Using estimated thermodynamic properties to model accessory phases: the case of tourmaline     

V. J. VAN HINSBERG  J. C. SCHUMACHER 《Journal of Metamorphic Geology》2007,25(7):769-779

Accessory phases and minor components in minerals are commonly ignored in thermodynamic modelling. Such an approach seems unwarranted, as accessory phases can represent a significant element reservoir and minor components can substantially change their host mineral's stability field. However, a lack of thermodynamic data prohibits assessment of these effects. In this contribution, the polyhedron method is used to estimate the thermodynamic properties of tourmaline, a common and widespread accessory phase, stable over a range of P–T–X conditions. The polyhedron method allows Δ H , S , V , C _P and V _m ( T , P ) properties to be estimated from a linear stoichiometric summation over the fractional properties of its polyhedron constituents. To allow for estimates of tourmaline, fractional thermodynamic properties for B^III and B^IV polyhedra were derived. Mixing contributions to molar volume were evaluated and symmetrical mixing parameters derived for Al-Mg, Al-Fe and Al-Li interaction on tourmaline's Y-site and T-site Al-Si interaction. Evaluation of the estimated properties using experimental and natural equilibria between tourmaline and melts, minerals and hydrothermal fluids, shows that reliable semi-quantitative results are obtained. The boron contents in fluids coexisting with tourmaline are calculated to within an order of magnitude of measured content, and where anchor-points are available, agreement improves to within a factor of 2. Including tourmaline in petrogenetic modelling of metamorphic rocks indicates that its presence leads to disappearance of staurolite and garnet, among others, and modifies the X _Mg of coexisting phases, in line with observations on natural rocks.  相似文献   

Ecogeomorphic state variables and phase‐space construction for quantifying the evolution of vegetated aeolian landscapes     

Andreas C. W. Baas  Joanna M. Nield 《地球表面变化过程与地形》2010,35(6):717-731

Cellular automaton modelling for the simulation of dune field formation and evolution has developed progressively in aeolian geomorphology in the last decade or so. A model that incorporates the effects of vegetation and its interactions with geomorphic landscape development – the Discrete Ecogeomorphic Aeolian Landscapes (DECAL) model – can replicate a number of important visual and qualitative aspects of the complex evolution of aeolian dune landscapes under the influence of vegetation dynamics in coastal environments. A key challenge in this research area is the analysis and comparison of both simulated and real‐world vegetated dune landscapes using objective and quantifiable principles. This study presents a methodological framework or protocol for numerically quantifying various ecogeomorphic attributes, using a suite of mathematically defined landscape metrics, to provide a rigorous and statistical evaluation of vegetated dune field evolution. Within this framework the model parameter space can be systematically explored and simulation outcomes can be methodically compared against real‐world landscapes. Based on a simplified scenario of parabolic dunes developing out of blow‐outs the resulting dune field realizations are investigated as a function of variable growth vigour of two simulated vegetation types (pioneer grass and successional woody shrub) by establishing a typological phase‐diagram of different landscape classes. The set of simulation outcomes furthermore defines a higher‐dimensional phase‐space, whose axes or dimensions can be interpreted by analysing how individual ecogeomorphic landscape metrics, or state variables, contribute to the data distribution. Principal component analysis can reduce this to a visual three‐dimensional (3D) phase‐space where landscape evolution can be plotted as time‐trajectories and where we can investigate the effects of changing environmental conditions partway through a simulation scenario. The use of landscape state variables and the construction of a 3D phase‐space presented here may provide a general template for quantifying many other eco‐geomorphic systems on the Earth's surface. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

Predicting river water temperatures using stochastic models: case study of the Moisie River (Québec,Canada)     

Behrouz Ahmadi‐Nedushan  André St‐Hilaire  Taha B. M. J. Ouarda  Laurent Bilodeau  Élaine Robichaud  Nathalie Thiémonge  Bernard Bobée 《水文研究》2007,21(1):21-34

Successful applications of stochastic models for simulating and predicting daily stream temperature have been reported in the literature. These stochastic models have been generally tested on small rivers and have used only air temperature as an exogenous variable. This study investigates the stochastic modelling of daily mean stream water temperatures on the Moisie River, a relatively large unregulated river located in Québec, Canada. The objective of the study is to compare different stochastic approaches previously used on small streams to relate mean daily water temperatures to air temperatures and streamflow indices. Various stochastic approaches are used to model the water temperature residuals, representing short‐term variations, which were obtained by subtracting the seasonal components from water temperature time‐series. The first three models, a multiple regression, a second‐order autoregressive model, and a Box and Jenkins model, used only lagged air temperature residuals as exogenous variables. The root‐mean‐square error (RMSE) for these models varied between 0·53 and 1·70 °C and the second‐order autoregressive model provided the best results. A statistical methodology using best subsets regression is proposed to model the combined effect of discharge and air temperature on stream temperatures. Various streamflow indices were considered as additional independent variables, and models with different number of variables were tested. The results indicated that the best model included relative change in flow as the most important streamflow index. The RMSE for this model was of the order of 0·51 °C, which shows a small improvement over the first three models that did not include streamflow indices. The ridge regression was applied to this model to alleviate the potential statistical inadequacies associated with multicollinearity. The amplitude and sign of the ridge regression coefficients seem to be more in agreement with prior expectations (e.g. positive correlation between water temperature residuals of different lags) and make more physical sense. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

Physically‐based modelling of double‐peak discharge responses at Slapton Wood catchment     

Stephen J Birkinshaw 《水文研究》2008,22(10):1419-1430

Heavy winter rainfall produces double‐peak hydrographs at the Slapton Wood catchment, Devon, UK. The first peak is saturation‐excess overland flow in the hillslope hollows and the second (i.e. the delayed peak) is subsurface stormflow. The physically‐based spatially‐distributed model SHETRAN is used to try to improve the understanding of the processes that cause the double peaks. A three‐stage (multi‐scale) approach to calibration is used: (1) water balance validation for vertical one‐dimensional flow at arable, grassland and woodland plots; (2) two‐dimensional flow for cross‐sections cutting across the stream valley; and (3) three‐dimensional flow in the full catchment. The main data are for rainfall, stream discharge, evaporation, soil water potential and phreatic surface level. At each scale there was successful comparison with measured responses, using as far as possible parameter values from measurements. There was some calibration but all calibrated values at one scale were used at a larger scale. A large proportion of the subsurface runoff enters the stream from three dry valleys (hillslope hollows), and previous studies have suggested convergence of the water in the three large hollows as being the major mechanism for the production of the delayed peaks. The SHETRAN modelling suggests that the hillslopes that drain directly into the stream are also involved in producing the delayed discharges. The model shows how in the summer most of the catchment is hydraulically disconnected from the stream. In the autumn the catchment eventually ‘wets up’ and shallow subsurface flows are produced, with water deflected laterally along the soil‐bedrock interface producing the delayed peak in the stream hydrograph. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

Implicit integration of a mixed isotropic–kinematic hardening plasticity model for structured clays     

Angelo Amorosi  Daniela Boldini  Vincenzo Germano 《国际地质力学数值与分析法杂志》2008,32(10):1173-1203

In recent years, a number of constitutive models have been proposed to describe mathematically the mechanical response of natural clays. Some of these models are characterized by complex formulations, often leading to non‐trivial problems in their numerical integration in finite elements codes. The paper describes a fully implicit stress‐point algorithm for the numerical integration of a single‐surface mixed isotropic–kinematic hardening plasticity model for structured clays. The formulation of the model stems from a compromise between its capability of reproducing the larger number of features characterizing the behaviour of structured clays and the possibility of developing a robust integration algorithm for its implementation in a finite elements code. The model is characterized by an ellipsoid‐shaped yield function, inside which a stress‐dependent reversible stiffness is accounted for by a non‐linear hyperelastic formulation. The isotropic part of the hardening law extends the standard Cam‐Clay one to include plastic strain‐driven softening due to bond degradation, while the kinematic hardening part controls the evolution of the position of the yield surface in the stress space. The proposed algorithm allows the consistent linearization of the constitutive equations guaranteeing the quadratic rate of asymptotic convergence in the global‐level Newton–Raphson iterative procedure. The accuracy and the convergence properties of the proposed algorithm are evaluated with reference to the numerical simulations of single element tests and the analysis of a typical geotechnical boundary value problem. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

Climate change and hydrology at the prairie margin: Historic and prospective future flows of Canada's Red Deer and other Rocky Mountain rivers          下载免费PDF全文

Laurens J. Philipsen  Karen M. Gill  Anita Shepherd  Stewart B. Rood 《水文研究》2018,32(17):2669-2684

The South Saskatchewan River Basin of southern Alberta drains the transboundary central Rocky Mountains region and provides the focus for irrigation agriculture in Canada. Following extensive development, two tributaries, the Oldman and Bow rivers, were closed for further water allocations, whereas the Red Deer River (RDR) remains open. The RDR basin is at the northern limit of the North American Great Plains and may be suitable for agricultural expansion with a warming climate. To consider irrigation development and ecological impacts, it is important to understand the regional hydrologic consequences of climate change. To analyse historic trends that could extend into the future, we developed century‐long discharge records for the RDR, by coordinating data across hydrometric gauges, estimating annual flows from seasonal records, and undertaking flow naturalization to compensate for river regulation. Analyses indicated some coordination with the Pacific decadal oscillation and slight decline in summer and annual flows from 1912 to 2016 (?0.13%/year, Sen's slope). Another forecasting approach involved regional downscaling from the global circulation models, CGCMI‐A, ECHAM4, HadCM3, and NCAR‐CCM3. These projected slight flow decreases from the mountain headwaters versus increases from the foothills and boreal regions, resulting in a slight increase in overall river flows (+0.1%/year). Prior projections from these and other global circulation models ranged from slight decrease to slight increase, and the average projection of ?0.05%/year approached the empirical trend. Assessments of other rivers draining the central and northern Rocky Mountains revealed a geographic transition in flow patterns over the past century. Flows from the rivers in Southern Alberta declined (around ?0.15%/year), in contrast to increasing flows in north‐eastern British Columbia and the Yukon. The RDR watershed approaches this transition, and this study thus revealed regional differentiation in the hydrological consequences from climate change.  相似文献   

The reaction history of kyanite in high‐P aluminous granulites          下载免费PDF全文

Jillian Kendrick  Aphrodite Indares 《Journal of Metamorphic Geology》2018,36(2):125-146

Cathodoluminescence (CL) mapping of kyanite in high pressure, aluminous granulites from the central Grenville Province reveals internal structures that are linked to their metamorphic reaction history. In two samples, individual kyanite crystals are shown to be composite porphyroblasts comprising three distinct generations, defined by their CL intensity and Cr (±V, Ti, Fe and Ga) content, and each separated by resorbed interfaces. In contrast, a sub‐aluminous sample contains two types of kyanite, one as resorbed inclusions in garnet and another in the groundmass or replacing garnet. These textural variants of kyanite are interpreted within the framework of phase equilibria modelling. In P–T pseudosections, a first generation of kyanite, which is only present in the most aluminous samples, is potentially linked to staurolite breakdown, and its resorption is consistent with a subsequent increase in pressure. This kyanite represents the earliest remnant of prograde metamorphism identifiable in these rocks. The second generation, present in the porphyroblasts in the same samples and as inclusions in garnet in the sub‐aluminous sample, is interpreted to be the peritectic product of muscovite dehydration melting. Resorption of this kyanite is consistent with subsequent continuous dehydration melting of biotite, which is also inferred based on microstructural considerations. The final generation of kyanite, present as rims on the prograde kyanite porphyroblasts in aluminous samples and as part of the groundmass or replacing garnet in the sub‐aluminous rock, is interpreted to have grown during melt crystallization upon retrogression. The presence of retrograde kyanite implies that the melt crystallized over a wide range of temperatures, and provides an important constraint on the P–T conditions of the metamorphic peak and on the retrograde P–T path. CL mapping is crucial for identifying retrograde kyanite in aluminous samples, as it preferentially overgrows existing kyanite rather than replacing other prograde phases. The scarcity of kyanite in sub‐aluminous rocks allows retrograde kyanite to grow as discrete crystals that can be identified by optical microscopy. This work attests to the potential of unconventional tools such as CL imaging for deciphering the metamorphic history of rocks.  相似文献   

An extended Greenwood‐Williamson modelbased normal interaction law for discrete element modelling of spherical particles with surface roughness          下载免费PDF全文

Tingting Zhao  Y.T. Feng  Min Wang 《国际地质力学数值与分析法杂志》2018,42(14):1624-1642

The current work aims to develop an improved random normal interaction law based on an extended Greenwood‐Williamson (GW) model for spherical particles with surface roughness in the discrete element modelling of particle systems. The extended GW model overcomes some theoretical defects of the classic GW model when incorporated into the discrete element framework. Based on 2 nondimensional forms in which only 2 surface roughness parameters are involved, an empirical formula of the improved interaction law is derived by the curve‐fitting technique. The resulting interaction law is incorporated into discrete element modelling to investigate the mechanical response of particle systems with different surface roughness. Numerical simulations are performed to model 1‐dimensional and 3‐dimensional compression tests to explore the macro and micro characteristics of granular particles with surface roughness. The results show that surface roughness makes the initial packing of a particle assembly looser and has a greater influence on looser packed samples as expected, but an assembly with moderate roughness may exhibit a higher strength. The limitations of the current development are also highlighted.  相似文献   

A top–down soil moisture and sap flux sampling design of a rain–snow transition mountain watershed     

Son Kyongho  Christina Tague 《水文研究》2019,33(11):1553-1568

This paper presents a top–down approach for soil moisture and sap flux sampling design with the goal of understanding ecohydrologic response to interannual climate variation in the rain–snow transition watersheds. The design is based on a priori estimates of soil moisture and transpiration patterns using a physical distributed model, Regional Hydro‐Ecologic Simulation System (RHESSys). RHESSys was initially calibrated with existing snow depth and streamflow data. Calibrated model estimates of seasonal trajectories of snowmelt, root‐zone soil moisture storage, and transpiration were used to develop five hydrologic similarity indicators and map these at (30 m) patch scale across the study watershed. The partitioning around medoids‐clustering algorithm was then used to define six distinctive spatially explicit clusters based on the five hydrologic similarity indictors. A representative site within each cluster was identified for sampling. For each site, soil moisture sensors were installed at the 30‐ and 90‐cm depths and at the five soil pits and a sap flux sensor at the averaged‐size white fir tree for each site. The model‐based cluster analysis suggests that the elevation gradient and topographically driven flow drainage patterns are the dominant drivers of spatial patterns of soil moisture and transpiration. The comparison of model‐based calculated hydrological similarity indicators with measured‐data‐based values shows that spatial patterns of field‐sampled soil moisture data typically fell within uncertainty bounds of model‐based estimates for each cluster. There were however several notable exceptions. The model failed to capture the soil moisture and sap flux dynamics in a riparian zone site and in a site where lateral subsurface flow may not follow surface topography. Results highlight the utility of using a hypothesis driven sampling strategy, based on a physically based model, for efficiently providing new information that can drive both future measurements and strategic refinements to model inputs, parameters, or structure that might reduce these errors. Future research will focus on strategies for using of finer scale representations of microclimate, topography, vegetation, and soil properties to improve models.  相似文献   

Evaluating lacustrine groundwater discharge to a large glacial lake using regional scale radon-222 surveys and groundwater modelling     

Hayley Wallace  E. J. Wexler  Spencer Malott  Clare E. Robinson 《水文研究》2021,35(4):e14165

Lacustrine groundwater discharge (LGD) can be an important pathway for delivering pollutants to lakes but this pathway is often poorly characterized. Evaluating the potential impact of LGD on lake water quality requires understanding the magnitude and spatial variability of LGD, as well as understanding the age and flow paths of the discharging groundwater (e.g., recharge area, groundwater flow paths, and travel times). This study first compares LGD rates along two ~40 km shoreline lengths of a large glacial lake, Lake Simcoe, Canada, that were independently estimated via a radon-222 (²²²Rn) field survey and via regional scale groundwater-surface water modelling. Backward particle tracking analysis is then used to examine the age and flow paths of the LGD and thereby assess the potential for the LGD to deliver anthropogenic pollutants to the lake. The field and modelling results compare well with respect to the magnitude and spatial variability of LGD. However, the comparison highlights the need for well-defined hydrogeological characterization if regional scale models are to be applied for LGD estimation. The particle tracking analysis indicates large variation in the groundwater flow path lengths and travels times (>1000 years to <50 years) for LGD along the shoreline. This illustrates that the LGD along different shoreline areas has varying potential to deliver anthropogenic pollutants to the lake. The study findings demonstrate the benefits of comparing independent field measured and model-simulated LGD estimates, and moreover suggest that it may be possible, in some cases, to use existing regional scale groundwater-surface water models, purpose-built for other water resource and quality objectives, to conduct preliminary evaluation of LGD contributions to lakes. Preliminary model-based evaluation would enable field efforts aiming to quantify and manage LGD to be better targeted rather than relying solely on regional scale field techniques that are often highly resource intensive.  相似文献