Flux comparison of Eulerian and Lagrangian estimates of Agulhas leakage: A case study using a numerical model

Estimating the magnitude of Agulhas leakage, the volume flux of water from the Indian to the Atlantic Ocean, is difficult because of the presence of other circulation systems in the Agulhas region. Indian Ocean water in the Atlantic Ocean is vigorously mixed and diluted in the Cape Basin. Eulerian integration methods, where the velocity field perpendicular to a section is integrated to yield a flux, have to be calibrated so that only the flux by Agulhas leakage is sampled. Two Eulerian methods for estimating the magnitude of Agulhas leakage are tested within a high-resolution two-way nested model with the goal to devise a mooring-based measurement strategy. At the GoodHope line, a section halfway through the Cape Basin, the integrated velocity perpendicular to that line is compared to the magnitude of Agulhas leakage as determined from the transport carried by numerical Lagrangian floats. In the first method, integration is limited to the flux of water warmer and more saline than specific threshold values. These threshold values are determined by maximizing the correlation with the float-determined time series. By using the threshold values, approximately half of the leakage can directly be measured. The total amount of Agulhas leakage can be estimated using a linear regression, within a 90% confidence band of 12 Sv. In the second method, a subregion of the GoodHope line is sought so that integration over that subregion yields an Eulerian flux as close to the float-determined leakage as possible. It appears that when integration is limited within the model to the upper 300 m of the water column within 900 km of the African coast the time series have the smallest root-mean-square difference. This method yields a root-mean-square error of only 5.2 Sv but the 90% confidence band of the estimate is 20 Sv. It is concluded that the optimum thermohaline threshold method leads to more accurate estimates even though the directly measured transport is a factor of two lower than the actual magnitude of Agulhas leakage in this model.

Lagrangian validation of numerical drifter trajectories using drifting buoys: Application to the Agulhas system

The skill of numerical Lagrangian drifter trajectories in three numerical models is assessed by comparing these numerically obtained paths to the trajectories of drifting buoys in the real ocean. The skill assessment is performed using the two-sample Kolmogorov–Smirnov statistical test. To demonstrate the assessment procedure, it is applied to three different models of the Agulhas region. The test can either be performed using crossing positions of one-dimensional sections in order to test model performance in specific locations, or using the total two-dimensional data set of trajectories. The test yields four quantities: a binary decision of model skill, a confidence level which can be used as a measure of goodness-of-fit of the model, a test statistic which can be used to determine the sensitivity of the confidence level, and cumulative distribution functions that aid in the qualitative analysis. The ordering of models by their confidence levels is the same as the ordering based on the qualitative analysis, which suggests that the method is suited for model validation. Only one of the three models, a 1/10° two-way nested regional ocean model, might have skill in the Agulhas region. The other two models, a 1/2° global model and a 1/8° assimilative model, might have skill only on some sections in the region

Numerical simulation of the 12 May 1997 CME Event: The role of magnetic reconnection

We perform a numerical study of the evolution of a Coronal Mass Ejection (CME) and its interaction with the coronal magnetic field based on the 12 May 1997, CME event using a global MagnetoHydroDynamic (MHD) model for the solar corona. The ambient solar wind steady-state solution is driven by photospheric magnetic field data, while the solar eruption is obtained by superimposing an unstable flux rope onto the steady-state solution. During the initial stage of CME expansion, the core flux rope reconnects with the neighboring field, which facilitates lateral expansion of the CME footprint in the low corona. The flux rope field also reconnects with the oppositely orientated overlying magnetic field in the manner of the breakout model. During this stage of the eruption, the simulated CME rotates counter-clockwise to achieve an orientation that is in agreement with the interplanetary flux rope observed at 1 AU. A significant component of the CME that expands into interplanetary space comprises one of the side lobes created mainly as a result of reconnection with the overlying field. Within 3 hours, reconnection effectively modifies the CME connectivity from the initial condition where both footpoints are rooted in the active region to a situation where one footpoint is displaced into the quiet Sun, at a significant distance (≈1R ) from the original source region. The expansion and rotation due to interaction with the overlying magnetic field stops when the CME reaches the outer edge of the helmet streamer belt, where the field is organized on a global scale. The simulation thus offers a new view of the role reconnection plays in rotating a CME flux rope and transporting its footpoints while preserving its core structure.

Adaptive approximate Bayesian computation

Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.'s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine importance sampling arguments bypasses this difficulty, in connection with the population Monte Carlo method of Cappe et al. (2004), and it includes an automatic scaling of the forward kernel. When applied to a population genetics example, it compares favourably with two other versions of the approximate algorithm.

Inferring population history with DIY ABC: a user-friendly approach to approximate Bayesian computation

Genetic data obtained on population samples convey information about their evolutionary history. Inference methods can extract part of this information but they require sophisticated statistical techniques that have been made available to the biologist community (through computer programs) only for simple and standard situations typically involving a small number of samples. We propose here a computer program (DIY ABC) for inference based on approximate Bayesian computation (ABC), in which scenarios can be customized by the user to fit many complex situations involving any number of populations and samples. Such scenarios involve any combination of population divergences, admixtures and population size changes. DIY ABC can be used to compare competing scenarios, estimate parameters for one or more scenarios and compute bias and precision measures for a given scenario and known values of parameters (the current version applies to unlinked microsatellite data). This article describes key methods used in the program and provides its main features. The analysis of one simulated and one real dataset, both with complex evolutionary scenarios, illustrates the main possibilities of DIY ABC.

An approximate Bayesian computation approach to overcome biases that arise when using amplified fragment length polymorphism markers to study population structure

There is great interest in using amplified fragment length polymorphism (AFLP) markers because they are inexpensive and easy to produce. It is, therefore, possible to generate a large number of markers that have a wide coverage of species genotnes. Several statistical methods have been proposed to study the genetic structure using AFLP's but they assume Hardy-Weinberg equilibrium and do not estimate the inbreeding coefficient, F-IS. A Bayesian method has been proposed by Holsinger and colleagues that relaxes these simplifying assumptions but we have identified two sources of bias that can influence estimates based on these markers: (i) the use of a uniform prior on ancestral allele frequencies and (ii) the ascertainment bias of AFLP markers. We present a new Bayesian method that avoids these biases by using an implementation based on the approximate Bayesian computation (ABC) algorithm. This new method estimates population-specific F-IS and F-ST values and offers users the possibility of taking into account the criteria for selecting the markers that are used in the analyses. The software is available at our web site (http://www-leca.uif-grenoble.fi-/logiciels.htm). Finally, we provide advice on how to avoid the effects of ascertainment bias.

Numerical abundance of invasive ants and monopolisation of exudate-producing resources - a chicken and egg situation

1. Invasive ants commonly reach abnormally high abundances and have severe impacts on the ecosystems they invade. Current invasion theory recognises that not only negative interactions, such as natural enemy release, but positive interactions, such as facilitation, are important in causing this increased abundance. 2. For invasive ants, facilitation can occur through mutualism with exudate-producing plants and insects. To obtain such partnerships, however, invaders must first displace native ants, whose communities are highly structured around such resources. 3. By manipulating the abundance of an invasive ant relative to a native, we show that a minimum threshold abundance exists for invasive ants to monopolise exudate-producing resources. In addition, we show that behavioural dominance is context dependent and varies with spatial location and numerical abundance. 4. Thus, we suggest a 'facilitation-threshold' hypothesis of ant invasion, whereby a minimum abundance of invasive ants is required before facilitation and behavioural dominance can drive abundance rapidly upwards through positive feedback.

ONeSAMP: a program to estimate effective population size using approximate Bayesian computation

The estimation of effective population size from one sample of genotypes has been problematic because most estimators have been proven imprecise or biased. We developed a web-based program, ONeSAMP that uses approximate Bayesian computation to estimate effective population size from a sample of microsatellite genotypes. ONeSAMP requires an input file of sampled individuals' microsatellite genotypes along with information about several sampling and biological parameters. ONeSAMP provides an estimate of effective population size, along with 95% credible limits. We illustrate the use of ONeSAMP with an example data set from a re-introduced population of ibex Capra ibex.

Comparative evaluation of a new effective population size estimator based on approximate Bayesian computation

We describe and evaluate a new estimator of the effective population size (N-e), a critical parameter in evolutionary and conservation biology. This new "SummStat" N-e. estimator is based upon the use of summary statistics in an approximate Bayesian computation framework to infer N-e. Simulations of a Wright-Fisher population with known N-e show that the SummStat estimator is useful across a realistic range of individuals and loci sampled, generations between samples, and N-e values. We also address the paucity of information about the relative performance of N-e estimators by comparing the SUMMStat estimator to two recently developed likelihood-based estimators and a traditional moment-based estimator. The SummStat estimator is the least biased of the four estimators compared. In 32 of 36 parameter combinations investigated rising initial allele frequencies drawn from a Dirichlet distribution, it has the lowest bias. The relative mean square error (RMSE) of the SummStat estimator was generally intermediate to the others. All of the estimators had RMSE > 1 when small samples (n = 20, five loci) were collected a generation apart. In contrast, when samples were separated by three or more generations and Ne less than or equal to 50, the SummStat and likelihood-based estimators all had greatly reduced RMSE. Under the conditions simulated, SummStat confidence intervals were more conservative than the likelihood-based estimators and more likely to include true N-e. The greatest strength of the SummStat estimator is its flexible structure. This flexibility allows it to incorporate any, potentially informative summary statistic from Population genetic data.

Effect of internal partitioning on indoor air quality of rooms with mixing ventilation - basic study

The internal partitioning, which is frequently introduced in open-space planning due to its flexibility, was tested to study its effects on the room air quality as well as ventilation performance. For the study, physical tests using a small model room and numerical modeling using CFD computation were utilized to evaluate different test conditions employing mixing ventilation from the ceiling. The partition parameters, such as its location, height, and the gap underneath, as well as contaminant source location were tested under isothermal conditions. This paper summarizes the results from the study.

Numerical study of 2D heat transfer in a scraped surface heat exchanger

A numerical study of fluid mechanics and heat transfer in a scraped surface heat exchanger with non-Newtonian power law fluids is undertaken. Numerical results are generated for 2D steady-state conditions using finite element methods. The effect of blade design and material properties, and especially the independent effects of shear thinning and heat thinning on the flow and heat transfer, are studied. The results show that the gaps at the root of the blades, where the blades are connected to the inner cylinder, remove the stagnation points, reduce the net force on the blades and shift the location of the central stagnation point. The shear thinning property of the fluid reduces the local viscous dissipation close to the singularity corners, i.e. near the tip of the blades, and as a result the local fluid temperature is regulated. The heat thinning effect is greatest for Newtonian fluids where the viscous dissipation and the local temperature are highest at the tip of the blades. Where comparison is possible, very good agreement is found between the numerical results and the available data. Aspects of scraped surface heat exchanger design are assessed in the light of the results. (C) 2003 Elsevier Ltd. All rights reserved.

Robust identification for linear-in-the-parameters models

In this paper new robust nonlinear model construction algorithms for a large class of linear-in-the-parameters models are introduced to enhance model robustness, including three algorithms using combined A- or D-optimality or PRESS statistic (Predicted REsidual Sum of Squares) with regularised orthogonal least squares algorithm respectively. A common characteristic of these algorithms is that the inherent computation efficiency associated with the orthogonalisation scheme in orthogonal least squares or regularised orthogonal least squares has been extended such that the new algorithms are computationally efficient. A numerical example is included to demonstrate effectiveness of the algorithms. Copyright (C) 2003 IFAC.