Table 2.

Point prediction performance measured in terms of the root-mean-square error (RMSE), the third quartile of the absolute error (Q₃AE) and the median absolute error (MdAE) for leave-one-observation-out (LOOO) cross-validation. The compared models are the RG spatial mean, the RG-like reference model (model 1), the locally stationary one-month and three-month spatial models (models 2 and 4) and the locally stationary three-month spatio-temporal model (model 5), all with a Gaussian nugget. The units are degrees Celsius and the percentages in the parentheses are improvements in comparison with the reference model.

pressure level	performance metric	spatial mean	reference model	space (one month)	space (three months)	space–time (three months)
10 dbar	RMSE	0.8889	0.6135	0.5876 (4.2%)	0.5667 (7.6%)	0.5072 (17.3%)
	Q3AE	0.8670	0.5026	0.4824 (4.0%)	0.4568 (9.1%)	0.3735 (25.7%)
	MdAE	0.4750	0.2556	0.2490 (2.6%)	0.2293 (10.3%)	0.1801 (29.5%)
300 dbar	RMSE	0.8149	0.5782	0.5692 (1.6%)	0.5675 (1.9%)	0.5124 (11.4%)
	Q3AE	0.6320	0.4213	0.4150 (1.5%)	0.4005 (4.9%)	0.3684 (12.6%)
	MdAE	0.3062	0.1991	0.1957 (1.7%)	0.1873 (5.9%)	0.1740 (12.6%)
1500 dbar	RMSE	0.1337	0.1014	0.0997 (1.7%)	0.0935 (7.8%)	0.0883 (12.9%)
	Q3AE	0.1043	0.0736	0.0725 (1.5%)	0.0678 (7.9%)	0.0641 (12.8%)
	MdAE	0.0530	0.0356	0.0355 (0.3%)	0.0328 (8.0%)	0.0311 (12.7%)