Barbara Mary Johnston

Australian dust storms in 2002–2003 and their impact on Southern Ocean biogeochemistry

During late 2002 and early 2003 southern Australia was in the grip of drought and experienced one of its most active dust storm seasons in the last 40 years with large dust plumes frequently advected over the adjacent Southern Ocean. We use meteorological records of dust activity, satellite ocean colour and aerosol optical depth data, and dust transport modeling to investigate the transport and deposition of mineral dust from Australia over adjacent ocean regions and to correlate it with biological response in phytoplankton standing stock as measured by chlorophyll-a concentration in five-degree latitude bands from 40-60°S. Seasonal maxima in mean surface chlorophyll-a of ~0.5 mg m-3 were not achieved until late Jan 2003 or during February in the more southerly bands, which when compared with a 9-year satellite mean climatology suggests the phenology of the bloom in 2002-03 was atypical. Contemporaneous field data on CO2 fugacity collected on transects between Tasmania and Antarctica show that significant atmospheric CO2 drawdown occurred as far south as 60°S during February 2003. Our results provide strong evidence for a large-scale natural dust fertilization event in the Australian sector of the Southern Ocean, and highlight the importance of dust-derived nutrients in the marine carbon cycle of the Southern Ocean.

A new method for the numerical evaluation of nearly singular integrals on triangular elements in the 3D boundary element method

A new method (the sinh-sigmoidal method) is proposed for the numerical evaluation of both nearly weakly and nearly strongly singular integrals on triangular boundary elements. These integrals arise in the 3D boundary element method when the source point is very close to the element of integration. The new polar coordinate-based method introduces a sinh transformation in the radial direction and a sigmoidal transformation in the angular direction, before the application of Gaussian quadrature. It also uses approximately twice as many quadrature points in the angular direction as in the radial direction, in response to a finding that the evaluation of these types of integrals is particularly sensitive to the placement of the quadrature points in the angular direction. Comparisons with various other methods demonstrate its accuracy and competitiveness. A major advantage of the new method is its ease of implementation and applicability to a wide class of integrals.

Time Reversibility, Correlation Decay and the Steady State Fluctuation Relation for Dissipation

Steady state fluctuation relations for nonequilibrium systems are under intense investigation because of their important practical implications in nanotechnology and biology. However the precise conditions under which they hold need clarification. Using the dissipation function, which is related to the entropy production of linear irreversible thermodynamics, we show time reversibility, ergodic consistency and a recently introduced form of correlation decay, called T-mixing, are sufficient conditions for steady state fluctuation relations to hold. Our results are not restricted to a particular model and show that the steady state fluctuation relation for the dissipation function holds near or far from equilibrium subject to these conditions. The dissipation function thus plays a comparable role in nonequilibrium systems to thermodynamic potentials in equilibrium systems.

Interannual variability in estimated biological productivity in the Australian sector of the Southern Ocean in 1997–2007

Changes in biological productivity in the Southern Ocean have the potential to have a significant effect on world climate. Here we use a combination of satellite, model and model reanalysis data to examine climate variability in the Australian sector of the Southern Ocean (110-160°E, 40-70°S) to identify the controls on chlorophyll-a (a proxy for phytoplankton biomass) and primary productivity and evaluate trends in these controls over the period 1997.2007. In summer, in the 65-70°S zone, sea-ice concentration together with the Southern Annular Mode explains 51% of the variance in chlorophyll-a, while mean wind stress and sea-surface temperature explains 55% of the variance in the 60-65°S zone. Further north, key controls are photosynthetically active radiation, sea-surface temperature, mixed layer depth and stratification. Trends in hydrodynamic variables are found to often be opposite in sign and up to an order of magnitude larger than those previously identified in the same sector for 1958-2005. Allowing for the effect of shorter time series on the magnitude of the trends, many recent trends seem to be outside the range of previous variability. These results are consistent with a shift in the ocean state in the past 10-15 yr, in response to a shift in climate.

Clenshaw-Curtis and Gauss-Legendre Quadrature for Certain Boundary Element Integrals

Following a recent article by Trefethen [SIAM Review, 50 (2008), pp. 67-87], the use of Clenshaw-Curtis quadrature rather than Gauss-Legendre quadrature for nearly singular integrals which arise in the boundary element method has been investigated. When these quadrature rules are used in association with the sinh-transformation, the authors have concluded, after considering asymptotic estimates of the truncation errors for certain proto-type functions arising in this context, that Gauss-Legendre quadrature should continue to be the preferred quadrature rule.

Long‐term trends in upper ocean structure and meridional circulation of the Southern Ocean south of Australia derived from the SODA reanalysis

Abstract Decadal-scale changes in the meridional circulation of the Southern Ocean south of Australia are studied, over the period 1958–2005, using Simple Ocean Data Assimilation (SODA) reanalysis data. Upper Circumpolar Deep Water (UCDW) is found to upwell nearer to the surface over time, while the mixed layer (ML) is found to deepen, leading to an increase in the number of times that UCDW intrudes into the ML. This entrainment of nutrients, especially iron, into the ML from UCDW, is crucial for primary production and appears to occur predominantly in summer/autumn, contrary to previous reports. ML temperature, density and salinity all show increasing trends in almost all seasons and latitudinal zones within the study region. A notable exception to the general increase in temperature occurs in the most southerly zone 60–65◦S in summer. An explanation for this apparent anomaly could be related to increased winds (in conjunction with the increasing trend in the Southern Annular Mode), which mix remnant winter water into the ML, negating the surface temperature increase. Unlike trends in ML variables, trends in UCDW variables appear to be decoupled from the surface trends and occur on time-scales that may be centennial rather than decadal.

Quantifying the effect of uncertainty in input parameters in a simplified bidomain model of partial thickness ischaemia

Reduced blood flow in the coronary arteries can lead to damaged heart tissue (myocardial ischaemia). Although one method for detecting myocardial ischaemia involves changes in the ST segment of the electrocardiogram, the relationship between these changes and subendocardial ischaemia is not fully understood. In this study, we modelled ST-segment epicardial potentials in a slab model of cardiac ventricular tissue, with a central ischaemic region, using the bidomain model, which considers conduction longitudinal, transverse and normal to the cardiac fibres. We systematically quantified the effect of uncertainty on the input parameters, fibre rotation angle, ischaemic depth, blood conductivity and six bidomain conductivities, on outputs that characterise the epicardial potential distribution. We found that three typical types of epicardial potential distributions (one minimum over the central ischaemic region, a tripole of minima, and two minima flanking a central maximum) could all occur for a wide range of ischaemic depths. In addition, the positions of the minima were affected by both the fibre rotation angle and the ischaemic depth, but not by changes in the conductivity values. We also showed that the magnitude of ST depression is affected only by changes in the longitudinal and normal conductivities, but not by the transverse conductivities.

Estimates of the error in Gauss-Legendre quadrature for double integrals

Error estimates are a very important aspect of numerical integration. It is desirable to know what level of truncation error might be expected for a given number of integration points. Here, we determine estimates for the truncation error when Gauss-Legendre quadrature is applied to the numerical evaluation of two dimensional integrals which arise in the boundary element method. Two examples are considered; one where the integrand contains poles, when its definition is extended into the complex plane, and another which contains branch points. In both cases we obtain error estimates which agree with the actual error to at least one significant digit.

Possible Four-Electrode Configurations for Measuring Cardiac Tissue Fiber Rotation

A number of electrode configurations, based on the usual four-electrode probe, are analysed in relation to the effect that changes in cardiac fiber rotation have on the potentials measured. Simulations are carried out using a mathematical model and a new solution technique, based on Fourier series followed by a simple one-dimensional finite difference scheme. This electrode analysis leads to the proposal of an in-principle method for determining cardiac fiber rotation

A multi-electrode array and inversion technique for retrieving six conductivities from heart potential measurements

A method for accurately finding cardiac bidomain conductivity parameters is a crucial part of efforts to study and understand the electrical functioning of the heart. The bidomain model considers current flowing along (longitudinal) and across (transverse) sheets of cardiac fibres, as well as between these sheets (normal), in both the extracellular and intracellular domains, which leads to six conductivity values. To match experimental studies, such a method must be able to determine these six conductivity values, not just the four where it is assumed that the transverse and normal conductivities are equal. This study presents a mathematical model, solution technique, multi-electrode array and two-pass inversion method, which can be used to retrieve all six conductivities from measurements of electrical potential made on the array. Simulated measurements of potential, to which noise is added, are used to demonstrate the ability of the method to retrieve the conductivity values. It is found that not only is it possible to accurately retrieve all six conductivity values, as well as a value for fibre rotation angle, but that the accuracy of such retrievals is comparable to the accuracy found in a previous study when only four conductivities (and fibre rotation) were retrieved.