# 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 Levenberg-Marquardt algorithm combines aspects of stochastic gradient and Gauss-Newton methods to perform iterative coefficient updates while managing regularization with \(\beta\). This allows for finding optimal coefficients that minimize the differences between model predictions and observed data while avoiding overfitting. Figure 6 presents an example of data retrieval from the simulated Uvsq-Sat NG Spectrometer (spectral resolution of 1 nm and SNR of 50), as achieved through the Levenberg-Marquardt algorithm. **--Step 6--** Quantification of uncertainties on the concentrations of gases as they can be observed via the Uvsq-Sat NG NIR Spectrometer (Figure 7). The Monte Carlo method is used to estimate the uncertainties of the normalized coefficients \(C_{1}\), \(C_{2}\), \(C_{3}\), and \(C_{4}\). It represents a powerful tool for addressing the uncertainties problem. The Levenberg-Marquardt algorithm is iteratively used in a loop to obtain multiple different sets of coefficients. In each iteration, a different random Gaussian noise is added. This procedure enables us to plot the associated Gaussians for each coefficient, contributing to the determination of the parameter corresponding to the uncertainty in the sought measurement. Finally, the normalized coefficients \(C_{1}\), \(C_{2}\), \(C_{3}\), and \(C_{4}\) are converted into physical values to provide the gas concentrations (CO\({}_{2}\), CH\({}_{4}\), O\({}_{2}\), and H\({}_{2}\)O), as they could be observed via the Uvsq-Sat NG Spectrometer from its dimensionless signal (TR\({}_{Spectro}(\lambda)\)). This approach allows us to obtain the uncertainties in gas concentrations determination with a 1-Sigma confidence level. Figure 7 depicts an illustrative case of extracting the concentrations of the four analyzed gases (CO\({}_{2}\), CH\({}_{4}\), O\({}_{2}\), and H\({}_{2}\)O) from the simulated Uvsq-Sat NG Spectrometer (spectral resolution of 1 nm and SNR of 50). The uncertainties in the concentrations retrieval of different atmospheric gases are significant (\(\pm\)11.3 ppm for CO\({}_{2}\), \(\pm\)120.2 ppb for CH\({}_{4}\)), considering the extremely low SNR values of the Uvsq-Sat NG NIR Spectrometer. A lower SNR signifies that the noise can obscure or distort the signal, leading to less dependable observations. In contrast, a higher  
Figure 3.3 Uvsq-Sat NG NIR Spectrometer data retrieval of the dimensionless signal (TR\({}_{Spectro}(\lambda)\)) as it can be observed via the spectrometer (spectral resolution of 1 nm and SNR of 50). The dark stars (noised data) represent data of the dimensionless signal (Step 4). The blue curve represents the best fit obtained using the Levenberg–Marquardt algorithm (Step 5). SNR implies that the strength of the desired signal is considerably higher than the level of unwanted noise, resulting in more accurate and precise measurements. Another analysis was conducted to investigate the impact of the spectrometer's spectral resolution and the influence of the SNR on the retrieval of gas concentrations. Table 5 provides a summary of these results, which emphasize the importance of having a spectrometer with a SNR of at least 1000, when its spectral resolution is 6 nm. In all the conducted simulations, the SNR is assumed to remain constant across wavelengths. A sensitivity analysis could be performed by allowing the SNR to change across different wavelengths. Considering that the Uvsq-Sat NG NIR Spectrometer can have a spectral resolution of 6 nm and a SNR of 2000, the retrieval of greenhouse gases (CO\({}_{2}\) and CH\({}_{4}\)) using the