# UVsq-Sat NG, a New CubeSat Pathfinder for Monitoring Earth Outgoing Energy and Greenhouse Gases
## 4 Methodology for Determining ERB and GHGs with Uvsq-Sat NG
The data series are normalized, taking into account the Solar Zenith Angle (\(SZA\)) and the satellite pointing axis (\(\theta\)) between the Nadir and the Zenith (Equation (2)), as depicted in the diagram illustrated in Figure 3.  
\[\mathrm{TR}_{n}(\lambda,T,P,L)=\mathrm{TR}(\lambda,T,P,L)\left(\frac{1}{\cos( \theta)}+\frac{1}{\cos(SZA)}\right) \tag{2}\]  
The high-resolution dimensionless transmittance functions (\(\mathrm{TR}_{n}(\lambda,T,P,L)\)) must be degraded to the resolution of the Uvsq-Sat NG NIR Spectrometer. Indeed, the spectrometer has a finite bandpass (or resolution), which is determined with the sensitivity of the spectrometer. The bandpass is defined as the Full Width at Half Maximum (FWHM) of the spectrometer's spectral response of the slit function (\(\mathrm{Sf}_{LoRes}\)), which depends on the wavelength (\(\lambda\)). The spectrometer slit functions and FWHM (assumed to fall within the range of 1 to 6 nm) will need to be measured accurately during ground-based calibration and Cal/Val as explained in Section 3.2.2. The convolution of the \(\mathrm{TR}_{n}(\lambda,T,P,L)\) high-resolution dimensionless transmittance functions via the Uvsq-Sat NG NIR Spectrometer slit functions (\(\mathrm{Sf}_{LoRes}\)) is given by the integral described in Equation (3). The integration interval (\(\Delta\lambda^{\prime}\)) is defined using the width of the slit functions. This approach allows us to  
Figure 4: **(top) Dimensionless transmittance functions (\(\mathrm{TR}(\
u,T,P,L)\)) for CO\({}_{2}\), CH\({}_{4}\), O\({}_{2}\), and H\({}_{2}\)O as a function of wavelength and for nominal mixing. (bottom) Dimensionless transmittance functions’ relative variations from a ‘maximum’ mixing ratio (430 ppm for CO\({}_{2}\), 2.0 ppm for CH\({}_{4}\), 0.22 for O\({}_{2}\), and 1.1 precipitable cm for H\({}_{2}\)O) to a nominal mixing ratio. **  
obtain dimensionless transmittance functions (Figure 5) at the spectrometer's resolution (TR\({}_{n}(\lambda,T,P,L)_{LoRes}\)). \[\text{TR}_{n}(\lambda)_{LoRes}=\text{TR}_{n}(\lambda,T,P,L)\otimes\text{sf}_{LoRes }=\int\text{TR}_{n}(\lambda^{\prime},T,P,L)\cdot\text{sf}_{LoRes}(\lambda- \lambda^{\prime})\;d\lambda^{\prime} \tag{3}\]  
Figure 5 shows that the spectral characteristics of the four gases remain distinguishable at the UVsq-Sat NG NIR Spectrometer's resolution, despite the attenuation and smoothing of absorption lines. These gases include O\({}_{2}\) near 1270 nm, CO\({}_{2}\) near 1600 nm, CH\({}_{4}\) near 1650 nm, and H\({}_{2}\)O at various wavelengths. **-Step 3**: Determination of the total dimensionless resulting transmittance function from the considered values of the gas mixing ratio. The total dimensionless resulting transmittance function (TR\({}_{n}^{tot}(\lambda,T,P,L)\), simplified to TR\({}_{n}^{tot}(\lambda)\)) is obtained from Equation (4). It depends on the desired mixing ratio, the nominal mixing ratio and the'maximum' mixing ratio of each gas. \[\text{TR}_{n}^{tot}(\lambda)=\text{TR}_{n}^{CO_{2}}(\lambda)\cdot\text{TR}_{n }^{CH_{4}}(\lambda)\cdot\text{TR}_{n}^{O_{2}}(\lambda)\cdot\text{TR}_{n}^{H_{ 2}O}(\lambda) \tag{4}\]  
Using the following linear interpolations:  
\[\text{TR}_{n}^{CO_{2}}(\lambda)=\text{TR}_{n}^{CO_{2}=420}(\lambda)+\text{C}_{ 1}\cdot\left(\text{TR}_{n}^{CO_{2}=430}(\lambda)-\text{TR}_{n}^{CO_{2}=420}( \lambda)\right)\]  
\[\text{TR}_{n}^{CH_{4}}(\lambda)=\text{TR}_{n}^{CH_{4}=1.9}(\lambda)+\text{C}_{ 2}\cdot\left(\text{TR}_{n}^{CH_{4}=2.0}(\lambda)-\text{TR}_{n}^{CH_{4}=1.9}( \lambda)\right)\]  
\[\text{TR}_{n}^{O_{2}}(\lambda)=\text{TR}_{n}^{O_{2}=0.21}(\lambda)+\text{C}_{ 3}\cdot\left(\text{TR}_{n}^{O_{2}=0.22}(\lambda)-\text{TR}_{n}^{O_{2}=0.21}( \lambda)\right)\]  
\[\text{TR}_{n}^{H_{2}O}(\lambda)=\text{TR}_{n}^{H_{2}O=1.0}(\lambda)+\text{C}_{ 4}\cdot\left(\text{TR}_{n}^{H_{2}O=1.1}(\lambda)-\text{TR}_{n}^{H_{2}O=1.0}( \lambda)\right)\]  
where C\({}_{1}\), C\({}_{2}\), C\({}_{3}\), and C\({}_{4}\) are normalized coefficients between 0 and 1 that determine a desired mixing ratio of the different gases.