Richard Karsten

Constructing the Residual Circulation of the ACC from Observations

The dynamics of the meridional overturning of the Antarctic Circumpolar Current (ACC) are best described in terms of a residual circulation that sums the transport of the wind-driven Ekman layer to the transport associated with eddies. Here an attempt is made to infer the residual circulation from observations by combining altimetric data and gridded hydrographic data to estimate eddy fluxes and winds to estimate Ekman transport. At the surface, a flow directed equatorward on the poleward flank of the ACC, and directed poleward on the equatorward flank of the ACC, is deduced. This convergence of flow into the axis of the ACC drives the subduction of the Antarctic Intermediate Water. Weak southward residual flow on the equatorward boundary of the ACC indicates that here Ekman transport is offset by eddy fluxes. The sense of the deduced residual circulation suggests that buoyancy is gained by the ocean through air‐sea flux poleward of the ACC, in broad agreement with observations. The surface residual circulation is mapped down to depth to yield two counterrotating meridional cells associated with the transformation of North Atlantic Deep Water and Subantarctic Mode Water into Antarctic Intermediate Water. The circulation suggested by these cells agrees remarkably well with the subsurface distribution of salinity and dissolved oxygen. The dependence of the residual circulation estimate on the magnitude of assumed eddy transfer and mixing coefficients is discussed.

The Role of Eddy Transfer in Setting the Stratification and Transport of a Circumpolar Current

Abstract High resolution numerical experiments of a circumpolar current are diagnosed to study how lateral and vertical transfer of buoyancy by geostrophic eddies balances advection by a meridional circulation driven by surface wind stresses and buoyancy fluxes. A theory is developed in the framework of the “residual circulation” to relate the vertical and horizontal stratification set up to the transfer properties of eddies and the patterns of imposed wind and buoyancy forcing. Simple expressions are found for the depth of penetration, stratification, baroclinic transport, and residual circulation of the current. Finally, the ideas are applied to the Antarctic Circumpolar Current (ACC) and yield predictions for how its properties depend on wind and buoyancy forcing.

Can Eddies Set Ocean Stratification

Abstract A simple theory is presented for the buoyancy anomaly and depth of penetration of a warm lens created by a surface buoyancy flux and Ekman pumping in an initially homogeneous, rotating fluid. It is assumed that the overturning of isopycnals induced by pumping and differential heating balances the counteroverturning tendency of baroclinic instability. Baroclinic eddies not only develop on the stratified lens, but also play a fundamental role in setting its stratification. The theory is successfully tested against numerical and laboratory experiments in which the mechanically induced deepening of a buoyant lens is arrested by its baroclinic instability. Finally the possibility is discussed that the eddy transfer process studied here might play a role in setting the stratification and depth of the main thermocline in the ocean.

A Computationally Stable Approach to Gaussian Process Interpolation of Deterministic Computer Simulation Data

For many expensive deterministic computer simulators, the outputs do not have replication error and the desired metamodel (or statistical emulator) is an interpolator of the observed data. Realizations of Gaussian spatial processes (GP) are commonly used to model such simulator outputs. Fitting a GP model to n data points requires the computation of the inverse and determinant of n×n correlation matrices, R, that are sometimes computationally unstable due to near-singularity of R. This happens if any pair of design points are very close together in the input space. The popular approach to overcome near-singularity is to introduce a small nugget (or jitter) parameter in the model that is estimated along with other model parameters. The inclusion of a nugget in the model often causes unnecessary over-smoothing of the data. In this article, we propose a lower bound on the nugget that minimizes the over-smoothing and an iterative regularization approach to construct a predictor that further improves the interpolation accuracy. We also show that the proposed predictor converges to the GP interpolator.

On tidal resonance in the global ocean and the back-effect of coastal tides upon open-ocean tides

Abstract The resonance of semi‐diurnal tidal elevations is investigated with a forward numerical forced damped global tide model and an analytical model of forced‐damped tides in a deep ocean basin coupled to a shelf. The analytical model contains the classical half‐wavelength and quarter‐wavelength resonances in the deep ocean and shelf, respectively, as well as a forcing‐scale dependence which depends on the ratio of the phase speed of open‐ocean gravity waves to that of the astronomical forcing. In the analytical model, when the deep ocean and shelf resonate separately at the same frequency, the resonance in the coupled system shifts to frequencies slightly higher and lower than the original frequency, such that a ‘double bump’ is seen in plots of elevation amplitude versus frequency. The addition of a shelf to a resonant open ocean tends to reduce open‐ocean tides, especially when the shelf is also near resonance. The magnitude of this ‘back‐effect’ is controlled by shelf friction. A weakly damped resonant shelf has a larger back‐effect on the open‐ocean tide than does a strongly damped shelf. Numerical simulations largely bear out the analytical model predictions, at least qualitatively. Idealized simulations show that continents enhance tides by enabling the half‐wavelength resonance. Simulations with realistic geometry and topography but varying longitudinal structure in the astronomical forcing display an influence of the forcing scale on tidal amplitudes somewhat similar to that seen in the analytical model. A frequency sweep in the semi‐diurnal band in experiments with realistic geometry and topography reveals weakly resonant peaks in the amplitudes of several shelf regions and in the globally averaged open‐ocean amplitudes. Finally, the back‐effect of the shelf upon the open ocean is seen in simulations in which locations of resonant coastal tides are blocked out and open‐ocean tidal elevations are significantly altered (increased, generally) as a result.

Assessment of arrays of in-stream tidal turbines in the Bay of Fundy

Theories of in-stream turbines are adapted to analyse the potential electricity generation and impact of turbine arrays deployed in Minas Passage, Bay of Fundy. Linear momentum actuator disc theory (LMADT) is combined with a theory that calculates the flux through the passage to determine both the turbine power and the impact of rows of turbine fences. For realistically small blockage ratios, the theory predicts that extracting 2000–2500 MW of turbine power will result in a reduction in the flow of less than 5 per cent. The theory also suggests that there is little reason to tune the turbines if the blockage ratio remains small. A turbine array model is derived that extends LMADT by using the velocity field from a numerical simulation of the flow through Minas Passage and modelling the turbine wakes. The model calculates the resulting speed of the flow through and around a turbine array, allowing for the sequential positioning of turbines in regions of strongest flow. The model estimates that over 2000 MW of power is possible with only a 2.5 per cent reduction in the flow. If turbines are restricted to depths less than 50 m, the potential power generation is reduced substantially, down to 300 MW. For large turbine arrays, the blockage ratios remain small and the turbines can produce maximum power with a drag coefficient equal to the Betz-limit value.

The semi‐diurnal tide in Hudson strait as a resonant channel oscillation

Abstract Tidal studies have shown that there exists a resonance of the semi‐diurnal tide in the Hudson Bay‐Hudson Strait system. The resonant response is particularly strong within Hudson Strait and Ungava Bay. It is shown here that the semi‐diurnal tide in Hudson Strait has characteristics that are similar to those of a half‐wavelength open channel resonance. A simple analytical model is developed to account for the salient aspects of the semi‐diurnal response in the strait. Non‐dimensional parameters that govern the response are identified and evaluated based on the physical dimensions of the region and results from a numerical tidal model. Taking account of the mechanical impedance presented to the channel by Hudson Bay, the results suggest that a channel mode is resonant near semi‐diurnal periodicities, in general agreement with observations and more complex tidal models of the region. The possibility that Ungava Bay may have a separate quarter‐wavelength resonance driven at the entrance to the continental shelf is also briefly explored.

ON THE POSSIBILITY OF COUNTER-PRODUCTIVE INTERVENTION: THE POPULATION MEAN FOR BLOWFLIES MODELS CAN BE AN INCREASING FUNCTION OF THE DEATH RATE

In this paper, the surprising observation is made that, in a single-species population, an increase in the death rate can in fact lead to an increase in mean population levels. Using a generalized blowflies model, this is shown — numerically as well as analytically — to be a consequence of both the delay and the nonlinearity in the model. Explicit criteria for the occurrence of the observed effects are derived from a Poincare-Lindstedt expansion. The ramifications of the results for pest management are discussed.

An Assessment of the Potential of Tidal Power From Minas Passage, Bay of Fundy, Using Three-Dimensional Models

Large tidal currents exist in Minas Passage, which connects Minas Basin to the Bay of Fundy off the northwestern coast of Nova Scotia. The strong currents through this deep, narrow channel make it a promising location for the generation of electrical power using instream turbines. These strong currents are clearly illustrated in the results of a high-resolution, three-dimensional model of the flow through Minas Passage presented here. The simulations also clearly indicate the asymmetry of the flood and ebb tides and the 3D structure of the flow. A previous study has indicated that as much as 7000 MW could be extracted from the tidal currents through Minas Passage. However, this estimate was based on a complete fence of turbines across the passage, in essence a tidal barrage. In this paper, the power potential of partial turbine fences is examined. In order to estimate the power potential of turbine arrays, the theory of partial turbine fences is adapted to the particular dynamics of Minas Passage. The theory estimates the potential power of the fence and the change in flow that would result. The results are presented in terms of the portion of the cross-sectional area that the turbines occupy and the drag coefficient of the turbines. When the turbine fence occupies a large portion of the passage, the potential power of the fence rises significantly, to a value much larger than estimates based on the kinetic energy flux. The increase in power comes from the increased tidal head that a large turbine fence creates and the resulting increase in the turbine drag. We also present the efficiency of the turbine fence — given as the ratio of the power associated with the turbine drag over the total power extracted from the flow — and the impact of the turbines on the tidal flow. The results of the theory are compared to numerical simulations of the flow through the passage with turbines represented as regions of increased drag. The numerical simulations give power values that are three to six time as high as the theory suggests is possible. This discrepancy is examined by plotting the changes in tidal currents caused by the turbine fence.Copyright

Simulating effects of environmental factors on biological control of Tetranychus urticae by Typhlodromus pyri in apple orchards

Successful biological control of mites is possible under various conditions, and identifying what are the requirements for robust control poses a challenge because interacting factors are involved. Process-based modeling can help to explore these interactions and identify under which conditions biological control is likely, and when not. Here, we present a process-based model for population interactions between the phytophagous mite, Tetranychus urticae, and its predator, Typhlodromus pyri, on apple trees. Temperature and leaf nitrogen concentration influence T. urticae rates of development and reproduction, while temperature and rate of ingestion of prey and pollen influence T. pyri rates of survival and reproduction. Predator and prey population dynamics are linked through a stage structured functional response model that accounts for spatial heterogeneity in population density throughout the trees. T. urticae biomass-days (BMD’s), which account for sizes of larvae, nymphs and adults, indicate level of mite-induced leaf damage. When BMD’s exceed 290 per leaf, there are economic losses. When BMD’s exceed 350 per leaf, T. urticae population growth is curbed and eventually the population decreases. Simulations were run to determine which conditions would lead to current year economic loss and increased risk of loss in the following year, i.e. where more T. urticae than T. pyri are present at the end of September. Risk was high with one or more of the following initial conditions: a high prey: predator ratio (10:1 or more); a low to intermediate (0.04–0.2 T. urticae per leaf) initial density; T. urticae with a higher initial proportion of adult females than T. pyri; and a delayed first detection of mites, whether in late July, or sometimes in late June, but not in early June. Warm summer weather, higher leaf nitrogen and T. urticae immigration into trees were also risk factors. Causes for these patterns based on biological characteristics of T. urticae and T. pyri are discussed, as are counter measures which can be taken to reduce risk.