Results of the cross-validation method for selecting the best kernel. Upper panel: we compared four kernels with multiplicative and additive kernels with a Matérn 3/2 (M3) or a square-exponential (SE) kernels with the temperature of the air in the container, and the spectro-graph, temperature of the Coudé tube, and pressure. The model that obtained the highest log-likelihood was preferred. This is the multiplicative M3 kernel (MM3) in hashed blue. Lower panel: comparison of the M3 or MM3 kernel with the difference number of housekeeping variables. We compared models with only one temperature (yellow and green), with pressure alone (red), with only three temperatures (purple), the multiplicative M3 kernel with three temperatures and pressure (blue), and the multiplicative M3 kernel with the addition of an SE kernel on time (pink).