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Namespaces | Functions
Saastamoinen.hpp File Reference

Saastamoinen troposphere correction model. More...

Go to the source code of this file.

Namespaces

namespace  NAV
 

Functions

double NAV::calcZHD_Saastamoinen (const Eigen::Vector3d &lla_pos, double p)
 Calculates the tropospheric zenith hydrostatic delay with the Saastamoinen model.
 
double NAV::calcZWD_Saastamoinen (double T, double e)
 Calculates the tropospheric zenith wet delay with the Saastamoinen model.
 

Detailed Description

Saastamoinen troposphere correction model.

Author
T. Topp (topp@.nosp@m.ins..nosp@m.uni-s.nosp@m.tutt.nosp@m.gart..nosp@m.de)
Date
2022-05-26

Algorithm description

Given the approximate position $ \phi $, $ \lambda $, $ h $, the elevation $ \varepsilon $ and the relative humidity $ h_{\mathrm{rel}} $ the tropospheric delay can be calculated using Saastamoinen's formulas.

A standard atmosphere is applied as a reference for the necessary parameters of the atmosphere.

  • total pressure in [hPa]

    \begin{equation} \label{eq:eq-Saastamoinen-pressure} p = 1013.25 \cdot \left(1-2.2557 \cdot 10^{-5} \cdot h \right)^{5.2568} \end{equation}

  • absolute temperature in [K]

    \begin{equation} \label{eq:eq-Saastamoinen-temperature} T = 15.0 - 6.5 \cdot 10^{-3} \cdot h + 273.15 \end{equation}

    where $ T_{0} = 15^{\circ} $ temperature at sea level

  • partial pressure of water vapor in [hPa]

    \begin{equation} \label{eq:eq-Saastamoinen-partial_pressure_water_vapor} e = 6.108 \cdot \exp \left\{ \frac{17.15 T-4684.0}{T-38.45} \right\} \cdot \frac{h_{\mathrm{rel}}}{100} \end{equation}

    where $ h_{\mathrm{rel}} = 0.7 $ is the relative humidity

  • zenith hydrostatic delay in [m] (see [11] Davis, Appendix A, eq. A11, p. 1604 or [8] Böhm ch. 1, eq. 3, p. 1)

    \begin{equation} \label{eq:eq-Saastamoinen-zhd} \Delta L_{\mathrm{h}}^{\mathrm{z}} = \dfrac{0.0022768 \cdot p}{1-0.00266 \cdot \cos 2 \varphi-0.00028 \cdot \dfrac{ h }{1000}} \end{equation}

  • zenith wet delay (see [45] Springer Handbook GNSS ch. 6, eq. 6.54, p. 173) in [m]

    \begin{equation} \label{eq:eq-Saastamoinen-zwd} \Delta L_{\mathrm{w}}^{\mathrm{z}} = 0.002277 \cdot \left(\frac{1255.0}{T} + 0.05 \right) \cdot e \end{equation}

  • zenith total delay in [m]

    \begin{equation} \label{eq:eq-Saastamoinen-ztd} \Delta L^{\mathrm{z}} = \Delta L_{\mathrm{h}}^{\mathrm{z}} + \Delta L_{\mathrm{w}}^{\mathrm{z}} \end{equation}

  • slant total delay along elevation angle in [m]

    \begin{equation} \label{eq:eq-Saastamoinen-std} \Delta L_{\mathrm{troposphere}} = \frac{\Delta L^{\mathrm{z}}}{\cos{ \left( z d \right) }} \end{equation}

    where $ zd $ is the zenith angle as $ \varepsilon=\frac{\pi}{2} - z d $ in [rad]

Definition in file Saastamoinen.hpp.