On the cumulant expansion up scaling of ground water contaminant transport equation with nonequilibrium sorption

The laboratory-scale ground water transport equation with nonequilibrium sorption reaction subjected to unsteady, nondivergence-free, and nonstationary velocity fields is up-scaled to the field-scale by using the ensemble-averaged equations obtained from the cumulant expansion ensemble-averaging method. It is found that existing ensemble-averaged equations obtained with the help of the cumulant expansion method for the system of linear partial differential equations are not second-order exact. Although the cumulant expansion methodology is designed for noncommuting operators, it is found that there are still commudativity requirements that need to be satisfied by the functions and constants exist in the coefficient matrix of the system of ordinary/partial differential equations. A reversibility requirement, which covers the commudativity requirements, is also proposed when applying the cumulant expansion method to a system of partial differential equations/a partial differential equation. The significance of the new velocity correction obtained in this study due to the applied second-order exact cumulant expansion is investigated on a numerical example with a linear trend in the distribution coefficient. It is found that the effect of the new velocity correction can be significant enough to affect the maximum concentration values and the plume center of mass in the case of a trending distribution coefficient in a physically heterogeneous environment.     

Dating carbonate rocks with in-situ produced cosmogenic Be: Why it often fails

Surface exposure dating of carbonate rocks using cosmogenic ¹⁰Be is problematic. We have performed step-wise leaching of calcite-rich samples in order to investigate the reasons for this. Results on different grain size fractions clearly indicate the source of atmospheric ¹⁰Be is clay. We demonstrate that partial-leaching procedures, which result in moderate pH levels will not release ¹⁰Be (in-situ produced or atmospheric) due to the instant re-absorption on grain surfaces. By contrast, under strongly acidic conditions, all absorbed ¹⁰Be is leached from aluminosilicates giving abnormally high ¹⁰Be concentrations and consequently exposure ages that are too old. Dating is only possible if samples do not contain any clay minerals or if they can be removed prior to carbonate dissolution.     

黄东海大气边界层高度时空变化特征

根据2006-2007年大连、青岛和台州逐日高分辨率L波段二次测风雷达探空资料、地面观测资料以及再分析资料,采用干绝热法和位温梯度法分别计算了各个台站的边界层高度,继而分析了黄东海边界层高度多时间尺度变化规律和空间演变特征.结果表明:(1)用清晨探空资料计算每日边界层高度,干绝热法比位温梯度法更为合理可靠;(2)沿海台站边界层高度有显著季节变化,夏季最低,秋季最高,这有别于陆地边界层普遍存在的夏季高、秋冬季节低的季节变化;(3)通过小波分析,发现边界层高度有显著的2～4 d天气尺度振荡和10～20 d准双周振荡;(4)黄东海上空海洋大气边界层在时间尺度上同样存在着明显的春夏季节低、秋冬季节高的季节变化特征,大部分海区空间上呈现西北低、东南高的分布形态.     

Cross-shelf transport into nearshore waters due to shoaling internal tides in San Pedro Bay, CA

In the summer of 2001, a coastal ocean measurement program in the southeastern portion of San Pedro Bay, CA, was designed and carried out. One aim of the program was to determine the strength and effectiveness of local cross-shelf transport processes. A particular objective was to assess the ability of semidiurnal internal tidal currents to move suspended material a net distance across the shelf. Hence, a dense array of moorings was deployed across the shelf to monitor the transport patterns associated with fluctuations in currents, temperature and salinity. An associated hydrographic program periodically monitored synoptic changes in the spatial patterns of temperature, salinity, nutrients and bacteria. This set of measurements show that a series of energetic internal tides can, but do not always, transport subthermocline water, dissolved and suspended material from the middle of the shelf into the surfzone. Effective cross-shelf transport occurs only when (1) internal tides at the shelf break are strong and (2) subtidal currents flow strongly downcoast. The subtidal downcoast flow causes isotherms to tilt upward toward the coast, which allows energetic, nonlinear internal tidal currents to carry subthermocline waters into the surfzone. During these events, which may last for several days, the transported water remains in the surfzone until the internal tidal current pulses and/or the downcoast subtidal currents disappear. This nonlinear internal tide cross-shelf transport process was capable of carrying water and the associated suspended or dissolved material from the mid-shelf into the surfzone, but there were no observation of transport from the shelf break into the surfzone. Dissolved nutrients and suspended particulates (such as phytoplankton) transported from the mid-shelf into the nearshore region by nonlinear internal tides may contribute to nearshore algal blooms, including harmful algal blooms that occur off local beaches.     

Coordinate mapping of analytical contaminant transport solutions to non-uniform flow fields

Existing analytical solutions to 2D and 3D contaminant transport problems are limited by the mathematically convenient assumption of uniform flow. An approximate method is developed herein for coordinate mapping of 2D (vertically-averaged) transport solutions to non-uniform steady-state irrotational and divergence-free flow fields in single-layer aquifers. The method enables existing analytical transport solutions to be applied to aquifer systems with wells, non-uniform saturated thickness, surface water features, and (to a limited degree) heterogeneous hydraulic conductivity and recharge. This mass-conservative coordinate mapping approach is inexact in its approximation of the dispersion process but is still sufficiently accurate for many simple flow systems. The degree of model error is directly proportional to the variation of velocity magnitude within the domain. These mapped analytical solutions are compared to numerical simulation results and the coordinate mapping errors are investigated. The methods described herein may be used in the traditional capacity of analytical transport models, i.e., screening and preliminary site assessment, without sacrificing accuracy by assuming locally uniform flow conditions or applying an ad-hoc coordinate transformation. The solutions benefit from the traditional advantages of analytical methods, particularly the removal of artifacts due to spatial and temporal discretization: no time-stepping or numerical discretization is required.     

A positive definite continuous FEM model for advection

This work introduces a continuous and sign-preserving finite element model (FEM) for advection problems. The model is formulated by integrating flux corrected transport technique (FCT) with the characteristic based (CB) FEM. Low order solution for the FCT has the form of element contribution and derives from an upwind monotone scheme with the minimum necessary diffusion for positivity. Selected numerical experiments illustrate the efficacy of the method by comparing results with some successful models, by demonstrating an approximate conservation of the accuracy of original CB algorithm once the complete procedure is operating, and by testing the model for severe time dependent advective flows.     

Comments on “Two-dimensional concentration distribution for mixing-controlled bioreactive transport in steady-state” by O.A. Cirpka and A.J. Valocchi

In this comment we present a re-analysis of the analytical solution presented by Cirpka and Valocchi for steady-state concentrations of dissolved bioreactive compounds and bacterial biomass in porous media. We discuss the validity range of the analytical solution. In particular, the criterion used to determine the sustainability of biomass is revisited. This re-analysis shows that the ω$\omega$ criterion used by Cirpka and Valocchi is only a necessary but not a sufficient criterion to determine the bioreactive zones. As a consequence, the analytical solution does not provide the exact distribution of compounds throughout the domain, but can serve as upper or lower boundaries for species concentrations at a given location. These conclusions are supported by the simulation results obtained from an established reactive transport model.     

Thermal conductive heating in fractured bedrock: Screening calculations to assess the effect of groundwater influx

A two-dimensional semi-analytical heat transfer solution is developed and a parameter sensitivity analysis performed to determine the relative importance of rock material properties (density, thermal conductivity and heat capacity) and hydrogeological properties (hydraulic gradient, fracture aperture, fracture spacing) on the ability to heat fractured rock using thermal conductive heating (TCH). The solution is developed using a Green’s function approach in which an integral equation is constructed for the temperature in the fracture. Subsurface temperature distributions are far more sensitive to hydrogeological properties than material properties. The bulk ground water influx (q) can provide a good estimate of the extent of influx cooling when influx is low to moderate, allowing the prediction of temperatures during heating without specific knowledge of the aperture and spacing of fractures. Target temperatures may not be reached or may be significantly delayed when the groundwater influx is large.     

The formation of headland/island sandbanks

There are four extensive sandbanks in the vicinity of the Isle of Portland, a headland in the English Channel. The formation and maintenance of the two most prominent of these sandbanks (one on either side of the headland) can largely be explained by net bedload convergence, driven by instantaneous headland eddies generated by tidal flow past the headland. However, there are also two less prominent sandbanks (again, one on either side of the headland), which are not located in zones of bedload convergence. It is suggested here that these latter two sandbanks were formed when the Isle of Portland was isolated from the mainland by a tidal strait. Relative sea-level data and radiocarbon dates indicate that this would have occurred ca. 9–7 ka BP, prior to the closure of the strait by sedimentation. Tidal flow through this strait generated eddy systems in addition to the headland eddies, leading to the formation of associated headland/island sandbanks. At 7 ka BP, sedimentation resulted in closure of the strait, leading to the present-day headland configuration, and subsequent reworking of these now moribund sandbanks formed by the strait. A series of idealised morphological model experiments, parameterised using bedrock depths and glacial isostatic adjustment model output of relative sea level, are here used to simulate this hypothesised sequence of sandbank evolution over the Holocene. The results of the model experiments are corroborated by in situ observations of bedforms and sediment characteristics, and by acoustic Doppler current profiler (ADCP) data applied to predictions of bedload transport over the sandbanks. In addition to demonstrating the mechanism which leads to the formation of sandbanks by tidal flow through a strait, the model results show that upon subsequent closure of such a strait, these sandbanks will no longer be actively maintained, in contrast to sandbanks which are continuously maintained by headland eddies.     

A parallel mesh-free contaminant transport model based on the Analytic Element and Streamline Methods

This paper introduces a new method for simulating large-scale subsurface contaminant transport that combines an Analytic Element Method (AEM) groundwater flow solution with a split-operator Streamline Method for modeling reactive transport. The key feature of the method is the manner in which the vertically integrated AEM flow solution is used to construct three-dimensional particle tracks that define the geometry of the Streamline Method. The inherently parallel nature of the algorithm supports the development of reactive transport models for spatial domains much larger than current grid-based methods. The applicability of the new approach is verified for cases with negligible transverse dispersion through comparisons to analytic solutions and existing numerical solutions, and parallel performance is demonstrated through a realistic test problem based on the regional-scale transport of agricultural contaminants from spatially distributed sources.