Angular Momentum Spins Up the Winds of Climate

#2068 "Mattawa Outward Bound" 24x48
Coriolis might have been deflecting our canoes to the right...
and I am pretty certain I saw vortices and deformation zones in the
current of the Mattawa... but angular momentum was preserved. 

Angular momentum is conserved in a closed system. Rotational energy is angular momentum that can be converted from one form to another but never lost - although we might not be able to get it back either.  

w= angular speed or rotation

The figure skater is everyone’s perfect analogy for angular momentum, although the skater is not a perfect closed system. The sound of the skate is a loss of rotational energy. Friction with the air and ice is another energy loss. The rotational speed is controlled by the "moment of the mass distribution" but with time, even the best skater will spin down to a standstill. The figure skater can control their rate of rotation. If they extend their arms and legs outward from the axis of rotation, their moment of mass distribution increases and they spin slower. Skaters spin faster by pulling their body inward to their rotational axis thus minimizing their moment of mass distribution. In all cases, their angular momentum is unchanged although they gradually spin down as that energy is lost.  The conservation of angular momentum through the re-distribution of mass can also be also studied using a swivel chair and exercise weights but the artistic impression points will not be nearly as impressive. 

Earth and the Moon as
seen from Mars orbit

Consider the earth. You might think that the spherical blue marble spinning in the vacuum of space is a perfectly rigid and closed system.  The earth might be close to that ideal but consider that scientists study the variable length of day (LOD). The "LOD" has actually increased over the 4.54 billion year history of the Earth due to tidal effects and the dissipation of angular momentum. The earth is spinning down. 

The Moon at about 1/81 the mass of Earth, is slowing the Earth's rotation. Days get about 2 milliseconds longer every 100 years. The moon has already stopped spinning and the tidal locking process will theoretically do the same to the Earth in 50 billion years. Weather would be very different on a stationary planet and your Coriolis hand will no longer work very well.  

Length of Day Deviations since 1965

The LOD also fluctuates on shorter times scales.  These miniscule variations have periods that range from a few weeks to years.

Outer Mantle - Liquid Outer Core- Solid Inner Core

The total angular momentum of Earth as a whole system must be constant. The relative movements and mass redistribution of Earth's core, mantle, crust, oceans, atmosphere, and cryosphere (cryosphere is the frozen water part of the Earth system) will result in variations in the spin (LOD) just  like the figure skater. A change of the angular momentum in one region must necessarily be balanced by angular momentum changes in the other regions.

The mass of the earth is far from evenly distributed. The continental plates are shifting. The polar ice caps are calving and breaking apart. Glaciers are melting. Mass is slowly being redistributed. The 'decade fluctuations' of Earth's rotation rate and LOD are thought to result from these fluctuations.

The LOD also varies significantly over time scales down to weeks.  We can blame these on the weather. Consider the water cycle for instance. Water evapourates into water vapour and rises, increasing the moment of that mass distribution. Precipitation falls to the ground and the moment of mass distribution decreases again. Storms can move this precipitation toward the poles and these movements also decrease the moment of mass distribution on the spherical globe. The increasing temperatures of climate change allow about 7 percent more water vapour to be held in the atmosphere for every degree Celsius of increase. The moment of inertia for that increased amount of water vapour higher in the atmosphere would be expected to slow down the Earth's spin - a longer LOD results. 

Observational evidence shows that there is no significant time delay between the change of  the atmospheric angular momentum and the corresponding impact on the LOD. The atmosphere and solid Earth are strongly coupled due to surface friction with a time constant of only about 7 days which is the spin-down time of the Ekman layer. We met Vagn Walfrid Ekman (1874 – 1954) in "Meteorology Meets Oceanography". This spin-down time is how long it takes to transfer atmospheric axial angular momentum to the Earth's surface and vice versa.

We need only consider the component of the zonal wind  (along the lines of latitude) at the ground to consider the transfer of axial angular momentum between the Earth and atmosphere. Textbooks  describe the rigid rotation of the atmosphere with the zonal wind with a speed of "u" at the equator relative to the ground. Super-rotation of the rigid atmosphere is when u > 0 and the rigid atmosphere is  rotating faster than the earth. If  u < 0 indicates then the rigid atmosphere is rotating slower than the Earth and "retrograding". The meridional wind (along the lines of longitude) and the vertical wind move the atmospheric angular momentum around the globe but these must balance out with time - due to the weather which is next week's Science Tuesday. 

Climatic Global Wind Patterns 

Surface friction allows the atmosphere to gain angular momentum from the Earth in the case of the atmospheric retrograde rotation or release it to Earth in the case of super-rotation. In the climatic average, the ground level zonal wind-component responsible for rigid rotation must be zero. This fact can explain the global wind patterns. The prevailing winds in the tropics and over the poles are easterly trade winds. Between 30 and 60 degrees the winds are westerly.  The atmosphere gains angular momentum from the Earth at low and high latitudes and repays that same amount back to the mid latitudes. Nature likes a balance. 

These musings and the posts of the last several weeks have been intended to ponder how complex yet beautiful the moving atmosphere can be - wind. We can now better understand the winds of weather from first principles - pressure gradient force, Coriolis force, centrifugal force, friction and finally the winds of climate (angular momentum balances). Some brilliant scientists were curious and discovered these natural wonders out over the last couple of centuries. It is important to remember these natural wonders and the scientists as well. 

The LOD might vary by a fraction of a millisecond as the atmospheric angular momentum is moved around the globe but that is not going to impact any forecast. Meteorologists simply do not have the time to worry about the LOD or to think of the angular momentum of the Earth and its components in order to forecast the wind. But next week we will look how these concepts might be used to better understand storms and the weather - know the wind; know the weather. Please stay tuned... 

Warmest regards and keep your paddle in the water,

Phil the Forecaster Chadwick