# Error Sources of Interferometric Synthetic Aperture Radar Satellites
## 3 Systematic Errors
### Propagation Path (Atmosphere)
#### 3.2.3 Liquid Water Delay
Second, the contribution from liquid water delay is as little as only 1-5% of the amount of wet delay since the droplets are too small to cause much scattering [28; 79]. However, it is apparent that this hypothesis is not realistic since clouds are an important and prevalent weather phenomenon. Moreover, although phase shifts caused by cloud droplets only produce limited signal delay in interferograms, it is only limited to the conditions of no precipitation. The delay caused by precipitation clouds could climb to a few millimeters, which can be influential for C-band and X-band sensors. In severe weather conditions, cumulus congestus clouds and cumulonimbus clouds can bring in more than 20 mm of delay and can be destructive. In addition to the errors caused by the liquid water delay itself, ignoring the liquid water delay will lead to a slight overestimation in computing PWV because the refractivity caused by scattering will be interpreted as being caused by water vapor [79]. The value of overestimation is defined as a quarter of a function of rain rate (mm/h) and temperature (\(K\); see Figure A-1 in [79]). For regions where the temperature is higher than 0 \({}^{\circ}\)C and the rain rate is lower than 16 mm/h, the overestimation of PWV is less than 5% [79]. Although the overestimation is subtle, it serves as an additional error source if liquid water delay is ignored. To sum up, the signal delay of C-band sensors caused by liquid water is limited under good weather conditions, especially when no clouds are present in the atmosphere. In this case, liquid water delay can be ignored. Nevertheless, if the weather worsens with increased liquid water content and cloud layer (cloudy sky, drizzle, or light rain), liquid water delay should be considered based on the required accuracy of the application. If the weather condition is severe (strong precipitation or thunderstorm), the influence from liquid water delay must be considered. Note that clouds and precipitation also modulate the observed water vapor quantities, so water vapor concentration is relatively high. As a result, regardless of the weather condition, water vapor (the medium for wet delay) is always the most dominant driving force of the delays [28]. The errors caused by the medium along the propagation path is one of the most complicated and significant contributions. Here we summarize the sources of the artifacts that occur along the propagation path (Table 5). \begin{table}
\begin{tabular}{l l l l l} \hline \hline \multirow{2}{*}{**Category**} & \multirow{2}{*}{**Ionospheric Advance**} & \multicolumn{2}{c}{**Topospheric Delay**} & \multirow{2}{*}{**Liquid Water Delay**} \\ \cline{3-3} \cline{5-5}  & & **Hydrostatic Delay** & & **Wet Delay** \\ \hline Atmospheric Layer & Ionosphere & Troposphere & Troposphere & Troposphere \\ Medium & Free electrons & Primarily nitrogen and oxygen & Water vapor & Liquid water droplets \\ Dispersive/Nondispersive & Dispersive & Nondispersive & Nondispersive & Mainly nondispersive \\ Influence of an increased medium & Decreased observed range & Increased observed range & Increased observed range & Increased observed range \\ Phase delay/advance & Phase advance & Phase delay & Phase delay & Phase delay \\ Interaction between radar wave & No & Refraction & Refraction & Forward scattering \\ and the medium & Faraday rotation & Non-polar (induced dipoles) & Non-polar (induced dipoles) & Polar (permanent dipole moment) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summary of the sources of errors that occur along the propagation path.