A stochastic model describing the impact of daily rainfall depth distribution on the soil water balance

Simplified, vertically-averaged soil moisture models have been widely used to describe and study eco-hydrological processes in water-limited ecosystems. The principal aim of these models is to understand how the main physical and biological processes linking soil, vegetation, and climate impact on the statistical properties of soil moisture. A key component of these models is the stochastic nature of daily rainfall, which is mathematically described as a compound Poisson process with daily rainfall amounts drawn from an exponential distribution. Since measurements show that the exponential distribution is often not the best candidate to fit daily rainfall, we compare the soil moisture probability density functions obtained from a soil water balance model with daily rainfall depths assumed to be distributed as exponential, mixed-exponential, and gamma. This model with different daily rainfall distributions is applied to a catchment in New South Wales, Australia, in order to show that the estimation of the seasonal statistics of soil moisture might be improved when using the distribution that better fits daily rainfall data. This study also shows that the choice of the daily rainfall distributions might considerably affect the estimation of vegetation water-stress, leakage and runoff occurrence, and the whole water balance.     

Evaluation of stochastic and artificial intelligence models in modeling and predicting of river daily flow time series

Stochastic Environmental Research and Risk Assessment - Modeling and forecasting the flow of rivers, especially in flood-prone areas using warning systems, enables officials to take the required...     

A stochastic conflict resolution model for water quality management in reservoir–river systems

In this paper, optimal operating rules for water quality management in reservoir–river systems are developed using a methodology combining a water quality simulation model and a stochastic GA-based conflict resolution technique. As different decision-makers and stakeholders are involved in the water quality management in reservoir–river systems, a new stochastic form of the Nash bargaining theory is used to resolve the existing conflict of interests related to water supply to different demands, allocated water quality and waste load allocation in downstream river. The expected value of the Nash product is considered as the objective function of the model which can incorporate the inherent uncertainty of reservoir inflow. A water quality simulation model is also developed to simulate the thermal stratification cycle in the reservoir, the quality of releases from different outlets as well as the temporal and spatial variation of the pollutants in the downstream river. In this study, a Varying Chromosome Length Genetic Algorithm (VLGA), which has computational advantages comparing to other alternative models, is used. VLGA provides a good initial solution for Simple Genetic Algorithms and comparing to Stochastic Dynamic Programming (SDP) reduces the number of state transitions checked in each stage. The proposed model, which is called Stochastic Varying Chromosome Length Genetic Algorithm with water Quality constraints (SVLGAQ), is applied to the Ghomrud Reservoir–River system in the central part of Iran. The results show, the proposed model for reservoir operation and waste load allocation can reduce the salinity of the allocated water demands as well as the salinity build-up in the reservoir.     

A conceptually based stochastic point process model for daily stream‐flow generation

Based on the stochastic and phenomenological aspects of hydrological processes, a conceptually based stochastic point process (SPP) model for daily stream‐flow generation is proposed in this paper. In which, storms are defined by a stochastic point process with marked values. All the random variables defining the process are assumed to be mutually independent, which constitutes a compound Poisson point process. The direct surface runoff is regarded as occurring from storage in a cascade of surface linear reservoirs and is responsible for the short‐term variation of the daily stream flows. The baseflow component is considered as coming from subsurface/groundwater storage and is responsible for the long‐term persistence of the storm time‐series. This type of model is proposed as a more realistic model of daily stream flow than models based on pure stochastic processes. Studies on the instantaneous unit hydrograph and the mechanism of baseflow could thereby provide some parameters for this model. Copyright © 2002 John Wiley & Sons, Ltd.     

Simulating daily, monthly and annual water balances in a land surface model using alternative root water uptake schemes

Hydrological simulations at multi-temporal time scales by a widely used land surface model (LSM) are investigated under contrasting vegetation and meteorological conditions. Our investigation focuses particularly on the effects of two different representations of root water uptake and root profile on simulated evapotranspiration (ET) and soil moisture by the Integrated BIosphere Simulator (IBIS). For this purpose, multi-year eddy covariance measurements, collected at four flux-tower sites across North America, were used to gauge IBIS simulations with: (a) its standard version (IBIS2.1), in which static root water uptake (RWU) and root profile schemes are incorporated; and (b) a modified version in which dynamic RWU and root profile schemes replaces the static schemes used in the standard version. Overall, our results suggest that the modified version of the model performs more realistically than the standard version, particularly when high atmospheric demand for evaporation is combined with high atmospheric vapour pressure deficit and low soil water availability. The overall correlation between simulated and measured monthly ET rates at the simulated sites reached 0.87 and 0.91 for the standard and the modified versions, respectively. Our results also show that the incorporation of the dynamic RWU in IBIS yields improved simulations of ET under very dry conditions, when soil moisture falls down to very low levels. This suggests that adequate representations of vegetation responses to drought are needed in LSMs as many state of the art climate models projections of future climate indicate more frequent and/or more intense drought events occurring in some regions of the globe. Our analysis also highlighted the urgent need for adequate methodologies to correct field measurements that exhibit energy imbalances in order to provide rigorous assessments of land surface model simulations of heat and mass exchanges between the land surface and the atmosphere.     

Ecohydrological modelling of flow duration curve in Mediterranean river basins

Flow duration curve provides an important synthesis of the relevant hydrological processes occurring at the basin scale, and, although it is typically obtained from field observations, different theoretical approaches finalized to its indirect reconstruction have been developed in recent years. In this study a recent ecohydrological model for the probabilistic characterization of base flows is tested through its application to a study catchment located in southern Italy, where long historical series of daily streamflow are available. The model, coupling soil moisture balance with a simplified scheme of the hydrological response of the basin, provides the daily flow duration curve. The original model is here modified in order to account for rainfall reduction due to canopy interception and stress its potential applicability to most of the ephemeral Mediterranean basins, where measurements of air temperature and rainfall often represent the only meteorological data available. The model shows a high sensitivity to two parameters related to the transport and evapotranspiration processes. Two different operational approaches for the identification of such parameters are explored and compared: by the first approach, these parameters are considered as time invariant quantities, while, in the second approach, empirical relationships between such parameters and the underlying climatic forcings are first derived and then adopted in the parameters calibration procedure. The model ability in reproducing the empirical flow duration curves and the model sensitivity to climate forcings, here referred as elasticity of the model, are investigated and it is shown how the adoption of the second approach leads to a general improvement of the model elasticity.     

A stochastic model reduction method for nonlinear unconfined flow with multiple random input fields

In this paper we present a stochastic model reduction method for efficiently solving nonlinear unconfined flow problems in heterogeneous random porous media. The input random fields of flow model are parameterized in a stochastic space for simulation. This often results in high stochastic dimensionality due to small correlation length of the covariance functions of the input fields. To efficiently treat the high-dimensional stochastic problem, we extend a recently proposed hybrid high-dimensional model representation (HDMR) technique to high-dimensional problems with multiple random input fields and integrate it with a sparse grid stochastic collocation method (SGSCM). Hybrid HDMR can decompose the high-dimensional model into a moderate M-dimensional model and a few one-dimensional models. The moderate dimensional model only depends on the most M important random dimensions, which are identified from the full stochastic space by sensitivity analysis. To extend the hybrid HDMR, we consider two different criteria for sensitivity test. Each of the derived low-dimensional stochastic models is solved by the SGSCM. This leads to a set of uncoupled deterministic problems at the collocation points, which can be solved by a deterministic solver. To demonstrate the efficiency and accuracy of the proposed method, a few numerical experiments are carried out for the unconfined flow problems in heterogeneous porous media with different correlation lengths. The results show that a good trade-off between computational complexity and approximation accuracy can be achieved for stochastic unconfined flow problems by selecting a suitable number of the most important dimensions in the M-dimensional model of hybrid HDMR.     

M5 model tree application in daily river flow forecasting in Sohu Stream, Turkey

This study investigate the potential of M5 model tree in predicting daily stream flows in Sohu river located within the municipal borders of Ankara, Turkey. The results of the M5 model tree was compared with support vector machines. Both modelling approaches were used to forecast up to 7-day ahead stream flow. A comparison of correlation coefficient and root mean square value indicates that M5 model tree approach works equally well to the SVM for same day discharge prediction. The M5 model tree also works well up to 7-day ahead discharge forecasting in comparison of SVM with this data set. An advantage of using M5 model tree approach is the availability of simple linear models to predict the discharge as well use of less computational time.     

A mean behavior model of aerobic biodegradation in heterogeneous formation

It has been observed that the field biodegradation rates for soluble hydrocarbon plumes are significantly smaller than the aerobic rates observed in the laboratory. It is believed that this difference is related to the fact that in the field oxygen and hydrocarbon must be mixed before the biodegradation reaction can occur, and that the effective degradation rate is controlled by the actual, not mean, concentrations of oxygen and hydrocarbon. In this work, we present a conceptual model of oxygen-mixing limited biodegradation, which indicates that the effective degradation rate should depend on the cross correlation between the oxygen and hydrocarbon concentration fluctuations. This is followed by a development of a rigorous, field-scale model.     

A mean behavior model of aerobic biodegradation in heterogeneous formation

It has been observed that the field biodegradation rates for soluble hydrocarbon plumes are significantly smaller than the aerobic rates observed in the laboratory. It is believed that this difference is related to the fact that in the field oxygen and hydrocarbon must be mixed before the biodegradation reaction can occur, and that the effective degradation rate is controlled by the actual, not mean, concentrations of oxygen and hydrocarbon. In this work, we present a conceptual model of oxygen-mixing limited biodegradation, which indicates that the effective degradation rate should depend on the cross correlation between the oxygen and hydrocarbon concentration fluctuations. This is followed by a development of a rigorous, field-scale model.     

Coupling snow accumulation and melt rate modules of monthly water balance models with the Jazim monthly water balance model

Several models for simulation of water balance processes in semi-arid mountainous basins were developed by coupling different modules of existing water balance models (WBM). Snow accumulation and snowmelt rate relationships extracted from the McCabe-Markstrom, Guo, Rao-Al Wagdany and WASMOD-M WBMs, originally developed for basins with humid climate, were coupled with the Jazim WBM, primarily developed for arid basins. Karaj Basin, central Iran, with snowy autumn–winter and dry summer periods, was selected to assess model performance. The model parameters were optimized using a genetic algorithm (GA). All coupled models performed better than the non-modified (original) WBMs in the study basin. The coupled Jazim–McCabe-Markstrom model provided the best performance in simulating low and high monthly flows. It estimated the snowmelt runoff values more accurately than other proposed coupled models because the linear relationships used in the snow module of the McCabe-Markstrom model are more compatible with snow variations in the Karaj Basin.     

A comparative study on a simple two-parameter monthly water balance model and the Kajiyama formula for monthly runoff estimation

ABSTRACT

A two-parameter monthly water balance model to simulate runoff can be used for a water resources planning programme and climate impact studies. However, the model estimates two parameters of transformation of time scale (c) and of the field capacity (SC) by a trial-and-error method. This study suggests a modified methodology to estimate the parameters c and SC using the meteorological and geological conditions. The modified model is compared with the Kajiyama formula to simulate the runoff in the Han River and International Hydrological Programme representative basins in South Korea. We show that the estimated c and SC can be used as the initial or optimal values for the monthly runoff simulation study in the model.

EDITOR M.C. Acreman; ASSOCIATE EDITOR S. Kanae     

Impacts of rising water demands in the Juba and Shabelle river basins on water availability in south Somalia

ABSTRACT

Somalia has frequently been affected by droughts, famines and water-related humanitarian crises. Water is scarce and the only perennial streams, the Juba and Shabelle rivers, are trans-boundary with river flows mainly originating from the Ethiopian highlands. In both riparian countries water demands are projected to increase. This paper reveals the impact of rising regional water abstractions on stream flows by illustrating sectoral demands and joining them into scenarios of medium and high population and economic growth. These scenarios are associated to the time horizons of 2035 and 2055, respectively. The scenarios disclose alarming trends especially for the Shabelle River: in the medium and high growth scenarios, water demands surpass the available river flows by 200 and 3500 hm³, respectively. The calculated deficits partly derive from conflicting assumptions about river flows by the two main riparian countries, an obstacle to any integrated planning efforts and sustained regional development.

EDITOR Z.W. Kundzewicz; ASSOCIATE EDITOR F. Hattermann     

A penalty finite difference model for Navier-Stokes flow problem in sedimentation basins

An explicit finite difference solution procedure for the 2D, unsteady, turbulent and incompressible Navier-Stokes flow problem is developed. The innovative feature of the numerical model is the use of a penalty function technique. To illustrate the effectiveness of the model, two numerically predicted flow patterns for laboratory size sedimentation tanks are compared to actual experimental results. The predicted flow pattern shows a satisfactory match with experimental data.     

Effects of model sensitivity and nonlinearity on nonlinear regression of ground water flow

Nonlinear regression is increasingly applied to the calibration of hydrologic models through the use of perturbation methods to compute the Jacobian or sensitivity matrix required by the Gauss-Newton optimization method. Sensitivities obtained by perturbation methods can be less accurate than those obtained by direct differentiation, however, and concern has arisen that the optimal parameter values and the associated parameter covariance matrix computed by perturbation could also be less accurate. Sensitivities computed by both perturbation and direct differentiation were applied in nonlinear regression calibration of seven ground water flow models. The two methods gave virtually identical optimum parameter values and covariances for the three models that were relatively linear and two of the models that were relatively nonlinear, but gave widely differing results for two other nonlinear models. The perturbation method performed better than direct differentiation in some regressions with the nonlinear models, apparently because approximate sensitivities computed for an interval yielded better search directions than did more accurately computed sensitivities for a point. The method selected to avoid overshooting minima on the error surface when updating parameter values with the Gauss-Newton procedure appears for nonlinear models to be more important than the method of sensitivity calculation in controlling regression convergence.     

A univariate model of river water nitrate time series

Four time series were taken from three catchments in the North and South of England. The sites chosen included two in predominantly agricultural catchments, one at the tidal limit and one downstream of a sewage treatment works. A time series model was constructed for each of these series as a means of decomposing the elements controlling river water nitrate concentrations and to assess whether this approach could provide a simple management tool for protecting water abstractions. Autoregressive (AR) modelling of the detrended and deseasoned time series showed a “memory effect”. This memory effect expressed itself as an increase in the winter–summer difference in nitrate levels that was dependent upon the nitrate concentration 12 or 6 months previously. Autoregressive moving average (ARMA) modelling showed that one of the series contained seasonal, non-stationary elements that appeared as an increasing trend in the winter–summer difference. The ARMA model was used to predict nitrate levels and predictions were tested against data held back from the model construction process – predictions gave average percentage errors of less than 10%. Empirical modelling can therefore provide a simple, efficient method for constructing management models for downstream water abstraction.     

A stochastic distributed model of soil erosion by overland flow

A model has been built to simulate runoff and erosion on slopes of varying form with soil of varying hydraulic conductivity, porosity, storage capacity, and particle size distribution. The model is based on known physical laws and takes into account spatially dependent random variation in the initial conditions of the soil. The rainfall is similarly both random and autocorrelated in space. Detailed results show how runoff is generated as a result of slow conductivity and high water table, how this leads to erosion, the degradation of the land surface, the capture of flow lines, and the development of networks of rills. The last accords well with results from laboratory experiments. Changing the initial conditions produces results that accord with intuition and reality.