Lecture 4 Effects of Cumulus on Large Scale Heat Budgets

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Lecture 4Effects 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

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Why?

• We can take observations at scales of 100s 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

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Define energy
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Relationship with 1st Law
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Mean Governing Equations
condensation
Average product gt includes subgrid scale
correlations, i.e. convection effects
evaporation
radiation
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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
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Apparent Moist Static Energy Source
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Integrate Q1
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Integrate Q2
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Check on Accuracy
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Cloud Model(Use Top Hat Averaging)
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Average includes cloud and environment
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Average includes cloud and environment
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Diagnose vertical mass flux
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Generalize a bit more
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Note the observable Q1, Q2 and QR imply effect of
cloud ensemble
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Cloud Model
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Idealization of Clouds
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Conservation Eqs. for individual cloud i
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Saturation Moist Static Energy
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Simplify
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Assumptions
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Assumptions
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Assumptions
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Summary
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Schematic of Model
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Relationship between clouds and Q1, Q2
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Total Ensemble Effect
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Conditions at Cloud Base
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Cloud Base (Continued)
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Iterative Solution
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Diagnostic flow from data
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Subgrid scale forcing Implied from large scale
flow
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Subgrid scale forcing Implied from large scale
flow