Multi‐scale assimilation of root zone soil water predictions

When hydrology model parameters are determined, a traditional data assimilation method (such as Kalman filter) and a hydrology model can estimate the root zone soil water with uncertain state variables (such as initial soil water content). The simulated result can be quite good. However, when a key soil hydraulic property, such as the saturated hydraulic conductivity, is overestimated or underestimated, the traditional soil water assimilation process will produce a persistent bias in its predictions. In this paper, we present and demonstrate a new multi‐scale assimilation method by combining the direct insertion assimilation method, particle swarm optimisation (PSO) algorithm and Richards equation. We study the possibility of estimating root zone soil water with a multi‐scale assimilation method by using observed in situ data from the Wudaogou experiment station, Huaihe River Basin, China. The results indicate there is a persistent bias between simulated and observed values when the direct insertion assimilation surface soil water content is used to estimate root zone soil water contents. Using a multi‐scale assimilation method (PSO algorithm and direct insertion assimilation) and an assumed bottom boundary condition, the results show some obvious improvement, but the root mean square error is still relatively large. When the bottom boundary condition is similar to the actual situation, the multi‐scale assimilation method can well represent the root zone soil water content. The results indicate that the method is useful in estimating root zone soil water when available soil water data are limited to the surface layer and the initial soil water content even when the soil hydraulic conductivities are uncertain. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Robust data assimilation in hydrological modeling – A comparison of Kalman and H-infinity filters

Hydrological model and observation errors are often non-Gaussian and/or biased, and the statistical properties of the errors are often unknown or not fully known. Thus, determining the true error covariance matrices is a challenge for data assimilation approaches such as the most widely used Kalman filter (KF) and its extensions, which assume Gaussian error nature and need fully known error statistics. This paper introduces H-infinite filter (HF) to hydrological modeling and compares HF with KF under various model and observation error conditions. HF is basically a robust version of KF. When model performance is not well known, or changes unpredictably, HF may be preferred over KF. HF is especially suitable for the cases where the estimation performance in the worst error case needs to be guaranteed. Through the application of HF to a hypothetical hydrologic model, this paper shows that HF is less sensitive to the uncertainty in the initial condition, corrects system bias more effectively, and converges to true state faster after interruptions than KF. In particular, HF performs better in dealing with instant human inputs (irrigation is used as an example), which are characterized by non-stationary, non-Gaussian and not fully known errors. However HF design can be more difficult than KF design due to the sensitivity of HF performance to design parameters (weights for model and observation error terms). Through sensitivity analysis, this paper shows the existence of a certain range of those parameters, in which the “best” value of the parameters is located. The tuning of HF design parameters, which can be based on users’ prior knowledge on the nature of model and observation errors, is critical for the implementation of HF.     

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.     

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.     

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.     

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.     

A calibration and temperature correction procedure for the water‐content reflectometer

Calibration is required for most soil moisture sensors if accurate measurements are to be obtained. This can be time consuming and costly, especially if field calibration is undertaken, but can be facilitated by a good understanding of the behaviour of the particular sensor being calibrated. We develop generalized temperature correction and soil water calibration relationships for Campbell Scientific CS615 water‐content reflectometer sensors. The temperature correction is estimated as a function of the raw sensor measurement. The calibration relationship requires one soil‐related parameter to be set. These relationships facilitate field calibration of these sensors to acceptable accuracies with only a small number of samples. Copyright © 2005 John Wiley & Sons, Ltd.     

Estimation of soil hydraulic properties and their uncertainty: comparison between laboratory and field experiment

Often the soil hydraulic parameters are obtained by the inversion of measured data (e.g. soil moisture, pressure head, and cumulative infiltration, etc.). However, the inverse problem in unsaturated zone is ill‐posed due to various reasons, and hence the parameters become non‐unique. The presence of multiple soil layers brings the additional complexities in the inverse modelling. The generalized likelihood uncertainty estimate (GLUE) is a useful approach to estimate the parameters and their uncertainty when dealing with soil moisture dynamics which is a highly non‐linear problem. Because the estimated parameters depend on the modelling scale, inverse modelling carried out on laboratory data and field data may provide independent estimates. The objective of this paper is to compare the parameters and their uncertainty estimated through experiments in the laboratory and in the field and to assess which of the soil hydraulic parameters are independent of the experiment. The first two layers in the field site are characterized by Loamy sand and Loamy. The mean soil moisture and pressure head at three depths are measured with an interval of half hour for a period of 1 week using the evaporation method for the laboratory experiment, whereas soil moisture at three different depths (60, 110, and 200 cm) is measured with an interval of 1 h for 2 years for the field experiment. A one‐dimensional soil moisture model on the basis of the finite difference method was used. The calibration and validation are approximately for 1 year each. The model performance was found to be good with root mean square error (RMSE) varying from 2 to 4 cm³ cm^?3. It is found from the two experiments that mean and uncertainty in the saturated soil moisture (θ_s) and shape parameter (n) of van Genuchten equations are similar for both the soil types. Copyright © 2010 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.     

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.     

Method development for estimating soil organic carbon content in an alpine region using soil moisture data

The high soil organic carbon(SOC) content in alpine meadow can significantly change soil hydrothermal properties and further affect the soil temperature and moisture as well as the surface water and energy budget. Therefore, this study first introduces a parameterization scheme to describe the effect of SOC content on soil hydraulic and thermal parameters in a land surface model(LSM), and then the SOC content is estimated by minimizing the difference between observed and simulated surface-layer soil moisture. The accuracy of the estimated SOC content was evaluated using in situ observation data at a soil moisture and temperature-measuring network in Naqu, central Tibetan Plateau. Sensitivity experiments show that the optimum time window for stabilizing the estimation results cannot be shorter than three years. In the experimental area, the estimated SOC content can generally reflect the spatial distribution of the measurements, with a root mean square error of 0.099 m^3 m^-3, a mean bias of 0.043 m^3 m^-3, and a correlation coefficient of 0.695. The estimated SOC content is not sensitive to the temporal frequency of the soil moisture data input. Even if the temporal frequency is as low as that of current soil moisture products derived from passive microwave satellites, the estimation result is still stable. Therefore, by combining a high-quality satellite soil moisture product and a parameter optimization method, it is possible to obtain grid-scale effective parameter values, such as SOC content,for an LSM and improve the simulation ability of the LSM.     

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.     

Effects of the roots of Cynodon dactylon and Schefflera heptaphylla on water infiltration rate and soil hydraulic conductivity

Water infiltration rate and hydraulic conductivity in vegetated soil are two vital hydrological parameters for agriculturists to determine availability of soil moisture for assessing crop growths and yields, and also for engineers to carry out stability calculations of vegetated slopes. However, any effects of roots on these two parameters are not well‐understood. This study aims to quantify the effects of a grass species, Cynodon dactylon, and a tree species, Schefflera heptaphylla, on infiltration rate and hydraulic conductivity in relation to their root characteristics and suction responses. The two selected species are commonly used for ecological restoration and rehabilitation in many parts of the world and South China, respectively. A series of in‐situ double‐ring infiltration tests was conducted during a wet summer, while the responses of soil suction were monitored by tensiometers. When compared to bare soil, the vegetated soil has lower infiltration rate and hydraulic conductivity. This results in at least 50% higher suction retained in the vegetated soil. It is revealed that the effects of root‐water uptake by the selected species on suction were insignificant because of the small evapotranspiration (<0.2 mm) when the tests were conducted under the wet climate. There appears to have no significant difference (less than 10%) of infiltration rates, hydraulic conductivity and suction retained between the grass‐covered and the tree‐covered soil. However, the grass and tree species having deeper root depth and greater Root Area Index (RAI) retained higher suction. Copyright © 2015 John Wiley & Sons, Ltd.     

Simultaneous estimation of surface soil moisture and soil properties with a dual ensemble Kalman smoother

In this paper, a new state-parameter estimation approach is presented based on the dual ensemble Kalman smoother(DEn KS) and simple biosphere model(Si B2) to sequentially estimate both the soil properties and soil moisture profile by assimilating surface soil moisture observations. The Arou observation station, located in the upper reaches of the Heihe River in northwestern China, was selected to test the proposed method. Three numeric experiments were designed and performed to analyze the influence of uncertainties in model parameters, atmospheric forcing, and the model's physical mechanics on soil moisture estimates. Several assimilation schemes based on the ensemble Kalman filter(En KF), ensemble Kalman smoother(En KS), and dual En KF(DEn KF) were also compared in this study. The results demonstrate that soil moisture and soil properties can be simultaneously estimated by state-parameter estimation methods, which can provide more accurate estimation of soil moisture than traditional filter methods such as En KF and En KS. The estimation accuracy of the model parameters decreased with increasing error sources. DEn KS outperformed DEn KF in estimating soil moisture in most cases, especially where few observations were available. This study demonstrates that the DEn KS approach is a useful and practical way to improve soil moisture estimation.     

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.     

Soil macroporosity and infiltration characteristics of a forest podzol

Spatial distribution of soil macroporosity was determined for a forest podzol from tension infiltrometer measurements at the soil surface. Surface‐derived macroporosity values were compared with point infiltration characteristics obtained from soil water content and soil water chemistry measurements during an experimental irrigation, and with parameters of a kinematic wave model applied to soil water content data. Macroporosity estimated by the tension infiltrometer ranged from 0·00087 to 0·0219% of soil volume, and infiltration at these two sites was dominated by propagation of a well‐defined wetting front through the soil profile and bypass flow via soil macropores, respectively. Infiltration at sites with intermediate macroporosities reflected a combination of these two processes, although results were inconclusive at one site owing to lateral flow at the base of the soil profile. There was no agreement between macroporosities estimated by the tension infiltrometer and the kinematic wave model. The maximum soil conductance parameter within the profile at a site, however, was related directly to the surface‐derived macroporosity. The partial agreement between surface‐derived macroporosity estimates and point infiltration characteristics shown here supports the use of tension infiltrometry as a rapid, non‐destructive method of assessing spatial variations in the relative contribution of macropore flow to the infiltration process. Copyright © 2000 John Wiley & Sons, Ltd.     

Ecohydrological modelling in a deciduous boreal forest: Model evaluation for application in non-stationary climates

Soil moisture is an important driver of growth in boreal Alaska, but estimating soil hydraulic parameters can be challenging in this data-sparse region. Parameter estimation is further complicated in regions with rapidly warming climate, where there is a need to minimize model error dependence on interannual climate variations. To better identify soil hydraulic parameters and quantify energy and water balance and soil moisture dynamics, we applied the physically based, one-dimensional ecohydrological Simultaneous Heat and Water (SHAW) model, loosely coupled with the Geophysical Institute of Permafrost Laboratory (GIPL) model, to an upland deciduous forest stand in interior Alaska over a 13-year period. Using a Generalized Likelihood Uncertainty Estimation parameterisation, SHAW reproduced interannual and vertical spatial variability of soil moisture during a five-year validation period quite well, with root mean squared error (RMSE) of volumetric water content at 0.5 m as low as 0.020 cm³/cm³. Many parameter sets reproduced reasonable soil moisture dynamics, suggesting considerable equifinality. Model performance generally declined in the eight-year validation period, indicating some overfitting and demonstrating the importance of interannual variability in model evaluation. We compared the performance of parameter sets selected based on traditional performance measures such as the RMSE that minimize error in soil moisture simulation, with one that is designed to minimize the dependence of model error on interannual climate variability using a new diagnostic approach we call CSMP, which stands for Climate Sensitivity of Model Performance. Use of the CSMP approach moderately decreases traditional model performance but may be more suitable for climate change applications, for which it is important that model error is independent from climate variability. These findings illustrate (1) that the SHAW model, coupled with GIPL, can adequately simulate soil moisture dynamics in this boreal deciduous region, (2) the importance of interannual variability in model parameterisation, and (3) a novel objective function for parameter selection to improve applicability in non-stationary climates.