Solute movement through intact columns of cryoturbated Upper Chalk

Cryoturbated Upper Chalk is a dichotomous porous medium wherein the intra-fragment porosity provides water storage and the inter-fragment porosity provides potential pathways for relatively rapid flow near saturation. Chloride tracer movement through 43 cm long and 45 cm diameter undisturbed chalk columns was studied at water application rates of 0.3, 1.0, and 1.5 cm h(-1). Microscale heterogeneity in effluent was recorded using a grid collection system consisting of 98 funnel-shaped cells each 3.5 cm in diameter. The total porosity of the columns was 0.47 +/- 0.02 m(3) m(-3), approximately 13% of pores were >15 mu m diameter, and the saturated hydraulic conductivity was 12.66 +/- 1.31 m day(-1). Although the column remained unsaturated during the leaching even at all application rates, proportionate flow through macropores increased as the application rate decreased. The number of dry cells (with 0 ml of effluent) increased as application rate decreased. Half of the leachate was collected from 15, 19 and 22 cells at 0.3, 1.0, 1.5 cm h(-1) application rates respectively. Similar breakthrough curves (BTCs) were obtained at all three application rates when plotted as a function of cumulative drainage, but they were distinctly different when plotted as a function of time. The BTCs indicate that the columns have similar drainage requirement irrespective of application rates, as the rise to the maxima (C/C-o) is almost similar. However, the time required to achieve that leaching requirement varies with application rates, and residence time was less in the case of a higher application rate. A two-region convection-dispersion model was used to describe the BTCs and fitted well (r(2) = 0.97-0-99). There was a linear relationship between dispersion coefficient and pore water velocity (correlation coefficient r = 0.95). The results demonstrate the microscale heterogeneity of hydrodynamic properties in the Upper Chalk. Copyright (C) 2007 John Wiley & Sons, Ltd.

Quantifying uncertainty in critical loads: (A) literature review

Critical loads are the basis for policies controlling emissions of acidic substances in Europe. The implementation of these policies involves large expenditures, and it is reasonable for policymakers to ask what degree of certainty can be attached to the underlying critical load and exceedance estimates. This paper is a literature review of studies which attempt to estimate the uncertainty attached to critical loads. Critical load models and uncertainty analysis are briefly outlined. Most studies have used Monte Carlo analysis of some form to investigate the propagation of uncertainties in the definition of the input parameters through to uncertainties in critical loads. Though the input parameters are often poorly known, the critical load uncertainties are typically surprisingly small because of a "compensation of errors" mechanism. These results depend on the quality of the uncertainty estimates of the input parameters, and a "pedigree" classification for these is proposed. Sensitivity analysis shows that some input parameters are more important in influencing critical load uncertainty than others, but there have not been enough studies to form a general picture. Methods used for dealing with spatial variation are briefly discussed. Application of alternative models to the same site or modifications of existing models can lead to widely differing critical loads, indicating that research into the underlying science needs to continue.

Quantifying uncertainty in critical loads: (B) acidity mass balance critical loads on a sensitive site

This paper reports an uncertainty analysis of critical loads for acid deposition for a site in southern England, using the Steady State Mass Balance Model. The uncertainty bounds, distribution type and correlation structure for each of the 18 input parameters was considered explicitly, and overall uncertainty estimated by Monte Carlo methods. Estimates of deposition uncertainty were made from measured data and an atmospheric dispersion model, and hence the uncertainty in exceedance could also be calculated. The uncertainties of the calculated critical loads were generally much lower than those of the input parameters due to a "compensation of errors" mechanism - coefficients of variation ranged from 13% for CLmaxN to 37% for CL(A). With 1990 deposition, the probability that the critical load was exceeded was > 0.99; to reduce this probability to 0.50, a 63% reduction in deposition is required; to 0.05, an 82% reduction. With 1997 deposition, which was lower than that in 1990, exceedance probabilities declined and uncertainties in exceedance narrowed as deposition uncertainty had less effect. The parameters contributing most to the uncertainty in critical loads were weathering rates, base cation uptake rates, and choice of critical chemical value, indicating possible research priorities. However, the different critical load parameters were to some extent sensitive to different input parameters. The application of such probabilistic results to environmental regulation is discussed.

Estimating uncertainty in terrestrial critical loads and their exceedances at four sites in the UK

Critical loads are the basis for policies controlling emissions of acidic substances in Europe and elsewhere. They are assessed by several elaborate and ingenious models, each of which requires many parameters, and have to be applied on a spatially-distributed basis. Often the values of the input parameters are poorly known, calling into question the validity of the calculated critical loads. This paper attempts to quantify the uncertainty in the critical loads due to this "parameter uncertainty", using examples from the UK. Models used for calculating critical loads for deposition of acidity and nitrogen in forest and heathland ecosystems were tested at four contrasting sites. Uncertainty was assessed by Monte Carlo methods. Each input parameter or variable was assigned a value, range and distribution in an objective a fashion as possible. Each model was run 5000 times at each site using parameters sampled from these input distributions. Output distributions of various critical load parameters were calculated. The results were surprising. Confidence limits of the calculated critical loads were typically considerably narrower than those of most of the input parameters. This may be due to a "compensation of errors" mechanism. The range of possible critical load values at a given site is however rather wide, and the tails of the distributions are typically long. The deposition reductions required for a high level of confidence that the critical load is not exceeded are thus likely to be large. The implication for pollutant regulation is that requiring a high probability of non-exceedance is likely to carry high costs. The relative contribution of the input variables to critical load uncertainty varied from site to site: any input variable could be important, and thus it was not possible to identify variables as likely targets for research into narrowing uncertainties. Sites where a number of good measurements of input parameters were available had lower uncertainties, so use of in situ measurement could be a valuable way of reducing critical load uncertainty at particularly valuable or disputed sites. From a restricted number of samples, uncertainties in heathland critical loads appear comparable to those of coniferous forest, and nutrient nitrogen critical loads to those of acidity. It was important to include correlations between input variables in the Monte Carlo analysis, but choice of statistical distribution type was of lesser importance. Overall, the analysis provided objective support for the continued use of critical loads in policy development. (c) 2007 Elsevier B.V. All rights reserved.

Individual differences in the effects of perceived controllability on pain perception: critical role of the prefrontal cortex

The degree to which perceived controllability alters the way a stressor is experienced varies greatly among individuals. We used functional magnetic resonance imaging to examine the neural activation associated with individual differences in the impact of perceived controllability on self-reported pain perception. Subjects with greater activation in response to uncontrollable (UC) rather than controllable (C) pain in the pregenual anterior cingulate cortex (pACC), periaqueductal gray (PAG), and posterior insula/SII reported higher levels of pain during the UC versus C conditions. Conversely, subjects with greater activation in the ventral lateral prefrontal cortex (VLPFC) in anticipation of pain in the UC versus C conditions reported less pain in response to UC versus C pain. Activation in the VLPFC was significantly correlated with the acceptance and denial subscales of the COPE inventory [Carver, C. S., Scheier, M. F., & Weintraub, J. K. Assessing coping strategies: A theoretically based approach. Journal of Personality and Social Psychology, 56, 267–283, 1989], supporting the interpretation that this anticipatory activation was associated with an attempt to cope with the emotional impact of uncontrollable pain. A regression model containing the two prefrontal clusters (VLPFC and pACC) predicted 64% of the variance in pain rating difference, with activation in the two additional regions (PAG and insula/SII) predicting almost no additional variance. In addition to supporting the conclusion that the impact of perceived controllability on pain perception varies highly between individuals, these findings suggest that these effects are primarily top-down, driven by processes in regions of the prefrontal cortex previously associated with cognitive modulation of pain and emotion regulation.