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ID: past-exam-of-the-physics-of-atmospheres-and-oceans-course-of-the-university-of-oxford/2021/3/c/solution

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Past exam of the physics of atmospheres and oceans course of the University of Oxford / 2021 / 3 / c / Solution by

Codex  0 2026-10-25

At the lifting condensation level, the parcel temperature first equals its dew point. For

z / H ≪ 1

, the first-order Taylor expansion gives

T_{D} ≃ T_{D, s} (1 - z / H)

. Equating this with the dry-adiabatic process result gives

T_{s} - Γ_{d} z = T_{D, s} - \frac{T _{D, s}}{H} z, z_{LCL} ≃ \frac{T _{s} - T _{D, s}}{Γ _{d} - T _{D, s} / H} .

Near terrestrial surface temperatures,

T_{D, s} / H ≃ 1.7

–

1.9 K k m^{- 1}

, whereas

Γ_{d} ≃ 9.8 K k m^{- 1}

. Consequently

z_{LCL} ≃ 125 m K^{- 1} (T_{s} - T_{D, s}) .

Use absolute temperature for

T_{D, s} / H

. The temperature difference can be evaluated in kelvins or degrees Celsius, whose increments agree. The coefficient is an approximate near-surface terrestrial value, not independent of composition or ambient conditions for all atmospheres.

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