On the equivalence of Eulerian and Lagrangian variables for the two-component Camassa-Holm system

The Camassa-Holm equation and its two-component Camassa-Holm system generalization both experience wave breaking in finite time. To analyze this, and to obtain solutions past wave breaking, it is common to reformulate the original equation given in Eulerian coordinates, into a system of ordinary differential equations in Lagrangian coordinates. It is of considerable interest to study the stability of solutions and how this is manifested in Eulerian and Lagrangian variables. We identify criteria of convergence, such that convergence in Eulerian coordinates is equivalent to convergence in Lagrangian coordinates. In addition, we show how one can approximate global conservative solutions of the scalar Camassa-Holm equation by smooth solutions of the two-component Camassa-Holm system that do not experience wave breaking

Deriving inherent optical properties from decomposition of hyperspectral non-water absorption

Semi-analytical algorithms (SAAs) developed for multispectral ocean color sensors have benefited from a variety of approaches for retrieving the magnitude and spectral shape of inherent optical properties (IOPs). SAAs generally follow two approaches: 1) simultaneous retrieval of all IOPs, resulting in pre-defined bio-optical models and spectral dependence between IOPs and 2) retrieval of bulk IOPs (absorption and backscattering) first followed by decomposition into separate components, allowing for independent retrievals of some components. Current algorithms used to decompose hyperspectral remotely-sensed reflectance into IOPs follow the first strategy. Here, a spectral deconvolution algorithm for incorporation into the second strategy is presented that decomposes at-w(λ) from in situ measurements and estimates absorption due to phytoplankton (aph(λ)) and colored detrital material (adg(λ)) free of explicit assumptions. The algorithm described here, Derivative Analysis and Iterative Spectral Evaluation of Absorption (DAISEA), provides estimates of aph(λ) and adg(λ) over a spectral range from 350 to 700 nm. Estimated aph(λ) and adg(λ) showed an average normalized root mean square difference of \u3c30% and \u3c20%, respectively, from 350 to 650 nm for the majority of optically distinct environments considered. Estimated Sdg median difference was \u3c20% for all environments considered, while distribution of Sdg uncertainty suggests that biogeochemical variability represented by Sdg can be estimated free of bias. DAISEA results suggest that hyperspectral satellite ocean color data will improve our ability to track biogeochemical processes affiliated with variability in adg(λ) and Sdg free of explicit assumptions

Prospectus, October 12, 1994

https://spark.parkland.edu/prospectus_1994/1016/thumbnail.jp

Optical Classification of an Urbanized Estuary Using Hyperspectral Remote Sensing Reflectance

Optical water classification based on remote sensing reflectance (Rrs(.)) data can provide insight into water components driving optical variability and inform the development and application of bio-optical algorithms in complex aquatic systems. In this study, we use an in situ dataset consisting of hyperspectral Rrs(.) and other biogeochemical and optical parameters collected over nearly five years across a heavily urbanized estuary, the Long Island Sound (LIS), east of New York City, USA, to optically classify LIS waters based on Rrs(.) spectral shape. We investigate the similarities and differences of discrete groupings (k-means clustering) and continuous spectral indexing using the Apparent Visible Wavelength (AVW) in relation to system biogeochemistry and water properties. Our Rrs(.) dataset in LIS was best described by three spectral clusters, the first two accounting for the majority (89%) of Rrs(.) observations and primarily driven by phytoplankton dynamics, with the third confined to measurements in river and river plume waters. We found AVW effective at tracking subtle changes in Rrs(.) spectral shape and fine-scale water quality features along river-to-ocean gradients. The recently developed Quality Water Index Polynomial (QWIP) was applied to evaluate three different atmospheric correction approaches for satellite-derived Rrs(.) from the Sentinel-3 Ocean and Land Colour Instrument (OLCI) sensor in LIS, finding Polymer to be the preferred approach. Our results suggest that integrative, continuous indices such as AVW can be effective indicators to assess nearshore biogeochemical variability and evaluate the quality of both in situ and satellite bio-optical datasets, as needed for improved ecosystem and water resource management in LIS and similar regions

Prospectus, March 29, 1995

*Content Warning* page 5 - Condom use - just for the health of it.https://spark.parkland.edu/prospectus_1995/1009/thumbnail.jp

Prospectus, February 1, 1995

https://spark.parkland.edu/prospectus_1995/1002/thumbnail.jp

Prospectus, December 14, 1994

https://spark.parkland.edu/prospectus_1994/1025/thumbnail.jp

Prospectus, October 5, 1994

https://spark.parkland.edu/prospectus_1994/1015/thumbnail.jp