Adjoint goal-based error norms for adaptive mesh ocean modelling

Flow in the world's oceans occurs at a wide range of spatial scales, from a fraction of a metre up to many thousands of kilometers. In particular, regions of intense flow are often highly localised, for example, western boundary currents, equatorial jets, overflows and convective plumes. Conventional numerical ocean models generally use static meshes. The use of dynamically-adaptive meshes has many potential advantages but needs to be guided by an error measure reflecting the underlying physics. A method of defining an error measure to guide an adaptive meshing algorithm for unstructured tetrahedral finite elements, utilizing an adjoint or goal-based method, is described here. This method is based upon a functional, encompassing important features of the flow structure. The sensitivity of this functional, with respect to the solution variables, is used as the basis from which an error measure is derived. This error measure acts to predict those areas of the domain where resolution should be changed. A barotropic wind driven gyre problem is used to demonstrate the capabilities of the method. The overall objective of this work is to develop robust error measures for use in an oceanographic context which will ensure areas of fine mesh resolution are used only where and when they are required. (c) 2006 Elsevier Ltd. All rights reserved.

Reconciling the electron counterstreaming and dropout occurrence rates with the heliospheric flux budget

Counterstreaming electrons (CSEs) are treated as signatures of closed magnetic flux, i.e., loops connected to the Sun at both ends. However, CSEs at 1 AU likely fade as the apex of a closed loop passes beyond some distance R, owing to scattering of the sunward beam along its continually increasing path length. The remaining antisunward beam at 1 AU would then give a false signature of open flux. Subsequent opening of a loop at the Sun by interchange reconnection with an open field line would produce an electron dropout (ED) at 1 AU, as if two open field lines were reconnecting to completely disconnect from the Sun. Thus EDs can be signatures of interchange reconnection as well as the commonly attributed disconnection. We incorporate CSE fadeout into a model that matches time-varying closed flux from interplanetary coronal mass ejections (ICMEs) to the solar cycle variation in heliospheric flux. Using the observed occurrence rate of CSEs at solar maximum, the model estimates R ∼ 8–10 AU. Hence we demonstrate that EDs should be much rarer than CSEs at 1 AU, as EDs can only be detected when the juncture points of reconnected field lines lie sunward of the detector, whereas CSEs continue to be detected in the legs of all loops that have expanded beyond the detector, out to R. We also demonstrate that if closed flux added to the heliosphere by ICMEs is instead balanced by disconnection elsewhere, then ED occurrence at 1 AU would still be rare, contrary to earlier expectations.

Constraining a North Atlantic Ocean general circulation model with chlorofluorocarbon observations

Measurements of anthropogenic tracers such as chlorofluorocarbons and tritium must be quantitatively combined with ocean general circulation models as a component of systematic model development. The authors have developed and tested an inverse method, using a Green's function, to constrain general circulation models with transient tracer data. Using this method chlorofluorocarbon-11 and -12 (CFC-11 and -12) observations are combined with a North Atlantic configuration of the Miami Isopycnic Coordinate Ocean Model with 4/3 degrees resolution. Systematic differences can be seen between the observed CFC concentrations and prior CFC fields simulated by the model. These differences are reduced by the inversion, which determines the optimal gas transfer across the air-sea interface, accounting for uncertainties in the tracer observations. After including the effects of unresolved variability in the CFC fields, the model is found to be inconsistent with the observations because the model/data misfit slightly exceeds the error estimates. By excluding observations in waters ventilated north of the Greenland-Scotland ridge (sigma (0) < 27.82 kg m(-3); shallower than about 2000 m), the fit is improved, indicating that the Nordic overflows are poorly represented in the model. Some systematic differences in the model/data residuals remain and are related, in part, to excessively deep model ventilation near Rockall and deficient ventilation in the main thermocline of the eastern subtropical gyre. Nevertheless, there do not appear to be gross errors in the basin-scale model circulation. Analysis of the CFC inventory using the constrained model suggests that the North Atlantic Ocean shallower than about 2000 m was near 20% saturated in the mid-1990s. Overall, this basin is a sink to 22% of the total atmosphere-to-ocean CFC-11 flux-twice the global average value. The average water mass formation rates over the CFC transient are 7.0 and 6.0 Sv (Sv = 10(6) m(3) s(-1)) for subtropical mode water and subpolar mode water, respectively.

Revisiting youden’s index as a useful measure of the misclassification error in meta-analysis of diagnostic studies

The paper considers meta-analysis of diagnostic studies that use a continuous score for classification of study participants into healthy or diseased groups. Classification is often done on the basis of a threshold or cut-off value, which might vary between studies. Consequently, conventional meta-analysis methodology focusing solely on separate analysis of sensitivity and specificity might be confounded by a potentially unknown variation of the cut-off value. To cope with this phenomena it is suggested to use, instead, an overall estimate of the misclassification error previously suggested and used as Youden’s index and; furthermore, it is argued that this index is less prone to between-study variation of cut-off values. A simple Mantel–Haenszel estimator as a summary measure of the overall misclassification error is suggested, which adjusts for a potential study effect. The measure of the misclassification error based on Youden’s index is advantageous in that it easily allows an extension to a likelihood approach, which is then able to cope with unobserved heterogeneity via a nonparametric mixture model. All methods are illustrated at hand of an example on a diagnostic meta-analysis on duplex doppler ultrasound, with angiography as the standard for stroke prevention.

Bayesian estimation and selection of nonlinear vector error correction models: The case of the sugar-ethanol-oil nexus in Brazil

Nonlinear adjustment toward long-run price equilibrium relationships in the sugar-ethanol-oil nexus in Brazil is examined. We develop generalized bivariate error correction models that allow for cointegration between sugar, ethanol, and oil prices, where dynamic adjustments are potentially nonlinear functions of the disequilibrium errors. A range of models are estimated using Bayesian Monte Carlo Markov Chain algorithms and compared using Bayesian model selection methods. The results suggest that the long-run drivers of Brazilian sugar prices are oil prices and that there are nonlinearities in the adjustment processes of sugar and ethanol prices to oil price but linear adjustment between ethanol and sugar prices.

Estimation of the stoichiometry of volatile fatty acid production in the rumen of lactating cows

The purpose of this study was to improve the prediction of the quantity and type of Volatile Fatty Acids (VFA) produced from fermented substrate in the rumen of lactating cows. A model was formulated that describes the conversion of substrate (soluble carbohydrates, starch, hemi-cellulose, cellulose, and protein) into VFA (acetate, propionate, butyrate, and other VFA). Inputs to the model were observed rates of true rumen digestion of substrates, whereas outputs were observed molar proportions of VFA in rumen fluid. A literature survey generated data of 182 diets (96 roughage and 86 concentrate diets). Coefficient values that define the conversion of a specific substrate into VFA were estimated meta-analytically by regression of the model against observed VFA molar proportions using non-linear regression techniques. Coefficient estimates significantly differed for acetate and propionate production in particular, between different types of substrate and between roughage and concentrate diets. Deviations of fitted from observed VFA molar proportions could be attributed to random error for 100%. In addition to regression against observed data, simulation studies were performed to investigate the potential of the estimation method. Fitted coefficient estimates from simulated data sets appeared accurate, as well as fitted rates of VFA production, although the model accounted for only a small fraction (maximally 45%) of the variation in VFA molar proportions. The simulation results showed that the latter result was merely a consequence of the statistical analysis chosen and should not be interpreted as an indication of inaccuracy of coefficient estimates. Deviations between fitted and observed values corresponded to those obtained in simulations. (c) 2005 Elsevier Ltd. All rights reserved.

Association between ovarian follicle development and pregnancy rates in dairy cows undergoing spontaneous oestrous cycles

Ovarian follicle development continues in a wave-like manner during the bovine oestrous cycle giving rise to variation in the duration of ovulatory follicle development. The objectives of the present study were to determine whether a relationship exists between the duration of ovulatory follicle development and pregnancy rates following artificial insemination (AI) in dairy cows undergoing spontaneous oestrous cycles, and to identify factors influencing follicle turnover and pregnancy rate and the relationship between these two variables. Follicle development was monitored by daily transrectal ultrasonography from 10 days after oestrus until the subsequent oestrus in 158 lactating dairy cows. The cows were artificially inseminated following the second observed oestrus and pregnancy was diagnosed 35 days later. The predominant pattern of follicle development was two follicle waves (74.7%) with three follicle waves in 22.1% of oestrous cycles and four or more follicle waves in 3.2% of oestrous cycles. The interval from ovulatory follicle emergence to oestrus (EOI) was 3 days longer (P < 0.0001) in cows with two follicle waves than in those with three waves. Ovulatory follicles from two-wave oestrous cycles grew more slowly but were approximately 2 mm larger (P < 0.0001) on the day of oestrus. Twin ovulations were observed in 14.2% of oestrous cycles and occurred more frequently (P < 0.001) in three-wave oestrous cycles; consequently EOI was shorter in cows with twin ovulations. Overall, 57.0% of the cows were diagnosed pregnant 35 days after AI. Linear logistic regression analysis revealed an inverse relationship between EOI and the proportion of cows diagnosed pregnant, among all cows (n = 158; P < 0.01) and amongst those with single ovulations (n = 145; P < 0.05). Mean EOI was approximately I day shorter (P < 0.01) in cows that became pregnant than in non-pregnant cows; however, pregnancy rates did not differ significantly among cows with different patterns of follicle development. These findings confirm and extend previous observations in pharmacologically manipulated cattle and show, for the first time, that in dairy cows undergoing spontaneous oestrous cycles, natural variation in the duration of post-emergence ovulatory follicle development has a significant effect on pregnancy rate, presumably reflecting variation in oocyte developmental competence.

Unravelling the rationale of 'overgrazing' and stocking rates in the beef production systems of Central Brazil using a bi-criteria compromise programming model

In Central Brazil, the long-term sustainability of beef cattle systems is under threat over vast tracts of farming areas, as more than half of the 50 million hectares of sown pastures are suffering from degradation. Overgrazing practised to maintain high stocking rates is regarded as one of the main causes. High stocking rates are deliberate and crucial decisions taken by the farmers, which appear paradoxical, even irrational given the state of knowledge regarding the consequences of overgrazing. The phenomenon however appears inextricably linked with the objectives that farmers hold. In this research those objectives were elicited first and from their ranking two, ‘asset value of cattle (representing cattle ownership)' and ‘present value of economic returns', were chosen to develop an original bi-criteria Compromise Programming model to test various hypotheses postulated to explain the overgrazing behaviour. As part of the model a pasture productivity index is derived to estimate the pasture recovery cost. Different scenarios based on farmers' attitudes towards overgrazing, pasture costs and capital availability were analysed. The results of the model runs show that benefits from holding more cattle can outweigh the increased pasture recovery and maintenance costs. This result undermines the hypothesis that farmers practise overgrazing because they are unaware or uncaring about overgrazing costs. An appropriate approach to the problem of pasture degradation requires information on the economics, and its interplay with farmers' objectives, for a wide range of pasture recovery and maintenance methods. Seen within the context of farmers' objectives, some level of overgrazing appears rational. Advocacy of the simple ‘no overgrazing' rule is an insufficient strategy to maintain the long-term sustainability of the beef production systems in Central Brazil.

Unravelling the rationale of 'overgrazing' and stocking rates in the beef production systems of Central Brazil using a bi-criteria compromise programming model

In Central Brazil, the long-term, sustainability of beef cattle systems is under threat over vast tracts of farming areas, as more than half of the 50 million hectares of sown pastures are suffering from. degradation. Overgrazing practised to maintain high stocking rates is regarded as one of the main causes. High stocking rates are deliberate and crucial decisions taken by the farmers, which appear paradoxical, even irrational given the state of knowledge regarding the consequences of overgrazing. The phenomenon however appears inextricably linked with the objectives that farmers hold. In this research those objectives were elicited first and from their ranking two, 'asset value of cattle (representing cattle ownership and 'present value of economic returns', were chosen to develop an original bi-criteria Compromise Programming model to test various hypotheses postulated to explain the overgrazing behaviour. As part of the model a pasture productivity index is derived to estimate the pasture recovery cost. Different scenarios based on farmers' attitudes towards overgrazing, pasture costs and capital availability were analysed. The results of the model runs show that benefits from holding more cattle can outweigh the increased pasture recovery and maintenance costs. This result undermines the hypothesis that farmers practise overgrazing because they are unaware or uncaring caring about overgrazing costs. An appropriate approach to the problem of pasture degradation requires information on the economics,and its interplay with farmers' objectives, for a wide range of pasture recovery and maintenance methods. Seen within the context of farmers' objectives, some level of overgrazing appears rational. Advocacy of the simple 'no overgrazing' rule is an insufficient strategy to maintain the long-term sustainability of the beef production systems in Central Brazil. (C) 2004 Elsevier Ltd. All rights reserved.

Senescence rates are determined by ranking on the fast-slow life-history continuum

Comparative analyses of survival senescence by using life tables have identified generalizations including the observation that mammals senesce faster than similar-sized birds. These generalizations have been challenged because of limitations of life-table approaches and the growing appreciation that senescence is more than an increasing probability of death. Without using life tables, we examine senescence rates in annual individual fitness using 20 individual-based data sets of terrestrial vertebrates with contrasting life histories and body size. We find that senescence is widespread in the wild and equally likely to occur in survival and reproduction. Additionally, mammals senesce faster than birds because they have a faster life history for a given body size. By allowing us to disentangle the effects of two major fitness components our methods allow an assessment of the robustness of the prevalent life-table approach. Focusing on one aspect of life history - survival or recruitment - can provide reliable information on overall senescence.

Comparison of survival rates of captive-reared and wild-bred Mauritius kestrels (Falco punctatus) in a re-introduced population

Re-introduction is a technique widely used in the conservation of threatened bird species. With advances in aviculture the use of captive-produced individuals as the release stock is becoming more commonplace, and ideally, survival of captive-produced, released individuals should be no different from their wild-bred counterparts. During the late 1980s the Critically Endangered Mauritius kestrel (Falco punctatus) was successfully re-introduced into the Bambous mountain range, Mauritius, some 30 years after its local extinction. Between 1987 and 2001 the developing population was closely monitored enabling us to construct re-sighting histories for 88 released and 284 wild-bred kestrels. We used age-structured models in the survival analysis software program MARK to determine if an individual's origin influenced its subsequent survival. Our analysis indicated no compelling evidence for reduced survival among juvenile captive-reared and released individuals, relative to their wild-bred counterparts, across the majority of cohorts and only limited evidence of a cohort-specific effect. This study illustrates that despite the lack of a formal experimental approach it is still feasible to conduct an assessment of re-introduction outcomes and techniques.