## 3 Error Characterization and Simulation Method  
### Errors Description  
#### 3.1.1 Instrument Uncertainties  
Instrument uncertainties come from the instrument itself, and usually cannot be corrected completely. The impacts of instrument uncertainties which cannot be corrected have to be assessed in order to quantify the accuracy of such a retrieval [25]. In a radiometer, the heterodyne mixer will convert the signal which is coming from the antenna to the intermediate frequency. Double sideband (DSB) and single sideband (SSB) are two modes of receivers commonly used in the radiometer. The SSB mode can keep the complete spectral lines, while the DSB mode can cover more spectral lines, since the upper and lower sideband signals will be folded together. In addition, the system temperature of the DSB receiver is lower than that of the SSB receiver. However, a sideband weight inconsistency commonly exists in the double-sideband radiometer. The theoretical value of the output radiance of a DSB receiver can be described as [26]:  
\[I_{IF}^{i}(v_{IF})=\frac{W_{S}(v)I_{A}^{i}(v)+W_{S}^{\prime}(v^{\prime})I_{A}^{ i}(v^{\prime})}{W_{S}(v)+W_{S}^{\prime}(v^{\prime})}, \tag{1}\]  
where \(i\) represents the channel, \(v\) represents the measurement frequency, \(v_{IF}\) is the intermediate frequency, \(I_{IF}\) is the radiance after the mixer, \(I_{A}\) is the radiance after the antenna, \(W_{S}\) and \(W_{S}^{\prime}\) are the lower and upper sideband response, respectively. In an ideal DSB radiometer, the sideband response of the lower and upper sideband should be consistent (0.5). In this simulation, an uncertainty of 0.2% is assumed in order to evaluate the retrieval error induced by the sideband weight. The assumed uncertainty of this sideband weight comes from our radiometer test. The stability of local oscillator frequency is very important, since it controls which line will be detected. Although it is a systematic error that can be corrected before launch, the local oscillator frequency will vary over the time in which one year goes by. A 0.5 MHz offset which may have \begin{table}
\begin{tabular}{c c} \hline \hline
**Characteristics** & **Value** \\ \hline Satellite altitude & 600 km \\ Scan altitude & 0–100 km \\ Spectrum integration time & 0.1 s (1 km) \\ Antenna vertical FOV & 5.5 km, 3.8 km, 3.3 km, 0.96 km \\ Spectrometer bandwidth & 2 GHz \\ Spectrometer resolution & 2 MHz \\ Local oscillator frequency & 117.55, 190.1, 239.66, 642.87 GHz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The main observation characteristics of the THz Atmospheric Limb Sounder (TALIS). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Radiometer (GHz)** & **Spectral Bands (GHz)** & **System Temperature (K)** \\ \hline \(118\) & 115.35–117.35, 117.75–119.75 & 1000 K, DSB \\  & 175.5–17.75, 202.7–204.7; & \\ \(190\) & 178.9–180.9, 199.3–201.3; & 1000 K, DSB \\  & 183.0–185.0, 195.2–197.2 & \\  & 229.66–231.66, 247.66–249.66; & \\ \(240\) & 232.16–234.16, 245.16–247.16; & 1000 K, DSB \\  & 234.66–236.66, 242.66–244.66 & \\  & 624.47–626.47, 659.27–661.27; & \\ \(643\) & 627.37–629.37, 656.37–658.37; & \\  & 632.37–634.37, 651.37–653.37; & \\  & 634.87–636.87, 648.87–650.87 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The spectral bands of the TALIS. occurred after several years is assumed to estimate the effect. This value of uncertainty is assumed according to the work by [PERSON] et al. (2018) [PERSON] et al. (2018). The geometrical tangent height is a key parameter, and is usually obtained from the satellite navigation system. However, the star tracker data is sometimes not very accurate, and the pointing angle (Line of sight, LOS) error should be considered. Fortunately, pointing can be retrieved along with temperature and species in a retrieval method. To estimate the effect, a 0.021\({}^{\circ}\) (-1 km) offset is added to the simulation, and it will be retrieved simultaneously with the products. The uncertainty of the pointing offset is assumed according to the work of [PERSON] et al. (2011) [PERSON] et al.