One‐dimensional dynamics of saturated incompressible porous media: analytical solutions and influence of inertia terms

The complexity of formulations for the hydromechanical coupled mechanics of porous media is typically minimised by simplifying assumptions such as neglecting the effect of inertia terms. For example, three formulations commonly employed to model practical problems are classified as fully dynamic, simplified dynamic and quasi‐static. Thus, depending on the porous media conditions, each formulation will have advantages and limitations. This paper presents a comprehensive analysis of these limitations when solving one‐dimensional fully saturated porous media problems in addition to a new solution that considers a more general loading situation. A phase diagram is developed to assist on the selection of which formulation is more appropriate and convenient regarding particular cases of porosity and hydraulic conductivity values. Non‐dimensional formulations are proposed to achieve this goal. Results using the analytical solutions are compared against numerical values obtained with the finite element method, and the effect of porosity is investigated. Copyright © 2016 John Wiley & Sons, Ltd.     

Calculating actual crop evapotranspiration under soil water stress conditions with appropriate numerical methods and time step

Calculation of actual crop evapotranspiration under soil water stress conditions is crucial for hydrological modeling and irrigation water management. Results of actual evapotranspiration depend on the estimation of water stress coefficient from soil water storage in the root zone, which varies with numerical methods and time step used. During soil water depletion periods without irrigation or precipitation, the actual crop evapotranspiration can be calculated by an analytical method and various numerical methods. We compared the results from several commonly used numerical methods, including the explicit, implicit and modified Euler methods, the midpoint method, and the Heun's third‐order method, with results of the analytical method as the bench mark. Results indicate that relative errors of actual crop evapotranspiration calculated with numerical methods in one time step are independent of the initial soil water storage in the range of soil water stress. Absolute values of relative error decrease with the order of numerical methods. They also decrease with the number of time step, which can ensure the numerical stability of successive simulation of soil water balance. Considering the calculation complexity and calculation errors caused by numerical approximation for different time step and maximum crop evapotranspiration, the explicit Euler method is recommended for the time step of 1 day (d) or 2 d for maximum crop evapotranspiration less than 5 mm/d, the midpoint method or the modified Euler method for the time step of up to one week or 10 d for maximum crop evapotranspiration less than 5 mm/d, and the Heun's third‐order method for the time step of up to 15 d. Copyright © 2011 John Wiley & Sons, Ltd.     

Appropriate Spatial Sampling of Rainfall or Flow Simulation/Echantillonnage Spatial de la Pluie Approprié pour la Simulation D'écoulements

Abstract

The objective of this study is to find the appropriate number and location of raingauges for a river basin for flow simulation by using statistical analyses and hydrological modelling. First, a statistical method is used to identify the appropriate number of raingauges. Herein the effect of the number of raingauges on the cross-correlation coefficient between areally averaged rainfall and discharge is investigated. Second, a lumped HBV model is used to investigate the effect of the number of raingauges on hydrological modelling performance. The Qingjiang River basin with 26 raingauges in China is used for a case study. The results show that both cross-correlation coefficient and modelling performance increase hyperbolically, and level off after five raingauges (therefore identified to be the appropriate number of rain-gauges) for this basin. The geographical locations of raingauges which give the best and worst hydrological modelling performance are identified, which shows that there is a strong dependence on the local geographical and climatic patterns.     

Fuzzy Optimization Neural Network Approach for Ice Forecast in the Inner Mongolia Reach of the Yellow River/Approche d'Optimisation Floue de Réseau de Neurones pour la Prévision de la Glace Dans le Tronçon de Mongolie Intérieure du Fleuve Jaune

Abstract

In ice forecasting, a key problem is the forecast of freeze-up and break-up dates. Ice-water mechanics and the principle of heat-exchange were mainly adopted in previous research. However, the mathematical models in these studies are complex and many parameters are required in relation to upstream and/or downstream gauging stations. Moreover, too many assumptions or simplifications for these parameters and constraints directly lead to low accuracy of the models and limitations as to their practical applications. This paper develops a fuzzy optimization neural network approach for the forecast of freeze-up date and break-up date. The Inner Mongolia reach lies in the top north of the Yellow River, China. Almost every year ice floods occur because of its special geographical location, hydrometeorological conditions and river course characteristics. Therefore, it is of particular importance for ice flood prevention to forecast freeze-up date and break-up date accurately. A case study in this region shows that the proposed methodology may allow obtaining useful results.     

Are artificial neural network techniques relevant for the estimation of longitudinal dispersion coefficient in rivers? / Les techniques de réseaux de neurones artificiels sont-elles pertinentes pour estimer le coefficient de dispersion longitudinale en rivières?

Abstract

Abstract Accurate application of the longitudinal dispersion model requires that specially designed experimental studies are performed in the river reach under consideration. Such studies are usually very expensive, so in order to quantify the longitudinal dispersion coefficient, as an alternative approach, various researchers have proposed numerous empirical formulae based on hydraulic and morphometric characteristics. The results are presented of the application of artificial neural networks as a parameter estimation technique. Five different cases were considered with the network trained for different arrangements of input nodes, such as channel depth, channel width, cross-sectionally averaged water velocity, shear velocity and sinuosity index. In the case where the sinuosity index is included as an input node, the results turned out to be better than those presented by other authors.     

Analytical and computational procedure for solving the consolidation problem of layered soils

One‐dimensional consolidation analysis of layered soils conventionally entails solving a system of differential equations subject to the flow conditions at the bounding upper and lower surfaces, as well as the continuity conditions at the interface of every pair of contiguous layers. Formidable computational efforts are required to solve the ensuing transcendental equations expressing the matching conditions at the interfaces, using this method. In this paper, the jump discontinuities in the flow parameters upon crossing from one layer to the other have been systematically built into a single partial differential equation governing the space–time variation of the excess pore pressure in the entire composite medium, by the use of the Heaviside distribution. Despite the presence of the discontinuities in the coefficients of the differential equation, a closed‐form solution in the sense of an infinite generalized Fourier series is obtained, in addition to which is the development of a Green's function for the differential problem. The eigenfunctions of the composite medium are the coordinate functions of the series, obtained computationally through the application of the extended equations of Galerkin. The analysis has been illustrated by solving the consolidation problem of a four‐layer composite, and the results obtained agree very well with the results obtained by previous researchers. Copyright © 2013 John Wiley & Sons, Ltd.     

Relations indices de Végétation–Pluie au Burkina Faso: Cas du Bassin Versant du Nakambé/Relationship between Rainfall and Vegetation Indexes in Burkina Faso: A Case Study of the Nakambé Basin

Abstract

This work deals with the problem of the use of remote sensing data derived from NOAA/AVHRR observations for monitoring the West African Sahel climatic variability. NDVI is widely used in hydrological and climatological research, and in the study of global climatic changes. The relationships between NDVI and climatic parameters are not well established yet and are the focus of many studies. The relationships between NDVI and rainfall were studied at a 10-day time step in the Nakambe River basin in Burkina Faso in the Sahelo-Sudanian area over the years 1982–1999. Good correlations were found in the annual evolution of these two variables. The statistical analysis shows a significant relationship between NDVI and the sum of the annual rainfall with determination coefficients greater than 0.80. At the spatial scale of 0.5° × 0.5°, the determination coefficient ranges from 0.91 to 0.96. It was also found that the NDVI is a good indicator of the determination of the beginning and the end of the rainy season. It gives reasonably good results in comparison with the other methods commonly used in the study region.     

Trend detection in river flow series: 1. Annual maximum flow / Détection de tendance dans des séries de débit fluvial: 1. Débit maximum annuel

Abstract

Results of a study on change detection in hydrological time series of annual maximum river flow are presented. Out of more than a thousand long time series made available by the Global Runoff Data Centre (GRDC) in Koblenz, Germany, a worldwide data set consisting of 195 long series of daily mean flow records was selected, based on such criteria as length of series, currency, lack of gaps and missing values, adequate geographical distribution, and priority to smaller catchments. The analysis of annual maximum flows does not support the hypothesis of ubiquitous growth of high flows. Although 27 cases of strong, statistically significant increase were identified by the Mann-Kendall test, there are 31 decreases as well, and most (137) time series do not show any significant changes (at the 10% level). Caution is advised in interpreting these results as flooding is a complex phenomenon, caused by a number of factors that can be associated with local, regional, and hemispheric climatic processes. Moreover, river flow has strong natural variability and exhibits long-term persistence which can confound the results of trend and significance tests.     

Influences of coupled wind–water processes on suspended sediment grain size: an example from tributaries of the Yellow River / Influences de processus couplés éoliens-hydriques sur la granulométrie des matières en suspension: exemple d'affluents du Fleuve Jaune

Abstract

Some unique coupled wind–water erosion processes exist in the desert-loess transitional zone in the middle Yellow River basin. Based on data from 40 stations on 29 rivers, a study was made on the influence of such processes on suspended sediment grain-size characteristics of the tributaries of the Yellow River. Results show that the percentage of >0.05-mm grain size decreases with the increased annual mean precipitation, but increases with the increase in the annual mean number of sand-dust storm days. The percentage of <0.01-mm grain size increases with the increase in the annual mean precipitation, but decreases with the increase in the annual number of sand-dust storm days. Based on annual mean data from 40 stations, multiple regression equations were established between the percentages of >0.05-mm grain size (r _>0.05) and <0.01-mm grain size (r _<0.01), annual mean precipitation (P _m) and annual mean number of sand-dust storm days (D _ss). On this basis, the relative contributions of the variations in D _ss and P _m to the variation in r _>0.05 and r _<0.01 were estimated. The results indicate that the variation in sand-dust storm frequency exerts greater influences on the variation in grain-size characteristics of suspended load than does the variation in annual mean precipitation. With the increase in the coupled wind–water processes index, expressed by P _m/D _ss, the percentage of >0.05-mm grain size in suspended sediment decreases and the percentage of <0.01-mm grain size increases. With the variation in P _m/D _ss, different combinations of r _>0.05 with r _<0.01 appear, which have some influence on the formation of hyperconcentrated flows. There exist some optimal ratios of coarse to fine fractions in suspended sediment that make sediment concentrations of hyperconcentrated flows the highest. The optimal r _>0.05/r _<0.01 value is related to some range of the index P _m/D _ss. When the P _m/D _ss index falls in this range, the optimum combination of relative coarse with fine sediments in the suspended load appears, and thus results in the peak values of sediment concentration.     

Partial L-moments for the analysis of censored flood samples / Utilisation des L-moments partiels pour l’analyse d’échantillons tronqués de crues

Abstract

Abstract A parameter estimation method is proposed for fitting the generalized extreme value (GEV) distribution to censored flood samples. Partial L-moments (PL-moments), which are variants of L-moments and analogous to ?partial probability weighted moments?, are defined for the analysis of such flood samples. Expressions are derived to calculate PL-moments directly from uncensored annual floods, and to fit the parameters of the GEV distribution using PL-moments. Results of Monte Carlo simulation study show that sampling properties of PL-moments, with censoring flood samples of up to 30% are similar to those of simple L-moments, and also that both PL-moment and LH-moments (higher-order L-moments) have similar sampling properties. Finally, simple L-moments, LH-moments, and PL-moments are used to fit the GEV distribution to 75 annual maximum flow series of Nepalese and Irish catchments, and it is found that, in some situations, both LH- and PL-moments can produce a better fit to the larger flow values than simple L-moments.