Stream tube integration method for analysing subsurface fluid flow

A stream tube integration method is introduced to solve transient subsurface fluid flow problems. The method combines a geometry-embedded form of Darcy's Law and the notion of location of average. Two types of problems, transient radial flow to a well of finite radius in an areally infinite aquifer and in a double porosity system, are solved by the stream tube integration method and the integral finite difference method. Results of the solutions show that the stream tube integration method, with fixed coarse mesh, are more accurate and better behaved than the integral finite difference method, with fine mesh. The fixed mesh stream tube integration method is readily extended to the moving mesh method. With much coarse mesh, the moving mesh technique can obtain the same accurate results as the fixed mesh stream tube integration method. It is suggested that the stream tube integration method is a viable way to state, solve, interpret and verify numerical solutions. The method provides efficient computation and improved accuracy for analysing subsurface fluid flow. © 1998 John Wiley & Sons, Ltd.     

A Tube Seepage Meter for In Situ Measurement of Seepage Rate and Groundwater Sampling

We designed and evaluated a “tube seepage meter” for point measurements of vertical seepage rates (q), collecting groundwater samples, and estimating vertical hydraulic conductivity (K) in streambeds. Laboratory testing in artificial streambeds show that seepage rates from the tube seepage meter agreed well with expected values. Results of field testing of the tube seepage meter in a sandy‐bottom stream with a mean seepage rate of about 0.5 m/day agreed well with Darcian estimates (vertical hydraulic conductivity times head gradient) when averaged over multiple measurements. The uncertainties in q and K were evaluated with a Monte Carlo method and are typically 20% and 60%, respectively, for field data, and depend on the magnitude of the hydraulic gradient and the uncertainty in head measurements. The primary advantages of the tube seepage meter are its small footprint, concurrent and colocated assessments of q and K, and that it can also be configured as a self‐purging groundwater‐sampling device.     

Three-dimensional decomposition method of global atmospheric circulation

By adopting the idea of three-dimensional Walker, Hadley and Rossby stream functions, the global atmospheric circulation can be considered as the sum of three stream functions from a global per- spective. Therefore, a mathematical model of three-dimensional decomposition of global atmospheric circulation is proposed and the existence and uniqueness of the model are proved. Besides, the model includes a numerical method leading to no truncation error in the discrete three-dimensional grid points. Results also show that the three-dimensional stream functions exist and are unique for a given velocity field. The mathematical model shows the generalized form of three-dimensional stream func- tions equal to the velocity field in representing the features of atmospheric motion. Besides, the vertical velocity calculated through the model can represent the main characteristics of the vertical motion. In sum, the three-dimensional decomposition of atmospheric circulation is convenient for the further in- vestigation of the features of global atmospheric motions.     

Neural network time series prediction of environmental variables in a small upland headwater in NE Scotland

Short‐term prediction of environmental variables such as stream flow rate is useful to members of the general public and environmental scientists alike, providing the ability to predict environmental disasters or scientifically interesting events. Here, a neural‐network based method is presented, which is capable of providing advance flood warnings or the prediction of high stream flow events for research purposes in a small upland headwater in NE Scotland. This method relies on training from past time series data acquired in the field, and provides the ability to predict a range of hydrological and meteorological variables up to 24 h ahead using feedback of predicted values at time t as new inputs for the next time step t + 1. The system is rapid and effective, relies on standard neural network training methods, and has the potential to be implemented in a web‐based monitoring and prediction package. The model design could be implemented at any study site where time series data has been gathered, and is sufficiently flexible to accept whatever data is available. Copyright © 2007 John Wiley & Sons, Ltd.     

Steady flow patterns in saturated and unsaturated,isotropic soils

A comprehensive analysis of steady flow patterns in saturated and unsaturated, possibly heterogeneous, isotropic soils is presented. It is shown that, at any point, the divergence of the unit tangent vector field to the streamlines is equal to the directional derivative along the streamlines of the orthogonal cross-sectional area of an infinitesimal stream tube divided by that area and also equal to the mean curvature of the surface of constant total head. Expressions are derived for the distribution of the flux, the water content, the velocity, the hydraulic conductivity, the total head, and the pressure head along a stream line or an infinitesimal, stream tube. Among the results is a simpler derivation, further interpretation, and extension of earlier work on calculating the hydraulic conductivity distribution from detailed measurements of the total head distribution in combination with measurements of the hydraulic conductivity at a few locations. In the last section, the jumps of various quantities at an interface are discussed.     

Analytical model for aquifer response incorporating distributed stream leakage

An analytical model of stream/aquifer interaction is proposed that predicts drawdown in an aquifer with leakage from a finite-width stream induced by pumping from a well. The model is formulated based on the assumptions of stream partial penetration, a semipervious streambed, and distributed recharge across a finite-width stream. Advantages of the analytical solution include its simple structure, consisting of the Theis well function with integral modifications. The solution is derived for the semi-infinite domain between the stream and pumping well, which is of primary interest to hydrogeologists. Previous stream/aquifer analytical models are compared to the analytical solution based on dimensionless drawdown profiles. Drawdown in the aquifer near a wide stream was found to be less than that predicted by a solution that ignored stream width. Deviations between the proposed analytical solutions and previous solutions increase as stream width increases. For a hypothetical stream/aquifer system, the proposed analytical solution was equivalent to prior solutions when the ratio of the distance between the stream and aquifer to the stream width was greater than 25. This analytical solution may provide improved estimates of aquifer and streambed leakage parameters by curve fitting experimental field drawdown data.     

Determination of magnetic cloud parameters and prediction of magnetic storm intensity

A program for identifying magnetic clouds in patrol satellite data, which recorded the interplanetary medium parameters near the magnetosphere, has been developed based on the cloud model in the form of a force-free cylindrical flux tube. The program makes it possible to also determine the entire magnetic field distribution in a cloud that approaches the Earth, using the initial satellite measurements. For this purpose, a model cloud (which has the maximal correlation coefficient with an analyzed cloud with respect to three magnetic field vector components and minimal rms deviations of the magnetic field and velocity components) is selected from the preliminarily created database including 2 million model clouds. The obtained magnetic field distribution in a cloud will make it possible to predict the intensity of a magnetic storm that this cloud will cause.     

Estimating overland flow erosion capacity using unit stream power

Soil erosion caused by water flow is a complex problem. Both empirical and physically based approaches were used for the estimation of surface erosion rates. Their applications are mainly limited to experimental areas or laboratory studies. The maximum sediment concentration overland flow can carry is not considered in most of the existing surface erosion models. The lack of erosion capacity limitation may cause over estimations of sediment concentration. A correlation analysis is used in this study to determine significant factors that impact surface erosion capacity. The result shows that the unit stream power is the most dominant factor for overland flow erosion which is consistent with experimental data. A bounded regression formula is used to reflect the limits that sediment concentration cannot be less than zero nor greater than a maximum value. The coefficients used in the model are calibrated using published laboratory data. The computed results agree with laboratory data very well. A one dimensional overland flow diffusive wave model is used in conjunction with the developed soil erosion equation to simulate field experimental results. This study concludes that the non-linear regression method using unit stream power as the dominant factor performs well for estimating overland flow erosion capacity.     

Flow depletion in a small stream caused by ground water abstraction from wells

The interaction between a gaining stream and a water-table aquifer is studied at an outwash plain. The aquifer is hydraulically well connected to the stream. Pumping tests were carried out in 1997 and 1998 in two wells 60 m from the stream, screening different depths of the aquifer. Drawdown was measured on both sides of the stream. Hydraulic head, drawdown, and stream depletion data were analyzed using numerical flow models. Similar models were fitted to each of two different data sets: Model A was fitted to steady-state hydraulic head and streamflow gain data not influenced by pumping; and model B was fitted to drawdown data measured during the 1998 pumping test. Each calibrated model closely fits its calibration data; however, predictions were biased if model A was used to predict the calibration data of model B, and vice versa. To further test the models, they were used to predict streamflow depletion during the two pumping tests as well as the drawdown during the 1997 test. Neither of these data were used for calibration. Model A predicted the measured depletions fairly accurately during both tests, whereas the predicted drawdowns in 1997 were significantly larger than actually measured. Contrary to this, the 1997 drawdowns predicted by model B were nearly unbiased; the predicted depletions deviate significantly from the measured depletions in 1997, but they compare well with the observations in 1998. Thus, although field work and analyses were extensive and done carefully to develop a ground water flow model that could predict both drawdown and streamflow depletion, the model predictions are biased. Analyses indicate that the deviations between model and data may be because of error in the models' representations of either the release of water from storage or of the hydrology in the riparian zone.     

A stream depletion field experiment

A field experiment was carried out to measure drawdowns in observation wells and stream depletion flows that occurred when water was abstracted from a well beside a stream. The field data is analyzed herein to determine the aquifer transmissivity, T, the aquifer storage coefficient, S, and a streambed leakage parameter, lambda, by comparing measurements with a solution obtained by Hunt (1999). The analysis uses early time drawdowns with a match-point method to determine T and S, and stream depletion measurements at later times are used to determine lambda. The final results are reasonably consistent for measurements taken in four observation wells. The advantages and disadvantages of this approach are discussed, and two alternative ways of estimating lambda are also discussed.     

New instrument for measuring water discharge by the salt dilution method

The instantaneous salt dilution method for water discharge measurements in open channels has been improved by the development of a new instrument measuring conductivity. The salt method consists of two parts: the calibration and the actual measurement in the stream. The calibration aims to calculate the linear relationship between electrical conductivity and salt concentration at various degrees of dilution in a salt solution. The original undiluted solution is injected into the water of a stream and the conductivity is measured downstream from the injection site. When measuring, the new instrument integrates the conductivity over time. From the value obtained on the instrument's display, the water discharge can easily be calculated on a hand-PC in the field. The instrument has eliminated the subsequent calculation work formerly necessary. It has increased the accuracy of the method and also reduced the need for field personnel during measurements.     

Sampling Fauna in Stream Sediments as well as Groundwater Using One Net Sampler

Groundwater bores act as traps. Net samplers are regularly used for sampling this type of trap for fauna. To enable direct comparisons of faunal communities in groundwater bores and stream sediments, stream sediment tubes were built similar to groundwater bores and were sampled with net samplers for fauna. These stream sediment tubes consisted of a tube anchored in the stream sediment, also called interstitial space. To test the efficacy of this trap method in stream sediments, it was compared to another type of trap, Hahn's trap. Faunal communities sampled by a net in the stream sediment tubes did not differ hugely from fauna in Hahn's trap samples. Physical and chemical factors of sampled water in both the stream sediment tubes, the surrounding interstitial sediments and the second type of traps, Hahn's traps, showed that water in both the tubes and Hahn's traps was closely related to interstitial water. The net sampler is inexpensive and easy to handle. It is suggested that sampling stream tubes with nets may be an appropriate method for long‐term monitoring studies.     

Fully coupled free‐surface flow and sediment transport modelling of flash floods in a desert stream in the Mojave Desert,California

For most of the year, a dry‐bed desert wash is void of water flow. Intensive rain events, however, could trigger significant flash floods that bring about highly complicated hydrodynamics and morphodynamics processes within a desert stream. We present a fully coupled three‐phase flow model of air, water, and sediment to simulate numerically the propagation of a flash flood in a field‐scale fluvial desert stream, the so‐called Tex Wash located in the Mojave Desert, California, United States. The turbulent flow of the flash flood is computed using the three‐dimensional unsteady Reynolds‐averaged Navier–Stokes equations closed with the shear stress transport k ? ω model. The free surface of the flash flood at the interface of air and water phases is computed with the level‐set method, which enables instantaneous tracking of the water surface as the flash flood propagates over the dry bed of the desert stream. The evolution of the desert fluvial stream's morphology, due to the action of the propagating flash flood on the mobile bed, is calculated using a Eulerian morphodynamics model based on the curvilinear immersed boundary method. The capabilities of the proposed numerical framework are demonstrated by applying it to simulate a flash flood event in a 0.65‐km ‐long reach of the Tex Wash, the intricate channel morphology of which is obtained using light imaging detection and ranging technology. The simulated region of the stream includes a number of bridge foundations. The simulation results of the model for the flash flood event revealed the formation of a highly complex flow field and scour patterns within the stream. Moreover, our simulation results showed that most scour processes take place during the steady phase of the flash flood, that is, after the flash flood fills the stream. The transient phase of the flash flood is rather short and contributes to a very limited amount of erosion within the desert stream.     

成都盆地南缘与新构造运动有关的河道演变及其对沉积作用影响初步探讨

本文利用2002年的ETM＋图像和该地区1：25万DEM数据,采用计算机图像处理和目视解译相结合的方法,辅以野外实测数据、历史资料进行综合分析,对该地区河道的演变特征和新构造进行详细解译。基本查清了新近系以来该地区河道的发展演变历程,岷江和青衣江都存在很大幅度的河道迁移现象,综合研究发现,河道迁移与该地区新构造运动密切相关。     

Assessing hydrological model predictive uncertainty using stochastically generated geological models

In distributed and coupled surface water–groundwater modelling, the uncertainty from the geological structure is unaccounted for if only one deterministic geological model is used. In the present study, the geological structural uncertainty is represented by multiple, stochastically generated geological models, which are used to develop hydrological model ensembles for the Norsminde catchment in Denmark. The geological models have been constructed using two types of field data, airborne geophysical data and borehole well log data. The use of airborne geophysical data in constructing stochastic geological models and followed by the application of such models to assess hydrological simulation uncertainty for both surface water and groundwater have not been previously studied. The results show that the hydrological ensemble based on geophysical data has a lower level of simulation uncertainty, but the ensemble based on borehole data is able to encapsulate more observation points for stream discharge simulation. The groundwater simulations are in general more sensitive to the changes in the geological structure than the stream discharge simulations, and in the deeper groundwater layers, there are larger variations between simulations within an ensemble than in the upper layers. The relationship between hydrological prediction uncertainties measured as the spread within the hydrological ensembles and the spatial aggregation scale of simulation results has been analysed using a representative elementary scale concept. The results show a clear increase of prediction uncertainty as the spatial scale decreases. Copyright © 2015 John Wiley & Sons, Ltd.     

Application of distributed hydrological models for predictions in ungauged basins: a method to quantify predictive uncertainty

Stream flow predictions in ungauged basins are one of the most challenging tasks in surface water hydrology because of nonavailability of data and system heterogeneity. This study proposes a method to quantify stream flow predictive uncertainty of distributed hydrologic models for ungauged basins. The method is based on the concepts of deriving probability distribution of model's sensitive parameters by using measured data from a gauged basin and transferring the distribution to hydrologically similar ungauged basins for stream flow predictions. A Monte Carlo simulation of the hydrologic model using sampled parameter sets with assumed probability distribution is conducted. The posterior probability distributions of the sensitive parameters are then computed using a Bayesian approach. In addition, preselected threshold values of likelihood measure of simulations are employed for sizing the parameter range, which helps reduce the predictive uncertainty. The proposed method is illustrated through two case studies using two hydrologically independent sub‐basins in the Cedar Creek watershed located in Texas, USA, using the Soil and Water Assessment Tool (SWAT) model. The probability distribution of the SWAT parameters is derived from the data from one of the sub‐basins and is applied for simulation in the other sub‐basin considered as pseudo‐ungauged. In order to assess the robustness of the method, the numerical exercise is repeated by reversing the gauged and pseudo‐ungauged basins. The results are subsequently compared with the measured stream flow from the sub‐basins. It is observed that the measured stream flow in the pseudo‐ungauged basin lies well within the estimated confidence band of predicted stream flow. Copyright © 2013 John Wiley & Sons, Ltd.     

Modelling discharge from a coastal watershed in southeast Sweden using an integrated framework

The field hydrology model DRAINMOD integrated with Arc Hydro in geographical information system (GIS) framework (Arc Hydro–DRAINMOD) was used to simulate the hydrological response of a coastal watershed in southeast Sweden. Arc Hydro–DRAINMOD uses a distributed approach to route water from each field edge to the watershed outlet. In the framework the Arc Hydro data model was used to describe the stream network in the watershed and to connect the individual simulated DRAINMOD‐field outflow time series from each plot using Arc Hydro schema‐links features, which were summed at Arc Hydro schema‐nodes features along the stream network to generate the stream network flow. Hydrology data collected during six periods between 2003 and 2008 were used to test Arc Hydro–DRAINMOD and its performance was evaluated by considering uncertainties in model inputs using generalized likelihood uncertainty estimation (GLUE). The GLUE estimates obtained (uncertainty bands 5% and 95%) agreed satisfactorily with measured monthly discharges. The percentage of time in which the observed discharges were bracketed by the uncertainty bands was 88% in calibration periods and 75% in validation periods. Although monthly time step simulations showed good agreement with observed discharges during the two main discharge events in spring, the contradictory daily time step results indicate that the watershed response simulations on a daily basis need to be improved. The uncertainty analysis showed that in periods of higher discharge, such as spring periods, the uncertainty in prediction was higher. It is important to note that these uncertainty estimations using the GLUE procedure include the uncertainties in measured discharge values, model inputs, boundary conditions and model structures. It was estimated that stream baseflow represented 42% of the total watershed discharge, but further research is needed to confirm this. These results show that the new Arc Hydro–DRAINMOD framework is applicable for predicting discharge from artificially drained watersheds in southeast Sweden. Copyright © 2010 John Wiley & Sons, Ltd.     

A stream tracer technique employing ionic tracers and specific conductance data applied to the Maimai catchment,New Zealand

The stream tracer technique and transient storage models (TSMs) have become common tools in stream solute and hyporheic exchange studies. The expense and logistics associated with water sample collection and analysis often results in limited temporal resolution of stream tracer breakthrough curves (BTCs). Samples are often collected without a priori or real‐time knowledge of BTC information, which can result in poor sample coverage of the critical shoulder (initial rise) and tail (post‐steady state fall) of the BTC. We illustrate the use of specific conductance (SC) measurements as a surrogate for conservative dissolved tracer (Br⁻) samples. The advantages of collecting SC data for use in the TSM are (1) cost, (2) ease of data collection, and (3) well‐defined breakthrough curves, which strengthen TSM parameter optimization. This method is based on developing an ion concentration (IC)–SC relationship from limited discrete tracer solute samples. SC data can be collected on a more frequent basis at no additional analysis cost. TSM simulations can then be run for the conservative tracer data derived from SC breakthrough curves and the IC–SC relationship. This technique was tested in a 120 m reach of stream (2–60 m subreaches) in the Maimai M15 catchment, New Zealand during baseflow recession. Dissolved LiBr was injected for 12·92 h, with Br⁻ as the conservative ion of interest. Four TSM simulations using the OTIS model are optimized using UCODE to fit (1) Br⁻ data derived from the Br⁻–SC relationship (n = 1307 observations at each of two stream sampling sites), (2) all stream Br⁻ data collected (n = 58 in upper reach, n = 60 in lower reach), (3) half of the stream Br⁻ data collected, and (4) 20 stream Br⁻ samples from each site. No two simulations resulted in the same optimal parameter values. Results suggest that the greater the frequency of observations, the greater the confidence in estimated parameter values. Br⁻–SC simulations resulted in the best overall model fits to the data, with the lowest calculated error variance of 6·37, narrowest 95% parameter estimate confidence intervals, and the highest correlation coefficient of 0·99 942, among the four simulations. This is largely due to the improved representation of the shoulder and tail of the BTC with this method. The IC–SC correlation method is robust in situations in which (1) changes in background SC data can be accounted for, and (2) the data used to define the IC–SC relationship are representative of the range of data collected. This method provides more efficient sample analysis, improved data resolution, and improved model results compared to the alternative stream tracer data gathering methods presented. Additionally, we describe a new parameterization of the cross‐sectional area of the stream during flow recession, as a function of discharge, based on a stream hydraulic geometry relationship. This variant of the OTIS model provides a more realistic representation of stream dynamics during unsteady discharge. Copyright © 2005 John Wiley & Sons, Ltd.     

海洋局域地磁正常场勒让德多项式模型的建立

研究了利用勒让德多项式构建局部海域地磁正常场模型的方法,给出了一种趋势面地磁数据滤波方法和模型截止阶数的确定方法,研究和分析了参与建模的地磁总强度数据的代表性和密度对地磁正常场模型精度的影响,最后提出了一种分区建模的思想.试验表明分区建模相对整体建模具有较高的精度.