Dual state-parameter estimation of root zone soil moisture by optimal parameter estimation and extended Kalman filter data assimilation

With well-determined hydraulic parameters in a hydrologic model, a traditional data assimilation method (such as the Kalman filter and its extensions) can be used to retrieve root zone soil moisture under uncertain initial state variables (e.g., initial soil moisture content) and good simulated results can be achieved. However, when the key soil hydraulic parameters are incorrect, the error is non-Gaussian, as the Kalman filter will produce a persistent bias in its predictions. In this paper, we propose a method coupling optimal parameters and extended Kalman filter data assimilation (OP-EKF) by combining optimal parameter estimation, the extended Kalman filter (EKF) assimilation method, a particle swarm optimization (PSO) algorithm, and Richards’ equation. We examine the accuracy of estimating root zone soil moisture through the optimal parameters and extended Kalman filter data assimilation method by using observed in situ data at the Meiling experimental station, China. Results indicate that merely using EKF for assimilating surface soil moisture content to obtain soil moisture content in the root zone will produce a persistent bias between simulated and observed values. Using the OP-EKF assimilation method, estimates were clearly improved. If the soil profile is heterogeneous, soil moisture retrieval is accurate in the 0-50 cm soil profile and is inaccurate at 100 cm depth. Results indicate that the method is useful for retrieving root zone soil moisture over large areas and long timescales even when available soil moisture data are limited to the surface layer, and soil moisture content are uncertain and soil hydraulic parameters are incorrect.     

Using a H∞ filter assimilation procedure to estimate root zone soil water content

Root zone soil water content impacts plant water availability, land energy and water balances. Because of unknown hydrological model error, observation errors and the statistical characteristics of the errors, the widely used Kalman filter (KF) and its extensions are challenged to retrieve the root zone soil water content using the surface soil water content. If the soil hydraulic parameters are poorly estimated, the KF and its extensions fail to accurately estimate the root zone soil water. The H‐infinity filter (HF) represents a robust version of the KF. The HF is widely used in data assimilation and is superior to the KF, especially when the performance of the model is not well understood. The objective of this study is to study the impact of uncertain soil hydraulic parameters, initial soil moisture content and observation period on the ability of HF assimilation to predict in situ soil water content. In this article, we study seven cases. The results show that the soil hydraulic parameters hold a critical role in the course of assimilation. When the soil hydraulic parameters are poorly estimated, an accurate estimation of root soil water content cannot be retrieved by the HF assimilation approach. When the estimated soil hydraulic parameters are similar to actual values, the soil water content at various depths can be accurately retrieved by the HF assimilation. The HF assimilation is not very sensitive to the initial soil water content, and the impact of the initial soil water content on the assimilation scheme can be eliminated after about 5–7 days. The observation interval is important for soil water profile distribution retrieval with the HF, and the shorter the observation interval, the shorter the time required to achieve actual soil water content. However, the retrieval results are not very accurate at a depth of 100 cm. Also it is complex to determine the weighting coefficient and the error attenuation parameter in the HF assimilation. In this article, the trial‐and‐error method was used to determine the weighting coefficient and the error attenuation parameter. After the first establishment of limited range of the parameters, ‘the best parameter set’ was selected from the range of values. For the soil conditions investigated, the HF assimilation results are better than the open‐loop results. Copyright © 2010 John Wiley & Sons, Ltd.     

On quantifying hydraulic conductance at the soil–root interface

This study sought to test a widely used hypothesis in water transport from soil to root: the soil textural effect on soil–root interfacial conductance can be quantified by the degree of soil water saturation. This hypothesis is inferred from basic soil physics and is commonly used in modelling root water uptake. However, it has never been subjected to rigorous experimental test. In the current study, the soil texture effect on the interfacial hydraulic conductance was evaluated on well‐watered pot‐grown cotton plants, with soil particle size ranges of 0–0.05, 0.05–0.1, 0.1–0.2, 0.2–0.3, 0.3–0.45, 0.45–0.6 and 0.6–1 mm in seven treatments, in addition to hydroponics. However, our experimental results showed that the volumetric soil water content, not degree of saturation, is the best explanatory variable for quantifying the interfacial effect on hydraulic conductance. Further analysis indicated that if temporal change of this interfacial effect on hydraulic conductance is the subject of concern, degree of saturation may still be a valid option. If soil textural or spatial variation in root water uptake is the subject of concern, volumetric soil water content is best suited to quantifying the interfacial effect on hydraulic conductance. Copyright © 2013 John Wiley & Sons, Ltd.     

Analytical solutions of infiltration process under ponding irrigation

The objective of this paper is to simulate the progress of the soil water content distribution in the soil profile with a water table at the bottom of the soil profile during ponding irrigation. This simulation can be done by solving the two‐dimensional Richards's equation for the assimilation of the advancing water jet, which uses the conditions of the two exponential functional forms k = k_s e^αψ and θ = θ_r + (θ_s − θ_r) e^αψ to represent the hydraulic conductivity and volumetric water content, with ψ the pressure as the third variable. We assume that the ground surface becomes ponded and saturated as soon as the water flux passes the dry ground surface. By the technique of transformation, the analytical solution of these two‐dimensional Richards' equations has enabled figures of volumetric water content distribution to be obtained in successive time periods after irrigation. For the example of loam soil, it can simulate the variation of volumetric water content during and after irrigation in the soil profile. The analytical solutions of this paper reflect the real situation simulated, and can be applied to verify those complicated solutions from other analytical models. Copyright © 2005 John Wiley & Sons, Ltd.     

Quantification of vertical water fluxes in the vadose zone using particle‐size distribution and pedology‐based approaches to model soil heterogeneities

One‐dimensional flow simulations were conducted at four locations of the shallow alluvial aquifer of the upper Rhine River (at the Erstein polder) to quantify the time‐dependent moisture distribution, the water flux and the water volume infiltrated in the unsaturated zone as a function of soil heterogeneities during a five‐day‐long flooding event. Three methods of estimating the hydraulic parameters of soil in the vadose zone were tested. They are based on the following: (1) experimental data, (2) soil particle‐size distribution and (3) pedology information on soils. Water fluxes calculated from modelling approaches 2 and 3 were compared with those of the experiment‐based values and the effect of these differences on the arrival time and velocity of water at the water table were analysed. Major differences in water fluxes were found among the methods of estimating the hydrodynamic parameters. At the Terrace location, the groundwater recharge predicted using soil data from methods 1 and 2 are approximately 4500 and 2400 mm, respectively. Flow simulations using soil data and the experiment‐based method show the highest velocities of infiltrating water at the soil surface and largest volume of groundwater infiltration but result in the lowest centres of the moisture content mass. The results obtained using soil data based on the pedological method are similar to those calculated using soil parameters based on the particle‐size distribution of extracted soil samples. Water pressure profiles calculated on Terrace and Channel location, 3 and 7 days after the inundation event agreed reasonably well with those observed when using hydrodynamic parameters from the experiment‐based method. However, the flow model using the pedology‐based parameters largely underestimates the time needed to achieve hydrostatic conditions of the soil water profile once water flooding at the soil surface stops. This can be mainly attributed to the low values of estimated van Genuchten parameter α. Copyright © 2012 John Wiley & Sons, Ltd.     

Modelling soil water dynamics considering measurement uncertainty

In shallow water table‐controlled environments, surface water management impacts groundwater table levels and soil water dynamics. The study goal was to simulate soil water dynamics in response to canal stage raises considering uncertainty in measured soil water content. Water and Agrochemicals in the soil, crop and Vadose Environment (WAVE) was applied to simulate unsaturated flow above a shallow aquifer. Global sensitivity analysis was performed to identify model input factors with the greatest influence on predicted soil water content. Nash–Sutcliffe increased and Root Mean Square Error reduced when uncertainties in measured data were considered in goodness‐of‐fit calculations using measurement probability distributions and probable asymmetric error boundaries, implying that appropriate model performance evaluation should be carried out using uncertainty ranges instead of single values. Although uncertainty in the experimental measured data limited evaluation of the absolute predictions by the model, WAVE was found a useful exploratory tool for estimating temporal variation in soil water content. Visual analysis of soil water content time series under proposed changes in canal stage management indicated that sites with land surface elevation of less than 2.0‐m NGVD29 were predicted to periodically experience saturated conditions in the root zone and shortening of the growing season if canal stage is raised more than 9 cm and maintained at this level. The models developed could be combined with high‐resolution digital elevation models in future studies to identify areas with the greatest risk of experiencing saturated root zone. The study also highlighted the need to incorporate measurement uncertainty when evaluating performance of unsaturated flow models. Copyright © 2014 John Wiley & Sons, Ltd.     

Spatio‐temporal heterogeneity in soil water stable isotopic composition and its ecohydrologic implications in semiarid ecosystems

Spatio‐temporal heterogeneity in soil water content is recognized as a common phenomenon, but heterogeneity in the hydrogen and oxygen isotope composition of soil water, which can reveal processes of water cycling within soils, has not been well studied. New advances are being driven by measurement approaches allowing sampling with high density in both space and time. Using in situ soil water vapour probe techniques, combined with conventional soil and plant water vacuum distillation extraction, we monitored the hydrogen and oxygen stable isotopic composition of soil and plant waters at paired sites dominated by grasses and Gambel's oak (Quercus gambelii) within a semiarid montane ecosystem over the course of a growing season. We found that sites spaced only 20 m apart had profoundly different soil water isotopic and volumetric conditions. We document patterns of depth‐ and time‐explicit variation in soil water isotopic conditions at these sites and consider mechanisms for the observed heterogeneity. We found that soil water content and isotopic variability were damped under Q. gambelii, perhaps due in part to hydraulic redistribution of deep soil water or groundwater by Q. gambelii in these soils relative to the grass‐dominated site. We also found some support for H isotope discrimination effects during water uptake by Q. gambelii. In this ecosystem, the soil water content was higher than that at the neighbouring Grass site, and thus, 25% more water was available for transpiration by Q. gambelii compared with the Grass site. This work highlights the role of plants in governing soil water variation and demonstrates that they can also strongly influence the isotope ratios of soil water. The resulting fine‐scale heterogeneity has implications for the use of isotope tracers to study soil hydrology and evaporation and transpiration fluxes to improve understanding of water cycling through the soil–plant–atmosphere continuum.     

Simulating soil‐water movement under a hedgerow surrounding a bottomland reveals the importance of transpiration in water balance

The objective of this study was to quantify components of the water balance related to root‐water uptake in the soil below a hedgerow. At this local scale, a two‐dimensional (2D) flow domain in the x–z plane 6 m long and 1·55 m deep was considered. An attempt was made to estimate transpiration using a simulation model. The SWMS‐2D model was modified and used to simulate temporally and spatially heterogeneous boundary conditions. A function with a variable spatial distribution of root‐water uptake was considered, and model calibration was performed by adjusting this root‐water uptake distribution. Observed data from a previous field study were compared against model predictions. During the validation step, satisfactory agreement was obtained, as the difference between observed and modelled pressure head values was less than 50 cm for 80% of the study data. Hedge transpiration capacity is a significant component of soil‐water balance in the summer, when predicted transpiration reaches about 5·6 mm day^?1. One of the most important findings is that hedge transpiration is nearly twice that of a forest canopy. In addition, soil‐water content is significantly different whether downslope or upslope depending on the root‐water uptake. The high transpiration rate was mainly due to the presence of a shallow water table below the hedgerow trees. Soil‐water content was not a limiting factor for transpiration in this context, as it could be in one with a much deeper water table. Hedgerow tree transpiration exerts a strong impact not only on water content within the vadose zone but also on the water‐table profile along the transect. Results obtained at the local scale reveal that the global impact of hedges at the catchment scale has been underestimated in the past. Transpiration rate exerts a major influence on water balance at both the seasonal and annual scales for watersheds with a dense network of hedgerows. Copyright © 2007 John Wiley & Sons, Ltd.     

Water mining from the deep critical zone by apple trees growing on loess

There have been significant recent advances in understanding the ecohydrology of deep soil. However, the links between root development and water usage in the deep critical zone remains poorly understood. To clarify the interaction between water use and root development in deep soil, we investigated soil water and root profiles beyond maximum rooting depth in five apple orchards planted on farmland with stand ages of 8, 11, 15, 18, and 22 years in a subhumid region on the Chinese Loess Plateau. Apple trees rooted progressively deeper for water with increasing stand age and reached 23.2 ± 0.8 m for the 22‐year‐old trees. Soil water deficit in deep soil increased with tree age and was 1,530 ± 43 mm for a stand age of 22 years. Measured root deepening rate was far great than the reported pore water velocity, which demonstrated that trees are mining resident old water. The deficits are not replenished during the life‐span of the orchard, showing a one‐way mining of the critical zone water. The one‐way root water mining may have changed the fine root profile from an exponential pattern in the 8‐year‐old orchard to a relative uniform distribution in older orchards. Our findings enhance our understanding of water‐root interaction in deep soil and reveal the unintended consequences of critical zone dewatering during the lifespan of apple trees.     

Estimating soil water fluxes from soil water records obtained using dielectric sensors

Accurate estimation of the soil water balance (SWB) is important for a number of applications (e.g. environmental, meteorological, agronomical and hydrological). The objective of this study was to develop and test techniques for the estimation of soil water fluxes and SWB components (particularly infiltration, evaporation and drainage below the root zone) from soil water records. The work presented here is based on profile soil moisture data measured using dielectric methods, at 30‐min resolution, at an experimental site with different vegetation covers (barley, sunflower and bare soil). Estimates of infiltration were derived by assuming that observed gains in the soil profile water content during rainfall were due to infiltration. Inaccuracies related to diurnal fluctuations present in the dielectric‐based soil water records are resolved by filtering the data with adequate threshold values. Inconsistencies caused by the redistribution of water after rain events were corrected by allowing for a redistribution period before computing water gains. Estimates of evaporation and drainage were derived from water losses above and below the deepest zero flux plane (ZFP), respectively. The evaporation estimates for the sunflower field were compared to evaporation data obtained with an eddy covariance (EC) system located elsewhere in the field. The EC estimate of total evaporation for the growing season was about 25% larger than that derived from the soil water records. This was consistent with differences in crop growth (based on direct measurements of biomass, and field mapping of vegetation using laser altimetry) between the EC footprint and the area of the field used for soil moisture monitoring. Copyright © 2007 John Wiley & Sons, Ltd.     

Soil water content in southern England derived from a cosmic‐ray soil moisture observing system – COSMOS‐UK

Cosmic‐ray soil moisture sensors have the advantage of a large measurement footprint (approximately 700 m in diameter) and are able to operate continuously to provide area‐averaged near‐surface (top 10–20 cm) volumetric soil moisture content at the field scale. This paper presents the application of this technique at four sites in southern England over almost 3 years. Results show the soil moisture response to contrasting climatic conditions during 2011–2014 and are the first such field‐scale measurements made in the UK. These four sites are prototype stations for a UK COsmic‐ray Soil Moisture Observing System, and particular consideration is given to sensor operating conditions in the UK. Comparison of these soil water content observations with the Joint UK Land Environment Simulator 10‐cm soil moisture layer shows that these data can be used to test and diagnose model performance and indicate the potential for assimilation of these data into hydro‐meteorological models. The application of these large‐area soil water content measurements to evaluate remotely sensed soil moisture products is also demonstrated. Numerous applications and the future development of a national COsmic‐ray Soil Moisture Observing System network are discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

The effect of conservation practices in sloped croplands on soil hydraulic properties and root‐zone moisture dynamics

Rain‐induced erosion and short‐term drought are the two factors that limit the productivity of croplands in the red soil region of subtropical China. The objective of this study was to estimate the effects of conservation practices on hydraulic properties and root‐zone water dynamics of the soil. A 3‐year experiment was performed on a slope at Xianning. Four treatments were evaluated for their ability to reduce soil erosion and improve soil water conditions. Compared with no practices (CK) and living grass strips (GS), the application of polyacrylamide (PAM) significantly reduced soil crust formation during intense rainfall, whereas rice straw mulching (SM) completely abolished soil crust formation. The SM and PAM treatments improved soil water‐stable aggregates, with a redistribution of micro‐aggregates into macro‐aggregates. PAM and SM significantly increased the soil water‐holding capacity. These practices mitigated the degradation of the soil saturated hydraulic conductivity (Ks) during intense rainfalls. These methods increased soil water storage but with limited effects during heavy rainfalls in the wet period. In contrast, during the dry period, SM had the highest soil water storage, followed by PAM and CK. Grass strips had the lowest soil water storage because of the water uptake during the vigorous grass growth. A slight decline in the soil moisture resulted in a significant decrease in the unsaturated hydraulic conductivity (Ku) of the topsoil. Therefore, the hydraulic conductivity in the field is governed by soil moisture, and the remaining soil moisture is more important than improving soil properties to resist short‐term droughts. As a result, SM is the most effective management practice when compared with PAM and GS, although they all protect the soil hydraulic properties during wet periods. These results suggest that mulching is the best strategy for water management in erosion‐threatened and drought‐threatened red soils. Copyright © 2014 John Wiley & Sons, Ltd.     

Vegetation impacts soil water content patterns by shaping canopy water fluxes and soil properties

Soil water content is a key variable for biogeochemical and atmospheric coupled processes. Its small‐scale heterogeneity impacts the partitioning of precipitation (e.g., deep percolation or transpiration) by triggering threshold processes and connecting flow paths. Forest hydrologists frequently hypothesized that throughfall and stemflow patterns induce soil water content heterogeneity, yet experimental validation is limited. Here, we pursued a pattern‐oriented approach to explore the relationship between net precipitation and soil water content. Both were measured in independent high‐resolution stratified random designs on a 1‐ha temperate mixed beech forest plot in Germany. We recorded throughfall (350 locations) and stemflow (65 trees) for 16 precipitation events in 2015. Soil water content was measured continuously in topsoil and subsoil (210 profiles). Soil wetting was only weakly related to net precipitation patterns. The precipitation‐induced pattern quickly dissipates and returns to a basic pattern, which is temporally stable. Instead, soil hydraulic properties (by the proxy of field capacity) were significantly correlated with this stable soil water content pattern, indicating that soil structure more than net precipitation drives soil water content heterogeneity. Also, both field capacity and soil water content were lower in the immediate vicinity of tree stems compared to further away at all times, including winter, despite stemflow occurrence. Thus, soil structure varies systematically according to vegetation in our site. We conclude that enhanced macroporosity increases gravity‐driven flow in stem proximal areas. Therefore, although soil water content patterns are little affected by net precipitation, the resulting soil water fluxes may strongly be affected. Specifically, this may further enhance the channelling of stemflow to greater depth and beyond the rooting zone.     

Responses of canopy transpiration and canopy conductance of peach (Prunus persica) trees to alternate partial root zone drip irrigation

We investigated canopy transpiration and canopy conductance of peach trees under three irrigation patterns: fixed 1/2 partial root zone drip irrigation (FPRDI), alternate 1/2 partial root zone drip irrigation (APRDI) and full root zone drip irrigation (FDI). Canopy transpiration was measured using heat pulse sensors, and canopy conductance was calculated using the Jarvis model and the inversion of the Penman–Monteith equation. Results showed that the transpiration rate and canopy conductance in FPRDI and APRDI were smaller than those in FDI. More significantly, the total irrigation amount was greatly reduced, by 34·7% and 39·6%, respectively for APRDI and FPRDI in the PRDI (partial root zone drip irrigation) treatment period. The daily transpiration was linearly related to the reference evapotranspiration in the three treatments, but daily transpiration of FDI is more than that of APRDI and FPRDI under the same evaporation demand, suggesting a restriction of transpiration water loss in the APRDI and FPRDI trees. FDI needed a higher soil water content to carry the same amount of transpiration as the APRDI and FPRDI trees, suggesting the hydraulic conductance of roots of APRDI and FPRDI trees was enhanced, and the roots had a greater water uptake than in FDI when the average soil water content in the root zone was the same. By a comparison between the transpiration rates predicted by the Penman–Monteith equation and the measured canopy transpiration rates for 60 days during the experimental period, an excellent correlation along the 1:1 line was found for all the treatments (R² > 0·80), proving the reliability of the methodology. Copyright © 2005 John Wiley & Sons, Ltd.     

THE INFLUENCE OF TOPOGRAPHY ON TIME AND SPACE DISTRIBUTION OF SOIL SURFACE WATER CONTENT

The distribution of water content in time and space at the soil surface has been investigated on a small farmland catchment (1.3 km² ) from four field surveys corresponding to different moisture statuses. For each survey, about 400 samples were collected at the soil surface at a depth of 5 cm along ten axes parallel to the greatest slope. The relationship between the measurements and the topography has been analysed. The structure of the data is well explained by a topographic index referring to the downslope conditions and defined as the elevation difference between the sample point and the stream point corresponding to the outlet of the water pathway derived from the digital elevation model (DEM). This index can be considered as an hydraulic head, at least for saturated conditions. A threshold for this index allows two domains within the catchment to be distinguished; an upper domain where the water content is nearly constant and varies slowly, and a lower domain where moisture status increases and is highly variable. The spatial distribution of these two domains is well correlated to the spatial distribution of the soils. Thus, both topography and the spatial distribution of soil appear to control the spatial distribution of surface water content at the 1-km² scale. © 1997 by John Wiley & Sons Ltd.     

A conceptual hydrologic model for a forested Carolina bay depressional wetland on the Coastal Plain of South Carolina,USA

This paper describes how climate influences the hydrology of an ephemeral depressional wetland. Surface water and groundwater elevation data were collected for 7 years in a Coastal Plain watershed in South Carolina USA containing depressional wetlands, known as Carolina bays. Rainfall and temperature data were compared with water‐table well and piezometer data in and around one wetland. Using these data a conceptual model was created that describes the hydrology of the system under wet, dry, and drought conditions. The data suggest this wetland operates as a focal point for groundwater recharge under most climate conditions. During years of below‐normal to normal rainfall the hydraulic gradient indicated the potential for groundwater recharge from the depression, whereas during years of above‐normal rainfall, the hydraulic gradient between the adjacent upland, the wetland margin, and the wetland centre showed the potential for groundwater discharge into the wetland. Using high‐resolution water‐level measurements, this groundwater discharge condition was found to hold true even during individual rainfall events, especially under wet antecedent soil conditions. The dynamic nature of the hydrology in this Carolina bay clearly indicates it is not an isolated system as previously believed, and our groundwater data expand upon previous hydrologic investigations at similar sites which do not account for the role of groundwater in estimating the water budget of such systems. Copyright © 2007 John Wiley & Sons, Ltd.     

Temporal stability of soil water content as affected by climate and soil hydraulic properties: a simulation study

Temporal stability of soil water content (TS SWC) is an often‐observed phenomenon, which characterization finds multiple applications. Climate and variability in soil properties are usually mentioned as factors of TS SWC, but their effects are far from clear. The objective of this work was to use SWC modeling to evaluate the effects of climate and soil hydraulic properties on the TS of soil water at different measurement schedules. We selected four representative climates found in USA and simulated the multiyear SWC dynamics for sandy loam, loam, and silty clay loam soils, all having the lognormal spatial distribution of the saturated hydraulic conductivity. The CLIMGEN and the HYDRUS6 codes were used to generate weather patterns and to simulate SWC, respectively. Four different methods were applied to select the representative location (RL). The low probability of having the same variability of mean relative differences of soil water under different climates was found in most of the cases. The probability that the variance of mean relative differences depended on sampling frequency was generally higher than 91% for the three soils. The interannual difference in mean relative differences variation from short and intensive summer campaigns was highly probable for all climates and soils. The RLs changed as climate and measurement scheduling changed, and they were less pronounced for coarse‐textured soils. The RL selection methods based solely on bias provided more consistency as compared with other methods. The TS appears to be the result of the interplay between climate, soil properties, and survey protocols. One implication of this factor interaction effect on TS SWC is that a simulation study can be useful to decide on the feasibility of including a search for TS‐based RLs for a specific site. Copyright © 2013 John Wiley & Sons, Ltd.     

Effective groundwater–surface water exchange at watershed scales

Coupled groundwater–surface water (GW–SW) models are capable of simulating complex hydrological systems when used at fine resolutions. However, properly characterizing bulk GW–SW fluxes for either coarsely resolved integrated models or basin‐discretized surface water models remains a challenge. Loss of subgrid detail, while beneficially decreasing computational cost, leads to a decrease in model accuracy as scale effects become important. Ideally, coarse low‐resolution models should be informed by expected subgrid behaviour, reducing the impact of scale effects. Determining how to best represent these fine‐scale details in lower‐resolution models is important for improving the accuracy and appropriateness of these models. To investigate some of these scale effects, we here explore the relationships between area‐averaged hydraulic head and bulk GW–SW exchange fluxes (e.g. evapotranspiration and discharge), all of which are presumed to be controlled predominantly by subgrid topographic effects. These relationships may be useful for simply upscaling models without the complete loss of crucial fine‐resolution subgrid details. Using finely resolved simulation output from Modflow for a fine‐resolution simulation and post‐processed results generated to represent coarser resolutions, upscaled flux relationships (UFRs) are generated for multiple terrains; these UFRs define the relationships that exist between average hydraulic head and average fluxes in unconfined aquifer systems. It is found that, for steady‐flow regimes, similar one‐to‐one power law relationships consistently exist between area‐averaged hydraulic heads, exchange fluxes and saturated area for a variety of terrains. Additionally, when the averaged values are properly normalized, the generated steady‐state UFRs for a single terrain are independent of hydraulic conductivity and potential evapotranspiration rates and apparently insensitive to the presence of mild heterogeneity. While some hysteresis is apparent in the relationships under transient conditions, transient artefacts are shown to be minor under some circumstances, indicating that UFRs may be applied to both steady‐state and transient scenarios. Simpler tests performed under saturated and variably saturated conditions in a cross‐sectional model show similar trends, suggesting that the UFR representation is extendable to systems where the vadose zone plays a significant role. It is suggested that relatively simple UFRs such as these may find use as an alternative to direct point upscaling or multi‐resolution models for estimating GW–SW exchange fluxes in coarse‐scale models. They also appear to justify the functional form of some classical models of baseflow and evapotranspiration used in conceptual surface water models. Copyright © 2015 John Wiley & Sons, Ltd.     

Influence of heterogeneity on unsaturated hydraulic properties: (1) local heterogeneity and scale effect

Spatial heterogeneity is ubiquitous in nature, which may significantly affect the soil hydraulic property curves. The models of a closed‐form functional relationship of soil hydraulic property curves (e.g. VG model or exponential model) are valid at point or local scale based on a point‐scale hydrological process, but how do scale effects of heterogeneity have an influence on the parameters of these models when the models are used in a larger scale process? This paper uses a two‐dimensional variably saturated flow and solute transport finite element model (VSAFT2) to simulate variations of pressure and moisture content in the soil flume under a constant head boundary condition. By changing different numerical simulation block sizes, a quantitative evaluation of parameter variations in the VG model, resulting from the scale effects, is presented. Results show that the parameters of soil hydraulic properties are independent of scale in homogeneous media. Parameters of α and n in homogeneous media, which are estimated by using the unsaturated hydraulic conductivity curve (UHC) or the soil water retention curve (WRC), are identical. Variations of local heterogeneities strongly affect the soil hydraulic properties, and the scale affects the results of the parameter estimations when numerical experiments are conducted. Furthermore, the discrepancy of each curve becomes considerable when moisture content becomes closer to a dry situation. Parameters estimated by UHC are totally different from the ones estimated by WRC. Copyright © 2012 John Wiley & Sons, Ltd.