Heights to pressures (using the ICAO atmosphere)

Converts heights to pressures (in $hPa$) using the ICAO atmosphere.

The pressure ($P$) is retrieved as follow:

• For $Z<11000$ gpm

  $$P=100.0-p_b\times P_{ICA{O}_{surface}}$$

  with

  $$p_b=(1.0-p_a{)}^{Z{P}_{11}}$$

  and

  $$p_a=L_{ICA{O}_{11}}\times Z\times \frac{1.0}{T_{ICA{O}_{surface}}}$$

• For $11000\le Z<20000.0$ gpm

  $$P=100.0\times {10}^{p_a}$$

  with

  $$p_a=\log (P_{ICA{O}_{11}})-p_b$$

and

$$p_b=\frac{g}{R_d}\times (Z-11000)\times \frac{1.0}{T_{ICA{O}_{iso}}};$$

• For $Z\ge 20000.0$ gpm

  $$P=100.0\times P_{ICA{O}_{22}}\times (1.0-P_a{)}^{Z{P}_{22}};$$

  with

  $$P_a=L_{ICA{O}_{22}}\times \frac{1.0}{T_{ICA{O}_{iso}}}\times (Z-20000)$$

With:

• Temperature of isothermal layer: $T_{ICA{O}_{iso}}=216.65$ K

• The assume surface temperature: $T_{ICA{O}_{surface}}=288.15$ K

• The assume surface pressure: $P_{ICA{O}_{surface}}=1013.25$ hPa

• The assumed pressure at 11,000 gpm: $P_{ICA{O}_{11}}=226.32$ hPa

• The assumed pressure at 22,000 gpm: $P_{ICA{O}_{22}}=54.7487$ hPa

• The lapse rate for levels up to 11,000 gpm: $L_{ICA{O}_{11}}=6.5\times {10}^{-03}$ K/m

• The lapse rate from 11,000 gpm to 22,000 gpm: $L_{ICA{O}_{22}}=-1.0\times {10}^{-03}$ K/m

• $Z{P}_{11}=\frac{g}{R_d\times L_{ICA{O}_{11}}}$

• $Z{P}_{22}=\frac{g}{R_d\times L_{ICA{O}_{22}}}$

• Specific gas constant for dry air: $R_d$

• Standard acceleration due to gravity: $g$

Saturated Vapor Pressure from T

The various formulations available to derive $e_{sat}$ (Saturated Vapor Pressure) from $T$ (temperature or dew point temperature) are:

• Rogers | default: Classical formula from Rogers and Yau (1989; Eq2.17)

  $$e_{sat}=1000\times 0.6112\times \exp (17.67\times \frac{T-2.7315\times {10}^2}{T-29.65})$$

• Sonntag: Eqn 7, Sonntag, D., Advancements in the field of hygrometry, Meteorol. Zeitschrift, N. F., 3, 51-66, 1994. Most radiosonde manufacturers use Wexler, or Hyland and Wexler or Sonntag formulations, which are all very similar (Holger Vomel, pers. comm., 2011)

  $$\begin{gathered} \begin{array}{r}\begin{array}{c}{e}_{sat}=\exp (\frac{-6096.9385}{T}+21.2409642-2.711193\times {10}^{-2} \\ \times T+1.673952\times {10}^{-5}\times T^2+2.433502\times \log (T))\end{array}\end{array} \end{gathered}$$

• Walko: Polynomial fit of Goff-Gratch (1946) formulation (Walko, 1991). The Walko formulation is computationally fastest of all methods, but becomes less accurate at extremely low temperatures, below roughly -70C.

  $$\begin{array}{r}\begin{array}{c}{e}_{sat}=c_0+x\times (c_1+x\times (c_2+x\times (c_3+x\times (c_4+\\ x\times (c_5+x\times (c_6+x\times (c_7+x\times c_8)))))))\end{array}\end{array}$$

  with:

  $$\begin{array}{r}\begin{array}{c}c=[610.5851,44.40316,1.430341,0.2641412\times {10}^{-1},\\ 0.2995057\times {10}^{-3},0.2031998\times {10}^{-5},0.6936113\times {10}^{-8},\\ 0.2564861\times {10}^{-11},-0.3704404\times {10}^{-13}]\end{array}\end{array}$$

• Murphy: Murphy and Koop, Review of the vapour pressure of ice and supercooled water for atmospheric applications, Q. J. R. Meteorol. Soc (2005), 131, pp. 1539-1565.

  $$\begin{gathered} \begin{array}{r}\begin{array}{c}{e}_{sat}=\exp (54.842763-\frac{6763.22}{T}-4.210\times \log (T) \\ +0.000367\times T+tanh(0.0415\times (T-218.8)) \\ \times (53.878-\frac{1331.22}{T}-9.44523\times \log (T) \\ +0.014025\times T))\end{array}\end{array} \end{gathered}$$