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In this synthesis, we assess present research and anticipate future development needs in modeling water quality in watersheds. We first discuss areas of potential improvement in the representation of freshwater systems pertaining to water quality, including representation of environmental interfaces, in-stream water quality and process interactions, soil health and land management, and (peri-)urban areas. In addition, we provide insights into the contemporary challenges in the practices of watershed water quality modeling, including quality control of monitoring data, model parameterization and calibration, uncertainty management, scale mismatches, and provisioning of modeling tools. Finally, we make three recommendations to provide a path forward for improving watershed water quality modeling science, infrastructure, and practices. These include building stronger collaborations between experimentalists and modelers, bridging gaps between modelers and stakeholders, and cultivating and applying procedural knowledge to better govern and support water quality modeling processes within organizations.

In this synthesis, we assess present research and anticipate future development needs in modeling water quality in watersheds. We first discuss areas of potential improvement in the representation of freshwater systems pertaining to water quality, including representation of environmental interfaces, in-stream water quality and process interactions, soil health and land management, and (peri-)urban areas. In addition, we provide insights into the contemporary challenges in the practices of watershed water quality modeling, including quality control of monitoring data, model parameterization and calibration, uncertainty management, scale mismatches, and provisioning of modeling tools. Finally, we make three recommendations to provide a path forward for improving watershed water quality modeling science, infrastructure, and practices. These include building stronger collaborations between experimentalists and modelers, bridging gaps between modelers and stakeholders, and cultivating and applying procedural knowledge to better govern and support water quality modeling processes within organizations.

The equilibrium shape of a thin inextensible membrane subject to solar radiation pressure under given boundary constraints is studied. The membrane is assumed to be insusceptible to elastic deformation and to have negligible bending resistance, and its steady-state shape is therefore described by a developable surface (i.e., a surface of zero Gaussian curvature), resulting from an equilibrium between radiation pressure and membrane tension forces. A quantitative understanding of the mechanics of such membranes is essential in characterizing the dynamics of solar sail spacecraft that use sail wing tip displacement as an attitude control mode. The analysis in this paper develops a theoretical foundation for the billowed wing shape. Under reasonable simplifying assumptions, the key result is that solar radiation pressure and a given wing tip displacement yield a billowed solar sail wing with the shape of a generalized cylinder (i.e., a developable ruled surface, whose rulings are all parallel, rather than a general developable with variable ruling directions). The base curve geometry for the solar sail is also determined as the solution to a boundary value problem. The results presented herein allow the shape of the billowed membrane to be computed to any desired precision, for any given tip displacement.

The equilibrium shape of a thin inextensible membrane subject to solar radiation pressure under given boundary constraints is studied. The membrane is assumed to be insusceptible to elastic deformation and to have negligible bending resistance, and its steady-state shape is therefore described by a developable surface (i.e., a surface of zero Gaussian curvature), resulting from an equilibrium between radiation pressure and membrane tension forces. A quantitative understanding of the mechanics of such membranes is essential in characterizing the dynamics of solar sail spacecraft that use sail wing tip displacement as an attitude control mode. The analysis in this paper develops a theoretical foundation for the billowed wing shape. Under reasonable simplifying assumptions, the key result is that solar radiation pressure and a given wing tip displacement yield a billowed solar sail wing with the shape of a generalized cylinder (i.e., a developable ruled surface, whose rulings are all parallel, rather than a general developable with variable ruling directions). The base curve geometry for the solar sail is also determined as the solution to a boundary value problem. The results presented herein allow the shape of the billowed membrane to be computed to any desired precision, for any given tip displacement.