We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

If model parameterizations of unresolved physics, such as the variety of upper ocean mixing processes, are to hold over the large range of time and space scales of importance to climate, they must be strongly physically based. Observations, theories, and models of oceanic vertical mixing are surveyed. Two distinct regimes are identified: ocean mixing in the boundary layer near the surface under a variety of surface forcing conditions (stabilizing, destabilizing, and wind driven), and mixing in the ocean interior due to internal waves, shear instability, and double diffusion (arising from the different molecular diffusion rates of heat and salt). Mixing schemes commonly applied to the upper ocean are shown not to contain some potentially important boundary layer physics. Therefore a new parameterization of oceanic boundary layer mixing is developed to accommodate some of this physics. It includes a scheme for determining the boundary layer depth h, where the turbulent contribution to the vertical shear of a bulk Richardson number is parameterized. Expressions for diffusivity and nonlocal transport throughout the boundary layer are given. The diffusivity is formulated to agree with similarity theory of turbulence in the surface layer and is subject to the conditions that both it and its vertical gradient match the interior values at h. This nonlocal “K profile parameterization” (KPP) is then verified and compared to alternatives, including its atmospheric counterparts. Its most important feature is shown to be the capability of the boundary layer to penetrate well into a stable thermocline in both convective and wind-driven situations. The diffusivities of the aforementioned three interior mixing processes are modeled as constants, functions of a gradient Richardson number (a measure of the relative importance of stratification to destabilizing shear), and functions of the double-diffusion density ratio, Rρ. Oceanic simulations of convective penetration, wind deepening, and diurnal cycling are used to determine appropriate values for various model parameters as weak functions of vertical resolution. Annual cycle simulations at ocean weather station Papa for 1961 and 1969–1974 are used to test the complete suite of parameterizations. Model and observed temperatures at all depths are shown to agree very well into September, after which systematic advective cooling in the ocean produces expected differences. It is argued that this cooling and a steady salt advection into the model are needed to balance the net annual surface heating and freshwater input. With these advections, good multiyear simulations of temperature and salinity can be achieved. These results and KPP simulations of the diurnal cycle at the Long-Term Upper Ocean Study (LOTUS) site are compared with the results of other models. It is demonstrated that the KPP model exchanges properties between the mixed layer and thermocline in a manner consistent with observations, and at least as well or better than alternatives.

Oceanic vertical mixing: a review and a model with a nonlocal boundary layer parameterization

In this paper we review on the technologies available to make globally quantitative observations of particles, in general, and plankton, in particular, in the world oceans, and for sizes varying from sub-micron to centimeters. Some of these technologies have been available for years while others have only recently emerged. Use of these technologies is critical to improve understanding of the processes that control abundances, distributions and composition of plankton, provide data necessary to constrain and improve ecosystem and biogeochemical models, and forecast changes in marine ecosystems in light of climate change. In this paper we begin by providing the motivation for plankton observations, quantification and diversity qualification on a global scale. We then expand on the state-of-the-art, detailing a variety of relevant and (mostly) mature technologies and measurements, including bulk measurements of plankton, pigment composition, uses of genomic, optical, acoustical methods and analysis using particles counters, flow cytometers and quantitative imaging devices. We follow by highlighting the requirements necessary for a plankton observing system, the approach to achieve it and associated challenges. We conclude with ranked action-item recommendations for the next ten years to move towards our vision of a holistic ocean-wide plankton observing system. Particularly, we suggest to begin with a demonstration project on a GO-SHIP line and/or a long-term observation site and expand from there ensuring that issues associated with methods, observation tools, data analysis, quality assessment and curation are addressed early in the implementation. Global coordination is key for the success of this vision and will bring new insights on processes associated with nutrient regeneration, ocean production, fisheries, and carbon sequestration.

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Globally consistent quantitative observations of planktonic ecosystems

Sorption of PAHs to microplastic and their bioavailability and toxicity to marine copepods under co-exposure conditions

The main characteristics of aqueous dispersions of nanoparticles are considered. One of the results of the work is the synthesis of calcium zirconate nanoparticles. The particles were obtained by the solution combustion method and analyzed by X-ray diffraction and X-ray fluorescence methods. The next step is to preparation of aqueous dispersion based on the synthesized nanoparticles, conducts studies on their stability, and carried out experiments to study the process of dispersion boiling. As a result, a conclusion has been made about a promising method of fixing nanoparticles on the heating surface. The obtained results showed that the heat exchange efficiency at the flat vertical heater is depended on exposure in the bubble boiling regime. The choice of nanoparticles and their concentration also have a significant influence at the discovered effect.

Санкт-Петербургский государственный университет культуры и искусств

Assessing impacts of simulated oil spills on the Northeast Arctic cod fishery.

Few-photon-induced breakup of helium is studied using a newly developed ab initio numerical framework for solving the six-dimensional time-dependent Schroedinger equation. We present details of the method and calculate (generalized) cross sections for the process of two-photon nonsequential (direct) double ionization at photon energies ranging from 39.4 to 54.4 eV, a process that has been very much debated in recent years and is not yet fully understood. In particular, we have studied the convergence property of the total cross section in the vicinity of the upper threshold ({approx} 54.4 eV) versus the pulse duration of the applied laser field. We find that the cross section exhibits an increasing trend near the threshold, as has also been observed by others, and show that this rise cannot solely be attributed to an unintended inclusion of the sequential two-photon double ionization process caused by the bandwidth of the applied field.

Numerical study of two-photon ionization of helium using an ab initio numerical framework

The use of wide-band transmittance imaging to size and classify suspended particulate matter in seawater.

Improving oil spill trajectory modelling in the Arctic

A spatially explicit coupled hydrodynamic-mass transport model system was used to simulate dispersal of particulate organic matter from Atlantic salmon (Salmo salar) farming in central Norway. Model setups of 32 m horizontal resolution were run for periods of up to 650 days for 3 sites of different oceanographic characteristics: one fjord location, one medium-exposed location influenced by fjord water and one coastal location. Records on feed used for each cage at each location were converted to feces released based on a published mass balance model. The results from the simulations were compared with scores from corresponding mandatory benthic surveys (MOM-B) of the sediment layer beneath the farms. The correspondence between simulated and measured thickness of the sediment layer was good, and improved with the inclusion of resuspension processes. At all sites the distribution of organic matter in the bottom layer was non-homogeneous, with significant temporal variation and transport and settling of matter up to at least 0.5 km away from one of the farms. Our results indicate that the monitoring practice used in Norway until now, with a few sediment grab samples taken mainly within the fish farm, may not adequately determine the areal impacts of all salmon farming operations. The patchy distribution of organic matter and the correspondence between simulation and survey results is attributed to the use of full 3D current fields of a high spatiotemporal resolution and a good model for resuspension processes that some previous model studies have failed to properly account for.

/pdf/spatiotemporal-dispersal-and-deposition-of-fish-farm-wastes-3dinzvtyg9.pdf

Raymond Nepstad

Papers

Assessing impacts of simulated oil spills on the Northeast Arctic cod fishery.

Numerical study of two-photon ionization of helium using an ab initio numerical framework

The use of wide-band transmittance imaging to size and classify suspended particulate matter in seawater.

Improving oil spill trajectory modelling in the Arctic

Spatiotemporal Dispersal and Deposition of Fish Farm Wastes: A Model Study from Central Norway