Background: Carbon storage and turnover in soils depend on the interplay of soil architecture, microbial activities and soil organic matter dynamics. For a fundamental understanding of the mechanisms that drive these processes, not only the exploitation of advanced experimental techniques down to the nanoscale is necessary, but also spatially explicit and dynamic image-based modeling at the pore scale.We present a modeling approach which is capable of transferring microscale information into macroscale simulations at the profile scale. This enables the prediction of future developments of carbon fluxes and the impact of changes in the environmental conditions linking scales.We consider a mathematical model for CO2 transport across soil profiles (macroscale) which is informed by a pore-scale (microscale) model for C turnover. It allows for the dynamic, self-organized re-arrangement of solid building units, aggregates and particulate organic matter (POM) based on surface interactions, realized by a cellular automaton method, and explicitly takes spatial effects on POM turnover such as occlusion into account. We further include the macroscopic environmental conditions water saturation, POM content, and oxygen concentration.The coupled simulations of macroscopic transport and pore scale carbon and aggregate turnover reveal the complex, nonlinear interplay of the underlying processes. Limitations by diffusive transport, oxygen availability, texture dependent occlusion and turnover of OM drive CO2 production and carbon storage.Zech, Prechtel, Ray (2024): Coupling scales in process-based soil organic carbon modeling including dynamic aggregation. J. Plant Nutr. Soil Sci.

<p>Advanced imaging techniques now allow to take snapshots of soils even down to the nanoscale. Nevertheless, assessing the temporal evolution of elemental distributions, distinguishing different liquid phases and identifying dynamic microbial processes is experimentally still challenging. Consequently mechanistic models operating at the pore scale facilitate the study and understanding of phenomena shaping soil structures as, e.g., carbon turnover, and vice versa.</p><p>We present an overview of a versatile hybrid discrete continuum modeling approach combining cellular automata and partial differential equations, which integrates the complex coupling of biological, chemical, and physical processes. Dynamic liquid and gaseous phases, diffusive processes for solutes, mobile bacteria transforming into immobile biomass, and ions are prescribed by means of partial differential equations. Furthermore the solid phase is dynamic, e.g. through aggregation of soil particles, the addition and decomposition of particulate organic matter, or the mechanical influence of roots and their exudates. The virtual soil structures rely on micro-CT images or particle libraries derived from dynamic image analysis of water-stable aggregates.</p><p>Applications include structure formation of clay minerals, the interplay between soil structural dynamics and organic matter turnover, or the impact/importance of liquid phase connectivity and substrate supply. Finally the mathematical homogenization technique is used to show a way how to incorporate information from the pore scale to macroscale models, e.g. by coupling microscale carbon turnover to profile-scale CO2 transport.</p>

<p>We present a spatially and temporally explicit mechanistic model for soil aggregation at the microscale. This consists of a cellular automaton model for the dynamic rearrangement of solid building units whose size and shape are derived from dynamic image analysis of wet-sieved, water stable aggregates. This model is combined with a particulate organic matter (POM) turnover model or a model for a growing fine root which exudes and distributes mucilage into the soil. Along this line the mutually interacting soil and POM dynamics and the intertwined processes at the root-soil interface are captured and evaluated simultaneously at the biologically relevant scale. Our comprehensive modeling toolbox allows us to conduct various simulation scenarios and to discriminate and evaluate the underlying processes and different drivers such as texture. We quantify our results by evaluating the stability of the created structures or the dynamical change in local porosity around a growing root. Finally, the insights gained at the microscale are used to parametrize a CO2 transport model at the profile scale. Thereby, the microbially mediated CO2 source is taken into account as well as the driver soil texture, and changing ambient environmental conditions such as water saturation, oxygen concentration and POM content.</p>

The structure of soil aggregates plays an important role for the turnover of particulate organic matter (POM) and vice versa. Analytical approaches usually do not disentangle the continuous re-organization of soil aggregates, caught between disintegration and assemblage. This led to a lack of understanding of the mechanistic relationship between aggregation and organic matter dynamics in soils. In this study, we took advantage of a process-based mechanistic model that describes the interaction between the dynamic (re-)arrangement of soil aggregates, based on dynamic image analysis data of wet-sieved aggregates, to analyze the turnover of POM, and simultaneous soil surface interactions in a spatially and temporally explicit way. Our novel modeling approach enabled us to unravel the temporal development of aggregate sizes, organic carbon (OC) turnover of POM, and surface coverage as affected by soil texture, POM input, and POM decomposition rate comparing a low and high clay soil (18% and 33% clay content). Our results reveal the importance of the dynamic re-arrangement of soil structure on POM-related turnover of OC in soils. Firstly, aggregation was largely determined by the POM input fostering aggregates through additional gluing joints outweighing soil texture at lower decomposition rate, whereas at higher decomposition rate, soil texture had a higher influence leading to larger aggregates in the high clay soil. Secondly, the POM storage increased with clay content, showing that surface interactions may delay the turnover of OC into CO2. Thirdly, we observed a structural priming effect in which the increased input of POM induced increased structural re-arrangement stimulating the mineralization of old POM. This work highlights that the dynamic re-arrangement of soil aggregates has important implications for OC turnover and is driven by underlying surface interactions where temporary gluing spots stabilize larger aggregates.

Microaggregates are hot spots of microbial activity at a scale that frequently poses a severe experimental challenge or defies a direct observation. Mathematical models that combine the mechanisms of spatially resolved organic matter transport with the processes of organic matter turnover can facilitate the understanding of soil microbial dynamics and the function of soils at these scales. In this study, we investigate microbial population dynamics and the turnover of particulate organic matter (POM) in soil micmaggregates. CT images of microaggregates obtained from samples of natural soils serve as basis for selecting the simulation domain. For different levels of water saturation, the fluid (liquid and gas) distribution within the pore space is calculated according to a morphological model. We consider bacteria and POM, which are heterogeneously distributed within the liquid phase. Dissolved organic carbon (DOC) is released by hydrolyzing POM, assuming a reaction following first-order kinetics. DOC spreads by diffusion and can subsequently be consumed by bacteria and turned into CO2. The growth of bacteria is realized by a cellular automaton framework (CAM) and based on Michaelis-Menten kinetics due to the uptake of DOC. Our simulations show that the heterogeneous distribution of substrate and bacteria results in an overall biodegradation kinetics and CO2 output that strongly depends on the microaggregate scale (<250 mu m). Only very specific cases can be distinguished globally, e.g., when the substrates are isolated from bacteria due to a disconnected liquid phase. Locally, however, heterogeneities in substrate distribution impact the development of bacteria populations, e.g., a smaller geodesic distance of bacteria to the substrate promotes bacterial growth locally.

Although advanced imaging techniques now allow snapshots even down to the nanoscale, the evolution of elemental distributions, different liquid phases and dynamic microbial processes still cannot always be assessed experimentally.Consequently mechanistic models operating at the pore scale facilitate the study and understanding of such phenomena.We present a versatile hybrid discrete continuum modeling approach combining cellular automata and partial differential equations which integrates the complex coupling of biological, chemical, and physical processes.Dynamic liquid and gas phases, diffusive processes for solutes, mobile bacteria transforming into immobile biomass, and ions are prescribed by means of partial differential equations.Furthermore the solid phase is dynamic, e.g. through aggregation of soil particles, growth of biofilms or the distribution of particulate organic matter in the system [1, 2, 3, 4].Finally mathematical homogenization techniques are used to show a way to incorporate information as the diffusivity from the pore scale to macroscale models [1,5].Applications include structure formation of clay minerals [4], the interplay of liquid phase connectivity, substrate supply and organic matter turnover [3], or the quantification of the effective diffusivity by upscaling on 3D geometries from CT scans of a loamy and a sandy soil.[1] N. Ray, A. Rupp and A. Prechtel.Discrete-continuum multiscale model for transport, biomass development and solid restructuring in porous media.

There is still no satisfactory understanding of the factors that enable soil microbial populations to be as highly diverse as they are. Mathematically based modeling can facilitate the understanding of their development and function in soils, e.g. with respect to habitat and carbon cycling. Our mechanistic model is based on [1,2] and allows studying the spatiotemporal dynamics of bacteria in unsaturated soil samples. In this presentation, different levels of saturation are investigated, for which the fluid (liquid and gas) distributions are calculated according to a morphological model. As in [3] various bacteria strains and organic matter are heterogeneously distributed in CT scans of various soil samples. The bacteria strains grow based on Michaelis-Menten kinetics due to the uptake of oxygen and dissolved organic carbon (DOC) present in the liquid phase. The development of bacterial colonies is realized in a cellular automaton framework (CAM) as presented in [1,2]. DOC is either present as a carbonaceous solution or hydrolized by a first order kinetic from heterogeneously distributed particulate organic matter (POM) sources. The diffusion of both nutrients oxygen and DOC are described by means of reactive transport equations, which include a Henry conditions for the transfer from/into the gas phase. We apply the local discontinuous Galerkin (LDG) method as a discretization scheme. Our simulations show that the impact heterogeneity in nutrient and bacteria distribution has on overall biodegradation kinetics strongly depends on the scale of interest. On the scale of soil microaggregates (<250 μm), only very specific cases can be distinguished globally, e.g. when nutrient sources are isolated from bacteria due to a disconnected liquid phase. Locally however, heterogeneities in nutrient distribution impact the development of bacteria populations, e.g. a lower geodesic distance of bacteria to nutrient promotes bacteria growth locally. Such local effects can have an important role for competing bacterial species. On larger scales (millimeter scale), such heterogeneities can also have a large impact. We conclude that the heterogeneous spatial structure must be resolved scale-dependently. [1] N. Ray, A. Rupp and A. Prechtel. Discrete-continuum multiscale model for transport, biomass development and solid restructuring in porous media, Adv. Water Resour. 107, 393-404 (2017), doi:10.1016/j.advwatres.2017.04.001. [2] A. Rupp, K. Totsche, A. Prechtel and N. Ray. Discrete-continuum multiphase model for structure formation in soils including electrostatic effects, Front. Environ. Sci. 6:96 (2018), doi:10.3389/fenvs.2018.00096. [3] X. Portell, V. Pot, P. Garnier, W. Otten and P.C. Baveye. Microscale heterogeneity of the spatial distribution of organic matter can promote bacterial biodiversity in soils: insights from computer simulations., Front. Microbiol. 9:1583 (2018), doi:10.3389/fmicb.2018.01583.

We assess the complex coupling of biological, chemical and physical processes with the help of a mechanistic modeling approach extending [Rupp 2019] The aim is to study the interplay of relevant mechanisms in silico and consequently gain a model-based understanding of dynamics in soils.The hybrid discrete-continuum model used explicitly represents the pore structure and allows for dynamic structural organization of the medium at the pore scale. The movement of interacting entities - nutrients, bacteria and possibly charged chemicals - in the fluid is described by means of the diffusion and Nernst-Planck equations with Henry's law at the liquid/gas interfaces. Homogeneous chemical reactions are considered using for instance the mass action law whereas heterogeneous reactions on the solid surface are incorporated via a kinetic Langmuir isotherm. A biomass phase can develop from agglomerations of bacteria and stabilising sticky agents may grow or decay at the solid surfaces. Root cells and an explicit phase of exudate as well as attachment properties of root hairs can be included. In addition to solving the continuous partial differential equations, a discrete cellular automaton method [Ray et al. 2017, Rupp et al 2018, Tang and Valocchi 2013] is used, enabling structural changes in the solid and biomass/mucilage phases at each time step. The partial differential equations are discretised with a local discontinuous Galerkin method which is able to handle discontinuities induced by the evolving geometry. Upscaling techniques enable the incorporation of information from the pore scale into the macroscale.In this study, we illustrate the ability of the approach to advance the understanding of specific process mechanisms. Microaggregates are the fundamental building blocks of soils and are thus important for soil structure, properties, and functions. Although there has been much research investigating the dynamics, stability, and structure of microaggregates, there is still a substantial lack in quantifying the relationships between the major driving forces (soil fauna, microorganisms, roots, organic and inorganic matter, and physical processes). As an example, we study structure formation of microaggregates as a function of the size and shape of the solid building units taking into account the effect of attraction and repulsion by charges. Biomass development and root exudate can significantly alter the macroscopic soil hydraulic properties. Using the model in hand, this effect can be quantified for different amount and spatial distribution of root exudate with geometries from CT-scans. In the natural environment, microbial communities are highly diverse. We employ the model to investigate the way spatial distribution of organic matter can influence bacterial dynamics.

Key functions of soils, such as permeability or habitat for microorganisms, are determined by structures at the microaggregate scale. The evolution of elemental distributions and dynamic processes can often not be assessed experimentally. So mechanistic models operating at the pore scale are needed. We consider the complex coupling of biological, chemical, and physical processes in a hybrid discrete-continuum modeling approach. It integrates dynamic wetting (liquid) and non-wetting (gas) phases including biofilms, diffusive processes for solutes, mobile bacteria transforming into immobile biomass, and ions which are prescribed by means of partial differential equations. Furthermore the growth of biofilms as, e.g., mucilage exuded by roots, or the distribution of particulate organic matter in the system, is incorporated in a cellular automaton framework (CAM) presented in [1, 2]. It also allows for structural changes of the porous medium itself (see, e.g. [3]). As the evolving computational domain leads to discrete discontinuities, we apply the local discontinuous Galerkin (LDG) method for the transport part. Mathematical upscaling techniques incorporate the information from the pore to the macroscale [1,4]. The model is applied for two research questions: We model the incorporation and turnover of particulate OM influencing soil aggregation, including ‘gluing’ hotspots, and show scenarios varying of OM input, turnover, or particle size distribution. Second, we quantify the effective diffusivity on 3D geometries from CT scans of a loamy and a sandy soil. Conventional models cannot account for natural pore geometries and varying phase properties. Upscaling allows also to quantify how root exudates (mucilage) can significantly alter the macroscopic soil hydraulic properties. [1] Ray, Rupp, Prechtel (2017). AWR (107), 393-404. [2] Rupp, Totsche, Prechtel, Ray (2018). Front. Env. Sci. (6) 96. [3] Zech, Dultz, Guggenberger, Prechtel, Ray (2020). Appl. Clay Sci. 198, 105845. [4] Ray, Rupp, Schulz, Knabner (2018). TPM 124(3), 803-824.

Microaggregates are the fundamental building blocks of soils and thus important for their structure, properties, and functions. Hence, experimental aggregate formation studies (Dultz et al. 2019) were conducted to reveal the mechanisms leading to the establishment of soil microaggregates from mixtures of the mineral building units goethite and illite. Mathematically based modeling can further illuminate the mechanisms and factors behind structure formation as well as facilitate this understanding, even if the experimental capability is limited. To this end, we present and extend a mechanistic modeling approach (Rupp et al. 2018, Rupp et al. 2019) which is based on a cellular automaton method that resolves explicitely particles at the micrometer scale. Thus it is capable to represent structural changes originating from (electrostatic) interaction of building units (aggregate forming materials). As prototypic building units goethite and illite with needle like and platy shapes of different size and charge are implemented. The operational, comprehensive model allows studying structure formation as a function of composition and charge of such mineral mixtures. Along this line, homoaggregation as well as heteroaggregation scenarios are investigated. The resulting microaggregates are investigated with respect to size, structure, and stability. Moreover, the role of the aspect ratio for stability, the point of zero charge for aggregation, and the amount of excess particles with respect to time is illustrated. Finally, the results are evaluated and compared to experimental data given in Dultz et al. (2019), and extend the scenarios studied there S. Dultz, S.K. Woche, R. Mikutta, M. Schrapel, G. Guggenberger (2019): Size and charge constraints in microaggregation: Model experiments with mineral particle size fractions. Applied Clay Science 170, 29-40. A. Rupp and K. Totsche and A. Prechtel and N. Ray (2018): Discrete-continuum multiphase model for structure formation in soils including electrostatic effects. Frontiers in Environmental Science, 6, 96. A. Rupp, T. Guhra, A. Meier, A. Prechtel, T. Ritschel, N. Ray, K.U. Totsche (2019): Application of a cellular automaton method to model the structure formation in soils under saturated conditions: A mechanistic approach. Frontiers in Environmental Science 7, 170.

Clay minerals and Feand Al-oxyhydroxides are considered as the most important materials for the formation of microaggregate building units in soils. The mode of aggregation and the resulting structure and stability are largely determined by their size, aspect ratio (AR), differences in surface charge (SC), and mixing ratio. Here, the impact of these parameters on the formation of microaggregate building units (BUs) was elucidated with a mechanistic model, i.e. using a twophase cellular automaton method, in which prototypes of illite and goethite were implemented. The simulations allowed assessing the formation of particle arrangements during aggregation, moreover building unit diameters, and the number of discrete particles. The contact area between particles was evaluated as a quantitative measure for stability. Homoaggregation of illite under the sole influence of attracting van der Waals forces enabling face-to-face as well as edge-to-face contacts, resulted in compact structures with a small mean diameter and specific surface area. In contrast, electrostatic attraction between negatively charged faces and positively charged edges favored formation of larger card-house structures, where low contact areas indicated the low stability of the resulting BUs. At constant AR, homoaggregation of illite of different particle size led to BUs of different stability, more precisely smaller particle sizes led to more stable BUs. Variation of the AR of illite, while keeping the particle size constant, revealed that most stable BUs arose from illite with smallest AR. Shielding of coarse goethite particles due to attachment of fine illite with negatively charged edges increased the number of discrete fine illite particles not aggregated. Aggregation of illite with positively charged edges was in fundamental difference to results from simulations with negative edges because of electrostatic attraction between illite particles. The simulation setting, without using fitting parameters resulted in an appropriate approximation of laboratory findings. The simulation clearly facilitated the understanding of microaggregate building unit formation and stability by illuminating turnover dynamics and provision of quantitative data.

Various processes such as heterogeneous reactions or biofilm growth alter a porous medium’s underlying geometric structure. This significantly affects its hydrodynamic parameters, in particular the medium’s effective permeability. An accurate, quantitative description of the permeability is, however, essential for predictive flow and transport modeling. Well-established relations such as the Kozeny–Carman equation or power law approaches including fitting parameters relate the porous medium’s porosity to a scalar permeability coefficient. Opposed to this, upscaling methods directly enable calculating the full, potentially anisotropic, permeability tensor. As input, only the geometric information in terms of a representative elementary volume is needed. To compute the porosity–permeability relations, supplementary cell problems must be solved numerically on this volume and their solutions must be integrated. We apply this approach to provide easy-to-use quantitative porosity–permeability relations that are based on representative single grain, platy, blocky, prismatic soil structures, porous networks, and real geometries obtained from CT-data. As a discretization method, we use discontinuous Galerkin method on structured grids. To make the relations explicit, interpolation of the obtained data is used. We compare the outcome with the well-established relations and investigate the ranges of the validity. From our investigations, we conclude whether Kozeny–Carman-type or power law-type porosity–permeability relations are more reasonable for various prototypic representative elementary volumes. Finally, we investigate the impact of a microporous solid matrix onto the permeability.