1. Lorenz energy cycle…summary

2. Review… Energy is conserved in the absence of sources/sinks (equations must satisfy this!) Within the “total energy”, energy can be converted from one type to another (interesting!) –e.g., PE  KE Energy analysis of baroclinic waves (2-level QG model) leads to the idea of ZAPE  EAPE  EKE to maintain growth/amplification of the eddies We have now expanded this idea beyond “just” synoptic-scale mid- latitude eddies to all eddies and the entire atmosphere! We write: Now need to find equations for ZKE etc. (i.e., for d(ZKE)/dt etc.)

3. Review… We take the momentum equation & zonally average to get an equation for This equation is then multiplied by “ubar” to get an equation for ZKE! Alternatively - multiply mean vorticity equation by “psi”  same result. By this approach, we get a set of 4 equations for the evolution of ZKE, EKE, ZAPE & EAPE. These are shown in the Lorenz energy cycle. We notice common terms in the equations - each “conversion” term appears in two equations with opposite signs - representing an energy conversion! All we need to do now is to figure what motions & phenomena are associated with each energy conversion. The “full story” is at the end of section 10.4 in JRH - you should read it!

4. ZAPEEAPE ZKE EKE G G D D {ZAPE  EAPE} {ZEKE  EKE} {EAPE  EKE} {ZKE  ZAPE}

5. ZAPEEAPE {ZAPE  EAPE} Conversion involves product: North-south eddy heat fluxes building up west-east temperature gradients. Can be any eddies BUT certainly occurs in synoptic eddies. Observationally a STRONG conversion ZAPE  EAPE.

6. EAPE EKE {EAPE  EKE} Conversion involves product: Correlation of warm air rising AND cold air sinking at SAME latitudes. Prevalent in synoptic storms. Can be contributions from all types of eddies! Observationally a STRONG conversion EAPE  EKE.

7. ZKE EKE {ZEKE  EKE} Conversion involves the product: Eddies cause the north-south flux of westerly momentum, and this can converge into a region and accelerate the background winds there. This would diminish EKE and build up ZKE.

8. ZAPE ZKE {ZKE  ZAPE} Conversion involves product: This involves warm air rising AND cold air sinking in the zonally- averaged sense at DIFFERENT latitudes. Warm air  + cooler air  in Hadley cell  ZAPE  EAPE … strong circulation, weak N-S temp. gradient Cooler air  + warmer air  in Ferrel cell  EAPE  ZAPE … weaker circulation, strong N-S temp. gradient Net effect???

9. Read the summary of the energy cycle on page 343!