Saastamoinen troposphere correction model. More...

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 + 273.16 \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 [43] 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]

Function Documentation

◆ calcZHD_Saastamoinen()

double NAV::calcZHD_Saastamoinen	(	const Eigen::Vector3d &	lla_pos,
		double	p )

Calculates the tropospheric zenith hydrostatic delay with the Saastamoinen model.

Parameters

[in]	lla_pos	[𝜙, λ, h]^T Geodetic latitude, longitude and height in [rad, rad, m]
[in]	p	Total barometric pressure in [millibar]

Returns: Range correction for troposphere and stratosphere for radio ranging in [m]

Note: See [39] Saastamoinen, p. 32; See [11] Davis, Appendix A, p. 1604; See [8] Böhm ch. 1, p. 1; See [42] RTKLIB ch. E.5 Troposphere and Ionosphere Models, sec. (1), p. 149

◆ calcZWD_Saastamoinen()

double NAV::calcZWD_Saastamoinen	(	double	T,
		double	e )

Calculates the tropospheric zenith wet delay with the Saastamoinen model.