Math 2.0

Geophysics Definition

Hadley cell and Held–Hou model

Builds on Thermal windCoriolis force

Definition

Consider an atmosphere on a planet of radius aa rotating with angular speed Ω\Omega, with gravitational acceleration gg and latitude φ\varphi. A Hadley cell is a thermally direct meridional overturning circulation of the zonally averaged flow. It has rising motion near the equator, poleward flow aloft, sinking in the subtropics and equatorward flow near the surface.

The Held–Hou model is the steady, axisymmetric model of such a cell in a Boussinesq atmosphere of depth HH with the following assumptions.

  1. Without the circulation the atmosphere would be in radiative equilibrium. Its potential temperature would decrease from equator to pole by the fraction ΔH\Delta_H of a reference value θ0\theta_0.
  2. The upper, poleward branch conserves angular momentum and starts from rest at the equator, so its zonal wind is uM(φ)=Ωasin⁡2φ/cos⁡φu_M(\varphi) = \Omega a \sin^2 \varphi / \cos \varphi.
  3. The temperature in the cell is in thermal wind balance with uMu_M.
  4. The temperature is continuous at the poleward edge φH\varphi_H of the cell. The cell neither gains nor loses heat in total, so its mean temperature equals the mean radiative equilibrium temperature.

Remarks

In the small-angle approximation these assumptions determine the edge of the cell, φH=(53gHΔHΩ2a2)1/2.\varphi_H = \left( \frac{5}{3} \frac{g H \Delta_H}{\Omega^2 a^2} \right)^{1/2}. Example: for the Earth, g=9.81g = 9.81 m/s2^2, H=104H = 10^4 m, ΔH=1/3\Delta_H = 1/3, Ω=7.29×10−5\Omega = 7.29 \times 10^{-5} s−1^{-1} and a=6.37×106a = 6.37 \times 10^6 m give φH≈0.5\varphi_H \approx 0.5 rad, about 29∘29^\circ, close to the observed edge of the Hadley cell. The model predicts a strong westerly jet at φH\varphi_H and, by Coriolis deflection of the return flow, easterly winds near the surface in the tropics.

Non-example: the observed winds in the upper branch are weaker than uMu_M, because eddies carry momentum. A flow with such eddy fluxes does not satisfy assumption 2, and the model overestimates the subtropical jet.

The model also predicts that the cell widens as Ω\Omega decreases, a trend seen in simulations of slowly rotating planets.

Reading path

To understand this page from the ground up, read these 29 pages in order. The foundations come first.

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Cross product, concept, no evidence levelCross productconceptDerivative, concept, no evidence levelDerivativeconceptEuclidean space, object, no evidence levelEuclidean spaceobjectEuclidean vector, concept, no evidence levelEuclidean vectorconceptGeostrophic balance, concept, no evidence levelGeostrophic balanceconceptIdentity matrix, object, no evidence levelIdentity matrixobjectMatrix, definition, no evidence levelMatrixdefinitionOrdinary differential equation, concept, no evidence levelOrdinary differential…conceptVector space, definition, no evidence levelVector spacedefinitionVelocity, concept, no evidence levelVelocityconceptClassical mechanics, concept, no evidence levelClassical mechanicsconceptSquare matrix, definition, no evidence levelSquare matrixdefinitionTranspose, definition, no evidence levelTransposedefinitionLinear map, definition, no evidence levelLinear mapdefinitionMomentum, concept, no evidence levelMomentumconceptInertial frame of reference, concept, no evidence levelInertial frame of ref…conceptMultilinear map, definition, no evidence levelMultilinear mapdefinitionOrthogonal matrix, definition, no evidence levelOrthogonal matrixdefinitionNewton's laws of motion, statement, no evidence levelNewton's laws of moti…statementAlternating multilinear map, definition, no evidence levelAlternating multiline…definitionOrthogonal group, object, no evidence levelOrthogonal groupobjectDeterminant, definition, no evidence levelDeterminantdefinitionSpecial orthogonal group, object, no evidence levelSpecial orthogonal gr…objectAngular velocity, concept, no evidence levelAngular velocityconceptRotating reference frame, concept, no evidence levelRotating reference fr…conceptFictitious force, concept, no evidence levelFictitious forceconceptCoriolis force, concept, no evidence levelCoriolis forceconceptThermal wind, statement, no evidence levelThermal windstatementHadley cell and Held–Hou model, definition, no evidence levelHadley cell and Held–…definition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
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  1. Cross product concept
  2. Derivative concept
  3. Euclidean space object
  4. Euclidean vector concept
  5. Geostrophic balance concept
  6. Identity matrix object
  7. Matrix definition
  8. Ordinary differential equation concept
  9. Vector space definition
  10. Velocity concept
  11. Classical mechanics concept
  12. Square matrix definition
  13. Transpose definition
  14. Linear map definition
  15. Momentum concept
  16. Inertial frame of reference concept
  17. Multilinear map definition
  18. Orthogonal matrix definition
  19. Newton's laws of motion statement
  20. Alternating multilinear map definition
  21. Orthogonal group object
  22. Determinant definition
  23. Special orthogonal group object
  24. Angular velocity concept
  25. Rotating reference frame concept
  26. Fictitious force concept
  27. Coriolis force concept
  28. Thermal wind statement
  29. Hadley cell and Held–Hou model definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Hadley_cell
About this page
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Kinddefinition
WritingW0 stub
MSC86A10, 76U60
DefinesHadley cell and Held–Hou model
UsesThermal wind, Coriolis force
Changed3 November 2026

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