:01 - In a numerical model, so I’ll be testing this in a numerical model, but in any situation you have to break up the atmosphere into layers, whether it’s layers in saturated static energy or in height, and those do map on to each other.

20:14 - So you break it up into layers and then what we’ll end up doing is calculating the perimeter over all clouds in each layer and then you can sum up all the perimeters eventually for all layers.

20:24 - Does that make sense? Okay, so here’s just another SHDOM illustration of the numerical model, and what I want to do is ask, what are the statistics that are in the Giga-LES in this revised parameter space? Now many people have studied them in space and time, what are they in this revised parameter space? Now, here’s the first thing is if we look at the value of the saturated static energy at cloud edge, it all seems to lie along this sort of bow feature right here.

21:04 - So do you see that there’s kind of a bow shape right here, we have height here, saturated static energy, this is at cloud edge.

21:16 - And here we have log 10 frequency, so look this is log 10 so it’s dropping off quite quickly on either side here.

21:23 - So this is almost like a knife edge in saturated static energy.

21:27 - All the clouds, it doesn’t matter what kind of clouds seem to lie along this line.

21:33 - Now above, this will be moist stability, so saturated static energy is increasing with height that’s stable.

21:38 - This is where the anvils are. Down here, we have the scattered cumulus is unstable so this is what leads to convection.

21:45 - Now, there are some fascinating properties about this, the value of h* at Cloud edge is equal to the cloud and clear sky domain mean value at that height.

21:59 - So if we were to look, draw a line here, well, this line is actually the average at any given height for the domain as a whole at that height.

22:15 - So it’s like cloud edge is like the fulcrum in that seesaw, so things are tipping back and forth, but the cloud edge has a value of saturate static energy that’s equal to the mean for the entire domain at that height.

22:32 - So that’s a pretty interesting property about cloud edge, that cloud edge seems like a very odd point to focus on, except it’s the same as the mean for the entire domain at that height.

22:45 - Okay, but then even more so where clouds are most common is where h* cloud edge is equal to the whole tropospheric domain for all heights.

22:58 - So if we average over the entire volume of the troposphere, then in the Giga-LES it has this value right here.

23:07 - It’s about three inches and 37. 5 kilojoules per kilogram.

23:12 - Well notice that the intersection point is right where the clouds are most common.

23:18 - That is the same height as the cirrus anvils.

23:21 - So the Cirrus anvils are occupying a value of the saturated static energy that is equivalent to the average saturated static energy value for the troposphere as a whole.

23:36 - So that I think is a pretty remarkable simplification.

23:39 - Is that roughly clear? I’m going to take it one step further.

23:48 - If we look at the deviation, then this falls off on either side.

23:55 - And you notice what well get in… What do we call a cirrus anvil? We call it an anvil? Well, an anvil has a particular shape.

24:00 - Well, it is dropping off from either side as some sort of perturbation from the tropospheric mean.

24:10 - So if you look at this, we get drop off. I mean, on either side, I’ve distorted this image just to make it fit, but the frequency of cloud occurrence drops off on either side of the mean.

24:25 - So that’s I think, interesting for the saturate static energy.

24:29 - Now the other thing I was looking at was the perimeter.

24:31 - Well, what are the statistics for a perimeter? And we look at this, and we see well, there’s a ton of different perimeters out here.

24:37 - But I think the first thing that might strike you is that we have a lot of small clouds and we have a small number of big clouds.

24:45 - Well, let’s say we just go to the high coordinate as a start.

24:50 - Now this would be a picture that would be fairly familiar, which is that if we look at the frequency, which is that bar there, and we look versus height in kilometers on the left axis and we have log 10 parameter, I’m using ? as a symbol for parameter along the X axis.

25:08 - And we see something that would be immediately familiar.

25:11 - We have a little peak of cumulus clouds down here, most clouds, 97% are above six kilometers in the Giga-LES.

25:19 - We still have a lot of small clouds up at high altitudes, but this is the only place we have the biggest clouds, which are of course, the Cirrus anvils.

25:32 - But now I’m going to show what this looks like in a spatial coordinate side originally introduced of number, perimeter, and saturated static energy.

25:42 - And all that complexity of the Giga-LES reduces to this shape, which is I think something extraordinarily simple.

25:50 - If we look at the Giga-LES results, basically a representation of a tropical cloud field as complex as this, in the coordinate system of saturated static energy, perimeter and number, then it’s just as simple symmetric shape.

26:06 - Which it’s simple enough… . Well just to summarize, here’s the anvils which are centered around the mean value right here of about 338 kilojoules per kilogram.

26:17 - You have some scattered Cu and Cirrus up over here, but then there’s this symmetry right here.

26:25 - So I think you would look at this and think about deterministic calculation with 10 to the 18 flops and required tremendous super computing time to calculate the cloud field and say, well, statistically, that actually reduces to something that’s just simple symmetry.

26:44 - Well it turns out that this can be derived from first principles.

26:49 - So then the paper I mentioned, what I showed was that there is a fairly simple derivation, I mean it took a lot of thinking to come with the derivation it took a while, but there is a derivation that reduces the shape and to a simple functional form, which is shown right here.

27:06 - The functional form can be expressed as this equation right here.

27:11 - Now, this is the tropospheric volume, this is a turbulent diffusivity that is a function of the spatial scale that’s considered.

27:20 - And that actually Richardson made progress for, there’s a four thirds Power law there that’s relevant related to the molecular diffusivity.

27:28 - This is almost like a Boltzmann distribution, really a gamma distribution, in terms of the ?h* which is the departure from the mean.

27:36 - So ?h* could be this way, or this way, it’s always positive.

27:41 - So this is a mean h* and then you’d have a perturbation either way.

27:46 - So that gives us an exponential distribution going this way, and then we have a Power law with a negative two exponent going this way for the perimeter distribution.

27:58 - So wherever we are here, we get a parallel, wherever we are here, or here, we get an exponential and this is a combination.

28:07 - And all these are tied to the Brunt-Vaisala frequency with respect to the moist adiabat which is N and that’s about ¹⁄₁₆₇ seconds in the model.

28:20 - So let me wonder about this question, when do we get power loss and when do we get exponential? Because we see both of these things throughout the throughout nature.

28:30 - Sometimes we see Power laws, sometimes we see exponential.

28:33 - Like for example in cloud size distributions, the clouds follow Power law, the droplets follow Power law, but then we get a Marshall Palmer distribution for precipitation.

28:43 - Why do we get a switch from a Power law to a negative exponential? And this is what I think is true, is if we look within an isentropic layer, then finite available resources are competing for resources.

28:58 - Any phenomenon is competing for available energy and matter and within an isentropic layer, well it’s within an isentrope we’ve already defined this as being a constant layer.

29:09 - But if there is a leak as in say with precipitation, where we’re losing something along the way, then we see a negative exponential.

29:19 - So that’s I think a simple shorthand for when we get one versus the other.

29:25 - So back to Richardson’s work. This is the interesting thing about Richardson, was that Richardson he did this numerical work, this deterministic approach, but he was a devout pacifist.

29:42 - And as a pacifist, he tried to come up with some simple way of understanding war.

29:49 - Now of course, you think of war as being a political struggle, there’s people involved, there’s people die, all these things.

30:00 - But then he was able to reduce war by looking at 100 years of data to a simple Power law with a slope of -2.

30:09 - And this is just a particular case here where he looks at…

30:14 - I just chose this figure in particular because I love this banditry in Manchoukuo during 1935.

30:20 - I mean, I would love to have some sort of figure in some paper that says that, but here’s log 10, the number of raids per unit range of membership.

30:30 - So this is like our number, and then log 10 the number of bandits in the group.

30:35 - Okay, and then here’s what he showed here, is the slope of -2. 29.

30:42 - I will make a caution here that if one is plotting, if one does it in a discrete form is just number versus the quantity, then one gets a slope of minus one, but in continuous form, where it’s number per thing as like DND log or whatever, then you get a slope of -2.

31:01 - So this is something to be aware of mathematically.

31:06 - So just tongue in cheek we could replace that with the log 10, the number of clouds and log 10 the perimeter of clouds, and we would get a similar slope here.

31:19 - And I think this is instructive because wars are about competition, right? And these clouds are competing, they’re competing for air.

31:30 - And so they’re competing for perimeter because it is across the perimeter that there are exchanges of air.

31:36 - But this -2 slope is everywhere I mean, in your brains, your neuronal firing is a -2 slope for the frequency of neuronal firing, the frequency of solar flares, the intensity of earthquakes, income distributions follow this, there’s a ton of societal phenomena that follow the same Power law.

31:58 - Wherever there’s competition, we tend to see this sort of relationship.

32:04 - So these clouds are interacting, I don’t think this is an accident that they follow this.

32:10 - So Richardson, he had this famous little poem, it was based off Jonathan Swift about fleas and perhaps you know it, “Big fleas have little fleas on their backs to bite them, and little fleas have lesser fleas, and so ad infinitum. ” I thought everyone would, but then I said this to my class and they were just shaking their heads so perhaps I’m just dating myself.

32:31 - But he was rift on the sense that big whorls have lesser little whorls that feed on their velocity, and little whorls have lesser whorls and so on to viscosity.

32:42 - And this is a little poem, but it’s quite a big insight for understanding turbulence and know how turbulence leads to the common graph micro scale.

32:52 - So this is pretty bad, but big clouds have little clouds that merge for their sustainment, and little clouds of bigger clouds that breathe in there detrainment.

33:03 - So the point here is that these clouds, they’re constantly changing size, they’re constantly feeding off one another.

33:13 - And it’s not like turbulence which is like a one way cascade, for clouds it’s a two way cascade where the big clouds are building off of little clouds.

33:24 - There’s a lot of work that goes into this now, there’s merging that goes on to make big clouds, but also the big clouds ultimately dissipate and break up into little clouds, or they exhale air that is available for little clouds entrain and then use for their growth.

33:46 - So just a little schematic here, let’s say we have a stream function around cloud edge where there’s some entrainment and detrainment.

33:54 - Well, air may rise along a moist adiabat, to stand along a dry adiabat, but we end up having a disequilibrium across cloud edge that creates to a buoyancy difference.

34:07 - And that drives flux, the diffusive flux across cloud edge in the closed circulation, but this air is ultimately available.

34:19 - These clouds are competing for the total circulation that’s for the entire troposphere within some isentropic layer.

34:27 - So this is a bit like fixed diffusion law, one looks at the rate of growth of a droplet, and there’s a similar equation that would be like the number of droplets or radius of the droplets and this would be saturation vapor density difference.

34:47 - But here for clouds is a similar thing, we have a total current here and that is constrained.

34:53 - And because it’s constrained with an isentropic layer of fixed thickness, the clouds must compete for the number of clouds times the length of the cloud, the perimeter of the cloud.

35:04 - And what that leads into is the property of scale and variance, which is that the number times the perimeter is a constant.

35:11 - So we have a large number of small clouds, a small number of big clouds, but the number times the perimeter of the clouds within a isentropic layer is invariant to the size of the clouds.

35:24 - So that’s scale and variance. So scale and variance are seen throughout nature.

35:28 - So then to move on to the exponential distribution, well that’s the other part of it.

35:35 - If you remember in statistical mechanics they introduces term beta which was in there, well, what’s this? How fast does it fall off? Within there’s something interesting that shows up, which is how fast it falls off has a characteristic depth, and that characteristic depth can be related to the relative humidity of the domain.

35:55 - Yes. Speaker 4: [inaudible 00:35:57] Is that conjecture or is that coming as a mathematical [inaudible 00:36:04]? Yeah, you can derive it.

36:07 - There’s- Speaker 4: The similarity theory? Similarity theory? Probably you could do from similarity theory, that’s not how I did it.

36:17 - I think it’s really related to a principle of detailed balance, when there are exchanges there have to be close changes across all size bins.

36:26 - And then if there isn’t loss from each size bin, then it leads mathematically to this property of scale and variance.

36:36 - I can’t reproduce them off the top of my head right now, but it’s in the paper.

36:40 - So I mean, here we think about some more general constraints here, that this departure can be related to the relative humidity of the domain.

36:52 - So then that’s another simplification. So this is coming back now, that’s the distributions.

37:05 - Just it to take the final step here, which is that this stability and the exchanges across cloud edge I think are linked through stability and perimeter.

37:19 - And there what we see is that if we integrate over all clouds of all perimeters, then we could get a total perimeter of all layers.

37:30 - So this addresses the question, if we break up the model into all layers, sum of over all clouds, of all perimeters, of all layers in this 100 meter grid box, 100 meter cube grid cell size, then that equals a total perimeter, and that total perimeter can be related to the stability very simply.

37:51 - So if we take the total perimeter, multiply it by turbulent diffusivity in 100 meter scale divided by the tropospheric volume, then that’s equal to the Brunt-Vaisala frequency with respect to the moist adiabat.

38:04 - So this is very nice I think because then it says that well, we could have one or the other, total cloud amount, or the stability and the two are linked through well, these parameters are just known.

38:16 - Well, does that work? Well, with regards to the distributions I didn’t mention that the agreement between theory and model was 10%, 13% for the exponential distribution, and 4% for the power.

38:30 - So the theory model very closely agree there.

38:35 - For total cloud perimeter, if we test this equation, if we calculate the total perimeter using the Giga-LES, tropospheric moist static stability as input, so we just put this from the Giga-LES what do we get out for prediction of the total cloud perimeter? Well, it’s 52 km/km?.

38:54 - So that would be a density dividing by the tropospheric volume.

38:59 - The actual total perimeter of summing over all clouds in all heights in the Giga-LES and the model resolution of 100 meters, 59 km/km?.

39:07 - So it’s very, very close. So this very simple theory reproduces all the complexity of the Giga-LES, at least statistically in terms of the distributions, and also the total cloud amount within very close agreement.

39:24 - So I want to go on to well, some possible implications, but are there any questions before we go on? Yeah.

39:33 - Speaker 5: How are you defining your cloud edge and how sensitive is this [inaudible 00:39:40]? Okay, so that’s a good question.

39:41 - So the cloud edge in the model like the Giga_LES is very easy, it’s just where it reaches saturation that’s cloud edge.

39:55 - So it’s the saturation adjustment scheme is what it’s called.

39:59 - So if, let’s say ice crystals are slow to evaporate, then it might become something a bit fuzzy, but in the model, it’s very easy to do.

40:11 - So that’s just the definition of cloud edge, is just where q is equal to q*.

40:17 - At cloud edge, the moist static energy is equal to the saturated static energy.

40:21 - So it’s that simple. Anything else? Okay.

40:27 - So now, this is the part, it’s more exploratory.

40:32 - I just want to think about what are possible ways we could use this? And I think this coordinates system is pretty unfamiliar, we think in spatial coordinates, non thermodynamic coordinates so what do we do with this? And I think, maybe one thing just thinking about us from a satellite perspective, here’s beautiful, epic pictures that we have all the time now.

40:57 - Could we use epic imagery? Well, we have a total perimeter there, we have total area even or total perimeter, there’s fractal relationship between perimeter and area, could we look at a picture like this and back out, let’s say a stability of the troposphere? Maybe it’s something worth exploring because of course, stability of the troposphere is a basic climate parameter.

41:27 - What about constraining cloud climate feedbacks? Is there a shorter way to do things now? Essentially, what we’re doing is we’re going straight to equilibrium here.

41:40 - It’s a bit like, there was a Berlin marathon about a decade ago where one of the runners was caught taking a shortcut, he found a shortcut in the Berlin marathon.

41:52 - So after I think 10 miles he just ran a few blocks over and went straight to the finish line.

41:59 - He was caught, not sweaty at all, raising his hands in victory and someone pointed out that he didn’t look very sweaty.

42:07 - Of course, perhaps that’s cheating, but if we can go straight to cloud climate feedbacks in a more direct way then doing numerical simulations, maybe it’s worth it.

42:18 - Well, I don’t know what to do here, but I’ll appreciate your input.

42:23 - Here’s one idea, here’s a some POLDER, that’s the French instrument, Oxygen A-band retrieval is a perimeter density over the Pacific during El Nino and La Ninas.

42:34 - And I’m very excited about these retrievals because it’s a passive measurement of cloud spatial structure.

42:42 - And I think, this has been worth a Nicola Ferlay has been doing with Anthony Davis, in part and there’s some room to go with this, but passive cloud structure is pretty interesting.

42:55 - So let’s say we look at El Nino to La Ninos sea surface temperature variations and look at the perimeter distributions.

43:03 - Well, here’s just the big one, the 2008, 2009 El Nino and we go from La Nina to El Nino there.

43:17 - And then if we look at the cloud perimeter distributions over the tropics during that time period, well, these are the distributions.

43:25 - We have a count per volume here, which we divide by the troposphere volume and this is the total perimeter logarithmically spaced.

43:35 - And we get these results right here. And well, this is nice, we see a parallel of minus two.

43:46 - Actually, the way this is plotted, this is minus one, that’s just because it was plotted in discrete form not continuous form.

43:53 - This is a Power law of minus two, shown here.

43:56 - I know Brian would admonish me for not actually fitting the data and just putting a parallel minus two and pretending they’re the same thing, but to me, they look close enough.

44:07 - Sorry, Brian. So, this is what’s predicted theoretically.

44:10 - So this is nice, is that the clouds display properties that are similar to what’s predicted theoretically.

44:16 - But also notice that there isn’t much variation between the El Nino and La Nina in terms of the distributions.

44:22 - And this is the thing about the total perimeter is constrained by the bulk tropospheric stability and stability is a quantity that does not change very much.

44:34 - Well, the dry one is 0. 01 per second, plus or minus a very little bit.

44:42 - So if the total parameter scales or the number scales as a Brunt-Vaisala frequency and this doesn’t change much, then maybe we wouldn’t expect much difference between El Nino and La Nina.

44:56 - Okay, well then how about this? What about climate sensitivity? So, I’m intrigued by this comment by Dennis Hartman in an introduction to a paper, I think it was by Tapio Schneider in PNAS.

45:12 - He made the point that net cloud waited a forcings near zero over the tropics.

45:16 - So the long wave and short wave roughly cancel averaged over the tropics.

45:21 - So that leads to this suggestion that if cloud area changes, the cloud distributions don’t, then there should be no cloud feedback.

45:32 - So we would have to get some change in the heights of these clouds and how they move around.

45:38 - If there’s just a change in the area then maybe we wouldn’t get a cloud feedback because they’d just continue to cancel in the future.

45:46 - Well, I think one thing you see here is that well, if it is possible to derive from first principles such very simple statistical distributions for the clouds, at least in a thermodynamic space, would you expect this to change in a warmer climate or would you expect this to be in variance? I think you might expect this to change a little bit as more latent heat is moved to the upper troposphere, this might increase a bit.

46:12 - So the total number of clouds might change, but maybe not their distributions.

46:17 - So the total perimeter of clouds, which can relate to the area might change a bit, it just increase this a little bit.

46:24 - I would guess just a few percent based on some just simple thermodynamics.

46:31 - So maybe it will be zero cloud feedback in the tropics, but that’s just a tentative thing.

46:38 - Well, then another aspect of this is that, there’s a hypothesis of what anvils will do, there’s the fixed anvil temperature, which Dennis Hartman suggested were due to the clear sky rate of cooling, there’s a transition from clear sky rate of cooling, but that’s quite abrupt on the upper troposphere.

46:59 - And that the cooling drops off very quickly and that leads to a point where vertical motions must also drop off.

47:07 - And the vertical motions drop off suddenly, then that suggests a point at which you would expect cloud anvils to choose down the altitude, it’s at about 200 hPas.

47:23 - And he was making the argument that this is determined by the Clausius-Clapeyron equation and in turn by the cloud temperature.

47:34 - So, he made the prediction that clouds would move higher that maintain a fixed anvil temperature.

47:41 - And this would be a positive cloud feedback, which is a bit counterintuitive because the temperature is fixed.

47:49 - But if clouds move higher and all else stays the same, then that works out to be a positive cloud feedback.

47:53 - That was adjusted to be a proportional height anvil temperature hypothesis that accounts for changing upper troposphere static stability.

48:04 - Well, I wonder if there’s constraints here, but if we look at the clouds just coming back to the original point, which is that the clouds seem to reside, the anvils seem to reside at this level that is equal to the saturated static energy mean value for the troposphere as a whole.

48:23 - So, the question I think might be not… Well, the question of what will happen to the anvils which is a key part of the climate feedback, maybe changed to what will happen to the troposphere mean saturated static energy? That may be another way to frame the question because that’s where the anvil seem to be is at this mean value, this intersection point.

48:48 - So I just got these results this morning, I’m just going to conclude with this from me and Glenn.

48:52 - So this is very hastily prepared, but these are RCE simulations that well, we only had eight hours to do the simulations.

49:00 - So they’re at 1,000 meters resolution, there 1,00 meters resolution, this is a side view and this is a top view.

49:10 - And maybe this is 305 K right here for the sea surface temperature, this is 301 K, clouds move a bit higher, maybe we get a few more clouds.

49:25 - If we look at these saturated static energy which is the dashed curve here, well, it’s a bit hard to see but I think there’s this little bit of a shift to higher altitudes.

49:40 - I think this is about the meaning right there and higher values of saturated static energy.

49:48 - So, I don’t know how to piece this together, but Ian Glenn helpfully suggested that we have a new hypothesis which is the fixed intervals of perimeter for fixed anvil perturbations and saturated static energy or FIPFABs.

50:07 - So, I have yet to process quite what he meant there, but I like the name.

50:13 - So, just to conclude here, I think these clouds are social, they converse at the edge, this is the interaction point between clouds and clear skies.

50:24 - That is a useful reference point, it’s like the fulcrum in the seesaw that can be related to a bulk tropospheric values because it is a shared quantity.

50:40 - And then that these clouds are actually sharing air, we can’t look at clouds individually and get anything meaningful out of this.

50:49 - And so we should focus statistically on clouds perhaps instead of deterministically, but within a coordinate system that may not feel immediately natural.

50:58 - At least to get some of these simplifications in that saturates static energy and cloud perimeter.

51:04 - And where this goes, I think needs more work and I’d love to explore this further.

51:09 - But the key things is that within saturated isentropic layers we get a parallel, the slope of minus two, but across isentropic layers, we get a Boltzmann distribution, a negative exponential.

51:25 - And that the scale height for that Boltzmann distribution drop off can be related to either the static stability actually, or the bulk relative humidity.

51:37 - So that’s simplifying and then the total cloud amount seems to be constrained by the stability or actually the relative humidity.

51:46 - And then we know what satellite observations simulations can best be applied to further test and constrain this? This is something I’d love to explore.

51:55 - And then I think perhaps a bit more provocatively, I would like to suggest that nowhere in these simplifications did aerosol cloud interactions come up or seem to need to, or precipitation parametrizations.

52:07 - I mean, all my finding in studying precipitation and snowflakes, actually, I’d love to show snowflakes and turbulence interactions, I’m really excited about this.

52:17 - But that’s where my work is, but I can’t find a place to insert, let’s say, a snowflake fall speed in a way that would change these statistical distributions.

52:28 - It’s just perimeter and saturated static energy and stability.

52:33 - Unless the aerosols are changing perhaps, to merge press black carbon, changing the stability of the troposphere, maybe that would be an avenue for doing it.

52:43 - I don’t see aerosol cloud interactions doing it because somehow that cloud field is going to have to find a way through interactions between clouds to satisfy these properties like scale and variance.

52:56 - And if they don’t, well, they’ll find a way to do it.

53:02 - One cloud is too much perimeter, well, then they’ll breathe through the trainment and provide air for all the small clouds to compensate and catch up.

53:13 - So, I’ll leave it at that. Thanks very much.

53:16 - Well, thanks very much Tim. What a provocative talk.

53:28 - So I’m supposed to have a microphone because we’re actually being recorded.

53:34 - So it’s up here. Do you see a microphone anywhere? Speaker 5: [inaudible 00:53:40] Oh, yeah, cool.

53:45 - Thank you. Okay, so we’re going to start with some order here.

53:50 - Let’s just start with Simon. Simon: I have two questions.

53:53 - When you sum over the perimeters when the cloud is overlapped, so you sum over each layer? Is that true? Yeah, in the model, you don’t care if it’s overlapped.

54:04 - You’re just summing over every layer. Simon: Oh, okay.

54:06 - And so the way to think about it is that in each layer, in the moist isentropic layer the clouds are competing, I think they have enough time to compete within that layer without considering interactions between layers.

54:27 - I’m not sure if that’s totally true, is that true? But nonetheless, that’s what we’re doing is we’re summing up over layers.

54:36 - Simon: Yeah. And my second question is related to cloud types, because different cloud types may have different way to exchange with its environment.

54:46 - So how these, I mean, can be represented in your simplified model here? It’s not.

55:01 - Sorry, I’m not sure I see why it would need to be represented.

55:07 - So, all cloud of whatever type have an edge.

55:11 - Simon: Yeah, for example- And they interact with their environment through that edge.

55:16 - Simon: Let me make it a simplified way. So say in the future of warming climate, can your model predict the ratio of convective cloud and stratiform cloud? The ratio will be different or not? Okay.

55:28 - So that’s reasonable. Well, what do you mean by convective and stratiform is perhaps part of the definition.

55:34 - And I think, perhaps there’s a perimeter to area ratio that is implicit in that definition.

55:42 - Is that possible? So if one has a perimeter to area ratio, that’s implicit in your definition of stratiform clouds versus convective clouds, well then sure I don’t think there’s any problem in doing that.

55:57 - However, I think the theory is talking about a continuum, there’s always a continuum so imposing some arbitrary separation might feel a little bit unnatural because of course, there’s plenty of clouds that are like stratocumulus that by definition are somewhere in between.

56:18 - Speaker 8: Thanks for a nice talk. So, does your model predict the increase of anvil clouds when the surface is warmer? Because a lot of cloud resolving model shows the anvil actually decreases when the surface warms.

56:35 - Okay, so that’s the thing is that the, yes, the model does predict an increase in perimeter density strictly.

56:45 - So that’s slightly harder to think about. But yes, it would predict an increase in perimeter I think.

56:50 - If you assume it as fixed tropospheric volume, which may be not quite right, but for fixed troposphere volume, then it’s natural to predict that the atmosphere will become more stable in a warmer climate.

57:05 - That’s a fairly easy thing to calculate for warmer sea surface temperature because there’s more latent heat to be evected to the upper troposphere and one can make a fairly simple calculation using Clausius-Clapeyron equation.

57:17 - I think that leads to… It’s in the paper, a simple calculation, but it was like a few percent per Kelvin in the increase in the area of the clouds.

57:29 - Now, I understand that that is opposite of what most GCM’s are predicting now, which is a reduction of cloud anvils.

57:40 - Speaker 8: Yes [inaudible 00:57:41]. Now, one thing I wonder, is whether or not this is just a limitation of the models because they can’t resolve all the smaller clouds of course, that I’m predicting.

57:52 - And I’m saying that the total cloud parameter will increase, I don’t necessarily know that that’s the anvils, it could be a lot of small clouds that are showing up as well.

58:03 - And those may not be actually represented at all in the GCM parametrization as that scattered Cirrus that shows up in the death throes of the cirrus anvils light time.

58:13 - So, I’d love to explore that further because I agree that that is a conflict between what this theory suggests and what most models suggest.

58:23 - Speaker 8: Yes. Thank you. Brian: So, we’ll have Mark and then [inaudible 00:58:30].

58:35 - Mark: Okay, so you showed a-band estimates, so we have satellite observations that you’re saying you can retrieve this perimeter parameter from.

58:41 - And you also talked about feedbacks, but could you comment about how things like cloud overlap would affect that? And if you’re running radiative transfer simulators to see whether your observed estimate of this thing is biased due to say cloud overlaps.

58:57 - Are you talking about in the satellite observations? Mark: Yeah, you’re talking about trying to retrieve these parameters and if you’re looking at a multi layer system passively, you’re going to miss a lot of perimeter of the clouds, right? That’s true.

59:11 - Mark: So could you comment on what you’ve thought about with that and how that might link to your estimates of feedbacks? Okay.

59:18 - I want to show you something. Well, Brian and I were talking about this.

59:21 - So this is an interior of a cloud measured using an instrument, the holodeck that was developed at Michigan Tech University.

59:33 - This is at scales and is in millimeters. Where’s the cloud overlap here? I mean, there is cloud overlap at all scales, okay? Even at the very, very smallest scales, there’s cloud overlap.

59:49 - Or I could go to something like this, these are snowflakes from an instrument I developed pictures.

59:54 - I see overlap there, I see overlap there. There is overlap at all scales.

60:01 - Now, an interesting property of the troposphere is that the spread and saturated static energy is if we go about… .

60:11 - Okay, this figure will do. The spread and saturated static energy here is what? About 10 kilojoules per kilogram? And the average is about what, 338 kilojoules per kilogram? So effectively, the entire troposphere can be treated as a moist isentrope and I understand that they may feel unnatural to think about it.

60:37 - But if one does ?h*/h*bar then that’s only about 3%.

60:44 - So, I’m not totally sure about this, but I think my answer is that the cloud overlap, well, no, you’re just looking down at an isentrope.

60:56 - And so whatever you see, is something that should be representative of the troposphere.

61:04 - And that one should, from a thermodynamic standpoint, and this is a thermodynamically based theory, should be acceptable.

61:11 - I’m not totally convinced by that because I thought about that question, Brian and I were talking about it on the way back here from the airport.

61:20 - And I agree that it’s an interesting thing to think about, but I think the cloud overlap is at all scales so I mean, what do you do? Mark: Thanks.

61:38 - Speaker 10: Great talk. My question is actually very similar to what Mark just asked.

61:48 - I was just curious about how you retrieve the perimeter from the polar measurements.

62:01 - Anthony Davis will probably be the best person to answer that.

62:06 - What’s Nicola doing there? Anthony Davis: Measuring [inaudible 01:02:12] top height up? I’m sorry.

62:15 - Yeah. So, this is top height and cloud top thickness.

62:17 - Anthony Davis: The product is cloud top height.

62:18 - Two bands. Anthony Davis: Yes. Just two bands, he can’t do any more than that.

62:23 - So that gives him a surface and from a surface, you can take slices and measure perimeters if you want.

62:33 - Did you try that? Well, that’s what we’ve done.

62:36 - Anthony Davis: That’s June, okay. Well no, actually, I think in this case all that was done was just look down and POLDER, it wasn’t actually setting up the structure of it, it was much more simple than that.

62:47 - But I think the intriguing thing to do is to look at…

62:52 - I don’t have it here. He’s done this wonderful, marvelous retrievals of a hurricane looking at the banded structures of hurricanes by using this technique.

63:01 - And the idea is, yes, you get cloud top height using this technique, but then also using some of the theory you developed, I think he’s getting some measure of cloud thickness for every single pixel.

63:11 - Anthony Davis: That’s correct. But I don’t see that happening here, not in this representation.

63:18 - I think that’s what he’s doing. Anthony Davis: Okay, well, I’ll have to read the paper.

63:25 - It’s his work in Marie Dumonds. Speaker 13: [inaudible 01:03:32] You’ve shown these universal scale laws seem to hold across a wide range of parameters, and you also showed the sense of the dependence, very simple dependence on these mean properties of the saturated energy.

63:51 - Why not just parametrize your clouds based on that quantity alone because you seem to have radiative properties appropriately represented by them? I didn’t quite understand.

64:00 - Speaker 13: Well, you can turn this around if you know the means saturated energy, can’t you say something about the cloud field that’s associated with it? Well, I guess I didn’t say that explicitly enough, but the point here is to have a point value.

64:16 - We could take a point value of the stability and maybe I’m misunderstanding, but we could take this, this is something you can get from the reanalysis rate analysis data, right? Speaker 13: Yeah.

64:29 - Well, then you have this and from that and the equation, a derive for the distribution one could unraffle this.

64:37 - So, for parametrization, sorry, I should have stated that more explicitly, but a GCM can do this.

64:45 - Speaker 13: Yeah, that’s basically my question- And then the GCM does this and then they can get the total perimeter without any effort and then this without any effort too and one is this physical distribution.

64:56 - Now then one doesn’t have this with respect to height, but I think one can do this.

65:01 - There’s some… Sorry, why am I spacing on the name? Sorry, the guy who did the work showing that how evaporation controls determines why you have anvils, more anvils than cumulus clouds slowed down.

65:20 - So if we just looked at this figure right here, a question I did not address, but I suspect the closest Clapeyron equation would simply explain is that this is symmetric, the average, but doesn’t explain why it’s all clouds up here.

65:40 - Strictly thermodynamically, you’ll expect equal distribution here and here, but that’s not what you see.

65:47 - And the explanation that’s been given is that clouds just evaporate much more quickly down here and that’s a function of the Clausius-Clapeyron equation.

65:56 - In fact, if you compare the temperatures here and the frequencies and two Clausius-Clapeyron equation for the saturates mixing ratio, it works out about right.

66:06 - So then, I think you might be able to do a complete picture, except I don’t have an explanation for this bow shape yet.

66:13 - So, there are places further to go but you’re totally right, that’s where I imagine parametrization leading.

66:21 - Brian: Okay, we’re running over. So let’s just take one more question.

66:28 - Speaker 15: So my question is a little bit on a tangent.

66:33 - I spent most of your talk thinking about that you’re talking about the chaos of cloud variability and how is that variability…

66:44 - You have passed constraints on this variability for the clouds, but why are the cloud chaos so different from say, momentum chaos, or energy chaos, that you have these constraints? Have you thought about what’s unique about this? I think what it is, is you found the property of clouds, which is the perimeter, and the perimeter is strained by the Clausius-Clapeyron and that limits the amount of chaos that that parameter can have.

67:14 - But it could be other properties of the cloud, like the mass of water in the cloud, that doesn’t have that constraint and it can go all over the place.

67:23 - Yeah, I think that’s [inaudible 01:07:24] model, there’s general approaches to model the water in the cloud, which is complicated and then once water gets into precipitation parametrizations.

67:34 - But the point is that the perimeter is directly linked to fluxes of mass and that is a constrained quantity.

67:46 - If we constrain the total flux of mass in the system at steady state, then the perimeter is constrained.

67:52 - It’s just an easier parameter to constrain.

67:55 - Speaker 15: But the flux is on a steady state.

67:59 - Well, for a climate condition, we would assume that they are.

68:03 - Speaker 15: Of a global ensemble? Of a global ensemble, yes.

68:06 - But their global ensemble might be defined as the tropics.

68:11 - So, in terms of reality, yeah, of course over shorter timescales everything interacts with everything else, the tropics interact with mid latitudes, and there’s all synoptic waves that come through.

68:24 - And that makes this more complicated. But imagine a GCM grid box, the implicit assumption is that there’s some sort of steady state within that grid box over the time scale that’s being calculated.

68:36 - Speaker 15: [inaudible 01:08:37]. Well okay, fine, but we have to approach this problem somehow.

68:43 - Okay? So, it’s a question of what is the timescale of interest? And if it’s a climatology, it’s a longer time scale and a larger spatial scale.

68:53 - So we do some averaging and there are fundamental properties like the mass flux that are constrained and that can ultimately be related to things like clear sky, top of the atmosphere rated cooling and water vapor concentrations and greenhouse gases.

69:08 - Brian: Well, thanks, everybody for sticking around, let’s thank Tim, one more time.

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