Emphasise will be given to simulation concepts for the vadose zone and to the limitations of avai... more Emphasise will be given to simulation concepts for the vadose zone and to the limitations of available software, e.g. related to boundary conditions. Classical water and solute transport formulas are investigated in relation to the used software. A practical approach is chosen to support the theoretical considerations, hence three simulation applications in very different fields: a) quantity measurement of soil water movement, b) thin layer in the vicinity of a foundation and c) solute transport simulation of a column experiment are summarised. The selected examples should especially enable engineers working in the field of water and environment an easier approach to simulation task and the underlying theory. A clear distinction is also made between skills and knowledge.
The large number of models for P dynamics in soil–plant systems focus on different scales and hav... more The large number of models for P dynamics in soil–plant systems focus on different scales and have different purposes. This chapter provides an overview of existing models and illustrates the scope and potential of current modelling techniques by using three case studies. We focus on plant traits that enhance plant phosphate uptake from soil. The first case study presents a model for phosphate uptake by mycorrhizal roots, the second study is based on a root system scale model that includes root plasticity, and the third presents a model for crop response to soil phosphate supply.
Water is one of the most important resources for plant growth and function. An accurate modelling... more Water is one of the most important resources for plant growth and function. An accurate modelling of the unsaturated flow is not only substantial to predict water uptake but also important to describe nutrient movement regarding water saturation and transport. In this work we present a model for water uptake. The model includes the simultaneous flow of water inside the soil and inside the root network. Water saturation in the soil volume is described by the Richards equation. Water flow inside the roots' xylem is calculated using the Poiseuille law for water flow in a cylindrical tube. The water saturation in the soil as well as water uptake of the root system is calculated numerically in three dimensions. We study water uptake of a maize plant in a confined pot under different supply scenarios. The main improvement of our approach is that the root surfaces act as spatial boundaries of the soil volume. Therefore water influx into the root is described by a surface flux instead of a volume flux, which is commonly given by an effective sink term. For the numerical computation we use the following software: The 3-dimensional maize root architecture is created by a root growth model based on L-Systems (Leitner et al 2009). A mesh of the surrounding soil volume is created using the meshing software DistMesh (Persson & Strang 2004). Using this mesh the partial differential equations are solved with the finite element method using Comsol Multiphysics 3.5a. Modelling results are related to accepted water uptake models from literature (Clausnitzer & Hopmans 1994, Roose & Fowler 2004, Javaux et al 2007). This new approach has several advantages. By considering the individual roots it is possible to analyse the influence of overlapping depletion zones due to inter root competition. Furthermore, such simulations can be used to estimate the influence of simplifying assumptions that are made in the development of effective models. The model can be easily combined with a nutrient uptake model. In this way the proposed method will be capable of analysing nutrient uptake considering inter root competition as well as the solubilising effect of combined root exudation. References Leitner D, Klepsch S, Bodner G and Schnepf A (2010). A dynamic root system growth model based on L-Systems - Tropisms and coupling to nutrient uptake from soil. Plant and Soil DOI: 10.1007/s11104-010-0284-7 Persson P O and Strang G (2004). A Simple Mesh Generator in MATLAB. SIAM Review 46 (2): 329-345 Clausnitzer V and Hopmans J W (1994). Simultaneous modeling of transient three-dimensional root growth and soil water flow. Plant and Soil 164(2): 299-314. Roose T and Fowler A C (2004). A model for water uptake by plant roots. Journal of Theoretical Biology 228(2): 155-171. Javaux M, Schröder T, Vanderborght J and Vereecken H (2008). Use of a three-dimensional detailed modeling approach for predicting root water uptake. Vadose Zone Journal 7(3): 1079-1088.
•Root hairs are known to be important in the uptake of sparingly soluble nutrients by plants, but... more •Root hairs are known to be important in the uptake of sparingly soluble nutrients by plants, but quantitative understanding of their role in this is weak. This limits, for example, the breeding of more nutrient-efficient crop genotypes.•We developed a mathematical model of nutrient transport and uptake in the root hair zone of single roots growing in soil or solution culture. Accounting for root hair geometry explicitly, we derived effective equations for the cumulative effect of root hair surfaces on uptake using the method of homogenization.•Analysis of the model shows that, depending on the morphological and physiological properties of the root hairs, one of three different effective models applies. They describe situations where: (1) a concentration gradient dynamically develops within the root hair zone; (2) the effect of root hair uptake is negligibly small; or (3) phosphate in the root hair zone is taken up instantaneously. Furthermore, we show that the influence of root hairs on rates of phosphate uptake is one order of magnitude greater in soil than solution culture.•The model provides a basis for quantifying the importance of root hair morphological and physiological properties in overall uptake, in order to design and interpret experiments in different circumstances.Root hairs are known to be important in the uptake of sparingly soluble nutrients by plants, but quantitative understanding of their role in this is weak. This limits, for example, the breeding of more nutrient-efficient crop genotypes.We developed a mathematical model of nutrient transport and uptake in the root hair zone of single roots growing in soil or solution culture. Accounting for root hair geometry explicitly, we derived effective equations for the cumulative effect of root hair surfaces on uptake using the method of homogenization.Analysis of the model shows that, depending on the morphological and physiological properties of the root hairs, one of three different effective models applies. They describe situations where: (1) a concentration gradient dynamically develops within the root hair zone; (2) the effect of root hair uptake is negligibly small; or (3) phosphate in the root hair zone is taken up instantaneously. Furthermore, we show that the influence of root hairs on rates of phosphate uptake is one order of magnitude greater in soil than solution culture.The model provides a basis for quantifying the importance of root hair morphological and physiological properties in overall uptake, in order to design and interpret experiments in different circumstances.
Mathematical and Computer Modelling of Dynamical Systems, 2010
Understanding the impact of root architecture on plant resource efficiency is important, in parti... more Understanding the impact of root architecture on plant resource efficiency is important, in particular, in the light of upcoming shortages of mineral fertilizers and changed environmental conditions. In the 1950s, a great number of root systems of European cultivated plants were excavated and studied by L. Kutschera (1960). Her work gave enormous insight into the variety of root system architectures and helped to realize the importance of belowground processes to plant productivity. We analysed the resulting hand drawings by using mathematical modelling and found root system parameters for a newly developed parametric L-System model. In this way we were able to first reproduce the illustrations, second computationally analyse root system traits and finally access the dynamic root architecture development.
We present a new numerical approach describing nutrient uptake in three dimensions. Dynamic bound... more We present a new numerical approach describing nutrient uptake in three dimensions. Dynamic boundary conditions are considered at the individual root surfaces within a root system. As an example, we compare the three‐dimensional simulation results of phosphate uptake by a young maize root system to the corresponding effective solution. We show that the two solutions are similar concerning phosphate uptake and the size of the depletion zones. The presented approach makes it possible to verify simplifications that are made in the development of effective models. Furthermore, it is possible to extend existing models by including spatial heterogeneities that will increase our understanding of rhizosphere processes.
Understanding the impact of roots and rhizosphere traits on plant resource efficiency is importan... more Understanding the impact of roots and rhizosphere traits on plant resource efficiency is important, in particular in the light of upcoming shortages of mineral fertilizers and climate change with increasing frequency of droughts. We developed a modular approach to root growth and architecture modelling with a special focus on soil root interactions. The dynamic three-dimensional model is based on L-Systems, rewriting systems well-known in plant architecture modelling. We implemented the model in Matlab in a way that simplifies introducing new features as required. Different kinds of tropisms were implemented as stochastic processes that determine the position of the different roots in space. A simulation study was presented for phosphate uptake by a maize root system in a pot experiment. Different sink terms were derived from the root architecture, and the effects of gravitropism and chemotropism were demonstrated. This root system model is an open and flexible tool which can easily be coupled to different kinds of soil models.
Prediction of the sorption behavior of environmental pollutants is of utmost importance within th... more Prediction of the sorption behavior of environmental pollutants is of utmost importance within the framework of risk assessments. In this work two approaches are presented with the aim to describe sorption of aromatic substances to geosorbents. First, analytical solutions of kinetic models were fitted to experimental data of batch sorption experiments with aniline and 1-naphthylamine onto animal manure-treated soil and the soil mineral montmorillonite. The models, accounting for equilibrium and nonequilibrium sorption coupled to transformation and/or irreversible sorption processes, could well reproduce the concentration course of the sorbates. Results suggest that the amounts transformed/degraded and irreversibly bound were higher for the soil than for the clay mineral. In the second part, quantum chemical calculations were performed on aniline and 1-naphthylamine interacting with acetic acid, acetamide, imidazole, and phenol as models of functional groups present in humic substances. Molecular modeling showed that formation of hydrogen bonds is the dominating binding mechanism in all modeled complexes, which are energetically very similar between aniline and 1-naphthylamine.
Nitrogen dynamics in semi-natural environments is crucial for the development and ecological stab... more Nitrogen dynamics in semi-natural environments is crucial for the development and ecological stability of these systems. The present paper shows the results of the reinvestigation of a 15N-tracer experiment, which was established in the Grossglockner massif in Austria at 2300 m a.s.l. in 1974/1975. We show that large quantities of nitrogen introduced by a single pulse labelling (amounting to approximately 1.7% of the nitrogen in the system) into an alpine grassland remain in the soil–plant system, with only 55% being lost during 27–28 years. In the first 10 cm of the four investigated soil profiles 40% of 15N was recovered, being mainly bound in organic forms. A simple site specific model was established on the basis of the results considering a biological, residual and labile N-pool, the latter being the source for N-losses. By the model a long mean residence time close to 100 years was derived for the remaining 15N.
Nitrogen dynamics in semi-natural environments is crucial for the development and ecological stab... more Nitrogen dynamics in semi-natural environments is crucial for the development and ecological stability of these systems. The present paper shows the results of the reinvestigation of a 15N-tracer experiment, which was established in the Grossglockner massif in Austria at 2300 m a.s.l. in 1974/1975. We show that large quantities of nitrogen introduced by a single pulse labelling (amounting to approximately 1.7% of the nitrogen in the system) into an alpine grassland remain in the soil–plant system, with only 55% being lost during 27–28 years. In the first 10 cm of the four investigated soil profiles 40% of 15N was recovered, being mainly bound in organic forms. A simple site specific model was established on the basis of the results considering a biological, residual and labile N-pool, the latter being the source for N-losses. By the model a long mean residence time close to 100 years was derived for the remaining 15N.
Emphasise will be given to simulation concepts for the vadose zone and to the limitations of avai... more Emphasise will be given to simulation concepts for the vadose zone and to the limitations of available software, e.g. related to boundary conditions. Classical water and solute transport formulas are investigated in relation to the used software. A practical approach is chosen to support the theoretical considerations, hence three simulation applications in very different fields: a) quantity measurement of soil water movement, b) thin layer in the vicinity of a foundation and c) solute transport simulation of a column experiment are summarised. The selected examples should especially enable engineers working in the field of water and environment an easier approach to simulation task and the underlying theory. A clear distinction is also made between skills and knowledge.
The large number of models for P dynamics in soil–plant systems focus on different scales and hav... more The large number of models for P dynamics in soil–plant systems focus on different scales and have different purposes. This chapter provides an overview of existing models and illustrates the scope and potential of current modelling techniques by using three case studies. We focus on plant traits that enhance plant phosphate uptake from soil. The first case study presents a model for phosphate uptake by mycorrhizal roots, the second study is based on a root system scale model that includes root plasticity, and the third presents a model for crop response to soil phosphate supply.
Water is one of the most important resources for plant growth and function. An accurate modelling... more Water is one of the most important resources for plant growth and function. An accurate modelling of the unsaturated flow is not only substantial to predict water uptake but also important to describe nutrient movement regarding water saturation and transport. In this work we present a model for water uptake. The model includes the simultaneous flow of water inside the soil and inside the root network. Water saturation in the soil volume is described by the Richards equation. Water flow inside the roots' xylem is calculated using the Poiseuille law for water flow in a cylindrical tube. The water saturation in the soil as well as water uptake of the root system is calculated numerically in three dimensions. We study water uptake of a maize plant in a confined pot under different supply scenarios. The main improvement of our approach is that the root surfaces act as spatial boundaries of the soil volume. Therefore water influx into the root is described by a surface flux instead of a volume flux, which is commonly given by an effective sink term. For the numerical computation we use the following software: The 3-dimensional maize root architecture is created by a root growth model based on L-Systems (Leitner et al 2009). A mesh of the surrounding soil volume is created using the meshing software DistMesh (Persson & Strang 2004). Using this mesh the partial differential equations are solved with the finite element method using Comsol Multiphysics 3.5a. Modelling results are related to accepted water uptake models from literature (Clausnitzer & Hopmans 1994, Roose & Fowler 2004, Javaux et al 2007). This new approach has several advantages. By considering the individual roots it is possible to analyse the influence of overlapping depletion zones due to inter root competition. Furthermore, such simulations can be used to estimate the influence of simplifying assumptions that are made in the development of effective models. The model can be easily combined with a nutrient uptake model. In this way the proposed method will be capable of analysing nutrient uptake considering inter root competition as well as the solubilising effect of combined root exudation. References Leitner D, Klepsch S, Bodner G and Schnepf A (2010). A dynamic root system growth model based on L-Systems - Tropisms and coupling to nutrient uptake from soil. Plant and Soil DOI: 10.1007/s11104-010-0284-7 Persson P O and Strang G (2004). A Simple Mesh Generator in MATLAB. SIAM Review 46 (2): 329-345 Clausnitzer V and Hopmans J W (1994). Simultaneous modeling of transient three-dimensional root growth and soil water flow. Plant and Soil 164(2): 299-314. Roose T and Fowler A C (2004). A model for water uptake by plant roots. Journal of Theoretical Biology 228(2): 155-171. Javaux M, Schröder T, Vanderborght J and Vereecken H (2008). Use of a three-dimensional detailed modeling approach for predicting root water uptake. Vadose Zone Journal 7(3): 1079-1088.
•Root hairs are known to be important in the uptake of sparingly soluble nutrients by plants, but... more •Root hairs are known to be important in the uptake of sparingly soluble nutrients by plants, but quantitative understanding of their role in this is weak. This limits, for example, the breeding of more nutrient-efficient crop genotypes.•We developed a mathematical model of nutrient transport and uptake in the root hair zone of single roots growing in soil or solution culture. Accounting for root hair geometry explicitly, we derived effective equations for the cumulative effect of root hair surfaces on uptake using the method of homogenization.•Analysis of the model shows that, depending on the morphological and physiological properties of the root hairs, one of three different effective models applies. They describe situations where: (1) a concentration gradient dynamically develops within the root hair zone; (2) the effect of root hair uptake is negligibly small; or (3) phosphate in the root hair zone is taken up instantaneously. Furthermore, we show that the influence of root hairs on rates of phosphate uptake is one order of magnitude greater in soil than solution culture.•The model provides a basis for quantifying the importance of root hair morphological and physiological properties in overall uptake, in order to design and interpret experiments in different circumstances.Root hairs are known to be important in the uptake of sparingly soluble nutrients by plants, but quantitative understanding of their role in this is weak. This limits, for example, the breeding of more nutrient-efficient crop genotypes.We developed a mathematical model of nutrient transport and uptake in the root hair zone of single roots growing in soil or solution culture. Accounting for root hair geometry explicitly, we derived effective equations for the cumulative effect of root hair surfaces on uptake using the method of homogenization.Analysis of the model shows that, depending on the morphological and physiological properties of the root hairs, one of three different effective models applies. They describe situations where: (1) a concentration gradient dynamically develops within the root hair zone; (2) the effect of root hair uptake is negligibly small; or (3) phosphate in the root hair zone is taken up instantaneously. Furthermore, we show that the influence of root hairs on rates of phosphate uptake is one order of magnitude greater in soil than solution culture.The model provides a basis for quantifying the importance of root hair morphological and physiological properties in overall uptake, in order to design and interpret experiments in different circumstances.
Mathematical and Computer Modelling of Dynamical Systems, 2010
Understanding the impact of root architecture on plant resource efficiency is important, in parti... more Understanding the impact of root architecture on plant resource efficiency is important, in particular, in the light of upcoming shortages of mineral fertilizers and changed environmental conditions. In the 1950s, a great number of root systems of European cultivated plants were excavated and studied by L. Kutschera (1960). Her work gave enormous insight into the variety of root system architectures and helped to realize the importance of belowground processes to plant productivity. We analysed the resulting hand drawings by using mathematical modelling and found root system parameters for a newly developed parametric L-System model. In this way we were able to first reproduce the illustrations, second computationally analyse root system traits and finally access the dynamic root architecture development.
We present a new numerical approach describing nutrient uptake in three dimensions. Dynamic bound... more We present a new numerical approach describing nutrient uptake in three dimensions. Dynamic boundary conditions are considered at the individual root surfaces within a root system. As an example, we compare the three‐dimensional simulation results of phosphate uptake by a young maize root system to the corresponding effective solution. We show that the two solutions are similar concerning phosphate uptake and the size of the depletion zones. The presented approach makes it possible to verify simplifications that are made in the development of effective models. Furthermore, it is possible to extend existing models by including spatial heterogeneities that will increase our understanding of rhizosphere processes.
Understanding the impact of roots and rhizosphere traits on plant resource efficiency is importan... more Understanding the impact of roots and rhizosphere traits on plant resource efficiency is important, in particular in the light of upcoming shortages of mineral fertilizers and climate change with increasing frequency of droughts. We developed a modular approach to root growth and architecture modelling with a special focus on soil root interactions. The dynamic three-dimensional model is based on L-Systems, rewriting systems well-known in plant architecture modelling. We implemented the model in Matlab in a way that simplifies introducing new features as required. Different kinds of tropisms were implemented as stochastic processes that determine the position of the different roots in space. A simulation study was presented for phosphate uptake by a maize root system in a pot experiment. Different sink terms were derived from the root architecture, and the effects of gravitropism and chemotropism were demonstrated. This root system model is an open and flexible tool which can easily be coupled to different kinds of soil models.
Prediction of the sorption behavior of environmental pollutants is of utmost importance within th... more Prediction of the sorption behavior of environmental pollutants is of utmost importance within the framework of risk assessments. In this work two approaches are presented with the aim to describe sorption of aromatic substances to geosorbents. First, analytical solutions of kinetic models were fitted to experimental data of batch sorption experiments with aniline and 1-naphthylamine onto animal manure-treated soil and the soil mineral montmorillonite. The models, accounting for equilibrium and nonequilibrium sorption coupled to transformation and/or irreversible sorption processes, could well reproduce the concentration course of the sorbates. Results suggest that the amounts transformed/degraded and irreversibly bound were higher for the soil than for the clay mineral. In the second part, quantum chemical calculations were performed on aniline and 1-naphthylamine interacting with acetic acid, acetamide, imidazole, and phenol as models of functional groups present in humic substances. Molecular modeling showed that formation of hydrogen bonds is the dominating binding mechanism in all modeled complexes, which are energetically very similar between aniline and 1-naphthylamine.
Nitrogen dynamics in semi-natural environments is crucial for the development and ecological stab... more Nitrogen dynamics in semi-natural environments is crucial for the development and ecological stability of these systems. The present paper shows the results of the reinvestigation of a 15N-tracer experiment, which was established in the Grossglockner massif in Austria at 2300 m a.s.l. in 1974/1975. We show that large quantities of nitrogen introduced by a single pulse labelling (amounting to approximately 1.7% of the nitrogen in the system) into an alpine grassland remain in the soil–plant system, with only 55% being lost during 27–28 years. In the first 10 cm of the four investigated soil profiles 40% of 15N was recovered, being mainly bound in organic forms. A simple site specific model was established on the basis of the results considering a biological, residual and labile N-pool, the latter being the source for N-losses. By the model a long mean residence time close to 100 years was derived for the remaining 15N.
Nitrogen dynamics in semi-natural environments is crucial for the development and ecological stab... more Nitrogen dynamics in semi-natural environments is crucial for the development and ecological stability of these systems. The present paper shows the results of the reinvestigation of a 15N-tracer experiment, which was established in the Grossglockner massif in Austria at 2300 m a.s.l. in 1974/1975. We show that large quantities of nitrogen introduced by a single pulse labelling (amounting to approximately 1.7% of the nitrogen in the system) into an alpine grassland remain in the soil–plant system, with only 55% being lost during 27–28 years. In the first 10 cm of the four investigated soil profiles 40% of 15N was recovered, being mainly bound in organic forms. A simple site specific model was established on the basis of the results considering a biological, residual and labile N-pool, the latter being the source for N-losses. By the model a long mean residence time close to 100 years was derived for the remaining 15N.
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