CONSERVATION OF ATMOSPHERIC ANGULAR MOMENTUM VARIATIONS WITH CLIMATIC CHANGE

[iapennell]

Dear Readers,

I would like to explain how a fundamental feature of the Global Circulation, that of the tendency of the atmosphere to rotate with the solid Earth around it's axis of rotation accommodates changing seasons functions. I also discuss how it accommodates some of the extreme conditions deduced by paleo-climatologists to have occurred across a large area of planet Earth during the most severe phase of the last Ice Age. Drought and severe cold seem to have featured heavily in both lower and higher latitudes during the most severe phase of the last Ice Age whilst drought was a feature feature of climate in the tropics and sub-tropics. This can only be explained in terms of persistent weather-patterns that have been observed to bring such conditions during the period of modern civilisation, that of strong high-pressure over higher latitudes keeping rain (or snow) bearing weather systems away, with the high-pressure delivering cold dry north-easterly winds across large areas of planet Earth. In the tropics too, drought is today associated with a strong sub-tropical high-pressure belt that brings dry, quite strong north-east winds (or south-east winds in the Southern Hemisphere) on the equatorward side. This is associated with the zone of hot, steamy rising air associated with Intertropical Convergence Zone (ITCZ) being restricted to being very close to the Equator with monsoons failing to penetrate tropical continents to bring seasonal rains. This is also a feature of Ice Ages where West Africa and southern Asia fail to get monsoon rains because they stay cooler (or at least fail to heat up more) than the hot equatorial seas to the south.

The modern understanding of how the atmosphere gains and loses Westerly Atmospheric Angular Momentum (AAM) by frictional interaction with the underlying surface is not consistent with a global climate whereby cool dry north-easterly winds can prevail over more than about 65% of the Earth's surface because of the Law of Conservation of Angular Momentum. It is then argued that because the atmosphere continues rotating with the Earth and because outside forces (from lunar tides, meteorites, etc.) are miniscule compared to the mass of the Earth's atmosphere and the momentum exchanges with the underlying surface, that what Westerly AAM is gained by the atmosphere in the tropics, subtropics and polar regions (due to the Polar Easterlies) has to be returned to the surface in middle latitudes. The atmosphere in low and very high latitudes does gain Westerly AAM through the frictional impact of surface easterlies on the seas and lands over which they travel and, indeed, Westerlies in higher latitudes, again through their frictional interaction with the underlying surface over which they blow, make those middle latitude locations the sink of Westerly AAM.

However, strong Westerlies in higher latitudes in autumn and winter are consistent with deep depressions which draw not only on sharp upper atmospheric temperature and pressure gradients aloft (i.e. through a strong Circumpolar Vortex) but also a source of warmth and latent heat to fuel these depressions effectively. And paleo-climatologists have deduced that winters at the height of the last Ice Age were dry and bitterly cold in the North whilst there were also strong dry North East Trade Winds bringing drought across Africa, southern Asia and central America with greater volumes of dust transported across the Atlantic from the Sahara to Brazil (Nigel Calder's 1974 publication on "The Weather Machine and the Threat of Ice" covers all these details).   And the Law of Conservation of Angular Momentum does not preclude the possibility that much stronger Westerlies could dominate in the Stratosphere and upper atmosphere whilst Easterlies predominate in the lower atmosphere and the Earth's rotation slows down enough to add a few milliseconds to the Length of Day: What matters is that the entire Earth Atmosphere system conserves axial Angular Momentum in the absence of outside forces.

Under such conditions, with very strong Westerly winds aloft high mountain areas alone (like the Himalayas) would become the sink for Westerly AAM as very strong Westerly winds blasted them at times.  In the absence of mountains, Westerly AAM would be brought down to the surface in areas of strong atmospheric subsidence when and where day-time solar heating of the surface and lowest layers of the atmosphere is sufficent to bring about stronger surface boundary layer convection- i.e. subtropical land areas in the Spring and Summer (beneath the descending air of a strong subtropical high-pressure belt). Such westerly (or more likely with the air moving equatorward with higher surface pressure to the north, north-westerly) winds would be very strong and return to the Earth Westerly AAM imputed to the atmosphere by north-easterlies over the rest of the Northern Hemisphere over the preceding year.  Such a situation would be more likely to develop in a severe Ice Age winter when extremely cold, dense air covers all middle and high latitude areas, the troposphere would correspondingly become a bit thinner north of the sub-tropics then the upper-air thermal and pressure- gradients become further strengthened around 25 to 30N: That would further increase the speed of the subtropical jet-stream and the westerly speed of the subsiding air beneath it.

Either way, in a severe Ice age Winter we have a situation whereby Westerly AAM is transferred from the surface into the atmospheric circulation (due to extensive Easterlies) , then is transferred upwards rather than polewards. That is not inconsistent with the Law of Conservation of Angular Momentum, but the sinks for Westerly AAM will also (likely) be in the tropics or sub-tropics (due to very strong Westerly jet-streams blasting subtropical mountains or (with daytime heating below) brought down to the surface in violent dusty squalls beneath the strongly- descending subtropical high-pressure belt (at about 25N). 

The Ferrel Cell in middle- latitudes, with surface south-westerlies and winds returning from higher latitudes would almost certainly cease to exist in a severe Ice Age winter (with all seas and lands frozen north of 30N)- to be replaced by a single Direct Cell extending from the Polar Regions to south of the Equator. Today, it is the returning flow of air from high-latitudes aloft- becoming relatively less "Westerly" as it moves into lower latitudes that today weakens the Westerlies moving north aloft from the Hadley Cell (by colliding into them), so that the air descending in subtropical highs does not have a strong Westerly component by the time it reaches the surface. If the mid-latitude and high-latitude oceans and lands are all frozen there is no Ferrel Cell, the air descending from beneath the subtropical highs moves strongly from the West as it descends- and it becomes subtropical Mountain Ranges like the Himalayas, Karakoram mountains and the High Atlas that the Westerlies hit (and are slowed down rapidly by). Unless the upper- air is much colder still (so as to encourage convection and cyclogenesis), frozen lands and seas with all the low- atmosphere being well below freezing-point do not lead to depression formation (or, with it, strong Westerlies on their southern flanks).  

continued below.        

[iapennell]

continued

During the summer half-year in the last Ice age there will still have been enough open water over oceans (and indeed warmth over land) south of about 45N to mean that the transfers of Westerly AAM happened in a manner close to how it is conventionally understood today: That is, with Westerly AAM being transferred polewards to furnish depressions (and Westerlies to the south of them) in higher latitudes. However, the zone of Westerlies would have been closer to the Equator- 30 to 45N rather than 40 to 70N (as in summer nowadays). With the Westerlies blowing in latitudes further from the axis of the Earth's rotation they will not have had to blow as strongly to remove Westerly AAM from the Global Circulation even though, as likely a steeper temperature and pressure gradient from the subtropical highs to the ITCZ will have furnished stronger North East Trade Winds. Also, unlike nowadays, the Himalayas and Karakoram mountains would have remained under the influence of some Westerlies beneath the subtropical jet - unlike in summer today. All of this would have increased the scope for blocking patterns to persist in high-latitudes to bring dry cold Easterly winds across Europe and North America (as discussed in Nigel Calder's "The Weather Machine and the Threat of Ice"). Clearly the existence of some open water in middle latitudes and an atmospheric temperature gradient between the Arctic and mid-latitudes had to lead to the formation of depressions- how else could the ice-sheets of northern Europe and North America have been furnished with snowfalls? However, it is clear that the more southerly zone of the weaker Westerlies even during the summer in an Ice Age can still (with help from the Himalayas also acting as a sink for Westerly AAM) satisfy the requirements for a sink for Westerly AAM to match the sources (Easterlies were prevalent across both high and higher middle latitudes in Ice Age summers, as well as in the tropics), and this also provides an explanation as to why extreme drought prevailed across such vast areas of the Northern Hemisphere.

Cold seas in mid latitudes and permanent ice on most land areas north of 45N will not have been conducive to deep depressions in general. However, strong temperature contrasts between the ice sheets and the warmer open North Atlantic will have furnished sufficient cyclogenesis (depression formation) in early autumn- before the sea froze over to bring snowfalls heavy enough to build up the ice over eastern Canada, but few major land areas (if any) saw sustained increases in precipitation during this period. Cold seas and oceans are not a good source of moisture and energy for depression formation (particularly where these freeze over), and this is something that is observed today. For instance, deep depressions virtually never penetrate Siberia between December and March and they weaken and fill rapidly if they penetrate interior Antarctica or- in winter- if they penetrate over the frozen Arctic Ocean.

The fluxes on Westerly AAM and the constraints of the Law of Conservation of Angular Momentum are secondary to the fact that hot air rises and cold air sinks, that colder air (particularly near the surface) encourages high surface pressure and out-flowing winds whilst warm surface and low- atmosphere conditions, particularly with cold air aloft encourages depressions, surface convection and squalls. Conservation of Angular Momentum and the position of fluxes of Westerly AAM on planet Earth almost has to play second-fiddle to the thermally- direct controls caused by warm air rising and cold air sinking- and often has to work around them.

continued below.          

Edited April 25, 2021 by iapennell

[iapennell]

Continued.

The conventional understanding of the atmospheric sinks and sources of Westerly AAM, so that the Earth Atmosphere System conserves total axial Angular Momentum, does not necessarily hold true in a manner that some meteorologists might expect for strong Global Warming either: Strong Global Warming would lead to melting of all the ice-caps whilst engendering more frequent (and severe) tropical depressions and hurricanes. Depressions in higher latitudes depend, amongst other things, on steep upper atmospheric temperature and pressure gradients between warmth over mid- latitudes and much colder conditions over the Arctic (and Antarctic). If you warm the Arctic and remove the ice-cap then, particularly in winter, you remove a key component of that which drives deep depressions and thus furnishes strong south-westerlies in the latitudes of the UK and western Europe.

An ice-free, much warmer Arctic is not likely to have "Polar Easterlies" because the upper-air would still be very cold and the warm water surface would fuel convection. Greenland, even without an ice-cap would still get very cold in the interior and this, with the ice-free Arctic Ocean (but still very cold air aloft) would encourage the formation of quite deep depressions which would move across the Arctic Ocean. Surrounding areas, such as coastal northern Siberia, Greenland and the Canadian Arctic islands would then be affected by strong Westerly winds- so the Arctic Region would (likely) become a sink for Westerly AAM- though not a major one on account of its closeness to the axis of Earth's rotation. Even so, a deep depression centred near the North Pole would have no Easterlies (as such) associated with it, the centre of the depression would invariably be north of wherever one was!

In a much warmer world more (and more intense) tropical depressions are liable to complicate the picture of where the sinks and sources of Westerly AAM are. On the whole, a deep tropical depression acts as a slight sink for Westerly AAM because the very strong Westerlies on the equator-ward flank (tropical depressions can never form within five degrees of the Equator) blow slightly further from the axis of the Earth's rotation (and, thus are more effective at removing Westerly AAM) than the easterlies poleward of the eye of the deep tropical depression. That said, deep tropical depressions tend to form close to (and move westwards along) the ITCZ when the ITCZ is well north or south of the Equator in whichever Hemisphere is experiencing summer/ autumn. Thus strong surface Easterlies add Westerly AAM to the Hemisphere in summer/ autumn but strong Westerlies extending equator-ward of the ITCZ remove it even more effectively from the Hemisphere experiencing winter/ spring. For the Northern Hemisphere, more hurricanes and typhoons would help strengthen the higher-latitude Westerlies between July and October- leading to windier, wetter summers but more tropical depressions south of the Equator during the Northern winter would help weaken the mid-latitude Westerlies- as would more depressions in the Arctic Ocean. This is because the Arctic and the area between the Equator and 10S would have strong Westerly winds- acting as efficient sinks for Westerly AAM- leaving rather less Westerly AAM for mid- latitudes of the Northern Hemisphere: Ergo more blocking highs and dry colder weather from the east is likely in Western Europe between January and May. 

Strong global warming would lead to more warming at high latitudes as ice caps melt and the darker surface, but the Equator would warm less. However, increased CO2 levels would concentrate most of the warming in the lower atmosphere so the steep atmospheric temperature gradient driving convection in the ITCZ would increase. By the same token warmer seas in the subtropics would help weaken the subtropical highs and help to reduce subsidence there- and reduced temperature and pressure gradients from the subtropical highs to the ITCZ would help weaken the easterly-quarter Trade Winds both north and south of the Equator. On balance, there would likely be a weaker Hadley Cell and the transfer of Westerly AAM from the surface in the tropics- then to higher latitudes would be reduced. This would also support generally weaker Westerlies in mid-latitudes, as would the sharply-reduced atmospheric temperature and pressure contrast between high latitudes and the sub-tropics. Warmer ocean surfaces in mid-latitudes would also help fuel deeper depressions, particularly in autumn and winter but the reduced atmospheric temperature contrasts between the Arctic and mid-latitudes would help weaken them. Depression tracks will also tend to higher latitudes. 

The distribution of the sinks and sources of Westerly AAM are likely to change substantially in a much warmer world than today. A weak temperature gradient from the sub-tropics to the Arctic will make mid-latitudes less of a sink for Westerly AAM than today, but deep depressions penetrating an ice-free Arctic will also make the Arctic a sink for Westerly AAM (taking up some of the slack for mid-latitudes), rather than a source for it (due to Polar Easterlies). The influence of more (and deeper) tropical depressions means that overall the tropics will be a bit less of a source of Westerly AAM than today, even if the Hadley Cell remains similar in strength. My contention is that the Hadley Cell weaken slightly overall as the impact of significantly reduced temperature/ pressure contrasts north and south outweigh the effects of stronger convection enhancing the ITCZ. However, another impact of the ITCZ moving well north and south of the Equator (due to more continents getting hotter than the Equator in summer) will be easterlies aloft in low latitudes- adding Westerly AAM to the atmosphere where these easterlies touch mountains (i.e. the northern Andes, mountains of East Africa), but this influence will be countered by more extensive monsoon south-westerlies affecting West Africa and south Asia and monsoon north-westerlies over Papua New Guinea and the tropical eastern Indian Ocean from December to March.  A warmer atmosphere will also have a deeper troposphere, particularly in northern latitudes which somewhat reduces the scope for the sub-tropical (Westerly) jet-stream to impinge on the Himalayas or the South American Andes. That removes one sink for Westerly AAM, but a weaker Circumpolar Vortex (due to a reduced poleward temperature gradient) would still encourage some depressions (with Westerlies to the south) to penetrate lower latitudes. 

On balance, a much warmer Earth would see a net reduction in Westerly AAM transferred to the atmosphere in the tropics, subtropics and the Arctic overall and a corresponding reduction in Westerly AAM reaching middle latitudes, at least in the North Hemisphere. Significantly, if the Arctic Ocean was totally ice-free and the Antarctic ice-sheet melted (which would raise sea-levels by almost 80 metres worldwide) there would be no Polar Easterlies as such, the Arctic would become a significant sink for Westerly AAM in winter with depressions pushing into the area.

In conclusion, therefore, either serious Global Warming or a return to much colder conditions globally would see a reduction in Westerly AAM transferred from high and low latitudes to middle-latitudes- but for different reasons: For instance, strong global warming leads to stronger tropical depressions which overall act as a sink for Westerly AAM, however strong Global Cooling towards Ice Age conditions encourages an upwards (rather than poleward) transfer of Westerly AAM leading- in time- to major mountain areas in lower latitudes becoming the sinks for Westerly AAM simply because low elevations at higher latitudes are no longer in a condition to receive it (at least not during the winter months). Whatever the reasons, the result is weaker Westerlies, or even north-easterlies instead for many mid-latitude areas. Strong global warming is capable if weakening the Westerlies blowing across the North Atlantic to such an extent that much colder winters with frequent easterly winds from Russia could, paradoxically affect the UK much more often.             

      

[iapennell]

NORTHERN HEMISPHERE SEVERE WINTER IN ICE-AGE: RELEVANCE OF THE "EKMAN SPIRAL" AFFECT ON ATMOSPHERIC CIRCULATION

A further consideration, with regards to the behaviour of the Global Circulation and Global (Westerly) Atmospheric Angular Momentum (GLAAM) sources and sinks is a feature called the Ekman Spiral, which is related to the Coriolis effect- and which affects related not only surface winds and ocean currents, but it also governs how air that is "dragged" along by faster moving air aloft moves.  The Ekman Spiral effect explains why surface atmospheric pressure becomes lower polewards of the subtropical high-pressure belt (in normal climatic conditions). The Ekman Spiral is illustrated here:

The above is an illustration of how the Ekman Spiral comes about in the Northern Hemisphere, in this case through the top 100- metre layer of an ocean in mid-latitudes normally affected by strong westerly winds. In Northern latitudes the force of the wind drags the water along in the direction of the wind but the Coriolis force- due to the effect of the Earth's rotation on the water itself acts to the right of motion of the water, causing the surface currents to be 45 degrees to the right. Thus, if the prevailing strong wind is Westerly, the current affected by the wind flows north-west to south-east (and at a lower speed). About 20 metres below the surface the north-westerly surface current drags along the waters below- from northwest to southeast, but the Coriolis Force again acts to the right- so that the flow of deeper water is more of a northerly (at even lower speed). This process repeats until (at 80 metres' depth) below the surface there is a very sluggish flow of water flowing in the opposite direction (from east to west). The tips of the vectors- of the wind- then the currents at the surface and a different depths describes a spiral shape- hence the Ekman Spiral. 

Much the same process happens high up in the atmosphere beneath the subtropical jet-stream (nowadays typically about 30- 35N and 30- 35S)  and some ten kilometres above sea- level initially). The subtropical jet-stream is so high and subsidence beneath it slow enough that the winds 10,000 metres above have little bearing on the winds at the surface. Typically, the strong 150 mph Westerlies of the subtropical jet-stream descend slowly and enters an area where pressure increases polewards- the Westerlies are thus pushed towards the Equator (where the Earth rotates more rapidly) and- in the process- lose their "Westerliness" relative to the underlying surface. The fast moving Westerlies of the subtropical jet-stream also try to drag the underlying air beneath it eastwards, but this underlying air is in the zone without a strong south to north pressure gradient (in the Northern Hemisphere) and it behaves like the surface of the sea under the influence of strong Westerlies: Because of the Coriolis force, this underlying air is pushed to the right (i.e back towards the Equator) as well as from west to east (at a lower speed to the subtropical jet-stream above). The net result of all these processes, under current climatic conditions, is that the subtropical jet-stream causes beneath it- an equatorward push of a substantial layer of the atmosphere in the subtropics. This leads to a situation whereby a considerable "depth of atmosphere" is constantly moved equatorwards of 35N and 35S, which in turn manifests as a sharp fall in surface pressures polewards of these latitudes. With ocean surfaces and lands in middle latitudes just 10C colder than 35N and 35S the dynamic "Ekman Spiral" process easily overcomes the propensity of cooler surfaces in mid- latitudes to help foster even higher surface pressure and the mid-latitude Ferrel Cell (with surface Westerlies) is the result- and the warmer Westerlies originating in somewhat lower latitudes, upon picking up moisture and interacting with cold air aloft (and meeting colder airmasses at high latitudes) further helps fuel higher-latitude depressions that strengthen the Ferrel Cell.

But there are clearly some situations where the whole house of cards maintaining the higher- latitude Westerlies falls flat.

Continued below.           

  

[iapennell]

Continued.

This Ekman Spiral effect beneath the subtropical jet-stream is only effective in creating the Ferrel Cell (with surface Westerlies in middle latitudes) when four conditions are met: 

Firstly, that subsidence beneath the subtropical jet-stream subsides subsides at the subtropical high fairly slowly- so that it can drag the air beneath it equatorwards before it impinges upon mountain ranges. If it is rapid the strong flow of air from west to east will hit mountains like the Himalayas and South American Andes before it has had a chance to move equatorwards (over areas the Earth rotates faster) and lose its "Westerliness". If the subtropical jet-stream descends fairly quickly it also pushes air eastwards lower down in the atmosphere before it itself moves equatorwards- and the lower altitude air would still have a considerable component from the west (as well as from higher latitudes) on hitting more extensive upland areas.

Secondly, the subtropical jet-stream needs to be polewards of 25N and 25S, in latitudes where the Coriolis force is sufficient to cause an effective Ekman Spiral effect. During the coldest winters in the last Ice Age the subtropical jet-stream would have been strong above 25N, where the Coriolis Force is little over two thirds what it is at 35N. A much colder, denser (and shallower) troposphere polewards of 25N, especially over the continents would have also intensified the pressure- gradients at the top of the troposphere further strengthening the subtropical jet-stream but the Coriolis/ Ekman effect on the air beneath with the strong Westerly sub-tropical jet-stream itself not being deflected equator-wards as much. Winds over the subtropics would- thus- have regularly have maintained a strong Westerly component even down to elevations as low as 3,000 metres (and that is with subtropical-high atmospheric subsidence rates similar to today). An equator-wards- positioned subtropical jet-stream would have meant more low- latitude mountains were the sink of Westerly GLAAM.

Thirdly, extreme cold over middle and high latitudes during the severest of Ice Age winters would have precluded the mid- latitude Westerly Ferrel Cell over large areas, particularly over the continents in the Northern Hemisphere. The situation would have been analogous to the situation over Asiatic Russia and Mongolia in winter today where intense cold and high-pressure are normal. If the lowest 3,000 metres of the atmosphere were 30C colder than today, but conditions aloft are little colder that increases the density of 30% of the atmosphere by 15%- which equates to a rise in sea- level pressure by 45 millibars- even assuming the Ekman Spiral effect beneath the subtropical jet-stream is trying to reduce surface barometric pressure in higher latitudes as it is today . The sinks for Westerly GLAAM would clearly be displaced from the entire region- upwards and equator-wards. The shallower troposphere over mid- latitudes that would ensue (5 to 6 km depth, not 9 km as nowadays) would enhance the baroclinic temperature and pressure gradients in the upper- air near the subtropical jet-stream, much colder air seeping from higher latitudes near the surface in the subtropics would intensify the subtropical high- pressure belts and precipitate more rapid descent of air in and beneath the subtropical jet-stream (the mountains beneath which would become major sinks of the Westerly AAM unable to make landfall in frigid high-pressure areas in higher latitudes). With no Ferrel Cell aloft over middle latitudes there's no return flow from higher latitudes aloft to slow down the subtropical jet-stream either- the strong Westerly subtropical jet-stream maintains its speed on descent until it hits something else to slow it down (like the Himalayas and Tibet).

Finally, during the coldest winters at the height of the last Ice Age the surface and lower atmosphere- with expanded pack-ice, deserts in low latitudes and ice-sheets in middle and high latitudes reflecting away the Sun's energy there would have been reduced temperature contrasts between a chilly surface and frigid Stratosphere. This would have applied almost everywhere on the planet and the result would have been a general decrease in the thickness of the troposphere by up to 1,000 metres compared to today (but a sharper decrease in its thickness in middle latitudes). This the strong sub-tropical Westerly jet-stream would have blown at a lower elevation and would have had less distance to descend before hitting extensive mountain areas. 

For all these reasons, during severe Ice Age winters in the Northern Hemisphere the transfers of GLAAM and Westerly AAM are radically altered from one where Westerly AAM is transferred from low latitudes and the highest latitudes to middle latitudes- to a budget of GLAAM whereby Westerly AAM is transferred from low-lying lands and seas in all latitudes to high mountain areas in all latitudes (except right on the Equator where weaker Easterlies blow).  The change to full Winter Ice age conditions would involve a permanent shift to stronger Westerlies aloft (over the Earth as a whole), more extensive Easterlies below and a slight reduction in the speed of the Earth's rotation (increasing the Length of Day by a few milliseconds). This is not inconsistent with the Law of Conservation of Angular Momentum since there need not be a net change in the axial Angular Momentum of the Earth- Atmosphere system for the above to happen.

The existence of the mid- latitude Ferrel Cell- with surface Westerlies angling in from lower latitudes to bring warmth and moisture and returning to the subtropics aloft- is sensitive to a number of factors coming together. Even today, there are times and places in higher latitudes where it is not found at the surface: Asiatic Russia in winter being a good example, as here early winter snowfalls encourage rapid surface cooling and the development of very cold high-pressure areas that displace the Westerlies upwards- and away from that region. This process would get underway earlier in the season and cover a much wider area during an Ice age. The Coriolis effect today acts on the subtropical jet-stream and the air below pulled along by the subtropical jet-stream: With current climatic conditions- with a deep troposphere and slow subsidence beneath the sub-tropical jet-stream and that subtropical jet-stream being far enough from the Equator the Coriolis forces can bring about a return of considerable depth of atmosphere towards the Equator- and helped by ice-free seas and oceans in higher latitudes- results in sharply lower pressure in high latitudes: So the Ekman Spiral effect helps to create the mild moist conditions that bring warmth and moisture to the North, but that happens under current climatic conditions.