A Hamiltonian Formulation for Long Internal Waves

A novel canonical Hamiltonian formalism is developed for long internal waves in a rotating environment. This includes the effects of background vorticity and shear on the waves. By restricting consideration to flows in hydrostatic balance, superimposed on a horizontally uniform background of vertical shear and vorticity, a particularly simple Hamiltonian structure arises, which can be thought of as describing a nonlinearly coupled infinite collection of shallow water systems. The kinetic equation describing the time evolution of the spectral energy of internal waves is subsequently derived, and a stationary Kolmogorov solution is found in the high frequency limit. This is surprisingly close to the Garrett--Munk spectrum of oceanic internal waves

AMM: Adaptive Multilinear Meshes

We present Adaptive Multilinear Meshes (AMM), a new framework that significantly reduces the memory footprint compared to existing data structures. AMM uses a hierarchy of cuboidal cells to create continuous, piecewise multilinear representation of uniformly sampled data. Furthermore, AMM can selectively relax or enforce constraints on conformity, continuity, and coverage, creating a highly adaptive and flexible representation to support a wide range of use cases. AMM supports incremental updates in both spatial resolution and numerical precision establishing the first practical data structure that can seamlessly explore the tradeoff between resolution and precision. We use tensor products of linear B-spline wavelets to create an adaptive representation and illustrate the advantages of our framework. AMM provides a simple interface for evaluating the function defined on the adaptive mesh, efficiently traversing the mesh, and manipulating the mesh, including incremental, partial updates. Our framework is easy to adopt for standard visualization and analysis tasks. As an example, we provide a VTK interface, through efficient on-demand conversion, which can be used directly by corresponding tools, such as VisIt, disseminating the advantages of faster processing and a smaller memory footprint to a wider audience. We demonstrate the advantages of our approach for simplifying scalar-valued data for commonly used visualization and analysis tasks using incremental construction, according to mixed resolution and precision data streams

Using Large Databases of Groundwater Chemistry in the Northern Midwest USA: The Effects of Geologic and Anthropogenic Factors

Regional geochemical databases for the northern Midwest USA are being compiled to examine the various geogenic and anthropogenic factors that control the chemistry of groundwater. At the regional scale, variations are seen that are attributable to agricultural and urban effects, or to geologic factors. Examples of the former include enrichments of nitrate in groundwater, while examples of the latter mainly highlight geochemical differences between carbonate rocks and all other rock types in the region. This paper examines a few of these regional effects and the spatial scales at which they can be observe

Seasonal kinetic energy variability of near-inertial motions

Author Posting. © American Meteorological Society, 2009. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 39 (2009): 1035-1049, doi:10.1175/2008JPO3920.1.Seasonal variability of near-inertial horizontal kinetic energy is examined using observations from a series of McLane Moored Profiler moorings located at 39°N, 69°W in the western North Atlantic Ocean in combination with a one-dimensional, depth-integrated kinetic energy model. The time-mean kinetic energy and shear vertical wavenumber spectra of the high-frequency motions at the mooring site are in reasonable agreement with the Garrett–Munk internal wave description. Time series of depth-dependent and depth-integrated near-inertial kinetic energy are calculated from available mooring data after filtering to isolate near-inertial-frequency motions. These data document a pronounced seasonal cycle featuring a wintertime maximum in the depth-integrated near-inertial kinetic energy deriving chiefly from the variability in the upper 500 m of the water column. The seasonal signal in the near-inertial kinetic energy is most prominent for motions with vertical wavelengths greater than 100 m but observable wintertime enhancement is seen down to wavelengths of the order of 10 m. Rotary vertical wavenumber spectra exhibit a dominance of clockwise-with-depth energy, indicative of downward energy propagation and implying a surface energy source. A simple depth-integrated near-inertial kinetic energy model consisting of a wind forcing term and a dissipation term captures the order of magnitude of the observed near-inertial kinetic energy as well as its seasonal cycle.Funding to initiate the McLane Moored Profiler observations at Line W were provided by grants from the G. Unger Vetlesen Foundation and the Comer Charitable Fund to the Woods Hole Oceanographic Institution’s Ocean and Climate Change Institute. Ongoing moored observations at Line W are supported by the National Science Foundation (NSF Grant OCE-0241354)

Quantifying the effect of riming on snowfall using ground-based observations

Ground-based observations of ice particle size distribution and ensemble mean density are used to quantify the effect of riming on snowfall. The rime mass fraction is derived from these measurements by following the approach that is used in a single ice-phase category microphysical scheme proposed for the use in numerical weather prediction models. One of the characteristics of the proposed scheme is that the prefactor of a power law relation that links mass and size of ice particles is determined by the rime mass fraction, while the exponent does not change. To derive the rime mass fraction, a mass-dimensional relation representative of unrimed snow is also determined. To check the validity of the proposed retrieval method, the derived rime mass fraction is converted to the effective liquid water path that is compared to microwave radiometer observations. Since dual-polarization radar observations are often used to detect riming, the impact of riming on dual-polarization radar variables is studied for differential reflectivity measurements. It is shown that the relation between rime mass fraction and differential reflectivity is ambiguous, other factors such as change in median volume diameter need also be considered. Given the current interest on sensitivity of precipitation to aerosol pollution, which could inhibit riming, the importance of riming for surface snow accumulation is investigated. It is found that riming is responsible for 5% to 40% of snowfall mass. The study is based on data collected at the University of Helsinki field station in Hyytiala during U.S. Department of Energy Biogenic Aerosols Effects on Clouds and Climate (BAECC) field campaign and the winter 2014/2015. In total 22 winter storms were analyzed, and detailed analysis of two events is presented to illustrate the study.Peer reviewe