Virtual temperature কী?

Example 21.4 (The air at Norman)

At the ground the sounding gives $p = 971.1\,\mathrm{hPa}$, $T = 19.0\,{}^{\circ}\mathrm{C}$ and a dew point of $18.5\,{}^{\circ}\mathrm{C}$. The vapour pressure is the saturation vapour pressure at the dew point, $e = e_s(18.5\,{}^{\circ}\mathrm{C}) = 21.5\,\mathrm{hPa}$ (Proposition 21.5 below). Then $r = 0.622 \times 21.5/(971.1 - 21.5) = 14.1\,\mathrm{g}/\mathrm{kg}$, $q = 13.9\,\mathrm{g}/\mathrm{kg}$, and $T_v - T = 0.61 \times 0.0141 \times 292.15\,\mathrm{K} = 2.5\,\mathrm{K}$: this air is as light as dry air two and a half degrees warmer.

Example 21.20 (The energy in the Norman sounding)

Lift the surface air of Example 21.4. It saturates at $964\,\mathrm{hPa}$, $64\,\mathrm{m}$ up, and follows a moist adiabat. Below $900\,\mathrm{hPa}$ the sounding is itself nearly saturated and the parcel stays a few tenths of a degree colder than its surroundings; then comes the inversion between $908\,\mathrm{hPa}$ and $889\,\mathrm{hPa}$, where the temperature rises by $4.1\,\mathrm{K}$ in $178\,\mathrm{m}$ and the parcel finds itself $5\,\mathrm{K}$ too cold. It becomes warmer than its surroundings only at $732\,\mathrm{hPa}$, $2.4\,\mathrm{km}$ above the ground, its LFC, and stays warmer up to its EL at $236\,\mathrm{hPa}$, $10.9\,\mathrm{km}$ above sea level, just below the tropopause the sounding reports at $235\,\mathrm{hPa}$. On a fine grid of pressures the areas of the skew-T figure are CAPE $= 2100\,\mathrm{J}/\mathrm{kg}$ and CIN $= -200\,\mathrm{J}/\mathrm{kg}$ with the temperature, and $2230\,\mathrm{J}/\mathrm{kg}$ and $-130\,\mathrm{J}/\mathrm{kg}$ with the virtual temperature: the moisture of the parcel adds its own buoyancy. Parcel theory gives $w_{\max} = \sqrt{2 \times 2100} = 65\,\mathrm{m}/\mathrm{s}$.