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    The fundamentals of Atmospheric Angular Momentum


    samadamsuk
    Paul

    Please be aware that these comments were copied here from a forum thread and that the date and time shown for each comment may not be accurate.

    Message added by Paul

    Hi All,

    I'm struggling a bit getting my head around the AM side of things, before I move on to the GWO orbits etc .. to be honest I have for a long time!, so I'm hoping I can tap in to the hive mind and get a better understanding ..

    My understanding is:

    1)Angular momentum is a property of the mass in motion about the earths axis (Understood!)

    2)That 'momentum' is from a combination of: The rotation speed, the mass, the length of the radius arm. In a closed system (i.e. the whole earth) AM is conserved. (Understood!)

    3)(Like a skater) - if the length of the radius arm is decreased, the rotation speed increases as the mass stays the same .. I get that bit (unless I have that incorrect of course - Understood!)

    4)I have read: Eastward winds circulate around the equator, in the same direction as the earths rotation. This means that parcels of air rotate more rapidly than the earth does (Understood!)

    5)I have also read: The frictional drag (surface friction I presume) that is acting to slow these winds down, transfers angular momentum from the earth to the atmosphere.... (Erm ...)

    This is the point I start dribbling.. to me if the easterly winds are travelling faster than the earths rotation, then any friction with the surface will slow these winds and transfer that energy to speeding up the earths rotation! (I have read that the  Length of day DOES change, much to my surprise!) - but if so then that's not in my book 'transfer of angular momentum from the earth to the atmosphere' - its the opposite.

    I also read, and didn't quite understand, that the direction of the air packet itself adds/subtracts to the overall mass from the centre, to the end of the radius arm in a rotating system - but this didn't clear anything up, unless that detracts from rotation in itself..

    In short, I'm a deeply confused man .. can you help! Springboarding off into GWO orbits and mountain torques won't help me - I need to get the absolute fundamentals here!

    Many thanks, Samos

     

     

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    I think I might have got the earths rotation the wrong way round! - in which case, point 5 makes more sense: 

    Friction Torque (From: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.225.904&rep=rep1&type=pdf)
    The friction torque is the torque that is exerted on the earth’s surface due to the frictional force that occurs because of the wind directly above the Earth’s surface moving relative to the solid earth. If there is an net global westerly surface wind (i.e. a surface wind from the west) the atmosphere will speed the earth’s rotation up, transfer angular momentum to the earth, and thus the atmosphere loses angular momentum. Analogously, if there is a net easterly surface wind (i.e. a surface wind from the east), the atmosphere slows down the rotation of the earth and angular momentum is transferred from the earth to the atmosphere

    That makes more sense... in which case as the earth is a closed system, that means the atmosphere as a whole wants to spend that new angular momentum windfall so we see polewards AM transport and increased westerlies at higher lattitudes to balance things out (?)..

    While these increased westerly's are ruining my golf it looks like mountain torques to the rescue to re-address the balance and bring the earths rotation speed back up:

    Mountain Torque is a function of pressure and orography and is the ‘turning force’ exerted due to a difference in pressure across any raised surface on the earth, but most significantly, mountains or mountain massifs. Consider a mountain with a high pressure on the west side of a mountain and low pressure on the east. The pressure system will exert an eastward torque that causes the earth to increase it’s rate of rotation, imparting angular momentum from the atmosphere to the solid earth. The opposite case, where there is higher pressure on the east side of the mountain, will slow the earth’s rotation down, reducing the solid earth’s angular momentum, and imparting it to the atmosphere. 
     

    As I understand it there is a time period where these negative and positive torques (fluxes) play out,  another snippet from the above link below

    Torques: A torque that increases the angular momentum of the atmosphere to be a positive torque, and one that decreases the angular momentum of the earth to be a negative one. 

    I can see now why the MJO and ENSO and all those shenanigans effect the AAM budget - they polarise the outcome due to persistant surface wind anomalies at the equator.

     

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    I'm aware I'm chatting to my self here .. I'll get help.. 

    Lastly then, I can see very roughly how the GWO fits in: 

    The GWO framework is similar to the MaddenJulian Oscillation (MJO) (Wheeler and Hendon, 2004) but incorporates midlatitude processes such as momentum transports and mountain/frictional torque events. The GWO is directly related to the variability of atmospheric angular momentum (AAM) and AAM tendency (dAAM/dt) which utilizes the GSDM phase space paradigm (Figure 1), categorized by eight stages (octants), like the MJO but shifted 22.5º.

    I'll try and get my head around the below another day! 


    image.thumb.png.003a79391ad70e0a3d19f7350216c381.png

    If anyone can add anything or set me straight, that would be great!

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    10 hours ago, samadamsuk said:

    I'm aware I'm chatting to my self here .. I'll get help.. 

    Lastly then, I can see very roughly how the GWO fits in: 

    The GWO framework is similar to the MaddenJulian Oscillation (MJO) (Wheeler and Hendon, 2004) but incorporates midlatitude processes such as momentum transports and mountain/frictional torque events. The GWO is directly related to the variability of atmospheric angular momentum (AAM) and AAM tendency (dAAM/dt) which utilizes the GSDM phase space paradigm (Figure 1), categorized by eight stages (octants), like the MJO but shifted 22.5º.

    I'll try and get my head around the below another day! 


    image.thumb.png.003a79391ad70e0a3d19f7350216c381.png

    If anyone can add anything or set me straight, that would be great!

    Keep going SMS...

    I am learning with you!

    Are you a member at Cirencester?

    MIA

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    Hi MIA,

    I will have a crack at the GWO tonight hopefully, and post my findings along with a big dollop of confusion! I'm still to not sure of the actual mechanism for increased atmospheric angular momentum above the equator to be balanced out at higher latitudes, but hopefully there are answers when I look at the GWO!

    I'm very close to Cirencester (South Cerney) - are you from this area?

     

    :) Sam

     

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    Hi All,

    I thought I'd put my findings on AAM into something that I think makes sense! I always worry that a guide is condescending - if it comes across as that, that's certainly not the intention - I need to break things down to very basic principles to understand something, so hopefully for those like me this'll take away a bit of the effort to wrap your head around AAM! Next will be GWO/GSDM.

    A big thankyou to Tamara for reaching out to me, and she is clearly as surprisingly nice as she is clever! Any mistakes anyone, point them out and I'll adjust.

     

    Principle of atmospheric angular momentum:

    To me I think the best approach to understand AM is to think about motion. 


    Straight line motion:
    If you push an object in space in a straight line, it takes energy to do that - the more mass there is in that object, the more energy it takes to push it!
    Without any forces then acting against that motion, the object will continue on forever - that motion is conserved. 
    If you then slow it down, it takes energy to do that - importantly energy is not lost - if you did this experiment in a box , i.e. a closed system, no energy within that system would be gained or lost.


    Rotational motion:
    The same principle of conservation of motion works for the rotating earth. The earth was set in motion at the point it was created, so effectively a whole lot of mass rotating around a point - it's still mass in motion.
    Important to note here that it's now important where the bulk of that mass is in relation to the centre of rotation .
    In a closed system (this time the whole earth + atmosphere), this motion is conserved, along the same principle as straight line motion.

    How are things conserved:    
    Rotation speed and mass distribution are the two parts of the equation - I hate equations though, so some analogies:
    The best analogy I can think of is to think of inflating the size and mass of the earth to the size of Jupiter - it's easy to see that the rotational speed would slow right down, unless it was given a push from an external source.
    Of course, inflating it to just the size of Jupiter, but keeping the mass the same, its relatively easy to see that the rotation speed would stay the same.


        The earth is a closed system - 
                1)No energy added, or taken away to the rotation
                2)No mass added, or taken away.


    There are (of course!, or why bother doing this!) though local regions around the earth that this balance is upset.
            How?
            1)Take a point above the equator, where easterly winds are flowing
            2)Take a line from the centre of the earth, up to 10HPA in the upper atmosphere - this is pretty well the total mass rotating around that     central point.
            3)The earth itself is rotating at say 1000 MPH. 
            4)The wind - relative to the point on the earths surface, is easterly at 20 Mph.
            5)In absolute terms, the atmosphere is rotating at 980 Mph!!
            6)That creates an imbalance - the same amount of mass (earth + atmosphere), rotating slower because of the wind of the wind direction.


    What is the result?
    It means that locally, the wind causes friction against the earths surface, slowing down the rotation of the earth, and so the momentum (angular momentum) is effectively transferred to the atmosphere.


    Surface Frictional Torque:
    The above is an example of surface frictional torque, working against the direction of the earths rotation. As different latitude have different prevailing wind directions, wind/friction can either impart AM to the atmosphere (tropics, poles), or with opposite wind flow, speed up the earths rotation and so impart AM to the earth (mid latitudes).


    Mountain Torques:    
    Mountain torques follow the same principle of the relative wind direction imparting AM to either the atmosphere, or earth, but work by creating a pressure difference from one side or the other.

    What the flux ?
    The above imbalances are imbalances on a regional scale. Angular momentum across the earth as a whole, is ultimately conserved. This is the most important point - an increase in AM in the atmosphere above the tropics will then propagate northwards via mass transport, and eddies, to the mid latitudes where the surface friction & mountains are acting to readdress the balance, and impart that AM back in to speeding up the earths rotation. This 'transmission' of one region to another of imparted AM is called the Flux.


    How is this useful for weather forecasting?
    The atmosphere across earth as a whole is working towards an equilibrium, a neutral state where the earth is rotation at it's average speed, and the atmosphere at average rotational speed. 
    The GWO tracks the journey of the global atmosphere as this imbalance/rebalance plays out in the global averaged AAM anomaly, and the fluxes that happen during the various stages have implications for all regions of the globe. 
    Numerical models do not incorporate the AM balance - they're concerned with discrete packets of atmosphere and their interaction over time to build out a global picture over time, and so this large scale process is of great interest. 
    The GSDM (Global Synoptic Dynamic Model) is (I believe) more of a framework than a computational forecasting model, but is an attempt to use the AAM/GWO cycle, along with the various weather phenomena, to combine the different frequencies and lifecycles of these phenomena into a more complete picture of what is happening.


    The Global picture:
    There is a global how angular momentum is effected per region (the GWO is concerned with the plus/minus anomaly, so this is the underlying standard situation on average) - there are however large variations from season to season - the below diagram takes a bit of getting used to! but bear with me..

        
     
    Below: At approx. 45 degrees north, the Frictional Torque (BLUE) is transferring Angular momentum from the atmosphere to the earth (Sink - the earth is spinning left to right, the wind is westerly (left to right) compared to this spin, so imparting additional rotation to the earth.


    The mountain Torque (RED) is also adding a sink, westerlies in the direction of rotation come up against the mountains.

    image.thumb.png.337df7d234b481803cad0edabc81fb69.png

     

    Below: (BLUE)At approx. 15N the trade winds are doing their thing and heading easterly, so an upwards arrow meaning surface friction slowing down the earth, and this imparting Angular Momentum to the atmosphere (17 Hadley's), and also mountain torque slowing imparting more angular momentum to the atmosphere, slowing down the earth, at (7 Hadley's)

    Clearly (I think!) angular momentum is being transferred to the atmosphere near the equator, and from the atmosphere to the earth at higher latitudes. 

    (RED)The horizontal arrows show atmospheric flux (The transport of Angular Momentum through the atmosphere from one region to another). Here it is being transported across 30N, poleward, and is large for the year as an average (and smallest in (June, July, August), largest (December, January, February).
     

    image.thumb.png.06ff1a6f16ffd9e25d886e750c567d3a.png


    Below: (RED)Due to the easterly regime in the polar part of the global circulation, the frictional, and mountain torques, are again imparting angular momentum to the atmosphere, as the wind direction is acting to slow the earths rotation and take on the AM within the atmosphere. Numbers are way down on the lower latitudes, and the AM flux from polar to mid latitude regions are typically 10% of the opposite moving AM in mid latitudes.

    Interestingly, there is also cross equator flux (Blue) - in the NH summer this is from SH to NH (14 Hadley's), and in the NW winter from NH to SH (4 Hadley's).

    image.thumb.png.d00f4ae500cf73569b736311b34e657f.png

    For reference, the full description: Horizontal arrows show atmospheric flux, encircled values show the contribution by miscellaneous torques, text at the bottom: Mountain Torque - italicised, frictional torque - upright, 

     

    A few general things to note:
    The seasonal variation of frictional torque in the NH is greater in the NH than the SH.
    Frictional Torque in each hemisphere is largest in that hemispheres winter (42vs14 in NH, 39vs30 in SH - a smaller range due to the surface being more % water)
    The principle source of momentum within the polar cap is mountain torque (values in italics, vertical arrows)
    Frictional Torques:
    Both eastward torque in the tropics, and westward torque in the temperate latitudes are stronger in the southern hemisphere than the NH.    
    There is a large annual variation in the tropics, with torque strongest in the  tropical region of the hemisphere that is experiencing winter.
    The annual variation is large in the temperate latitudes of the NH, but small in the SH.
    Mountain Torques:
    Mountain torques are most significant in the NH.
    Mountain torques are almost as large as frictional torques in spring and summer.
    Mountain torques generally drain momentum in middle latitudes (Sink), and impart eastward momentum in both high latitudes and the tropics (Source)
     

    Samos :)

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    Wow SMS

    I nearly understood the whole of it on my first read.!!

    Well done.

    As to golf -

    The wife and I play a lot of golf together on travels around the UK.

    We use it as a means of seeing the whole of the UK.  We love it!

    She has a friend who lives in Minchinhampton who is very poorly.

    When we visit her we take the golf clubs....

    So we play the old course (wonderful!), and more recently we have played the main course there (Cirencester).

    I have played about 1200 courses now in the UK. About a half of those that can be played.!!

    I hope to be able to complete many more!

    Not hinting by the way!

    MIA

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    Hi MIA,

    Glad it was readable!

    Life's a search for good people - would love to join you for a game one-day!

    BR, Samos

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