An integral-balance nonlinear model to simulate changes in soil moisture,groundwater and surface runoff dynamics at the hillslope scale

We present a system of ordinary differential equations (ODEs) capable of reproducing simultaneously the aggregated behavior of changes in water storage in the hillslope surface, the unsaturated and the saturated soil layers and the channel that drains the hillslope. The system of equations can be viewed as a two-state integral-balance model for soil moisture and groundwater dynamics. Development of the model was motivated by the need for landscape representation through hillslopes and channels organized following stream drainage network topology. Such a representation, with the basic discretization unit of a hillslope, allows ODEs-based simulation of the water transport in a basin. This, in turn, admits the use of highly efficient numerical solvers that enable space–time scaling studies. The goal of this paper is to investigate whether a nonlinear ODE system can effectively replicate observations of water storage in the unsaturated and saturated layers of the soil. Our first finding is that a previously proposed ODE hillslope model, based on readily available data, is capable of reproducing streamflow fluctuations but fails to reproduce the interactions between the surface and subsurface components at the hillslope scale. However, the more complex ODE model that we present in this paper achieves this goal. In our model, fluxes in the soil are described using a Taylor expansion of the underlying storage flux relationship. We tested the model using data collected in the Shale Hills watershed, a 7.9-ha forested site in central Pennsylvania, during an artificial drainage experiment in August 1974 where soil moisture in the unsaturated zone, groundwater dynamics and surface runoff were monitored. The ODE model can be used as an alternative to spatially explicit hillslope models, based on systems of partial differential equations, which require more computational power to resolve fluxes at the hillslope scale. Therefore, it is appropriate to be coupled to runoff routing models to investigate the effect of runoff and its uncertainty propagation across scales. However, this improved performance comes at the expense of introducing two additional parameters that have no obvious physical interpretation. We discuss the implications of this for hydrologic studies across scales.     

Equation of a Barotropic Fluid on a Rotating Spherical Surface and its Inertial Manifold

The inertial manifold is a positive invariant set which exponentially attracts all the trajectories of a dissipative dynamic system. It was introduced for the purpose of studying the asymptotic behaviour of such systems. The initial infinitely dimensional dynamic system, generated by a partial differential evolution equation, can be projected on to it, in order to obtain the final system of ordinary differential equations (inertial equations). These equations then simulate the initial object. Although the inertial manifold is an object relatively simpler than the attractor (a very complicated set of non-integer dimension may be an attractor) it is more difficult to prove its existence than that of the attractor. The equation of a barotropic fluid on a rotating spherical surface is one of the examples of dissipative dynamic systems with an inertial manifold. This kindles the hope that also the equations of the dynamics of the real atmosphere will have an inertial manifold. The reduction of the sample system to this Lipschitz manifold of finite dimension thus justifies us in analysing the behaviour of the atmosphere on non-linear models of finite dimensions and few parameters, in a finite system of ordinary differential equations.     

An insight into the dynamics of Lake Nainital (Kumaun Himalaya,India) using stable isotope data / Un aperçu de la dynamique du Lac Nainital (Himalaya Kumaun,Inde) à partir de données isotopiques stables

Abstract

Abstract The water balance of Lake Nainital in the Kumaun Himalaya, India was previously computed using water budgeting and other indirect methods. An important data set of stable oxygen and hydrogen isotopic composition of water sources of the lake region was also presented and used to verify the annual estimates of subsurface flow/water balance. In the present study, the same data set has been used to investigate the dynamics of this lake in terms of the seasonal processes operative during the annual hydrological cycle: increased inflow during the monsoon, delayed groundwater inflow, and stratification and mixing of water. Based on the available data, a simple two-box model was used to constrain the values of exchange coefficients between the hypolimnion and epilimnion layers and to estimate evaporation and outflow components from the isotopic data.     

Seasonal and storm flow dynamics of dissolved organic carbon in a Mediterranean mountain catchment (Vallcebre,eastern Pyrenees)

To improve understanding of DOC dynamics in seasonal Mediterranean environments, rainfall, soil water, groundwater and stream water samples were taken during a 27-month period in the Can Vila catchment (northeast Spain). Using these data, we characterized DOC dynamics in the different hydrological compartments and analysed the factors affecting them. We also analysed DOC dynamics during storm events and the factors that control DOC delivery to the stream. The results show some seasonality in rainwater and soil water DOC concentrations, while no clear seasonality was observed in stream water and groundwater, where DOC dynamics were strongly related to discharge and water table variations. For storm events with several discharge peaks, the slope of the discharge–DOC concentration relationship was higher for the first peak. The rather similar dynamics of stream water DOC concentration in all floods contrast with the observed diversity of hydrological processes. This raises the question of the origin of the observed rapid DOC increase.

EDITOR M.C. Acreman

ASSOCIATE EDITOR K. Heal     

Development and demonstration of a structured hydrological feature coding system for Europe

Abstract

Validation of large amounts of digital hydrological data and eventual exchange of data between various organisations can benefit from the development of a structured hydrological feature coding system. In this article we describe the development of such a system and present its implementation in the CCM2 structured hydrological feature data set, covering Europe to the Urals and including Turkey. We discuss the coding of river basins, catchments, lakes and rivers. The proposed coding system is largely inspired by the work of Otto Pfafstetter with additions for coding oceans, seas, islands and lakes. Furthermore the coding system can be transferred to features that geometrically intersect the coded hydrological features and we propose some rules on how to establish this transfer.

Citation de Jager, A. L. & Vogt, J. V. (2010) Development and demonstration of a structured hydrological feature coding system for Europe. Hydrol. Sci. J. 55(5), 661–675.     

Sustainable groundwater management of the stressed Coastal aquifer in the Gaza region

Abstract

This study proposes an empirical approach that can lead to the sustainable management of groundwater resources. This approach enables a comprehensive understanding of an aquifer, delineates distinct hydrological scenarios, and recommends a set of operational activities for each sub-region of the aquifer. The paper focuses on the Coastal aquifer of the Gaza Strip region which has been divided into three sub-regions. The southern sub-region (WSW) is classified as scenario “+a2”, which indicates that it can be used as a multi-annual groundwater reservoir. The northern sub-region (NW-E) is designated scenario “-a2”, where the recommended operational measures include injection of freshwater in wells and cleaning of the surface environment. The third sub-region (CSE), is classified as scenario “-b2”, which requires severe management measures to correct both a negative hydrological and environmental situation. The approach also involves on-going monitoring of the aquifer, and can be considered as an empirical tool to provide preliminary guidelines for long-term groundwater management.     

Improving rainfall–runoff modelling through the control of uncertainties under increasing climate variability in the Ouémé River basin (Benin,West Africa)

ABSTRACT

The objective of this paper is to understand how the natural dynamics of a time-varying catchment, i.e. the rainfall pattern, transforms the random component of rainfall and how this transformation influences the river discharge. To this end, this paper develops a rainfall–runoff modelling approach that aims to capture the multiple sources and types of uncertainty in a single framework. The main assumption is that hydrological systems are nonlinear dynamical systems which can be described by stochastic differential equations (SDE). The dynamics of the system is based on the least action principle (LAP) as derived from Noether’s theorem. The inflow process is considered as a sum of deterministic and random components. Using data from the Ouémé River basin (Benin, West Africa), the basic properties for the random component are considered and the triple relationship between the structure of the inflowing rainfall, the corresponding SDE that describes the river basin and the associated Fokker-Planck equations (FPE) is analysed.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR D. Gerten     

Modelling climate and land-use change impacts with SWIM: lessons learnt from multiple applications

Abstract

The Soil and Water Integrated Model (SWIM) is a continuous-time semi-distributed ecohydrological model, integrating hydrological processes, vegetation, nutrients and erosion. It was developed for impact assessment at the river basin scale. SWIM is coupled to GIS and has modest data requirements. During the last decade SWIM was extensively tested in mesoscale and large catchments for hydrological processes (discharge, groundwater), nutrients, extreme events (floods and low flows), crop yield and erosion. Several modules were developed further (wetlands and snow dynamics) or introduced (glaciers, reservoirs). After validation, SWIM can be applied for impact assessment. Four exemplary studies are presented here, and several questions important to the impact modelling community are discussed. For which processes and areas can the model be used? Where are the limits in model application? How to apply the model in data-poor situations or in ungauged basins? How to use the model in basins subject to strong anthropogenic pressure?

Editor D. Koutsoyiannis; Associate editor C. Perrin     

Evaluation of the soil water balance in an alluvial flood plain with a shallow groundwater table

Abstract

Many of the hydrological and ecological functions of alluvial flood plains within watersheds depend on the water flow exchanges between the vadoze soil zone and the shallow groundwater. The water balance of the soil in the flood plain is investigated, in order to evaluate the main hydrological processes that underlie the temporal dynamics of soil moisture and groundwater levels. The soil moisture and the groundwater level in the flood plain were monitored continuously for a three-year period. These data were integrated with the results derived from applying a physically-based numerical model which simulated the variably-saturated vertical water flow in the soil. The analysis indicated that the simultaneous processes of lateral groundwater flow and the vertical recharge from the unsaturated zone caused the observed water table fluctuations. The importance of these flows in determining the rises in the water table varied, depending on soil moisture and groundwater depth before precipitation. The monitoring period included two hydrological years (September 2009–September 2011). About 13% of the precipitation vertically recharged the groundwater in the first year and about 50% in the second. The difference in the two recharge coefficients was in part due to the lower groundwater levels in the recharge season of the first hydrological year, compared to those observed in the second. In the latter year, the shallow groundwater increased the soil moisture in the unsaturated zone due to capillary rise, and so the mean hydraulic conductivity of the unsaturated soil was high. This moisture state of soil favoured a more efficient conversion of infiltrated precipitation into vertical groundwater recharge. The results show that groundwater dynamics in the flood plain are an important source of temporal variability in soil moisture and vertical recharge processes, and this variability must be properly taken into account when the water balance is investigated in shallow groundwater environments.

Citation Pirastru, M. and Niedda, M., 2013. Evaluation of the soil water balance in an alluvial flood plain with a shallow groundwater table. Hydrological Sciences Journal, 58 (4), 898–911.     

Automated first and second order moment equations for a set of stochastic differential equations of type AŻ+BZ=C(t)

The generation of the second and higher order moment equations for a set of stochastic differential equations based on Ito's differential lemma is difficult, even for small system of equations. From the knowledge of the statistical properties of the Gaussian white noises associated with the parameters and input coefficients of a set of stochastic differential equations of typeA.+B.Z=C(t), a way to automatically generate the second order moment equations in a computer is presented in this paper. The resulting set of first and second order moment equations is also presented in the same state-space form of the original set of stochastic differential equations through a vectorization of the correlation matrix, which takes advantage of its symmetry. The procedure involved here avoids the inversion of matrixA to apply Ito's differential lemma. Therefore, the presented numerical implementation reduces the computational effort required in the formulation and solution of the moment equations. Moreover, other robust and efficient numerical deterministic integration schemes can be equally applied to the solution of the moment equations.     

Onset of an energy cascade and nonperiodic behaviour in the nonlinear propagation of MHD waves in the solar atmosphere

Abstract

We study the nonlinear stability of MHD waves propagating in a two-dimensional, compressible, highly magnetized, viscous plasma. These waves are driven by a weak, shear body force which could be imposed by large scale internal fluctuations present in the solar atmosphere.

The effects of anisotropic viscosity (leading to a cubic damping) and of the nonlinear coupling of the Alfven and the magnetoacoustic waves are analysed using Galerkin and multiple-scale analysis: the MHD equations are reduced to a set of nonlinear ordinary differential equations which is then suitably truncated to give a model dynamical system, representing the interaction of two complex Galerkin modes.

For propagation oblique to the background magnetic field, analytical integration shows that the low-wavenumber mode is physically unstable. For propagation parallel to the background magnetic field the high-wavenumber wave can undergo saddlenode bifurcations, in way that is similar to the van der Pol oscillator; these bifurcations lead to the appearance of a hysteresis cycle.

A numerical integration of the dynamical system shows that a sequence of Hopf bifurcations takes place as the Reynolds number is increased, up to the onset of nonperiodic behaviour. It also shows that energy can be transferred from the low- wavenumber to the high-wavenumber mode.     

System dynamics model for predicting floods from snowmelt in North American prairie watersheds

This study uses a system dynamics approach to explore hydrological processes in the geographic locations where the main contribution to flooding is coming from the snowmelt. Temperature is identified as a critical factor that affects watershed hydrological processes. Based on the dynamic processes of the hydrologic cycle occurring in a watershed, the feedback relationships linking the watershed structure, as well as the climate factors, to the streamflow generation were identified prior to the development of a system dynamics model. The model is used to simulate flood patterns generated by snowmelt under temperature change in the spring. Model structure captures a vertical water balance using five tanks representing snow, interception, surface, subsurface and groundwater storage. Calibration and verification results show that temperature change and snowmelt play a key role in flood generation. Results indicate that simulated values match observed data very well. The goodness‐of‐fit between simulated and observed peak flow data is measured using coefficient of efficiency, coefficient of determination and square of the residual mass curve coefficient. For the Assiniboine River all three measures were in the interval between 0·92 and 0·96 and for the Red River between 0·89 and 0·97. The model is capable of capturing the essential dynamics of streamflow formation. Model input requires a set of initial values for all state variables and the time series of daily temperature and precipitation information. Data from the Red River Basin, shared by Canada and the USA, are used in the model development and testing. Copyright © 2002 John Wiley & Sons, Ltd.     

Assessment of the hydrological status of Doñana dune ponds: a natural World Heritage Site under threat

ABSTRACT

The hydrological response of shallow ponds to groundwater withdrawal has been of growing concern in the Doñana National Park (southern Spain) in recent decades. This study examines the role of groundwater in maintaining the hydroperiod (i.e. the hydrological regime) in the park’s main dune ponds, by quantifying the groundwater fluxes to/from them. The hydrological characterization was performed by applying different methodologies. Daily hydrological balances registered in the ponds revealed groundwater contributions ranging from 80% of the total water inflows (i.e. groundwater discharge) to a net groundwater recharge from the ponds to the aquifer, and enabled the studied water bodies to be classified as discharge or recharge systems. The recharge systems must have been influenced by the lowering of piezometric levels due to groundwater extraction for urban supply in a nearby coastal resort.     

Groundwater system response at sites with different agricultural land uses: case of the Guarani Aquifer outcrop area,Brotas/SP-Brazil

A system identification approach can be incorporated in groundwater time series analysis, revealing information concerning the local hydrogeological situation. The aim of this work was to analyse water table fluctuations in an outcrop area of the Guarani Aquifer System (GAS) in Brotas/SP, Brazil, using data from a groundwater monitoring network. The water table dynamic was modelled using continuous time series models that reference the hydrogeological system upon which they operate. The model’s climatological inputs of precipitation and evapotranspiration generate impulse response (IR) functions with parameters that can be related to the physical conditions concerning the hydrological processes involved. The interpretation of the model parameters from two sets of monitoring wells selected at different land-use sites is presented, exemplifying the effect of different water table depths and the distance to the nearest drainage location. Systematic trends of water table depths were also identified from model parameters at specific periods and related to plant development, crop harvest and land-use changes.

EDITOR D. Koutsoyiannis

ASSOCIATE EDITOR L. Ruiz     

Evaluating the performance of climate models in reproducing the hydrological characteristics of rainfall events

ABSTRACT

Rainfall events largely control hydrological processes occurring on and in the ground, but the performance of climate models in reproducing rainfall events has not been investigated enough to guide selection among the models when making hydrological projections. We proposed to compare the durations, intensities, and pause periods, as well as depths of rainfall events when assessing the accuracy of general circulation models (GCMs) in reproducing the hydrological characteristics of observed rainfall. We also compared the sizes of design storm events and the frequency and severity of drought to demonstrate the consequences of GCM selection. The results show that rainfall and extreme hydrological event projections could significantly vary depending on climate model selection and weather stations, suggesting the need for a careful and comprehensive evaluation of GCM in the hydrological analysis of climate change. The proposed methods are expected to help to improve the accuracy of future hydrological projections for water resources planning.     

A parcel formulation of Hamiltonian layer models

Starting from the three-dimensional hydrostatic primitive equations, we derive Hamiltonian N-layer models with isentropic tropospheric and isentropic or isothermal stratospheric layers. Our construction employs a new parcel Hamiltonian formulation which describes the fluid as a continuum of Hamiltonian ordinary differential equations bound together by integral transport laws. In particular, we show that this parcel Hamiltonian structure is compatible with the stacking of layers under isentropic or isothermal constraints. The appeal of the parcel formulation is the simplification of various calculations, in particular the derivation of the continuum Poisson bracket and the proof of the Jacobi identity. A comparison and connection is made between the Hamiltonian dynamics of fluid parcels and the Hamiltonian system of partial differential equations. The parcel formulation can be seen as a precursor and tool for the study of Hamiltonian numerical schemes.     

The development of stochastic space transformation and diagrammatic perturbation techniques in subsurface hydrology

This paper develops concepts and methods to study stochastic hydrologic models. Problems regarding the application of the existing stochastic approaches in the study of groundwater flow are acknowledged, and an attempt is made to develop efficient means for their solution. These problems include: the spatial multi-dimensionality of the differential equation models governing transport-type phenomena; physically unrealistic assumptions and approximations and the inadequacy of the ordinary perturbation techniques. Multi-dimensionality creates serious mathematical and technical difficulties in the stochastic analysis of groundwater flow, due to the need for large mesh sizes and the poorly conditioned matrices arising from numerical approximations. An alternative to the purely computational approach is to simplify the complex partial differential equations analytically. This can be achieved efficiently by means of a space transformation approach, which transforms the original multi-dimensional problem to a much simpler unidimensional space. The space transformation method is applied to stochastic partial differential equations whose coefficients are random functions of space and/or time. Such equations constitute an integral part of groundwater flow and solute transport. Ordinary perturbation methods for studying stochastic flow equations are in many cases physically inadequate and may lead to questionable approximations of the actual flow. To address these problems, a perturbation analysis based on Feynman-diagram expansions is proposed in this paper. This approach incorporates important information on spatial variability and fulfills essential physical requirements, both important advantages over ordinary hydrologic perturbation techniques. Moreover, the diagram-expansion approach reduces the original stochastic flow problem to a closed set of equations for the mean and the covariance function.     

Comparative hydrogeology – reference analysis of groundwater dynamics from neighbouring observation wells

ABSTRACT

Groundwater level fluctuations are caused by spatial and temporal superposition of processes within and outside the aquifer system. Most of the subsurface processes are usually observed on a small scale. Upscaling to the regional scale, as required for future climate change scenarios, is difficult due to data scarcity and increasing complexity. In contrast to the limited availability of system characteristics, high-resolution data records of groundwater hydrographs are more generally available. Exploiting the information contained in these records should thus be a priority for analysis of the chronical lack of data describing groundwater system characteristics. This study analyses the applicability of 63 indices derived from daily hydrographs to quantify different dynamics of groundwater levels in unconfined gravel aquifers from three groundwater regions (Bavaria, Germany). Based on the results of two different skill tests, the study aids index selection for different dynamic components of groundwater hydrographs.     

The development of stochastic space transformation and diagrammatic perturbation techniques in subsurface hydrology

This paper develops concepts and methods to study stochastic hydrologic models. Problems regarding the application of the existing stochastic approaches in the study of groundwater flow are acknowledged, and an attempt is made to develop efficient means for their solution. These problems include: the spatial multi-dimensionality of the differential equation models governing transport-type phenomena; physically unrealistic assumptions and approximations and the inadequacy of the ordinary perturbation techniques. Multi-dimensionality creates serious mathematical and technical difficulties in the stochastic analysis of groundwater flow, due to the need for large mesh sizes and the poorly conditioned matrices arising from numerical approximations. An alternative to the purely computational approach is to simplify the complex partial differential equations analytically. This can be achieved efficiently by means of a space transformation approach, which transforms the original multi-dimensional problem to a much simpler unidimensional space. The space transformation method is applied to stochastic partial differential equations whose coefficients are random functions of space and/or time. Such equations constitute an integral part of groundwater flow and solute transport. Ordinary perturbation methods for studying stochastic flow equations are in many cases physically inadequate and may lead to questionable approximations of the actual flow. To address these problems, a perturbation analysis based on Feynman-diagram expansions is proposed in this paper. This approach incorporates important information on spatial variability and fulfills essential physical requirements, both important advantages over ordinary hydrologic perturbation techniques. Moreover, the diagram-expansion approach reduces the original stochastic flow problem to a closed set of equations for the mean and the covariance function.     

Hydrological simulation of a conservation bench terrace system in a subhumid climate

Abstract

A finite element model to simulate runoff and soil erosion from agricultural lands has been developed. The sequential solutions of the governing differential equations were found: Richards' equation with a sink term for infiltration and soil water dynamics under cropped conditions; St Venant equation with kinematic wave approximation for overland and channel flow; and sediment continuity equation, for soil erosion. The model developed earlier has been improved to simulate erosion/deposition in impoundments and predicted and observed soil loss values were in reasonably good agreement when the model was tested for a conservation bench terrace (CBT) system. The finite element model was extensively applied to study the hydrological behaviour of a CBT system vis-à-vis the conventional system of sloping borders. The model estimates runoff and soil loss reasonably well, under varying conditions of rainfall and at different crop growth stages. The probable reasons for discrepancies between observation and simulation are reported and discussed. Sensitivity analysis was carried out to study the effect of various hydrological, soil and topographical parameters, such as ratio of contributing to receiving areas, weir length, depth of impoundment, slope of contributing area, etc. on the flow behaviour in a CBT system.