Dynamics
Energetics of General Circulation
In the previous lecture we discussed the
characteristics of the general circulation of the
atmosphere
In today’s lecture we want to focus on how these
characteristics affect the energy balance in
different regions of the earth
• How the general circulation results in the transfer of
energy from the equator to the poles
• How the general circulation affects other climate variable
(namely moisture and momentum)
Dynamics
Energetics of General Circulation
The atmospheric energy balance can be written as:
Therefore, we can write the local rate of change as:
If we take the vertical average of this equation, we get four terms
related to energy in the atmosphere
•
•
•
•
Internal - energy associated with the temperature of the atmosphere
Potential - energy associated with vertical “position” of the atmosphere
Kinetic - energy associated with large-scale motions
Latent - energy associate with phase change of water
Hence, we can write the total energy of the atmosphere as:
We can estimate the size of the various terms
Dynamics
Energetics of General Circulation
If we assume a hydrostatic atmosphere, we can write the total
internal energy as:
Changing the vertical coordinate from z to p gives:
Next, we can write the potential energy as:
Integrating by parts gives:
Dynamics
Energetics of General Circulation
So we find that the ratio of the internal energy to the potential
energy is fixed:
This implies that much of the internal energy of the atmosphere is
required simply to maintain the potential energy associated with
the structure of the atmosphere (this is implicit in the hydrostatic
assumption)
We can now calculate the total kinetic energy:
If we assume that |u| ~ 15m/s, then the ratio of kinetic to total
internal energy (potential and internal) is:
Hence, kinetic energy is a very small fraction of the total energy in
the atmosphere
Dynamics
Energetics of General Circulation
It can be shown that of the total energy in the atmosphere, only
about 0.5% is available for conversion into kinetic energy (i.e. the
generation of motion); the rest is tied up in maintaining the
hydrostatic structure of the atmosphere
First we can write the change of potential energy as:
This implies that potential energy is converted through vertical
motions in the atmosphere
Dynamics
Energetics of General Circulation
Next we can write the change of internal energy as:
Here we see that internal energy is created/destroyed via heating
and work done via compression/expansion
If we use the momentum equation multiplied by u, we can
calculate the rate of change of kinetic energy:
Hence, kinetic energy is converted via work done against a
pressure gradient as well as work done against the force of gravity
From our discussion about internal energy, there was a term
related to:
This suggests a mechanism for converting internal energy to
kinetic energy via compression and expansion
Dynamics
Energetics of General Circulation
In addition, from before, the change in potential energy is related
to:
This suggests a mechanism for converting potential energy to
kinetic energy
The final term we need is the one related to latent heat:
Here, the evaporation/condensation term is essentially the
conversion of latent heat into sensible heat, I.e. it represents a
heating/cooling of the atmosphere
Hence, this suggests a mechanism for converting latent heat to
internal energy
Dynamics
Energetics of General Circulation
Now we can put all four terms together to get a sense of the
flow of energy within the atmospheric system
We can also estimate the zonal averages of the different
transport terms
Transport associated with mean and transient processes
Dynamics
Energetics of General Circulation
Just as the general circulation of the atmosphere transports
energy it also transports moisture
• This transport results in convergence and divergence of
moisture in particular regions of the globe
In addition, the general circulation also transports
momentum
Dynamics
Energetics of General Circulation
Form
Designation
Size
% of Total
Internal
rcvT
1800x105
J/m2
70%
Potential
rgz
700
27
Latent
rLq
70
2.7
Kinetic
(1/2)ru2
1.3
0.05
Dynamics
Energetics of General Circulation
Q/t
Latent
Evap.
rLq
Internal
-L(e-c)
rgw
Potential
rgz
rcvT
-uP
Friction
Kinetic
-u
r(1/2u2)
Friction
Dynamics
Energetics of General Circulation
Dynamics
Energetics of General Circulation
Dynamics
Energetics of General Circulation
Dynamics
Energetics of General Circulation
Dynamics
Energetics of General Circulation