Saastamoinen Tropospheric Delay

Saastamoinen tropospheric delay, in brief

A Saastamoinen-style model estimates the neutral-atmosphere signal delay using meteorological quantities and a mapping from zenith to the satellite direction. Pressure, temperature, water-vapour pressure, height and angular units need explicit conventions. The model does not eliminate all atmospheric uncertainty.

Prepared by OpenGNSSLabUpdated 30 September 2026Sources, reproducibility and corrections

Learning objectives

Separate hydrostatic and wet delay components.
Estimate pressure, temperature, and water vapor pressure.
Map zenith delay to the line of sight.

Delay structure

The neutral atmosphere delays GNSS code and phase measurements. Saastamoinen separates the delay into a stable hydrostatic part and a more variable wet part.

In the zenith direction, the total is usually around 2 to 2.5 m. At lower elevation angles, mapping to the slant path can multiply the delay.

Example inputs

Parameter	Value
Station height	1200 m
Latitude	35.7 deg = 0.623 rad
Relative humidity	0.40
Satellite elevation	30 deg

Step 1

Standard atmosphere variables

When local meteorological observations are unavailable, estimate pressure, temperature, and water vapor pressure from height and humidity.

p=1013.25(1-2.2557\times10^{-5}h)^{5.2568}=887.6\ \text{hPa}

T=15-6.5\times10^{-3}h+273.15=280.35\ \text{K}

e_s=6.108\exp\left(\frac{17.15T-4684}{T-38.45}\right)=9.86\ \text{hPa}

e=e_sRH=3.94\ \text{hPa}

Step 2

Zenith hydrostatic delay

The hydrostatic term dominates the total delay and depends mainly on surface pressure.

ZHD=0.0022768\frac{p}{1-0.00266\cos(2\varphi)-0.00028h_{km}}

ZHD=0.0022768\frac{887.6}{0.998824}=2.025\ \text{m}

Step 3

Zenith wet delay

The wet term is smaller here because the example uses relatively dry conditions.

ZWD=0.002277\left(\frac{1255}{T}+0.05\right)e

ZWD=0.002277(4.526)(3.94)=0.0406\ \text{m}

Step 4

Map to the satellite line of sight

With a 30 degree elevation, the zenith angle is 60 degrees and the simple mapping factor is 1/cos z = 2.

z=90^\circ-e=60^\circ,\qquad \cos z=0.5

T_h=\frac{2.025}{0.5}=4.05\ \text{m}

T_w=\frac{0.0406}{0.5}=0.0812\ \text{m}

T_{trop}=T_h+T_w=4.1312\ \text{m}

Typical ranges

Condition	Typical delay
Zenith	2 to 2.5 m
Elevation 30 deg	4 to 5 m
Elevation below 15 deg	10 to 20 m
Wet component	3 to 20 cm

Result

Computed result

4.1312 m

For this Tehran example and 30 degree satellite elevation, the Saastamoinen slant delay is about 4.13 m.

What you should understand now

The hydrostatic delay is large and predictable.
The wet delay is smaller but can be more variable.
Elevation angle can dominate the slant delay through the mapping function.

Help improve this tutorial

Point out numerical ambiguity, missing prerequisites, or a step that needs a fuller derivation.

Saastamoinen Tropospheric Delay