Terrestrial vegetation plays a central role in regulating the carbon and water cycles, and adjusting planetary albedo. As such, a clear understanding and accurate characterization of vegetation dynamics is critical to understanding and modeling the broader climate system. Maximum tree height is an important feature of forest vegetation because it is directly related to the overall scale of many ecological and environmental quantities and is an important indicator for understanding several properties of plant communities, including total standing biomass and resource use. We present a model that predicts local maximal tree height across the entire continental United States, in good agreement with data. The model combines scaling laws, which encode the average, base-line behavior of many tree characteristics, with energy budgets constrained by local resource limitations, such as precipitation, temperature and solar radiation. In addition to predicting maximum tree height in an environment, our framework can be extended to predict how other tree traits, such as stomatal density, depend on these resource constraints. Furthermore, it offers predictions for the relationship between height and whole canopy albedo, which is important for understanding the Earth's radiative budget, a critical component of the climate system. Because our model focuses on dominant features, which are represented by a small set of mechanisms, it can be easily integrated into more complicated ecological or climate models.

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Long-term environmental performance assessments of natural processes, including erosion, are critically important for waste repository site evaluation. However, assessing a site’s ability to continuously function is challenging due to parameter uncertainty and compounding nonlinear processes. In lieu of unavailable site data for model calibration, we present a workflow to include multiple sources of surrogate data and reduced-order models to validate parameters for a long-term erosion assessment of a low-level radioactive nuclear waste repository. We apply this new workflow to a low-level waste repository on mesas in Los Alamos National Laboratory in New Mexico. To account for parameter uncertainty, we simulate high-, moderate-, and low-erosion cases. The assessment extends to 10,000 years, which results in large erosion uncertainties, but is necessary given the nature of the interred waste. Our long-term erosion analysis shows that high-erosion scenarios produce rounded mesa tops and partially filled canyons, diverging from the moderate-erosion case that results in gullies and sharp mesa rims. Our novel model parameterization workflow and modeling exercise demonstrates the utility of long-term assessments, identifies sources of erosion forecast uncertainty, and demonstrates the utility of landscape evolution model development. We conclude with a discussion on methods to reduce assessment uncertainty and increase model confidence.

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Two forms of the so-called mixed-potential electric field integral equation (MPIE) are developed for two-dimensional, perfectly conducting (PC) surfaces of arbitrary shape in the presence of an infinite, PC wedge, subject to transverse electric excitation. One of the MPIEs is based on the Coulomb gauge while the other employs the Lorentz gauge. In either case the effect of the wedge is incorporated in the integral equation by means of the appropriate Green's functions, leaving the current distribution on the arbitrary surface as the only unknown. The Green' s functions are derived by the eigenfunction expansion technique. A well-established moment method procedure is adapted to numerically solve both forms of the MPIE. Computed results are presented for several cases of interest, and the relative merits of the Coulomb and Lorentz gauge MPIEs are discussed.