By Richard Willoughby
May 2021
(The author appreciates the availability NASA’s Earth Observations satellite data sets used in this analysis.)
This is a three part series that analyses the role of atmospheric water in regulating Earth’s thermal balance.
Part 2 Discusses the mechanism of deep convection concluding with the persistency of clouds over ocean warm pools.
Part 3 Examines the global ocean energy balance over an annual cycle month-by-month to identify the role of atmospheric water in regulating the energy balance.
Part 2: Deep Convection and Development of Convective Potential Energy
Water in the atmosphere behaves differently to the other gases. Water vapour has the lowest density of the common constituent gasses. Water exists in the atmosphere as a gas, liquid and solid. All three phases are effective emitters of long wave radiation and ice in the atmosphere forms highly reflective cloud.
The unique properties of water in the atmosphere create convective instability that is observed to limit the ocean surface temperature in tropical warm pools to an annual average of 30C, detailed in Part 1 above. The primary cause of convective instability that drives deep convection is the buoyancy of water vapour. The development of convective potential relies on the ability of atmospheric water, in all phases, to cool by radiated heat transfer.
Level of Free Convection
Convective instability can only occur when the mass of water vapour in the atmosphere exceeds 30kg/sq.m; equivalent to 30mm water vapour. Once the level of water vapour exceeds 30mm, the atmosphere can partition into a zone of free convection in contact with the surface and an upper zone that is not involved in the surface vertical convection current. The upper altitude of the surface mixing zone is termed the Level of Free Convection (LFC).
To better appreciate how the LFC develops, it is useful to examine the conditions of a saturated air column over a surface at 300K (27C). Such conditions are observed over ocean surfaces at the onset of the deep convective cycle. Figure 10 compares the density of air with altitude and the density of water vapour with altitude.
Figure 10: Variation of moist air density with altitude and water vapour density with altitude in saturated column above 300K surface
With reference to Figure 10, it is observed that the density of the water only makes a small contribution to the total air density and falls off rapidly with altitude such that water has negligible mass above 14,000m. Moreover, this is for a saturated column but water vapour can be present over a wide range of relative humidity at any altitude from zero up to the saturated level. Figure 11 compares the density change of moist air with altitude and the density contribution of water in saturated air.
Figure 11: Formation of level of free convection in saturated air column above 300K surface
With reference to Figure 11, it is observed that the density of water with elevation is greater at ground level than the change in density of air with elevation. At 5000m and 6g/Cu.m, the density of the water vapour reduces faster than the density change of the total mixture with altitude. That transition creates the condition where dry air will be supported by a moist air column below. Similarly, a rising air column, under thermal equilibrium, will not rise above the LFC.
An LFC can exist in any air column where the total water column exceeds 30mm irrespective of relative humidity. The free convection zone below the LFC will increase in water vapour above a warming ocean surface while the water vapour above the LFC is solidifying or condensing as it cools via radiated heat loss. Given sufficient time, the water vapour above the LFC solidifies and condenses to leave dry air while the zone below the LFC becomes saturated. This condition can be better appreciated with reference to Figure 12 for the atmospheric conditions above a 303K surface.
Figure 12: Developing convective potential over a 303K ocean surface
The atmospheric temperature profile will follow a saturated adiabat from the surface to the LFC then progress upward along the dry adiabat that passes through the LFC. Under these surface conditions and relative humidity, the LFC is at 6300m where the temperature is just above freezing at 276K.
Convective Available Potential Energy
The partitioning of the atmosphere above and below the LFC can exist while the column is in thermal equilibrium. If there is a disturbance that causes a small parcel of moist air to penetrate into the dry zone, its lower density and, therefore, buoyancy will cause it to rise and it will be followed by more moist air until the zone above the LFC becomes supersaturated. This is the process of cloudburst whereby moist buoyant air bursts into the upper dry zone once the thermal equilibrium is upset and convective instability ensues. The supersaturated air above the LFC gives rise to local precipitation that can grow to intense rain if moist air converges laterally from more stable zones.
With reference to Figure 12, the work done by the rising moist air during cloudburst is determined by the area on the chart between the moist adiabat and the dry adiabat above the LFC. The low level of moisture above 14,000m or 220C means this condition limits the development of convective potential to below this altitude above ocean warm pools limiting at 303K. The maximum possible Convective Available Potential Energy (CAPE) above a surface at 303K is 6000J/kg. This requires the CAPE to be fully developed before instability occurs. Observations above tropical warm pools indicate the convective potential rarely exceeds 4000J/kg in these regions. The maximum updraft velocity during cloudburst is the square root of the CAPE*2. A CAPE of 4000J/kg would consequently create a maximum updraft velocity of 98m/s.
Convective Instability and Cloud Cover
The atmospheric column becomes supersaturated during cloudburst. Water vapour can extend to at least 14,000m during cloudburst and produces high level cumulus cloud that effectively blocks surface insolation at the onset of the convective cycle and each subsequent cloudburst. The outgoing long wave radiation is absorbed by the water vapour, water condensate and, finally, the ice high in the atmosphere that will have a radiating temperature as low as 220K with a corresponding OLR radiating power of 130W/sq.m with average outgoing long wave power of 210W/sq.m over 30C warm pools. By contrast, the peak reflective power can be as high as 1000W/sq.m in peak insolation as observed at the tropical moored buoys.
The precipitation following cloudburst subsides leaving the zone above the LFC saturated but set to again develop convective potential. During this stage, most long wave radiation from tropical warm pools exits above the LFC to solidify the water vapour thus forming persistent cirrus cloud that deepens during the CAPE development phase.
The persistency of the cirrus cloud is better appreciated with reference to distribution of water vapour above the LFC and the level of freezing for stated surface temperature as set out in the following Table 1.
Table 1: Distribution of water vapour above the LFC and the level of freezing under saturated conditions for nominated surface temperature
The table sets out the limiting conditions but only for the CAPE development phase when cirrus cloud deepens and then thins before the cycle repeats. At 300K, the clear sky conditions can persist for approximately 37% of the CAPE development phase if the divergence does not disrupt the cycle. The ice forming the cirrus cloud melts as it descends below the level of freezing and continues to descend below the LFC as water condensate. The cirrus cloud dissipates while the exiting OLR is condensing the water vapour below the level of freezing but above the LFC. Usually the air above 300K water surface diverges to air over warmer water and this disrupts the regular convective cycle such that clear sky persists for longer than 37% of the time. On the other hand, convergence of moist air to warm pools at 303K, where clear sky would be expected 24% of the CAPE development stage, reduces the proportion of clear sky to a level where the surface heat fluxes, including cooling precipitate, are balanced and 303K is the upper temperature limit. Without convergence playing a role, the radiated heat fluxes balance when the surface reaches 305K with clear skies 17% of the CAPE development stage. A surface temperature of 306K has not been observed in open ocean warm pools. At this temperature, the sky above the ocean would maintain persistent cloud, cycling from cumulus to thickening cirrus then thinning cirrus but no clear sky before the next cloudburst.
The location of the warmest pool experiences convergence of mid-level moist air and cooler adjacent zones experience corresponding divergence. This results in the warmest pool experiencing precipitation of up to 15mm/day, twice the daily rate of condensate production, while adjacent locations 2.5mm/day, under half the daily condensate production.
Typical long wave radiating power over a tropical warm pool is 210W/sq.m. This corresponds to water vapour solidification/condensing rate of 7.3mm/day. Hence, above a warm pool of 303K (30C), it takes a maximum of 45 hours for a convective cycle to solidify/condense 13.8mm of water vapour if it is not disrupted by divergence of moist air and shorter if it reaches instability before the CAPE reaches full potential. Observed convective cycles rarely run to full potential.
The Persian Gulf
The surface temperature in the Persian Gulf has been observed to reach 307K in August but examining the atmospheric profile shows the mid-level moisture content is too low to create the LFC needed before deep convection can develop. The Persian Gulf experiences high rates of evaporation but the prevailing dry north-westerly winds transport the high level moisture laterally to the Arabian Sea. Cloudbursts are rare events in the Persian Gulf.
Data Sources
https://neo.sci.gsfc.nasa.gov/view.php?datasetId=CERES_LWFLUX_Mhttps://neo.sci.gsfc.nasa.gov/view.php?datasetId=CERES_SWFLUX_Mhttps://neo.sci.gsfc.nasa.gov/view.php?datasetId=MYD28Mhttps://neo.sci.gsfc.nasa.gov/view.php?datasetId=MYD28M
I have used many months from these sets. All the charts and images are independently produced meaning not copied images from these links.
There is also data from the moored buoys that I refer to:https://www.pmel.noaa.gov/tao/drupal/disdel/
O.T. but an interesting story… https://www.theatlantic.com/international/archive/2021/05/joe-biden-china-infrastructure/618921/?utm_source=pocket-newtab
Sixty-five percent of China’s electric power is still generated by coal:
I’ve read that 36 degress C, ie ~309 K, has been recorded in the Persian Gulf.
From part 1 yesterday, “The Persian Gulf is the only body of water to regularly exceed 34C”. 36C would theoretically be possible, albeit rare.
https://wattsupwiththat.com/2021/05/23/ocean-surface-temperature-limit-part-1/
The plot in part 1 showed yellow at 34C. It is actually yellow for 34C and above. I will make a change to the wording.
I have observed 35C in the shallow water near the south-eastern shore from MODIS.
Rick
The south-eastern shore of the Persian Gulf is the site of one of the world’s most significant modern carbonate ramp environments and onshore coastal Sabkha.
The nearshore coastal environment of this carbonate ramp generates warm dense saline bottom water which exits the Persian Gulf through the Straits of Hormuz, into the Gulf of Oman from where it descends into the depths of the Arabian Sea.
For further details of this reverse-flow, estuarine circulation system of the Persian Gulf see
Reynolds, R.M., 1993. Physical oceanography of the Gulf, Strait of Hormuz, and the Gulf of Oman—Results from the Mt Mitchell expedition. Marine pollution bulletin, 27, pp.35-59.
.
I lived there (Dubai/Sharjah) and can confirm that the summer temperature of the Gulf waters is uncomfortably high – like a warm bath.
“… The maximum possible Convective Available Potential Energy (CAPE) above a surface at 303K is 6000J/kg. This requires the CAPE to be fully developed before instability occurs. Observations above tropical warm pools indicate the convective potential rarely exceeds 4000J/kg in these regions. The maximum updraft velocity during cloudburst is the square root of the CAPE*2. A CAPE of 4000J/kg would consequently create a maximum updraft velocity of 98m/s. ”
—————-
Think about this for a moment. 98 m/s is 219 mph and rising to 45,000 feet. That is explosive!
Serious convective potential in the Bay of Bengal yesterday:
https://earth.nullschool.net/#2021/05/22/2300Z/wind/isobaric/500hPa/overlay=cape/orthographic=77.07,10.69,530/loc=81.722,11.064
Water gets blasted way up above freezing:
https://earth.nullschool.net/#2021/05/22/2300Z/wind/isobaric/250hPa/overlay=relative_humidity/orthographic=77.07,10.69,530/loc=83.177,10.142
Some comes down immediately but the column is saturated well above freezing and that solidifies as it cools to form reflective cloud.
The.cooling power needed to develop CAPE to keep driving this process across the tropical oceans is awesome.
The air rising at over 200 mph entrains a lot of momentum energy which is released when the column stops rising. Is this energy significant with respect to the heat of condensation and heat of freezing when clouds form? If so, is it included in model parameterizations?
Literally far off topic, yet this all makes me think of the great red spot on Jupiter. What kind of colossal energy source is driving that massive storm – and maintaining it for centuries?
It seems it reaches much higher and is colder than the clouds around it. Yet it also seems to be greatly heating the atmosphere above it – the stupendous amount of sound it generates converts to heat. Yet, the storm hasn’t dissipated.
Can’t comment on the relative effect, but the energy will be dissipated in vortex shedding and lead to a temperature increase.
I decided not to make any substantive comment until reading all three parts.
So, a quick non substantive comment. The direction this seems to be going partly validates WE thermoregulation hypothesis. Key will be part 3, since I think WE’s recent equivalent ‘part 3’ post on inferred ECS is likely incorrect because of implied time frames. Is more likely something like TCR. Already said so in a comment to that post. Observational ECS is about 1.7 plus or minus something. That value can be approximately derived several different independent ways, as previously commented several times. Anything much less, or much more, is likely incorrect.
Good to know you are following with interest. Part 3 is where the heretic is exposed and will be the most controversial – I expect.
Maybe I’m dense but I don’t understand figure 11.
Robert
You are probably not dense – the fact that you question the chart suggests otherwise. It is actually comparing a CHANGE in air density with a water vapour density. So the comparison for that scale is only validated by the fact that relative humidity can be whatever it will be from a range zero to 100% – or supersaturated during cloudburst. Normally there can be water up to saturation or no water.
So above the crossover point, the water vapour can disappear and the air above is not going to change density enough to sink. In other words, saturated air’s loss in density with altitude is less than the change in density with total loss of water. Remove the water and the dry air density above the LFC is still lower than the moist air density below. The air can dry without losing enough buoyancy to sink.
It took me a long time to understand this and be comfortable with that chart.
Might use some of this comment to help convey the importance of this. It is the key to understanding the upper temperature limit of open ocean water.
This is why the process of water fall-out by the precipitation mechanism is critical to how this works. Gravity removes the water and so the dried air cannot reabsorb the water vapour on descent, the water has gone back down all by itself. The dry air is stuck up there and can only desecend in one of the following ways:
It takes a bit of pondering to realize that Fig 10 is at lapse rate temperature also….
Can someone explain how CO2 warms water? Before you answer, study the physics of the CO2 molecule and LWIR between 13 and 18µ’s interaction with water. Also, H2O absorbs those same wavelengths and is far more prevalent than CO2 above the oceans.
CO,
Water is warmed the same way land is warmed. SWR from the sun adds energy and more ghgs (WV, CO2 and insignificants) slow the rate of energy leaving. WV increase has been about 10 times more effective than CO2 on average at slowing the rate of energy leaving. https://watervaporandwarming.blogspot.com
Any decent engineering heat transfer analysis textbook shows how the radiation calculations are made.
The bottom line is small changes in water vapor can offset a large molar change in the non-condensing GHGE component. That is where the climate dowsers get it fundamentally wrong. And they likely know it.
COO, Let’s try this…..
Sunlight warms the ocean, not CO2. Let’s pretend all the CO2 is in one patch, say 15% of sky. The CO2 patch in the sky lets sunlight through but absorbs and emits IR at a temperature intermediate between the surface and outer space. IF you go through the SB radiation calcs, you will see that the same amount of Sunlight will now heat the ocean a little bit more because that intermediate temp 15% CO2 patch is blocking the ocean’s view of 15% of cold outer space that the warm ocean would otherwise radiate to.
The difference isn’t much. Clouds reflect far more incoming SW than CO2 absorbs of the outgoing IR.
But, the atmosphere has to warm first, and that isn’t what’s happening, the oceans are warming first
Better reread what I wrote, Bob…
CO2 doesn’t absorb all the upwelling IR just certain freqs, and half of the IR it emits is directed back toward space. So the 15% of sky is not an opaque IR ceiling it is more like a tinted IR sunroof.
While it’s true that any one blob of atmosphere sends half its IR emissions upward and half downward, that’s not the net effect of the atmosphere as a whole. Overall, for every watt of longwave radiation the atmosphere sends to space, it sends 2.5 watts to the surface.
(This happens because the surface primarily sees longwave emissions from the warmer lower atmosphere, while space primarily sees longwave emissions from a higher, cooler part of the atmosphere.)
If you include water vapor, clouds, CO₂, etc., then I understand that, on average, something like 92% of longwave radiation emitted by the surface is intercepted by the atmosphere.
My understanding would be that, say on the attached graphic, the part of the curve that follows the 297 C curve is where the satellite actually is seeing IR from the surface. So in this specific case, about 80% of the area under the curve has NOT been intercepted by the atmosphere. A mind meld of our “understandings” might be in order…..
I’ve been puzzled by this myself. Diagrams of “Earth’s energy budget” seem to typically report just a tiny fraction of LW radiation from Earth’s surface going directly to space. One older chart showed 9 of 117 units emitted by the surface going to space. A chart in Wikipedia shows 12 of 117 units going to space, which would imply 90% absorption by the atmosphere. Yet, diagrams like the one you offer seem to suggest a much higher percentage of surface-emitted radiation reaching space.
Kiehl and Trenberth (Table 2) say 390 W/m² is emitted by the surface and 235 W/m² (or 60% as much) is emitted at TOA into space, which implies an absorption by the atmosphere of at least 40%. K&T show a figure somewhat like yours (their Fig. 1), but the black-body radiation curve for the (global average) surface temperature shows a larger gap from measurements than what appears in the (Tropical Western Pacific) figure you’ve offered. I find it hard to explain the apparent difference in your chart and theirs. How could a smaller surface LW radiation be absorbed in the tropics than would be absorbed overall. Maybe some difference in assumed emissivity is in play?
How can one reconcile a claim that 90% of surface radiation is absorbed by the atmosphere with an observation than TOA emission is 60% as much as surface emission? Well, maybe it could all work out in a self-consistent fashion if around 30% of surface LW emissions were absorbed in the lower atmosphere and then re-emitted?
Half of the mass of the atmosphere is below 5 km, and in the case of tropical storms, I’d expect the highly-absorbing cloud base to be really low…
Absorption and re-emission would need to happen at a fairly low altitude if it’s going to match the black-body emission curve for a near-surface temperature. In the K&W version of the plot, there is a gap between the temperature of most emissions and the temperature of the surface, so maybe there’s room for much of the emission to be in the low atmosphere?
I’ve spent some time trying to sort through all this. I’m not as satisfied as I’d like to be that it all makes sense. But, that’s the current state of my investigation. If you or others learn more about this, I’d be interested in hearing about it.
Very interesting meteorological perspective. Excellent description of some mechanisms of tropospheric adjustment to surface temperature perturbations. It might be worth mentioning that the specific values and limits proposed are atmospheric properties that emerge under earth standard pressure.
I appreciate the favourable comments
You raise a good point on the surface pressure. All the atmospheric columns used for this analysis are at 101000Pa. I will state that.
I started to think that I might be on to something by looking at what happens when the ocean has 200m less water and there are massive ice mountains displacing atmospheric air. I expected the increase in surface pressure would make a significant difference to the limiting temperature. At 105000Pa it raised the surface temperature by more than 1C but less than 2 for the same separation of LFC and freezing.
Maybe enough to pull the globe out of glaciation but others have shown good evidence for dust to start the melting process.
I could not find any references on ocean surface pressure during glaciation to support the hypothesis.
The lingering question I have in relation to this type of analysis is what, if any, processes exist to control the total area of warm pools reaching the proposed limits. Other than geographical limitations of ocean and coastlines I do not see anything here to suggest that the the total area of warm pools is fixed or limited. Perhaps this will be discussed in part 3?
In regard to ambient air pressure during different geological periods there exists very little available proxy information other than, perhaps, ambient air temperature. The biologists and paleontologists might have the best shot by looking at the structures of plants and animals from those periods. It is a curiosity to understand pressure differences between today’s ice-house (Quaternary) and previous Hot-House periods (Mesozoic, Paleozoic). There may even be minor differences between the glacial and interglacials of the Quaternary. Atmospheric mass-balance concepts might offer clues.
cheers
Does the size of massive land animals (dinosaurs) offer any hint to the ambient air pressure that was around them?
I have no idea biology is way out of my comfort zone. I’ve seen estimates that surface pressure was up to 5x that of today (i.e. 5 bar) 65 Mya. Some estimate a total of up to 90-100bar of CO2 tied up in carbonate rocks from early gaseous Earth atmosphere a few billion years ago. This would be similar to Venus today. Others say early Earth atmosphere could have been very thin (0.5 bar) and so they rely on greenhouse to explain the temps. So it’s conceivable that atmospheric pressure does vary over different timescales but the estimates are all over the map. Nobody knows. Looking at temperature estimates over the most recent few hundred thousand years it seems possible total pressure varies by 10-20% among interglacial/glacial periods. This area of research has been completely abandoned in favour of radiative energy balance physics relying on albedo and greenhouse gases. I expect some day it may come back into fashion. I can’t see any other explanation other than albedo/cloud/water vapour effects must emerge under a temperature regime based on pressure and solar input. Otherwise there would not be 3 phases of water to begin with to act as some dynamic variable control (glacier, ocean, cloud etc).
Dr. Octave Levenspiel of U of Oregon had articles on his website showing his calculations that the Earth’s atmospheric pressure was higher and oxygen content greater in the times of dinosaurs, pterodactyls, and giant dragonflies. Since his passing, his website has been reduced, some remaining at
levenspiel.com/dinosaurs/
Rick,
The total ice volume of Antarctica is some 26.5 million cubic kilometers spread over an area of 14 million sq km. Suppose that during the last glacial maximum we had 2 Antarctics worth of ice in the northern hemisphere, one on North America and one on Europe extending into Siberia. Then not only would the sea level be lower, but this extra 50 million cubic km of ice would remove air space above the present land masses. That air has to go somewhere.
Total surface area of the oceans is 360 million sq km so the sea level drop will be 140 metres (assuming a tank shaped ocean). Now the environmental lapse rate is 6.5 Kelvin per Kilometre so the air temperature rise at the new lower sea level in the tropics during the ice age will be 0.9 Kelvin. A small but not zero temperature increase.
The interesting question is this – What will be the surface pressure increase due to the ice volume held at altitude on the continents? The average surface elevation of Antarctica is 1.9 km and the surface area of the Earth is 510 million sq km, so if we assume that 1 atmosphere pressure covers this area (it doesn’t because of the elevation of the Antarctic ice block). and that the troposphere is 12 km thick, then we have a planetary volume of air of 6,120 M cu km. If we reduce the accomodation space for the air by 50 M cu km to 6,070 M cu km then the proportional increase in atmospheric pressure will be 1.008 and so the sea-level surface pressure will rise from 1013 mbar to 1021 mbar
Does this even sound right? After all the volume ice stored on land is equaivalent to the volume of seawater removed from the oceans, so no change in accomodation volume. Maybe this is not so, air is a compressioble fluid and so a lower surface datum during ice ages will produce a higher surface air pressure?
Please argue at will.
If you dig a mineshaft, the shaft fills with a column of air. The volume of material that composed the shaft gets moved up to the surface where it displaces the same “volume” of air, but the air displaced is slightly lower density than the air in the mineshaft.
The air at the bottom of the shaft will be at higher pressure, by the hydrostatic head of the air column. A very, very much smaller effect is that the height of the atmosphere, and thus the atmospheric pressure at the mine’s surface level will be minusculely lower because of the mass of air that used to be in the atmosphere that is now down in the mineshaft. Don’t know if this helps envision your glacier melt situation or not.
DMacKenzie,
Thanks for chipping in to help me out of the hole I have dug for myself 🙂
In a very real sense the oceans occupy a very wide hole in the surface of the Earth. So by reducing sea level and piling ice up onto the land the air will then start at a lower surface datum and also in a smaller surface area (the surface area of the ocean hole). The continents and ice caps will be above this new lower datum sea level and so the average surface air pressure at sea level will rise. The tricky part of the calculation is establishing by how much datum surface air pressure will increase.
Yes, the ocean is big mineshaft covering 70% of the Earth. In the basic “mineshaft case” the calcs would be relatively simple. But start throwing in lapse rates with elevations and radiative temperature of the planet with ocean or ice albedo…..
Philip
I did similar sums and concluded it would not be enough to make much difference.
Thanks Rick
It is a fun exercise to do and it is always worth checking assumptions.
Richard,
This is a really interesting comment and bears direct analogy with the impact of polar katabatic winds that spread out over the southern hemisphere Ross and Weddell seas on the margins of the Southern Ocean, and also the Sea of Okhotsk, the winter exit point to the Pacific Ocean from the Siberian winter cold air pool. There are some superb examples of how dry air passing out to sea gathers moisture and forms clouds downwind.
The Persian Gulf is simply too small, The Shamal Wind is a katabatic wind descending from the Zagros Mountains and when it passes over the Gulf it is a direct tropical analogy of the cold polar katabatic winds.
Hi Rick,
just support of your counting from other side. From my photovoltaic collectors I see that total daily energy is roughly equivalent of 5 hours of maximum sun illumination. That is 1kW/m2 for 5 hours, giving 5kWh of energy.
If you transform it to latent condensation heat, it is 7.37kg of evaporated water by sun daily. This is corresponding with your value of condensed water by longwave radiation per m2 per day 7.3mm.
This is only confirming that Earth is just big heat pipe, with column of water down and vapor up.
What energy you put in, same energy you get out.
Column profile is given by gravity, atmosphere density. Temperature has upper limit of 30C, after this limit only speed of processes is increasing.
That is about it.
And there is another obvious thing. I realized and counted this few months ago.
Absolute humidity at sea level is around 28g of water per m3 at 30C.So how high you will propel this humid air with daily solar energy?
1m3 of air is around 1.13kg, what is ratio of 40.36. That means 1kg of water vapor must propel 40.36kg of air.
So let’s take mentioned 7.39kg of water, we need to propel 7.39×40.36=298kg of moist air.
Potential energy is m.g.h, weight, gravitational constant, height.
We have energy Q=5kWh=18MJ.
h=Q/m.g
h=18,000,000J/298kg.10ms^-2
h=6040m
And we have our LFC.
How do the Great Lakes factor in to this ? The Great Lakes have a surface area of 94,250 sq. mi. and the Persian/Arabian Gulf 96, 912 sq. mi.. The fact that the Lakes are in the center of a continental land mass makes for some interesting weather phenomena.
It’s doubtful that the surface temperature of the Great Lakes would ever reach 300 K (about 80.3 F) due to their high latitude and being fed by freshwater rivers, so that the effects Rick talks about over tropical oceans would not occur there.
The Great Lakes do have a major effect on climate, particularly in areas to the south and east, during late autumn and early winter, when northwesterly winds around storms centered in New England or Labrador blow cold, dry air over the lakes. While there is still open water in the Great Lakes, water is evaporated easily into the cold, dry air, which quickly saturates, then precipitates out as rain or snow downwind, particularly if the terrain is at higher elevation. This “lake effect snow” tends to lessen later in winter as the Great Lakes freeze over, and the source of moisture is reduced.
Rick:
I’m afraid I’m still struggling with figure 11. The diagram key (in yellow) and the description at the bottom of the diagram seem to contradict. Is the blue line the density of moist air, the density of water vapour, or the rate of change of either of those?
John
You are not alone. It took me a long time to reconcile placing the CHANGE in density of moist air with just THE density of water vapour on the same chart. What validates it is that the water vapour can exist at any relative humidity (plus supersaturated in some circumstances).
Considering altitudes higher than the intersection, the air can become dry but will still be buoyant on the layer below. The complete loss of water is too small to make enough density difference to cause the dry air to sink below the altitude of intersection of the curves.
So moist air at thermal equilibrium is more buoyant than dry but the LFC occurs because there is a point where dry air will actually sits on moist air below.
You can observe this in radiosonde skew-t plots. There will be a pressure (altitude) where the humidity just goes sideways (drops rapidly).
Very interesting post. Many thanks for sharing your energy with us.
Rick: I have been thinking about the elevated SST during PETM, could this be related to the icefree polar conditions leading to high ocean bottom temperatures? Or to rephrase it differently: is the maximum SST related to ocean bottom temperature?
Hans,
Sorry, but you have that the wrong way round. The ocean currents are the primary mechanism by which energy is transported from the tropics to the poles.
The global ocean can operate in two distinctly different modes:
During the PETM the circumpolar Southern Ocean was not yet fully formed (Australia: The Land Where Time Began) and the Tethys Ocean was still not yet fully consumed by the plate collision between India and Asia, so warm dense tropical bottom water was still able to deliver energy to the ice free paleo Arctic Ocean.
Hans
The deep oceans do not have much impact on the surface conditions in the present era. The tropics pump the water into the atmosphere and it eventually drops out at higher latitudes where it renters the ocean at lower temperature. The present return channel from the poles to the tropics sits between 500m and 1000m:
The channel would have been returning warmer water in the Eocene but the tropical surface would be warmer than the return water. The temperature limiting process is related to the surface temperature of the water.
One point that I have not mentioned specifically in this Part is that the atmospheric conditions are above a surface pressure of 1010mb. Increasing atmospheric pressure will increase the upper surface temperature but it is not a significant sensitivity. Taking the pressure to 1050mb increases the upper surface limit by more than 1C but less than 2C. The reverse happens if the surface pressure is lower.
I would expect if all the ice was removed; sea levels higher and more total water vapour that will not change the surface pressure much. I can imagine an increase in surface pressure during glaciation with ice mountains displacing more air and sea surface lower but I have not found evidence for this.
I have an opinion that the higher temperatures observed in the Evans paper is more location based. Land can certainly disrupt deep convection as the Persian Gulf demonstrates. Evans readings in the Equatorial Pacific were not the high values like around Bali. This is his comment overall:
When samples are taken from beaches then they are not going to be particularly representative of warm pools in open oceans. If you were taking samples in the Persian Gulf today, there may be evidence of 36C because it certainly occurs but only for a few months each year. There are not many deep ocean sites. This from Evans on deep oceans:
There are a myriad of factors that could have an impact on the inferred temperature and the actual temperature. I expect that the 36C is anomalous. I can accept 32C is a possibility and would like to look at surface pressures during the era.
Thanks Rick.
This is, of course, captured in climate models. /sarc
Hello gents, sorry for cutting in but I asked this question to “adiabatic experts” and they never answered. It puzzles me for I searched manuals and they all appear to cover the lapse rate very well in ascension but not as well in descension.
So I’ll try my fortunes with you guys,
Question: What causes the parcel of air in the dry adiabatic lapse rate to descend once it has risen enough to be stably buoyant under its potential energy?
It can’t possible be “stuck” there so something alters it. A physicist I been talking to claims the only way it can descend is by ejecting energy through ghgs. I don’t disagree ghgs eject energy, and the higher up near the tropopause the more likely that energy will be ejected out into space but the answer doesn’t seem to cover more meteorological practical functions.
Thoughts?
The only location where the surface temperature is near static day and night is the tropical warm pools but the deep convection over them is different to what occurs in most other location.
For example, land temperature is never constant. It warms in the day and cools at night. Any air above the surface will establish vertical and lateral convective current. Dry air just follows the dry adiabat up and down in those surface forced circulations.
I’m a physicist who at one point thought ejecting energy through GHGs was the only way that air could end up descending…
Upon further analysis, I’ve realized that cooling by GHGs is one factor, but horizontal circulation to a cooler part of the globe can occur because (1) the pressure gradient with altitude in cooler and warmer parts of the globe is different, and (2) heat exchange can occur between high altitude and low altitude air currents (perhaps radiative heat exchange with the surface might be important too?).
So, there are a lot of factors that come into play…
I appreciate the input. This was his reply which left me more than a little confused…
“Problem is they can never sink again if the whole process had no way to get rid of some of the inner energy. It is simply prohibited by Archimede‘s principle: Something less dense will never sink through something more dense. But it must start sinking somehow so that the pressure gradient can apply the volume work to the sinking air parcel. No initial energy loss to start the sinking – no further sinking. If you shift a parcel of air up and it decompresses adiabatically, only two things could compress it again: Work or loss of inner energy. To get the work of compression it must sink to regions of higher pressure. To sink, it would need to reduce volume first, otherwise Archimede‘s principle prohibits sinking. How to reduce volume without work? Way two or no way at all. At this stage the physics is quite simple.”
@CDM
Ask him to explain how whirlpools form.
I think the problem is he’s not thinking through the consequences of having a heat sink at ground level.
If there are both heat sinks and heat sources at ground level, you’ll end up with an atmospheric circulation pattern that has air descending towards the sink and rising over the source. You also end up with lateral air movement, with a low altitude air current from the heat sink towards the heat source, and a high altitude current from the heat source towards the heat sink.
The necessity of such circulation arising becomes clear if you examine the pressure profiles over the heat sink and heat source. dP/dz = -ρ⋅g, but the density ρ is larger near the heat sink than it is near the heat source, which means the pressure gradient is steeper over the heat sink than over the heat source. That means that pressure cannot be equalized horizontally at all altitudes. When you look at the pressure difference near the surface, it implies air motion from the sink towards the source, while the pressure difference at altitude implies air motion in the opposite direction.
For all this to work, it’s essential that there be some measure of heat exchange between the high and low air currents, so that the high altitude air is cooler by the time it gets to a location over the heat sink.
The air sinking over the heat sink can be essentially neutrally buoyant (when one takes adabatic lapse rate into account) and will be driven to descend by the pressure differentials. Or, something like that.
The point is, the system cannot be in equilibrium without such a circulation pattern forming. Examining the pressure differentials reveals this.
I believe the system can be understood as a form of heat engine, so that there is work being done to drive the air circulation.
(I talk about all this in this comment, which might or might not add anything helpful.)
Richard, I very much appreciate the subject matter you’re writing about. I wish it was easier to be clear what is conventional meteorological analysis and what, if anything, might be your own personal interpretation. I’m imagining that most of what you write about here reflects standard analysis? If so, could you point to some relevant references?
I’m particularly curious about this statement: “Convective instability can only occur when the mass of water vapour in the atmosphere exceeds 30kg/sq.m; equivalent to 30mm water vapour.” Could you point me to a reference that could help me unpack the underlying physics of this particular assertion?
I really want to understand what you’re saying. To that end, I’m willing to ask some “dumb questions” to try to accelerate my understanding. Would you be willing to respond?
Are you saying that no Level of Free Convection (LFC) can exist if there is less water vapor in the atmospheric column?
Do you have any reference to where this number comes from?
Are you saying that the LFC reaches the surface at this level of water vapor?
I’m having trouble figuring out what you’re plotting in Figure 11. What is meant by “the density change of moist air”? How do the curves in this figure relate to the curves in Figure 10? There is a curve related to “density of moist air” in both figures, but the magnitudes are vastly different, so it seems like you can’t be plotting the same quantity.
As I understand it, air is unsaturated (“dry”) from the surface to the LFC, then saturated (“moist”) from the LFC to the Equilibrium Level (EL), then becomes unsaturated (“dry”) above that.
So, I don’t know what you mean that “dry air will be supported by a moist air column below.” Are you talking about the dry air above the EL?
I’m confused by that. I thought that the LFC is the level at which moist convection begins (not ends), so that a rising air column easily rises above the LFC?
I thought the LFC defines where “free convection” begins, not where it ends? So, I’m confused by your calling the zone below the LFC the “free convection zone.”
In descriptions I’ve seen of LFC, they talk about following a dry adiabat up to the level of the LCL (Lifting Condensation Level), then following a moist adiabat. Following a dry adiat doesn’t resume until one exceeds the EL (Equilibrium Level). So, it seems like you’ve got the description backwards. Am I missing something?
Bob,
I know that I am going to regret doing this because from my perspective as a radiative physicist you come from the dark side. Over the centuries physicists have done incredible damage to the geosciences and the current destruction of climatology and her replacement by “climate science“ is just the latest example of this brutal process. So, when you say I am here to learn, or worse I am here to help, then like many on my side I head for the hills and duck down behind the rocks.
Why do I do this? Well History of Science is a good guide here. Some basic background. My father was a mathematics teacher who taught applied mathematics to engineers at university level. He maintained that mathematics was the Queen of the Sciences, mathematicians explored ideas, decades, sometimes centuries before any practical use of their work could be established. My own view is that physics is simply a glorified exercise in curve fitting, very abstruse curve fitting perhaps, but when all is said and done physics is the follower and not the leader of scientific thought.
I am not a mathematician, but I am an explorer. So, let’s see where we are.
You state that you used to think that the presence of greenhouse gases was the only way that an atmosphere can cool and so descend. There are two separate issues here cooling and descent.
The cooling, process of radiative emission by mass requires shear wave flexure, because it is shear motion that couples mass to radiative emission. So, while polyatomic molecules have flexural motion, it is sold particles that are the most efficient thermal emitters because of the multiplicity of modes of flexural vibration that solids can undergo. Consequently, if we have a condensing volatile at elevation in a planetary atmosphere then these ice particles will both form a veil, blocking incoming solar radiation and also be a layer with efficient emission of thermal radiation to space.
The next point I want to mention is the issue of planetary rotation. I do not even pretend to understand this subject but I can and do make observations of what is seen. The process of rotation fundamentally limits the ability of a fluid to advect across the surface of a globe. The more rapid the rotation the less far the fluid can travel. Earth and Mars for example have 3 atmospheric cells per hemisphere, Jupiter has nine, Venus and Titan by contrast have only one. This issue of rotation and vorticity creates the circumstance by which upper air can undergo forced descent before all possible thermal radiative cooling to space has occurred. By this means energy can be retained in a planetary atmosphere.
Then there is the issue of latent heat, in the case of water this involves both vapour to liquid and also liquid to solid transformations. This power assist process of energy release on lifting creates an imbalance when precipitation and gravity separation remove the water back to the surface. But there is an additional factor, upper seeding by falling ice crystals from cirrus clouds can and does cool the air below these topside ice clouds by latent heat absorption, so here is another dynamic mechanism by which upper air can be cooled and so forced to descend. And so, it goes on. Meteorology is a complex field, that requires a lifetimes study before you begin to realise that we really don’t know very much for sure.
To be clear about the context for your response, I’m guessing that perhaps you meant to respond to this comment (which talked about what it takes to allow uplifted convecting air to return to the surface)?
I’ll be sorry if it turns out that way.
Maybe it’s just the “far side”?
I want to acknowledge that it may seem risky to engage with me. Thanks for trying.
It sounds like there’s a lot of pain there. I’d be interested to better understand that, if you choose to share.
Some people are take on their parents attitudes, and some people reject their parents’ attitudes. So, I’m not entirely clear on what lesson you might have taken from your fathers’ views.
(My own father is a biologist who got into science as his way out of dairy farming.)
That doesn’t match my sense of physics, but it’s good to know where you’re coming from.
I said that, but that statement was only a crude approximation of what I used to think.
What was more literally the case was that I used to think that a “high heat sink” was necessary to sustain convective circulation. Cooling by GHG is one form of “high heat sink” but not the only one, as you point out.
Sure, solids and liquids tend to be more efficient absorbers and emitters of radiation than gases, though gases in large quantities can have significant radiative effects.
Interesting. Makes sense in broad terms.
I never thought there was any requirement that air had to experience “all possible thermal radiative cooling” before it could descend.
I’d be interested in understanding what you mean by “an imbalance” here. What sort of imbalance?
I’m guessing that means water vapor condenses around those ice crystal “seeds,” releasing its latent heat? And that perhaps some of that latent heat goes into melting the ice, so that the air has less energy content than it would have had if the water vapor had condensed otherwise? That’s the cooling being referred to?
If so, makes sense.
* * *
Thanks.
Bob,
This is fundamental Meteorology 101. Clouds can and do evaporate all the time.
It is the physical separation by gravity of water (either in its condensed droplet or solid crystal form) by precipitation from the cloud that creates the physical imbalance which makes it impossible for air lifted by convection to return back down along the moist adiabat. Upper air in the absence of surrounding water is constrained to follow the dry adiabat on descent.
Once again you prove by this statement that you just don’t get it.
I am talking about the sublimation of virga as ice crystals from advected cirrus clouds above fall under gravity into dry air below.
Go out, look up and watch the sky. Observation of nature is the basis of all science.
The whole tone of your reply that follows this statement is a poster child example of why it is pointless to engage with you.
Ok. It makes sense that, in the absence of water droplets (or ice crystals?) that could re-hydrate descending air, that air can’t follow the moist adiabat.
Does the need to follow the dry adiabat mean that the air can’t descend? Or simply that it will get hotter as it descends?
Of course I don’t get it. I’m trying to learn something. I’m taking your words, trying to make sense of them, and reflecting my best guess, so that you can tell me where I’ve gone wrong. I’m not sure how else to learn from what you’re saying.
Ok, that makes sense. Thanks for clarifying.
I wasn’t sure why you used the term “seeding” — that’s what led me to guess that you might be talking about ice crystals acting as nucleation “seeds” stimulating condensation. I guess you must have meant something else.
I’d love to know what you’re talking about. What “tone” do you think is present in my reply?
it’s really hard to accurately transmit and interpret tone in writing.
I tend to be really straightforward in what I write, without any hidden meaning. Yet, I don’t make sense to everybody, and so some people assume a meaning that’s not there. I don’t know if you’re doing that or not, but maybe?
I’d love to be given the benefit of the doubt, with regard to my intentions.
Bob,
You are clearly a very clever guy.
However, you continually make mistakes and then make inferences based on these mistakes which are wrong.
Then you invite confirmation of your error.
You are setting traps with the clear intention of discrediting.
Under no circumstances will I trust you.
Thanks for letting me know what’s at the root of your suspicion.
I doubt you’ll believe me, but I never set verbal traps. I find that sort of behavior disturbing and unpleasant, even reprehensible, and to be avoided at all costs. It’s not aligned with my core values. Once in a very rare while I’ll notice that something could seem to be setting up a “gotcha!” Whenever I notice that, I change what I was going to write.
Sometimes I suspect that someone is wrong, but don’t know for sure because they’re not expressing themselves clearly enough to be sure what they mean. When that happens, I do my best not to hide my potential disagreement, but to suspend judgment and try to find out what they really mean.
I ask for clarity for the sake of clarity, not because I want to set a trap.
In the case of your recent post, I had no suspicion at all that you were saying anything wrong. I assumed what you were writing about was likely valid.
I was just seeking clarity to understand your meaning. Nothing more.
I haven’t seen evidence that I make mistakes more often than anyone else. However, unlike others, I’m pretty transparent about explicitly sharing what I’m thinking, and that makes it easier to notice if I make a mistake. That supports me learning faster than I might otherwise.
I think other people make mistakes all the time, but don’t even notice it because they’re not willing to make their thinking explicit and examine it.
* * *
I often find it frustrating how unclear some things are. Often, people don’t seem to realize the number of unspoken assumptions that are implicit in their words. Without knowing those assumptions, “message received” is often not the same as “message sent.”
I’m not interested in pretending to understand something when I don’t. I really want to understand what people are saying.
One of my favorite strategies for trying to achieve understanding is to offer a guess as to what the other person might mean, so they can tell me what I understood, and where I failed to get their meaning.
This can offer a really effective way of understanding someone’s meaning more clearly.
I’m not assuming I know what the other means. I’m letting them know that I’m not sure what they mean, and I’m letting them in on my guess about what I’m thinking they might mean so they can let me know if I’ve understood them or not, and correct any wrong guesses.
It doesn’t bother me at all to learn that I’ve guessed wrong. I’m not assuming I’m right. I’m just trying to make sense of things.
I’m sorry if this style of seeking clarity is frustrating for you or others.
Would it help if I more explicitly said, “I’m not sure I understand you?”
I don’t want to be annoying.
Is there any way I could seek clarity that you might find less triggering?
No.
But you are.
No, a leopard cannot change its spots.
As you are clearly addicted to this process and cannot stop, I will help you by making this my last response to you here.
I’m intrigued by this work, but also have a number of questions (e.g., here or here). The author has not, as yet, chosen to address my questions.
I’m curious: Is any reader of this essay able to follow it well enough that you understand how Table 1 is calculated, and why it is an appropriate calculation to make?