Integrated Calendar

Clouds are among the most influential components of Earth’s radiation budget, modulating radiative transfer across the electromagnetic spectrum. As a result, even processes that contribute relatively weak radiative effects, such as those occurring in clouds’ surroundings, can be substantial compared to clear-sky conditions and therefore important to Earth’s energy budget and the climate it sustains. Over the past two decades, studies have highlighted several mechanisms contributing to the radiative signatures around clouds, including three-dimensional radiative transfer, enhanced aerosol humidification, and subvisible cloud features. Recent work by Eytan et al. (2025) has provided the first quantification of the top-of-atmosphere (TOA) radiative impact of these near-cloud regions. Their findings suggest a shortwave effect of ~9 W/m² over the ocean in the local afternoon, implying that clouds indirectly amplify the aerosol direct radiative effect. In the longwave, a mean effect of ~1 W/m² corresponds to the radiative forcing of an additional ~90 ppm of CO₂, highlighting these regions' climate relevance. In this talk, I will introduce a new framework for partitioning the sky into three radiative categories: cloudy, pure clear-sky, and cloud-influenced clear-sky. I will demonstrate how this refined classification reveals near-cloud regions' hidden but crucial contribution to all-sky radiative fluxes. We will explore how these contributions vary with cloud type, spatial cloud patterns, and background aerosol loading. By explicitly accounting for these previously overlooked regions, this new paradigm opens the door to a more comprehensive understanding of the processes involved in the cloud’s role in Earth’s energy budget and in aerosol–cloud interactions, which are two of the largest sources of uncertainty in climate projections according to the latest IPCC report. Ultimately, this work aims to establish a more unified approach to treating the atmosphere, from dry aerosols to clouds, and to deepen our understanding of how clouds and their surrounding environments influence Earth’s climate. In doing so, it offers a promising path toward reducing one of the most persistent uncertainties in climate change projections.

I will introduce the analytic structure theory of Lie groups through their connection with Lie algebras, which capture the infinitesimal behavior of the group. We will explore how the exponential map and the Baker–Campbell–Hausdorff formula bridge the two, leading to key insights such as the local-to-global correspondence and automatic analyticity of Lie groups. I will mostly follow pages 25–51 in Terrence Tao’s book.