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## Modeling the Basics, A mathematical summary of condensation in climate models.

Posted by Jeff Id on October 21, 2010

An important point often made by critics of climate models is that they often represent our best guess at specific phenomena.  One of the biggest uncertainties in climate models is in proper modeling of atmospheric moisture.  Considering that H2O is widely accepted to be the strongest of all greenhouse gasses, water is fairly important component of climate models.  As is often the case at tAV, I’m not the guy who figured this out but am the one who will attempt to translate the deficiency in models as I currently understand it.

Based on Makarieva et al. recent multi-author paper (M10) on the driving force behind winds several here at the Air Vent have discovered that the climate model CAM3.0 linked here doesn’t include precipitation condensation based pressure loss in its cloud parametrization. The model doesn’t even attempt a simulation for what I believe will soon be accepted as the primary driver of most winds including tornadoes and hurricanes, not just globally on earth but solar system wide.  Jupiter’s red spot, bands in Saturn, all of it powered by condensation based pressure changes.   Why is that so important? Because the additional energy stored in water vapor which translates into lower than modeled pressure and higher than modeled windspeeds in hadley cell updrafts.

Ask yourself to explain what powers a tornado, and soon you’ll find yourself describing strong temperature inversions where the hot surface air breaks through the cold upper air or something of that sort.  In fact, that is what we’ve all been taught since junior high.  M10 teaches that there is a component of basic gas physics missing from this explanatoin — condensation.

The water vapor component of saturated air at 30C has a Water vapor is about 0.6PSI where as standard air pressure at sea level is 14.7 PSI.  When the vapor condenses, it no longer contributes to the gas pressure in the region of condensation much as it takes up nearly zero volume at that point.  The air pressure in the saturated volume would drop by the vapor pressure amount when condensed.  The pressure doesn’t sound like much but remember, we already have a model which creates some convection without it and 0.6PSI over a square yard is 780 lbs of additional upward force.  That’s not all though, the heat release during condensation creates an additional pressure loss warming the surrounding air reducing the air pressure even further.  The net effect is all toward powerful amplification of updrafts in a condensation environment.

I’m not intending to do the calculations any further here, because it is basic knowledge.  None of what I’ve written above is in any way new and all of it has been known longer and more completely than we have known about CO2 absorbing infrared radiation.  In fact, 20 years ago in my undergraduate thermodynamics class we were forced to calculate all of these factors for a variety of mixed gasses.  So when I first read Anastassia’s paper on what powers hurricanes, it made perfect sense to me.  Except for the part where she claimed it wasn’t part of mainstream literature.

Nick Stokes, who takes too much criticism some times, summed it up best, brackets are mine.

I have to say that it’s still not clear to me where condensation comes in in 3.3.6. However, I remain sure that they haven’t just forgotten about it. This stuff [models] has been around for thirty years, reviewed by thousands.

For some background reading  Nick linked to the Zhang paper from which the cloud parametrization for CAM3.0 was adopted. Paper here and he also pointed out some very similar equations to M10 right from the CAM model there is a difference though.

From the CAM3.0 global climate model, chapter 3.3.2 paraphrased style, it’s not a direct quote and I’m not the original author 😉

The conservation of total air mass using as the prognostic variable can be written as

Eq 3.365

Similarly, the mass conservation law for tracer species (or water vapor) can be written as

Eq 3.366

There is no “law” of conservation of water vapor to my knowledge.  Water vapor can condense, especially when V can be in the vertical direction toward lower pressure.  This is clearly a simplification of the situation as mass of water vapor is obviously not conserved during condensation in an air volume.

q is the specific humidity of water vapor in this case.  Pi is the pseudo density of the air.  These conventions are different from molar density that M10 uses but they are interchangeable for the following points.  M10 equation 34 is actually nearly identical but have an additional tweak to insure that water vapor is not conserved.

Eq 34 from linked M10 paper.

Calling your attention just to the right side of the equation for S ≡,   w is velocity in the vertical z direction, Nv is the molar density of water vapor.  So the first term  w · dNv/dz is the change in water vapor density that is multiplied times vertical velocity resulting in a term for the change in water vapor density with respect to time, functionally identical to the first term in eq 3.366 which says change in total vapor mass in the volume vs time.  The second term  in  eq34  w · Nv/N*dN/dz is the change in total mass  with respect to z distance which when multiplied by w velocity (distance/time), it is the change in total mass vs time created by air flow.  Again functionally nearly identical to the second term of eq 3.366 on which the model is based except that term 2 of 3.366 only addresses the water vapor while eq34 addresses total air mass.  They are the same equation– almost.

The difference is that the model eq 2 above is set equal to zero representing conservaton of water vapor mass, whereas M10 has the equation set equal to S. Were it set to zero, the volume of vapor in term 1 would always equal term 2 and there would be no change in vapor density ratio – no condensation.  IN eq 34 ‘S’ represents the condensation mass.

From M10

S (Eq. 34) is the sink term describing the non-conservation of the condensable component (water vapor).

See, Nick and I aren’t alone,  the authors of M10 have never heard of conservation of water vapor either.   Several of us scoured section after section of the model looking for where this effect was included.   In the section on moisture, I found that while they used partial pressures to determine q, they didn’t recalculate pressure based on the new value maintaining conservation of water vapor mass.  Surface pressure is held fixed as is the column’s molar gas mass even though they are calculating a condensation/evaporation process.  The expansion and contraction processes are simply not calculated.

I commented to Nick, on the CAM model:

All they update is the q in 3.417 with no adjustment for the pressure created from the condensation. In fact they hold it to zero change during the update to maintain conservation of air mass (total gas mass and pressure) while changing q. By doing that in a condensation region, they’ve lost their conservation of mass in the form of condensate and increased the total energy per volume.

As further confirmation,  Reader RuhRoh, discovered this little gem in a different model ‘CCM’ confirming quite clearly what we are discussing:

These conservation errors result in small imbalances ( << 1 W/m2) in the CCM. We note that there are also small inconsistencies present in conservation that are associated with the use of a moist mixing ratio, and moist surface pressure in the model. In principle, as any process removes water vapor from a cell, the surface pressure (PS), and the mass of air (dp) should change in a grid volume. This ought to also imply a change to any mass specific quantity affected by the parameterization. These changes are ignored in CCM parameterizations from one process to the next. We typically insist that processes conserve assuming a fixed mass of air (and hence a fixed surface pressure) within a parameterization.

Holding pressure fixed to conserve a mass of air ignoring the water vapor removal.  Now that we’ve established that at least two climate models ignore this part, we caught some attention from modeler Gavin Schmidt of Real Climate who wrote.

Most GCMs use the hydrostatic approximation in which the pressure at any point is exactly equal to the weight of the air column above it. Very high resolution weather models sometimes use the proper non-hydrostatic equations, but this isn’t very important at coarse scale (I’m sure there is a paper that has demonstrated this somewhere).

While it sounds like a perfectly valid way to calculate pressure, the fact that delta P from condensation is not accounted for means that models will underrate the estimated flow to some degree in moist hadley cell regions.  You can understand the thought process of the scientists when the models were developed.  The mass of the vapor is small in comparison to the surrounding air, so as water condenses they work to capture only the energy of the condensation holding mass constant.  This creates an imbalance in condensation where the mass in a volume after condensation is greater than the mass before.  This imbalance shows up later in a minor energy imbalance corrected elsewhere in the model.  Since the imbalance is small the effect is assumed to be small and everyone is happy.

None of this is unreasonable in my view, except that total energy in the volume is not the same as total gas pressure in the volume and you’ve now lost 0.6 psi from the flow in a hurricane model.  But there is another detail we should talk about.  The moisture is a continuing massive source of stored potential energy in the lower atmosphere.  As global warming occurs from CO2 buildup, the lower atmosphere is expected to contain more vapor per unit volume.  Basic physics right?  The increased vapor would result in increased condensation and increased regions of updraft pumping more heat into the upper atmosphere where it can be radiated to space.  Due to the warmer temperature profile in the tropics, heat from the surface could be carried quite a bit higher in the atmosphere before freezing occurs perhaps making the tropics a very effective.

So then the  whole question comes down to, does this pressure change make much difference or is it just a fudge factor?

Well Makarieva et al. also proved the effect can drive hurricanes and tornadoes.

It is not small, and as my understanding grows seems correct that it isn’t standard in climate or weather science.  It’s shocking, but this powerful and well known condensation effect appears to be missing from all of the climate models.

1. ### Phillip Bratbysaid

Yes, never heard of the conservation of phase law.

2. ### AMacsaid

0.6 psi looks much too high. Say you start with H20-saturated air at 30C, and processes (adiabatic expansion etc) bring you to 25C. The amount of condensation will then be

(saturation @ 30C) – (saturation @ 25C)

Which would lead to some value much less than 0.6 psi with respect to pressure changes. It seems to me that 0.6 psi is

(saturation @ 30C) – (0% rel humidity @ 30C).

3. ### Craig Loehlesaid

It is worse than you think. Consider a summer landscape in which the surface is heated differentially. Warm spots give more warm air which start to create updrafts which create cummulus clouds (or even thunderstorm clouds) and the system starts pumping heat upwards. IF however, you consider the entire landscape AVERAGE temperature (which the climate models must do at a very large grid scale), it may be too low to create an updraft like this. This larger scale averaged simulated land unit will get warmer than a real one because it will not start pumping heat so soon. Add to this the effect of failure to consider the condensation volume loss, and you create a serious deficiency in the heat pump effect of thunderstorms. It is not merely that there is some small conservation error that can be fixed at the end: rather, the neglect of this factor diminishes the function of the localized and important heat pump of the thunderstorm/hurricane type system (by reducing the growth in wind speed and updraft) which pumps a lot of heat, especially in the tropics. The assumption of adiabatic cooling ignores all of this and treats the atmosphere as always smooth and at equilibrium. False assumption and only necessary because of the scale at which the models operate. It is in fact known that the models under-simulate thunderstorms.

4. ### Jeff Idsaid

I still wonder if someone will be able to step up and show us where this is wrong. This isn’t small news at this point.

Craig wrote:

“It is in fact known that the models under-simulate thunderstorms.”

See, I didn’t know that and have read very little about models. The above sure looks like a good explanation as to why that happens.

5. ### Craig Loehlesaid

It is like simulating a boiling pot of water with a single column of water using only heat transfer and not allowing bubbling. It will give wrong answers.

6. ### Anastassia Makarievasaid

In M10 it is stated that precipitation alone produces pressure gradients of sufficient magnitude to drive the trade winds. This leaves a minor role for differential heating. If one claims that the main effect is missing from GCMs, one is challenged to explain how GCMs reproduce the observed velocity and pressure field.

On pages 11-12 Lorenz 1967 lists the governing equations for atmospheric dynamics. The equation of motion (1) lists the forces that act to change the kinetic energy of the air. Note that there is no explicit driver of circulation in this equation. In other words, there is no information about what would make the air move. We can only see that the motion can be sustained if there is some pressure gradient.

Neither does the conservation of mass equation (2) contain a driver of motion. Ideal gas law (5) relates temperature and pressure. Thus, the driver of motion as conventionally considered is contained in the conservation of energy equation (3). This equation accomodates the parameters of differential heating and heat conductivity and latent heat release in the Q variable.

Ultimately, therefore, the information about pressure gradient comes into (1) from (3). Lorenz even re-writes this equation in terms of pressure (4). The problem is to know what pressure gradient would correspond to a given distribution of heat sources. Apparently, the larger the latitudinal gradient of solar power, the larger the resulting pressure gradient. The problem is to know the proportionality coefficient. Here it is my understanding that the attempts to derive the value of this coefficient from basic atmospheric parameters fail (hence the explicit problems with theory I discussed in the previous thread). The coefficient appears to be too low. In GCMs, it is simply taken from observations, such that the resulting pressure gradient conforms to the reality.

When you already have the correct pressure gradient in Eq. (1), manipulations with conservation of mass equation will produce nothing. Even if you put the precipitation term there, it will make a minor difference — because you have already got the right gradient in Eq. (1). This explains why including or excluding vapor non-conservation from existing GCMs is not relevant at all. The key issue is that modern GCMs take information about pressure gradient from conservation of energy equation.

This is just a highly formalized description of model logic and physics as I see it. The error is not in the fact that zero is put into the conservation of energy. The error is to artificially inflate the pressure gradient that would correspond to the existing differential heating. I will next dwell on the alternative logic of condensation-induced dynamics.

7. ### Craig Loehlesaid

Re: #6. This shows that the claim that the models are “pure physics” is not true. Also, if the pressure gradient is empirical, how will this properly reflect changing conditions? Finally, by under-representing the heat-pump effect of condensation driven convection, the models fail to properly model the negative feedback effect of these heat-pumps. Stronger heating leads to more convection and more heat dissipation.

8. ### Will Kernkampsaid

Jeff,

When the water condenses, it is still in the airmass as droplets. Only when these droplets coagulate and rain out to the ground do you get the pressure effect you start the discussion off with. Until such time, you could preserve the amount of water (vapor+droplets) in the way shown. You would then ignore the small density effect.

Later in the discussion you start to address cloud resolution problems due to grid cell size. This appears to be a key challenge for the GCM’s. I would be very interested in a detailed comparison of how these models approximate cloud formation and rain amounts.

Will

9. ### Jeff Idsaid

#6 and #7, The explanation makes sense but again, I don’t see where this adjustment to pressure gradient is included in the models. Is there some example of it?

10. ### Jeff Idsaid

#8 If water condenses at the top of a column, there is a pressure drop in the volume where the water condensed, this doesn’t address the bottom of the column. It causes a drop in pressure at the point where it occurred. At the bottom of the column there would also be a slight drop until the condensed moisture reached terminal velocity then it would remain the same as before the condensation, of course mass would be flowing up and out of the column so pressure would gradually reduce further as things moved along.

11. ### Gavinsaid

Hey, I can get as excited by new results as the next guy, but you are a long way off base with this summary.

First of all, there is a contradiction between your claim about Makareiva’s paper and her statement on the previous thread. She stated that the issue was what happens when water mass is removed from the column (#93), not the process of condensation. (Although she appears to go back on that in comment #151 – and you wonder why people are confused!).

Let’s try and disaggregate the issues:

1) what happens during condensation in the free atmosphere with no removal of mass (i.e. cloud formation)
2) what is the impact of changes in column water amounts on pressure gradients

You want to focus on 1), which is fine. But since I already mentioned that climate models acknowledge that (2) is assumed away and that they are working on seeing whether it’s important (likely answer, not very), I’m a little surprised that this isn’t where you want to go. But let’s move on.

You’re claims about 1) are indeed exciting, but I don’t think they stand up to scrutiny, the main reason being that the analogies you are using (steam engines, collapsing coke cans etc.) are all examples of condensation taking place in constant volumes – implying that the pressure will vary. However, the free atmosphere is not a constant volume, and what is occuring is happening at constant pressure.

Think about the conditions at exactly the level at which condensation wants to occur (for some reason we have a super saturated air parcel just sitting there). The pressure at this level is set by the mass of the column above it (we can assume a hydrostatic column without any problem). But since the pressure is set externally to the parcel, it cannot change if the parcel undergoes some thermodynamic shift (which could be because of condensation, or radiative transfer etc.).

What happens if you condense some of the vapour to liquid at constant pressure? There is obviously latent heat release but let’s ignore that for now, i.e. assume L=0, and so the temperature is constant. The new gas phase constituents will have a different density, and the condensate will start to settle. Changes in density will mean that the parcel is either pushing on the environment (or vie versa). Since dry air is actually denser than moist air (at the same temperature), the buoyancy forces on this parcel will be pushing it down with respect to the rest of the environment.

(In the real world, the effect of latent heat is much more important and the gas phase will be made more buoyant (not less) as a function of condensation. Thus enhanced upward flow (which sustains large scale convection) is only because of the latent heat, not anything else. If you turn off latent heating, you would greatly reduce the circulation. That might be a fun GCM experiment to try – what happens as LHE –> 0… hmmm…).

The bottom line is that latent heat effects are by far the dominant contribution to density changes, and the reason why GCMs have had reasonable Hadley Circulations for decades is because they get that right. I don’t think there is anything to point 1), and while point 2) is obviously correct (though not widely used in models), it’s impact will be small.

PS. It is not sufficient to find lists of things that GCMs do badly and simply assume that some new idea is the reason why…

12. ### Anastassia Makarievasaid

Let us now suppose that differential heating makes a negligible contribution. We will consider a two-component atmosphere. Equation of motion will remain the same, but instead of one equation of conservation of mass we will have two equations, one for dry air and another for vapor, Eqs. 32 and 33. We now get a new variable, density of vapor Nv, but presuming that we are talking about saturated atmosphere, we will take information about Nv from ambient temperature using the Clausius-Clapeyron law. We know that non-conservation occurs due to adiabatic ascent and hence express the condensation rate as Eq. 34.

Let us summarize what we have at this stage: instead of equation of motion and conservation equation, we now have three equations. We’ve got a new equation and we will take the information about pressure gradient from it. As it is specified in Eq. 37.

The conservation of energy equation will be used to specify temperature gradients. Here horizontal temperature gradients can be arbitrarily small, because condensation is mostly determined by the vertical adiabatic change of temperature. Differential heating will make a minor correction to circulation. Unlike in GCMs, we will not have to tune anything to observations to roughly represent the circulation. We obtain the characteristic magnitude of circulation from basic atmospheric parameters.

Therefore, the key point is which equation to use to specify the pressure gradient. The key error is physical. Eq. 33, with condensation specified by Eq. 34, speaks of tiny magnitudes Nv $<<$ Nd compared to Eq. 32. However, it contains all information about large pressure gradients. The key error has been to ignore the vapor physics because Nv is considered to be small. In reality, relating to pressure differences that drive the observed winds, it is huge.

Again, it is very rough basic logic.

13. ### Pat Franksaid

Jeff, “That’s not all though, the heat release during condensation creates an additional pressure loss warming the surrounding air reducing the air pressure even further.

It seems to me that the release of the heat of condensation will increase the pressure exerted by the remaining molecules, while the condensation itself will decrease the pressure of the volume (loss of water vapor). I haven’t done a calculation to see if the higher pressure caused by heat will fully compensate the lower pressure due to loss of water molecules.

But just from equilibrium PV=nRT considerations, if dV=0 (V1=V2 is given) and dT=0 (T1=T2 if loss of latent heat is complete), then the pressure in the rising volume will decrease with the mole fraction “n” of water vapor condensing out into droplets. The value of T2 depends on how much of the released latent heat migrates out of the rising air volume. If T2 is greater than T1 the pressure drop will be less than prescribed by the change in “n.” But T2 will have to increase by the same fraction that n has decreased in order for P1 = P2.

But if the phase-change heat is lost to surrounding cooler air so that dT=0, then following condensation the lower density will cause the packet of air to rise further, entering a higher and yet cooler air mass. Condensation will then recur, internal air pressure will drop, and the process will be repeated.

So, the air in that volume will continue to rise, losing water vapor to condensation all along the way, and continually emitting the released latent heat into the surrounding air, until the rising air mass becomes dry.

If the latent heat flux warms the surrounding air, the density of that air will decrease and become entrained in the rising plume. Condensation of water when a warm moist packet enters a cooler air mass would seem to power a thermal updraft.

14. ### Anastassia Makarievasaid

When gas is added to the atmosphere in one place, and disappears from it in another, this process is associated with formation of a pressure gradient. Pressure is higher where gas is produced and lower where it disappears. One can pose a stationary problem of finding the pressure difference between the two regions depending on peculiarities of the two processes (gas removal and gas addition).

If we look at the atmosphere, we can see that such a problem is highly applicable and relevant. It is relevant not only for the Hadley cell, but also for quasi-stationary systems like hurricanes and tornadoes. However, highly surprisingly, we do not find any treatment of this problem in the meteorological theory. The stationary gradient caused by mass changes has never been evaluated in theory.

In our work we show that the gradients that are associated with these processes are very large in the atmospheric context. It is shown from basic physical principles, without empirical parameterizations or whatsoever tuning. It is difficult for me to see how the existing GCMs can escape a major re-write unless somebody comes forward and shows, from basic physical principles, not models, where we could err.

15. ### Anastassia Makarievasaid

#7 Craig,

Re: #6. This shows that the claim that the models are “pure physics” is not true.

What we are proposing is pure physics for sure, it is too transparent. And the physics we propose (a major role for mass removal) is not compatible with what GCMs show (a minor role for mass removal). One of the two must be wrong. I have suggested my version of why GCMs are wrong based on my analysis of what the climate theorists say. Let us see what will be said on our pure physics.

16. ### Craig Loehlesaid

re #15 by “models” I meant the GCMs.

17. ### Nick Stokessaid

Jeff,
I’ve been tracing the story of sources in the CAM3 documentation. 3.36 is the sort of equation you want to see – a vapor equation with S clearly there on the RHS.

Then they go into semi-implicit stuff, where water vapor seems to be not one of the variables included (as you’d expect). The trail picks up in 3.18 – tracer transport. They give an equation where they explicitly say they are excluding sources and sinks. But they are only excluded for the moment.

In terminology that may cause further excitement here, they have Sec 3.1.19 on “Mass fixers”. This goes rather thoroughly into the sequencing. They solve for a part stage ignoring sources, then they account for the effect of the sources over that time. This is a key section.

You might like to follow their discussion of a “small error” following Eq 3.244.

Something else to note is the “stats calcs” in 3.1.21. I’ve mentioned that any good CFD program will monitor some things that should be “conserved”. I’ve used quotes, because there may be sources, but the numerics should not be one. It’s a check on numerical accuracy and a warning of instability. But is also serves as a check on model correctness. If you’re summing the total wv routinely, as they are (3.262), then they will be checking total water.

So that’s the background. There’s still more detail I’m looking at.

18. ### glaciermansaid

I remember seeing Willis Eschenbach’s talk on Thunderstorms being the pump that regulates heat, especially in the tropics.

Seeing this thread and the previous one made me remember it. How much are the GCMs under accounting for thunderstorm heat pump effect? Knowing this would answer a lot of questions, maybe even find the “missing heat” – http://www2.ucar.edu/news/missing-heat-may-affect-future-climate-change.

19. ### Steve Fitzpatricksaid

I have to admit to being more than a little puzzled by this talk of pressure reduction due to condensation. Maybe I am missing something important.

The condensation takes place due to cooing as an air parcel rises, and that cooling is from adiabatic expansion. In other words, the condensation (and “loss” of gas volume due to condensation) is driven by a net expansion of the air as it’s altitude increases and the ambient pressure falls. An order of magnitude estimate is the expansion of a dry parcel of air rising from the ground to 12 Km is about 4 fold. The net expansion of a moist parcel would (of course) be lowered a bit by the condensation of water vapor (it represents as much as 6-7% of the parcel volume at ground level), but at the same time the volume would be increased by the latent heat liberated by the condensation process… the moist parcel doesn’t cool so much as the dry one so this adds to volume. At no time during the ascent of a moist parcel does it seem to me that a net “loss” of volume could possibly take place… it is continuously expanding. And it pretty much has to be at the pressure which corresponds to it’s physical height all along the way as it rises.

So I am honestly confused when someone says that pressure falls as a result of condensation; it seems to me the exact opposite is what is happening, condensation increases because pressure falls and causes adiabatic cooling.

20. ### jimsaid

Water has a molecular weight of 18. Oxygen 32. Nitrogen 28. So removing water vapor makes the air more dense, not less. The heat generated might well have the opposite effect.

Water vapor
The addition of water vapor to air (making the air humid) reduces the density of the air, which may at first appear contrary to logic.

This occurs because the molecular mass of water (18 g/mol) is less than the molecular mass of dry air (around 29 g/mol). For any gas, at a given temperature and pressure, the number of molecules present is constant for a particular volume (see Avogadro’s Law). So when water molecules (vapor) are added to a given volume of air, the dry air molecules must decrease by the same number, to keep the pressure or temperature from increasing. Hence the mass per unit volume of the gas (its density) decreases.

21. ### Terrysaid

#19 Steve

As I understand it, the fundamental gas-phase physics (ie condensation, expansion etc) are not at issue here, it is the mass balance of H2O that is the problem. Ie, the models do not re-adjust the parcel for the new total H2O mass in the vapour phase once condensation has occurred, rather the parcel is assumed to still contain the same total as was present before condensation occurred. On a small scale it is not significant, but on large scales it is.

On a separate issue (but probably related) I also seem to recall that the GCM’s are constrained to hold the global RH to 70%. If this mass balance issue turns out to be significant what does holding RH to 70% do in conjunction with it (I could be wrong on this RH constraint tho)

22. ### Jeff Idsaid

I don’t have much time again but apparently the description wasn’t clear enough. As a saturated cubic meter of air rises pressures and temperature drop. The resulting condensation removes molecules from the gas pressure portion of the equation, pressure drops and more air is sucked into the volume from around it. This occurs even with heating from condensation because the condensation would stop if the mass warmed instead of cooled. It only means the mass cools slower and think about what that means to our chunk of air’s density compared to surrounding air and upward motion.

I really need to say again though that I don’t know how much is or is not included in all of the climate models or the magnitude of the effect. Some of the models are ignoring that component though. Some interesting off-line comments have been made as well which just leave me more confused.

23. ### Steve Fitzpatricksaid

#21,

Ok. But 1) the total mass difference can be not more than about 3%, and 2) there is no change in the mass of teh rising parcel due to condensation per se, the mass of cloud particles (condensate) remains in the rising air parcel. It is only if rain droplets fall out of the (cloudy) parcel that the mass loss takes place.

Is it the potential loss of 3% mass that this is all about?

24. ### Terrysaid

#23

It is higher than that when the air is supersaturated as it is in clouds. Also when it is cumulatively applied to convection cells, the effect could be quite significant. I will have to defer to model experts and await the answer.

25. ### Curtsaid

Steve #23:

“Is it the potential loss of 3% mass that this is all about?”

3% mass loss, if it does translate into anything like 3% pressure drop, could be a huge effect. Think of the winds generated between a high-pressure system at 30 inches Hg and a low-pressure system at 29 inches Hg (sorry for the English units).

Right now, I’m agnostic on this — it’s been too long since I worked with these issues in detail to offer an informed opinion.

26. ### Craig Loehlesaid

Not all condensation occurs due to rising of a parcel of air. Some occurs due to mixing of air masses, which is how you get a line of rain when cold air pushes into warm, or due to cooling as the sun goes down. Yesterday was calm but became windy at sunset–due to pressure changes of condensation?

I would very much like to see some form of physical experiment regarding the condensation issue. In the absence of this I have been looking at clouds. If the latent heat of condensation were not fully transferred to the air parcel suspending condensing water vapour, then the relevant air parcel should be reduced in volume and buoyancy. This should result in certain cloud formation characteristics –

– clouds should form in clumps around sites of initial condensation. The reduction of volume at the initial condensation site within the air parcel should cause a temporary pressure gradient leading to more rapid condensation around that point.

– If there is reduction of buoyancy of the air parcel in which the water vapour is condensing, most clouds should remain close to their formation altitude.

I feel that it is quite plausible that not all the latent heat of condensation is transferred to an air parcel in which water vapour is condensing. Those experiments with saturated air in adiabatic chambers, in which the transfer of the latent heat of condensation is seen to be almost fully transferred to the air molecules may not be analogous to the real world as they occur within a closed (radiation trapping) vessel.

28. ### MikeNsaid

>An important point often made by critics of climate models is that they often represent our best guess at specific phenomena.

This isn’t a point made by critics; it is made by proponents. Tamino wrote that they represent everything we know about the physical world, contrary to my claim that they are curve fitting.

29. ### jimsaid

#23 Cloud particles are made of liquid water. They would occupy less volume than the equa-molar amount (same number of molecules) of water vapor. The cloud would be more dense than the same volume with water vapor only. Of course the heat of condensation will heat the entire mass which is probably why clouds tend to rise.

30. ### jimsaid

#27 I believe clouds are generally so large that the condensation/cloud formation process could be considered adiabatic on short time scales.

31. ### Steve Fitzpatricksaid

#25,
“3% mass loss, if it does translate into anything like 3% pressure drop, could be a huge effect.”

Yes, but it is hard for me to see how 3% mass loss translates into a significant pressure drop anywhere. The pressure of the rising parcel can never be significantly different from the normal atmospheric pressure at the altitude of the parcel. The pressure is pretty much fixed by altitude. Yes, there are significant differences in pressure versus height profiles for large systems like hurricanes, but that is not the case for your run-of-the-mill convective cloud. What does change (a lot!) is the temperature, due to the latent heat of condensation, compared to the average temperature versus altitude profile of the atmosphere. When the cell tops out, it is much warmer than the surrounding (non-cloudy) air. These convective cells carry a huge amount of heat from the (moist) surface to the upper troposphere, where it can radiate to space, and so cools the Earth.

If the GCM’s do not properly treat the change in mass when rain falls, then this could (of course) introduce some inaccuracy; I just don’t see gross errors from this issue alone. Bigger fish to fry exist.. like the substantial under estimate of total evaporation from the surface of a warming ocean, which substantially reduces the cooling you would expect for convective cells as the ocean temperature rises due to radiative forcing.

It seems to me the GCM’s have important inaccuracies, but this does not look to me like one of them.

32. ### Windy Wilsonsaid

When I saw the title I thought it would be about the Global Warming “scientists” rocking back in their chairs, staring at the air vent in the ceiling until the number came to them.
This is even better, as it shoots major holes in their models.

Please try to explain the scientific stuff, I had hs chem and physics 40 years ago when it was halfway worth the time, and while I get a lot of mileage out of the physics class, there are some things that need a bit more explanation.

(btw, this whole reliance on computer models to substantiate one’s hypothesis is only possible because the leftists consider it somehow possible to computer-model stuff that never happened before, like animal tests of cosmetics and stuff).

I am trying to think of ways to empirically test the hypothesis that water vapour condensing within an air parcel may reduce the volume of the air parcel and ultimately be the main driver of winds within weather systems. As far as I can see tests in closed adiabatic chambers may give a result showing that more of the heat released by vapour condensing is transferred to the surrounding air than actually occurs in nature.

One way to test may be to launch large balloons containing air parcels to be tested. The balloons could be of the inelastic clear polyethylene type, and would be only 1/4 inflated with air to be tested at ground level. A smaller helium filled standard weather balloon could be attached to the crown to compensate for the weight of the envelope and instruments. A controlled warm moist air parcel could then be lifted and allowed to expand. The flight profile, temperature, and infra red radiation of various air parcels could be then observed. If a moist air parcel shows a decrease in vertical speed or a step change in a steadily decreasing speed after reaching condensation level, this may indicate the hypothesis is correct.

Current understanding indicates that the latent heat released as water vapour condenses heats the air in which the water is contained causing it to expand to compensate or slightly overcompensate for the loss of water vapour volume. Possibly this effect is only momentary, as the heated air molecules radiate more strongly from their increased energy state. Possibly some of the heat released during condensation is radiated out of the air parcel before it can heat the air molecules.

I am seeing this as a four dimensional problem that requires a four dimensional empirical experiment. I wonder if other readers have suggestions for empirical testing? I’m not sure blackboards and chalk can give real world answers for this one.

34. ### Paul Linsaysaid

One thing that puzzles me in this discussion is the “heating of the air” due to condensation. It’s unquestioned in the discussion so far, but I’m not sure that it will.

Condensation is a quantum mechanical process, a water vapor molecule bonds to the water molecules on the surface of a droplet of water. The bonding is going to release a photon(s?) which will radiate away from the droplet. It’s not a given that the photon will actually heat anything.

Suppose first that the emitted photons are confined to a narrow spectral peak. Unless by some miracle the wavelength is in one of the CO2 bands, it’s simply going to escape and the energy will be lost to some distant volume of air to be absorbed by water vapor or escape to space. (There are no nearby water molecules to absorb the radiation, they’ve all condensed out.)

The opposite extreme is that the bonding radiation has a blackbody distribution. Then a fraction of the radiated photons will be absorbed by the CO2 bands which in turn can heat the local N2 and O2 by collisional excitation. But only a fraction will be absorbed, the rest will escape.

Inside a cloud, the radiation will be absorbed by the water droplets in short order. However in a clear sky, it’s not clear that the radiation will do much, if any, heating that could oppose the pressure drop caused by the condensation.

35. ### TimTheToolMansaid

How do the models model the other end of the process? ie pressure changes due to evaporation at the Earth’s surface? Or is this less relevent because it tends to be a smaller pressure change over a much larger area?

36. ### Anastassia Makarievasaid

#21 Terry

Ie, the models do not re-adjust the parcel for the new total H2O mass in the vapour phase once condensation has occurred, rather the parcel is assumed to still contain the same total as was present before condensation occurred. On a small scale it is not significant, but on large scales it is.

I thought this can be right. In terms of our papers, it is equivalent to substituting S for Sd. This gives dp/dx = 0. We discuss it in Section 4.2.

I’d like to once again draw attention of those people who would read our paper in more detail to the following. The effect of mass sink on pressure we are talking about is proportional to Nv, a small share of total air density. If we put Sd instead of S (34) into the continuity equation, we do not get any pressure gradient, dp/dx = 0. Yet Sd (mass sink) differs from real S by a small term of the order of Nv/N. So we can say that we do account for the mass sink! Yet the effect is overlooked. I think this is what could be going on in GCMs.

37. ### Brian Hsaid

Jeff;
You mention raindrops at terminal velocity; they are losing their potential energy at a fixed rate as they fall, to friction. Which is/generates heat, no? So falling rain warms the air, and then the surface when it impacts.

38. ### Dan Hughessaid

Click to access 3310964.pdf

General derivation of basic equations for mixtures of materials. Many others are available. Check the references in this report.

39. ### Frank K.said

Gavin sez:

“Youre claims about 1) are indeed exciting, but I dont think they stand up to scrutiny, the main reason being that the analogies you are using (steam engines, collapsing coke cans etc.) are all examples of condensation taking place in constant volumes implying that the pressure will vary.”

Err…I believe a collapsing coke can and a steam engine (cylinder) are not constant volumes! Constant mass, but not constant volume (although a steam engine is not even constant mass in the real world).

How’s the Model E documentation coming along, Gavin?

40. ### Morgansaid

Gavin: “It is not sufficient to find lists of things that GCMs do badly and simply assume that some new idea is the reason why…” Windy: “…because the leftists consider it somehow possible to computer-model stuff that never happened before” Frank K: “How’s the Model E documentation coming along, Gavin?”

I’d hate for this thread to devolve into a snark-fest, because it is a really interesting read for me as a pure naif in the area. So for purely selfish reasons, let me ask everyone to be charitable and assume that people are approaching the relevant questions with their own limited but not necessarily naive understanding of (a) what the relevant physics are, (b) how those physics would ideally be modeled, (c) what the impact of deviations from ideal are, and (d) what the models actually do. And also that people are being honest?

Morgan.

100% agreed.

42. ### anna vsaid

Paul Linsay said

One thing that puzzles me in this discussion is the “heating of the air” due to condensation. It’s unquestioned in the discussion so far, but I’m not sure that it will.

Condensation is a quantum mechanical process, a water vapor molecule bonds to the water molecules on the surface of a droplet of water. The bonding is going to release a photon(s?) which will radiate away from the droplet. It’s not a given that the photon will actually heat anything.

It will heat because of momentum conservation, i.e. part of the energy released will go into conserving the momentum the photon takes away and will increase the kinetic energy of the molecule, which is heat. I do not know the amount, but heat it will.

One of the unfortunate side effects of the misuse of physics in climate studies is that radiation is harped on ad nauseam, as if the only way energy manifests is through radiation.

43. ### DeWitt Paynesaid

Adiabatic expansion of a mass of air starting at 300 K and saturated with water vapor has a lapse rate of about 3 K/km compared to ~10 K/km for dry air or the 6.5 K/km of the US standard atmosphere. So as the pressure decreases, the moist air will have a larger volume and lower density than the dry air because it’s warmer. The temperature difference increases with altitude. If all the heat, latent and sensible, were transferred to the surrounding air, the resulting expansion of the surrounding air would far exceed any loss in volume from the condensation of water. OTOH, if the heat is radiated to space then there will be a significant drop in volume. So it seems to me that where the heat goes is the most important factor.

44. ### Anastassia Makarievasaid

#43 DeWitt,

Let me point out that in Fig. 1c in M10 the joint effect of latent heat release AND mass removal on the difference in air pressure between dry and moist columns are described as dependent on height z.

Shown in Fig. 1c is that if you replace a dry air column by moist saturated one, the lower atmosphere pressure will be dominated by mass removal up to a certain height. I am not aware that such a graph would have ever been attempted in the meteorological literature and the characteristic height zc calculated.

In the meantime, this height can have the physical meaning of the point where circulation changes its direction (i.e. air converging to the low pressure area in the lower atmosphere, at zc starts flowing back). We show that zc decreases with decreasing temperature. This general dependence may help explain the tendency of why the cloud height is never as large in the polar regions as it can be in the tropics.

Changing temperature of the air column does not change surface pressure.

45. ### Anastassia Makarievasaid

#26 Craig,

Sure not all condensation is due to adiabatic ascent! Regarding dry winds — every circulation, including the one driven by condensation, has an ascending (wet) and descending (dry) parts. So if the wind is dry here, it may be a consequence of the fact that it rains somewhere else.

By the way, regarding heating. This summer in Russia there was anomalous heat over a thousand kilometers. This heat-struck territory was some 10 degrees (!) warmer than the neighboring regions. One could expect the warm air to ascend, after all. When, if not now, people thought. But what do you think? The air descended instead, and did so for two months, while the rising air flow somehow appeared in the neighboring colder regions in Europe that got flooded.

One should really hunt hard to find warm air to ascend (especially if the air is dry). Let us take hurricanes, for example. The warmest part of the hurricane is the eye — here the air descends. The ambient environment is warmer then the hurricane — but again, the air descends outside the hurricane. The coldest part of the hurricane is near the eyewall — and what do you think? The air ascends right there, and violently so! If you do not believe me, take a look at Fig. 4c of Montgomery et al. 2006, where temperature profiles of an intense hurricane are considered.

Of course, we can think of the many explanations of why differential heating, which should make warm air rise, actually makes it descend. But is feels sometimes that the explanation that we are proposing might be simpler: the air rises where it rains (independent of temperature), because condensation lowers pressure and facilitates convergence. And convergence gives a positive feedback to the ascent.

So, if you have warm moist air and suddenly the temperature drops, a squall can be initiated.

46. ### Frank K.said

Morgan said
October 22, 2010 at 9:39 am

You’re right – I’ll refrain from snark and let this thread focus on the physics. Apologies.

47. ### Steven Moshersaid

Morgan.

100% agreed.

this is physics. . just the maths. please

48. ### AEAsaid

For reference, the winds outside my window are blustery at a pressure gradient of about 0.2%/hundred miles:
http://www.usairnet.com/weather/maps/current/

49. ### Andrewsaid

6-“Neither does the conservation of mass equation (2) contain a driver of motion. Ideal gas law (5) relates temperature and pressure. Thus, the driver of motion as conventionally considered is contained in the conservation of energy equation (3). This equation accomodates the parameters of differential heating and heat conductivity and latent heat release in the Q variable.”

I’m not sure if this matters to what you were saying, but the ideal gas law is not really appropriate for water vapor, especially when it condenses, as the ideal gas law doesn’t say anything about phase changes. If you are going to use equations for water vapor, they need to be more precise equations of state.

No one here was thinking water vapor behaved like an ideal gas, right?

Anastassia,
Ignoring precipitation issues, from my reading of your discussion paper you are indicating that the latent heat released from water vapour condensing within a moist air parcel does not sufficiently heat the surrounding air molecules within the air parcel to prevent a loss of volume.

Previous thinking has been that the volume of a moist air parcel would be maintained or even slightly increase as water vapour condenses. Your work would represent a significant change in the understanding of the physical effects resulting from the phase change of water molecules in the atmosphere. Such a change to current theory would certainly require empirical confirmation.

Do you or your fellow authors have any suggestions as to how this theory can be empirically tested? Are there instruments that could be used to observe cloud formation? Is there a test apparatus that would be able to answer this in the lab? I would greatly appreciate your thoughts on empirical testing.

51. ### cementafriendsaid

I noted that Gavin had a say at 11.
The major problem with GCMs is that there has been no input from professional engineers (particularly chemical and mechanical) who understand heat transfer, fluid dynamics and thermodynamics.
Hey, Gavin did you know that there is a Schmidt number, which is dimensionless (viscosity/ (density*diffusivity)). It is a wonder you did not suggest it should be put in a model in say section 4.11.1. Of course, it is not named after you but in the climate game there is no need to deny the truth of any statement (such as temperature change preceding CO2 change)
Jeff ID did you (as an aeronautical engineer) note there is no mention of Reynolds number (length*density*velocity/viscosity) particularly in association with drag in section 4.10
Section 4.9(Parameterization of Longwave Radiation) has some hypotheses which are probably the largest area of exaggeration and error. Firstly, the major absorbers/emitters (4.9.1) are water(liquid&solid) in clouds and then water vapor. Aerosols (dust, salt, soot -particularly from forest fires etc) do deserve a mention because of the large absorptivity range. However, CO2 should be relegated to section 4.9.3 Trace gases. The inclusion of CFCs in this section is just bloating the model to make it look more important.
As others have said the models need to be reworked by people of understand the theory- ie engineers
Anastassia M has a useful input but she should be looking at Fluid Dynamics Journals (and publishing there) eg http://www.springerlink.com/content/0935-4964/open/ , (Two-fluid formulation of the cloud-top mixing layer for direct numerical simulation; Juan Pedro Mellado, Bjorn Stevens, Heiko Schmidt and Norbert Peters Online First™, 2 February 2010. Here is one from some Russian authors http://www.springerlink.com/content/9gv24v2073hg1202/ (Background current concept and chaotic advection in an oceanic vortex flow E. Ryzhov, K. Koshel and D. Stepanov). This one mentions high Reynolds numbers http://www.springerlink.com/content/1q0727403287681q/ (Kinetic theory of stellar systems, two-dimensional vortices and HMF model, Pierre-Henri Chavanis). Please note I do not subscribe to the journal. I am on the editorial board of a journal concerned with processes and process research. I do wide searches to try and keep up to date.
Keep well everyone

52. ### Nick Stokessaid

#51
“Hey, Gavin did you know that there is a Schmidt number, which is dimensionless (viscosity/ (density*diffusivity)).
there is no mention of Reynolds number (length*density*velocity/viscosity)”

There are good reasons why GCMs don’t have much use for these numbers. Note that they both involve viscosity. So what would you use. Molecular viscosity? Molecular diffusion is really small, and everything is turbulent.

Eddy viscosity? Well, it isn’t just a number; it varies a lot. The reason why Sc and Re are so handy is that you can work them out from things you know in advance.

But the other thing about the atmosphere is that on a large scale it is anisotropic. Behaviour in the vertical is very different to the horizontal. If you did have a useful viscosity it would be a tensor, not a number,

GCM’s work on a very anisotropic grid. Cells about 100 km across, and depth on the km scale or less. Consequently horizontal diffusion can be ignored. There are no numbers to attach to viscosity in that direction at all.

53. ### John F. Pittmansaid

Re: Nick Stokes (Oct 23 04:45), you have put your finger on one of the problems, if not the main problem for engineers such as myself who do heat transfer. Yes, it would be a tensor. The problem is that the models are treating the correction, as outlined in the above thread, and others, as a scalar. The claim I would like to point to ia that horizontal diffusion can be ignored from a previous thread by RuhRoh

These conservation errors result in small imbalances ( << 1 W/m2) in the CCM. We note that there are also small inconsistencies present in conservation that are associated with the use of a moist mixing ratio, and moist surface pressure in the model. In principle, as any process removes water vapor from a cell, the surface pressure (PS), and the mass of air (dp) should change in a grid volume. This ought to also imply a change to any mass specific quantity affected by the parameterization. These changes are ignored in CCM parameterizations from one process to the next. We typically insist that processes conserve assuming a fixed mass of air (and hence a fixed surface pressure) within a parameterization. "

However, the models are boundary value with attendant initial value constraints. I think we will find a skeptic reception to a claim that horizontal does not matter about a tensor in a 3d differencing model from those of us who do heat transfer. It is not called thermoscalers, but thermodynamics. Even worse than being a tensor, it is a tensor in a field where the specific heat can change. These assumptions or differences in models should or will impact heat transfer. But I agree with Gavin, is it significant?

While I think, the addition of an empirical correction to force the model to conform that was posted earlier, is a typical elegant engineering approach 😉 , it does beg the question as to why MMH10 found what they did. Usually a test that showed a bias in parameterization, would lead to a correction factor such that the model conformed to reality.

54. ### Frank K.said

Nick Stokes said
October 23, 2010 at 4:45 am

Actually many CFD codes use non-dimensional forms of the governing equations such that common dimensionless numbers (such as Reynolds number, Mach number) can be set as part of the model inputs. GCMs are of course different and may or may not employ non-dimensional variables.

You are correct that horizontal diffusion is small in atmospheric flows, but some codes like CAM 3.0 appear to include it, as shown in their superb documentation (3.1.6):

http://www.cesm.ucar.edu/models/atm-cam/docs/description/

Finally, which 100:1 cells sizes are ideed anisotropic, aero CFD solvers routinely employ much higher cell aspect ratios to capture boundary layer behavior on aircraft wings and fuselages, where Reynolds numbers are on the order of 10^6 or more.

55. ### Frank K.said

Sorry – should be “…while 100:1 cells sizes are indeed anisotropic…”

56. ### Luciasaid

Jeff/Gavin

Most GCMs use the hydrostatic approximation in which the pressure at any point is exactly equal to the weight of the air column above it. Very high resolution weather models sometimes use the proper non-hydrostatic equations, but this isn’t very important at coarse scale (I’m sure there is a paper that has demonstrated this somewhere).

I’m puzzled– does gavin mean they ” the pressure at any point is exactly equal to the weight of the air column above it.” As in, exactly and for all purposes including the pressure term in the momentum equation? And even for a perfectly vertical tube whose diameter goes to zero? And accounting for the honest to goodness density of the air at all points in the tube?

Because if the thermodynamic pressure varies exactly this way, for all purposes the term should drop out of the honest to goodness momentum equations that at the greatest level of generality include the full honest to goodness thermodynamic pressure and gravity terms to represent the body force. You could then code to your hearts content ignoring pressure in the momentum equation and pressure would do nothing. (Which would usually give really wrong answers for most flows including simple ones like flow of water in horizontal pipes.)

Yet, it appears Nick’s model does contain a pressure term in the momentum equation. Do you have a link to Gavin’s comment? Did he say something to put this in context?

57. ### Luciasaid

Hmm… I guess what I mean is if pressure is exactly of sets weight, gradient of pressure exactly balances body forces in the direction of gravity. So, it drops out in that direction. Pressure doesn’t necessarily drop out of equations orthogonal to the body force. But still, isn’t this a problem if the pressure gradient drops out in the vertical direction?

58. ### Luciasaid

Do you or your fellow authors have any suggestions as to how this theory can be empirically tested? Are there instruments that could be used to observe cloud formation? Is there a test apparatus that would be able to answer this in the lab? I would greatly appreciate your thoughts on empirical testing.

Here’s a thought: Derive a formulation for the speed of sound (∂p/∂ρ) at constant S in the water vapor. Then maybe measure the speed of sound in steam held near it’s vapor pressure so that condensation and evaporation and see if their model gets the correct speed of sound?

This could also be done in moist air over a range of relative humidities.

If their formulation is right, they should get the correct speed of sound. Some careful measurements of pressure, temperature etc. would be required, but it might be do-able.

There should be some limiting cases that would be amenable to doing an experiment.

59. ### Frank K.said

Lucia,

Look at the Lorenz text that Dr. Makarieva link to above:

Click to access General_Circ_WMO_1967_Part1.pdf

Page 16 of the text discusses the hydrostatic approximation, which (from what I understand) eliminates sound waves as solutions to the primitive equations, and also can be arrived at from a scale analysis (like the boundary layer equations).

Of course, you can also eliminate pressure from the momentum equations by casting them as an equation for vorticity (recall the good ol’ vorticity-stream function CFD methods…).

BTW NCAR’s CAM 3.0 uses vorticity as a dependent variable.

60. ### Antonio Nobresaid

In trying to answer your appeal for an empirical test for the loss of pressure in cloud formation/condensation, it occurred to me to ask the help of an aeronautical engineer (Jeff Id, or anyone?) to explain an anecdotal experience I logged while flying in the Amazon. Gazing through the window on the aircraft wing, I notice that while flying in blue skies, without turbulence, the plane flies straight and calm. Then as the plane cuts through an individualized big cloud (cumulus for example), the first reaction as it crosses the cloud boundary is “to fall”, not to rise as the conventional cloud paradigm would entail (ascending convective currents within the cloud). I’ve logged this experience dozens of time, it is always the same, plane crosses the cloud and falls. When it gets back to clear sky, in the other end of the cloud, the wing flexes upward with a bump. My aeronautical lay explanation for this is that the density of air within a cloud, due to condensation, is slightly lower than outside the cloud. If planes can be used as good measurement platforms, there will be plenty of empirical tests for the theoretical evidences introduced by our colleagues Anastassia and Viktor.

61. ### Al Tekhasskisaid

Nick (#52) wrote:

“There are good reasons why GCMs don’t have much use for these numbers. Note that they both involve viscosity. So what would you use. Molecular viscosity? Molecular diffusion is really small, and everything is turbulent.”

No, these reasons are not good. Removal of viscosity is done out of serious necessity, the calculational necessity. Uncertainty of “what to choose” is unscientific excuse. Think in this simple terms: GCMs neglect viscosity and are based on ideal non-viscous fluid. Motion of this fluid would never stop even without any forces, and will accelerate if forces exist. Clearly the long-term behavior of this system is not what one would expect from nature, but this is exactly what the goal of climate modeling is – long term behavior of weather. Introduction of damping at computational level is artificial kludge, it acts on different level of solutions, and therefore there is no guarantee that the long term behavior of GCMs is correct. Probably this is why the climate attractor in these models is always a simple fixed point.

62. ### Bob Kosssaid

Judith Curry just put up a post on the Makarieva paper.
http://judithcurry.com/2010/10/23/water-vapor-mischief/

63. ### Nick Stokessaid

Al #61,
I don’t think they ignore vertical diffusion of momentum. There’s a whole section of the CAM3 doc:
4.11 Vertical Diffusion and Boundary Layer Processes
So they are not ignoring viscosity altogether.

I think they ignore hosizontal diffusion of momentum because it is genuinely small on the grid scale, not just of necessity. But in any case, the point is that if it’s not in the calc, you can’t put a number on it for Re calculation.

Of course another issue with Re is that the atmosphere doesn’t have obvious characteristic lengths that you could use.

64. ### Gavinsaid

#52 speaking of the Schmidt number, it does come into GCMs – in particular in the formulation of the evaporative flux it controls the humidity roughness length (after Brutsaert (1982)).

Interestingly, much of the difference between the evaporative flux between water isotopologues (H218O vs H216O for instance) occurs because the Schmidt number is different for each species.

65. ### luciasaid

Of course, you can also eliminate pressure from the momentum equations by casting them as an equation for vorticity (recall the good ol’ vorticity-stream function CFD methods…).

Yes. But recasting in different variables that don’t happen to show P explicitly is not what’s worrying me.

66. ### Frank K.said

“Yes. But recasting in different variables that don’t happen to show P explicitly is not what’s worrying me.”

OK. What is worrying you?? If it’s the way the pressure gradient is treated in GCMs, read the Lorentz text I cited earlier.

67. ### Frank K.said

Nick Stokes:

“I think they ignore hosizontal diffusion of momentum because it is genuinely small on the grid scale.”

CAM 3.0 doesn’t ignore it. See 3.1.6 of the documentation.

68. ### Nick Stokessaid

Frank K 67,
Indeed there is horizontal diffusion. It sounds though as if it is artificial viscosity introduced for numerical reasons, rather than any physical viscosity.

#60 Antonio,
Thank you for your response. I only have a VFR license, so I have avoided flying through clouds and have not noticed this effect. I could see the use of a light weight UAV as being suitable for this type of empirical testing. If condensing water vapour is causing a loss of volume in an air parcel, a vehicle with low inertia should also show a slight horizontal acceleration on entry and a slight deceleration on exit from the cloud. The best results would probably obtained by flying the UAV through clouds that are forming rapidly. After a cloud has reached a stable size, pressure would quickly equalize.

The Aerosonde UAV may be suitable.
http://www.aerosonde.com/products/products.html

70. ### Brian Hsaid

Oh, beautiful!
In an SA article subtly dissing Judith Curry, “Iconoclast” posts the following:

14. Iconoclast 05:06 PM 10/23/10

The proposition that the average temperature of the earth’s surface is warming because of increased emissions of human-produced greenhouse gases cannot be tested by any known scientific procedure

It is impossible to position temperature sensors randomly over the earth’s surface (including the 71% of ocean, and all the deserts, forests, and icecaps) and maintain it in constant condition long enough to tell if any average is increasing. Even if this were done the difference between the temperature during day and night is so great that no rational aveage can be derived.

Measurements at weather stations are quite unsuitable since they are not positioned representatively and they only measure maximum and minimum once a day, from which no average can be derived. They also constantly change in number, location and surroundings. Recent studies show that most of the current stations are unable to measure temperature to better than a degree or two

The assumptions of climate models are absurd. They assume the earth is flat, that the sun shines with equal intensity day and night, and the earth is in equilibrium, with the energy received equal to that emitted.

Half of the time there is no sun, where the temperature regime is quite different from the day.

No part of the earth ever is in energy equilibrium, neither is there any evidence of an overall “balance”.

It is unsurprising that such models are incapable of predicting sny future climate behsviour, even if this could be measured satisfactorily.

There are no representative measurements of the concentration of atmospheric csrbon dioxide over any land surface, where “greenhouse warming” is supposed to happen.

After twenty years of study, and as expert reviewer to the IPCC from the very beginning , I can only conclude that the whole affair is a gigantic fraud

Every paragraph a gem.

71. ### Frank K.said

Frank K 67,
“Indeed there is horizontal diffusion. It sounds though as if it is artificial viscosity introduced for numerical reasons, rather than any physical viscosity.”

I think the biharmonic operator is used for stability, but the horizontal diffusion appears to be physical (though perhaps an option – i.e. you can turn it off if need be).

72. ### Anastassia Makarievasaid

#58 Lucia,

Here’s a thought: Derive a formulation for the speed of sound (∂p/∂ρ) at constant S in the water vapor. Then maybe measure the speed of sound in steam held near it’s vapor pressure so that condensation and evaporation and see if their model gets the correct speed of sound?

This is a very genuine and insightful comment. I promise to handle it reasonably soon. I will leave a note here.

73. ### Dan Hughessaid

Pressure wave sped in mixtures of all kinds has already been done many times:

http://journals.ametsoc.org/doi/abs/10.1175/1520-0469(1971)028%3C0202%3AMOTAOS%3E2.0.CO%3B2

http://www.amazon.com/Multiphase-Flow-Dynamics-1-Fundamentals/dp/3540698329/ref=sr_1_8?s=books&ie=UTF8&qid=1287928360&sr=1-8

74. ### luciasaid

>>K. What is worrying you?? If it’s the way the pressure gradient is treated in GCMs, read the Lorentz text I cited earlier.

Yes. That’s what I want to know. I want to figure out if it’s lietrally done the way Gavin says and if so why or under what circumstances it makes sense. I’m reading the Lorenz paper– sorry I failed to say thanks for the link. It’s what I wanted.

No one minds resting equations in terms of vorticiity in a way that changes the variabiles, so that a particular variable drops out. Vorticity, stream functions, potential functions what not– not a problem provided the map back into a set of equations that weren’t “simplified” in a way that is unphysical.

75. ### luciasaid

Anastassia Makarieva said

I promise to handle it reasonably soon. I will leave a note here.

Drop a note at my blog, or let jeff share your email. If I think of other ideas, I’ll let you know. (I was thinking of a few in the tub. There may be some flow visualization technqiues that might be useful to add. If you do this, it might be nice to also see the size of water droplets that form etc. In the longer run, that would be interesting.

76. ### luciasaid

Dan–

Pressure wave sped in mixtures of all kinds has already been done many times:

Of course this speed of sound has been studied both analytically and experimentally in some mixtures– some theory for bubbly flows and/or particulate flows discussed in Wallis’s 1969 fluid dynamics text book. That text doesn’t seem to inlcude phase change– (But I plan to look more carefully so I could tell Anastassia if I find it.)

It seems unlikely to have been done in “all” kinds of multiphase flows. There are so many!

I think Anastassia Makarieva should check the nuclear/mech eng. literature (and all literature) to see if the specific case of interest has been done. If you know the case of sound propagating through water vapor when P= vapor pressure at that the temperature, permitting for the possibility of phase change as the wave propagates, why not tell us who did it?

Is that specific solution and/or experimental confirmation in one of those books? If so– who did it?

77. ### ESsaid

There can be condensation with no wind. For instance, where I am today the visibility is just a few feet in fog, but there is zero wind.

78. ### Jorgesaid

Hi Lucia –

I came across this in a quick search. I suspect the main thrust of the paper is not to do with the present subject but it does include this in the abstract.

“The sound speed in a single-component two-phase system, such as a water-steam mixture, depends on whether or not equilibrium between the phases on the saturation curve is maintained. Heat and mass transfer which occur when equilibrium is maintained cause the sound speed to be much lower than under non-equilibrium conditions in which heat and mass transfer are absent. The sound speed in a water-steam mixture may be as low as 1 m s−1.”

http://www.agu.org/pubs/crossref/1977/JB082i020p02895.shtml

It is behind a pay wall so I don´t know if it is just calculation or if there is experiment to confirm.

79. ### Nick Stokessaid

“The sound speed in a water-steam mixture may be as low as 1 m s−1”
Hey, I can walk faster that that!
(not to say they’re wrong, but…)

80. ### Dereksaid

Would topography have any effect. ?
Climate models as I understand model a flat surface (it’s one of the reasons I refer to AGW believers as “flat earthers”).
Surely you can’t ignore the Rockies or the Urals, or the Himalayas, and therefore Monsoons.
Or are these “topographic” omissions “corrected for” by more (unmentioned and specifically spatially placed) fudge factors.

Makes me ask do the climate models model temperature inversions, or the mistral (Maestrale) type winds as well.

81. ### Frank K.said

“The sound speed in a water-steam mixture may be as low as 1 m s−1″
Hey, I can walk faster that that!
(not to say they’re wrong, but…)

Does that mean you would break the sound barrier, Nick? :^)

(I can run up to 9 mph = 4 m/s on the treadmill at our gym – hey that’s Mach 4!)

82. ### Dan Hughessaid

For the case of thermodynamic equilibrium the sound speed at the liquid side of the co- existence region is discontinuous. The sound speed drops from the all-liquid value to an extremely small value. I recall that it approaches zero as the liquid mass fraction approaches zero from inside the co-existence region. The change from a high vapor mass fraction to the all-vapor state on the other side of the co-existence region is much less of a change that on the liquid side. This is standard thermodynamics and is available from many textbooks. Near the all-saturated-liquid side of the co-existence region values less than 1 m s-1will be indicated by the thermodynamic-equilibrium approach.

Thermodynamic equilibrium, of course, ignores the meta-stable states between the co-existence line and the spinodal lines for superheated liquid and sub-cooled vapor inside the co-existence region. Consideration of the presence of these lines in which meta-stable states are allowed will very likely remove the discontinuities. Thermodynamic equilibrium also has automatically built-in values for the mass and energy exchange processes. A frozen-composition model for use inside the co-existence region avoids the discontinuous nature of the equilibrium-mixture approach.

For a moist-air mixture of a non-condensable gas and the vapor phase of water, the sound speed goes like an inverse weighting of the square of the sound speeds with the weight factors being the mass fractions of the components of the mixture. Again, equilibrium and frozen-composition approaches are available. Models for mass and energy exchanges between the gas and the vapor will affect the value of the sound speed. The references listed above by me will provide additional information. The frozen composition approach, no mass and energy exchanges, will again provide a more continuous values.

For a mixture of moist air plus liquid water, I think the sound speed will go like a mass-fraction weighting of the inverse squared speeds of each component. Again, mass and energy exchange between all the fluids will affect the sound speed. As the models for mass and energy exchanges are made to approach the equilibrium values the sound speed will approach the equilibrium value.

83. ### luciasaid

Nick

“The sound speed in a water-steam mixture may be as low as 1 m s−1″
Hey, I can walk faster that that!
(not to say they’re wrong, but…)

Read Wallis 1967 for discussions in a textbook. The speed of sound in multiphase mixtures can be quite low. Wallis doesn’t seem to discuss bubbly flows– which, if my memory serves correctly, is the case where it can get very, very low.

This isn’t just weird theoretical stuff. People have applied the theory to design things like nozzles.

While I can’t say for sure whether Anastasia’s specific case has been investigated in the engineering literature, I would not be surprised if it was. The reason I am suggesting Dan be specific it to help Anastasia find stuff if it exists. The experiment she wants may turn out to have been done at any time between the 50-now. (Or it hasn’t been done.)

But the speed of sound in multiphase flows can be really, really low.

84. ### La presión de Makarieva « PlazaMoyua.orgsaid

[…] Modeling the Basics, A mathematical summary of condensation in climate models. […]

85. ### Dan Hughessaid

I am on the road for another Moto Road Trip down to Georgia.I don’t have any reference materials with me and won’t be taking time to be specific by using Web resources. I’m on vacation after all.

I suspect the gas, vapor, liquid mixture has been investigated in depth. The references listed above might be good starting points. The book by Kolev has info about several mixtures.

As I am working from memory, my comments need to be verified.

86. ### Michael Tobissaid

Fascinating but confusing. Clarification would be welcome.

My confusions:

1) These concerns are focused where there are nonhydrostatic phenomena. In hydrostatic models these are bulk parameterized anyway. So why doesn’t it all come out in the wash? Most GCMs do not represent the physics in question at all since they fail to resolve it.

2) All else equal (temperature, ambient pressure), a parcel with condensate removed will have higher, not lower density as well as lower volume. What a nonhydrostatic model would do with such a parcel may be an interesting question. You should ask the weather guys, not the climate guys, since our models do not resolve the phenomenon, as I said above. But if it is physically real, wouldn’t it suppress rather than enhance convection?

3) Is it really true that condensate does not participate in the hydrostatic balance? Why? An iceberg floating in water participates in the hydrostatic balance of the ocean. The ocean does not “see” the volume displaced by non-liquid as vaccuum. Does a fluid with a heavy colloidal suspension not flow under an otherwise identical fluid that has no colloids? This seems an easy experiment.

4) Why don’t stratus formations lift and grow? Could we get a condensation instability in a closed lucite box? Imagine gradually cooling a moist near-saturated cube of air until condensation just starts. Would the condensation run away in an unstable way?

It’s just a box of rain. I don’t know who put it there. Believe it if you need it or leave it if you dare.

87. ### mushroom georgesaid

If M10 is correct, does this mean the “Missing Hot Spot” in the upper troposphere just went sideways making wind?

88. ### ESsaid

Latent heat development in convection clouds has been known for a long time. In 1833 James Espy wrote a summary of his theory of the upward movement of the air in storms (convection) and of their self-sustaining power from the evolution of latent heat. He wrote “The Philosphy of Storms” in 1840.
http://en.wikipedia.org/wiki/James_Pollard_Espy
Epsy knew that air must be cooled to its dew point temperature for condensation to occur. He was wrong on some things, but he was generally correct on how cumulus clouds form, according to a text I read on meteorology. His book is available online. The Section First and Introduction give his theory: