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.     

New class of solutions for water infiltration problems in unsaturated soils

This paper presents the results of approximate analytical solutions to Richards' equation, which governs the problem of unsaturated flow in porous media. The existing methods generally fall within the category of numerical and analytical methods, often having many restrictions for practical situations. In the present study, two approximate analytical methods known as the differential transform method (DTM) and homotopy perturbation method (HPM) were employed to find analytical solutions to Richards' equation. The methods were found to be robust in finding solutions practically identical to those from the existing analytical and numerical methods. Two representative examples were considered in order to evaluate the accuracy of the solutions obtained by DTM and HPM, revealing high level of accuracy in both cases.     

Remarks upon numerical solutions of infiltration into a soil profile

Abstract

A methodology of time-step estimation for numerically solving the Richards equation is discussed. Its importance in simulating water movement in unsaturated—saturated soils is shown for infiltration into a soil profile by applying various time-step estimations and boundary conditions for different soils. In order to test the results of the computations, infiltration theory was applied. According to infiltration theory, the pressure head in the initially unsaturated part will not take positive values as long as the moisture front has not reached the phreatic level, or, in the case of a profile with a free-draining lower boundary, it is not saturated at the base. In other cases, the appearance of positive values of the pressure head produces incorrect values for the inflow rate q.     

Higher and lowest order mixed finite element approximation of subsurface flow problems with solutions of low regularity

In this work we study mixed finite element approximations of Richards’ equation for simulating variably saturated subsurface flow and simultaneous reactive solute transport. Whereas higher order schemes have proved their ability to approximate reliably reactive solute transport (cf., e.g. [Bause M, Knabner P. Numerical simulation of contaminant biodegradation by higher order methods and adaptive time stepping. Comput Visual Sci 7;2004:61–78]), the Raviart–Thomas mixed finite element method (RT₀) with a first order accurate flux approximation is popular for computing the underlying water flow field (cf. [Bause M, Knabner P. Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods. Adv Water Resour 27;2004:565–581, Farthing MW, Kees CE, Miller CT. Mixed finite element methods and higher order temporal approximations for variably saturated groundwater flow. Adv Water Resour 26;2003:373–394, Starke G. Least-squares mixed finite element solution of variably saturated subsurface flow problems. SIAM J Sci Comput 21;2000:1869–1885, Younes A, Mosé R, Ackerer P, Chavent G. A new formulation of the mixed finite element method for solving elliptic and parabolic PDE with triangular elements. J Comp Phys 149;1999:148–167, Woodward CS, Dawson CN. Analysis of expanded mixed finite element methods for a nonlinear parabolic equation modeling flow into variably saturated porous media. SIAM J Numer Anal 37;2000:701–724]). This combination might be non-optimal. Higher order techniques could increase the accuracy of the flow field calculation and thereby improve the prediction of the solute transport. Here, we analyse the application of the Brezzi-Douglas-Marini element (BDM₁) with a second order accurate flux approximation to elliptic, parabolic and degenerate problems whose solutions lack the regularity that is assumed in optimal order error analyses. For the flow field calculation a superiority of the BDM₁ approach to the RT₀ one is observed, which however is less significant for the accompanying solute transport.     

基于最小作用原理的Richards方程变分解

经典的Richards入渗控制方程属于偏微分方程,具有强烈的非线性,难以求得解析解。以入渗时间为最小作用量,基于Richards方程建立关于入渗路径的时间泛函,将考虑重力项的非饱和土垂直入渗问题转化为泛函极值问题,并构造等价的Euler-Lagrange方程进行求解。计算结果表明,扩散系数D（?）与概化湿润锋距离具有函数关系,当扩散系数D（?）形式已知时,可求得最优路径下湿润锋处含水率、较远处湿润锋最小含水率、土壤含水率最大熵分布3个问题,并基于最优路径检验了本研究条件下,Boltzmann变换和线性变换求解Richards方程的精度。求解过程未引进新变量化简Richards方程,不改变原方程结构,因此其解具有普遍性,可作为非饱和土力学计算的一个补充。     

非饱和土壤渗透的快速数值计算

给出非饱和土壤渗透计算求解理查兹方程的有限差分法。该计算值与实测值吻合较好。这个方法使用了水土势双曲正弦变换的隐式差分格式。砂土、壤土及粘土范围内的渗透过程在微机上几十秒钟内即可被模拟出来,其误差很小。非饱和土壤的渗透特性可以划分为地表积水前、地表积水后及退水过程三种类型。     

非饱和土入渗的数值模拟

入渗引起土中孔隙水压力的变化,是影响非饱和土性状的最重要的原因之一。因此,正确地分析和模拟非饱和土入渗过程具有重要意义。通过对一维和二维降雨入渗问题的研究,展示了湿润锋面、地下水位面及孔隙水压力分布随时间的变化,使得对入渗问题的认识更加直观和清楚。     

Solving the nonstationary Richards equation with adaptive hp-FEM

This paper examines the potential of the adaptive hp-FEM method for the numerical solution of time-dependent variably saturated Darcian flow problems described by the Richards equation. The method is illustrated on three model problems: a benchmark with known exact solution, groundwater seepage into a dry lysimeter box with time-dependent boundary conditions, and capillary barrier behavior under an intense infiltration. In the second part of the paper we present the weak formulation of the Richards equation for the Newton’s and Picard’s methods, give a brief overview of adaptive hp-FEM with emphasis on aspects that are usually not discussed in the literature, and we briefly introduce the open source adaptive hp-FEM library HERMES that was used to generate numerical results for this paper. All computations that we present are easily reproducible.     

Optimal root profiles in water-limited ecosystems

The vertical distribution of roots in the soil is of central importance to the mass and energy exchange between the land and the atmosphere. It has been demonstrated that the vertical root profiles which maximize transpiration in numerical experiments reflect well the characteristics of root profiles observed in nature for water-limited ecosystems. Previous research has demonstrated how the optimal vertical root profile depends on both the mean annual precipitation (MAP) and the soil texture. Recently, in the climate literature, it has been suggested Chou et al. (2012) [5] that increased greenhouse forcing in the tropics can lead to a simultaneous decrease in the frequency and increase in the intensity of precipitation. In this paper we demonstrate how such a change in the statistical structure of rainfall, even with no change to MAP, requires deeper root distributions to maintain optimal water use. These results raise interesting questions for future studies of nutrient dynamics, the cost of additional below ground carbon allocation, and inter plant functional type competition.