A numerical hillslope hydrodynamic model is of great importance in facilitating the understanding of rainfall-runoff mechanism.However,most of the currently existing models do not consider the effect of coupled hydrod...A numerical hillslope hydrodynamic model is of great importance in facilitating the understanding of rainfall-runoff mechanism.However,most of the currently existing models do not consider the effect of coupled hydrodynamic processes as runoff,subsurface flow or groundwater flow.In this study,the Tsinghua Hillslope Runoff Model based on multiple hydrodynamic process,THRM model,is developed,which couples with Saint Venant equation for surface runoff and Richards equation for variably saturated soil water movement(including subsurface flow and groundwater flow).A finite difference scheme with improved boundary conditions is adopted in this research.It is revealed from the simulation that the THRM model has a high computational efficiency and stability in simulating subsurface flow of the experimental hillslope,which is valuable in assessing the hillslope runoff generation mechanism.A model based sensitivity analysis is also carried out.The impact of boundary condition,grid size and initial soil moisture on simulation result and model stability are revealed,which provides insightful references to understand the mechanism of subsurface flow.展开更多
The rubber tree physiological and ecological process quantitatively described by using mathematical method is an important means to the analysis of rubber tree growth process and mechanism. The study on growth simulat...The rubber tree physiological and ecological process quantitatively described by using mathematical method is an important means to the analysis of rubber tree growth process and mechanism. The study on growth simulation model of rubber tree will lay the foundation for the application of rubber tree cultivation intelligent decision system. A Richards equation was formulated to describe the height and stem diameter growth dynamics of the annual rubber seedlings. An area correlation analysis was done according to the closeness of the observed parameters to the dynamic curve on the gray system composed of the seedling growth increment and the meteorological factors including aerial temperature, precipitation and solar radiation hours that influence upon the seedling growth. The results showed that rubber seedling response fitted the Richards equation quite well. The growth increment displayed a distinct alternation of 'slow—fast—slow— fast—slow' rhythm. The growth course of the seedlings might be partitioned into three periods of time by the sequential clustering analysis, namely pre-growing, fast-growing, late-growing stage. The tray correlation analysis revealed that air temperature had the most significant influence while precipitation had the least impact on height growth of the rubber seedlings. In conclusion, the air temperature had the most significant influence while solar radiation hours had the least impact on stem diameter growth of the rubber seedlings.展开更多
We obtain the global attractivity and global asymptotical stability of positive equilibria to a 3-dimensional Richards model with delays. Our results do not depend on the size-asymmetry parameter which measures the de...We obtain the global attractivity and global asymptotical stability of positive equilibria to a 3-dimensional Richards model with delays. Our results do not depend on the size-asymmetry parameter which measures the degree of the curvature of size-growth among individuals over the entire growth curve, and the shape parameter which affects the shape of model curve. Lastly, we gave a numerical simulation to verify the feasibility of our main results.展开更多
Machine learning(ML)provides a new surrogate method for investigating groundwater flow dynamics in unsaturated soils.Traditional pure data-driven methods(e.g.deep neural network,DNN)can provide rapid predictions,but t...Machine learning(ML)provides a new surrogate method for investigating groundwater flow dynamics in unsaturated soils.Traditional pure data-driven methods(e.g.deep neural network,DNN)can provide rapid predictions,but they do require sufficient on-site data for accurate training,and lack interpretability to the physical processes within the data.In this paper,we provide a physics and equalityconstrained artificial neural network(PECANN),to derive unsaturated infiltration solutions with a small amount of initial and boundary data.PECANN takes the physics-informed neural network(PINN)as a foundation,encodes the unsaturated infiltration physical laws(i.e.Richards equation,RE)into the loss function,and uses the augmented Lagrangian method to constrain the learning process of the solutions of RE by adding stronger penalty for the initial and boundary conditions.Four unsaturated infiltration cases are designed to test the training performance of PECANN,i.e.one-dimensional(1D)steady-state unsaturated infiltration,1D transient-state infiltration,two-dimensional(2D)transient-state infiltration,and 1D coupled unsaturated infiltration and deformation.The predicted results of PECANN are compared with the finite difference solutions or analytical solutions.The results indicate that PECANN can accurately capture the variations of pressure head during the unsaturated infiltration,and present higher precision and robustness than DNN and PINN.It is also revealed that PECANN can achieve the same accuracy as the finite difference method with fewer initial and boundary training data.Additionally,we investigate the effect of the hyperparameters of PECANN on solving RE problem.PECANN provides an effective tool for simulating unsaturated infiltration.展开更多
The objective of the present study was to develop a computer software for simulating the temporal development of plant disease epidemics using Richards, logistic, Gompertz, monomolecular, and exponential functions, re...The objective of the present study was to develop a computer software for simulating the temporal development of plant disease epidemics using Richards, logistic, Gompertz, monomolecular, and exponential functions, respectively, and for predicting disease with a fitted model. The software was programmed using Visual Basic （VB6.0） and packaged with the Wise Installation System. The Fibonacci （＇0.618＇） section strategy was used to find out the most appropriate value for the shape parameter （m） in Richards function simulation through looping procedures. The software program was repeatedly tested, debugged and edited until it was run through favorably and produced ideal outputs. It was named Epitimulator based on the phrase ＇epidemic time simulator＇ and has been registered by the National Copyright Department of China （Reg. no. 2007SR18489）. It can be installed and run on personal computers with all versions of Windows operational systems. Data of disease index and survey time are keyed in or imported from Access files. The output of fitted models and related data of parameters can be pasted into Microsoft Excel worksheet or into Word document for editing as required and the simulated disease progress curves can be stored in separate graphic files. After being finally tested and completed, Epitimulator was applied to simulate the epidemic progress of corn northern leaf blight （Exserohilum turcicum） with recorded data from field surveys of corn crops and the fitted models were output. Comparison of the simulation results showed that the disease progress was always best described by Richards function, which resulted in the most accurate simulation model. Result also showed that forecast of northern leaf blight development was highly accurate by using the computed progress model from Richards function.展开更多
A numerical model of two-dimensional soil water movement under surface drip irrigation condition was developed. The physical process of soil water movement is described by 2D Richards equation,and the upper boundary c...A numerical model of two-dimensional soil water movement under surface drip irrigation condition was developed. The physical process of soil water movement is described by 2D Richards equation,and the upper boundary condition is depicted by the improved moving ponded area boundary. The partial differential equation(PDE) is transformed into ordinary differential equations(ODEs) through spatial semi-discretization and numerically solved by an ordinary differential equation solver(CVODE) . The numerical and field experiments indicate the good performance of the model in terms of accuracy and efficiency. The model provides a useful tool for long-term simulation of soil water movement under surface drip irrigation. Also,the model can serve as a general 2D Richards equation solver for variably saturated soil water movement,which is named as TIVS model(Tsinghua Integrated Variably Saturated soil water movement model).展开更多
Scale adaptable hydrological models have attracted more and more attentions in the hydrological modeling research community, and the constitutive relationship at the macro-scale is one of the most important issues, up...Scale adaptable hydrological models have attracted more and more attentions in the hydrological modeling research community, and the constitutive relationship at the macro-scale is one of the most important issues, upon which there are not enough research activities yet. Taking the constitutive relationships of soil water movement--soil water retention curve (SWRC) as an example, this study extends the definition of SWRC at the micro-scale to that at the macro-scale, and aided by Monte Carlo method we demonstrate that soil property and the spatial distribution of soil moisture will affect the features of SWRC greatly. Furthermore, we assume that the spatial distribution of soil moisture is the result of self-organization of climate, soil, ground water and soil water movement under the specific boundary conditions, and we also carry out numerical experiments of soil water movement at the vertical direction in order to explore the relationship between SWRC at the macro-scale and the combinations of climate, soil, and groundwater. The results show that SWRCs at the macro-scale and micro-scale presents totally different features, e.g., the essential hysteresis phenomenon which is exaggerated with increasing aridity index and rising groundwater table. Soil property plays an important role in the shape of SWRC which will even lead to a rectangular shape under drier conditions, and power function form of SWRC widely adopted in hydrological model might be revised for most situations at the macro-scale.展开更多
Multiple-dimensional water flow in variably saturated soils plays an important role in ecological systems such as irrigation and water uptake by plant roots; its quantitative description is usually based on the Richa...Multiple-dimensional water flow in variably saturated soils plays an important role in ecological systems such as irrigation and water uptake by plant roots; its quantitative description is usually based on the Richards＇ equation. Because of the nonlinearity of the Richards＇ equation and the complexity of natural soils, most practical simulations rely on numerical solutions with the nonlinearity solved by iterations. The commonly used iterations for solving the nonlinearity are Picard and Newton methods with the former converging at first-order rate and the later at second-order rate. A recent theoretical analysis by the authors, however, revealed that for solving the diffusive flow, the classical Picard method is actually a chord-Newton method, converging at a rate faster than first order; its linear convergence rate is due to the treatment of the gravity term. To improve computational efficiency, a similar chord-Newton method as for solving the diffusive term was proposed to solve the gravity term. Testing examples for one-dimensional flow showed significant improvement. The core of this method is to produce a diagonally dominant matrix in the linear system so as to improve the iteration-toiteration stability and hence the convergence. In this paper, we develop a similar method for multiple-dimensional flow and compare its performance with the classical Picard and Newton methods for water flow in soils characterised by a wide range of van Genuchten parameters.展开更多
In this paper, we present a generalization of the commonly used growth models. We introduce Koya-Goshu biological growth model, as a more general solution of the rate-state ordinary differential equation. It is shown ...In this paper, we present a generalization of the commonly used growth models. We introduce Koya-Goshu biological growth model, as a more general solution of the rate-state ordinary differential equation. It is shown that the commonly used growth models such as Brody, Von Bertalanffy, Richards, Weibull, Monomolecular, Mitscherlich, Gompertz, Logistic, and generalized Logistic functions are its special cases. We have constructed growth and relative growth functions as solutions of the rate-state equation. The generalized growth function is the most flexible so that it can be useful in model selection problems. It is also capable of generating new useful models that have never been used so far. The function incorporates two parameters with one influencing growth pattern and the other influencing asymptotic behaviors. The relationships among these growth models are studies in details and provided in a flow chart.展开更多
作为一名英语教师,学会正确地运用理论于实际教学中尤为重要的。在平时的空闲时间,我会阅读各种英语专业的书籍。其中对我影响最大的是由人民教育出版社于2013年6月1日出版的,英国剑桥大学Jack Richards和Charles Lockhart合著的Reflect...作为一名英语教师,学会正确地运用理论于实际教学中尤为重要的。在平时的空闲时间,我会阅读各种英语专业的书籍。其中对我影响最大的是由人民教育出版社于2013年6月1日出版的,英国剑桥大学Jack Richards和Charles Lockhart合著的Reflective Teaching in Second Language Classrooms,即《第二语言课堂的反思性教学》。展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.51190092,51109110,51222901)the Co-ordination Program of State Key Laboratory of Hydro-Science and Engineering(Grant No.2012-KY-03)
文摘A numerical hillslope hydrodynamic model is of great importance in facilitating the understanding of rainfall-runoff mechanism.However,most of the currently existing models do not consider the effect of coupled hydrodynamic processes as runoff,subsurface flow or groundwater flow.In this study,the Tsinghua Hillslope Runoff Model based on multiple hydrodynamic process,THRM model,is developed,which couples with Saint Venant equation for surface runoff and Richards equation for variably saturated soil water movement(including subsurface flow and groundwater flow).A finite difference scheme with improved boundary conditions is adopted in this research.It is revealed from the simulation that the THRM model has a high computational efficiency and stability in simulating subsurface flow of the experimental hillslope,which is valuable in assessing the hillslope runoff generation mechanism.A model based sensitivity analysis is also carried out.The impact of boundary condition,grid size and initial soil moisture on simulation result and model stability are revealed,which provides insightful references to understand the mechanism of subsurface flow.
文摘The rubber tree physiological and ecological process quantitatively described by using mathematical method is an important means to the analysis of rubber tree growth process and mechanism. The study on growth simulation model of rubber tree will lay the foundation for the application of rubber tree cultivation intelligent decision system. A Richards equation was formulated to describe the height and stem diameter growth dynamics of the annual rubber seedlings. An area correlation analysis was done according to the closeness of the observed parameters to the dynamic curve on the gray system composed of the seedling growth increment and the meteorological factors including aerial temperature, precipitation and solar radiation hours that influence upon the seedling growth. The results showed that rubber seedling response fitted the Richards equation quite well. The growth increment displayed a distinct alternation of 'slow—fast—slow— fast—slow' rhythm. The growth course of the seedlings might be partitioned into three periods of time by the sequential clustering analysis, namely pre-growing, fast-growing, late-growing stage. The tray correlation analysis revealed that air temperature had the most significant influence while precipitation had the least impact on height growth of the rubber seedlings. In conclusion, the air temperature had the most significant influence while solar radiation hours had the least impact on stem diameter growth of the rubber seedlings.
基金supported by the National Natural Science Foundation of China (No.39970112 and 30470268)China-Germany Agricultural Cooperation Research Project (No.06/07 and 08/09)
文摘We obtain the global attractivity and global asymptotical stability of positive equilibria to a 3-dimensional Richards model with delays. Our results do not depend on the size-asymmetry parameter which measures the degree of the curvature of size-growth among individuals over the entire growth curve, and the shape parameter which affects the shape of model curve. Lastly, we gave a numerical simulation to verify the feasibility of our main results.
基金funding support from the science and technology innovation Program of Hunan Province(Grant No.2023RC1017)Hunan Provincial Postgraduate Research and Innovation Project(Grant No.CX20220109)National Natural Science Foundation of China Youth Fund(Grant No.52208378).
文摘Machine learning(ML)provides a new surrogate method for investigating groundwater flow dynamics in unsaturated soils.Traditional pure data-driven methods(e.g.deep neural network,DNN)can provide rapid predictions,but they do require sufficient on-site data for accurate training,and lack interpretability to the physical processes within the data.In this paper,we provide a physics and equalityconstrained artificial neural network(PECANN),to derive unsaturated infiltration solutions with a small amount of initial and boundary data.PECANN takes the physics-informed neural network(PINN)as a foundation,encodes the unsaturated infiltration physical laws(i.e.Richards equation,RE)into the loss function,and uses the augmented Lagrangian method to constrain the learning process of the solutions of RE by adding stronger penalty for the initial and boundary conditions.Four unsaturated infiltration cases are designed to test the training performance of PECANN,i.e.one-dimensional(1D)steady-state unsaturated infiltration,1D transient-state infiltration,two-dimensional(2D)transient-state infiltration,and 1D coupled unsaturated infiltration and deformation.The predicted results of PECANN are compared with the finite difference solutions or analytical solutions.The results indicate that PECANN can accurately capture the variations of pressure head during the unsaturated infiltration,and present higher precision and robustness than DNN and PINN.It is also revealed that PECANN can achieve the same accuracy as the finite difference method with fewer initial and boundary training data.Additionally,we investigate the effect of the hyperparameters of PECANN on solving RE problem.PECANN provides an effective tool for simulating unsaturated infiltration.
基金supported by the National Programs of Public-Beneficiary Sectors Funds,Ministryof Science and Technology,China(200803024)
文摘The objective of the present study was to develop a computer software for simulating the temporal development of plant disease epidemics using Richards, logistic, Gompertz, monomolecular, and exponential functions, respectively, and for predicting disease with a fitted model. The software was programmed using Visual Basic （VB6.0） and packaged with the Wise Installation System. The Fibonacci （＇0.618＇） section strategy was used to find out the most appropriate value for the shape parameter （m） in Richards function simulation through looping procedures. The software program was repeatedly tested, debugged and edited until it was run through favorably and produced ideal outputs. It was named Epitimulator based on the phrase ＇epidemic time simulator＇ and has been registered by the National Copyright Department of China （Reg. no. 2007SR18489）. It can be installed and run on personal computers with all versions of Windows operational systems. Data of disease index and survey time are keyed in or imported from Access files. The output of fitted models and related data of parameters can be pasted into Microsoft Excel worksheet or into Word document for editing as required and the simulated disease progress curves can be stored in separate graphic files. After being finally tested and completed, Epitimulator was applied to simulate the epidemic progress of corn northern leaf blight （Exserohilum turcicum） with recorded data from field surveys of corn crops and the fitted models were output. Comparison of the simulation results showed that the disease progress was always best described by Richards function, which resulted in the most accurate simulation model. Result also showed that forecast of northern leaf blight development was highly accurate by using the computed progress model from Richards function.
基金supported by the "Eleventh Five-year Plan" Project (Grant No.2007BAD38B01)
文摘A numerical model of two-dimensional soil water movement under surface drip irrigation condition was developed. The physical process of soil water movement is described by 2D Richards equation,and the upper boundary condition is depicted by the improved moving ponded area boundary. The partial differential equation(PDE) is transformed into ordinary differential equations(ODEs) through spatial semi-discretization and numerically solved by an ordinary differential equation solver(CVODE) . The numerical and field experiments indicate the good performance of the model in terms of accuracy and efficiency. The model provides a useful tool for long-term simulation of soil water movement under surface drip irrigation. Also,the model can serve as a general 2D Richards equation solver for variably saturated soil water movement,which is named as TIVS model(Tsinghua Integrated Variably Saturated soil water movement model).
基金Supported by the National Natural Science Foundation of China (Grant Nos. 50779022 and 50509013)
文摘Scale adaptable hydrological models have attracted more and more attentions in the hydrological modeling research community, and the constitutive relationship at the macro-scale is one of the most important issues, upon which there are not enough research activities yet. Taking the constitutive relationships of soil water movement--soil water retention curve (SWRC) as an example, this study extends the definition of SWRC at the micro-scale to that at the macro-scale, and aided by Monte Carlo method we demonstrate that soil property and the spatial distribution of soil moisture will affect the features of SWRC greatly. Furthermore, we assume that the spatial distribution of soil moisture is the result of self-organization of climate, soil, ground water and soil water movement under the specific boundary conditions, and we also carry out numerical experiments of soil water movement at the vertical direction in order to explore the relationship between SWRC at the macro-scale and the combinations of climate, soil, and groundwater. The results show that SWRCs at the macro-scale and micro-scale presents totally different features, e.g., the essential hysteresis phenomenon which is exaggerated with increasing aridity index and rising groundwater table. Soil property plays an important role in the shape of SWRC which will even lead to a rectangular shape under drier conditions, and power function form of SWRC widely adopted in hydrological model might be revised for most situations at the macro-scale.
文摘Multiple-dimensional water flow in variably saturated soils plays an important role in ecological systems such as irrigation and water uptake by plant roots; its quantitative description is usually based on the Richards＇ equation. Because of the nonlinearity of the Richards＇ equation and the complexity of natural soils, most practical simulations rely on numerical solutions with the nonlinearity solved by iterations. The commonly used iterations for solving the nonlinearity are Picard and Newton methods with the former converging at first-order rate and the later at second-order rate. A recent theoretical analysis by the authors, however, revealed that for solving the diffusive flow, the classical Picard method is actually a chord-Newton method, converging at a rate faster than first order; its linear convergence rate is due to the treatment of the gravity term. To improve computational efficiency, a similar chord-Newton method as for solving the diffusive term was proposed to solve the gravity term. Testing examples for one-dimensional flow showed significant improvement. The core of this method is to produce a diagonally dominant matrix in the linear system so as to improve the iteration-toiteration stability and hence the convergence. In this paper, we develop a similar method for multiple-dimensional flow and compare its performance with the classical Picard and Newton methods for water flow in soils characterised by a wide range of van Genuchten parameters.
文摘In this paper, we present a generalization of the commonly used growth models. We introduce Koya-Goshu biological growth model, as a more general solution of the rate-state ordinary differential equation. It is shown that the commonly used growth models such as Brody, Von Bertalanffy, Richards, Weibull, Monomolecular, Mitscherlich, Gompertz, Logistic, and generalized Logistic functions are its special cases. We have constructed growth and relative growth functions as solutions of the rate-state equation. The generalized growth function is the most flexible so that it can be useful in model selection problems. It is also capable of generating new useful models that have never been used so far. The function incorporates two parameters with one influencing growth pattern and the other influencing asymptotic behaviors. The relationships among these growth models are studies in details and provided in a flow chart.
文摘作为一名英语教师,学会正确地运用理论于实际教学中尤为重要的。在平时的空闲时间,我会阅读各种英语专业的书籍。其中对我影响最大的是由人民教育出版社于2013年6月1日出版的,英国剑桥大学Jack Richards和Charles Lockhart合著的Reflective Teaching in Second Language Classrooms,即《第二语言课堂的反思性教学》。
