Power function decay of hydraulic conductivity for a TOPMODEL‐based infiltration routine

TOPMODEL rainfall‐runoff hydrologic concepts are based on soil saturation processes, where soil controls on hydrograph recession have been represented by linear, exponential, and power function decay with soil depth. Although these decay formulations have been incorporated into baseflow decay and topographic index computations, only the linear and exponential forms have been incorporated into infiltration subroutines. This study develops a power function formulation of the Green and Ampt infiltration equation for the case where the power n = 1 and 2. This new function was created to represent field measurements in the New York City, USA, Ward Pound Ridge drinking water supply area, and provide support for similar sites reported by other researchers. Derivation of the power‐function‐based Green and Ampt model begins with the Green and Ampt formulation used by Beven in deriving an exponential decay model. Differences between the linear, exponential, and power function infiltration scenarios are sensitive to the relative difference between rainfall rates and hydraulic conductivity. Using a low‐frequency 30 min design storm with 4·8 cm h^?1 rain, the n = 2 power function formulation allows for a faster decay of infiltration and more rapid generation of runoff. Infiltration excess runoff is rare in most forested watersheds, and advantages of the power function infiltration routine may primarily include replication of field‐observed processes in urbanized areas and numerical consistency with power function decay of baseflow and topographic index distributions. Equation development is presented within a TOPMODEL‐based Ward Pound Ridge rainfall‐runoff simulation. Copyright © 2006 John Wiley & Sons, Ltd.     

Use of spatially distributed water table observations to constrain uncertainty in a rainfall–runoff model

The Generalised Likelihood Uncertainty Estimation (GLUE) methodology is used to investigate how distributed water table observations modify simulation and parameter uncertainty for the hydrological model TOPMODEL, applied to the Sæternbekken Minifelt catchment in Norway. Errors in simulating observed flows, continuously-logged borehole water levels and more extensive, spatially distributed water table depths are combined using Bayes' equation within a `likelihood measure' L. It is shown how the distributions of L for the TOPMODEL parameters change as the different types of observed data are considered. These distributions are also used to construct corresponding simulation uncertainty bounds for flows, borehole water levels, and water table depths within the spatially-extensive piezometer network. Qualitatively wide uncertainty bounds for water table simulations are thought to be consistent with the simplified nature of the distributed model.     

Increased flexibility in base flow modelling using a power law transmissivity profile

The hydrological catchment model known as TOPMODEL, in its original and most widely‐used form, assumed that subsurface transmissivity decreases exponentially as subsurface water storage decreases. It has been shown that this leads to recession curves of discharge Q that take the form ? dQ/dt = aQ^b, where a is a constant and b = 2. In order to reproduce a wider range of recession, or base flow, behaviour, a power function for transmissivity was subsequently incorporated into TOPMODEL as an alternative to the exponential function. This was claimed to extend the realistic values of b to range from 1 to 2, inclusive. We show here that the power transmissivity function can also generate values of b > 2 without making unrealistic assumptions (beyond those arguably made in the original TOPMODEL), thus generating recession curves consistent with catchments showing prolonged base flow. Furthermore, the power transmissivity function can generate recession curves that steepen with time (b < 1). Copyright © 2007 John Wiley & Sons, Ltd.     

Refined conceptualization of TOPMODEL for shallow subsurface flows

The TOPMODEL framework was used to derive expressions that account for saturated and unsaturated flow through shallow soil on a hillslope. The resulting equations were the basis for a shallow‐soil TOPMODEL (STOPMODEL). The common TOPMODEL theory implicitly assumes a water table below the entire watershed and this does not conceptually apply to systems hydrologically controlled by shallow interflow of perched groundwater. STOPMODEL provides an approach for extending TOPMODEL's conceptualization to apply to shallow, interflow‐driven watersheds by using soil moisture deficit instead of water table depth as the state variable. Deriving STOPMODEL by using a hydraulic conductivity function that changes exponentially with soil moisture content results in equations that look very similar to those commonly associated with TOPMODEL. This alternative way of conceptualizing TOPMODEL makes the modelling approach available to researchers, planners, and engineers who work in areas where TOPMODEL was previously believed to be unsuited, such as the New York City Watershed in the Catskills region of New York State. Copyright © 2002 John Wiley & Sons, Ltd.     

Water storage dynamics in a till hillslope: the foundation for modeling flows and turnover times

Studies on hydrology, biogeochemistry, or mineral weathering often rely on assumptions about flow paths, water storage dynamics, and transit times. Testing these assumptions requires detailed hydrometric data that are usually unavailable at the catchment scale. Hillslope studies provide an alternative for obtaining a better understanding, but even on such well‐defined and delimited scales, it is rare to have a comprehensive set of hydrometric observations from the water divide down to the stream that can constrain efforts to quantify water storage, movement, and turnover time. Here, we quantified water storage with daily resolution in a hillslope during the course of almost an entire year using hydrological measurements at the study site and an extended version of the vertical equilibrium model. We used an exponential function to simulate the relationship between hillslope discharge and water table; this was used to derive transmissivity profiles along the hillslope and map mean pore water velocities in the saturated zone. Based on the transmissivity profiles, the soil layer transmitting 99% of lateral flow to the stream had a depth that ranged from 8.9 m at the water divide to under 1 m closer to the stream. During the study period, the total storage of this layer varied from 1189 to 1485 mm, resulting in a turnover time of 2172 days. From the pore water velocities, we mapped the time it would take a water particle situated at any point of the saturated zone anywhere along the hillslope to exit as runoff. Our calculations point to the strengths as well as limitations of simple hydrometric data for inferring hydrological properties and water travel times in the subsurface.     

Simulation and comparative study of two types of Topographic Index model for a homogeneous mountain catchment

In order to expand the application range of the classic Topographic Index model (TOPMODEL) and develop a more appropriate submodel of hydrological processes for use in the land surface model, two types of TOPMODEL are investigated, one with saturated hydraulic conductivity change with depth obeying exponential law (classical e-TOPMODEL or e-TOPMODEL for short) and the other obeying general power law (general p-TOPMODEL or p-TOPMODEL for short). Using observation date in the Suomo River catchment located in the upper reaches of the Yangtze River, the sensitivity study of the p-TOPMODEL was conducted and the simulated results from the model were examined and evaluated first, and then the results were compared with the results from the e-TOPMODEL to find the similarities and differences between the two types of models. The main conclusions obtained from the above studies are (1) topographic index and its distribution derived from the p-TOPPMODEL for the Suomo Basin are sensitive to changes of parameter n and m; (2) changes of n and m have impacts on the simulation results of various hydrological components (such as daily runoff, monthly averaged runoff, monthly averaged surface runoff and subsurface runoff), but have the weaker impacts on forty-year averaged total runoff; and (3) for the same value of m, the simulated results of e-TOPMODEL display higher surface runoff and lower subsurface runoff than the general p-TOPMODEL does but multi-year averaged total runoffs produced from the two types of TOPMODEL show insignificant difference. The differences between the two types of models indicate that it is necessary to pay close attention to correct selection from different hydrological models for use in land surface model development. The result mentioned above is useful to provide some referential information for the model selection.     

Changes in Entrapped Gas Content and Hydraulic Conductivity with Pressure

Water table fluctuations continuously introduce entrapped air bubbles into the otherwise saturated capillary fringe and groundwater zone, which reduces the effective (quasi‐saturated) hydraulic conductivity, K_quasi, thus impacting groundwater flow, aquifer recharge and solute and contaminant transport. These entrapped gases will be susceptible to compression or expansion with changes in water pressure, as would be expected with water table (and barometric pressure) fluctuations. Here we undertake laboratory experiments using sand‐packed columns to quantify the effect of water table changes of up to 250 cm on the entrapped gas content and the quasi‐saturated hydraulic conductivity, and discuss our ability to account for these mechanisms in ground water models. Initial entrapped air contents ranged between 0.080 and 0.158, with a corresponding K_quasi ranging between 2 and 6 times lower compared to the K_s value. The application of 250 cm of water pressure caused an 18% to 26% reduction in the entrapped air content, resulting in an increase in K_quasi by 1.16 to 1.57 times compared to its initial (0 cm water pressure) value. The change in entrapped air content measured at pressure step intervals of 50 cm, was essentially linear, and could be modeled according to the ideal gas law. Meanwhile, the changes in K_quasi with compression–expansion of the bubbles because of pressure changes could be adequately captured with several current hydraulic conductivity models.     

Mechanisms and pathways of lateral flow on aspen‐forested,Luvisolic soils,Western Boreal Plains,Alberta, Canada

Rainfall simulation experiments by Redding and Devito ( 2008 , Hydrological Processes 23: 4287–4300) on two adjacent plots of contrasting antecedent soil moisture storage on an aspen‐forested hillslope on the Boreal Plain showed that lateral flow generation occurred only once large soil storage capacity was saturated combined with a minimum event precipitation of 15–20 mm. This paper extends the results of Redding and Devito ( 2008 , Hydrological Processes 23: 4287–4300) with detailed analysis of pore pressure, soil moisture and tracer data from the rainfall simulation experiments, which is used to identify lateral flow generation mechanisms and flow pathways. Lateral flow was not generated until soils were wet into the fine textured C horizon. Lateral flow occurred dominantly through the clay‐rich Bt horizon by way of root channels. Lateral flow during the largest event was dominated by event water, and precipitation intensity was critical in lateral flow generation. Lateral flow was initiated as preferential flow near the soil surface into root channels, followed by development of a perched water table at depth, which also interacted with preferential flow pathways to move water laterally by the transmissivity feedback mechanism. The results indicate that lateral flow generated by rainfall on these hillslopes is uncommon because of the generally high available soil moisture storage capacity and the low probability of rainfall events of sufficient magnitude and intensity. Copyright © 2010 John Wiley & Sons, Ltd.     

Using internal catchment information to reduce the uncertainty of discharge and baseflow predictions

The semi-distributed hydrological model TOPMODEL was tested with data from the Can Vila research basin (Vallcebre) in order to verify its adequacy for simulating runoff and the relative contributions from saturated overland flow and groundwater flow. After a test of the overall performance of the model, only data from a wet period were selected for this work. The test was performed using the GLUE method. The model was conditioned on continuous discharge and water table records. Furthermore, point measurements of recession flow simultaneous with water table depth and the extent of saturated areas were used to condition the distributions of the more relevant parameters, using new or updated evaluation measures. A wide range of parameter sets provided acceptable results for flow simulation when the model was conditioned on flow data alone, and the uncertainty of prediction of the contribution from groundwater was extremely large. However, conditioning on water table records and the distribution of parameters obtained from point observations strongly reduced the uncertainty of predictions for both stream flow and groundwater contribution.     

Generalization of TOPMODEL for a power law transmissivity profile

A generalization of the TOPMODEL equations for a power law vertical profile of hydraulic conductivity is introduced. The exponential profile of TOPMODEL is obtained as a limit case of the new general form. © 1997 John Wiley & Sons, Ltd.     

A BTOP model to extend TOPMODEL for distributed hydrological simulation of large basins

Topography is a dominant factor in hillslope hydrology. TOPMODEL, which uses a topographical index derived from a simplified steady state assumption of mass balance and empirical equations of motion over a hillslope, has many advantages in this respect. Its use has been demonstrated in many small basins (catchment areas of the order of 2–500 km²) but not in large basins (catchment areas of the order of 10 000–100 000 km²). The objective of this paper is to introduce the Block‐wise TOPMODEL (BTOP) as an extension of the TOPMODEL concept in a grid based framework for distributed hydrological simulation of large river basins. This extension was made by redefining the topographical index by using an effective contributing area af(a) (0?f(a)?1) per unit grid cell area instead of the upstream catchment area per unit contour length and introducing a concept of mean groundwater travel distance. Further the transmissivity parameter T₀ was replaced by a groundwater dischargeability D which can provide a link between hill slope hydrology and macro hydrology. The BTOP model uses all the original TOPMODEL equations in their basic form. The BTOP model has been used as the core hydrological module of an integrated distributed hydrological model YHyM with advanced modules of precipitation, evapotranspiration, flow routing etc. Although the model has been successfully applied to many catchments around the world since 1999, there has not been a comprehensive theoretical basis presented in such applications. In this paper, an attempt is made to address this issue highlighted with an example application using the Mekong basin. Copyright © 2007 John Wiley & Sons, Ltd.     

The in(a/tan/β) index: How to calculate it and how to use it within the topmodel framework

Topographic indices may be used to attempt to approximate the likely distribution of variable source areas within a catchment. One such index has been applied widely using the distribution function catchment model, TOPMODEL, of Beven and Kirkby (1979). Validation of the spatial predictions of TOPMODEL may be affected by the algorithm used to calculate the model's topographic index. A number of digital terrain analysis (DTA) methods are therefore described for use in calculating the TOPMODEL topographic index, In(a/tanβ) (a = upslope contributing area per unit contour; tanβ = local slope angle). The spatial pattern and statistical distribution of the index is shown to be substantially different for different calculation procedures and differing pixel resolutions. It is shown that an interaction between hillslope contributing area accumulation and the analytical definition of the channel network has a major influence on calculated In(a/tanβ) index patterns. A number of DTA tests were performed to explore this interaction. The tests suggested that an ‘optimum’ channel initiation threshold (CIT) may be identified for positioning river headwaters in a raster digital terrain model (DTM). This threshold was found to be dependent on DTM grid resolution. Grid resolution is also suggested to have implications for the validation of spatial model predictions, implying that ‘optimum’ TOPMODEL parameter sets may be unique to the grid scale used in their derivation. Combining existing DTA procedures with an identified CIT, a procedure is described to vary the directional diffusion of contributing area accumulation with distance from the channel network.     

Development of a one-parameter variable source area runoff model for ungauged basins

This research develops a one-parameter model of saturated source area dynamics and the spatial distribution of soil moisture. The single required parameter is the maximum soil moisture deficit within the catchment. The concept behind the development of the model comes from the fact that the complexity of topographically-driven runoff generation can be reduced through the use of geomorphological scaling relations. The scaling formulation allows the prediction of the dynamics of saturated source areas as a function of basin-wide soil moisture state. This model offers a number of potential advantages. Firstly, the model parameter is independent of topographic index distribution and its associated scale effects. Secondly, it may be possible to measure this single parameter using field measurements or perhaps remote sensing, which gives the model significant potential for application in ungauged basins. Finally, the fact that this parameter is a physical characteristic of the basin, estimation of this parameter avoids regionalization and parameter transferability problems. The model is tested using rainfall–runoff data from the 10.4 ha experimental catchment known as Tarrawara in Australia, the 37 km² Town Creek catchment in U.S.A., and the 620 km² Balaphi and the 850 km² Likhu sub-catchments of the Koshi river in Nepal. In sub-catchments of Koshi river, the simulation results compare favorably against the calibrated TOPMODEL both in terms of direct runoff and the spatial distribution of soil moisture state. In the Tarrawara and Town Brook catchments, simulation results compare favorably against observed storm runoff using all observed data, without calibration.     

Vegetation water sources in California's Sierra Nevada (USA) are young and change over time,a multi-isotope (δ18O, δ2H, 3H) tracer approach.

Sierra Nevada forests transpire a significant amount of California's water resources, sparking interest in applying forest management to improve California's water supply. Determining the source water of evapotranspiration enables forest managers to make informed decisions. To this end, a significant interest in critical zone science is to develop new methods to work across time scales to predict subsurface water storage and use. In this study, forest vegetation accessed young water and switched sources depending on availability, suggesting that forest drought vulnerability may depend on the range of water sources available (rain, snowmelt and deeply stored water). This finding also suggests that changes in transpiration rates may have immediate effects on water sources in close proximity to vegetation, and delayed effects on storage and runoff. New δ¹⁸O, δ²H and ³H data were used to track precipitation, runoff, evapotranspiration and storage through the critical zone seasonally, including seasons where evapotranspiration and snowmelt were in phase (winter snowmelt) and out of phase (seasonally dry summer). The main source of this headwater catchment's runoff is derived from its meadow saturated zone water, which was dominated by snowmelt. Water that originated as snowmelt contributed to transpiration, unless other sources, such as recent rain, became available. In cases where xylem δ¹⁸O and δ²H signatures matched those of deeper saturated zone water, ³H data showed that xylem water was distinctly younger than the deep saturated zone water. During 2016, which experienced relatively normal snowpack in winter and seasonally dry summer conditions, mean summer saturated zone water and vegetation water were similar in δ¹⁸O, −12.4 ± 0.04 ‰ and − 12.5 ± 0.3 ‰, respectively, but were distinctly different in ³H, 5.5 ± 0.2 pCi/L and 13.7 ± 1.1 pCi/L, respectively. While δ¹⁸O shows that vegetation and meadow saturated zone water have similar origins, ³H shows they have dissimilar ages.     

Numerical investigation of saturated source area behavior at the small catchment scale

The objective of this research is to explore the relationship between small catchment properties and the temporal growth and decay of saturated source areas (SSA). A simple physics-based hydrologic model, which we call the Sandbox model, is developed for this purpose. A thorough sensitivity analysis is undertaken to evaluate model response to variations in model parameters. Sandbox model output is compared to that from the semi-distributed conceptual model, TOPMODEL, a model with a wide spread acceptance. Plotting the temporal evolution of the extent of saturated source area versus catchment average soil water content during a number of wetting and drying cycles shows a wide variety of trajectories or hysteretic loops. A parametric analysis was performed to quantify the impact of hypothetical catchment properties on the relationship between saturated area extent and basin-average soil water content, revealing hysteretic behavior. It is shown that this hysteresis is the result of changes in groundwater table slope, which is usually less than, and seldom equal to, the land-surface slope in non-saturated areas.     

A network‐index‐based version of TOPMODEL for use with high‐resolution digital topographic data

This paper describes the preliminary development of a network‐index approach to modify and to extend the classic TOPMODEL. Application of the basic Beven and Kirkby form of TOPMODEL to high‐resolution (2·0 m) laser altimetric data (based upon the UK Environment Agency's light detection and ranging (LIDAR) system) to a 13·8 km² catchment in an upland environment identified many saturated areas that remained unconnected from the drainage network even during an extreme flood event. This is shown to be a particular problem with using high‐resolution topographic data, especially over large appreciable areas. To deal with the hydrological consequences of disconnected areas, we present a simple network index modification in which saturated areas are only considered to contribute when the topographic index indicates continuous saturation through the length of a flow path to the point where the path becomes a stream. This is combined with an enhanced method for dealing with the problem of pits and hollows, which is shown to become more acute with higher resolution topographic data. The paper concludes by noting the implications of the research as presented for both methodological and substantive research that is currently under way. Copyright © 2004 John Wiley & Sons, Ltd.     

Sensitivity analysis of extended TOPMODEL for agricultural watersheds equipped with tile drains

An extension of TOPMODEL was developed for rainfall–runoff simulation in agricultural watersheds equipped with tile drains. Tile drain functions are incorporated into the framework of TOPMODEL. Nine possible flow generation scenarios are suggested for tile-drained watersheds and applied in the modelling procedure. In the model development, two methods of simulation of the flow in the unsaturated zone were compared: the traditional, physically based storage approach and a new approach using a transfer function. A regionalized sensitivity analysis was used to determine the sensitivity of parameters and to compare the behaviour of the transfer function with that of the simple storage-related formulation. The number of accepted combinations of parameter values, on average, was higher for the transfer function approach than when using a Monte Carlo method of parameter estimation. Since the rainfall–runoff response pattern tends to vary seasonally, seven events distributed throughout a year were used in the sensitivity analysis to investigate the seasonal variation of the hydrological characteristics. © 1997 John Wiley & Sons, Ltd.     

Propagation of seismic waves through liquefied soils

To predict the earthquake response of saturated porous media it is essential to correctly simulate the generation, redistribution, and dissipation of excess pore water pressure during and after earthquake shaking. To this end, a reliable numerical tool requires a dynamic, fully coupled formulation for solid–fluid interaction and a versatile constitutive model. Presented in this paper is a 3D finite element framework that has been developed and utilized for this purpose. The framework employs fully coupled dynamic field equations with a u–p–U formulation for simulation of pore fluid and solid skeleton interaction and a SANISAND constitutive model for response of solid skeleton. After a detailed verification and validation of the formulation and implementation of the developed numerical tool, it is employed in the seismic response of saturated porous media. The study includes examination of the mechanism of propagation of the earthquake-induced shear waves and liquefaction phenomenon in uniform and layered profiles of saturated sand deposits.     

太湖水体秋季散射特性及其相关因素分析

水体散射特性的研究是水色遥感和水生态学研究中重要的组成部分.通过对2007-11-08至2007-11-21在太湖获取的水体固有光学属性和室内水样分析数据的分析,研究太湖水体散射特性及其相关因素.结果表明,太湖水体散射系数与波长之间存在幂函数递减规律,平均幂指数为0.82±0.21,变异系数为25.39%;粒径分布斜率与幂指数以及散射系数ln(550nm)/1n(756nm)之间存在线性相关,R2分别为0.894和0.783;后向散射率与无机悬浮物浓度之间指数负相关R2=0.854;折射指数与无机悬浮物浓度和无机物与有机物的比例之间指数负相关,R2分别为0.851和0.781.     

On the transport of moisture in polythermal glaciers

Abstract

We reconsider the problem of formulation of a model for polythermal glaciers, focussing attention in particular on the temperate zone where ice and water can coexist at the melting temperature. The energy equation for the ice-water mixture in this zone introduces a moisture flux, and a constitutive law for this flux is required. By analogy with the flow through a porous medium, we use Darcy's law (i.e. the second momentum equation of a two-phase flow model with “porous” geometry), and then require a mechanical constitutive relation relating the water pressure p _w to the average ice pressure p _i . Experience in two phase flows suggests that p _w =p _i may be problematical, and experience in soil mechanics suggests it is inaccurate. A constitutive relation is therefore presented based on work of Nye (1976), and its effect on the well-posedness of the model is examined. Considerations of the sort presented here have clear relevance in the formulation of similar problems in other geophysical situations, notably mantle convection.