## 3 Results
### Application of the Model for Spectral Irradiance Estimation  
Next, we chose at random a subset of instances from the testing set, and applied our model to estimate the full spectral irradiance from 360 nm to 780 nm using only the readings from the low-cost sensor ensemble, the SR data, and the computed solar zenith and azimuth angles. Figure 9 depicts the estimated irradiance spectra for two representative cases: the top panel corresponding to a day reported as mostly cloudy [53], and the lower panel corresponding to a day reported as relatively clear [54] in the local meteorological records. It is seen how the contrasting weather conditions are reflected in the spectra; the clear-sky spectrum displaying defined peaks in the shorter wavelengths characteristic of a blue sky, whereas the cloudier instance displays a comparatively flattened and diffused shape especially across the blue to red portion of the spectrum. This spectral smoothing arises from enhanced scattering and absorption by cloud water droplets, resulting in a whiter sky appearance. Figure 10 compares the estimated spectra and the corresponding ground-truth spectra measured by the reference instrument. The comparison shows that the ML model effectively captures the overall spectral shape and irradiance values. Figure 8: Relative MSE values across the 421 spectral bins evaluated on the test set. Figure 7: MSE values on each of the 421 spectral bins evaluated on the training and testing sets. We then selected sets of consecutive time points that were available in the testing set from the same two days to build a time series of SSI and further observe how the respective weather conditions of the day are reflected in the irradiance patterns. Figure 11  
Figure 10: Irradiance spectrum estimated using the model compared with the ground-truth spectra measured by the reference instrument. The top panel corresponds to a cloudy day and the lower panel corresponds to a clear-sky day. Figure 9: Irradiance spectra estimated using the model. The top panel corresponds to a cloudy day and the lower panel corresponds to a clear-sky day. depicts the wavelength-resolved SSI estimated by the model across short time intervals on a generally cloudy day (top panel) and a generally clear-sky day (lower panel). The clear-sky weather is clearly apparent in the lower heatmap by the bright, well-defined band corresponding to the blue region of light, sharply contrasting with the adjacent wavelength bands, whereas the top panel corresponding to comparatively cloudier conditions exhibits muted contrast across most of the spectral range. Microscopic water droplets, which form clouds, are excellent sources of Mie scattering [55], which is relatively wavelength-independent, resulting in a more uniform distribution of visible light wavelengths. In contrast, on clearer days, unhindered by clouds, Rayleigh scattering [56] from atmospheric constituents is more prominent. Rayleigh scattering is wavelength-dependent, and most effective at shorter wavelengths, thereby accounting for the peak in the blue-violet region. Figure 12 compares the spectral heatmaps generated by the model with the ground-truth measurements from the reference instrument, using the relative absolute error (RAE). The RAE is defined as:  
\[\text{RAE}=\frac{|\hat{y}-y|}{|y|} \tag{1}\]  
where \(\hat{y}\) is the model-estimated spectral irradiance value and \(y\) is the ground-truth or the corresponding reference instrument reading. In both cases, a substantial majority of estimates fall below approximately 15% RAE. Although the second case includes some points with RAEs around 20%, these represent a smaller proportion of the total. In environmental sensing, an RAE below 20% is often acceptable, considering intrinsic challenges such as sensor noise and atmospheric variability. Figure 11: Wavelength-resolved SSI estimated by the model for brief intervals of time. The top panel corresponds to a cloudy day and the lower panel corresponds to a clear-sky day.