A nonlinear function approach for the normalized complementary relationship evaporation model

A nonlinear function approach for the normalized complementary relationship evaporation model that is different from the methodology maintaining the symmetric complementary relationship with appropriate definitions of potential and wet‐environment evaporation is proposed and verified. This approach employs the definitions used in the advection‐aridity model, wherein the potential is estimated using the Penman equation. Normalized by Penman potential evaporation, the complementary relationship model is expressed as a function describing the relationship between the evaporation ratio (the ratio of the actual to the Penman potential evaporation) and the proportion of the radiation term in Penman potential evaporation. The new nonlinear function proposed in the current study is approximately equivalent to the advection‐aridity and the modified Granger models under conditions that are neither too wet nor too dry, but is more reasonable under arid and wet conditions. The new nonlinear function model performs well in estimating actual evaporation, as verified by the observed data from four sites under different land covers. Copyright © 2011 John Wiley & Sons, Ltd.     

A finite element solution for the fractional advection–dispersion equation

The fractional advection–dispersion equation (FADE) known as its non-local dispersion, has been proven to be a promising tool to simulate anomalous solute transport in groundwater. We present an unconditionally stable finite element (FEM) approach to solve the one-dimensional FADE based on the Caputo definition of the fractional derivative with considering its singularity at the boundaries. The stability and accuracy of the FEM solution is verified against the analytical solution, and the sensitivity of the FEM solution to the fractional order α and the skewness parameter β is analyzed. We find that the proposed numerical approach converge to the numerical solution of the advection–dispersion equation (ADE) as the fractional order α equals 2. The problem caused by using the first- or third-kind boundary with an integral-order derivative at the inlet is remedied by using the third-kind boundary with a fractional-order derivative there. The problems for concentration estimation at boundaries caused by the singularity of the fractional derivative can be solved by using the concept of transition probability conservation. The FEM solution of this study has smaller numerical dispersion than that of the FD solution by Meerschaert and Tadjeran (J Comput Appl Math 2004). For a given α, the spatial distribution of concentration exhibits a symmetric non-Fickian behavior when β = 0. The spatial distribution of concentration shows a Fickian behavior on the left-hand side of the spatial domain and a notable non-Fickian behavior on the right-hand side of the spatial domain when β = 1, whereas when β = −1 the spatial distribution of concentration is the opposite of that of β = 1. Finally, the numerical approach is applied to simulate the atrazine transport in a saturated soil column and the results indicat that the FEM solution of the FADE could better simulate the atrazine transport process than that of the ADE, especially at the tail of the breakthrough curves.     

Seasonal variability of the complementary relationship in the Asian monsoon region

The complementary relationship (CR) between potential evaporation (LE_p) and actual evaporation (LE) is widely used to explain the evaporation paradox and to estimate LE, in which wet environment evaporation (LE_w) is usually calculated using the Priestley–Taylor equation. However, in many studies on the CR, it has been found that the Priestley–Taylor parameter α is not a constant. Through seasonal variation of α for estimating LE_w in the CR, this paper analyses its seasonal variability. Based on flux observation data at two flux experiment sites (Kogma in Thailand and Weishan in China) in the Asian monsoon region, seasonal variability of the CR is detected, i.e. the α value is larger in winter than in summer. This seasonal variability might be caused by seasonal variability in the transport of water vapor and sensible heat between oceans and continent. The monsoon increases air humidity and lowers air temperature in summer, which leads to a decrease in α; it increases atmospheric air temperature and vapor content in winter, increasing α. Nevertheless, during May–September, α has a range of 1.06–1.16 at the Kogma site and 1.00–1.36 at the Weishan site, which is approximate to the typical range 1.1–1.4. Copyright © 2012 John Wiley & Sons, Ltd.     

Testing a conceptual hillslope recession model based on the storage–discharge relationship with the Richards equation

The conceptual recession model based on the storage–discharge relationship was proposed to account for the unsaturated–saturated water storage interaction. The recession model was formulated by combining the constitutive storage–discharge relationship with the integral balance equation for unsaturated and saturated water storage. The functional form of the constitutive storage–discharge relationship was determined from the spatial integration of the Richards equation. The performance of the recession model was tested by comparing with the solution of the Richards equation for different simulation geometric shapes and soil types. The conceptual recession model incorporating the unsaturated–saturated water storage interaction was in good agreement with the recession response of the Richards equation. However, the recession model that neglected the unsaturated–saturated water storage interaction was comparable to the Richards equation only for soils with the weak interaction between unsaturated water storage and saturated water storage. This result suggests the important role of the unsaturated–saturated water storage interaction in the formulation of the recession process when the derivative of the functional relationship between the unsaturated water storage and saturated water storage becomes significant. Copyright © 2007 John Wiley & Sons, Ltd.     

Multi‐model ensemble prediction of terrestrial evapotranspiration across north China using Bayesian model averaging

Using high‐quality dataset from 12 flux towers in north China, the performance of four evapotranspiration (ET) models and the multi‐model ensemble approaches including the simple averaging (SA) and Bayesian model average (BMA) were systematically evaluated in this study. The four models were the single‐layer Penman–Monteith (P–M) model, the two‐layer Shuttleworthe–Wallace (S–W) model, the advection–aridity (A–A) model, and a modified Priestley–Taylor (PT‐JPL). Based on the mean value of Taylor skill (S) and the regression slope between measured and simulated ET values across all sites, the order of overall performance of the individual models from the best to the worst were: S–W (0.88, 0.87), PT‐JPL (0.80, 1.17), P–M (0.63, 1.73) and A–A (0.60, 1.68) [statistics stated as (Taylor skill, regression slope)]. Here, all models used the same values of parameters, LAI and fractional vegetation cover as well as the forcing meteorological data. Thus, the differences in model performance were mainly attributed to errors in model structure. To the ensemble approach, the BMA method has the advantage of generating more skillful and reliable predictions than the SA scheme. However, successful implementation of BMA requires accurate estimates of its parameters, and some degradation in performance were observed when the BMA parameters generated from the training period were used for the validation period. Thus, it is necessary to explore the seasonal variations of the BMA parameters according the different growth stages. Finally, the optimal conditional density function of half‐hourly ET approximated well by the double‐exponential distribution. Copyright © 2016 John Wiley & Sons, Ltd.     

On a monotonicity preserving Eulerian–Lagrangian localized adjoint method for advection–diffusion equations

Eulerian–Lagrangian localized adjoint methods (ELLAMs) provide a general approach to the solution of advection-dominated advection–diffusion equations allowing large time steps while maintaining good accuracy. Moreover, the methods can treat systematically any type of boundary condition and are mass conservative. However, all ELLAMs developed so far suffer from non-physical oscillations and are usually implemented on structured grids. In this paper, we propose a finite volume ELLAM which incorporates a novel correction step rendering the method monotone while maintaining conservation of mass. The method has been implemented on fully unstructured meshes in two space dimensions. Numerical results demonstrate the applicability of the method for problems with highly non-uniform flow fields arising from heterogeneous porous media.     

Long-term pan evaporation observations as a resource to understand the water cycle trend: case studies from Australia

Abstract

Acceleration of the global water cycle over recent decades remains uncertain because of the high inter-annual variability of its components. Observations of pan evaporation (E_pan), a proxy of potential evapotranspiration (ET_p), may help to identify trends in the water cycle over long periods. The complementary relationship (CR) states that ET_p and actual evapotranspiration (ET_a) depend on each other in a complementary manner, through land–atmosphere feedbacks in water-limited environments. Using a long-term series of E_pan observations in Australia, we estimated monthly ET_a by the CR and compared our estimates with ET_a measured at eddy covariance Fluxnet stations. The results confirm that our approach, entirely data-driven, can reliably estimate ET_a only in water-limited conditions. Furthermore, our analysis indicated that ET_a did not show any significant trend in the last 30 years, while short-term analysis may indicate a rapid climate change that is not perceived in a long-term perspective.

Editor Z.W. Kundzewicz; Associate editor D. Gerten

Citation Lugato, E., Alberti, G., Gioli. B., Kaplan, J.O., Peressotti, A., and Miglietta, F., 2013. Long-term pan evaporation observations as a resource to understand the water cycle trend: case studies from Australia. Hydrological Sciences Journal, 58 (6), 1287–1296.     

Bare soil evaporation under high evaporation demand: a proposed modification to the FAO-56 model

Abstract

This study evaluates the evaporation component of the FAO-56 model under high evaporation demand. To perform this, two data sets were used as field evaluation, and a second model was used for comparison (a model based on the square root of time, SRT). The results show that although FAO-56, the field data and the SRT model present similar cumulative evaporation over the study period (approximately one month), when the data are analysed daily, FAO-56 overestimated evaporation at the beginning of the process and underestimated it at the end. A correction for FAO-56 is proposed to amend the mismatch between FAO-56 and the field-measured data under high evaporation conditions. Consequently, the parameters used by the FAO-56 evaporation component are discussed.

Citation Torres, E. A. & Calera, A. (2010) Bare soil evaporation under high evaporation demand: a proposed modification to the FAO-56 model. Hydrol. Sci. J. 55(3), 303–315.     

Stable oxygen and hydrogen isotopes as indicators of lake water recharge and evaporation in the lakes of the Yinchuan Plain

The Yinchuan Plain has more than 2000 years of history of irrigation by diverting water from the Yellow River. Currently, the amount of water diverted from the Yellow River is about 21.7 times the water formed on the plain as a result of precipitation and inflow of groundwater. Under the intensive influence of irrigation, the plain changed from a desert into a rich and populous area, earning its name as ‘South China Beyond the Great Wall’, with lakes scattered across the Yinchuan Plain just as stars in the sky. In this research, 17 representative lakes were sampled to analyze and study ²H and ¹⁸O content; the results showed that lakes on the plain have undergone obvious non‐equilibrium evaporation. Recharges of the lakes can be divided into three types: recharge from the Yellow River, from groundwater and from both of these. The Craig–Gordon non‐equilibrium evaporation model for isotope fractionation was used to estimate the evaporation proportion of each lake. The results showed that evaporation from lakes on Yinchuan Plain is generally extensive under the dry climatic conditions. Most lakes have an evaporation proportion of over 25%, with the largest originating from Shahu lake and Gaomiaohu lake in the northern part of the plain, at 42.5% and 42.8%, respectively. The evaporation proportions calculated on the basis of ¹⁸O and ²H are very close to each other. This shows that the method used in this paper is feasible for estimating the evaporation proportions of lakes in areas with a heavy anthropogenic influence. Copyright © 2013 John Wiley & Sons, Ltd.     

A simple rainfall–runoff model based on hydrological units applied to the Teba catchment (south‐east Spain)

A hydrological model (YWB, yearly water balance) has been developed to model the daily rainfall–runoff relationship of the 202 km² Teba river catchment, located in semi‐arid south‐eastern Spain. The period of available data (1976–1993) includes some very rainy years with intensive storms (responsible for flooding parts of the town of Malaga) and also some very dry years. The YWB model is in essence a simple tank model in which the catchment is subdivided into a limited number of meaningful hydrological units. Instead of generating per unit surface runoff resulting from infiltration excess, runoff has been made the result of storage excess. Actual evapotranspiration is obtained by means of curves, included in the software, representing the relationship between the ratio of actual to potential evapotranspiration as a function of soil moisture content for three soil texture classes. The total runoff generated is split between base flow and surface runoff according to a given baseflow index. The two components are routed separately and subsequently joined. A large number of sequential years can be processed, and the results of each year are summarized by a water balance table and a daily based rainfall runoff time series. An attempt has been made to restrict the amount of input data to the minimum. Interactive manual calibration is advocated in order to allow better incorporation of field evidence and the experience of the model user. Field observations allowed for an approximate calibration at the hydrological unit level. Copyright © 2001 John Wiley & Sons, Ltd.     

Comparison of methods for applying the Priestley–Taylor equation at a regional scale

The scenario assumed for this study was that of a region with a complete or first‐order weather station surrounded by a network of second‐order stations, where only monthly air temperature data were available. The objective was to evaluate procedures to estimate the monthly α parameter of the Priestley–Taylor equation in the second‐order stations by adjusting and extrapolating α values determined at the first‐order station. These procedures were applied in two climatic zones of north‐east Spain with semi‐arid continental and semi‐arid Mediterranean climates, respectively. Procedure A assumed α to be constant over each zone for each month (direct extrapolation). Procedure B accounted for differences in vapour pressure deficit and available energy for evapotranspiration between the first‐ and second‐order stations. Procedure C was based on equating the Penman–Monteith (P–M) and Priestley–Taylor (P–T) equations on a monthly basis to solve for α. Methods to estimate monthly mean vapour pressure deficit, net radiation and wind speed were developed and evaluated. A total of 11 automated first‐order weather stations with a minimum period of record of 6 years (ranging from 6 to 10 years) were used for this study. Six of these stations were located in the continental zone and five in the Mediterranean zone. One station in each zone was assumed to be first‐order whereas the remainder were taken as second‐order stations. Monthly α parameters were calibrated using P–M reference crop evapotranspiration (ET₀) values, calculated hourly and integrated for monthly periods, which were taken as ‘true’ values of ET₀. For the extrapolation of monthly α parameters, procedure A was found to perform slightly better than procedure B in the Mediterranean zone. The opposite was true in the continental zone. Procedure C had the worst performance owing to the non‐linearity of the P–M equation and errors in the estimation of monthly available energy, vapour pressure deficit and wind speed. Procedures A and B are simpler and performed better. Overall, monthly P–T ET₀ estimates using extrapolated α parameters and R_n?G values were in a reasonable agreement with P–M ET₀ calculated on an hourly basis and integrated for monthly periods. The methods presented for the spatial extrapolation of monthly available energy, vapour pressure deficit and wind speed from first‐ to second‐order stations could be useful for other applications. Copyright © 2001 John Wiley & Sons, Ltd.     

A coupled one‐dimensional viscoelastic–plastic model for aquitard consolidation caused by hydraulic head variations in aquifers

Accurate and practical calculation of aquitard consolidation is required for a reliable analysis of land subsidence caused by groundwater overexploitation in a multilayered aquifer system because aquitards are generally more compressible than aquifers are. This study proposes a coupled one‐dimensional viscoelastic–plastic consolidation model that considers the combined effect of changes in soil parameters and body force to simulate aquitard consolidation caused by hydraulic head variations in neighbouring aquifers. The proposed model uses variable total stress and simultaneously solves hydraulic head and vertical soil displacement. The constitutive relation based on the Voigt model with different elastic moduli of the spring in normally consolidated and overconsolidated soils is used to describe the viscoelastic–plastic deformation mechanism of aquitards. In addition, the proposed model considers the combined effect of variations in hydraulic conductivity, elastic moduli, and body force on the calculation of aquitard consolidation. Three hypothetical scenarios with various hydraulic head variations in aquifers are used to examine the coupled one‐dimensional viscoelastic–plastic consolidation model. The results show that neglecting plasticity and viscosity of soil causes aquitard consolidation to be respectively underestimated and overestimated. In addition, ignoring body force variation underestimates aquitard consolidation, whereas neglecting soil parameters variation overestimates aquitard consolidation. Two real case scenarios are also studied to further demonstrate the applicability of the coupled one‐dimensional viscoelastic–plastic consolidation model. Copyright © 2015 John Wiley & Sons, Ltd.     

Impacts of model initialization on an integrated surface water–groundwater model

Integrated hydrologic models characterize catchment responses by coupling the subsurface flow with land surface processes. One of the major areas of uncertainty in such models is the specification of the initial condition and its influence on subsequent simulations. A key challenge in model initialization is that it requires spatially distributed information on model states, groundwater levels and soil moisture, even when such data are not routinely available. Here, the impact of uncertainty in initial condition was explored across a 208 km² catchment in Denmark using the ParFlow.CLM model. The initialization impact was assessed under two meteorological conditions (wet vs dry) using five depth to water table and soil moisture distributions obtained from various equilibrium states (thermal, root zone, discharge, saturated and unsaturated zone equilibrium) during the model spin‐up. Each of these equilibrium states correspond to varying computation times to achieve stability in a particular aspect of the system state. Results identified particular sensitivity in modelled recharge and stream flow to the different initializations, but reduced sensitivity in modelled energy fluxes. Analysis also suggests that to simulate a year that is wetter than the spin‐up period, an initialization based on discharge equilibrium is adequate to capture the direction and magnitude of surface water–groundwater exchanges. For a drier or hydrologically similar year to the spin‐up period, an initialization based on groundwater equilibrium is required. Variability of monthly subsurface storage changes and discharge bias at the scale of a hydrological event show that the initialization impacts do not diminish as the simulations progress, highlighting the importance of robust and accurate initialization in capturing surface water–groundwater dynamics. Copyright © 2015 John Wiley & Sons, Ltd.     

A coupling model of FE–BE–IE–IBE for non-linear layered soil–structure interactions

A coupling model of Finite Elements (FEs), Boundary Elements (BEs), Infinite Elements (IEs) and Infinite Boundary Elements (IBEs) is presented for analysis of soil–structure interaction (SSI). The radiation effects of the infinite layered soil are taken into account by FE–IE coupling, while the underlying bed rock half-space is discretized into BE–IBE coupling whereby the non-horizontal bed rock surface can be accounted for. Displacement compatabilities are satisfied for all types of aforementioned elements. The equivalent linear approach is employed for approximation of nonlinearity of the near field soil. This model has some advantages over the current SSI program in considering the bed rock half-space and non-vertical wave incidence from the far field. Examples of verification demonstrate the applicability and accuracy of the method when compared with the FLUSH program. Finally, the effects of the relative modulus ratio E_r/E_s of rock and soil and the incident angles of non-vertical waves on the responses of the structure and the soil are examined. Copyright © 1999 John Wiley & Sons, Ltd.     

Zircon fission‐track and U–Pb double dating using femtosecond laser ablation–inductively coupled plasma–mass spectrometry: A technical note

We present a new LA–ICP–MS system for zircon fission‐track (FT) and U–Pb double dating, whereby a femtosecond laser combined with galvanometric optics simultaneously ablates multiple spots to measure average surface U contents. The U contents of zircon measured by LA–ICP–MS and standardized with the NIST SRM610 glass are comparable to those measured by the induced FT method, and have smaller analytical errors. LA–ICP–MS FT dating of seven zircon samples including three IUGS age standards is as accurate as the external detector method, but can give a higher‐precision age depending on the counting statistics of the U content measurement. Double dating of the IUGS age standards gives FT and U–Pb ages that are in agreement. A chip of the Nancy 91500 zircon has a homogeneous U content of 84 ppm, suggesting the possibility of using this zircon as a matrix‐matched U‐standard for FT dating. When using the Nancy 91500 zircon as a U‐standard, a zeta calibration value of 42–43 year cm² for LA–ICP–MS FT dating is obtained. While this value is strictly valid only for the particular session, it can serve as a reference for other studies.     

Patterns and dynamics of river–aquifer exchange with variably-saturated flow using a fully-coupled model

The parallel physically-based surface–subsurface model PARFLOW was used to investigate the spatial patterns and temporal dynamics of river–aquifer exchange in a heterogeneous alluvial river–aquifer system with deep water table. Aquifer heterogeneity at two scales was incorporated into the model. The architecture of the alluvial hydrofacies was represented based on conditioned geostatistical indicator simulations. Subscale variability of hydraulic conductivities (K) within hydrofacies bodies was created with a parallel Gaussian simulation. The effects of subscale heterogeneity were investigated in a Monte Carlo framework. Dynamics and patterns of river–aquifer exchange were simulated for a 30-day flow event. Simulation results show the rapid formation of saturated connections between the river channel and the deep water table at preferential flow zones that are characterized by high conductivity hydrofacies. Where the river intersects low conductivity hydrofacies shallow perched saturated zones immediately below the river form, but seepage to the deep water table remains unsaturated and seepage rates are low. Preferential flow zones, although only taking up around 50% of the river channel, account for more than 98% of total seepage. Groundwater recharge is most efficiently realized through these zones. Subscale variability of K_sat slightly increased seepage volumes, but did not change the general seepage patterns (preferential flow zones versus perched zones). Overall it is concluded that typical alluvial heterogeneity (hydrofacies architecture) is an important control of river–aquifer exchange in rivers overlying deep water tables. Simulated patterns and dynamics are in line with field observations and results from previous modeling studies using simpler models. Alluvial heterogeneity results in distinct patterns and dynamics of river–aquifer exchange with implications for groundwater recharge and the management of riparian zones (e.g. river channel-floodplain connectivity via saturated zones).     

用稳定同位素方法估算大型浅水湖泊蒸发量——以太湖为例

湖泊蒸发量的准确估算对于水文学、气象学和湖泊学等研究有重要的意义.基于2013-2015年太湖水量收支资料、气象观测数据和稳定同位素观测资料,采用稳定同位素质量守恒模型、水量平衡法和Priestley-Taylor模型估算太湖蒸发量,分析太湖蒸发量的季节变化和年际变化特征,并以Priestley-Taylor模型结果为参考值,评价水量平衡法和同位素质量守恒方程的计算精度.结果表明:5-9月太湖蒸发量较高,冬季最低.2013-2015年太湖年总蒸发量分别为1069、894和935 mm,蒸发量的年际变化受到天气条件的影响.2013年12月2014年11月期间,用Priestley-Taylor模型计算的湖泊蒸发量为885 mm;同位素质量守恒模型的估算结果较一致,为893 mm;而水量平衡方程的估算结果明显偏高,为1247 mm.