Lecture 4 Effects of Cumulus on Large Scale Heat Budgets Yanai, Esbensen and Chu (1972) The key paper outlining a framework for diagnostic studies of convective scale interaction
Why? We can take observations at scales of 100’s of km only We can notice that dynamic and thermodynamic evolution of the flow is occurring due to the impacts of cumulus scale features that we cannot directly see We need a consistent framework to assess this “apparent” effect
Define energy
Relationship with 1st Law
Mean Governing Equations condensation Average product => includes subgrid scale correlations, i.e. convection effects evaporation radiation
We can separate convection effects from effects of mena flow Apparent Heat Source Apparent Moisture Sink Large Scale Response Convective Scale Forcing Can be Measured Can be inferred
Apparent Moist Static Energy Source
Integrate Q1
Integrate Q2
Check on Accuracy
Cloud Model (Use Top Hat Averaging)
Average includes cloud and environment
Average includes cloud and environment
Diagnose vertical mass flux
Generalize a bit more
Note the observable Q1, Q2 and QR imply effect of cloud ensemble
Cloud Model
Idealization of Clouds
Conservation Eqs. for individual cloud “i”
Saturation Moist Static Energy
Simplify
Assumptions
Assumptions
Assumptions
Summary
Schematic of Model
Relationship between clouds and Q1, Q2
Total Ensemble Effect
Conditions at Cloud Base
Cloud Base (Continued)
Iterative Solution
Diagnostic flow from data
Subgrid scale forcing Implied from large scale flow
Subgrid scale forcing Implied from large scale flow