Jan W. Hopmans

One‐, two‐, and three‐dimensional root water uptake functions for transient modeling

Although solutions of multidimensional transient water flow can be obtained by numerical modeling, their application may be limited as root water uptake is generally considered to be one- or two-dimensional only. This is especially the case for trees. The first objective of this paper is to test the suitability of a three-dimensional root water uptake model for the simultaneous simulation of transient soil water flow around an almond tree. The soil hydraulic and root water uptake parameters were optimized by minimizing the residuals between measured and simulated water content data. Water content was measured in a three-dimensional grid around a sprinkler-irrigated almond tree for a 16 day period, following irrigation. A second objective was to compare the performance and results of the three-dimensional flow model with one- and two- dimensional root water uptake models. For this purpose, measured water contents were aggregated in the x and y direction in the one-dimensional case and in the radial direction for the two-dimensional uptake model. For the estimation of root water uptake model parameters a genetic algorithm was used to estimate the approximate global minimum of the parameter space, whereas final parameters were determined using the Simplex optimization algorithm. With the optimized root water uptake parameters, simulated and measured water contents during the 16-day period were in excellent agreement for all root water uptake models. Most significantly, the spatial variation in flux density below the rooting zone decreased when reducing multidimensional root water uptake to fewer dimensions, thereby justifying the proposed multidimensional approach.

Simultaneous modeling of transient three-dimensional root growth and soil water flow

A model is presented for the simultaneous, dynamic simulation of soil water movement and plant root growth. Root apices are translocated in individual growth events as a function of current local soil conditions. A three-dimensional finite-element grid over the considered soil domain serves to define the spatial distribution of soil physical properties and as framework for the transient water flow model. Examples illustrate how field-observed morphology of root systems can be approximated by including even a coarsely discretized description of the soil environment. Intended as a tool for testing of hypotheses on soil-plant interaction, simulations can be performed for different levels of model complexity, depending on how much information is available. At the simplest level, root growth is simulated without soil water uptake, whereas the most comprehensive level includes growth of the shoot and dynamic assimilate allocation to root and shoot.

Sustainability of irrigated agriculture in the San Joaquin Valley, California

The sustainability of irrigated agriculture in many arid and semiarid areas of the world is at risk because of a combination of several interrelated factors, including lack of fresh water, lack of drainage, the presence of high water tables, and salinization of soil and groundwater resources. Nowhere in the United States are these issues more apparent than in the San Joaquin Valley of California. A solid understanding of salinization processes at regional spatial and decadal time scales is required to evaluate the sustainability of irrigated agriculture. A hydro-salinity model was developed to integrate subsurface hydrology with reactive salt transport for a 1,400-km2 study area in the San Joaquin Valley. The model was used to reconstruct historical changes in salt storage by irrigated agriculture over the past 60 years. We show that patterns in soil and groundwater salinity were caused by spatial variations in soil hydrology, the change from local groundwater to snowmelt water as the main irrigation water supply, and by occasional droughts. Gypsum dissolution was a critical component of the regional salt balance. Although results show that the total salt input and output were about equal for the past 20 years, the model also predicts salinization of the deeper aquifers, thereby questioning the sustainability of irrigated agriculture.

Transient three-dimensional modeling of soil water and solute transport with simultaneous root growth, root water and nutrient uptake

A three-dimensional solute transport model was developed and linked to a three-dimensional transient model for soil water flow and root growth. The simulation domain is discretized into a grid of finite elements by which the soil physical properties are spatially distributed. Solute transport modeling includes passive and active nutrient uptake by roots as well as zero- and first-order source/sink terms. Root water uptake modeling accounts for matric and osmotic potential effects on water and passive nutrient uptake. Root age effects on root water and nutrient uptake activity have been included, as well as the influence of nutrient deficiency and ion toxicity on root growth. Examples illustrate simulations with different levels of model complexity, depending on the amount of information available to the user. At the simplest level, root growth is simulated as a function of mechanical soil strength only. Application of the intermediate level with root water and nutrient uptake simulates the influence of timing and amount of NO3 application on leaching. The most comprehensive level includes simulation of root and shoot growth as influenced by soil water and nutrient status, temperature, and dynamic allocation of assimilate to root and shoot.

Current Capabilities and Future Needs of Root Water and Nutrient Uptake Modeling

The importance of root function in water and nutrient transport is becoming increasingly clear, as constraints on agricultural resources are imposed due to water limitations and environmental concerns. Both are driven by the increasing need to expand global food production. However, the historical neglect of consideration of water and nutrient uptake processes below ground has created a knowledge gap concerning the plant responses of nutrient and water limitations to crop production. The review includes sections on (i) notation and definitions of water potential, (ii) the physical coupling of plant transpiration and plant assimilation by way of the principles of diffusion of water vapor and carbon dioxide, (iii) apoplastic and symplastic water and nutrient pathways in plants, (iv) active and passive nutrient uptake, and (v) a discussion of the current state-of-the-art in multidimensional soil water flow and chemical transport modeling. The subsequent review of water uptake, nutrient uptake, and simultaneous water and nutrient uptake addresses shortcomings of current theory and modeling concepts. The review concludes with an example illustrating a possible multidimensional approach for simultaneous water and nutrient uptake modeling. Specific recommendations identify the need for coupling water and nutrient transport and uptake, including salinity effects on root water uptake and the provision of simultaneous passive and active nutrient uptake. It considers the requirement for multidimensional dedicated root water and nutrient uptake experiments to validate and calibrate hypothesized coupled root uptake models.

Indirect estimation of soil thermal properties and water flux using heat pulse probe measurements: Geometry and dispersion effects

from 1.0 to >10 m d � 1 . We also demonstrate the general application of inverse modeling to estimate soil thermal properties and their functional dependence on volumetric water content in a separate numerical experiment. We suggest that inverse modeling of HPP temperature data may allow simultaneous estimation of soil water retention (when combined with matric potential measurements) and unsaturated hydraulic conductivity (through water flux estimation) from simple laboratory experiments. INDEX TERMS: 1866 Hydrology: Soil moisture; 1875 Hydrology: Unsaturated zone; 1894 Hydrology: Instruments and techniques; KEYWORDS: Soil water flow; soil heat flow; inverse modeling; dispersivity

Three dimensional imaging of plant roots in situ with X-ray Computed Tomography

X-ray Computed Tomography (CT) is a non-invasive technique that allows forthree-dimensional, nondestructive imaging of heterogeneous materials. Todate, few studies have examined the potential of CT to quantify plant rootsin situ. Pre-germinated bean plants were grown for 14 days in PVC containers(10 cm long×5.0 cm internal diameter) containing a sandy soil medium ina growth chamber under optimum growing conditions. The stems of the beanplants were excised and their root systems imaged with a high-energyindustrial tomography unit (420 kV). Forty individual horizontal tomograms,each 200 μm thick were combined into a 3-D data set for a total rootingdepth of 0.8 cm starting at the base of the hypocotyl. This volumetric dataset was analyzed for root volume through estimation of relative fractions ofroot and soil matrix within each voxel for the entire 3-D data set. Therendering of iso-attenuation surfaces illustrated the spatial arrangement ofroots with diameters equal and larger than 0.36 mm. In addition, bean rootsystems were destructively sampled at 1-cm depth increments and analyzed fordry weight, total root length and root diameter. Destructive root samplingyielded a root length per unit volume (Lv) between 44 and 60 cm cm-3soil, whereas the CT-measured Lv was about 76 cm cm-3.

Parameter estimation of two-fluid capillary pressure–saturation and permeability functions

Abstract Accurate characterization and modeling of subsurface flow in multi-fluid soil systems require development of a rapid, reproducible experimental method that yields the information necessary to determine the parameters of the capillary pressure–saturation and permeability functions. Previous work has demonstrated that parameter optimization using inverse modeling is a powerful approach to indirectly determine these constitutive relationships for air–water systems. We consider extension of the inverse parameter estimation method to the modified multi-step outflow method for two-fluid (air–water, air–oil and oil–water) flow systems. The wellposedness of the proposed parameter estimation problem is evaluated by its accuracy, uniqueness and parameter uncertainty. Seven different parametric models for the capillary pressure–saturation and permeability functions were tested in their ability to fit the multi-step outflow experimental data; these included the van Genuchten–Mualem (VGM) model, van Genuchten–Burdine (VGB), Brooks–Corey–Mualem (BCM), Brooks–Corey–Burdine (BCB), Brutsaert–Burdine (BRB), Gardner–Mualem (GDM) and Lognormal Distribution–Mualem (LNM) models. The VGB, BCM and BCB models fitted the multi-step outflow data poorly, and resulted in relatively large values for the root-mean-squared residuals. It was concluded that the remaining VGM, LNM, BRB and GDM models successfully characterized the multi-step experimental data for two-fluid flow systems. Although having one parameter less than the other models, the GDM models performance was excellent. Finally, we conclude that optimized capillary pressure–saturation functions for the oil–water and air–oil could be predicted from the respective air–water function using interfacial tension ratios.

Quantitative Analysis of Flow Processes in a Sand Using Synchrotron-Based X-ray Microtomography

Pore-scale multiphase flow experiments were developed to nondestructively visualize water flow in a sample of porous material using X-ray microtomography. The samples were exposed to similar boundary conditions as in a previous investigation, which examined the effect of initial flow rate on observed dynamic effects in the measured capillary pressure–saturation curves; a significantly higher residual saturation and higher capillary pressures were found when the sample was drained fast using a high air-phase pressure. Prior work applying the X-ray microtomography technique to pore-scale multiphase flow problems has been of a mostly qualitative nature and no experiments have been presented in the existing literature where a truly quantitative approach to investigating the multiphase flow process has been taken, including a thorough image-processing scheme. The tomographic images presented here show, both by qualitative comparison and quantitative analysis in the form of a nearest neighbor analysis, that the dynamic effects seen in previous experiments are likely due to the fast and preferential drainage of large pores in the sample. Once a continuous drained path has been established through the sample, further drainage of the remaining pores, which have been disconnected from the main flowing water continuum, is prevented.

Reclaiming freshwater sustainability in the Cadillac Desert

Increasing human appropriation of freshwater resources presents a tangible limit to the sustainability of cities, agriculture, and ecosystems in the western United States. Marc Reisner tackles this theme in his 1986 classic Cadillac Desert: The American West and Its Disappearing Water. Reisners analysis paints a portrait of region-wide hydrologic dysfunction in the western United States, suggesting that the storage capacity of reservoirs will be impaired by sediment infilling, croplands will be rendered infertile by salt, and water scarcity will pit growing desert cities against agribusiness in the face of dwindling water resources. Here we evaluate these claims using the best available data and scientific tools. Our analysis provides strong scientific support for many of Reisners claims, except the notion that reservoir storage is imminently threatened by sediment. More broadly, we estimate that the equivalent of nearly 76% of streamflow in the Cadillac Desert region is currently appropriated by humans, and this figure could rise to nearly 86% under a doubling of the regions population. Thus, Reisners incisive journalism led him to the same conclusions as those rendered by copious data, modern scientific tools, and the application of a more genuine scientific method. We close with a prospectus for reclaiming freshwater sustainability in the Cadillac Desert, including a suite of recommendations for reducing region-wide human appropriation of streamflow to a target level of 60%.