A variable sorptivity infiltration equation

Horizontal and vertical one-dimensional infiltration are compared when they both occur in a homogeneous isotropic porous body initially at a uniform low water content _n under constant concentration (₀) or constant pressure head (H ₀) conditions. From a consideration of the physics governing infiltration under such conditions, the conclusion is reached that the magnitude of the pressure head gradient atx=0, wherex=0 denotes the infiltration surface in the horizontal case, must be larger than the magnitude of the pressure head gradient atz=0, wherez=0 denotes the infiltration surface in the vertical case, for all finitet>0, so that for the hydraulic head gradient atz=0 to be greater than (1/2K ₀)S _x t ^–1/2 but smaller than [(1/2K ₀)S _x t ^–1/2+1],K ₀ being the hydraulic conductivity at ₀ andS _x the sorptivity during horizontal infiltration. On these grounds, it is further argued that if the sorptivityS _z is introduced for the case of vertical infiltration, then it must be equal toS _x fort=0 only and that it must decrease with time. Results obtained by solving soil-water flow equations for the infiltration conditions defined above, and from experiment, support the above conclusions. An equation for the relationship between cumulative infiltration and time during vertical infiltration is developed after assuming thatS _z decreases with time in an exponential manner. Cumulative infiltration versus time relationships given by this equation are compared with those obtained from the numerical solution of the soil-water flow equation and from experiment.     

Combined analytical solution of overland flow and sediment transport

With reference to the kinematic wave theory coupled with the hypothesis of constant linear velocity for the rating curve, rising limb analytical solutions have been calculated for overland flow, over an Hortonian-infiltrating surface, and sediment discharge. These analytical solutions are certainly easier to use than the numerical integration of the basic equations and they may be used to obtain an initial evaluation of the parameters of more complex models generally devised for complicated cases.Notation a exponent of the Horton law [T^–1] - b exponent of the rill erosion equation - B inter-rill erosion coefficient [ML^–m–2T ^m–1] - c sediment concentration [ML^–3] - c _o reference sediment concentration [ML^–3] - E _I inter-rill erosion [ML^–2T^–1] - E _R rill erosion [ML^–2T^–1] - f _c final infiltration rate of the soil [LT^–1] - f _o initial infiltration rate of the soil [LT^–1] - h flow depth [L] - h _o reference flow depth [L] - i infiltration rate [LT^–1] - k rill erosion coefficient [ML^–1–b T^–1] - K integration constant - L() Laplace transformation - m exponent of the inter-rill erosion equation - n Manning's coefficient [L^–1/3T] - p rainfall intensity [LT^–1] - q water discharge per unit width [L²T^–1] - q _s sediment discharge per unit width [ML^–1T^–1] - t time [T] - t _p ponding time [T] - x distance along the flow direction [L] Greek Letters coefficient of the stage-discharge equation [L^2–T^–1] - exponent of the stage-discharge equation - rill erosion coefficient [L^–1]     

融冰洪水演进的马斯京根模型

为解决参数率定过程复杂的问题,将河段内的融冰产生的流量视为河段下断面出流的一部分,构建出适用于文开河融冰时期洪水演进的马斯京根模型,并将优化算法应用到模型参数率定的过程中。以黄河宁蒙河段为例,采用试错法、非线性规划法和智能算法中的遗传算法这3种方法对所构建的模型参数进行率定。模拟结果表明:3种方法所模拟的出流过程线均合格;整体上,非线性规划法模拟的精度最高,其洪水的确定性系数D_c为0.980,过程平均相对误差RE为4.840%;而试错法模拟的洪峰流量更为准确,且冰期模拟精度高于无冰期。本研究为融冰洪水演进的模拟提供了一种新方法。     

Time-dependent soil-water distribution under a circular trickle source

Soil-water distribution in homogeneous soil profiles of Yolo clay loam and Yolo sand (Typic xerorthents) irrigated from a circular source of water, was measured several times after the initiation of irrigation. The effect of trickle discharge rates and soil type on the locations of the wetting front and soil-water distribution was considered. Soil-water tension and hydraulic conductivity, as functions of soil-water content, were also measured. The theories of time-dependent, linearized infiltration from a circular source and a finite-element solution of the two-dimensional transient soil-water equation were compared with the experimental results. In general, for both soils the computer horizontal and vertical advances of the wetting front were closely related to those observed. With both theories, a better prediction of the wetting front position for the clay loam soil than for the sandy soil is shown. The calculated and measured horizontal vertical advances did not agree over long periods of time. With the linearized solution, overestimated and underestimated vertical advances for the clay and sandy soils, respectively, were shown. The finite-element model approximate in a better way the vertical advances than the linearized solution, while an opposite tendency for the horizontal advances indicated, especially in sandy soil.Notation k constant (dK/d) - K hydraulic conductivity - K ₀ saturated hydraulic conductivity - J ₀,J ₁ Bessel functions of the first kind - h soil water tension - q Q/r ₀ ² - Q discharge rate - r cylindrical coordinate; also horizontal distance in soil surface - R dimensionless quantity forr - r ₀ constant pond radius - R ₀ dimensionless quantity forr ₀ - t time - T dimensionless quantity fort - x, y Cartesian coordinates - z vertical coordinate; also vertical distance along thez axis chosen positively downward - Z dimensionless quantity forz - empirical soil characteristic constant - dummy variable of integration - volumetric soil water content - matrix flux potential - dimensionless quantity for      

The Influence of Conceptual Flow Simulation Model Parameters on Model Solution

This article investigates the influence of conceptual flow simulation model parameters (i.e coefficients and constants that need to be estimated in calibration) on model solution (surface runoff) to understand the characteristics of the model. A new conceptual watershed yield model (WYM) was employed. There are four physical parameters, two fitting coefficients and two initial estimates of the surface water and groundwater storagesthat control the functioning of the model. The conceptual model was applied on Ling River near Kahuta and detailed sensitivity analysis was performed to explore the most sensitive model parameters. The most sensitive model parameters worked out were C _g (a fitting coefficient, which reflects the rate at whichgroundwater runoff occurs), w _r (watershed retention is the initial rainfall losses before runoff begins), p _gr (inputparameter that reflects the discharge capacity of the groundwateraquifer). The model parameters like i _c (infiltration coefficient), g _wsm (input parameter that depends on the subsurface storage available in the watershed) and e _p (input parameter) have negligible effect on model solution. It was observed that w _r (watershed retention) is the only surface runoff controlling parameter and p _gr and C _g are the groundwater runoff controlling parameters.     

Estimation of Clark’s Instantaneous Unit Hydrograph Parameters and Development of Direct Surface Runoff Hydrograph

We present a method to estimate Time of Concentration (T _c) and Storage Coefficient (R) to develop Clark’s Instantaneous Unit Hydrograph (CIUH). T _c is estimated from Time Area Diagram of the catchment and R is determined using optimization approach based on Downhill Simplex technique (code written in FORTRAN). Four different objective functions are used in optimization to determine R. The sum of least squares objective function is used in a novel way by relating it to slope of a linear regression best fit line drawn between observed and simulated peak discharge values to find R. Physical parameters (delineation, land slope, stream lengths and associated drainage areas) of the catchment are derived from SPOT satellite imageries of the basin using ERDAS: Arc GIS is used for geographic data processing. Ten randomly selected rainfall–runoff events are used for calibration and five for validation. Using CIUH, a Direct surface runoff hydrograph (DSRH) is developed. Kaha catchment (5,598 km²), part of Indus river system, located in semi-arid region of Pakistan and dominated by hill torrent flows is used to demonstrate the applicability of proposed approach. Model results during validation are very good with model efficiency of more than 95% and root mean square error of less than 6%. Impact of variation in model parameters T _c and R on DSRH is investigated. It is identified that DSRH is more sensitive to R compared to T _c. Relatively equal values of R and T _c reveal that shape of DSRH for a large catchment depends on both runoff diffusion and translation flow effects. The runoff diffusion effect is found to be dominant.     

考虑雾化雨条件下边坡的稳定性分析

以锦屏水电站边坡为例,将渗流理论引入边坡的稳定分析,结合数值分析软件SLIDE,研究了边坡在不同降雨入渗深度下动水压力、安全系数的变化情况及规律,提出了降雨入渗及排水加固后的边坡稳定性评价方法。分析结果表明 随着雾化雨的降雨入渗,动水压力有不断增大的趋势,安全系数有不断减小的趋势,降雨入渗雾化3 d后,坡体下部已达到完全饱和状态,持续的雾化雨作用对坡体下部地下水位的改变不大,形成了稳定水流,边坡的安全系数也没有太大变化;同时,采用固定的土性参数来计算边坡的稳定性还不能全面地评价边坡的稳定性,土体抗剪强度参数c和φ的变异性及其相关性是影响边坡可靠度指标的一个极其重要的因素。     

Analytical solutions of unsteady drainage problems for soils subjected to variable recharge from a semi-confined aquifer

In drainage of agricultural lands, the upward vertical recharge from a semi-confined aquifer depends on the difference of the piezometric heads on the two sides of the semi-impermeable layer through which this recharge takes place. This means that the recharge through the semi-impermeable base depends on the unknown height of the unsteady water table. In the nonhomogeneous Boussinesq equation, which describes the drainage problems, the downward uniform rate of the recharge from rain or irrigation and the recharge from the semiconfined aquifer are expressed by two terms. By solving the Boussinesq equation expressions for the nondimensional height of the water table and the nondimensional discharge of the drains per unit drained area are obtained for three different initial conditions. Some known solutions are shown as special cases of the present solutions. Variation of nondimensional water table heights at half distance of the drain spacing and the nondimensional discharge of the drains with nondimensional time have been graphically illustrated with the help of synthetic examples.Notation B _s thickness of the semi-impervious layer [L] - c hydraulic resistance of the semi-impervious layer [T] - D depth of the drains from the base [L] - d _e equivalent depth [L] - h=h(x, t) height of the water table [L] - h ₀ initial height of the water table [L] - h _t water table height at mid-distance of drains att [L] - h _j ,h _k water table height at mid-distance of drains at timej andfk, respectively [L] - H ₀ piezometric head in the semi-confined aquifer [L] - K hydraulic conductivity of the soil [LT^–1] - K _s hydraulic conductivity of the semi-impervious layer [LT^–1] - k ₀,k ₁,k ₂ nondimensional constants - L distance between the drains [L] - q ₀ upward recharge per unit surface area through the semi-impervious layer [LT^–1] - q _t discharge per unit drainable area of drains at timet [LT^–1] - R,R ₀ recharge per unit surface area from rain or irrigation during the unsteady and steady-state, respectively, [LT^–1] - S specific yield of the soil - t time of observation [T] - x distance measured from the drain [L] - leakage factor [L] - nondimensional distance - nondimensional time     

洪涝灾害三参数损失函数的构建Ⅰ——基本原理

为把握快速城镇化、社会经济增长、防洪工程标准提高背景下暴雨洪涝灾害风险的演变趋势,基于洪水风险理论及城市洪涝灾害的连锁性与损失突变性特征,探讨了洪涝灾害风险演变驱动机制,构建了具有物理意义的三参数洪涝灾害损失-重现期(D-R)风险函数,明确了曲线形态中临界洪灾损失值Dc、临界重现期Rc、区域脆弱性综合指数k等控制参数的物理意义。该函数可作为洪涝灾害风险评估与预测的一种便捷手段,找到洪涝灾害风险演化的转折点,可为防灾减灾决策提供依据,同时也可应用于对防洪工程体系减灾效益的评估。     

A Modified SCS-CN Method Incorporating Storm Duration and Antecedent Soil Moisture Estimation for Runoff Prediction

In one of the widely used methods to estimate surface runoff - Soil Conservation Service Curve Number (SCS-CN), the antecedent moisture condition (AMC) is categorized into three AMC levels causing irrational abrupt jumps in estimated runoff. A few improved SCS-CN methods have been developed to overcome several in-built inconsistencies in the soil moisture accounting (SMA) procedure that lies behind the SCS-CN method. However, these methods still inherit the structural inconsistency in the SMA procedure. In this study, a modified SCS-CN method was proposed based on the revised SMA procedure incorporating storm duration and a physical formulation for estimating antecedent soil moisture (V ₀ ). The proposed formulation for V ₀ estimation has shown a high degree of applicability in simulating the temporal pattern of soil moisture in the experimental plot. The modified method was calibrated and validated using a dataset of 189 storm-runoff events from two experimental watersheds in the Chinese Loess Plateau. The results indicated that the proposed method, which boosted the model efficiencies to 88% in both calibration and validation cases, performed better than the original SCS-CN and the Singh et al. (2015) method, a modified SCS-CN method based on SMA. The proposed method was then applied to a third watershed using the tabulated CN value and the parameters of the minimum infiltration rate (f _c ) and coefficient (β) derived for the first two watersheds. The root mean square error between the measured and predicted runoff values was improved from 6 mm to 1 mm. Moreover, the parameter sensitivity analysis indicated that the potential maximum retention (S) parameter is the most sensitive, followed by f _c . It can be concluded that the modified SCS-CN method, may predict surface runoff more accurately in the Chinese Loess Plateau.     

Comparative Evaluation of Analytic Solutions in Predicting Soil Moisture Profiles in Vertical One-Dimensional Infiltration under Ponded and Constant Flux Boundary Conditions

The problem of vertical one-dimensional infiltration for both ponded and constant flux boundary conditions was studied through the use of existing analytic solutions. Main objective was to compare the soil moisture profile developed under constant flux boundary condition at the time of ponding , with that moisture profile developed under ponded conditions at an earlier time . Time t _C denotes the time when the decreasing infiltration rate for the ponded conditions becomes equal to the constant flux _q , applied for the constant flux case. One might state that the analytical solutions, for both cases do not give identical profiles. An approximate coincidence might be brought about through a modification in the diffusivity which, in many respects, seems justified. Practical outcome of the above analysis is the determination of the time of ponding T, after which surface runoff starts, for the constant flux case. This is of practical significance either under natural conditions of rainfall or under conditions of sprinkle-irrigation, since surface runoff is directly related with soil erosion and waste of irrigation water. Therefore any attempt to determine the time of ponding T is well merited.     

Evaluation of Class A Pan Coefficient Models for Estimation of Reference Crop Evapotranspiration in Cold Semi-Arid and Warm Arid Climates

Evapotranspiration and evaporation measurements are important parameters for many agricultural activities such as water resource management and environmental studies. There are several models which can determine pan coefficient (K _Pan), using wind speed, relative humidity and fetch length conditions. This paper analyses seven exiting pan models to estimate K _Pan values for two different climates of Iran. Monthly mean reference crop evapotranspiration (ET₀) was calculated according to the pan-ET₀ model. The results showed that estimated pan coefficients by majority of the suggested models were not statistically accurate to be used in the pan-ET₀ conversion method. However, for the cold semi-arid climate condition, the best K _Pan models for estimation of ET₀ were Orang and Raghuwanshi–Wallender, respectively. Also, the Snyder and Orang models were best fitted models for warm arid climate, respectively. The mean annual value of K _Pan, determined by Penman–Monteith FAO 56 (PMF-56) standard model for warm arid sites, was approximately 32% higher than the corresponding value in the cold semi-arid climate. Similarly, the mean annual ET₀ in the warm arid sites was 66% higher, compared to the ET₀ of the cold semi-arid sites. These types of warm arid and semi-arid climates are found widely throughout the world.     

Spatial Distributions of Soil Surface-Layer Saturated Hydraulic Conductivity and Controlling Factors on Dam Farmlands

Saturated hydraulic conductivity (Ks) is a critical soil property affecting water flow and solute transport. In the Loess Plateau of China, sloping farmlands have been increasingly replaced by dam farmlands to achieve higher crop yields and more importantly to control soil erosions. It is necessary to understand the spatial pattern of near-surface K _S on those newly formed dam farmlands, because the land surface processes (e.g., erosion that is controlled by overland flow) are largely determined by the spatial distribution of near-surface Ks. In this study, near-surface Ks (e.g., 5 cm depth of the surface layers) was measured using 336 undisturbed soil samples collected from two dam farmlands located in the Liudaogou catchment, a heavily studied catchment in the Loess Plateau of China. Based on classical and geostatistical analyses, the soil properties at the filled dam farmland showed more spatial variations compared to the silting dam farmland. Statistical scale-invariance was evaluated using the Hurst scaling parameter (H) for different soil parameters. The H values ranged from 0.646 to 0.877, indicating certain degrees of statistical scale-invariance and long-range dependency within the spatial range. The bulk density (D_b), saturated water content (SW), sand content (SA), silt content (SI), and clay content (CL) were shown to affect the K _S values significantly with SW, SI, and CL negatively and SA and D_b positively correlated with K _S . The highest K _S value was found at the middle portion of the dam farmlands and the lowest value was found at the locations with the minimum occurrence of surface runoff. In addition, the areas with lowest K _S values corresponded to the areas with the highest CL, SI, and SW. The results showed that disturbing soil structure by planting crops would benefit the floodwater control on dam farmlands due to increased Ks and the flooding on dam farmlands would be eased due to the silting process.     

Influence of horizontal eddy viscosity and bottom friction coefficients on morphodynamic evaluations

The horizontal eddy viscosity (ε) and bottom friction coefficient (K_br) are important hydrodynamic parameters in the computation of flow fields that dictate the morphodynamics. The effect of the variations in ε and K_br as well as their combination on the prediction of hydrodynamics and morphodynamics in the Cochin harbor and adjoining nearshore area (9.9312° N, 76.2673° E) has been investigated in detail. A tidal circulation model to solve the shallow water equation is applied with the different parameterizations of ε and K_br. In order to understand its effect, ε is expressed as a function of depth averaged velocity and length scale of computation mesh, whereas K_br is expressed as a function of depth. The validation of the model is carried out with the measured currents. The improvement in the hydrodynamic and morphodynamic predictions is demonstrated by implementing the spatially and temporally varying ε The predictions are further improved by implementing a spatially varying K_br. It is seen that the simulations with varying ε and K_br predict the morphodynamic behavior close to the field values. The performance of the model predictions is discussed in terms of R², RMSE and BSS (Brier Skill Score).     

Stability of fluid flow in a Brinkman porous medium–A numerical study

The stability of fluid flow in a horizontal layer of Brinkman porous medium with fluid viscosity different from effective viscosity is investigated. A modified Orr-Sommerfeld equation is derived and solved numerically using the Chebyshev collocation method. The critical Reynolds number cRe, the critical wave number αc and the critical wave speed cc are computed for various values of porous parameter and ratio of viscosities. Based on these parameters, the stability characteristics of the system are discussed in detail. Streamlines are presented for selected values of parameters at their critical state.     

用畦灌试验资料推求土壤入渗参数的非线性回归法

本文对利用畦灌试验资料推求土壤入渗参数的Maheshwari法和Esfandiari法进行改进,把利用模式搜索技术进行参数计算,改为利用非线性回归法进行多次逼近计算,使计算工作量大大减少。实测资料的验证表明,改进后的方法具有更高的计算精度。在此基础上,本文对Maheshwari法、Esfandiari法及经过改进的算法进行了评价,认为几种算法各有优缺点,使用时应根据试验资料及观测精度选择。     

On the predictability of the water-table variation in a ditch-drainage system

The irrigation in regions of brackish groundwater in many parts of the world results in the rise of the water-table very close to the groundsurface. The salinity of the productive soils is therefore increased. A proper layout of the ditch-drainage system and the prediction of the spatio-temporal variation of the water table under such conditions are of crucial importance in order to control the undesirable growth of the water-table. In this paper, an approximate solution of the nonlinear Boussinesq equation has been derived to describe the water-table variations in a ditch-drainage system with a random initial condition and transient recharge. The applications of the solution is discussed with the help of a synthetic example.Notations a lower value of the random variable representing the initial water-table height at the groundwater divide - a+b upper value of the random variable representing the initial water-table height at the groundwater divide - h variable water-table height measured from the base of the aquifer - K hydraulic conductivity - L half width between ditches - m ₀ initial water-table height at the groundwater divide - N(t) rate of transient recharge at time t - N ₀ initial rate of transient recharge - P N ₀/K - S Specific yield - t time of observation - t ₀ logarithmic decrement of the recharge function - T Kt/SL - x distance measured from the ditch boundary - X x/L - Y h/L - Y mean of Y - Y Variance of Y     

Design of earthen vegetated open channels

Modified formulas for Manning's equation are developed for use in the design of earthen open channels with submerged aquatic weeds. The proposed relations have their basis in field and experimental data. A multiple regression analysis was used to develop a relationship between the mean velocity, hydraulic radius, and water surface slope. The new formulas are dependent on the distribution of weeds along the channel's wetted perimeter and the percentage of vegetation density with respect to the cross-section area of the waterway.Notation A cross-section area - A _w area of weeds - B ₁ top width of channel flow - g acceleration of gravity - h height of roughness element - n Manning's coefficient - Q discharge of flow - R hydraulic radius - S water surface slope - S ₀ bed surface slope - V mean flow velocity     

Optimal allocation of water resources in large river basins: I. Theory

The major purpose of this paper is to present the useful techniques in the optimal allocation of water resources (OAWR) and to demonstrate using water resources applications how these methods can be conveniently employed in practice for systematically studying both simple and complex water resources problems. Formal modelling techniques in multiobjective decision-making provide many benefits to professionals working in water resources and elsewhere. A new Large-system Hierarchical Dynamic Programming (LHDP) method to solve the model can be carried out to ascertain the consequences of meaningful parameter changes upon the optimal or compromise solution.As a case study, the techniques and methods are applied to the OAWR of the Yellow River Basin (YRB) of China. The next paper shares with the reader recent research results on the OAWRYRB.Notation L _i inflows from the trunk stream in the subregioni. - S _i run-off volume of the river sectioni. - Q _i net inflows of intervals in the subregioni. - W _i volumes of water drawn the trunk stream ofi into subdistricti. - H _i volumes of water returning to the trunk stream in the subdistricti. - B _i(W _i) the maximum net benefits (in hundred million yuan) from the annual-water consumption ofW _iin subregioni. - W _ik the annual-water consumption (in hundred million m³) of sectorK in subregioni, k = 1, 2, 3, 4. - B _ik(W _ik the maximum net benefits (in hundred million yuan) from the annual consumptionW _ikof sectork in subregioni. - BS _i(S _i) the maximum net benefits (in hundred million yuan) obtained from the optimal allocation of the run-off volumeS _iof river trunki among different sectors within the months of a year.     

西藏高海拔地区气象数据缺失条件下的ET0计算研究

西藏高海拔地区低氧低压(平均不足海平面的2/3)、太阳辐射强(年太阳辐射6 000~8 000 MJ/m2)、近地层空气湿度变化大,加之西藏地区气象资料系列短、站点少,该地区ET_0计算具有特殊性及不便性。本研究基于西藏地区9个典型站点20年逐日气象资料,通过引入海拔因子与修正温度常数对Hargreaves(HS)模型进行改进,旨在得到一种少参、准确的高海拔地区ET_0简易计算方法。结果表明,海拔2 000 m以上地区Hargreaves-Elevation(HS-E)改进模型在不同时间尺度条件下的修正结果均明显优于HS模型且避免了原HS模型在高海拔地区ET_0计算出现负值的情况,提升了ET_0计算值的实用性与精度。以PM模型ET_0计算值为标准进行误差分析,HS-E模型逐日ET_0计算的纳什效率系数(NSE)、均方根误差(RMSE)和平均相对误差(MRE)分别为0.8、0.53mm/d和13.80%,逐月ET_0计算的NSE、RMSE和MRE分别为0.84、11.90 mm/month和12.50%;对比不同时间尺度条件下(日、月)误差分析结果可知,计算时间尺度越大HS-E模型结果越优。HS-E改进模型在高海拔地区适应性较强,具有较高的计算精度,可作为西藏海拔2000 m以上地区气象数据缺失条件下ET_0计算的推荐模型。