Keynote talk: David Neelin, UCLA: "Unforeseen directions of Arakawa’s hypothesis”

our next speaker is Dave Nealon, he's a distinguished professor at UCLA in climate dynamics and coupled ocean atmosphere modeling and Dave got his BSc and MSc at Toronto, the University of Toronto, he got his PhD at Princeton and he leads the CSI climate group. systems interaction group at UCLA and one of the things that distinguishes his research has been the development of simplified models of the tropical ocean and he developed a sequence of hierarchy-type models that he called quasi-equilibrium tropical circulation models or, for short, qtcms and I think they lead to a lot of information and part of that is that you can make analytical progress with these models.

Yes, if you want to read more about that, it's in the general circulation modeling book that Dave Randall edited. which was published in 2000 and that's why the title of this

talk

today is more almost than balance

unforeseen

directions

of the

arakawa

hypothesis

thank you thank you um I chose this title because it appealed to me and Faya also liked it um in a quick test and then as it was Coming to organize the

talk

, there were so many

directions

in which the quasi-balance had gone that it was essentially impossible to do a complete and proper review, so what I will do is try my way through it, highlighting in particular some of the ways where it has gone is reflected in the work of several of the early career people listed here, including Kathleen skiro, who are all here, and Todd emeniger, who is also here, and then Leilani dulerov was a student who worked with fias and me and Christian Martinez Lobos.

He is now an assistant professor at the Adolfo Urbanías University. So here's the list of things I want to touch on and I'll try to keep it consistent as I go through these various directions that the quasi-balance has gone. I'll come back to this scheme from time to time and try to make it fun as we go, so at first it was okay Erico and Schubert weren't quite the start, but there were many elements that were later adapted in later parameterizations of All Sorts, including , of course these are the cloud spectrum and the fact that you have drag on each of these clouds and one of the things we'll touch on again is that you know within this canonical vertical profile of the ambient wet energy and the saturation version of That if an elevated column is to the right of this line, it means it is warmer than the environment and is there to float, so a spectrum of trailing columns was imagined and this led to this infamous fruit hearth equation. which we heard about last night from Wayne and us.

We'll come back to this, there were a few things that I think should probably be revisited from this, but it's all very revealing going forward, one of the first things that was done with Carrie Emanuel quasi-balance LED and kind of What attracted us to Chris Brotherton and me is the realization that if you're connecting the boundary layer to the free troposphere, you have a deep layer of heat over a warm region, you're going to be creating very clinical pressure gradients, so this will have an immediate effect. large scale impacts and by working that over the years and over time, I also realized that the fact that you have a deep spine immediately implies a vertical spine, a warm and deep spine immediately applies a vertical structure of humidity and that immediately applies an amount of work. that has to be done to lift a large-scale plot and that was the derivation of the gross wet stability in the vertically continuous coordinates, the reduced amount of work that has to be done to move a large-scale plot up or down the scale. air mass up or down in a region of convection due to partial cancellation by convective heating and then Wayne was kind enough to mention the qtcm which I'm not going to talk about today, but I wanted to point out that, um, the various things that were studied by us and others, um in terms of the way waves propagate or if you take the limit where you assume that waves go very fast and that the Coriolis force is not important even in the tropics, you get the version of weak temperature gradient of This tends to spread due to El Niño warming or whatever else is happening including global warming, a large scale temperature pattern and if you have rapid convective adjustment at all times then your lower troposphere and the upper troposphere have to be in balance with each other, so all kinds of consequences will be connected from this warming.

The other thing that was prescient that we'll come back to is that Akio was aware that the quasi-equilibrium or highlighted that quasi-Colombia would be a curve here, he's plotting it in a space of relative humidity and essentially a quantity similar to a vertical lapse rate. for wet instability and indicates that its quasi-equilibrium can be anywhere along this line. This has since been quantified in a couple of ways, including I. Today we will show that an earlier version was just in terms of the critical value at which you get a strong increase in precipitation as a function of water vapor for a given temperature , so this water vapor temperature plane can be mapped onto this plane and there.

There will be even closer mapping later and then from the initial context. I want to mention that this is from um Shu in 1992, um, that Akio and his collaborators were very aware of the fact that there were going to be variations on small-scale quasi-equilibrium and this was one of the motivations for introducing stochastic convective parameterizations of the I won't have time to say anything, but I will talk about the importance of variants on the state of quasi-equilibrium, another thing to throw away. The thing is that the adjustment time scale, which is supposed to be essentially infinitely fast in a strict quality balance, is very important and you can see this when implemented in, for example, Schubert relaxed error color or others. quasi-equality based schemes that say to dissipate Cape with a certain time scale and we will return to those time scales as well.

Well, point two of the outline is probably the longest section of convective onset and its consequences, so I want to start with some things from Kathleen and Fayez's income in combination if you have a temperature and humidity input to the environment and you also have observations of precipitation, you can infer the dependence of precipitation on the temperature and humidity profile and we have done this in a couple of different ways, one is if you know the way If the mass flux increases with height, then you have an idea of drag broadly, not necessarily turbulent drag at the edges of receding clouds, but includes dynamic drags that may arrive as a more coherent flow, and of course these interact with each other. others importantly, um, so if you know how mass flux increases with height in a typical column, you know the typical way you get boundary layer air slightly above the lower free troposphere, etc., and that can give you a weighting for temperature and humidity, so you can do this by estimating things with a mass with a radar wind profiler, that was Kathleen's approach or you can do this as an inverse problem, reverse engineering and that was Phias' approach and both emerged. with a very similar answer, which is that you tend to get a lot of boundary layer-like air coming from the lower troposphere every time you have strong convection and this is going to start abruptly and then there's a little bit of margin here I won't go into detail about the onset of large-scale saturation, so one of the consequences of quasi-equilibrium and this onset is surprisingly that you can effectively derive the shape of the precipitation probability distribution, so that The intensity of precipitation or the accumulation of precipitation over events typically have a range that is approximately exponential, so in other words you have a scale of precipitation and prophecy, the probability falls as indicated in this linear record and then if you convert this to a logarithmic graph, you'll see that this one is roughly a three-scale scale free roughly the power law in the lower extreme range and that comes up very easily with just two ingredients: one you need a sharp rise or threshold for the onset of terminal precipitation and number two is that you need fluctuations across that precipitation threshold and this is just to indicate in a buoyancy measure what this empirical expectation of ambient temperature and humidity or equivalent potential temperature is. and its saturation value from the boundary layer and the lower free troposphere in a way that has been made to match this sharp increase in precipitation as a function of all the important thermodynamic quantities that could be influencing that, so that's the reverse engineering problem and then in this uh and this is similar but much more similar but much sharper than if you do the same thing as a function. of, say, column water vapor and temperature, which is a little more traditional.

I'll show that as well and then the probability density function of this buoyancy has a sharp peak very close to the start and then these fluctuations over that, so I'm going to emphasize that where you sit is primarily an estimate of the cause of the equilibrium in the that you are trying to be and the variations are a combination of the grand scale pushing you up and the convection trying to adjust you, but at a finite pace. and of course you can do this vertically too. This shows the virtual temperature difference, so it's an input to the buoyancy for a particular drag parameterization that essentially gives you equal weighting of all levels in the lower free troposphere in terms of the mass coming. and if you color code this by water vapor, you can compare it to the onset of precipitation and find that you need quite a bit of entertainment in the lower troposphere to match this kind of onset, so that's older work, now let me .

Show this in the water vapor domain, so this is the same conditional average rapid onset of precipitation based on a cruder measure of buoyancy which is just column water vapor minus for each temperature the critical value where you get this sharp rise and in fact that's how I got that curve like temperature and water vapor that we showed earlier in the warm up when you collapse like that you get essentially what turns out to be a measure of buoyancy and several different tropospheric temperatures or you can do saturation, the vertically integrated saturation value collapses into a similar curve, so that's your start and then if you do it in a column of water vapor, you can see that you spend a lot of time that can vary from condition to condition. in the non-precipitation regime, but you tend to do similar things when you get to the precipitation regime here and it starts to rain rapidly and dissipate buoyancy.

Well, back to the precipitation distributions, this is the power law range and exponential cutoff shown in log. record precipitation observations from accumulations over events plus daily averages and here is a stochastic model that essentially takes the observed onset roughly as a ramp function and puts it in and can very easily reproduce these same types of curves in the shallow end . This essentially scale-free part of the range in the journal simply comes from the fact that you're averaging a bunch of accumulations, so you move them to the larger end, so that's the explanation that comes from convective cause equilibrium, the quasi-equilibrium is the drift in moisture and buoyancy that tends to push you back towards this threshold, the grand scale is giving you these fluctuations, plus you have fluctuations internal to the precipitation itself and as you wander back and forth across this threshold, that gives you the power law essentially. scale-free range and when you still have larger events, like the slow drift starts to matter, then you get a balance between the drift and the large-scale inputs and that's the convective part plus the balance, but with a time scale finite and that gives you this. part of the range, so when you part, when you take the quasi-equilibrium, you allow deviations from it, you allow a finite time scale, you get this precipitation distribution, if you violate this in some important way, like if you make your process too deterministic, it can ruin it.

This is our grade range very easily, if you mess up the time scale or the amount of variation that you have, whether on a large scale or within your precipitating processes, you can mess up this medium to large range of events with the shear scale. . Well, I want to add another little thing that is almost equilibrium, but what about the upper end of this water vapor distribution shown here for the precipitation point, so you can see it has a nice peak here and this is a logarithmic scale? for different temperatures and different colors, this is how often you sit in this column of water vapor relative to its critical valueat each temperature, so what is happening up here?

So you have balance, the beak almost gives you the width and then I'm jokingly calling this, it almost needs a name, uh, ideas welcome. As you move towards that upper end and, if you can, if you check what's there, have you just discovered that if you apply a simple criterion for mesoscale convective systems, the probability that you are at a pixel that is within a mesoscale convective system and it's reaching 90 to 97 percent here at this high end, so you're almost always organized convection to get to this water vapor and I'll come back to that and Interestingly, the fraction of precipitation that is in MCS it's not as big, but it's still in the 70 to 90 percent range, so there's a lot of organization here, so let me move on to a simpler measure of this organization when talking about mesoscale convective systems, there are a lot of criteria you want to satisfy, but a simple way to look at it is with precipitation clusters, you just take all the pixels that are connected to each other and that have precipitation at some minimum threshold and in the observations again you get this power law range for the integrated precipitation over the entire cluster here multiplied by the latent heat of condensation, so it's in gigawatts the expressed latent heat, you know this power law range and then a roughly exponentially scaled part distribution here and therefore The analogy with the theory of what is happening in precipitation distributions as a function of time suggests that this would include physical importance and would be susceptible to change under global warming, so what is a simple model you can do for this? take the same stochastic model.

This is fias' work again. It's like a version of the qtcm that was mentioned, but without any dynamics, you just have the humidity and temperature equation and you're using the weak temperature gradient approximation so that the temperature across the domain is assumed to adjust quickly horizontally. through waves. You can reproduce the statistics of these groups in terms of probability distribution quite easily, with the slope of power loss being almost the same as the one observed and the cutoff here, it's kind of interesting. I'm going to quickly scan this because it has a lot of inputs so you can do a lot of experiments playing with your wet physics and a lot of those wet physics parameters, including the humidity value at which your precipitation starts. increasing something that is affected by global warming affects that scale so it's a physical scale set by wet physics and that's important because there are things that would have such a limit that it would be like filtration that wouldn't really be physical so what if I want to understand that one thing you can do is map everything into a stochastic branching process and then look at the kind of probability of generating a neighbor given that you have precipitation and a point is the key metric and if you use that to remap all of these boundaries As a function of these parameters you get a pretty good collapse, suggesting that for the physics of causal equilibrium at the grid point you need a measure of how well a point is precipitation or the dynamics in the vicinity of the grid point. precipitation tends to generate. precipitating the neighbors and that's enough to give you a great measure of what's happening at this boundary, so something that may not have been applied yet, but that needs to be applied to diagnose this in full models, okay, so this is talking about something so fast coming from Leilani dulgarov um if you look at this in the observations of these integrated precipitation over the Cumulus Clouds and you look at them in a group of coupled models from phase six of the internal comparison project, you will find that the models they work decently by having this scale free range followed by a range characteristic that is characterized by a scale here and that when you go to a global warming scenario, in this case a typical commercial type scenario for these six cmx models, you get a increase in all of these, it's roughly scale with clausius clipheron in most models, but some are the closest club here on and the fact that you're changing this scale on a logarithmic chart implies that your risk rates are going to change approximately exponentially and in fact that happens, so under global warming a slight change here can lead to a big change in the probability of larger groups forming and all of this essentially comes from the type of dynamics very simple humid taken advantage of by having quasi-clerbium slightly different from quasi, so let's go back to a more convective onset and its consequences, um, the next thing you'll see do and again, this is a fiiasis job is to break things down into two main contributions that would be assigned to things that are very recognizable to Akio Arakawa.

This empirical buoyancy, the measure of buoyancy is empirical because of the wait in the vertical that you're giving the environment that Let's assume it flows into its convective column, so it corresponds to a lot of drag in the lower free troposphere. You can do this based on the subsaturation of the lower free troposphere versus a layer-like parameter that compares the equivalent boundary layer potential. temperature to the saturation equivalent potential temperature above it, uh, and when you look in, you know, reanalyze in this case the temperature and the humidity and the precipitation observed from a satellite retrieval, uh, in fact, you find that you get an angle in this space in the same way.

Accu Arakawa anticipated it in that scheme a long time ago, but now it's quantified and you have the slope of precipitation based on where you move in this buoyancy-like space and you can do things like, you know, if you want to condense this. compose a finite difference vector that essentially approximates a gradient version of this with a direction in which precipitation is increasing and how much it's increasing and you can use that to diagnose models. I'm not going to go into the details here, but Suffice it to say that in many of the models the surface may have a much less pronounced precipitation increase depending on the buoyancy inputs or it may be facing in the wrong direction where you essentially have to get too close. to saturation at the bottom. free troposphere to get rain compared to observations, on the other hand some models do reasonably well on this and here is just another condensation of this into fewer dimensions so you can see the increase in conditional average precipitation with buoyancy, some models are very weak, some here are observations in black here and some in, you know, have a two week rate of increase, so you wouldn't dissipate your buoyancy fast enough and then some of them are in the wrong direction, uh, in this subsaturation plane and the layer. as quantity, so they depend too much on undersaturation.

Now I wanted to include some Todd stuff and I'm going to touch on this real quick if you don't mind, and Todd's poster is on the wall if you want. to check it, so if you are still studying these models and want to discover a little more of the underlying physics, you can remember this figure at the beginning with the canonical wet static energy or the equivalent potential temperature and its saturation value with which I was comparing the lifted plots, so here are those two

arakawa

quantities shown here, this is the saturation value and this is the equivalent potential temperature of the environment and this is averaged over rainfall events, so By taking out cases that they would be very far from quasi equilibrium now, one thing you notice is that in the observations in black here is an observation of the site of our arm and a reanalysis of the era, both are shown in both agree, there is a steep slope. of this, as already seen in arakawa, is something that involves a substantial amount or is consistent with a large amount of drag in the lower free troposphere if there is something like a balance of convective cause that tends to make buoyancy small so your columns are not far from the ground state so it involves quite a bit of drag and a lot of the models are getting something like that and this is the equivalent potential temperature of the boundary layer mapped here so I can do the vertical comparison and I can see that if there was no drag, most of these models would be very unstable, there are some models that basically go straight here, that means they have very little drag and there are a lot of movements that some people discuss in terms of particular cloud types and I'm not going to name names, but I think it's a numerical instability of some kind, this momentum just isn't really seen in the observations in any kind of averaging, so this is something you already know. addressing what your convective scheme is doing uh is probably a really good goal for some of the numbers, the fancy numbers, for example, that we saw in John Sebring's first talk, um, so, um, but moving on from this, let's try condense this. and I'm just going to scan this because some of you will know it by heart and some of you won't, but if you take an equation from the training column and it has, let's say, a roughly constant train speed for sake.

As an argument, here you are bringing a certain amount of mass from the environment into the plot and then as you go along you are going to make the approximation that the plot is not that far from the environment for this purpose, that is a low level. buoyancy approximation and then you know how to further approximate this as a finite or vertically integrated difference across the layer and you end up with a measure of something that would be the drag if you were actually in convective quality equilibrium which is a function of the boundary layer Air Compared to sort of the mid-troposphere values, we decided to call it pseudo drag because we're not really sure that those conditions hold up well, although they seem to work pretty well, but it's a useful indicator of a combination of that decay rate that would be a convective instability if you weren't training like crazy versus the undersaturation of the environment essentially um, so here's this quantity, this pseudo drag here for these models versus the critical value of this empirical buoyancy at which convection begins, so you'll see that this it's a pretty good predictor of the value that convection starts and you can also do the exercise of estimating the same from reanalysis and observations of the arm and get measurements of where you should be on this and you can exclude some models. like MPI models on the low end and others like NASA guess pretty well on the big end using a diagnostic like this.

Well, I had to put in one extra thing, which is as soon as you get two dimensions and this was already in Arakawa. diagram like a schematic arrow, you know forcing this way to fit that way, um, if you have a mode of your distribution set by a combination of what the large scale is trying to do versus what the convection is trying to do back, you'll have There's a circulation around that almost always and you can diagnose it and Brandon Walden has really been going to town on this and diagnosing this and it's very interesting to see the way you trend now this is in a reanalysis data set for the The temperature and humidity you tend to circulate up in the Cape and then down in a subset and vice versa, which reasonably suggests what you would anticipate, but you also have to remember that there are variations that come and go across these constant lines. buoyancy here empirical buoyancy constant um the variations go strongly this way uh or this way or this way Crossing that line and that stochastic or short time scale fitted effect is going to be extremely important for the precipitation distributions that I mentioned before, okay, let's try it to draw some consequences for tropical wave theory and um, this is the same curve again, slightly different version here done with essential wet enthalpy variables instead of the equivalent potential temperature of precipitation as a function of the buoyancy measure again, it is estimated that the lower troposphere to avoid problems with the level of freezing and because if you are built in a lower troposphere you tend to continue, but Kathleen in her article verified that you could do this through the troposphere complete and behaved basically the same way, so you have a buoyancy that depends on the boundary layer, wet enthalpy, humidity and temperature if you linearize this rain, so this is effectively an empirical convective parameterization for a deep model in Barrel Clinic mode if you don't need to know details about the vertical structure.

So you can linearize this and find out different adjustment times in the different thermodynamic directions here. Broken down by a boundary layer, a direct direction of humidity and temperature, and I'm just going to show things compacted again in thetemperature and humidity. instructions and the main point is that the ones that adjust the humidity are substantially longer empirically than the ones that adjust the temperature, so the layer adjustment, as expected, goes fast and the humidity adjustment goes slower and Dave nods because yes, of course you would. This is to be expected and comes from an empirical estimate.

Okay, so this is from an eigenvalue problem that Fayaz did, where you can actually see the directions in a temperature and humidity plane in which the convective adjustment is done, so I'm just pointing out that you can do, you know, exactly the problem that Arakawa intuitively solved in the back of his head all those years ago and then you put this back into the aerberoclinic wave model and these have a long history and I only got some, you know, early work out of it. which we did things from Dave Raymond and Lincoln and uh and Adam Silver Maloney, so these are based on the wave number where you've done a Fourier transform in the X direction for your tropical waves and your As you go to the long scale By changing the time scale to a large scale, you know the typical settling time of the gravity wave and as you move towards the short end it tends to be essentially closer to the weak temperature gradient approximation where the waves go faster compared to their spatial characteristic.

The scale when you have these different, empirical wavenumbers becomes a very simple dispersion relationship and let me point out the version down here that has a little bit of wind-induced surface heat exchange.o Unstable evaporation, wind feedback or infection of zonal humidity, the branch of the quasi-stationary mode that would simply move with the wind obtained in the weak temperature gradient approximation is simply continuously connected to a mode that essentially has its temperature and humidity in convective equilibrium. at all times as it evolves and you can move directly on that Branch through some unknown intermediate stage which theory has not been properly realized, but when they occur these time scales connect directly to each other as there have been giant fights in the community . about the extent to which humidity modes with a weak temperature gradient can be used to explain large scale things like the Madden Julian oscillation and this says that they mix continuously, there is no real fight, you just need to match these approximations correctly .

That brings us to the last two brief things that I want to outline today, so empirically it looks like deep convection and I say it has trouble avoiding drag, which is a little anthropomorphic, but you tend to have substantial amounts of drag. through the lower free tropo the lower free troposphere um empirically if you want to explain the dependence of the strong precipitation parts of that diagram, then this has nothing to do with weak precipitation or shallow convection etc., it sounds like you're in a regime that is more like what mesoscale people have been telling us for years: there is a substantial input through a deep layer and it is not necessarily as coherent as it is schematized in the typical mesoscale, but there is a combination of turbulence and somewhat coherent movements that you already know. and you're getting air through a deep layer, so a couple of things: These are observations from Kathleen's analysis of the radar wind profile that I showed you earlier with the mass flux increasing steadily but not quite uniformly at through the um uh.

The entire lower troposphere, which means you're getting mass through these lower four kilometers. Here's an analytical result which is the point of Yi Hung's article here which I'll get to in a moment to show that you can get it quite easily and then. Here's just an estimate of if you go into the fitting radar measurements and look for connected features only from the rain identified as convective, so it doesn't include all the stratiform stuff that's schematized here, just the convective part here and measure the size of the convective characteristic. You can do the length of a chord in two ways or you can take the square root of the area of ​​the feature and what you find is that there is a substantial amount of this rain that is happening on features that are not that small, now you have to remember that you know . the smallest you could get, as you know, four kilometers from the trim radar, but there's a substantial amount of precipitation coming out of things that aren't that small horizontally, okay, so, um, um, this is the repeat of the two elements here. from Kathleen, the mass flow response to buoyancy increases through the bottom layer and oh yeah and I explained everything in the above so I just want to say if you want more details on that CE in this poster but here's the part where we borrow material that's pretty well known at the mesoscale but doesn't seem to have been well imported into the parameterization realm yet, although several people, including Mitch Moncrief, have been talking about certain things for years, so before, when you have buoyancy. forcing you would also have a dynamic portion in this equation that you will have, it is generally expressed in terms of temperature of pressure gradients that are not local.

Here everything is written for vertical acceleration as you would if you were treating things for effective buoyancy, you would move this equation around, but essentially the acceleration of your updraft will depend in a non-local way. You are undoing an elliptical operator in your buoyancy and in the vertical this means that you are going to tend. To get influence below and above your bubble, now you have to be careful because as soon as you get vertical motion, you will start generating negative buoyancy if something doesn't balance it out, i.e. convective heating, so this is a good way to generate a convective cold top where you get a lot of cold compensating for the negative buoyancy right at the top, but if your updraft is compensating for its vertical motion by condensation, you can get extension below, so by just doing a couple of things here you can see all four as a function of type. of a characteristic width of the diameter of, say, a cylinder or sorry, in this case it's a single wavelength, you can get substantial penetration beneath a region of buoyancy in the vertical direction shown here and one other thing to remember is that in terms of scales if let's say a massive convection that is united in a region and this has been produced stochastically by ehang based on a series of superimposed cylinders of different buoyancy values.

There is a lot of waiting on large scales because their domain is expanded. in the convective region, but you have a whole domain here that does nothing, has no buoyancy, so you have quite a bit of projection at larger scales, which will then be if the vertical scale of the character is what you care about. buoyancy and vertical speed versus how far you are from the surface, which is a couple of kilometers, it's not hard to have a lot of force on that horizontal scale and then you can try this, you know if you could throw together or what, um yhung .

He likes to call a bunch of positive buoyancy negatives and make several random assemblies of this. The non-local part tends to be very robust, so if you're putting together a bunch of observations of an updraft, what happens to the averaged updrafts? together you will tend to get this increase which is not necessarily quite linear, but it has a lot of weight in both the boundary layer and the lower troposphere, coming out again and again in a very robust way, not that there is always a magical linear increase. of mass flow with height, but it will tend to show up a lot, so the last thing is protected convection, um, uh, because this is fun, and again, this is with fires, so we just said that deep convection really strong that is causing a lot of precipitation production, it is usually not able to prevent a lot of masks from entering the lower free troposphere, which incurs a strong dependence on how dry it is in the lower free troposphere , so what if able to avoid that dry air entrainment and given that we have an empirical buoyancy estimator we can estimate we can do the thought experiment.

Let's take this as a function of precipitation versus approximate buoyancy is a ramp function and see how well we do. to predict, say, the average precipitation and then imagine that that individual area has been protected in some way, it could be by something that disrupts the drag, you could imagine putting a chimney around it in the larger scale geoengineering type of case or a balloon, or you could just Imagine you're in a vortex that protects you from a lot of motion or you have a lot of moist air around you like in a mesoscale system, so it just replaces the entrained dry air you're seeing in your observation data set. in this case a reanalysis with almost saturated air, so here is the observed precipitation from a quarterly estimate.

Here's the reconstructed precipitation when you have the water vapor and the temperature from the reanalysis, so it works out pretty well and this is what happens when you then go. go ahead and do this protected convection, so this is a measure of how much, under normal circumstances, dry air prevents precipitation and I should point out a couple of things, one is the color scale change up here, this is four millimeters and half. per hour and this is 0.6 millimeters per hour and you should think of this as Point by Point, this couldn't happen all at once because you couldn't have as much heating, it would be offset by other things in the climate system, but Think about This is used as a measure of what would happen if you protected one point at a time and plotted the precipitation it could receive and, furthermore, it is worth emphasizing that this is being done with instantaneous values ​​of three hours by three hours and then adding them to make it if we were protecting a particular region long term, that is, there are big effects in many places of the dried urine treatment and then there are some places where it is really big in the Gulf in the Caribbean, as you can see by comparing the colors here with Colors down here in the reconstructed regular precipitation that knows dry air, so what if you want to test this in a model and the first place we've done it is in the community atmosphere model.

So up here is just that estimate that you saw and it's only shown in individual sets of grid boxes, there are some that correspond to some grid boxes of the atmospheric model and down here you're doing the experiment in the camera. We've done this a couple of different ways that you can turn off. the drag or you can just say yeah, the air coming in, we're going to say it's almost saturated and the color changes again here, you know, notice that this is three millimeters per hour and uh, the kind of normal range. this green is normal precipitation, you know, today it's six to 12 millimeters a day, it would be in this range of sort of dark green here, so essentially you can have sustained storms for long periods of time in many places if you just do it. you would do.

There is no dry air to be drawn in and kill them, so this is very suggestive. For example, Brian Tang and Kerry Emanuel have a ventilation theory for the impact of dry air on hurricanes. This says turn off the dry air ventilation and you will be able to sustain yourself. your hurricane from the kind of typical temperature state that you have, really emphasizes the role of this dry air and gives you a way to numerically estimate its impact in a similar way if you were in a mesoscale convective system and your plumes shoot up and You're in pre-humidified air where convection has already humidified the air around you, you'll tend to get some of this effect in those places, as long as you're not pulling in large amounts of air from the front.

Um, so a strong measure of how important dry air entrainment can be brings me to the summary that I've broken down into a couple of slides, so Erica was convective because the balance has really hit a lot of places, in fact, more than I have been. I could cover here, but among the ones I would send as a souvenir is when you include a finite time scale in the convective quasi-equilibrium, you get as a gift the probability distribution of rainfall and the quantitative aspects of the variations over convection. The balance of causes determines important things about the distribution of precipitation and it is important to say the changes in precipitation under global warming, which I cut from the talk so as not to extend it in time, but we show it for the precipitation groups, so than the distribution of precipitation groups shown here with the global distribution. warming versus regular climate in red and blue has related mechanisms, so the threshold is important sets the quasi-equilibrium value sets the finite time scale fluctuations on thisbetween the large scale and precipitation pushing back stochastically sets this quasi and then at the very high end, you're getting into a situation that I jokingly called very quasi where a lot of organization appears and you tend to have interactions with neighbors within the convection and Then Erica was of the opinion that having a quasi-equilibrium curve can be quantified in a space that is no different than the space that Arakawa was imagining and is something that our current numerical models actually have quite a bit of trouble achieving correctly and while we are in that, if you have that empirically estimated time scale.

Can you say anything meaningful about the expected evolution of tropical wave types and about the large impact of dry air entrainment on precipitation in our current climate and, finally, this is despite the entrainment in which Arakal was present when viewing majestically? growing exponentially or linearly increasing with height in the training columns, each nibbling air a little more or a little less around their edges will probably have to be replaced by something containing a lot of what is often called dynamic drag which is mainly found in the lower troposphere and only closes in the upper troposphere, however the seeds of this were already there in Arakawa's work and when Kerry, Chris and I were initially thinking about the large scale impacts of equilibrium of convective causes we temporarily forgot and now that everything has to be worked backwards for the effects of a large scale in the balance of the convective cause and finally I had to finish with the canonical photo of Akio, so greetings to all, you have time to questions and I think I can switch to this microphone so it can be passed around the room. um uh thank you Dave for bringing us um since this symposium is about some history, I want to mention something in historical development that continues to be a puzzle and you're not willing to improve the puzzle table, but it's something that you already know from the beginning. days of just working on General Matters of proactive convection actually and everything that came out of this idea of ​​being exchanged, the clue, I mean, in the case of the glue, is at the core of the particular parameterization that um Appeal and Wayne developed , but there was a time actually there.

It was a different current that emerged based on real observations in the days when scientists were bravely manning airplanes and clouds, starting with, I think, Jack Warner's word in the 1950s, also, of course, Joanne Lankas, who demonstrated conclusively that yes, of course, the clouds are swapping, but I also thought at the time I dismissed the idea that we were creating a track model as a specific way of dealing with that and this work was Yes, Jack Warner and then David Raymond and Alan live with observations of Community aircraft and show that the real clouds did not hit that model very well and in fact, in the lower purpose here, most of the transports were coming out of the subcloud.

The scale is not like the column versus the environment, but subclass scale columns that go up and down in the transport phase and this is what is called buoyancy, it still runs the type of model and from all those observations are very persuasive and there was a moment, I think, in the In the '90s, the field seemed to embrace this and everything was retrained, including the model, and I don't know how that happened or why it happened and I'm not sure it's wrong that That happened, but it baffled me, that's how it is. All the motion evaporated and that makes a big difference, so to summarize, this saturation decay that they need in a tropical atmosphere can also be consistent with a zero buoyancy override guarantee model if and only if you take into account the virtual. effects of water vapor water condensed and one of you and I killed that and I've repeated what he and I did with modern radio zones.

It's really beautiful, it could be a complete coincidence, but the tropical atmosphere floats almost perfectly neutrally on an elevated plot. conversely from the top of the mix layer, I don't think it's conclusive proof of that, obviously it's been a puzzle why the controversy went away or maybe it didn't and I'm just not aware of that, yeah I mean , I can offer several thoughts on that like Steve on apparently Ken too, um, but one is so um, yeah, I mean the virtual effects, um, you know, which are substantial and should be included and are often neglected because simplicity, um, uh, the kind of empirical thing we're trying to explain here if you know why to get right, to get a strong relationship with precipitation, you have to have a lot of influence from the ambient air in the lower free troposphere and, therefore, some form of that air entering the package is the simplest explanation for that.

Another idea is that in terms of buoyancy classification, if you're moving conserved quantities up and down and back and forth, and you know people. They often do things like they only count things when they start moving up as part of an updraft, and then if they go up and down and up and down, they count them again as an updraft, even though it was recycling the same conserved thing. quantities whereas the type of flow implied by the larger scale region that is generally buoyant would reach far beyond all of those smaller scale circulations and would take some of that ambient air and inevitably bring it in where the turbulence would then interact with it so that some of those lumbering little scales maybe just spinning their wheels and that's a guess, not a quantified statement, um, but you know there's this empirical fact that you have a strong dependence on ambient air, uh, in the troposphere. free bottom and this is a cheap way of explaining that, but all those things that you say are precise and interesting and need to move forward, and the buoyancy tartar is supposed to also address some of that, you know that tends to your general movement ascending of the greats.

The scale upstream is going to ignore some of those small-scale things. Various thoughts, cool sets of different types of clouds are made up of subcloud elements. Actually a major peer review, but they produce the same profiles. There is actually consistency in these in this memory, so all. True, many thanks to David.