Search Results (109)

Rainfall-induced landslides are widely distributed in many countries. Rainfall impacts the hydraulic dynamics of groundwater and, therefore, slope stability. We derive an analytical solution of slope stability considering effective rainfall based on the Richards equation. We define effective rainfall as the total volume of rainfall stored within a given range of the unsaturated zone during rainfall events. The slope stability at the depth of interest is provided as a function of effective rainfall. The validity of analytical solutions of system states related to effective rainfall, for infinite slopes of a granite residual soil, is verified by comparing them with the corresponding numerical solutions. Additionally, three approaches to global sensitivity analysis are used to compute the sensitivity of the slope stability to a variety of factors of interest. These factors are the reciprocal of the air-entry value of the soil α, the thickness of the unsaturated zone L, the cohesion of soil c, the internal friction angle ϕ related to the effective normal stress, the slope angle β, the unit weights of soil particles γ_s, and the saturated hydraulic conductivity K_s. The results show the following: (1) The analytical solutions are accurate in terms of the relative differences between the analytical and the numerical solutions, which are within 5.00% when considering the latter as references. (2) The temporal evolutions of the shear strength of soil can be sequentially characterized as four periods: (i) strength improvement due to the increasing weight of soil caused by rainfall infiltration, (ii) strength reduction controlled by the increasing pore water pressure, (iii) strength reduction due to the effect of hydrostatic pressure in the transient saturation zone, and (iv) stable strength when all the soil is saturated. (3) The large α corresponds to high effective rainfall. (4) The factors ranked in descending order of sensitivity are as follows: α > L > c > β > γ_s > K_s > ϕ. Full article

The North China Plain is a crucial agricultural region in China, but irregular precipitation patterns have led to significant water shortages. To address this, analyzing the high-resolution dynamics of root-zone soil moisture transport is essential for optimizing irrigation strategies and improving water resource efficiency. The Richards equation is a robust model for describing soil moisture transport dynamics across multiple soil layers, yet its application at large spatial scales is hindered by its sensitivity to boundary conditions and model parameters. This study introduces a novel approach that, for the first time, employs a continuous time series of near-surface soil moisture as the upper boundary condition in the Richards equation to estimate high-resolution root-zone soil moisture in the North China Plain, thus enabling its large-scale application. Singular spectrum analysis (SSA) was first applied to reconstruct site-specific time series, filling in missing and singular values. Leveraging observational data from 617 monitoring sites across the North China Plain and multiple spatial covariates, we developed a machine learning model to estimate near-surface soil moisture at a 1 km resolution. This high-resolution, continuous near-surface soil moisture series then served as the upper boundary condition for the Richards equation, facilitating the estimation of root-zone soil moisture across the region. The results indicated that the machine learning model achieved a correlation coefficient (R) of 0.92 for estimating spatial near-surface soil moisture. Analysis of spatial covariates showed that atmospheric forcing factors, particularly temperature and evaporation, had the most substantial impact on model performance, followed by static factors such as latitude, longitude, and soil texture. With a continuous time series of near-surface soil moisture, the Richards equation method accurately predicted multi-layer soil moisture and demonstrated its applicability for large-scale spatial use. The model yielded R values of 0.97, 0.78, 0.618, and 0.43, with RMSEs of 0.024, 0.06, 0.08, and 0.11, respectively, for soil layers at depths of 10 cm, 20 cm, 40 cm, and 100 cm across the North China Plain. Full article

Soil structure, a critical indicator of soil quality, significantly influences agricultural productivity by impacting on the soil’s capacity to retain and deliver water, nutrients, and salts. Quantitative study of soil structure has always been a challenge because it involves complex spatial-temporal variability. This study employs multifractal analysis to assess the temporal variation in soil pore distribution, a pivotal factor in soil structure. Field observation data were collected in a sandy loam area of the People’s Victory Canal Irrigation scheme in Henan Province, China. A 200 m × 200 m test plot with five sampling points was used to collect soil samples at three depth layers (10–30 cm, 30–50 cm, and 50–70 cm) for soil water retention curve and particle size composition analysis, with a total of seven sampling events throughout the growing season. The results revealed that while soil particle-size distribution (Particle-SD) showed minor temporal changes, soil pore-size distribution (Pore-SD) experienced significant temporal fluctuations over a cropping season, both following a generalized power law, indicative of multifractal traits. Multifractal parameters of Pore-SD were significantly correlated with soil bulk density, with the strongest correlation in the topsoil layer (10–30 cm). The dynamic changes in soil pore structure suggest potential variations during saturation–unsaturation cycles, which could be crucial for soil water movement simulations using the Richards equation. The study concludes that incorporating time-varying parameters in simulating soil water transport can enhance the accuracy of predictions. Full article

The stand basal area, closely related to age, site quality, and stand density, is an important factor for predicting forest growth and yield. The accurate estimation of site quality is especially a key component in the stand basal area model. We utilized sample plots with Picea asperata Mast. as the dominant species in the multi-period National Forest Inventory (NFI) dataset to establish a site index (SI) model including climate effects through the difference form of theoretical growth equations and mixed-effects models. We combined the SI calculated from the SI model, stand age, and stand density index to construct a basal area growth model for Picea asperata Mast. stands. The results show that the Korf model is the best SI base model for Picea asperata Mast. The mean temperatures in summer and winter precipitation were used as the fixed parameters to construct a nonlinear model. Ultimately, elevation, origin, and region, as random effects, were incorporated into the mixed-effects model. The coefficients (R²) of determination of the base model, the nonlinear model including climate, and the nonlinear mixed-effects model are 0.869, 0.899, and 0.921, with root-mean-square errors (RMSEs) of 1.320, 1.315, and 1.301, respectively. Among the basal area models, the Richards model has higher precision. And the basal area model including an SI incorporating climatic factors had a higher determination coefficient (R²) of 0.918 than that of the model including an SI without considering climatic effects. The mixed-effects model incorporating climatic and topographic factors shows a better fitting performance of SI, resulting in a higher precision of the basal area model. This indicates that in the development of forest growth models, both biophysical and climatic factors should be comprehensively considered. Full article

Lateral flow immunoassay (LFIA) is extensively utilized for point-of-care testing due to its ease of operation, cost-effectiveness, and swift results. This study investigates the flow dynamics and reaction mechanisms in LFIA by developing a three-dimensional model using the Richards equation and porous media transport, and employing numerical simulations through the finite element method. The study delves into the transport and diffusion behaviors of each reaction component in both sandwich LFIA and competitive LFIA under non-uniform flow conditions. Additionally, the impact of various parameters (such as reporter particle concentration, initial capture probe concentrations for the T-line and C-line, and reaction rate constants) on LFIA performance is analyzed. The findings reveal that, in sandwich LFIA, optimizing parameters like increasing reporter particle concentration and initial capture probe concentration for the T-line, as well as adjusting reaction rate constants, can effectively enhance detection sensitivity and broaden the working range. Conversely, in competitive LFIA, the effects are inverse. This model offers valuable insights for the design and enhancement of LFIA assays. Full article

This paper considers the application of a scenario simulation technique to assess subsurface drip irrigation system efficiency while using it to irrigate crops grown under raised bed technology. For simulating purposes, we use a model based on the two-dimensional Richards equation stated in terms of water head in a curvilinear domain. Solutions to problems are obtained using a finite-difference scheme with dynamic time step change. Using the data from pressure measurements obtained while growing potatoes on sandy loess soil in production conditions, we performed a calibration of the model using the particle swarm optimization algorithm. Further, the accuracy of the model was tested and average absolute errors in the range from 3.16 to 5.29 kPa were obtained. Having a calibrated model, we performed a series of simulations with different irrigation pipeline placements determining the configuration under which water losses are minimal. The simulated configuration, under which infiltration losses were minimal, was the installation of pipelines under the raised bed at the depth of 10 cm below the soil surface. The results confirm that the applied technique can be used for decision-making support while designing subsurface drip irrigation systems combined with raised bed growing technology. Full article

In this study, the biomass expansion factor (BEF) method was combined with the tree growth function in order to obtain a more accurate growth function of tree species through the fitting of different growth functions to tree growth, and to determine the characteristics of the forest carbon stock as well as the carbon sink potential of Huangshan National Forest Park (HNFP) in China. The carbon sink potential of each tree species and the integrated influencing factors, such as the stand and soil, were directly represented by structural equation modelling (SEM) to clarify the size and path of each influencing factor against the carbon sink potential. The results showed the following: (1) the logistic growth function fitting results for the seven major tree species in HNFP were better than those from the Richard–Chapman growth function, and the R² was greater than 0.90. (2) In 2014, the total carbon stock of the forest in HNFP was approximately 9.59 × 10⁵ t, and the pattern of carbon density, in general, was higher in the central region and the northeastern region and lower in the northern and southern regions, while the distribution of carbon density was lower in the northern and southern regions. The carbon density pattern generally showed a higher distribution in the central and northeastern regions and a lower distribution in the northern and southern regions; most of the high-carbon-density areas were distributed in blocks, while the low-carbon-density areas were distributed sporadically. (3) The total carbon sink of the forest in HNFP was 8.26 × 10³ t in 2014–2015, and due to the large age structure of the regional tree species, the carbon sinks of each tree species and the total carbon sink of HNFP showed a projected downward trend from 2014 to 2060. (4) For different tree species, the influencing factors on carbon sink potential are not the same, and the main influence factors involve slope position, slope, altitude, soil thickness, etc. This study identified the carbon stock and carbon sink values of the forest in HNFP, and the factors affecting the carbon sink potential obtained by SEM can provide a basis for the selection of new afforestation sites in the region as well as new ideas and methods to achieve peak carbon and carbon neutrality both regionally and nationally in the future. Full article

The dynamic interaction between subsurface flow and soil mechanics is often simplified in the stability assessment of variably saturated landslide-prone hillslopes. The aim of this study is to analyze the impact of conventional simplifications in coupling and modeling strategies on stability assessment of such hillslopes in response to precipitation using the local factor of safety (LFS) concept. More specifically, it investigates (1) the impact of neglecting poroelasticity, (2) transitioning from full coupling between hydrological and mechanical models to sequential coupling, and (3) reducing the two-phase flow system to a one-phase flow system (Richards’ equation). Two rainfall scenarios, with the same total amount of rainfall but two different relatively high (4 mm h⁻¹) and low (1 mm h⁻¹) intensities are considered. The simulation results of the simplified approaches are compared to a comprehensive, fully coupled poroelastic hydromechanical model with a two-phase flow system. It was found that the most significant difference from the comprehensive model occurs in areas experiencing the most transient changes due to rainfall infiltration in all three simplified models. Among these simplifications, the transformation of the two-phase flow system to a one-phase flow system showed the most pronounced impact on the simulated local factor of safety (LFS), with a maximum increase of +21.5% observed at the end of the high-intensity rainfall event. Conversely, using a rigid soil without poroelasticity or employing a sequential coupling approach with no iteration between hydromechanical parameters has a relatively minor effect on the simulated LFS, resulting in maximum increases of +2.0% and +1.9%, respectively. In summary, all three simplified models yield LFS results that are reasonably consistent with the comprehensive poroelastic fully coupled model with two-phase flow, but simulations are more computationally efficient when utilizing a rigid porous media and one-phase flow based on Richards’ equation. Full article

A time stepping quasilinearization approach to the mixed (or coupled) form of one and two dimensional Richards’ equations is developed. For numerical solution of the linear ordinary differential equation (ODE) for 1D case and elliptic for 2D case, obtained after this semidiscretization, a finite volume method is used for direct problems arising on each time level. Next, we propose a version of the decomposition method for the numerical solution of the inverse ODE and 2D elliptic boundary problems. Computational results for some soil types and its related parameters reported in the literature are presented. Full article

Soil moisture is important for understanding climate, water resources, water storage, and land use management. This study used Sentinel-2 (S-2) satellite optical data to retrieve surface soil moisture at a 10 m scale on grassland sites with low hydraulic conductivity soil in a climate dominated by heavy rainfall. Soil moisture was estimated after modifying the Optical Trapezoidal Model to account for mixed land cover in such conditions. The method uses data from a short-wave infra-red band, which is sensitive to soil moisture, and four vegetation indices from optical bands, which are sensitive to overlying vegetation. Scatter plots of these data from multiple, infrequent satellite passes are used to define the range of surface moisture conditions. The saturated and dry edges are clearly non-linear, regardless of the choice of vegetation index. Land cover masks are used to generate scatter plots from data only over grassland sites. The Enhanced Vegetation Index demonstrated advantages over other vegetation indices for surface moisture estimation over the entire range of grassland conditions. In poorly drained soils, the time lag between satellite surface moisture retrievals and in situ sensor soil moisture at depth must be part of the validation process. This was achieved by combining an approximate solution to the Richards’ Equation, along with measurements of saturated and residual moisture from soil samples, to optimise the correlations between measurements from satellites and sensors at a 15 cm depth. Time lags of 2–4 days resulted in a reduction of the root mean square errors between volumetric soil moisture predicted from S-2 data and that measured by in situ sensors, from ~0.1 m³/m³ to <0.06 m³/m³. The surface moisture results for two grassland sites were analysed using statistical concepts based upon the temporal stability of soil water content, an ideal framework for the intermittent Sentinel-2 data in conditions of persistent cloud cover. The analysis could discriminate between different natural drainages and surface soil textures in grassland areas and could identify sub-surface artificial drainage channels. The techniques are transferable for land-use and agricultural management in diverse environmental conditions without the need for extensive and expensive in situ sensor networks. Full article

A mechanistic model was developed to simulate one-dimensional pesticide transport in two-stage vertical flow constructed wetland. The two pesticides taken under study were carbendazim and chlorothalonil. The water flow patterns within the constructed wetland were simulated using the Richards equation. Water content and vertical flux, which are the outputs of the substrate water flow model, were used to calculate the substrate moisture-related parameters and advection term in the solute transport model. The governing solute transport equation took into account a total of six processes: advection, molecular diffusion, dispersion, adsorption to the solid surface, degradation and volatilization. A total of 14 simulation cases, corresponding with available experimental data, were used to calibrate the model, followed by further simulations with standardized influent pesticide concentrations. The simulations indicated that the constructed wetland reached a steady state of pesticide removal after 7 days of operation. Two distinct water flow patterns emerged under saturated and unsaturated conditions. The patterns observed while varying the hydraulic loading rates were similar for each individual saturation condition. Two-factor ANOVA of the simulated data further revealed that the carbendazim and chlorothalonil removal was dependent on the hydraulic loading rates, but it was independent of the influent pesticide concentration. Analysis of the simulated pesticide removal showed that degradation emerged as the predominant removal process over time for both the pesticides. The model developed in this study can be an important tool for the design and construction of treatment wetlands for pesticide removal from wastewater. Full article

Matter grows and self-assembles to produce complex structures such as virus capsids, carbon fullerenes, proteins, glasses, etc. Due to its complexity, performing pen-and-paper calculations to explain and describe such assemblies is cumbersome. Many years ago, Richard Kerner presented a pen-and-paper path integral approach to understanding self-organized matter. Although this approach successfully addressed many important problems, including the yield of fullerene formation, the glass transition temperature of doped chalcogenide glasses, the fraction of boroxol rings in B2O3 glasses, the first theoretical explanation for the empirical recipe of window and Pyrex glass and the understanding of virus capsid self-assembly, it still is not the primary choice when tackling similar problems. The reason lies in the fact that it diverges from mainstream approaches based on the energy landscape paradigm and non-equilibrium thermodynamics. In this context, a critical review is presented, demonstrating that the Richard Kerner method is, in fact, a clever way to identify relevant configurations. Its equations are simplified common physical sense versions of those found in the energy landscape kinetic equations. Subsequently, the utilization of equilibrium Boltzmann factors in the transition Markov chain probabilities is analyzed within the context of local two-level energy landscape models kinetics. This analysis demonstrates that their use remains valid when the local energy barrier between reaction coordinate states is small compared to the thermal energy. This finding places the Richard Kerner model on par with other more sophisticated methods and, hopefully, will promote its adoption as an initial and useful choice for describing the self-agglomeration of matter. Full article

The Chinese fir (Cunninghamia lanceolata) is the largest tree species used for afforestation in China. The purpose of this study was to explore the effects of site quality, stand density, and tree species composition on the growth and yield of mixed Chinese fir forests and to build prediction models for their stand average DBH (diameter at breast height), average height, and volume. Using 430 plots of mixed Chinese fir forests in the Fujian Province of China, the optimal base models for predicting stand average DBH, average height, and volume were selected from the Schumacher, Korf, Logistic, Mitscherlich, and Richards equations. On this basis, the site class index (SCI), stand density index (SDI), and tree species composition coefficient (TSCC) were introduced to improve the model’s performance, and the applicability of the different models was evaluated. The optimal base models for the average DBH, average height, and stand volume of mixed Chinese fir forests all used the Richards equation. The best fitting effect was obtained when the SCI was introduced into parameter a in the average height model, while the inclusion of the TSCC did not improve the model significantly. The fitting effects of the average DBH and stand volume models were both best in the form of y=a1SCIa2[1−exp⁡(−b1SDIb2)t]c when the SCI and SDI were introduced. When the TSCC was further included, the fitting effects of the stand average DBH and volume models were significantly improved, with their R² increased by 47.47% and 58.45%, respectively, compared to the base models. The optimal models developed in this study showed good applicability; the residuals were small and distributed uniformly. We found that the SCI had an impact on the maximum values of the stand average DBH, average height, and volume; the SDI was closely related to the growth rate of the diameter and volume, while the TSCC influenced the maximum values of the stand average DBH and volume. The model system established in this study can provide a reference for the harvest prediction and mixing ratio optimization of mixed Chinese fir forests. Full article

The sustainable exploitation of groundwater resources is a multifaceted and complex problem, which is controlled, among many other factors and processes, by water flow in porous soils and sediments. Modeling water flow in unsaturated, non-deformable porous media is commonly based on a partial differential equation, which translates the mass conservation principle into mathematical terms. Such an equation assumes that the variation of the volumetric water content (θ) in the medium is balanced by the net flux of water flow, i.e., the divergence of specific discharge, if source/sink terms are negligible. Specific discharge is in turn related to the matric potential (h), through the non-linear Darcy–Buckingham law. The resulting equation can be rewritten in different ways, in order to express it as a partial differential equation where a single physical quantity is considered to be a dependent variable. Namely, the most common instances are the Fokker–Planck Equation (for θ), and the Richards Equation (for h). The other two forms can be given for generalized matric flux potential (Φ) and for hydraulic conductivity (K). The latter two cases are shown to limit the non-linearity to multiplicative terms for an exponential K-to-h relationship. Different types of boundary conditions are examined for the four different formalisms. Moreover, remarks given on the physico-mathematical properties of the relationships between K, h, and θ could be useful for further theoretical and practical studies. Full article

To model dynamic systems in various situations results in an ordinary differential equation of the form dydt=g(y,t,θ), where g denotes a function and θ stands for a parameter or vector of unknown parameters that require estimation from observations. In order to consider environmental fluctuations and numerous uncontrollable factors, such as those found in forestry, a stochastic noise process ϵt may be added to the aforementioned equation. Thus, a stochastic differential equation is obtained: dYtdt=f(Yt,t,θ)+ϵt. This paper introduces a method and procedure for parameter estimation in a stochastic differential equation utilising the Richards model, facilitating growth prediction in a forest’s tree population. The fundamental concept of the approach involves assuming that a deterministic differential equation controls the development of a forest stand, and that randomness comes into play at the moment of observation. The technique is utilised in conjunction with the logistic model to examine the progression of an agricultural epidemic induced by a virus. As an alternative estimation method, we present the Random Time Transformation (RTT) method. Thus, this paper’s primary contribution is the application of the RTT method to estimate the Richards model, which has not been conducted previously. The literature often uses the logistic or Gompertz models due to difficulties in estimating the parameter form of the Richards model. Lastly, we assess the effectiveness of the RTT Method applied to the Chapman–Richards model using both simulated and real-life data. Full article