# 氣溫垂直遞減率

## 數學表示

${\displaystyle \gamma =-{\frac {dT}{dz}}}$

${\displaystyle \gamma }$為氣溫垂直遞減率，T為溫度，z為海拔高度。

## 種類

• 環境溫度遞減率 – 平穩大氣下，氣溫隨海拔變化的比率
• 絕熱遞減率 – 固定量的空氣絕熱上升或下降時，氣溫隨海拔變化的比率。絕熱遞減率有兩種：[1]
• 乾絕熱直減率
• 飽和絕熱直減率

${\displaystyle PdV=-VdP/\gamma }$

${\displaystyle mc_{v}dT-VdP/\gamma =0}$

${\displaystyle c_{p}dT-\alpha dP=0}$

${\displaystyle dP=-\rho gdz}$

${\displaystyle \Gamma _{d}=-{\frac {dT}{dz}}={\frac {g}{c_{p}}}=9.8\ ^{\circ }\mathrm {C} /\mathrm {km} }$

${\displaystyle \Gamma _{w}=g\,{\frac {1+{\dfrac {H_{v}\,r}{R_{sd}\,T}}}{c_{pd}+{\dfrac {H_{v}^{2}\,r}{R_{sw}\,T^{2}}}}}=g\,{\frac {1+{\dfrac {H_{v}\,r}{R_{sd}\,T}}}{c_{pd}+{\dfrac {H_{v}^{2}\,r\,\epsilon }{R_{sd}\,T^{2}}}}}}$

${\displaystyle \Gamma _{w}}$ =飽和絕熱遞減率=K/m
${\displaystyle g}$ =地球重力加速度=9.8076 m/s2
${\displaystyle H_{v}}$ =水的汽化熱=2501000 J/kg
${\displaystyle R_{sd}}$ =乾燥空氣的氣體常數= 287 J kg−1 K−1
${\displaystyle R_{sw}}$ =水蒸氣的氣體常數= 461.5 J kg−1 K−1
${\displaystyle \epsilon ={\frac {R_{sd}}{R_{sw}}}}$ ＝乾燥空氣與水蒸氣的氣體常數的無因次比值=0.622
${\displaystyle e}$ =飽和空氣的水蒸氣分壓
${\displaystyle p}$ =飽和空氣的氣壓
${\displaystyle r=\epsilon e/(p-e)}$ =水蒸氣的質量與乾燥空氣質量的混合比例
${\displaystyle T}$ =飽和空氣的溫度，單位K
${\displaystyle c_{pd}}$ =乾燥空氣在定壓下的比熱=

1003.5 J kg−1 K−1

## 參考

1. ^ Adiabatic Lapse Rate,頁面存檔備份，存於互聯網檔案館IUPAC Goldbook
2. ^ Danielson, Levin, and Abrams, Meteorology, McGraw Hill, 2003
3. ^ Landau and Lifshitz, Fluid Mechanics, Pergamon, 1979
4. ^ Kittel and Kroemer, Thermal Physics, Freeman, 1980; chapter 6, problem 11頁面存檔備份，存於互聯網檔案館
5. ^ 存档副本. [2016-01-06]. （原始內容存檔於2016-03-03）.