Skip to content

Latest commit

 

History

History
142 lines (81 loc) · 3.94 KB

formula_part1.rst

File metadata and controls

142 lines (81 loc) · 3.94 KB
Raw

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_{ICAO_{surface}}

    with

    p_{b} = (1.0 - p_{a})^{ZP_{11}}

    and

    p_{a} = L_{ICAO_{11}} \times Z \times \frac{1.0}{T_{ICAO_{surface}}}

  • For 11000 \leq Z < 20000.0 gpm

    P = 100.0 \times 10^{p_{a}}

    with

    p_{a} = \log(P_{ICAO_{11}}) - p_{b}

and

p_{b} = \frac{g}{R_{d}} \times (Z - 11000) \times \frac{1.0}{T_{ICAO_{iso}}};

  • For Z \geq 20000.0 gpm

    P = 100.0 \times P_{ICAO_{22}} \times (1.0 - P_{a})^{ZP_{22}};

    with

    P_{a} = L_{ICAO_{22}} \times \frac{1.0}{T_{ICAO_{iso}}} \times (Z - 20000)
With:
  • Temperature of isothermal layer: T_{ICAO_{iso}} = 216.65 K
  • The assume surface temperature: T_{ICAO_{surface}} = 288.15 K
  • The assume surface pressure: P_{ICAO_{surface}} = 1013.25 hPa
  • The assumed pressure at 11,000 gpm: P_{ICAO_{11}} = 226.32 hPa
  • The assumed pressure at 22,000 gpm: P_{ICAO_{22}} = 54.7487 hPa
  • The lapse rate for levels up to 11,000 gpm: L_{ICAO_{11}} = 6.5 \times 10^{-03} K/m
  • The lapse rate from 11,000 gpm to 22,000 gpm: L_{ICAO_{22}} = -1.0 \times 10^{-03} K/m
  • ZP_{11} = \frac{g}{R_{d} \times L_{ICAO_{11}}}
  • ZP_{22} = \frac{g}{R_{d} \times L_{ICAO_{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\left(17.67 \times \frac{T - 2.7315 \times 10^{2}}{T - 29.65}\right)

  • 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)

    e_{sat} = \exp\left(\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)\right)

  • 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.

    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})))))))

    with:

    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}]

  • 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.

    e_{sat} = \exp\left(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)\right)