CAN THE STRONG SUMMER SUN AND THE CONSERVATION OF ANGULAR MOMENTUM STOP SEVERE WINTER COLD OVER BRITAIN?: YES IT CAN!

iapennell · January 3, 2014

3rd January 2014

Happy New Year fellow Weather-enthusiasts! How are you faring with all the wind and the wet (and little frost or snow)!

Judging from the weather-patterns that have affected northern Britain- and not just the South- so far during Autumn/Winter 2013/14 the Ferrel Westerlies (that part of the Global Winds that blow from the subtropical highs to the "sub-polar lows" and angle in from the south-west in the Northern Hemisphere) have been pretty vigorous and persistent haven't they?! They have brought plenty of rain but also mild temperatures: Even at my weather station near Alston (high up in the North Pennines) there was no air frost 'til November and (so far) no really hard frost for the winter season (and little real snow).

The weather we experience in Britain is caused by the Sun which beats down on the tropics throughout the year and beats down on the high latitudes of the Northern Hemisphere during the summer half-year. It is also caused by the differential heating between the tropics and the poles and the fact that the Earth rotates which greatly modulates the weather that can be experienced in higher latitudes. This is fairly standard textbook stuff but can the strong Summer Sun and the year-round strong Sun over the tropics combined with the Earth's rotation really be capable of protecting higher northern latitudes so completely against fierce winter cold??

At the latitude of Northern Britain (55N) during the period from early November through til early February the sun never gets more than 20 degrees above the horizon at noon and it is up for less than nine hours per day: The solar constant is 1380 Watts per square metre but such is the low elevation of the Sun that even if all the radiant heat were absorbed by the surface (over this nine hours the Sun is on average just thirteen degrees above the horizon at most) a maximum of just ten mega-joules of heat would be absorbed by each square metre of land and surrounding sea. However according to standard texts the Earth-atmosphere system radiates as a black body at -18C (in winter this would normally be a bit lower but the clear skies needed to assume total absorption of solar energy at the surface would certainly cancel this effect- even allowing for the effects of water vapour and CO₂)- the total heat loss from our square-metre surface would be at least 240 Watts per square metre, which over 24 hours amounts to over 20 megajoules. So overall there is a radiative heat loss of over ten megajoules per square metre per day during the winter months at higher northern latitudes.

Given the specific heat capacity of the entire atmosphere and the first 10 cm of the ground likely to be affected by radiative cooling over relatively short periods (up to two weeks) (this is no more than 15 MJ per degree Celcius even with moist ground) it is clear that if heat-advection were to cease over the UK during the winter temperatures would drop over land by more than 10C per fifteen days: High-level cloud cover would reduce the net long-wave heat loss but it would also reflect over 65% of the weak winter sun's heat so we are still looking at a strong net heat loss upwards of 10 MJ per square metres per day in this situation; moisture condensing out of the atmosphere would increase the specific heat capacity somewhat so that the first 10C cooling would be delayed just a few days but then the condensation out onto the surface as reflective frost and ice and the loss of water vapour (a greenhouse gas) from the atmosphere would ensure the net radiative heat loss increased and this cooling would also become concentrated near the surface. Catastrophic levels of frost (i.e below -30C) would occur within a month over mainland Britain in the absence of any winds advecting milder air from the ocean (which cools more slowly).

Clearly, this sort of thing rarely happens in Britain, and nothing like it has happened this winter so far. The winds blowing in from the west and south-west have been very effective at counteracting a ten megajoule-per-square-metre-per-day heat loss over Northern Britain this season! But is it really possible for the Summer Sun over the oceans and the strong all-year sun in low latitudes (combined with the Earth rotating once in 23 hours and 56 minutes) to generate sufficient SW winds over Britain to stop the country freezing? Lets see!

Now our SW winds tend to originate from over the North Atlantic close to 40N. Here in summer the subtropical high brings clear skies and the Summer Sun beats down at least 14 hours per day and reaching more than 60 degrees above the horizon at noon from mid-April to late August. The effective elevation of the Sun for 14 hours every day is at least 34 degrees for over four months: The Solar Constant is 1365 Watts per square metre (the Earth being a bit further from the Sun during the Northern Summer), and thus a payload of over 38.5 Megajoules of solar insolation per square metre beats down on this region of the North Atlantic every day for over four months. As the sun gets high in the sky and the atmosphere is clear (thanks to the subtropical high) over 90% of this energy is absorbed by the dark ocean surface; which means at least 35 MJ/m²/day of energy is absorbed. The net long-wave heat loss over this region will be a bit higher than the global averaghe averaged throughout the year but clear skies only increase the net heat loss some 40 Watts per square metre compared to the norm (particularly over an ocean with heat-trapping water vapour in the low atmosphere). The high atmosphere in lower latitudes is also colder so radiatively this largely cancels out the effect of warmer surface conditions- and an ocean at 40N (even in summer) wont be that much warmer as to make much difference. So a long-wave heat loss of 280 Watts per square metre from the Earth-atmosphere system over the North Atlantic (A -18C effective temperature equates to 240 W/m² heat loss). That means a total long-wave heat loss of 24 MJ/m² per day, which leaves us with a net heat input each day for over four months of at least 14 MJ/m² per day. Over the 130 days between mid April and late August it means that the North Atlantic at 40N absorbs a massive 1.9 Gigajoules of energy per square metre- thats a lot of heat! We are basing our calculations here on the elevation of the Sun in April and late August; not June (let us remember) so this figure is going to be a conservative estimate of the net heat input to the North Atlantic at 40N in the summer!!

Now, question is; whether the Earth-atmosphere system at 40N over the North Atlantic can more than lose that 1.9 Gigajoules of heat during the rest of the year: Over a period of almost eight months from late August to mid April the Sun will move from north of the equator to over 23 degrees south, then back again north of the equator by the end of the period. During that time the Sun will (on average) be near 13S because its transitions across the equator are rapid but the change of latitude (declination) of the Sun slows near the solstice. The sun will reach a maximum elevation of 37 degrees at noon (averaged over this period) and the day-length will on average be ten hours. The average elevation of the sun during the average ten hours it will be above the horizon will be 25 degrees. This means that, given the Solar Constant will be 1380 W/m² over this period, that for on average ten hours each day just over 580 Watts/m² will be incident on this part of the North Atlantic. That is a total of 21 MJ per day. However- during the autumn and winter when the sun is lower in the sky the effective reflectivity of water surfaces increases- the sun being on average 25 degrees above the horizon means an albedo of about 0.3. With the jet-stream moving a bit further south in winter frontal influences will bring some cloud to the North Atlantic at 40N at times, so we can confidently assert that our effective albedo will be near 0.4 for this region: Thus we can calculate a solar input over almost eight months averaging out at just 13 MJ per day.

The net radiative heat loss (given the input of high cloud at times and slightly cooler water surfaces in winter) will be closer to the global average, even if we assume that the subtropical high would bring clear skies most of the time. Working on the basis of an effective temperature of -16C for the Earth-Atmosphere system over the North Atlantic equates to 247 W/m² long-wave radiative heat loss (or 21.3 MJ/m²/day). So, the net daily heat loss over almost eight months is 8.3 MJ per day;- or about 1.9 Gigajoules per square metre over this entire period.

Over the year it means there is a net heat loss of precisely zero joules of energy over the North Atlantic at 40N- and that is (remember) predicated on conservative estimates for summer insolation for the region. This would (of course) be irrelevant if the North Atlantic cooled and warmed rapidly in response to the seasons;- if winter cooling could make the North Atlantic very cold the SW winds reaching Britain would hardly prevent severe cold in this country. So does the effective thrmal capacity of the ocean have an effect? yes it does because the specific heat capacity of water is 4200 joules/kg/C and each cubic metre of ocean contains 1,000 kg of water. Solar heating and surface cooling of ocean water is spread over a large depth- over 100 metres with seasonal heating and cooling. This means that the effective heat capacity of the North Atlantic for our calculations increases to over 420 MJ/C/m² of ocean surface- so our 1.9 Gigajoules/m² seasonal heating-cooling is only really capable of changing the temperature of the North Atlantic at 40N by 4.5C at most!

This part of the North Atlantic at near 40N has a mean temperature a little warmer than the mean global average because air subsiding in the subtropical high is warm having originated (largely) over the tropics; also as pointed out above the summer estimates for solar insolation are a little conservative. Mean temperatures throughout the year are 15C, which given the possible amplitude variations in sea-surface temperature mean that the North Atlantic can reach 18C at the end of summer but fail to cool below 12C by late winter.

Cold air from North America can affect the North Atlantic at 40N, but given the heat capacity of the ocean and the persistence of the subtropical high in this region the North Atlantic at 40N will still never cool below 10C even by early March. And that discounts the influence of the North Atlantic drift (bringing warm waters from even further south) and the ongoing fact of warm advection from the subsidence of air (via the subtropical high) that has its origins in the deep tropics!

So during the mid-winter period the North Atlantic at 40N will not be colder than 12C (and will probably be a degree or so warmer than this further to the east). The question is, is this sufficient to mean frost-free conditions for the UK??

Well, let us assume a parcel of air moves from 40N over the North Atlantic in an east-NE'ly direction towards northern Britain. This airmass moves at 15 mph and moves 2000 miles to reach northern Britain in just five and a half days. The net radiative heat loss of the entire airmass averages 10 MJ/m²/day over the average latitude of its transition towards the UK (47.5N, this value is typical for a moist oceanic atmosphere over these latitudes in winter) whilst the specific heat capacity of the column of atmosphere moving east-NE is 12 MJ/m²/C, taking into account some condensation of moisture will occur but that the very high atmosphere is moving more directly west to east. The airmass would cool by just over 0.8C per day and it means that our airmass would (other things being equal) have a sea level temperature of about 7.5C on reaching the Cumbrian/SW Scotland Coast. Of course, other things are not equal because the airmass will be modulated from below by the North Atlantic as it moves over progressively cooler waters (though still well above freezing point) and by possible interaction with colder (returning Ferrel) Westerlies from higher latitudes aloft. However, this does serve to illustrate that enough heat is absorbed over lower latitudes of the North Atlantic to render the deep west to southwest airstreams reaching Britain mild (even in mid-winter).

But the next question is: Do stiff, moist and mild SW winds have to be a feature of our winters? Why do these necessarily occur and not bitterly cold north-easterlies off Siberia? To answer that question we need to look at the Earth's rotation and the application of the law of Conservation of Angular Momentum to the Global Winds. The differential heating of the deep tropics and higher latitudes play a role too.

In the deep tropics the Sun beats down strongly throughout the year: Near the equator there is a net heating of the Earth-Atmosphere system that results from the excess of solar insolation over outgoing radiation that adds a net 1.5 Gigajoules of heat energy per square metre each year. This excess energy results in the hot seas and hot, steamy jungles near the equator which in turn power the myriad clusters of thunderstorms that define the Intertropical Convergence Zone (ITCZ). Winds blow from relatively cooler regions (with correspondingly denser air) well to the north and south of the ITCZ: Because of the rotation of the Earth these winds blowing towards the ITCZ start with less absolute westerly angular momentum than the equator which (furthest from the axis of Earth's rotation) moves west to east at 1000 miles per day; hence the winds converging on the ITCZ blow in more from the east relative to the equatorial lands upon which they encounter. In the Northern Hemisphere, north of the ITCZ, these are the NE Trade Winds.

Now these NE winds blow in a direction counter to the Earth's rotation and their frictional interaction with the land and sea over which they blow imparts westerly momentum to the atmosphere whilst trying to retard the Earth's rotation by a very small amount. The excess Westerly momentum has to go somewhere, otherwise the Earth would slow down over time and the upper atmosphere would start moving from west to east at many 1000's of miles per hour- and eventually either shoot off into space through great centrifugal force or cause utterly devastating wind-storms where convection and down-draughts brought the upper air to the surface. Clearly this does not happen, which means that the forces of westerly and easterly winds must balance over the globe.

Now the heat of the equator compared to the cooler regions around 35N during the Northern Winter are quite suffice to cause surface pressure differences of 20 milibars beween 35N and 5N: This suffices to cause persistent 15 mph NE Trade Winds over this entire latitude range all around the World. Now, the frictional impact of these winds on any given surface quadruples with a doubling of the speed so 30 mph SW winds over just quarter of the area would provide the sink for the atmospheric westerly momentum caused by the NE Trade Winds. However, the Westerlies in higher latitudes have to blow harder because the surfaces there are closer to the axis of the Earth's rotation: It follows that at 60N double the force will be required to have the same effect as near the equator! To counteract the effect of the 15 mph NE Trade Winds between 35N and 5N there needs to be- between 40N and 60N- 26 mph SW winds assuming that there are not also easterly winds in high latitudes. The winds in higher latitudes will infact be more from the west-SW (due to a stronger Coriolis Effect) so this speed reduces a bit to 24 mph all around the Northern Hemisphere between 40N and 60N; however easterlies in high latitudes and easterlies associated with high-pressure over Siberia and Mongolia both increases the need for a greater sink for atmospheric Westerly momentum and removes the area of mid-latitudes whereby this could be achieved. That would dictate a need for 30 mph Westerly/SW winds blowing towards NW Europe.

However, mountain ranges in the Northern Hemisphere (such as the Rockies in North America, the Pamirs in Central Asia, etc) intercept the much strong westerly winds that encircle the Arctic at elevation and so are a major sink for this net "Westerly momentum", and the outlet of such momentum is loaded heavily to locations with violent westerly gales (the frictional force of the wind goes up with the square of its speed). This explains why winds of 26 mph from the west or SW don't blow most of the time over Britain in winter (though it may well have seemed like it in December 2013!). It does, however explain why the prevailing winter winds in Britain (particularly in the North) come from the west and south-west; and the numbers are perfectly adequate to demonstrate scope for there to be a continuous flow of mild and moist air over the Region for much of the winter.

So then, the heat balance of the North Atlantic at 40N, the strong equatorial sun driving the ITCZ and the Trade Winds and the resultant need for Westerlies to act as a sink to counterract the frictional effect of all those NE Trade Winds (again caused by the Earth's rotation, and all dictated by the Law of Conservation of Angular Momentum);- ALTOGETHER RESULTS in the windy, wet, sometimes stormy,- but yet consistently mild autumn/winter weather that we have had across the country this year!

All these physical laws governing the Global Weather patterns explain why I am unconvinced by some meteorologists assertions that massive "Blocking highs" can form with impunity and bring bitter NE winds across vast areas of middle latitudes for months on end in the winter. This does happen occasionally over quite wide areas and they can last for some weeks (i.e. December 2010); but this tends to require a wholesale shift of the zones of outlet of "Westerly Momentum" into lower latitudes with the jet streams hitting the Himalayas in a major way. This tends not to happen without something pretty major interrupting the Global Circulation.

I hope you found the calculations and explanations for our mild and stormy winter weather interesting!

Ian Pennell

Edited January 16, 2014 by Osbourne One-Nil

PolarWarsaw · January 3, 2014

Looks like a very interesting read, but it's too big (font wise) to read properly. Did you happen to spill pop on your CAPS button? Any chance this can be made smaller as it's easier to read.

feb1991blizzard · January 3, 2014

Looks like a very interesting read, but it's too big (font wise) to read properly. Did you happen to spill pop on your CAPS button? Any chance this can be made smaller as it's easier to read.

Yes.