Richards Equation-based Model Research Articles

Dynamic and empirical methods for field capacity estimation in fine textured soils with a coarse interlayer

Field capacity (FC) is an important soil hydraulic concept in soil science and irrigation management. It is generally determined from soil water content in a soil layer when soil profile reaches a steady pressure head or negligible drainage flux from an initially saturated soil. However, the proposed criteria are mainly tested for uniform soils and vary with soil textures. To quantify FC in layered soils, a Richards equation-based model was used to describe water flow in fine-textured soils with a coarse interlayer. With calibrated soil hydraulic parameters for loam and sand from infiltration measurements, drainage from saturation was simulated in the loam with a sand interlayer. A relative drainage rate (δ) was defined as a function of water storage and drainage flux to analyze soil water status at FC. Soil water content in the upper loam layer of layered profiles was improved compared with that in the uniform loam, which was negatively correlated with buried depth but positively correlated with thickness of the sand layer for a specified δ. Under different buried depths and thicknesses, soil water content decreased with the decline of δ and decreased rapidly as δ reduced to 1 % d−1. The drainage flux at δ = 1 % d−1 changed within a range of 0.056–0.26 cm d−1, and soil water content reached to 0.278–0.346 cm3 cm−3, which accounted for 70–87 % of the saturated water content of loam. Although the FC in the upper fine-textured soil layer varied for different buried depths and thicknesses of coarse interlayer, the proposed dynamic method is reliable and universal to estimate the FC in the above layered soils at δ = 1 % d−1. An empirical equation was also developed to calculate the FC in fine-textured soils with different buried depths and thicknesses of a coarse interlayer based on the critical δ value.

Parameterizing field capacity as the upper limit of available water in bucket-type hydrological models

• FC was calibrated in a bucket model (BM) to best mimic a Richards equation-based model. • FC calibrated for BM depended on soil, crop, and was strongly influenced by climate type. • FC calibrated for BM was more than one pF-unit closer to saturation than what is usually considered. • Pressure heads commonly used for FC underestimated crop available water in BM. Field capacity (FC) was originally defined as a soil profile property without relation to crop water uptake. Nevertheless, it has been frequently used as the upper limit for available water in bucket-type models. We aimed to find the value of FC in the bucket-type model WOFOST that best simulates the water balance predicted by the Richards equation-based model SWAP, here considered as a benchmark. With an equal description of plant growth, we calibrated FC in WOFOST by minimizing the root mean square deviation between selected outputs (targets) from WOFOST and SWAP. The calibrated FC value depended on the target, soil type, climate, and crop drought sensitivity. Using common soil-based values for FC, available water was underestimated up to 60%. Crop production parameters were insensitive to FC, and although best values for FC were close to saturation, crop production results were similar to employing a common pF value between 1.0 and 2.0.

Polynomial functions to predict flux-based field capacity from soil hydraulic parameters

We propose two new polynomials as pedotransfer function, PTF, to predict the flux-based Field Capacity water content, ΘFC. The inputs for the PTF are the bottom flux criterium, the profile depth, and the retention and conductivity parameters of the Van Genuchten – Mualem model, VGM. A first polynomial was developed including all VGM parameters and a second polynomial considers VGM parameter l equal to 0.5, the most commonly applied value. The polynomials were built using stepwise multiple linear regression and a generated dataset over a wide range of VGM model parameters. The “observed values” for the polynomial calibration were acquired from internal drainage simulations performed by the Richards equation-based model SWAP. The derived polynomials predicted the simulated ΘFC with high accuracy. The RMSD between observed and predicted ΘFC on tested datasets, for the complete version and the l = 0.5 polynomial version were, respectively, 0.01912 and 0.01362. The proposed polynomials may be combined with other PTFs providing the VGM parameters from texture and/or other basic data. Examples of predicted FC water content and pF are shown on texture triangles using the Rosetta PTF to predict VGM parameters from soil texture data. For stand-alone use, the polynomials allow predicting the flux-based ΘFC from VGM parameters without the need for numerical simulations.

Wave-driven Groundwater Flows in Sandy Beaches: A Richards Equation-based Model

Clément, J.-B.; Sous, D.; Golay, F. and Ersoy M., 2020. Wave-driven groundwater flows in sandy beaches: A Richards equation-based model. In: Malvárez, G. and Navas, F. (eds.), Global Coastal Issues of 2020. Journal of Coastal Research, Special Issue No. 95, pp. 1047–1051. Coconut Creek (Florida), ISSN0749-0208.A groundwater model is developed to simulate flows under the swash zone of sandy beach. Variably saturated beach is described by Richards equation, which is solved by the Rivage code thanks to a discontinuous Galerkin method. The SWASH code is used to simulate wave propagation in nearshore waters and compute suitable boundary conditions at the beachface to force Richards equation. An idealized case is considered to investigate the beach groundwater response to the action of swash cycles associated with long IG-like waves: infiltration/ exfiltration, water table, hydraulic head and pore velocities are outlined. A good qualitative agreement is found with observations from experimental studies in the literature.

Machine Learning vs. Physics-Based Modeling for Real-Time Irrigation Management

Real-time monitoring of soil matric potential has now become a common practice for precision irrigation management. Some crops, such as cranberries, are susceptible to both water and anoxic stresses. Excessive variations in soil matric potential in the root zone may reduce plant transpiration, due to either saturated or dry soil conditions, thereby reducing productivity. A timely supply of the right amount of water is, therefore, fundamental for efficient irrigation management. In this paper, we compare the capabilities of a machine learning-based model and a physics-based model to predict soil matric potential in the root zone. The machine learning model is a random forest algorithm, while the physics-based model is a two-dimensional solver of Richards equation (HYDRUS 2D). After training and calibration on a dataset collected in a cranberry field located in Quebec (Canada), the performance of the two models is evaluated for 30 different time frames of 72-h soil matric potential forecasts. The results highlight that both models can accurately forecast the soil matric potential in the root zone. The machine learning-based model can achieve better performance when compared to the physics-based model, but forecasting accuracy decreases rapidly toward the end of the 72-h lead time, while the error for the Richards equation-based model does not increase with time and remain small compared to the typical measurement error.

A Modified Green-Ampt Model and Parameter Determination for Water Infiltration in Fine-textured Soil with Coarse Interlayer

A modified Green-Ampt model was developed to simulate water infiltration in fine-textured soil with a coarse interlayer. Because under such a soil structure, the two soils may not be fully saturated during infiltration, the model introduced two parameters—that is, the saturation coefficients a and b, to reflect the incomplete saturation condition and their influence on infiltration processes. In order to analyze the variation pattern of the two parameters in the above proposed model, scenarios were set for soil column infiltration in fine-textured soil with a coarse interlayer under different buried depths. A Richards equation-based model (RE-Model) was built for simulating the above scenarios and to obtain the evolution of soil water content along the soil profiles. Simulation results show that the infiltration rate decreased to a constant value when the wetting front crossed the upper interface between the fine and coarse soil layer. The soil matrix suction (ψ2) at the upper interface remained unchanged after the wetting front advanced into the coarse layer, and the steady value of ψ2 showed a linear relationship with the buried depth of the coarse layer. Based on the simulation results of the RE-Model, a method was proposed to determine the saturation coefficients related to the relative hydraulic conductivity and water content at ψ2 in the modified Green-Ampt model. Then, the modified model was tested under various infiltration conditions with different soil layered structures, and the results showed good agreement with the experimental data.

Transient unsaturated flow in the drainage layer of a highway: solution and drainage performance

In order to quickly remove water entering pavement layers so as to mitigate water-induced damage, drainage layers are widely used in highway pavements. This paper introduces a 1-D mathematical model in order to quantify the transient behaviour of the groundwater flow in the drainage layer of highway pavements. The model takes into account the capillary effect and the nonlinear relationship between hydraulic conductivity and saturation. The analytical solution is obtained and validated against the 2-D Richards equation-based model. Then, sensitivity analysis is carried out and the results show that the drainage time is reduced and drainage efficiency is enhanced by capillarity. The drainage capacity (the total water drained from the drainage layer) depends on the water retention curve (e.g. αG in the Gardner equation). In view of material selection, a relatively low value of αG helps improve the drainage capacity of the drainage layer, whereas a suitable amount of fine particles also leads to a better drainage performance. Furthermore, the drainage material with hydraulic properties is recommended in terms of drainage performance improvement and strength requirement. The analytical solution, which is simple and easy to use, provides guidance for assessing the capillary effects on the effectiveness and efficiency of subsurface drainage systems of a highway.

An analytical solution for predicting the transient seepage from a subsurface drainage system

Subsurface drainage systems have been widely used to deal with soil salinization and waterlogging problems around the world. In this paper, a mathematical model was introduced to quantify the transient behavior of the groundwater table and the seepage from a subsurface drainage system. Based on the assumption of a hydrostatic pressure distribution, the model considered the pore-water flow in both the phreatic and vadose soil zones. An approximate analytical solution for the model was derived to quantify the drainage of soils which were initially water-saturated. The analytical solution was validated against laboratory experiments and a 2-D Richards equation-based model, and found to predict well the transient water seepage from the subsurface drainage system. A saturated flow-based model was also tested and found to over-predict the time required for drainage and the total water seepage by nearly one order of magnitude, in comparison with the experimental results and the present analytical solution. During drainage, a vadose zone with a significant water storage capacity developed above the phreatic surface. A considerable amount of water still remained in the vadose zone at the steady state with the water table situated at the drain bottom. Sensitivity analyses demonstrated that effects of the vadose zone were intensified with an increased thickness of capillary fringe, capillary rise and/or burying depth of drains, in terms of the required drainage time and total water seepage. The analytical solution provides guidance for assessing the capillary effects on the effectiveness and efficiency of subsurface drainage systems for combating soil salinization and waterlogging problems.

Boussinesq Equation-Based Model for Flow in the Drainage Layer of Highway with Capillarity Correction

The current engineering design of the highway drainage layer is typically based on the groundwater table elevation predicted by saturated flow models. Capillary effects may become significant, with unsaturated flow playing an important role in conducting water out of the drainage layer. With the capillarity neglected, saturated flow models such as the Boussinesq equation-based model (BM) and the Laplace equation-based model (LM) over predict the groundwater table elevation. This paper aims to modify the traditional BM to account for the capillary effects on the drainage. A correction term was added to the BM to incorporate predominantly horizontal flow in the unsaturated zone above the water-table, with vertical flow neglected. Analytical solutions to the governing equation were developed for both flat and sloping drainage layers. The modified model and analytical solutions were validated against predictions of a Richards equation-based model (RM) that simulated the variably saturated flow directly. The results showed that the assumption of negligible vertical flow made in the modified Boussinesq equation model (MBM) was sound. With capillary effects incorporated, this model predicted well the behavior of the water-table as simulated by the RM with relative errors typically less than 2% for the base case considered. The improvement made through the capillarity correction will enable the MBM to be used for analyzing and predicting the groundwater table in the design of the highway drainage layer.

Information content and complexity of simulated soil water fluxes

The accuracy-based performance measures may not suffice to discriminate among soil water flow models. The objective of this work was to attempt using information theory measures to discriminate between different models for the same site. The Richards equation-based model HYDRUS-1D and a water budget-type model MWBUS were used to simulate one-year long observations of soil water contents and infiltration fluxes at various depths in a 1-m deep loamy Eutric Regosol in Bekkevoort, Belgium. We used the (a) metric entropy and (b) the mean information gain as information content measures, and (c) the effective measure complexity and (d) the fluctuation complexity as complexity measures. To compute the information content and complexity measures, time series of fluxes were encoded with the binary alphabet; fluxes greater (less) than the median value were encoded with one (zero). Fifty Monte Carlo simulation runs were performed with both models using hydraulic properties measured along a trench. The two models had the similar accuracy of water flux simulations. Precipitation input data demonstrated a moderate complexity and relatively high information content. Model outputs showed distinct differences in their relationships between complexity and information content. Overall, more complex simulated soil flux time series were obtained with the HYDRUS-1D model that was perceived to be conceptually more complex than the WMBUS model. An increase in the complexity of water flux time series occurred in parallel with the decrease in the information content. Using both complexity and information content measures allowed us to discriminate between the soil water models that gave the same accuracy of soil water flux estimates.