Background
Earth’s climate depends on the balance between the sunlight it absorbs and reflects, and the heat it radiates back to space as infrared light, the outgoing longwave radiation (OLR). This balance is monitored mainly by large satellite missions such as NASA’s CERES (Loeb et al., 2018). Small, low-cost instruments could complement them, but their data are hard to use alone. CLARA, a compact radiometer developed at PMOD/WRC in Davos and flying on the Norwegian microsatellite NorSat-1 (Walter et al., 2017; Haberreiter et al., 2026), measures OLR only on the night side of its orbit, along narrow ground tracks with variable coverage as well as partially long interruptions, including a nine-month gap in 2021–22 due to problems with the operation of the satellite. In an average month it observes about a fifth of the globe. We asked whether these sparse measurements can be turned into complete monthly maps of night-time OLR, with reliable uncertainties, by combining them with ERA5, a reanalysis that reconstructs the global atmosphere (Hersbach et al., 2020).
Data and method
We used CLARA data from January 2020 to September 2026, kept night-side footprints viewed at moderate angles (225,460 samples) and averaged them on a 5° × monthly grid. CLARA records radiance (W m−2 sr−1), whereas ERA5 provides flux (W m−2), so we compare the two through correlations and relative changes. CLARA reproduces ERA5’s equator-to-pole pattern (correlation 0.93) with damped contrasts, and relative to ERA5 its level rises by 23 % across the 2021–22 gap, indicating a change in operation and the instrument performance. As ERA5 agrees closely with CERES (correlation 0.99), these differences stem from CLARA.
We modelled CLARA as a linear function of ERA5, which also absorbs the unit conversion, with a step at the gap, plus a spatio-temporal Gaussian process: a statistical model that learns how the remaining differences are correlated in space, across seasons and between years. The noise reflects the number of overpasses behind each monthly value, and a sparse variational approximation (Titsias, 2009) handles the 37,898 observed cell-months. We compared three covariance functions (exponential, Gaussian, Matérn 3/2) by blocked cross-validation, holding out entire regions, half-years or both, so that every prediction is tested on unseen data. Reduced models without the Gaussian process, without ERA5, or without both show what each ingredient contributes.
Results
The exponential covariance predicted the held-out monthly CLARA values best: the root-mean-square difference between predicted and observed OLR of a cell-month was 39.3 W m−2 sr−1, 22 % of the mean observed value, although the three variants were statistically indistinguishable. Compared with a constant before and after the gap (46.4 W m−2 sr−1, 26 %), the Gaussian process alone reduced this error by 12 %, ERA5 alone by 14 % and both together by 15 %; adding ERA5 to the Gaussian process helped significantly in all three validation designs. The predicted uncertainties are well calibrated: 94 % of held-out values fall within the 95 % prediction intervals. About two thirds of the variance that ERA5 does not explain is sampling noise, and errors are larger after the gap, where a monthly cell value typically rests on a single overpass. The final product covers every 5° cell and month from 2020 to 2026 (209,952 values), each with its uncertainty.
Relevance
The approach turns fragmentary measurements from a small, low-cost instrument into a gap-free monthly record with honest uncertainties, comparable with other satellite products: an important step towards routinely filling CLARA’s data gaps. It quantifies instrument effects relevant to future missions, such as the shift across the gap, and transfers to other small satellites, helping Davos-built instruments monitor Earth’s energy budget, a key indicator of climate change.
References
Haberreiter, M., Finsterle, W., Montillet, J.-P., et al. (2026). Total solar irradiance and Outgoing Longwave Radiation as observed with the CLARA radiometer onboard NorSat-1: In-flight performance and data release. Under revision.
Hersbach, H., et al. (2020). The ERA5 global reanalysis. Quarterly Journal of the Royal Meteorological Society, 146, 1999–2049. https://doi.org/10.1002/qj.3803
Loeb, N. G., et al. (2018). Clouds and the Earth’s Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) top-of-atmosphere (TOA) Edition-4.0 data product. Journal of Climate, 31, 895–918. https://doi.org/10.1175/JCLI-D-17-0208.1
Titsias, M. (2009). Variational learning of inducing variables in sparse Gaussian processes. Proceedings of the 12th International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 5, 567–574.
Walter, B., Levesque, P.-L., Kopp, G., Andersen, B., Beck, I., Finsterle, W., et al. (2017). The CLARA/NORSAT-1 solar absolute radiometer: instrument design, characterization and calibration. Metrologia, 54(5), 674–682. https://doi.org/10.1088/1681-7575/aa7a63