Modelling the influence of mechanical-ecohydrological feedback on the nonlinear dynamics of peatlands

Peatlands are complex systems that exhibit nonlinear dynamics due to internal and external feedback mechanisms. However, the feedback of vegetation on peat volume changes that potentially affect peatland dynamics is not well understood. Here, we analyse the consequences of coupling between plant functional types with peat stiffness on a nonequilibrium model of a peatland by developing MPeat model. In this formulation, the peat systems prefer to exist in two possible states defined by two limit cycles, one corresponding to a wet and the other to a dry attractor. These states can also coexist under the same net rainfall indicating bistability in which a crucial drying threshold leads to a tipping point and associated regime shift from soft-wet to stiff-dry states with related changes in rates of carbon storage. While the shift from wet to dry states constitutes a tipping point, to shift from the dry to wet states requires more sustained increases in net rainfall, indicating that dry state is the more stable attractor as the peatland grows. As the model peatland evolves, the response of surface motion, carbon accumulation, and water table depth to the same external forcing becomes increasingly higher amplitude indicating that a degree of caution may be required when interpreting the paleorecord. Investigation of the behaviour of these states in response to seasonal variations in water budget suggests that the wet state will display high amplitude and later peak timing when compared to the dry state, a phenomenon that is observed in measures of surface motion. Our study highlights the possible importance of mechanical-ecohydrological feedback and, in particular, the role of the coupling between the proportion of plant functional types, peat Young's modulus, plant weight, and water table position in influencing peatland regime shifts, critical thresholds or tipping points, and both short- and long-term peatland dynamical behaviour

MPeat2D - a fully coupled mechanical-ecohydrological model of peatland development in two dimensions

Higher-dimensional models of peatland development are required to analyse the influence of spatial heterogeneity and complex feedback mechanisms on peatland behaviour. However, the current models exclude the mechanical process that leads to uncertainties in simulating the spatial variability in the water table position , vegetation composition, and peat physical properties. Here, we propose MPeat2D, a peatland development model in two dimensions, which considers mechanical, ecological, and hydrological processes together with the essential feedback from spatial interactions. MPeat2D employs poroelasticity theory that couples fluid flow and solid deformation to model the influence of peat volume changes on peatland ecology and hydrology. To validate the poroelasticity formulation, the comparisons between numerical and analytical solutions of Mandel's problems for two-dimensional test cases are conducted. The application of MPeat2D is illustrated by simulating peatland growth over 5000 years above a flat and impermeable substrate with free-draining boundaries at the edges, using constant and variable climate. In both climatic scenarios, MPeat2D produces lateral variability in the water table depth, which results in the variation in the vegetation composition. Furthermore, the drop in the water table at the margin increases the compaction effect, leading to a higher value of bulk density and a lower value of active porosity and hydraulic conductivity. These spatial variations obtained from MPeat2D are consistent with the field observations, suggesting plausible outputs from the proposed model. By comparing the results of MPeat2D to a one-dimensional model and a two-dimensional model without the mechanical process, we argue that mechanical-ecohydrological feedbacks are important for analysing spatial heterogeneity, shape, carbon accumulation, and resilience of peatlands

Modelling and upscaling of transport in carbonates during dissolution: validation and calibration with NMR experiments

We present an experimental and numerical study of transport in carbonates during dissolution and its upscaling from the pore (∼ μm) to core (∼ cm) scale. For the experimental part, we use nuclear magnetic resonance (NMR) to probe molecular displacements (propagators) of an aqueous hydrochloric acid (HCl) solution through a Ketton limestone core. A series of propagator profiles are obtained at a large number of spatial points along the core at multiple time-steps during dissolution. For the numerical part, first, the transport model—a particle-tracking method based on Continuous Time Random Walks (CTRW) by Rhodes et al. (2008)—is validated at the pore scale by matching to the NMR-measured propagators in a beadpack, Bentheimer sandstone, and Portland carbonate Scheven et al. (2005). It was found that the emerging distribution of particle transit times in these samples can be approximated satisfactorily using the power law function ψ(t) ∼ t −1 −β, where 0 < β < 2. Next, the evolution of the propagators during reaction is modelled: at the pore scale, the experimental data is used to calibrate the CTRW parameters; then the shape of the propagators is predicted at later observation times. Finally, a numerical upscaling technique is employed to obtain CTRW parameters for the core. From the NMR-measured propagators, an increasing frequency of displacements in stagnant regions was apparent as the reaction progressed. The present model predicts that non-Fickian behaviour exhibited at the pore scale persists on the centimetre scale

The impact of porous media heterogeneity on non-Darcy flow behaviour from pore-scale simulation

The effect of pore-scale heterogeneity on non-Darcy flow behaviour is investigated by means of direct flow simulations on 3-D images of a beadpack, Bentheimer sandstone and Estaillades carbonate. The critical Reynolds number indicating the cessation of the creeping Darcy flow regime in Estaillades carbonate is two orders of magnitude smaller than in Bentheimer sandstone, and is three orders of magnitude smaller than in the beadpack. It is inferred from the examination of flow field features that the emergence of steady eddies in pore space of Estaillades at elevated fluid velocities accounts for the early transition away from the Darcy flow regime. The non-Darcy coefficient β, the onset of non-Darcy flow, and the Darcy permeability for all samples are obtained and compared to available experimental data demonstrating the predictive capability of our approach. X-ray imaging along with direct pore-scale simulation of flow provides a viable alternative to experiments and empirical correlations for predicting non-Darcy flow parameters such as the β factor, and the onset of non-Darcy flow

MPeat—A fully coupled mechanical-ecohydrological model of peatland development

Mathematical models of long-term peatland development have been produced to analyse peatland behaviour. However, existing models ignore the mechanical processes that have the potential to provide important feedback. Here, we propose a one-dimensional model, MPeat, that couples mechanical, ecological and hydrological processes via poroelasticity theory, which couples fluid flow and solid deformation. Poroelasticity formulation in the MPeat is divided into two categories, fully saturated and unsaturated. To validate this formulation, we compare numerical solutions of the fully saturated case with analytical solutions of Terzaghi's problem. Two groups of MPeat simulations are run over 6,000 years using constant and variable climate, and the results are compared to those of two other peat growth models, DigiBog and the Holocene Peat Model. Under both climatic conditions, MPeat generates the expected changes in bulk density, active porosity and hydraulic conductivity at the transition from the unsaturated to the saturated zone. The range of values of peat physical properties simulated by MPeat shows good agreement with field measurement, indicating plausible outputs of the proposed model. Compared to the other peat growth models, the results generated by MPeat illustrate the importance of poroelasticity to the behaviour of peatland. In particular, the inclusion of poroelasticity produces shallower water table depth, accumulates greater quantities of carbon and buffers the effect of climate changes on water table depth and carbon accumulation rates. These results illustrate the importance of mechanical feedbacks on peatland ecohydrology and carbon stock resilience