An emulator approach to stratocumulus susceptibility

The climatic relevance of aerosol–cloud interactions depends on the sensitivity of the radiative effect of clouds to cloud droplet number inline-formulaN, and liquid water path LWP. We derive the dependence of cloud fraction CF, cloud albedo inline-formulaA_C, and the relative cloud radiative effect inline-formula $M3inlinescrollmathml\text{rCRE}=\text{CF}\cdot A_{\text{C}}$ 75pt13ptsvg-formulamathimg04b90a5dc217adf737c6571084a1e32c acp-19-10191-2019-ie00001.svg75pt13ptacp-19-10191-2019-ie00001.png on inline-formulaN and LWP from 159 large-eddy simulations of nocturnal stratocumulus. These simulations vary in their initial conditions for temperature, moisture, boundary-layer height, and aerosol concentration but share boundary conditions for surface fluxes and subsidence. Our approach is based on Gaussian-process emulation, a statistical technique related to machine learning. We succeed in building emulators that accurately predict simulated values of CF, inline-formulaA_C, and rCRE for given values of inline-formulaN and LWP. Emulator-derived susceptibilities inline-formula $M7inlinescrollmathml\partial \ln \text{rCRE}/\partial \ln N$ 79pt14ptsvg-formulamathimg754867febeb12f3e2702559dae288dbe acp-19-10191-2019-ie00002.svg79pt14ptacp-19-10191-2019-ie00002.png and inline-formula $M8inlinescrollmathml\partial \ln \text{rCRE}/\partial \ln \text{LWP}$ 94pt14ptsvg-formulamathimg13d5a44c4b9d759c1e81a57e52a37726 acp-19-10191-2019-ie00003.svg94pt14ptacp-19-10191-2019-ie00003.png cover the nondrizzling, fully overcast regime as well as the drizzling regime with broken cloud cover. Theoretical results, which are limited to the nondrizzling regime, are reproduced. The susceptibility inline-formula $M9inlinescrollmathml\partial \ln \text{rCRE}/\partial \ln N$ 79pt14ptsvg-formulamathimgfebfb39e1021efe691810f564824a15b acp-19-10191-2019-ie00004.svg79pt14ptacp-19-10191-2019-ie00004.png captures the strong sensitivity of the cloud radiative effect to cloud fraction, while the susceptibility inline-formula $M10inlinescrollmathml\partial \ln \text{rCRE}/\partial \ln \text{LWP}$ 94pt14ptsvg-formulamathimg9db89e2bed541b688ed7a46d4da6c12d acp-19-10191-2019-ie00005.svg94pt14ptacp-19-10191-2019-ie00005.png describes the influence of cloud amount on cloud albedo irrespective of cloud fraction. Our emulation-based approach provides a powerful tool for summarizing complex data in a simple framework that captures the sensitivities of cloud-field properties over a wide range of states.