Analytical solution for the advection–dispersion transport equation in layered media

The advection–dispersion transport equation with first-order decay was solved analytically for multi-layered media using the classic integral transform technique (CITT). The solution procedure used an associated non-self-adjoint advection–diffusion eigenvalue problem that had the same form and coefficients as the original problem. The generalized solution of the eigenvalue problem for any numbers of layers was developed using mathematical induction, establishing recurrence formulas and a transcendental equation for determining the eigenvalues. The orthogonality property of the eigenfunctions was found using an integrating factor that transformed the non-self-adjoint advection–diffusion eigenvalue problem into a purely diffusive, self-adjoint problem. The performance of the closed-form analytical solution was evaluated by solving the advection–dispersion transport equation for two- and five-layer media test cases which have been previously reported in the literature. Additionally, a solution featuring first-order decay was developed. The analytical solution reproduced results from the literature, and it was found that the rate of convergence for the current solution was superior to that of previously published solutions.Indisponível

Analytical solution of the advection–diffusion transport equation using a change-of-variable and integral transform technique

This paper presents a formal exact solution of the linear advection–diffusion transport equation with constant coefficients for both transient and steady-state regimes. A classical mathematical substitution transforms the original advection–diffusion equation into an exclusively diffusive equation. The new diffusive problem is solved analytically using the classic version of Generalized Integral Transform Technique (GITT), resulting in an explicit formal solution. The new solution is shown to converge faster than a hybrid analytical–numerical solution previously obtained by applying the GITT directly to the advection–diffusion transport equation.Indisponível

Reviews and syntheses : Turning the challenges of partitioning ecosystem evaporation and transpiration into opportunities

Evaporation (E) and transpiration (T) respond differently to ongoing changes in climate, atmospheric composition, and land use. It is difficult to partition ecosystem-scale evapotranspiration (ET) measurements into E and T, which makes it difficult to validate satellite data and land surface models. Here, we review current progress in partitioning E and T and provide a prospectus for how to improve theory and observations going forward. Recent advancements in analytical techniques create new opportunities for partitioning E and T at the ecosystem scale, but their assumptions have yet to be fully tested. For example, many approaches to partition E and T rely on the notion that plant canopy conductance and ecosystem water use efficiency exhibit optimal responses to atmospheric vapor pressure deficit (D). We use observations from 240 eddy covariance flux towers to demonstrate that optimal ecosystem response to D is a reasonable assumption, in agreement with recent studies, but more analysis is necessary to determine the conditions for which this assumption holds. Another critical assumption for many partitioning approaches is that ET can be approximated as T during ideal transpiring conditions, which has been challenged by observational studies. We demonstrate that T can exceed 95% of ET from certain ecosystems, but other ecosystems do not appear to reach this value, which suggests that this assumption is ecosystem-dependent with implications for partitioning. It is important to further improve approaches for partitioning E and T, yet few multi-method comparisons have been undertaken to date. Advances in our understanding of carbon-water coupling at the stomatal, leaf, and canopy level open new perspectives on how to quantify T via its strong coupling with photosynthesis. Photosynthesis can be constrained at the ecosystem and global scales with emerging data sources including solar-induced fluorescence, carbonyl sulfide flux measurements, thermography, and more. Such comparisons would improve our mechanistic understanding of ecosystem water fluxes and provide the observations necessary to validate remote sensing algorithms and land surface models to understand the changing global water cycle.Peer reviewe

Comparison of measured and simulated water storage in dryland terraces of the Loess Plateau, China

In the hilly regions of China, developing sustainable agriculture requires implementing conservation management practices that prevent soil erosion and conserve soil and water resources. In the semiarid northwest Loess Plateau, the primary conservation management practice is terracing. Numerical simulation of soil water dynamics in terraces is potentially an efficient means of investigating the effects of terrace design on moisture retention, but little information is available on the accuracy of such simulations. In this work, we evaluated the accuracy of HYDRUS-2D simulations of water infiltration and redistribution in fallow, level, dryland terraces located in the Loess Plateau. The simulated soil water content distributions were in good agreement with experimental data. Modeling analyses showed that about one-third of the evaporative water losses occurred from the terrace riser surface. To prevent such losses, it is advisable to mulch the riser and minimize the riser surface area. The simulations also demonstrated that with other dimensions equal, wide terraces retain more water on a percentage basis than narrow ones due to a lower evaporating surface area are per unit volume of water storage. With other design considerations being equal, wide beds and minimal riser surface areas will likely enhance water capture and retention. Future analyses of terrace moisture dynamics may additionally include simulations of root water uptake, surface ponding, and runoff.Computer models Soil moisture HYDRUS-2D Terrace Dryland agriculture Conservation

Moving Forward on Remote Sensing of Soil Salinity at Regional Scale

Soil salinity undermines global agriculture by reducing crop yield and impairing soil quality. Irrigation management can help control salinity levels within the soil root-zone. To best manage water and soil resources, accurate regional-scale inventories of soil salinity are needed. The past decade has seen several successful applications of soil salinity remote sensing. Two salinity remote sensing approaches exist: direct assessment based on analysis of surface soil reflectance (the most popular approach), and indirect assessment of root-zone (e.g., 0-1 m) soil salinity based on analysis of crop canopy reflectance. In this perspective paper, we call on researchers and funding agencies to pay greater attention to the indirect approach because it is better suited for surveying agriculturally important lands. A joint effort between agricultural producers, irrigation specialists, environmental scientists, and policy makers is needed to better manage saline agricultural soils, especially because of projected future water scarcity in arid and semi-arid irrigated areas. The remote sensing community should focus on providing the best tools for mapping and monitoring salinity in such areas, which are of vital relevance to global food production

Impact of Drought and Changing Water Sources on Water Use and Soil Salinity of Almond and Pistachio Orchards: 2. Modeling

California is increasingly experiencing drought conditions that restrict irrigation deliveries to perennial nut crops such as almonds and pistachios. During drought, poorer quality groundwater is often used to maintain these crops, but this use often results in secondary salinization that requires skilled management. Process-based models can help improve management guidelines under these challenging circumstances. The main objective of this work was to assess seasonal soil salinity and root water uptake as a function of irrigation water salinity and annual rain amounts. The manuscript presents a comparison of three-year experimental and numerically simulated root zone salinities in and below the root zone of almond and pistachio drip-irrigated orchards at multiple locations in the San Joaquin Valley (SJV), California, with different meteorological characteristics. The HYDRUS-1D numerical model was calibrated and validated using field measurements of soil water contents and soil solute bulk electrical conductivities at four root zone depths and measured soil hydraulic conductivities. The remaining soil hydraulic parameters were estimated inversely. Observations and simulations showed that the effects of rain on root zone salinity were higher in fields with initially low salinities than in fields with high salinities. The maximum reduction in simulated root water uptake (7%) occurred in response to initially high soil salinity conditions and saline irrigation water. The minimum reduction in simulated water uptake (2.5%) occurred in response to initially low soil salinity conditions and a wet rain year. Simulated water uptake reductions and leaching fractions varied at early and late times of the growing season, depending on irrigation water salinity. Root water uptake reduction was highly correlated with the cumulative effects of using saline waters in prior years, more than salt leaching during a particular season, even when rain was sufficient to leach salts during a wet year

Workflow to establish time-specific zones in precision agriculture by spatiotemporal integration of plant and soil sensing data

Management zones (MZs) are used in precision agriculture to diversify agronomic management across a field. According to current common practices, MZs are often spatially static: they are developed once and used thereafter. However, the soil⁻plant relationship often varies over time and space, decreasing the efficiency of static MZ designs. Therefore, we propose a novel workflow for time-specific MZ delineation based on integration of plant and soil sensing data. The workflow includes four steps: (1) geospatial sensor measurements are used to describe soil spatial variability and in-season plant growth status; (2) moving-window regression modelling is used to characterize the sub-field changes of the soil⁻plant relationship; (3) soil information and sub-field indicator(s) of the soil⁻plant relationship (i.e., the local regression slope coefficient[s]) are used to delineate time-specific MZs using fuzzy cluster analysis; and (4) MZ delineation is evaluated and interpreted. We illustrate the workflow with an idealized, yet realistic, example using synthetic data and with an experimental example from a 21-ha maize field in Italy using two years of maize growth, soil apparent electrical conductivity and normalized difference vegetation index (NDVI) data. In both examples, the MZs were characterized by unique combinations of soil properties and soil⁻plant relationships. The proposed approach provides an opportunity to address the spatiotemporal nature of changes in crop genetics × environment × management interactions