Models of maar volcanoes,Lunar Crater (Nevada,USA)

Maar volcanoes are generally understood to be the result of highly energetic, explosive interaction between magma and water (groundwater or surface water). Two end-member conceptual models have been proposed to explain the dimensions (diameter, depth) of maar craters: (1) an incremental growth model, where a crater grows due to subsidence and ejection of debris over the course of many explosions, and the final size is an integrated result of multiple explosive events; (2) a model in which the dimensions of a maar crater are the result of the largest single explosion during the lifetime of the maar (major-explosion dominated model). In the latter case, the maar size can be used to estimate the energy and depth of the largest explosion, which in turn allows estimation of the magma mass involved. This paper describes Lunar Crater maar (Nevada, USA) and tests the two models as explanations for the characteristics of the volcano, in particular the major-explosion dominated model. This model implies magma mass and supply rates that are unrealistic, and the tephra at the maar do not contain key features observed in the ejecta at large single-explosion craters. The incremental growth model seems most suitable based upon geological evidence.     

Real-time flood forecasting with the use of inadequate data

Abstract

A modelling scheme is developed for real-time flood forecasting. It is composed of (a) a rainfall forecasting model, (b) a conceptual rainfall-runoff model, and (c) a stochastic error model of the ARMA family for forecast error correction. Initialization of the rainfall-runoff model is based on running this model on a daily basis for a certain period prior to the flood onset while parameters of the error model are updated through the Recursive Least Squares algorithm. The scheme is suitable for the early stages of operation of flood forecasting systems in the presence of inadequate historical data. A validation framework is set up which simulates real-time flood forecasting conditions. Thus, the effects of the procedures for rainfall-runoff model initialization, forecast error correction and rainfall forecasting are assessed. Two well-known conceptual rainfall-runoff models (the Soil Moisture Accounting model of the US National Weather Service River Forecast Service—SMA-NWSRFS and TANK) together with data from a Greek basin are used for illustration purposes.     

Fracture control of ground water flow and water chemistry in a rock aquitard

There are few studies on the hydrogeology of sedimentary rock aquitards although they are important controls in regional ground water flow systems. We formulate and test a three-dimensional (3D) conceptual model of ground water flow and hydrochemistry in a fractured sedimentary rock aquitard to show that flow dynamics within the aquitard are more complex than previously believed. Similar conceptual models, based on regional observations and recently emerging principles of mechanical stratigraphy in heterogeneous sedimentary rocks, have previously been applied only to aquifers, but we show that they are potentially applicable to aquitards. The major elements of this conceptual model, which is based on detailed information from two sites in the Maquoketa Formation in southeastern Wisconsin, include orders of magnitude contrast between hydraulic diffusivity (K/S(s)) of fractured zones and relatively intact aquitard rock matrix, laterally extensive bedding-plane fracture zones extending over distances of over 10 km, very low vertical hydraulic conductivity of thick shale-rich intervals of the aquitard, and a vertical hydraulic head profile controlled by a lateral boundary at the aquitard subcrop, where numerous surface water bodies dominate the shallow aquifer system. Results from a 3D numerical flow model based on this conceptual model are consistent with field observations, which did not fit the typical conceptual model of strictly vertical flow through an aquitard. The 3D flow through an aquitard has implications for predicting ground water flow and for planning and protecting water supplies.     

SLURP model and GIS for estimation of runoff in a part of Satluj catchment,India

Abstract

The snow and rain in the Himalayas are the main sources of supply for the rivers in the Indo-Gangetic plains. Irrigation, hydropower generation, and water supply are very much dependent on the availability of water in the Himalaya rivers. Mathematical models serve as important aids for the estimation of water availability in rivers. In the present study the SLURP watershed model is applied to a rainfed area of the Satluj catchment located in the western Himalayas, India. The SLURP model developed at NHRI, Canada, is a distributed conceptual model which simulates the behaviour of a watershed by carrying out vertical water balances for each element of a matrix of landcovers and subareas of a watershed and then routing the resulting runoff between subareas. The ILWIS geographic information system was used to prepare the input data required for SLURP and land use data were obtained from the IRS satellite LISS II visible and near infrared sensors. The simulated flows at the Bhakhra Dam outlet of the Satluj catchment were computed and found to compare well with the observed flows.     

Hydro-economic models: Concepts, design, applications, and future prospects

Future water management will shift from building new water supply systems to better operating existing ones. The variation of water values in time and space will increasingly motivate efforts to address water scarcity and reduce water conflicts. Hydro-economic models represent spatially distributed water resource systems, infrastructure, management options and economic values in an integrated manner. In these tools water allocations and management are either driven by the economic value of water or economically evaluated to provide policy insights and reveal opportunities for better management. A central concept is that water demands are not fixed requirements but rather functions where quantities of water use at different times have varying total and marginal economic values. This paper reviews techniques to characterize the economic value of water use and include such values in mathematical models. We identify the key steps in model design and diverse problems, formulations, levels of integration, spatial and temporal scales, and solution techniques addressed and used by over 80 hydro-economic modeling efforts dating back 45-years from 23 countries. We list current limitations of the approach, suggest directions for future work, and recommend ways to improve policy relevance.     

A mathematical model to aid management of outflow from the Okavango swamp,Botswana

A series of mathematical models permitted a 20-year sequence of flows to be routed through the complex river and swamp system thus facilitating simulation of the behaviour of the Mopipi off-channel storage from which the Orapa Diamond Mine draws its water supply. From the results of the simulation it was possible to judge the reliability of the Orapa water supply scheme.Although the scheme would evidently have met the design demand throughout the simulation period, the source area, located many kilometres upstream of Orapa, is highly sensitive to relatively minor vegetational changes and possibly also to seismic activity. For this reason, coupled with the fact that future developmental pressures are likely to conflict with the desire to preserve this wilderness environment, it seems imperative that the scope of the model be widened to embrace the whole of the Okavango delta and that ecological studies be directed towards establishing interrelationships among the biological, hydrological and other parameters of the broader conceptual model.     

An evaluation of approaches for modelling hydrological processes in high‐elevation,glacierized Andean watersheds

We use two hydrological models of varying complexity to study the Juncal River Basin in the Central Andes of Chile with the aim to understand the degree of conceptualization and the spatial structure that are needed to model present and future streamflows. We use a conceptual semi‐distributed model based on elevation bands [Water Evaluation and Planning (WEAP)], frequently used for water management, and a physically oriented, fully distributed model [Topographic Kinematic Wave Approximation and Integration ETH Zurich (TOPKAPI‐ETH)] developed for research purposes mainly. We evaluate the ability of the two models to reproduce the key hydrological processes in the basin with emphasis on snow accumulation and melt, streamflow and the relationships between internal processes. Both models are capable of reproducing observed runoff and the evolution of Moderate‐resolution Imaging Spectroradiometer snow cover adequately. In spite of WEAP's simple and conceptual approach for modelling snowmelt and its lack of glacier representation and snow gravitational redistribution as well as a proper routing algorithm, this model can reproduce historical data with a similar goodness of fit as the more complex TOPKAPI‐ETH. We show that the performance of both models can be improved by using measured precipitation gradients of higher temporal resolution. In contrast to the good performance of the conceptual model for the present climate, however, we demonstrate that the simplifications in WEAP lead to error compensation, which results in different predictions in simulated melt and runoff for a potentially warmer future climate. TOPKAPI‐ETH, using a more physical representation of processes, depends less on calibration and thus is less subject to a compensation of errors through different model components. Our results show that data obtained locally in ad hoc short‐term field campaigns are needed to complement data extrapolated from long‐term records for simulating changes in the water cycle of high‐elevation catchments but that these data can only be efficiently used by a model applying a spatially distributed physical representation of hydrological processes. Copyright © 2013 John Wiley & Sons, Ltd.     

Death valley regional ground-water flow model calibration using optimal parameter estimation methods and geoscientific information systems

A regional-scale, steady-state, saturated-zone ground-water flow model was constructed to evaluate potential regional ground-water flow in the vicinity of Yucca Mountain, Nevada. The model was limited to three layers in an effort to evaluate the characteristics governing large-scale subsurface flow. Geoscientific information systems (GSIS) were used to characterize the complex surface and subsurface hydrogeologic conditions of the area, and this characterization was used to construct likely conceptual models of the flow system. Subsurface properties in this system vary dramatically, producing high contrasts and abrupt contacts. This characteristic, combined with the large scale of the model, make zonation the logical choice for representing the hydraulic-conductivity distribution. Different conceptual models were evaluated using sensitivity analysis and were tested by using nonlinear regression to determine parameter values that are optimal, in that they provide the best match between the measured and simulated heads and flows. The different conceptual models were judged based both on the fit achieved to measured heads and spring flows, and the plausibility of the optimal parameter values. One of the conceptual models considered appears to represent the system most realistically. Any apparent model error is probably caused by the coarse vertical and horizontal discretization.     

A framework for dealing with uncertainty due to model structure error

Although uncertainty about structures of environmental models (conceptual uncertainty) is often acknowledged to be the main source of uncertainty in model predictions, it is rarely considered in environmental modelling. Rather, formal uncertainty analyses have traditionally focused on model parameters and input data as the principal source of uncertainty in model predictions. The traditional approach to model uncertainty analysis, which considers only a single conceptual model, may fail to adequately sample the relevant space of plausible conceptual models. As such, it is prone to modelling bias and underestimation of predictive uncertainty.     

A general Bayesian framework for calibrating and evaluating stochastic models of annual multi-site hydrological data

Multi-site simulation of hydrological data are required for drought risk assessment of large multi-reservoir water supply systems. In this paper, a general Bayesian framework is presented for the calibration and evaluation of multi-site hydrological data at annual timescales. Models included within this framework are the hidden Markov model (HMM) and the widely used lag-1 autoregressive (AR(1)) model. These models are extended by the inclusion of a Box–Cox transformation and a spatial correlation function in a multi-site setting. Parameter uncertainty is evaluated using Markov chain Monte Carlo techniques. Models are evaluated by their ability to reproduce a range of important extreme statistics and compared using Bayesian model selection techniques which evaluate model probabilities. The case study, using multi-site annual rainfall data situated within catchments which contribute to Sydney’s main water supply, provided the following results: Firstly, in terms of model probabilities and diagnostics, the inclusion of the Box–Cox transformation was preferred. Secondly the AR(1) and HMM performed similarly, while some other proposed AR(1)/HMM models with regionally pooled parameters had greater posterior probability than these two models. The practical significance of parameter and model uncertainty was illustrated using a case study involving drought security analysis for urban water supply. It was shown that ignoring parameter uncertainty resulted in a significant overestimate of reservoir yield and an underestimation of system vulnerability to severe drought.     

Error covariance calculation for forecast bias estimation in hydrologic data assimilation

To date, an outstanding issue in hydrologic data assimilation is a proper way of dealing with forecast bias. A frequently used method to bypass this problem is to rescale the observations to the model climatology. While this approach improves the variability in the modeled soil wetness and discharge, it is not designed to correct the results for any bias. Alternatively, attempts have been made towards incorporating dynamic bias estimates into the assimilation algorithm. Persistent bias models are most often used to propagate the bias estimate, where the a priori forecast bias error covariance is calculated as a constant fraction of the unbiased a priori state error covariance. The latter approach is a simplification to the explicit propagation of the bias error covariance. The objective of this paper is to examine to which extent the choice for the propagation of the bias estimate and its error covariance influence the filter performance. An Observation System Simulation Experiment (OSSE) has been performed, in which ground water storage observations are assimilated into a biased conceptual hydrologic model. The magnitudes of the forecast bias and state error covariances are calibrated by optimizing the innovation statistics of groundwater storage. The obtained bias propagation models are found to be identical to persistent bias models. After calibration, both approaches for the estimation of the forecast bias error covariance lead to similar results, with a realistic attribution of error variances to the bias and state estimate, and significant reductions of the bias in both the estimates of groundwater storage and discharge. Overall, the results in this paper justify the use of the traditional approach for online bias estimation with a persistent bias model and a simplified forecast bias error covariance estimation.     

From models to performance assessment: the conceptualization problem

Today, models are ubiquitous tools for ground water analyses. The intent of this paper is to explore philosophically the role of the conceptual model in analysis. Selection of the appropriate conceptual model is an a priori decision by the analyst. Calibration is an integral part of the modeling process. Unfortunately a wrong or incomplete conceptual model can often be adequately calibrated; good calibration of a model does not ensure a correct conceptual model. Petroleum engineers have another term for calibration; they refer to it as history matching. A caveat to the idea of history matching is that we can make a prediction with some confidence equal to the period of the history match. In other words, if we have matched a 10-year history, we can predict for 10 years with reasonable confidence; beyond 10 years the confidence in the prediction diminishes rapidly. The same rule of thumb applies to ground water model analyses. Nuclear waste disposal poses a difficult problem because the time horizon, 1000 years or longer, is well beyond the possibility of the history match (or period of calibration) in the traditional analysis. Nonetheless, numerical models appear to be the tool of choice for analyzing the safety of waste facilities. Models have a well-recognized inherent uncertainty. Performance assessment, the technique for assessing the safety of nuclear waste facilities, involves an ensemble of cascading models. Performance assessment with its ensemble of models multiplies the inherent uncertainty of the single model. The closer we can approach the idea of a long history with which to match the models, even models of nuclear waste facilities, the more confidence we will have in the analysis (and the models, including performance assessment). This thesis argues for prolonged periods of observation (perhaps as long as 300 to 1000 years) before a nuclear waste facility is finally closed.     

Application of tank,NAM, ARMA and neural network models to flood forecasting

Two lumped conceptual hydrological models, namely tank and NAM and a neural network model are applied to flood forecasting in two river basins in Thailand, the Wichianburi on the Pasak River and the Tha Wang Pha on the Nan River using the flood forecasting procedure developed in this study. The tank and NAM models were calibrated and verified and found to give similar results. The results were found to improve significantly by coupling stochastic and deterministic models (tank and NAM) for updating forecast output. The neural network (NN) model was compared with the tank and NAM models. The NN model does not require knowledge of catchment characteristics and internal hydrological processes. The training process or calibration is relatively simple and less time consuming compared with the extensive calibration effort required by the tank and NAM models. The NN model gives good forecasts based on available rainfall, evaporation and runoff data. The black‐box nature of the NN model and the need for selecting parameters based on trial and error or rule‐of‐thumb, however, characterizes its inherent weakness. The performance of the three models was evaluated statistically. Copyright © 2000 John Wiley & Sons, Ltd.     

Use of point scale models to improve conceptual understanding in complex aquifers: An example from a sandstone aquifer in the Eden valley,Cumbria, UK

Understanding catchment functioning is increasingly important to enable water resources to be quantified and used sustainably, flood risk to be minimized, as well as to protect the system from degradation by pollution. Developing conceptual understanding of groundwater systems and their encapsulation in models is an important part of this understanding, but they are resource intensive to create and calibrate. The relative lack of data or the particular complexity of a groundwater system can prevent the development of a satisfactory conceptual understanding of the hydrological behaviour, which can be used to construct an adequate distributed model. A time series of daily groundwater levels from the Permo-Triassic sandstones situated in the River Eden Valley, Cumbria, UK have been analysed. These hydrographs show a range of behaviours and therefore have previously been studied using statistical and time series analysis techniques. This paper describes the application of AquiMOD, impulse response function (IRF) and combined AquiMOD-IRF methods to characterize the daily groundwater hydrographs. The best approach for each characteristic type of response has been determined and related to the geological and hydrogeological framework found at each borehole location. It is clear that AquiMOD, IRF and a combination of AquiMOD with IRF can be deployed to reproduce hydrograph responses in a range of hydrogeological settings. Importantly the choice of different techniques demonstrates the influence of differing processes and hydrogeological settings. Further they can distinguish the influences of differing hydrogeological environments and the impacts these have on the groundwater flow processes. They can be used, as shown in this paper, in a staged approach to help develop reliable and comprehensive conceptual models of groundwater flow. This can then be used as a solid basis for the development of distributed models, particularly as the latter are resource expensive to build and to calibrate effectively. This approach of using simple models and techniques first identifies specific aspects of catchment functioning, for example influence of the river, that can be later tested in a distributed model.     

Analysis of Wellbore Skin Samples—Typology,Composition, and Hydraulic Properties

The presence of a wellbore skin layer, formed during the drilling process, is a major impediment for the energy‐efficient use of water wells. Many models exist that predict its potential impacts on well hydraulics, but so far its relevant hydraulic parameters were only estimates or, at best, model results. Here, we present data on the typology, thickness, composition, and hydraulic properties obtained from the sampling of excavated dewatering wells in lignite surface mines and from inclined core drilling into the annulus of an abandoned water well. Despite the limited number of samples, several types of skin were identified. Both surface cake filtration and particle straining in the aquifer occur. The presence of microcracks may be a determining feature for the hydraulic conductivity of skin layers. In the case of the well‐developed water supply well, no skin layer was detected. The observed types and properties of wellbore skin samples can be used to test the many mathematical skin models.     

Error control of iterative linear solvers for integrated groundwater models

An open problem that arises when using modern iterative linear solvers, such as the preconditioned conjugate gradient method or Generalized Minimum RESidual (GMRES) method, is how to choose the residual tolerance in the linear solver to be consistent with the tolerance on the solution error. This problem is especially acute for integrated groundwater models, which are implicitly coupled to another model, such as surface water models, and resolve both multiple scales of flow and temporal interaction terms, giving rise to linear systems with variable scaling. This article uses the theory of "forward error bound estimation" to explain the correspondence between the residual error in the preconditioned linear system and the solution error. Using examples of linear systems from models developed by the US Geological Survey and the California State Department of Water Resources, we observe that this error bound guides the choice of a practical measure for controlling the error in linear systems. We implemented a preconditioned GMRES algorithm and benchmarked it against the Successive Over-Relaxation (SOR) method, the most widely known iterative solver for nonsymmetric coefficient matrices. With forward error control, GMRES can easily replace the SOR method in legacy groundwater modeling packages, resulting in the overall simulation speedups as large as 7.74×. This research is expected to broadly impact groundwater modelers through the demonstration of a practical and general approach for setting the residual tolerance in line with the solution error tolerance and presentation of GMRES performance benchmarking results.     

Stochastic observation error and uncertainty in water quality evaluation

When evaluating water quality, the influence of physical weight of the observed index is normally taken into account, but the influence of stochastic observation error (SOE) is not adequately considered. Using Monte Carlo simulation, combined with Shannon entropy, the Principle of Maximum Entropy (POME) and Tsallis entropy, this study investigates the influence of stochastic observation error (SOE) for two cases of the observed index: small observation error and large observation error. Randomness and fuzziness represent two types of uncertainties that are deemed significant and should be considered simultaneously when developing or evaluating water quality models. To that end, three models are employed here: two of the models, named as model I and model II, consider both the fuzziness and randomness, and another model, considers only fuzziness. The results from three representative lakes in China show that for all three models, the influence of stochastic observation error (SOE) on water quality evaluation can be significant irrespective of whether the water quality index has a small observation error or a large observation error. Furthermore, when there is a significant difference in the accuracy of observations, the influence of stochastic observation error (SOE) on water quality evaluation increases. The water quality index whose SOE is minimum determines the results of evaluation.     

Ground water budget analysis and cross-formational leakage in an arid basin

Ground water budget analysis in arid basins is substantially aided by integrated use of numerical models and environmental isotopes. Spatial variability of recharge, storage of water of both modern and pluvial age, and complex three-dimensional flow processes in these basins provide challenges to the development of a good conceptual model. Ground water age dating and mixing analysis with isotopic tracers complement standard hydrogeologic data that are collected and processed as an initial step in the development and calibration of a numerical model. Environmental isotopes can confirm or refute a priori assumptions of ground water flow, such as the general assumption that natural recharge occurs primarily along mountains and mountain fronts. Isotopes also serve as powerful tools during postaudits of numerical models. Ground water models provide a means of developing ground water budgets for entire model domains or for smaller regions within the model domain. These ground water budgets can be used to evaluate the impacts of pumping and estimate the magnitude of capture in the form of induced recharge from streams, as well as quantify storage changes within the system. The coupled analyses of ground water budget analysis and isotope sampling and analysis provide a means to confirm, refute, or modify conceptual models of ground water flow.