Methods
A parsimonious regression, not a GCM. The authors estimate annual total cloud cover from a water-cycle indicator, the Atlantic Multidecadal Oscillation, and the cold tail of global temperature. Skill is claimed in-sample (1935–1980), out-of-sample (1981–2018), and against a 19th-century parish diary. The model card is the part the paper did not archive: the scaling, the moisture envelope, the hand-placed shape, and which series are real.
The published equation
WCI carries soil moisture and storm rainfall as an interaction: drought does not cut cloud cover by the same amount in a stormy year as in a quiet one. AMO and GTA25 enter with negative sign. Dotted words open a textbook note and a lab note.
α, β, σ, γ, η are the paper’s published modifiers. A and B are the scale and intercept needed to put the linear combination into cloud-fraction units for the western Mediterranean (companion whole-Med reconstruction used B ≈ 0.60; this basin is clearer). The AMO symbol in the equation is one term. The file behind it is mis-specified relative to a detrended AMO, and this atlas also feeds that file into PDSI and GTA, so the fitted γ is not the whole Atlantic effect on the curve below. Skill is judged on the calibration window.
Calibration scatter · Fig. 4A
Modeled versus analog observed TCC, 1935–1980. r = 0.67, RMSE = 0.009. The paper shows 90% and 95% prediction bands; a handful of years fall outside, as here.
Residual histogram · Fig. 4B
Residuals of the calibration fit. Approximate normality is the authors’ justification for using the linear envelope as an uncertainty band.
Calibration and validation in time
Split at 1980/81. Validation r = 0.98. High late-period skill is partly the shared decline — a trend both the predictors and CRU cloud cover exhibit — not only year-to-year weather.
Water-cycle indicator vs TCC · Fig. 7A
Paper: two calibration points sit outside the 95% band. Wetter soils and stormier summers map onto higher cloud fraction.
AMO vs TCC · Fig. 7B
Paper: four points outside 95%. Negative slope: a warm North Atlantic is a clearer western Mediterranean, via SST gradients and a shifted storm track.
Domain and spatial structure · Fig. 3
Western Mediterranean land: roughly Iberia, southern France, Maghreb and western Italy. CM-SAF 1982–2018 shows low, homogeneous cover in the south and higher, more variable cover in the north.
How the millennium is filled
- Predictors with millennial coverage (Mann AMO, tree-ring PDSI, TSI, volcanoes) are pushed through Eq. 2 for every year 969–2022. The Mann index is the weak point: its 2σ band includes zero in most years, and 1850–2006 keeps a warming trend the standard AMO removes.
- Uncertainty is the 21-year moving standard deviation of the reconstruction — a smoothness envelope, not a full ensemble of proxy errors.
- Independent qualitative checks: Atlas cedar drought (MCA drier than LIA), Moroccan speleothem wetness from the 15th century, Iberian rainy 17th century, and the Carcaixent sky diary (1837–1878). The cedar and speleothem comparisons are climate moisture. They are not a ranking of river flow before and after the basin was re-engineered.
- Interannual variance is a warm-season (April–August) phenomenon; summer storms are the hinge between soil moisture and cloud.
Each slider is one methodological choice, not a new climate. The dashed line stays put. Moving several at once adds their cloud effects, including the cross-term when a detrended index is also counted only once. Nothing here refits the paper’s coefficients.
1990–2022 mean 36.9% · +0.1 points vs the curve as used