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A select few Derivations of Climate Physics

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  • Course
  • Physics
  • Institution
  • Swansea University (SWAN)
  • Book
  • Elementary Climate Physics

Climate Physics derivations such as -Solar Constant -Adiabatic Lapse Rate -Poisson's equation (potential temperature) -Pressure using the Hydrostatic equation

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Document information

  • March 21, 2024
  • 9
  • 2023/2024
  • Class notes
  • Dirk
  • Select classes

Subjects

  • climate physics
  • solar constant
  • lapse rate
  • climate
  • adiabatic lapse rate
  • potential temperature
  • pressure
  • hydrostatic equation
  • poisson equation
  • vertical temperature profile

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USEFUL DERIVATIONS


Contents

1

1 Solar Constant 2

2 Pressure using Hydrostatic Equation 3

3 Adiabatic Lapse Rate 5

4 Poisson’s Equation/ Potential Temperature 7




1

, 1 Solar Constant




Solar constant S is defined as the amount of energy per meter squared received at the mean
sun-Earth radius.


We assume that we are considering a black-body so the total amount of radiation emitted from
the sun is


B(T ) = σT 4 [W m−2 ]


Power of the sun can be defined as


PSun = σT 4 × 4πRSun
2




Now we can define the solar constant as

2
S= PSun
2
4πRSE
= σTs4 ( RR2s )
SE

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