2025 Theses Doctoral

Computational and Theoretical Approaches to Spectral Challenges in Atmospheric Radiation

Czarnecki, Paulina

Atmospheric longwave (thermal) and shortwave (solar) radiation sets the Earth's energy balance, playing a crucial role in weather and climate. While the fundamental physics of radiation are well-known, radiative flux can vary by orders of magnitude across space, time, and frequency, making the total flow of energy through the atmosphere difficult to compute and understand. This doctoral thesis focuses on simplifying the spectral dimension via developing algorithms for more efficient, accurate, and transparent calculation of radiation for Earth system modeling as well as theoretical work with the goal of clarifying underlying physical relationships.

The first half of the dissertation explores the mathematical optimization of spectral integration by reducing the complexity of the spectral dimension. In the first chapter, we describe a novel method called data-driven quadrature (DDQ), which uses a linear weighted sum of monochromatic calculations at a small set of optimally-chosen frequencies to calculate the broadband (spectrally-integrated) thermal flux. We evaluate the method against two modern parameterizations (correlated 𝑘-distributions) and find that we can achieve comparable errors with 32 spectral points, an orders-of-magnitude dimension reduction from the millions of absorption lines that make up the electromagnetic spectrum. The second chapter follows up on the first, updating the optimization algorithm to support shortwave calculations, which must additionally be robust to variations in solar zenith angle and surface reflectivity. We expand both the longwave and shortwave schemes to capture variability in major greenhouse gas concentrations with potential application to different climate scenarios and rigorously evaluate the scheme in clear and cloudy skies.

The second half of the dissertation focuses on understanding interactions between radiation and the climate system via pencil-and-paper theory. In the third chapter, we derive analytical models of radiative forcing by well-mixed greenhouse gases including methane (CH₄), nitrous oxide (N₂O), and chlorofluorocarbons (CFCs). Radiative forcing by an optically thin absorber (e.g., CFC-12) is governed by emission throughout the troposphere and scaled by the total change in gas concentration, such that a linear increase in gas abundance yields a linear increase in forcing. Conversely, gases that are both optically thin and optically thick across their absorption spectrum, such as N₂ and CH₄, can be understood as a combination of the two regimes, yielding a super-logarithmic relationship to concentration. Our theory is in excellent agreement with full-physics line-by-line calculations in atmospheres with and without spectral overlap by water vapor.

Finally, the fourth chapter explores the spectral overlap of greenhouse gases with clouds in the longwave. We derive analytical models describing the radiative impact of clouds and test our ideas in output from a cutting-edge global storm resolving model. Low clouds exert a limited cloud radiative effect not only because their temperatures are similar to the surface temperature, as commonly cited, but because of masking by water vapor absorption. As surface temperatures change, feedbacks by gases continue to play a role in cloudy column; additionally, clouds that warm with the atmosphere can provide a stabilizing feedback when they mask the otherwise amplifying feedback of the water vapor continuum.

Together, these four chapters contribute to both computational tractability and analytical understanding of the flows of radiant energy through Earth's atmosphere.