7.1 Numerical Flow and Transport Models

The sophistication of the model chosen for a project must reflect the nature of the domain being simulated, the degree of parameterization, availability of parameter data, and the objective. Modeling of peatland systems and their interaction with adjacent or underlying mineral groundwater systems requires a two- or three-dimensional approach.

Given the relatively thin peat layer (from a hydrogeological perspective) and the proximity of the water table to the surface, the dominant processes can usually be represented by a model that incorporates only saturated flow processes; with coupling to the atmosphere represented by an appropriate surface boundary condition. Freely available and well-documented models such as MODFLOW, which represent the partial differential equations for flow, provide a useful approach for assessing landscape scale influences on peatland function. For example, Reeve and others (2000) demonstrated the importance of the permeability of the underlying mineral deposit on the nature of vertical flow in bog peatlands. Where underlain by low permeability deposits, simulated flow in peatlands was primarily horizontal with laterally varying, isolated flow cells associated with meso-scale peatland features. In contrast, in areas with relatively high permeability underlying mineral deposits, simulated flow was primarily vertical. Quillet and others (2017) showed—using a saturated flow model—how a permeable esker deposit controlled the topographic slope of the adjacent peatland, and the importance of vertical heterogeneity in the peat deposit for maintaining appropriate water tables. Lower peat hydraulic conductivity associated with enhanced decomposition near bog peatland margins was shown to enhance water storage, which is favorable for peatland development (Lapen et al., 2005).

Sutton (2021) simulated three-dimensional saturated flow and transport in a constructed upland fen peatland system and showed the spatial pattern of salt contamination in the fen peatland reflected the design of the system, including features such as recharge basins in the upland. This, and most other studies, do not explicitly represent the effect of ground freezing in simulation studies. Given the proximity of the water table to the surface in peatlands, the hydraulic properties of the near-surface layers can change profoundly with freezing, and this requires explicit representation of thermal processes in order to simulate winter conditions (McKenzie et al., 2007).

A particular challenge associated with representing flow and transport at the landscape scale is the high degree of discretization required to represent the exponential decrease in hydraulic conductivity with depth, particularly in the upper layers. This feature of peatlands controls the transmissivity feedback mechanism that was described earlier, wherein horizontal flow is highly dependent on water table elevation because water table elevation dictates the extent to which high permeability layers are engaged in the flow process. Higher levels of model discretization require more detailed parameterization and thus, more computational resources. The latter argument diminishes with the availability of increasing computer processing power, but the need for accurate parameter values increases accordingly.

To represent vertical flow and transport, which is important to surface-vegetation— atmosphere transfers, a one-dimensional approach is often sufficient. Typically, these onedimensional approaches explicitly represent variably saturated conditions in the profile. Given the availability, relative simplicity, and limited computational demand of freely available numerical models (e.g., Hydrus 1D; Simunek, 2005), considerable insight has been gained into what governs flow and transport in peat profiles. In general, this is done by solving for water flow with Richard’s Equation in conjunction with a soil hydraulic property model, such as the van Genuchten—Mualem relationships (Mualem, 1976; van Genuchten, 1980), as discussed in Section 3.2 Unsaturated Zone Properties and Processes and represented by Equation 5 and 6. When simulating variably saturated water flow in peatlands, the upper boundary conditions (i.e., precipitation and evapotranspiration) are the key drivers of the hydrologic system.