Speaker: Yi Zhang, NYU
Title: "A Planck–optical depth power law in a moist atmosphere"
Abstract:
Water vapor plays two major roles in the Earth’s atmosphere – it condenses and radiates. As a condensable gas, its concentration is strongly shaped by temperature through the Clausius-Clapeyron relation; as a radiatively active gas, it absorbs and emits infrared radiation across a broad range of wavenumbers and acts as a dominant greenhouse gas. Because of these dual roles, Planck emission expressed in optical-depth space for water vapor approximately follows a power law, with the exponent γ being the ratio of photon energy to latent heat per water molecule. This power law traces back to the Boltzmann factor in both the Clausius-Clapeyron relation and Planck’s function. The power law enables analytic solutions of the Schwarzschild equation for upward and downward longwave fluxes, from which atmospheric cooling, outgoing longwave radiation (OLR), and surface downward longwave radiation (DLR) follow directly as functions of surface Planck emission and column-integrated optical depth. The nondimensional parameter γ encapsulates the dual role of water vapor as a condensable and a greenhouse gas, and the same potentially applies to other planetary atmospheres in which the condensable also absorbs planetary radiation.
Bio:
Yi Zhang is an assistant professor of mathematics and atmosphere/ocean science at the Courant Institute of NYU. She earned her PhD from the Program of Atmospheric and Oceanic Sciences from Princeton University in 2021 and her Bachelor’s degree in Physics from Peking University in 2016. She was a Miller Postdoctoral Fellow at the University of California, Berkeley from 2021 to 2023. Her research interests include atmospheric dynamics, thermodynamics, radiative transfer, and extreme events.
In person attendance at this seminar is only open to Columbia University affiliates.