The Effects of Tidal Forcing on Nutrient Fluxes in the Tidal, Freshwater James River Estuary, VA

A 12-month study (January to December 2015) focused on the effects of tidal forcing on nutrient fluxes in the tidal, freshwater segment of the James River Estuary (JRE). Discrete sampling of nutrient chemistry and continuous monitoring of tidal discharge were used to determine the volume and timing of the tides, and differences in nutrient concentrations between incoming and outgoing tides. The goal of this study was to improve understanding of tidal influence on nutrient fluxes and their role in nutrient transport to the lower estuary. Results suggested that differences in nutrient concentrations between incoming and outgoing tides were small throughout the year. This finding suggests that nutrient fluxes at the study site, near the tidal fresh-oligohaline boundary of the James, are largely determined by tidal volume owing to weak concentrations gradients. Changes in water quality during seaward and landward tidal excursions into deeper versus shallower segments were analyzed to infer biogeochemical processes. Differences in oxygen production and nitrate utilization suggest greater autotrophy during landward excursions, consistent with more favorable light conditions. This work was conducted as a collaborative effort between Virginia Commonwealth University, the USGS, Randolph-Macon College, and Washington and Lee University participating in the “Mountains to the Sea” project

Kolmogorov widths under holomorphic mappings

If $L$ is a bounded linear operator mapping the Banach space $X$ into the Banach space $Y$ and $K$ is a compact set in $X$, then the Kolmogorov widths of the image $L(K)$ do not exceed those of $K$ multiplied by the norm of $L$. We extend this result from linear maps to holomorphic mappings $u$ from $X$ to $Y$ in the following sense: when the $n$ widths of $K$ are $O(n^{-r})$ for some r\textgreater{}1, then those of $u(K)$ are $O(n^{-s})$ for any s \textless{} r-1, We then use these results to prove various theorems about Kolmogorov widths of manifolds consisting of solutions to certain parametrized PDEs. Results of this type are important in the numerical analysis of reduced bases and other reduced modeling methods, since the best possible performance of such methods is governed by the rate of decay of the Kolmogorov widths of the solution manifold

Approximation of high-dimensional parametric PDEs

Parametrized families of PDEs arise in various contexts such as inverse problems, control and optimization, risk assessment, and uncertainty quantification. In most of these applications, the number of parameters is large or perhaps even infinite. Thus, the development of numerical methods for these parametric problems is faced with the possible curse of dimensionality. This article is directed at (i) identifying and understanding which properties of parametric equations allow one to avoid this curse and (ii) developing and analyzing effective numerical methodd which fully exploit these properties and, in turn, are immune to the growth in dimensionality. The first part of this article studies the smoothness and approximability of the solution map, that is, the map $a\mapsto u(a)$ where $a$ is the parameter value and $u(a)$ is the corresponding solution to the PDE. It is shown that for many relevant parametric PDEs, the parametric smoothness of this map is typically holomorphic and also highly anisotropic in that the relevant parameters are of widely varying importance in describing the solution. These two properties are then exploited to establish convergence rates of $n$-term approximations to the solution map for which each term is separable in the parametric and physical variables. These results reveal that, at least on a theoretical level, the solution map can be well approximated by discretizations of moderate complexity, thereby showing how the curse of dimensionality is broken. This theoretical analysis is carried out through concepts of approximation theory such as best $n$-term approximation, sparsity, and $n$-widths. These notions determine a priori the best possible performance of numerical methods and thus serve as a benchmark for concrete algorithms. The second part of this article turns to the development of numerical algorithms based on the theoretically established sparse separable approximations. The numerical methods studied fall into two general categories. The first uses polynomial expansions in terms of the parameters to approximate the solution map. The second one searches for suitable low dimensional spaces for simultaneously approximating all members of the parametric family. The numerical implementation of these approaches is carried out through adaptive and greedy algorithms. An a priori analysis of the performance of these algorithms establishes how well they meet the theoretical benchmarks

\u3cem\u3eLaunching through the Surf\u3c/em\u3e Traveling Exhibit Panel 15: Yamhill County Connections

McMinnville and other Yamhill County cities have had a close association with Pacific City and the dory fleet since the late 1800s. Panel 15 is the first of two panels that chronicle the issues and the people who have forged those ties. The panel features vintage photographs from the collections of dory fishers interviewed for the project.https://digitalcommons.linfield.edu/dory_exhibit/1014/thumbnail.jp

\u3cem\u3eLaunching through the Surf\u3c/em\u3e Traveling Exhibit Panel 13: Blessing of the Fleet

Like many fishing communities, the Pacific City dory community honors its fleet, asks for bountiful and safe fishing for the coming season, and remembers those who have died during the year at the annual Blessing of the Fleet. The ceremony is held on the beach the first Saturday in June. In a similar vein, the community celebrates the dories and honors those who made significant contributions to the fleet and the community during the Memorial Wall Ceremony. This observance normally takes place during Dory Days. Panel 13 describes both of these events.https://digitalcommons.linfield.edu/dory_exhibit/1012/thumbnail.jp

\u3cem\u3eLaunching through the Surf\u3c/em\u3e Traveling Exhibit Panel 02: Historical Highlights

The first of three panels in the exhibit that provide general historical highlights about the Dory Fleet, panel two features a timeline of events from 1855 to 1935. It incorporates a section from the Oregon House Calendar of 1927, chronicling the introduction and passage of House Bill 282. This legislation closed the Nestucca River to commercial fishing. The panel also includes an excerpt from the 1927 version of the Oregon Voters’ Pamphlet that describes an initiative to overturn the legislative action.https://digitalcommons.linfield.edu/dory_exhibit/1001/thumbnail.jp

\u3cem\u3eLaunching through the Surf\u3c/em\u3e Traveling Exhibit Panel 01: Title

Panel one serves as the title panel of the traveling exhibit. It was adapted from the cover designed by Candido Salinas for the Fall 2012 issue of the Linfield Magazine. The panel features a vintage photograph from the Coon Family Collection depicting double-enders launching from the beach in 1957.https://digitalcommons.linfield.edu/dory_exhibit/1000/thumbnail.jp

\u3cem\u3eLaunching through the Surf\u3c/em\u3e Traveling Exhibit Panel 11: Turning Oars for a Dory

Exhibit panel 11 describes the procedure for turning oars for a dory. Partners Paul Hanneman and Terry Learned have crafted the Cape Kiwanda Wood Products dory oars since the early 1960s. During the spring of 2012, project collaborator Tyrone Marshall photographed the process.https://digitalcommons.linfield.edu/dory_exhibit/1010/thumbnail.jp

\u3cem\u3eLaunching through the Surf\u3c/em\u3e Traveling Exhibit Panel 14: The Memorial Wall

Incorporating drawings and photographs from the Tom Donohue Collection, panel 14 documents the process of building the Memorial Wall at Cape Kiwanda, as well as its dedication in 2009.https://digitalcommons.linfield.edu/dory_exhibit/1013/thumbnail.jp

\u3cem\u3eLaunching through the Surf\u3c/em\u3e Traveling Exhibit Panel 18: The Project - The Play

Panel 18 depicts the development of the production of Kickin’ Sand and Tellin’ Lies, a play based on the oral histories collected during the project. The play was performed in November 2012 at the Marshall Theatre on the Linfield College campus in McMinnville and at the Kiawanda Community Center in Pacific City. It is the second of three exhibit panels that chronicle the Launching through the Surf project.https://digitalcommons.linfield.edu/dory_exhibit/1017/thumbnail.jp