Capabilities and limitations of detailed hillslope hydrological modelling

Hillslope hydrological modelling is considered to be of great importance for the understanding and quantification of hydrological processes in hilly or mountainous landscapes. In recent years a few comprehensive hydrological models have been developed at the hillslope scale which have resulted in an advanced representation of hillslope hydrological processes (including their interactions), and in some operational applications, such as in runoff and erosion studies at the field scale or lateral flow simulation in environmental and geotechnical engineering. An overview of the objectives of hillslope hydrological modelling is given, followed by a brief introduction of an exemplary comprehensive hillslope model, which stimulates a series of hydrological processes such as interception, evapotranspiration, infiltration into the soil matrix and into macropores, lateral and vertical subsurface soil water flow both in the matrix and preferential flow paths, surface runoff and channel discharge. Several examples of this model are presented and discussed in order to determine the model's capabilities and limitations. Finally, conclusions about the limitations of detailed hillslope modelling are drawn and an outlook on the future prospects of hydrological models on the hillslope scale is given.The model presented performed reasonable calculations of Hortonian surface runoff and subsequent erosion processes, given detailed information of initial soil water content and soil hydraulic conditions. The vertical and lateral soil moisture dynamics were also represented quite well. However, the given examples of model applications show that quite detailed climatic and soil data are required to obtain satisfactory results. The limitations of detailed hillslope hydrological modelling arise from different points: difficulties in the representations of certain processes (e.g. surface crusting, unsaturated–saturated soil moisture flow, macropore flow), problems of small‐scale variability, a general scarcity of detailed soil data, incomplete process parametrization and problems with the interdependent linkage of several hillslopes and channel–hillslope interactions. Copyright © 1999 John Wiley & Sons, Ltd.     

The influence of preferential flow on hillslope hydrology in a semi‐arid watershed (in the Spanish Dehesas)

Preferential flow is known to influence hillslope hydrology in many areas around the world. Most research on preferential flow has been performed in temperate regions. Preferential infiltration has also been found in semi‐arid regions, but its impact on the hydrology of these regions is poorly known. The aim of this study is to describe and quantify the influence of preferential flow on the hillslope hydrology from small scale (infiltration) to large scale (subsurface stormflow) in a semi‐arid Dehesa landscape. Precipitation, soil moisture content, piezometric water level and discharge data were used to analyse the hydrological functioning of a catchment in Spain. Variability of soil moisture content during the transition from dry to wet season (September to November) within horizontal soil layers leads to the conclusion that there is preferential infiltration into the soils. When the rainfall intensity is high, a water level rapidly builds up in the piezometer pipes in the area, sometimes even reaching soil surface. This water level also drops back to bedrock within a few hours (under dry catchment conditions) to days (under wet catchment conditions). As the soil matrix is not necessarily wet while this water layer is built up, it is thought to be a transient water table in large connected pores which drain partly to the matrix, partly fill up bedrock irregularities and partly drain through subsurface flow to the channels. When the soil matrix becomes wetter the loss of water from macropores to the matrix and bedrock decreases and subsurface stormflow increases. It may be concluded that the hillslope hydrological system consists of a fine matrix domain and a macropore domain, which have their own flow characteristics but which also interact, depending on the soil matrix and macropore moisture contents. The macropore flow can result in subsurface flow, ranging from 13% contribution to total discharge for a large event of high intensity rainfall or high discharge to 80% of total discharge for a small event with low intensity rainfall or low discharge. During large events the fraction of subsurface stormflow in the discharge is suppressed by the large amount of surface runoff. Copyright © 2008 John Wiley & Sons, Ltd.     

Gypsies in the palace: experimentalist's view on the use of 3‐D physics‐based simulation of hillslope hydrological response

As a fundamental unit of the landscape, hillslopes are studied for their retention and release of water and nutrients across a wide range of ecosystems. The understanding of these near‐surface processes is relevant to issues of runoff generation, groundwater–surface water interactions, catchment export of nutrients, dissolved organic carbon, contaminants (e.g. mercury) and ultimately surface water health. We develop a 3‐D physics‐based representation of the Panola Mountain Research Watershed experimental hillslope using the TOUGH2 sub‐surface flow and transport simulator. A recent investigation of sub‐surface flow within this experimental hillslope has generated important knowledge of threshold rainfall‐runoff response and its relation to patterns of transient water table development. This work has identified components of the 3‐D sub‐surface, such as bedrock topography, that contribute to changing connectivity in saturated zones and the generation of sub‐surface stormflow. Here, we test the ability of a 3‐D hillslope model (both calibrated and uncalibrated) to simulate forested hillslope rainfall‐runoff response and internal transient sub‐surface stormflow dynamics. We also provide a transparent illustration of physics‐based model development, issues of parameterization, examples of model rejection and usefulness of data types (e.g. runoff, mean soil moisture and transient water table depth) to the model enterprise. Our simulations show the inability of an uncalibrated model based on laboratory and field characterization of soil properties and topography to successfully simulate the integrated hydrological response or the distributed water table within the soil profile. Although not an uncommon result, the failure of the field‐based characterized model to represent system behaviour is an important challenge that continues to vex scientists at many scales. We focus our attention particularly on examining the influence of bedrock permeability, soil anisotropy and drainable porosity on the development of patterns of transient groundwater and sub‐surface flow. Internal dynamics of transient water table development prove to be essential in determining appropriate model parameterization. Copyright © 2010 John Wiley & Sons, Ltd.     

Effects of hillslope topography on hydrological responses in a weathered granite mountain,Japan: comparison of the runoff response between the valley‐head and the side slope

To evaluate the effects of hillslope topography on storm runoff in a weathered granite mountain, discharge rate, soil pore water pressures, and water chemistry were observed on two types of hillslope: a valley‐head (a concave hillslope) and a side slope (a planar hillslope). Hydrological responses on the valley‐head and side slope reflected their respective topographic characteristics and varied with the rainfall magnitude. During small rainfall events (<35 mm), runoff from the side slope occurred rapidly relative to the valley‐head. The valley‐head showed little response in storm runoff. As rainfall amounts increased (35–60 mm), the valley‐head yielded a higher flow relative to the side slope. For large rainfall events (>60 mm), runoff from both hillslopes increased with rainfall, although that from the valley‐head was larger than that from the side slope. The differences in the runoff responses were caused by differences in the roles of lower‐slope soils and the convergence of the hillslope. During small rainfall events, the side slope could store little water; in contrast, all rainwater could be stored in the soils at the valley‐head hollow. As the amount of rainfall increased, the subsurface saturated area of the valley‐head extended from the bottom to the upper portion of the slope, with the contributions of transient groundwater via lateral preferential flowpaths due to the high concentration of subsurface water. Conversely, saturated subsurface flow did not contribute to runoff responses, and the subsurface saturated area at the side slope did not extend to the upper slope for the same storm size. During large rainfall events, expansion of the subsurface saturated area was observed in both hillslopes. Thus, differences in the concentration of subsurface water, reflecting hillslope topography, may create differences in the extension of the subsurface saturated area, as well as variability in runoff responses. Copyright © 2007 John Wiley & Sons, Ltd.     

First‐order exchange coefficient coupling for simulating surface water–groundwater interactions: parameter sensitivity and consistency with a physics‐based approach

Distributed hydrologic models capable of simulating fully‐coupled surface water and groundwater flow are increasingly used to examine problems in the hydrologic sciences. Several techniques are currently available to couple the surface and subsurface; the two most frequently employed approaches are first‐order exchange coefficients (a.k.a., the surface conductance method) and enforced continuity of pressure and flux at the surface‐subsurface boundary condition. The effort reported here examines the parameter sensitivity of simulated hydrologic response for the first‐order exchange coefficients at a well‐characterized field site using the fully coupled Integrated Hydrology Model (InHM). This investigation demonstrates that the first‐order exchange coefficients can be selected such that the simulated hydrologic response is insensitive to the parameter choice, while simulation time is considerably reduced. Alternatively, the ability to choose a first‐order exchange coefficient that intentionally decouples the surface and subsurface facilitates concept‐development simulations to examine real‐world situations where the surface‐subsurface exchange is impaired. While the parameters comprising the first‐order exchange coefficient cannot be directly estimated or measured, the insensitivity of the simulated flow system to these parameters (when chosen appropriately) combined with the ability to mimic actual physical processes suggests that the first‐order exchange coefficient approach can be consistent with a physics‐based framework. Copyright © 2009 John Wiley & Sons, Ltd.     

Understanding coastal wetland hydrology with a new regional‐scale,process‐based hydrological model

Coastal wetlands represent an ecotone between ocean and terrestrial ecosystems, providing important services, including flood mitigation, fresh water supply, erosion control, carbon sequestration, and wildlife habitat. The environmental setting of a wetland and the hydrological connectivity between a wetland and adjacent terrestrial and aquatic systems together determine wetland hydrology. Yet little is known about regional‐scale hydrological interactions among uplands, coastal wetlands, and coastal processes, such as tides, sea level rise, and saltwater intrusion, which together control the dynamics of wetland hydrology. This study presents a new regional‐scale, physically based, distributed wetland hydrological model, PIHM‐Wetland, which integrates the surface and subsurface hydrology with coastal processes and accounts for the influence of wetland inundation on energy budgets and evapotranspiration (ET). The model was validated using in situ hydro‐meteorological measurements and Moderate Resolution Imaging Spectroradiometer (MODIS) ET data for a forested and herbaceous wetland in North Carolina, USA, which confirmed that the model accurately represents the major wetland hydrological behaviours. Modelling results indicate that topographic gradient is a primary control of groundwater flow direction in adjacent uplands. However, seasonal climate patterns become the dominant control of groundwater flow at lower coastal plain and land–ocean interface. We found that coastal processes largely influence groundwater table (GWT) dynamics in the coastal zone, 300 to 800 m from the coastline in our study area. Among all the coastal processes, tides are the dominant control on GWT variation. Because of inundation, forested and herbaceous wetlands absorb an additional 6% and 10%, respectively, of shortwave radiation annually, resulting in a significant increase in ET. Inundation alters ET partitioning through canopy evaporation, transpiration, and soil evaporation, the effect of which is stronger in cool seasons than in warm seasons. The PIHM‐Wetland model provides a new tool that improves the understanding of wetland hydrological processes on a regional scale. Insights from this modelling study provide benchmarks for future research on the effects of sea level rise and climate change on coastal wetland functions and services.     

Finite‐element analysis of laminated rubber bearing of building frame under seismic excitation

Finite element analysis is carried out for a building frame supported by laminated rubber bearings to simultaneously investigate global displacement and local stress responses under seismic excitation. The frame members and the rubber bearings are discretized into hexahedral solid elements with more than 3 million degrees of freedom. The material property of rubber is represented by the Ogden model, and the frame is assumed to remain in elastic range. It is shown that the time histories of non‐uniform stress distribution and rocking behavior of the rubber bearings under a frame subjected to seismic excitation can be successfully evaluated, and detailed responses of base and frame can be evaluated through large‐scale finite element analysis. Copyright © 2015 John Wiley & Sons, Ltd.     

Physics‐based numerical modelling of large braided rivers dominated by suspended sediment

Physics‐based models have been increasingly developed in recent years and applied to simulate the braiding process and evolution of channel units in braided rivers. However, limited attention is given to lowland braided rivers where the transport of suspended sediment plays a dominant role. In the present study, a numerical model based on the basic physics laws of hydrodynamics and sediment transport is used to simulate the evolution process of a braided river dominated by suspended load transport. The model employs a fractional method to simulate the transport of graded sediments and uses a multiple‐bed‐layer approach to represent the sediment sorting process. An idealized braided river has been produced, with the hydrodynamic, sediment transport and morphological processes being analysed. In particular, the formation process of local pool–bar units in the predicted river has been investigated. A sensitivity analysis has also been undertaken to investigate the effects of grid resolution and an upstream perturbation on the model prediction. A variety of methods are applied to analyse the geometrical and topographical properties of the modelled river. Self‐organizing characteristics related to river geometry and topography are analysed by state‐space plots, which indicate a close relationship with the periodical erosion and deposition cycles of braiding. Cross‐sectional topography and slope frequency display similar geometries to natural rivers. Scaling characteristics are found by correlation analysis of bar parameters. Copyright © 2014 John Wiley & Sons, Ltd.     

A discrete particle representation of hillslope hydrology: hypothesis testing in reproducing a tracer experiment at Gårdsjön,Sweden

Despite the long history of the continuum equation approach in hydrology, it is not a necessary approach to the formulation of a physically based representation of hillslope hydrology. The Multiple Interacting Pathways (MIPs) model is a discrete realization that allows hillslope response and transport to be simultaneously explored in a way that reflects the potential occurrence of preferential flows and lengths of pathways. The MIPs model uses random particle tracking methods to represent the flow of water within the subsurface alongside velocity distributions that acknowledge preferential flows and transition probability matrices, which control flow pathways. An initial realization of this model is presented here in application to a tracer experiment carried out in Gårdsjön, Sweden. The model is used as an exploratory tool, testing several hypotheses in relation to this experiment. Copyright © 2011 John Wiley & Sons, Ltd.     

Simulated effect of a forest road on near‐surface hydrologic response: redux

In the work reported here the comprehensive physics‐based Integrated Hydrology Model (InHM) was employed to conduct both three‐ and two‐dimensional (3D and 2D) hydrologic‐response simulations for the small upland catchment known as C3 (located within the H. J. Andrews Experimental Forest in Oregon). Results from the 3D simulations for the steep unchannelled C3 (i) identify subsurface stormflow as the dominant hydrologic‐response mechanism and (ii) show the effect of the down‐gradient forest road on both the surface and subsurface flow systems. Comparison of the 3D results with the 2D results clearly illustrates the importance of convergent subsurface flow (e.g. greater pore‐water pressures in the hollow of the catchment for the 3D scenario). A simple infinite‐slope model, driven by subsurface pore‐water pressures generated from the 3D and 2D hydrologic‐response simulations, was employed to estimate slope stability along the long‐profile of the C3 hollow axis. As expected, the likelihood of slope failure is underestimated for the lower pore pressures from the 2D hydrologic‐response simulation compared, in a relative sense, to the higher pore pressures from the 3D hydrologic response simulation. The effort reported herein provides a firm quantitative foundation for generalizing the effects that forest roads can have on near‐surface hydrologic response and slope stability at the catchment scale. Copyright © 2006 John Wiley & Sons, Ltd.     

Modelling the potential impacts of groundwater hydrology on long‐term drainage basin evolution

Fluvial erosion processes are driven by water discharge on the land surface, which is produced by surface runoff and groundwater discharge. Although groundwater is often neglected in long‐term landscape evolution problems, water table levels control patterns of Dunne runoff production, and groundwater discharge can contribute significantly to storm flows. In this analysis, we investigate the role that groundwater movement plays in long‐term drainage basin evolution by modifying a widely used landscape evolution model to include a more detailed representation of basin hydrology. Precipitation is generated by a stochastic process, and the precipitation is partitioned between surface runoff and groundwater recharge using a specified infiltration capacity. Groundwater flow is simulated by a dynamic two‐dimensional Dupuit equation for an unconfined aquifer with an irregular underlying impervious layer. The model is applied to the WE‐38 basin, an experimental catchment in Pennsylvania, because 60–80 per cent of the discharge is derived from groundwater and substantial hydrologic and geomorphic information is available. The hydrologic model is first calibrated to match the observed streamflows, and then the combined hydrologic/geomorphic model is used to simulate scenarios with different infiltration capacities. The results of this modelling exercise indicate that the basin can be divided into three zones with distinct streamflow‐generating characteristics, and different parts of the basin can have different geomorphic effective events. Over long periods of time, scenarios in which groundwater discharge is large tend to modify the topography in a way that promotes groundwater discharge and inhibits Dunne runoff. Copyright © 2006 John Wiley & Sons, Ltd.     

Development and testing of a physically based,three-dimensional model of surface and subsurface hydrology

We present a numerical, catchment-scale model that solves flow equations of surface and subsurface flow in a three-dimensional domain. Surface flow is described by the two-dimensional parabolic approximation of the St. Venant equation, using Manning’s equation of motion; subsurface flow is described by the three-dimensional Richards’ equation for the unsaturated zone and by three-dimensional Darcy’s law for the saturated zone, using an integrated finite difference formulation. The hydrological component is a dynamic link library implemented within a comprehensive model which simulates surface energy, radiation budget, snow melt, potential evapotranspiration, plant development and plant water uptake. We tested the model by comparing distributed and integrated three-dimensional simulated and observed perched water depth (PWD), stream flow data, and soil water contents for a small catchment. Additional tests were performed for the snow melting algorithm as well as the different hydrological processes involved. The model successfully described the water balance and its components as evidenced by good agreement between measured and modelled data.     

Sub‐grid scale parameterization of hillslope runoff and erosion processes for catchment‐scale models of semi‐arid landscapes

The processes of hillslope runoff and erosion are typically represented at coarse spatial resolution in catchment‐scale models due to computational limitations. Such representation typically fails to incorporate the important effects of topographic heterogeneity on runoff generation, overland flow, and soil erosion. These limitations currently undermine the application of distributed catchment models to understand the importance of thresholds and connectivity on hillslope and catchment‐scale runoff and erosion, particularly in semi‐arid environments. This paper presents a method for incorporating high‐resolution topographic data to improve sub‐grid scale parameterization of hillslope overland flow and erosion models. Results derived from simulations conducted using a kinematic wave overland flow model at 0.5 m spatial resolution are used to parameterize the depth–discharge relationship in the overland flow model when applied at 16 m resolution. The high‐resolution simulations are also used to derive a more realistic parameterization of excess flow shear stress for use in the 16 m resolution erosion model. Incorporating the sub‐grid scale parameterization in the coarse‐resolution model (16 m) leads to improved predictions of overland flow and erosion when evaluated using results derived from high‐resolution (0.5 m) model simulations. The improvement in performance is observed for a range of event magnitudes and is most notable for erosion estimates due to the non‐linear dependency between the rates of erosion and overland flow. Copyright © 2013 John Wiley & Sons, Ltd.     

Role of temporal resolution of meteorological inputs for process‐based snow modelling

Accurate snow accumulation and melt simulations are crucial for understanding and predicting hydrological dynamics in mountainous settings. As snow models require temporally varying meteorological inputs, time resolution of these inputs is likely to play an important role on the model accuracy. Because meteorological data at a fine temporal resolution (~1 hr) are generally not available in many snow‐dominated settings, it is important to evaluate the role of meteorological inputs temporal resolution on the performance of process‐based snow models. The objective of this work is to assess the loss in model accuracy with temporal resolution of meteorological inputs, for a range of climatic conditions and topographic elevations. To this end, a process‐based snow model was run using 1‐, 3‐, and 6‐hourly inputs for wet, average, and dry years over Boise River Basin (6,963 km²), which spans rain dominated (≤1,400 m), rain–snow transition (>1,400 and ≤1,900 m), snow dominated below tree line (>1,900 and ≤2,400 m), and above tree line (>2,400 m) elevations. The results show that sensitivity of the model accuracy to the inputs time step generally decreases with increasing elevation from rain dominated to snow dominated above tree line. Using longer than hourly inputs causes substantial underestimation of snow cover area (SCA) and snow water equivalent (SWE) in rain‐dominated and rain–snow transition elevations, due to the precipitation phase mischaracterization. In snow‐dominated elevations, the melt rate is underestimated due to errors in estimation of net snow cover energy input. In addition, the errors in SCA and SWE estimates generally decrease toward years with low snow mass, that is, dry years. The results indicate significant increases in errors in estimates of SCA and SWE as the temporal resolution of meteorological inputs becomes coarser than an hour. However, use of 3‐hourly inputs can provide accurate estimates at snow‐dominated elevations. The study underscores the need to record meteorological variables at an hourly time step for accurate process‐based snow modelling.     

Two‐dimensional physically based finite element runoff model for small agricultural watersheds: I. Model development

Soil erosion by water is the root cause of ecological degradation in the Shiwalik foothills of Northern India. Simulation of runoff and its component processes is a pre‐requisite to develop the management strategies to tackle the problem, successfully. A two‐dimensional physically based distributed numerical model, ROMO2D has been developed to simulate runoff from small agricultural watersheds on an event basis. The model employs the 2‐D Richards equation with sink term to simulate infiltration and soil moisture dynamics in the vadoze zone under variable rainfall conditions, and 2‐D Saint‐Venant equations under the kinematic wave approximation along with Manning's equation as the stage‐discharge equation for runoff routing. The various flow‐governing equations have been solved numerically by employing a Galerkin finite element method for spatial discretization using quadrilateral elements and finite difference techniques for temporal solutions. The ROMO2D computer program has been developed as a class‐based program, coded in C + + in such a way that with minor modifications, the model can be used to simulate runoff on a continuous basis. The model writes output for a runoff hydrograph of each storm. Model development is described in this paper and the results of model testing and field application are to be presented in a subsequent paper. Copyright © 2008 John Wiley & Sons, Ltd.     

Isotope hydrology of a tropical coffee agroforestry watershed: Seasonal and event‐based analyses

Stable isotope variations are extremely useful for flow partitioning within the hydrologic cycle but remain poorly understood throughout the tropics, particularly in watersheds with rapidly infiltrating soils, such as Andisols in Central America. This study examines the fluctuations of stable isotope ratios (δ¹⁸O and δ²H) in the hydrologic components of a tropical coffee agroforestry watershed (~1 km²) with Andisol soils in Costa Rica. Samples were collected in precipitation, groundwater, springs, and stream water over 2 years. The local meteoric water line for the study site was δ²H = 8.5 δ¹⁸O + 18.02 (r² = 0.97, n = 198). The isotope ratios in precipitation exhibited an enriched trend during the dry season and a notable depletion at the beginning of the wet season. The δ¹⁸O compositions in groundwater (average = ?6.4‰, σ = 0.7) and stream water (average = ?6.7‰, σ = 0.6) were relatively stable over time, and both components exhibited more enriched values in 2013, which was the drier year. No strong correlation was observed between the isotope ratios and the precipitation amount at the event or daily time‐step, but a correlation was observed on a monthly scale. Stream water and base flow hydrograph separations based on isotope end‐member estimations showed that pre‐event water originating from base flow was prevalent. However, isotope data indicate that event water originating from springs appears to have been the primary driver of initial rises in stream flow and peak flows. These results indicate that isotope sampling improves the understanding of water balance components, even in a tropical humid location, where significant variations in rainfall challenge current modelling efforts. Further research using fine‐scale hydrometric and isotopic data would enhance understanding the processes driving spring flow generation in watersheds.     

A temperature‐precipitation‐based model of thirty‐year mean snowpack accumulation and melt in Oregon,USA

High‐resolution, spatially extensive climate grids can be useful in regional hydrologic applications. However, in regions where precipitation is dominated by snow, snowmelt models are often used to account for timing and magnitude of water delivery. We developed an empirical, nonlinear model to estimate 30‐year means of monthly snowpack and snowmelt throughout Oregon. Precipitation and temperature for the period 1971–2000, derived from 400‐m resolution PRISM data, and potential evapotranspiration (estimated from temperature and day length) drive the model. The model was calibrated using mean monthly data from 45 SNOTEL sites and accurately estimated snowpack at 25 validation sites: R² = 0·76, Nash‐Sutcliffe Efficiency (NSE) = 0·80. Calibrating it with data from all 70 SNOTEL sites gave somewhat better results (R² = 0·84, NSE = 0·85). We separately applied the model to SNOTEL stations located < 200 and ≥ 200 km from the Oregon coast, since they have different climatic conditions. The model performed equally well for both areas. We used the model to modify moisture surplus (precipitation minus potential evapotranspiration) to account for snowpack accumulation and snowmelt. The resulting values accurately reflect the shape and magnitude of runoff at a snow‐dominated basin, with low winter values and a June peak. Our findings suggest that the model is robust with respect to different climatic conditions, and that it can be used to estimate potential runoff in snow‐dominated basins. The model may allow high‐resolution, regional hydrologic comparisons to be made across basins that are differentially affected by snowpack, and may prove useful for investigating regional hydrologic response to climate change. Published in 2011 by John Wiley & Sons, Ltd.