A time dependent mixing model to close PDF equations for transport in heterogeneous aquifers

Probability density function (PDF) methods are a promising alternative to predicting the transport of solutes in groundwater under uncertainty. They make it possible to derive the evolution equations of the mean concentration and the concentration variance, used in moment methods. The mixing model, describing the transport of the PDF in concentration space, is essential for both methods. Finding a satisfactory mixing model is still an open question and due to the rather elaborate PDF methods, a difficult undertaking. Both the PDF equation and the concentration variance equation depend on the same mixing model. This connection is used to find and test an improved mixing model for the much easier to handle concentration variance. Subsequently, this mixing model is transferred to the PDF equation and tested. The newly proposed mixing model yields significantly improved results for both variance modelling and PDF modelling.     

地震海洋学方法在海洋混合参数提取中的研究与应用——以南海内波和地中海涡旋为例

混合是海洋中普遍存在的一种海水运动形式,对多个海洋学分支的研究具有重要的影响.随着物理海洋学的研究重心从大尺度向中小尺度现象过渡,近年来混合问题的研究重心也逐渐转向了中小尺度现象.内波与中尺度涡都是非常重要的中小尺度物理海洋学现象,对海洋能量在不同尺度中的级联发挥着重要的作用.本文基于地震海洋学研究了海洋混合参数的提取方法,并以南海内波和地中海涡旋为例进行了计算和分析.结果显示,南海内波在200~600m深度范围内所引起的混合可达10-2.79 m2·s-1左右,比大洋的统计结果10-5 m2·s-1高出两个数量级以上.而地中海涡旋所引起的湍流混合率可达10-3.44 m2·s-1左右,与大洋统计结果相比高出1.5个数量级左右,并且地中海涡旋下边界的混合要强于上边界,这一特征与前人的研究一致,另外涡旋上边界之上以及侧边界的外侧也具有非常高的混合率.     

Sensitivity analysis of the probability distribution of groundwater level series based on information entropy

Information entropy is an effective method to analyze uncertainty in various processes. The principle of maximum entropy (POME) provides a guide line for the parameter estimation of probability density function (PDF). Mutual entropy analysis is well qualified for delineating the nonlinear and complex multivariable relationship. The probability distribution of model output is the element of model uncertainty analysis. In this paper, a synthetic groundwater flow field is build to produce groundwater level series (GLS). The probability distribution of GLS is obtained by the frequency analysis method based on POME and Chi-Squared test. The important uncertainty factors that affect the parameters of PDF of GLS are assessed by the sensitivity analysis methods, which include stepwise regression analysis and mutual entropy analysis. Results of this analysis indicate that most of the GLS follow normal distribution (or log-normal distribution), while a few obey others. The mean and variance of normal GLS are affected differently by the input variables of groundwater model. Mutual entropy analysis is more competitive and appropriate for delineating the nonlinear and nonmonotonic multivariable relationship than stepwise regression analysis.     

Pervasive,Preferential Flow through Mega-Thick Unsaturated Zones in the Southern Great Basin

Recharge from preferential flow through mega-thick (100–1000 m) unsaturated zones is a pervasive phenomenon, as demonstrated with a case study of volcanic highland recharge areas in the Great Basin province in southern Nevada, USA. Statistically significant rising water-level trends occur for most study-area wells and resulted from a relatively wet period (1969–2005) in south-central Nevada. Wet and dry winters control water-level trends, with water levels rising within a few months to a year following a wet-winter recharge event and declining during sustained dry periods. Even though a megadrought has persisted since 2000, this drought condition did not preclude major recharge events. Modern groundwater reaching the water table is consistent with previous geochemical studies of the study area that indicate mixing of modern and late Pleistocene recharge water. First-order approximations and simple mixing models of modern and late Pleistocene water indicate that 10% to 40% of recharge is preferential flow and that modern recharge may play a larger role in the water budget than previously thought.     

Heat budget of the surface mixed layer south of Africa

ARGO hydrographic profiles, two hydrographic transects and satellite measurements of air–sea exchange parameters were used to characterize the properties and seasonal heat budget variations of the Surface Mixed Layer (SML) south of Africa. The analysis distinguishes the Subtropical domain (STZ) and the Subantarctic Zone (SAZ), Polar Frontal Zone (PFZ) and Antarctic Zone (AZ) of the Antarctic Circumpolar Current. While no Subantarctic Mode Water forms in that region, occurrences of deep SML (up to ∼450 m) are observed in the SAZ in anticyclones detached from the Agulhas Current retroflection or Agulhas Return Current. These are present latitudinally throughout the SAZ, but preferentially at longitudes 10–20° E where, according to previous results, the Subtropical Front is interrupted. Likely owing to this exchange window and to transfers at the Subantarctic Front also enhanced by the anticyclones, the SAZ shows a wide range of properties largely encroaching upon those of the neighbouring domains. Heat budget computations in each zone reveal significant meridional changes of regime. While air–sea heat fluxes dictate the heat budget seasonal variability everywhere, heat is mostly brought through lateral geostrophic advection by the Agulhas Current in the STZ, through lateral diffusion in the SAZ and through air–sea fluxes in the PFZ and AZ. The cooling contributions are by Ekman advection everywhere, lateral diffusion in the STZ (also favoured by the ∼10° breach in the Subtropical Front) and geostrophic advection in the SAZ. The latter likely reflects an eastward draining of water warmed through mixing of the subtropical eddies.     

城市化对石家庄站日气温变化的影响

利用1962—2011年逐日平均、最低和最高气温资料,对比分析了石家庄站和藁城站平均、最低和最高气温的概率分布特征.石家庄站是我国少有的自建站以来从未迁址的城市气象站,而附近的藁城站可近似看作乡村气象站.结果表明:城市化致使石家庄站1962—2011年平均、最低和最高气温的概率密度分布向高温方向偏移,其中对最低气温分布的影响尤其明显,对最高气温分布的影响很小;受城市化影响,石家庄站最低气温概率密度分布的高温部分增温比低温部分增温更加明显,最低气温分布形状更加扁平;相对于1962—1986年,1987—2011年石家庄站平均、最低和最高气温概率密度分布均向高温方向偏移,其中最低气温偏移最为明显,并导致1962—2011年整个分析时期最低气温分布出现非正态性;城市化对石家庄站气温分布的影响在冬、春季比夏、秋季更显著,最显著的城市化影响出现在冬季最低气温上;石家庄站基于最低气温的极端气温指数趋势受城市化影响严重,冷夜日数和暖夜日数的城市化影响分别为-1.13d/10a、1.48d/10a,但基于最高气温的冷昼和暖昼日数等极端气温指数变化趋势受城市化影响不明显.出现这种现象的主要原因是城市化对最低、最高气温分布的影响存在差异.     

Determination of the freshwater budget of tidal flats from measurements near a tidal inlet

The freshwater budget of a tidal flat area is evaluated from long-term hydrographic time series from an observation pole positioned in a tidal channel in the Hörnum Basin (Germany). For each tidal cycle, the freshwater budget is calculated from the total imported and exported water volumes and the corresponding mean densities. The variability of the budget on a tidal scale is characterised by a period of twice the tidal period, exhibiting a minimum when the tidal flats are dry around daylight hours during the foregoing low tide, and a maximum when low tide occurs at night; enhanced evaporation on the flats at daylight hours is identified as the driving process. On the average over one year, while winter observations are missing, the freshwater budget is negative for the years 2002–2005 and positive only for 2006. The interannual mean is negative and amounts to a freshwater loss of about 2 mm day⁻¹, although the large-scale climate in this region is humid. The results demonstrate that the bulk parametrisations for the latent and sensible heat flux between the ocean and the atmosphere must not be applied for the tidelands.     

Combination of CFCs and stable isotopes to characterize the mechanism of groundwater–surface water interactions in a headwater basin of the North China Plain

Mountainous areas are characterized by steep slopes and rocky landforms, with hydrological conditions varying rapidly from upstream to downstream, creating variable interactions between groundwater and surface water. In this study, mechanisms of groundwater–surface water interactions within a headwater catchment of the North China Plain were assessed along the stream length and during different seasons, using hydrochemical and stable isotope data, and groundwater residence times estimated using chlorofluorocarbons. These tracers indicate that the river is gaining, due to groundwater discharge in the headwater catchment both in the dry and rainy seasons. Residence time estimation of groundwater using chlorofluorocarbons data reveals that groundwater flow in the shallow sedimentary aquifer is dominated by the binary mixing of water approximating a piston flow model along 2 flow paths: old water, carried by a regional flow system along the direction of river flow, along with young water, which enters the river through local flow systems from hilly areas adjacent to the river valley (particularly during the rainy season). The larger mixing ratio of young water from lateral groundwater recharge and return flow of irrigation during the rainy season result in higher ion concentrations in groundwater than in the dry season. The binary mixing model showed that the ratio of young water versus total groundwater ranged from 0.88 to 0.22 and 1.0 to 0.74 in the upper and lower reaches, respectively. In the middle reach, meandering stream morphology allows some loss of river water back into the aquifer, leading to increasing estimates of the ratio of young water (from 0.22 to 1). This is also explained by declining groundwater levels near the river, due to groundwater extraction for agricultural irrigation. The switch from a greater predominance of regional flow in the dry season, to more localized groundwater flow paths in the wet season is an important groundwater–surface water interactions mechanism, with important catchment management implications.     

Translating CFC-based piston ages into probability density functions of ground-water age in karst

Temporal age distributions are equivalent to probability density functions (PDFs) of transit time. The type and shape of a PDF provides important information related to ground-water mixing at the well or spring and the complex nature of flow networks in karst aquifers. Chlorofluorocarbon (CFC) concentrations measured for samples from 12 locations in the karstic Madison aquifer were used to evaluate the suitability of various PDF types for this aquifer. Parameters of PDFs could not be estimated within acceptable confidence intervals for any of the individual sites. Therefore, metrics derived from CFC-based apparent ages were used to evaluate results of PDF modeling in a more general approach. The ranges of these metrics were established as criteria against which families of PDFs could be evaluated for their applicability to different parts of the aquifer. Seven PDF types, including five unimodal and two bimodal models, were evaluated. Model results indicate that unimodal models may be applicable to areas close to conduits that have younger piston (i.e., apparent) ages and that bimodal models probably are applicable to areas farther from conduits that have older piston ages. The two components of a bimodal PDF are interpreted as representing conduit and diffuse flow, and transit times of as much as two decades may separate these PDF components. Areas near conduits may be dominated by conduit flow, whereas areas farther from conduits having bimodal distributions probably have good hydraulic connection to both diffuse and conduit flow.     

Thermal characterization of the Vulcano fumarole field

Ground-based thermal infrared surveys can contribute to complete heat budget inventories for fumarole fields. However, variations in atmospheric conditions, plume condensation and mixed-pixel effects can complicate vent area and temperature measurements. Analysis of vent temperature frequency distributions can be used, however, to characterise and quantify thermal regions within a field. We examine this using four thermal infrared thermometer and thermal image surveys of the Vulcano Fossa fumarole field (Italy) during June 2004 and July 2005. These surveys show that regions occupied by low temperature vents are characterised by distributions that are tightly clustered around the mean (i.e., the standard deviation is low), highly peaked (positive kurtosis) and skewed in the low temperature direction (negative skewness). This population is associated with wet fumaroles, where boiling controls maximum temperature to cause a narrow distribution with a mode at 90–100°C. In contrast, high temperature vent regions have distributions that are widely spread about the mean (i.e., the standard deviation is high), relatively flat (negative kurtosis) and skewed in the high temperature direction (positive skewness). In this dry case, fumaroles are water-free so that maximum temperatures are not fixed by boiling. As a result greater temperature variation is possible. We use these results to define two vent types at Vulcano on the basis of their thermal characteristics: (1) concentrated (localized) regions of high temperature vents, and (2) dispersed low temperature vents. These occur within a much larger region of diffuse heat emission across which surfaces are heated by steam condensation, the heat from which causes elevated surface temperatures. For Vulcano's lower fumarole zone, high and low temperature vents occupied total areas of 3 and 6 m², respectively, and occurred within a larger (430 m²) vent-free zone of diffuse heat emission. For this lower zone, we estimate that 21–43 × 10³ W of heat was lost by diffuse heat emission. A further 4.5 × 10³ W was lost by radiation from high temperature vents, and 6.5 × 10³ W from low temperature vents. Thus, radiative heat losses from high and low temperature vents within Vulcano's lower fumarole zone respectively account for 10% and 15% of the total heat lost from this zone. This shows that radiation from open vents can account for a non-trivial portion of the total fumarole field heat budget.     

Sensitivity analysis of a deterministic water temperature model to forest canopy and soil temperature in Catamaran Brook (New Brunswick,Canada)

A coupled deterministic hydrological and water temperature model, CEQUEAU, was modified to include soil temperature and crown closure in its calculation of local advective terms in the heat budget. The modified model was than tested to verify its sensitivity to these modifications. An analysis of the heat budget of a small forested catchment in eastern Canada revealed that the advective term related to interflow plays a significant role in the daily water heat budget, providing on average 28% of the local advective budget (which also includes advective heat terms from surface runoff and groundwater) and nearly 14% of the total heat budget (which includes all radiative terms at the water surface, convection and evaporation, as well as the local advective terms). Relative sensitivity indices (RSIs) were used to verify the impact of the newly introduced parameters and variables. Among them, parameters related to the forest cover (crown closure and leaf area index) have a maximum RSI of ?0·6; i.e. a 100% increase in value produces a 60% decrease in the local advective term. Parameters with the greatest influence are the volume of water contributing to interflow and the amplitude of the net radiative flux at the soil surface, which, if doubled, would double the contribution of the local interflow advective term to the heat budget. Copyright © 2003 John Wiley & Sons, Ltd.     

Maintenance of the mean kinetic energy in the global ocean by the barotropic and baroclinic energy routes: the roles of JEBAR and Ekman dynamics

In order to determine the maintenance mechanisms of the currents of the global ocean, this study investigates the budget of the annual mean kinetic energy (KE) in a high-resolution (0.1° × 0.1°) semi-global ocean simulation. The analysis is based on a separation of the mean KE using the barotropic (i.e., depth-averaged) and baroclinic (the residual) components of velocity. The barotropic and baroclinic KEs dominate in higher and lower latitudes, respectively, with their global average being comparable to each other. The working rates of wind forcing on the barotropic and baroclinic circulations in the global ocean are 243 and 747 gigawatts, respectively. This study presents at least three new results for the budget of the barotropic KE. Firstly, an energy diagram is rederived to show that the work of the barotropic component of the horizontal pressure gradient (HPG) is connected to the work related to the joint effect of baroclinicity and bottom relief (JEBAR), and then to the budget of potential energy (PE). Secondly, the model analysis shows that the globally averaged work of the barotropic HPG (which is connected to the work related to JEBAR and then to the budget of the PE) is nearly zero. This indicates that the wind- and buoyancy-induced barotropic circulations in the global ocean are of the same strength with opposite sign. Thirdly, it is found that the work of the wind forcing on the barotropic component of the simulated Antarctic Circumpolar Current (ACC) is canceled by the combined effect, in equal measure, of the work of the barotropic HPG and the work of dissipative processes for mean KE. This result makes a significant contribution to the discussion on the depth-integrated momentum balance of the ACC. The barotropic KE is dissipated by the effects of bottom frictional stress, lateral frictional stress, and the Reynolds stress, of which more than half is attributed to an unexpectedly large contribution from biharmonic horizontal friction. Future studies should pay more attention to the role of biharmonic friction used in high-resolution numerical models.     

A hillslope forest floor (duff) water budget and the transition to local control

The partially decomposed organic layer (duff: F and H layers) of the forest floor is an important boundary between the soil and atmospheric processes. Here we use both empirical data and a three‐dimensional coupled heat and water budget model to explain the duff hydrological hillslope shift between very brief wet periods when lateral flow in the duff and infiltration into the mineral soil occur and dry periods when evaporative flow dominates and both lateral and mineral soil flow are not important. The duff moisture transitions from wet to dry periods were the result of low lateral flow which moves liquid and water vapour only centimetres to metres, very rapidly and mostly in the H layer immediately after precipitation. During wet periods, the net lateral fluxes were negative on divergent areas and positive on convergent areas of the hillslope, leading to a net moisture loss in divergent areas and a net gain in convergent areas. The response to lateral flow in the H layer was more rapid than in the F layer. The transition from the lateral downwards flow to mineral soil to evaporative control was within approximately 48 h of precipitation. Canopy species and aspect were important with lodgepole pine, southwest aspect and 4‐cm deep duff controlled by evaporative processes while Engelmann spruce, northeast aspect and 30‐cm duff were more controlled by hillslope redistribution processes. Copyright © 2010 John Wiley & Sons, Ltd.     

我国上空平流层中微量气体的垂直分布和变化趋势

利用1992～2005年卤素掩星试验（HALOE）的观测资料分析了中国上空平流层的几种微量气体（NO, NO2, HF, HCl, CH4, H2O 和O3）混合比的垂直分布和变化趋势,以期为研究平流层的辐射和化学过程提供一些有用的数据. 文中除给出我国上空平流层各高度上平均的各种微量气体的含量外,还给出青藏高原上空这些微量气体的含量. 分析结果表明,平流层各种微量气体混合比的垂直分布有其不同的特征,在对流层上层到平流层底部各种微量气体的混合比分布和季节变化与平流层相比有明显的差异;分析结果还表明,这些微量气体的季节变化、准两年周期振荡和长期变化趋势都很明显,并且在平流层的不同高度上它们的变化趋势是不相同的. 在平流层中层,NO, NO2, HCl 和H2O 混合比在1998年以前都是增加而后则是明显下降的,但O3相反,在1998年以前明显减少,1998年后其减少的趋势不明显. 这表明,近年来平流层中层这些微量气体的减少使得它们对臭氧的破坏有所缓解. 但在平流层下层,臭氧的耗损仍然很明显.     

Field data and flow system response in clay (vertisol) shale terrain,north central Texas,USA

The water budget in clay shale terrain is controlled by a complex interaction between the vertisol soil layer, the underlying fractured rock, land use, topography, and seasonal trends in rainfall and evapotranspiration. Rainfall, runoff, lateral flow, soil moisture, and groundwater levels were monitored over an annual recharge cycle. Four phases of soil–aquifer response were noted over the study period: (1) dry‐season cracking of soils; (2) runoff initiation, lateral flow and aquifer recharge; (3) crack closure and down‐slope movement of subsurface water, with surface seepage; (4) a drying phase. Surface flow predominated within the watershed (25% of rainfall), but lateral flow through the soil zone continued for most of the year and contributed 11% of stream flow through surface seepage. Actual flow through the fractured shale makes up a small fraction of the water budget but does appear to influence surface seepage by its effect on valley‐bottom storage. When the valley soil storage is full, lateral flow exits onto the valley‐bottom surface as seasonal seeps. Well response varied with depth and hillslope position. FLOWTUBE model results and regional recharge estimates are consistent with an aquifer recharge of 1·6% of annual precipitation calculated from well heights and specific yield of the shale aquifer. Copyright © 2005 John Wiley & Sons, Ltd.     

Modelling the chloride signal at Plynlimon,Wales, using a modified dynamic TOPMODEL incorporating conservative chemical mixing (with uncertainty)

The application of a modified version of dynamic TOPMODEL for two subcatchments at Plynlimon, Wales is described. Conservative chemical mixing within mobile and immobile stores has been added to the hydrological model in an attempt to simulate observed stream chloride concentrations. The model was not fully able to simulate the observed behaviour, in particular the short‐ to medium‐term dynamics. One of the primary problems highlighted by the study was the representation of dry deposition and cloud‐droplet‐deposited chloride, which formed a significant part of the long‐term chloride mass budget. Equifinality of parameter sets inhibited the ability to determine the effective catchment mixing volumes and coefficients or the most likely partition between occult mass inputs and chloride mass inputs determined by catchment immobile‐store antecedent conditions. Some success was achieved, in as much as some aspects of the dynamic behaviour of the signal were satisfactorily simulated, although spectral analysis showed that the model could not fully reproduce the 1/f power spectra of observed stream chloride concentrations with its implications of a wide distribution of residence times for water in the catchment. Copyright © 2006 John Wiley & Sons, Ltd.     

Mixed deposits of complex magmatic and phreatomagmatic volcanism: an example from Crater Hill,Auckland, New Zealand

 A series of alternating phreatomagmatic ("wet") and magmatic ("dry") basaltic pyroclastic deposits forming the Crater Hill tuff ring in New Zealand contains one unit (M1) which can only be interpreted as the products of mixing of ejecta from simultaneous wet and dry explosions at different portions of a multiple vent system. The principal characteristics of M1 are (a) rapid lateral changes in the thicknesses of, and proportions in juvenile components in individual beds, and (b) wide ranges of juvenile clast densities in every sample. M1 appears to have been associated with an elongate source of highly variable and fluctuating magma : water ratios and magma discharge rates. This contrasts with the only other documented mixed (wet and dry) basaltic pyroclastic deposits where mixing from two point sources of quite different but stable character has been inferred. Received: July 11, 1995 / Accepted: February 13, 1996     

Preliminary laboratory studies of the optical scattering properties of the crystal clouds

Ice crystal clouds have an influence on the radiative budget of the earth; however, the exact size and nature of this influence has yet to be determined. A laboratory cloud chamber experiment has been set up to provide data on the optical scattering behaviour of ice crystals at a visible wavelength in order to gain information which can be used in climate models concerning the radiative characteristics of cirrus clouds. A PMS grey-scale probe is used to monitor simultaneously the cloud microphysical properties in order to correlate these closely with the observed radiative properties. Preliminary results show that ice crystals scatter considerably more at 90° than do water droplets, and that the halo effects are visible in a laboratorygenerated cloud when the ice crystal concentration is sufficiently small to prevent masking from multiple scattering.     

Fractal generation of surface area of porous media

Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure with predefined statistical and scaling properties is somewhat scarcer. In the present paper a new numerical method for generating a three-dimensional porous medium with any desired probability density function (PDF) and autocorrelation function (ACF) is presented. The well-known Turning Bands Method (TBM) is modified to generate three-dimensional synthetic isotropic and anisotropic porous media with a Gaussian PDF and exponential-decay ACF. Porous media with other PDF's and ACF's are constructed with a nonlinear, iterative PDF and ACF transformation, whereby the arbitrary PDF is converted to an equivalent Gaussian PDF which is then simulated with the classical TBM. Employing a new method for the estimation of the surface area for a given porosity, the fractal dimensions of the surface area of the synthetic porous media generated in this way are then measured by classical fractal perimeter/area relationships. Different 3D porous media are simulated by varying the porosity and the correlation structure of the random field. The performance of the simulations is evaluated by checking the ensemble statistics, the mean, variance and ACF of the simulated random field. For a porous medium with Gaussian PDF, an average fractal dimension of approximately 2.76 is obtained which is in the range of values of actually measured fractal dimensions of molecular surfaces. For a porous medium with a non-Gaussian quadratic PDF the calculated fractal dimension appears to be consistently higher and averages 2.82. The results also show that the fractal dimension is neither strongly dependent of the porosity nor of the degree of anisotropy assumed.     

Contribution of baseflow during dry spells in irregular channel cross section

The discharge and water level of a gaining stream are known to be maintained during dry spells by baseflow, which is defined as discharge from underground storage. However, the effect of baseflow on a real river is not well known because direct measurements of baseflow in field are difficult to conduct. Therefore, this study attempts to clarify the contribution of baseflow to streamflow and the extent to which the water level is maintained even during dry spells. A digital filter technique is applied to the records of daily mean streamflow in order to estimate the amount of baseflow, and the lateral distribution method is applied to irregular cross sections at observational sites to obtain the stage–discharge rate curve. Through a comparison of the observed data and calculation results, the amount of baseflow is estimated across the channel, in addition to the maximum water level retained during dry spells in relation to the baseflow. Finally, based on the results of an energy conservation model, this study proposes that the source of the amount of baseflow estimated across a channel section may be different from that of the water level maintained during dry spells.