This study examines shallow cumulus cloud fields and their surface shortwave radiative effects using large-eddy simulation (LES) along with observations across multiple days at the Atmospheric Radiation Measurement Southern Great Plains atmospheric observatory. Pronounced differences are found between probability density functions (PDFs) of downwelling surface solar irradiance derived from observations and LES one-dimensional (1D) online radiation calculations. The shape of the observed PDF is bimodal, which is only reproduced by offline three-dimensional (3D) radiative transfer calculations, demonstrating PDF bimodality as a 3D radiative signature of continental shallow cumuli. Local differences between 3D and 1D radiative transfer calculations of downwelling surface solar irradiance are, on average, larger than 150 W m−2 on one afternoon. The differences are substantially reduced when spatially averaged over the LES domain and temporally averaged over the diurnal cycle, but systematic 3D biases ranging from 2 to 8 W m−2 persist across different days. Covariations between the domain-averaged surface irradiance, framed as a surface cloud radiative effect, and the simulated cloud fraction are found to follow a consistent diurnal relationship, often exhibiting hysteresis. In contrast, observations show highly variable behavior. By subsampling the LES domain, it is shown that this is due to the limited sampling density of inherently 3D observations. These findings help to define observational requirements for detecting such relationships, provide valuable insight for evaluating weather and climate models against surface observations as they push to ever higher resolutions, and have important implications for future assessments of solar renewable energy potential.

Shallow cumulus clouds exhibit highly three-dimensional (3-D) spatial structure leading to complex variability in the surface solar irradiance (SSI) beneath. This variability is captured by the typically bimodal shape of the SSI probability density function (PDF). Using large eddy simulation to generate well-resolved cloud fields and Monte Carlo 3-D radiative transfer to reproduce realistic associated SSI PDFs, we seek direct relationships between the cloud field properties and the SSI PDF shape. Applying both random forest and artificial neural network algorithms, we find variations in the two modes of the SSI PDF are well predicted by just a handful of cloud field properties. The two algorithms utilize cloud properties similarly, with indistinguishable performance despite their different architectures. These results offer a marked improvement in realism relative to one-dimensional radiative transfer while bypassing computationally expensive 3-D radiative transfer, with immediate application to renewable energy assessments, and potential for several other geophysical applications. Plain Language Summary When sunlight is intercepted by broken clouds, it is not straightforward to calculate how much of the sunlight reaches the ground in the cloud shadows or the gaps between them. To account for this properly in atmospheric models typically requires tracking the exact path of sunlight through the Earth-Atmosphere system, which can be a cumbersome task. We present an alternative approach to calculate how frequently different amounts of sunlight reach the surface under broken cloud scenes. This new approach uses just a few key pieces of information about the clouds to make predictions. Compared with existing approaches, the predicted surface sunlight is substantially more realistic. Results are consistent across two different algorithms tested and arrive at predictions in similar ways. The combined accuracy and efficiency of the new approach has several applications.