虛溫

介紹

引言

${\displaystyle {R_{x}}={\frac {R^{*}}{M_{x}}}\,,}$

${\displaystyle {M_{air}}={\frac {e}{p}}M_{v}+{\frac {p_{d}}{p}}M_{d}\,,}$

${\displaystyle e}$${\displaystyle p_{d}}$${\displaystyle M_{v}}$${\displaystyle M_{d}}$分別代表水氣和乾空氣的莫耳質量。根據道爾頓分壓定律，氣體總壓可表示如下：

${\displaystyle {p}={p_{d}}+{e}\,.}$

推導過程

${\displaystyle {\rho }={\frac {m_{d}+m_{v}}{V}}=\rho _{d}+\rho _{v}\,,}$

${\displaystyle {e}=\rho _{v}R_{v}T\,}$ and ${\displaystyle {p_{d}}=\rho _{d}R_{d}T\,.}$

${\displaystyle {\rho }={\frac {p-e}{R_{d}T}}+{\frac {e}{R_{v}T}}\,.}$

${\displaystyle {p}={\rho }R_{d}T_{v}\,,}$

${\displaystyle {T_{v}}={\frac {T}{1-{\frac {e}{p}}(1-{\epsilon })}}\,.}$

形式變化

${\displaystyle {\frac {e}{p}}={\frac {w}{w+{\epsilon }}}\,,}$

${\displaystyle {T_{v}}=T{\frac {w+\epsilon }{\epsilon (1+w)}}\,.}$

${\displaystyle {T_{v}}\approx T(1+0.61w)\,.}$

${\displaystyle {T_{v}}\approx T+{\frac {w}{6}}\,.}$[3]

參考資料

1. ^ Bailey, Desmond T. Upper-air Monitoring. Meteorological Monitoring Guidance for Regulatory Modeling Applications (PDF). John Irwin. Research Triangle Park, NC: United States Environmental Protection Agency. February 2000: 9–14 [June 1987]. EPA-454/R-99-005.
2. ^ AMS Glossary. American Meteorological Society. [2014-06-30].
3. ^ U.S. Air Force. The Use of the Skew-T Log p Diagram in Analysis and Forecasting. United States Air Force. 1990: 4–9. AWS-TR79/006.
4. ^ The Effect of Neglecting the Virtual Temperature Correction on CAPE calculations, Weather and Forecasting 1994; 9: 625-629. American Meteorological Society. [2010-06-02].
5. ^ Tropical cyclone genesis potential index in climate models. International Research Institute for Climate and Society. [2009-12-10].