General Circulation and Kinetic Energy

Model output from Warren M. Washington, 1969: http://www.ucar.edu/library/collections/washington/timeline/timeline.php?startdate=1963-01-01&enddate=1969-12-31

Application of the Primitive Equations• Primitive equations govern the evolution of the atmosphere

and therefore are useful to forecast the weather and also for climate simulations. They are:

pc

J

p

T

dt

dT

z

pwpdp

t

psss

ps s

VV0

Vp

p

RT

p

FVkV

fdt

d HORIZONTAL MOTION 2 COMPONENTS u,v (PROGNOSTIC)

HYPSOMETRIC EQUATION: DIAGNOSTIC

THERMODYNAMIC ENERGY EQUATION (PROGNOSTIC)

CONTINUITY

BOTTOM BOUNDARY CONDITIONS

• 1) Imagine that you are using an atmospheric model of primitive equations. This model starts from a state of rest. The atmosphere is stably stratified and there is friction at the surface

• t=0 :Tropics begin to warm and polar regions coool in response to the distribution of diabatic heating. Changes in geopotential will begin

• Resulting pressure gradients will start the circulation in upper levels (like a planetary sea breeze as we discussed before)

• 2) Changes in the distribution of mass will occur due to the upper troposphere circulation. Mass will increase in high latitudes => High pressure at the surface and decrease in the tropics => low pressure at the surface

• As a consequence a circulation pole-equator will start at the surface (gradient forces in the movement equation). Coriolis will deflect westward the pole-equator low level circulation

• 3) Coriolis deflects eastward the upper-level Equator-Pole circulation

• Transport of westerly momentum from low to high latitudes (conservation of momentum)

• 4) The flow becomes progressively more zonal with each successive time step until the geostrophic balance between coriolis and gradient force is observed

NH

• 5) As required by the thermal wind balance, the vertical wind shear between the low level easterlies and upper level westerlies increases in proportion to the strengthening equator-to-pole temperature gradient forced by the meridional gradient of the diabatic heating

• Frictional drag limits the strength of the surface easterlies but the westerlies aloft become stronger with each successive time step

• When the meridional temperature gradient reaches a critical value, the simulated circulation changes: baroclinic instability spontaneously breaks out in midlatitudes imparting a wave like character to the flow.

• In the developing waves, warm, humid subtropical air masses flow poleward ahead of the eastward moving surface cyclones

• Cold, dry polar air masses flow equatorward behind the cyclones

Northern Hemisphere

• ~45o net poleward flux of sensible and latent heat arresting the buildup of the equator-to-pole temperature gradient

• Note the tilting of these waves

• The poleward moving air to east of the troughts exhibits a stronger westerly wind component than the equatorward moving air to the west of the troughs : net poleward flux of westerly momentum from the subtropics to midlatitudes

• Surface winds in midlatitudes shift from easterly to westerly

• Ferrel cell is associated with the baroclinic waves and is characterized by ascent on the polar flank and descent on the equatorward flank

• With the development of baroclinic waves the Hadley cell withdraw into the tropics and a subsidence develops at subtropical (~30o) latitudes: These regions coincide with the subtropical anticyclones

The kinetic energy cycle: potential energy converted into kinetic energy

Frictional dissipation and Kinetic energy• Frictional dissipation at

the surface and in the atmosphere continually depletes the kinetic energy of the large-scale wind systems

• The source of kinetic energy is the release of potential energy through the sinking of colder, denser air and the rising of warmer, less dense air

• (lowering of the atmosphere’s center of mass)

• Color shading indicates the distribution of temperature and density, with cooler, denser fluid represented by blue. The sloping black lines represent pressure surface. When warm air rises and cold air sinks, the potential energy that is released does work on the horizontal field forcing to flow across the isobars from higher toward lower pressure

p

p

• The equation for the time rate of change of kinetic energy:

VFVV

V 2

2V

dt

d

dt

d

Frictional Force: dissipation of kinetic energy

The only source of Kinetic energy

VFVV

V 2

2V

dt

d

dt

d

• The dissipation term is more intense close to the Earth’s surface. It acts to reduce the wind speed. Coriolis is never strong enough to balance pressure gradient forces. The resulting imbalance and cross isobar flow toward lower pressure maintains the kinetic energy and the surface wind speed in the presence of frictional dissipation (remember that F is always opposite to the wind direction)

Conversion of potential to kinetic Energy in The Hadley Cell

OMEGA - January

HADLEY

July

Meridional Winds in the Hadley Cell

Pres

sure

January

OMEGA - January

HADLEY

Hadley cell: warm light air rises and cold denser air sinks: release potential energy and convert it into kinetic energy of the horizontal flowCells like that are referred to as:Thermally direct

FerrelFerrel

Ferrel cell: warm light sink and cold denser air rises: Thermally indirect

Other examples of direct cells:

• Monsoons (warm air ascend over continents and cold air descends over the oceans)

• Tropical cyclones (warm air ascends in the core of the cyclones)

Direct cells deplete atmosphere's reservoir of potential energy: what does restore it?

• 1) radiative transfer (warms the air in the tropics and cools in high latitudes (maintains the equator-to pole contrasts and pressure gradients):

2) release of latent heat by convective clouds

• warms the middle of the atmosphere and expands the atmosphere column.

• As the result air expands in the lower troposphere and compresses in the upper troposphere, lifting the air at intermediate levels and maintaining the height of the atmosphere’s center of mass against the lowering produced by thermally direct circulations

Surface Heating

Warming due to latent heat

Φ2

Φ1

Temperature: effect of convection on large scale in tropical regions

Next classes we will be talking about weather systems