Machine learning reveals strong grid-scale dependence in the satellite <i>N</i> _d –LWP relationship

Abstract. The relationship between cloud droplet number concentration (Nd) and liquid water path (LWP) is highly uncertain yet crucial for determining the impact of aerosol-cloud interactions (ACI) on Earth's radiation budget. The Nd-LWP relationship is examined using a machine learning (ML) random forest model applied to five years of satellite data at grid resolutions ranging from 10° to 0.05° in 12 distinct regions. In the subtropics, the shape of the Nd-LWP relationship switches from an inverted-V at 1° grid-resolution to an “M” shape at 0.1° resolution with decreased dln⁡LWPdln⁡Nd sensitivity. Tropical and midlatitude regions generally show a more positive sensitivity. Cloud sampling and filtering also influence this slope, wherein the exclusion of thin clouds, as commonly performed to reduce retrieval uncertainty, leads to strongly negative sensitivity across all regions. Precipitation is primarily responsible for driving the strength of the sensitivity, with strong positive slopes in raining clouds and negative and/or neutral responses found in non-raining clouds. A new method to compute radiative forcing from the ML model shows a robust Twomey radiative forcing across all regions and grid resolutions. However, LWP and cloud fraction adjustments to the radiative forcing, which are ∼50 % or smaller than the Twomey effect, decrease to negligible values with higher spatial resolution data. As Earth system models move toward higher spatial resolutions in the future, evaluating the LWP and CF adjustment contributions to the radiative forcing budget at these finer resolutions will be essential for evaluation and model development.