Dynamics

1. 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)

2. 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

3. 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:

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. Dynamics • Energetics of General Circulation

11. Dynamics Q/t • Energetics of General Circulation Latent rLq Internal rcvT Evap. -L(e-c) Friction rgw -uP Potential rgz Kinetic (1/2u2) -u Friction

12. Dynamics • Energetics of General Circulation

13. Dynamics • Energetics of General Circulation

14. Dynamics • Energetics of General Circulation

15. Dynamics • Energetics of General Circulation

16. Dynamics • Energetics of General Circulation