Table 1 Discovered and estimated absolute (non-standardised) linear direct causal effects for the discovered graph (Fig. 2a)

1

AOD → Cloud: aerosols serving as CNN/INPs and enhancing cloud formation (ACI, i.e, cloud fraction adjustment)¹⁶

+

0.6 [0.4; 0.8]

[0.59; 1.07] from¹⁶

2

Cloud → SW: increased cloud cover blocks SW from reaching the surface^9,80

-

−105.3[−157.5; −59.9]Wm⁻²

[−177; 0]Wm⁻² from⁸⁰

3

SW \(\to \,{{\rm{T}}}_{\max }\): surface warming by SW absorption^9,81

+

0.02* [0.004; 0.04]

0.1K/Wm⁻² from⁸¹

4

CC \(\to \,{{\rm{T}}}_{\max }\): non-radiative cooling of clouds, e.g., evaporative cooling following precipitation⁵¹. This effect is only significant during summer and short time scales and the reversed, i.e, reduced precipitation, has been identified as a driver of summer heat waves⁸².

-

−3.3* [−6.05; −1.1]

−0.71⁵¹

5

AOD → SW: ARI¹⁶ through scattering and absorption. Because clouds are represented as cloud area fraction, cloud albedo changes (Twomey effect¹⁷) are also contained in this link.

-

−66.4*[−99.8; −30.95]

ARI: [−27; −20]Wm⁻² from¹⁶ for global annual estimates

6

Clouds \(\to \,{{\rm{T}}}_{\min }\): LW warming at night⁹

+

2.1 [−0.3; 4.5]

[1; 3] K⁸³

7

AOD \(\to \,{{\rm{T}}}_{\min }\) : LW warming through ARI at night^18,19

+

1.9 [0.6; 3.6]

[0.39; 4.56] K (methods)

8

\({{\rm{T}}}_{\min }\,\to \,{{\rm{T}}}_{\max }\)

+

0.5 [0.2; 0.8];

[0;1] due to

9

\({{\rm{T}}}_{\max }\,\to \,{{\rm{T}}}_{\min }\): temporal auto-dependency from sequential measurements

+

0.4 [0.3; 0.5]

temporal auto-dependency