Part 1: Come Watson! The game is afoot!

The problem: To avoid future over-abstraction we need to understand how recharge will be affected by changing climate conditions.

The case: What is the best model for groundwater recharge?

The perpetrators: SMWB or Darcy-Richard's Equation

Okay so groundwater modelling isn't so dramatic that it can be used in a Sherlock Holmes mystery (I think I am just a bit too over-enthusiastic from watching 'The Abominable Bride' ) but the choice of groundwater modelling is an interesting case.

Before we get into the nitty-gritty, we need the background information for the case:

Soil Structure

Soil consists of particles (that will aggregate according to their properties), micropores and macropores. Macropores are large, visible pores usually greater than 0.08mm and can continue for a several meters vertically or horizontally. They are caused by the growth and decay of roots and mycelia, drought, and burrowing animals.

Source: US Department of the Interior, Bureau of Reclamation

The diagram on the left illustrates the different water zones. In the soil zone there will be time and space variation in moisture content, and from the dashed line indicating the bottom of the soil zone to the water table we expect to see downward percolation to the water table only.

Water moves through the soil as matrix flow; the slow and even movement of water through pore space following convective-dispersion theory, and preferential flow; the sudden and uneven movement of water.

It is through macropores that preferential flow mainly occurs and being able to accurately model preferential flow is at the forefront of groundwater modelling.

The Soil Moisture Water Balance (SMWB) theory and Darcy-Richard's equations are the two most widely used methods and are different from each other. One is more conceptual where the other is more physically based.

SMWB

The Soil Moisture Water Balance equation, is a bucket approach and states that recharge occurs when the field capacity (which is the total amount of water that the soil can hold against gravity) of the soil has been met. Moisture is removed from the soil by evaporation and evapotranspiration, and a particular fraction can be held near the surface depending on soil type even when there is a deficit. Key parameters for SMWB models are:

- field capacity
- vegetation cover
- rooting depths
- evapotranspiration
- bare soil evaporation

The SMWB method is conceptual as it incorporates no physically based calculation of how water moves through the unsaturated zone to the aquifer. It quantifies the amount of water that becomes recharge from a set input.

It can only be used to model direct recharge (i.e. from irrigation or precipitation) and not groundwater flows or exchanges. Additionally, the time lag between infiltration and appearance in groundwater stores has to be estimated, usually by cross-correlating rainfall and groundwater reservoir levels.

Darcy-Richard's Equation

The Richard's equation is derived from Darcey's law of saturated flow through porous media and the

Source: USGS 

 law of conservation of mass, and describes how water moves through unsaturated soils. In the Richard's equation water moves due to gravity, hydraulic head and capillarity and it's flow is restrained by the hydraulic conductivity of the soil.

Models such as HYDRUS, and MODFLOW that employ the Richard's equation to model water flow in the unsaturated zone and Darcy's law to model water flow in the saturated zone are considered physically based models as the model is based on physical principles. Often a simplification of the Richard's equation is used, where the vertical force is assumed to be gravity only and the hydraulic head is ignored. MIKESHE software employs this method. Unlike SWMB models these equation can be employed to model groundwater flows and exchanges such as transfers to and from surface water stores. The diagram on the right illustrates what MODFLOW can model.

The same parameters used for SMWB are needed along with additional parameters and a more complex model domain. Most notably the soil needs to be discretized: each cell is assigned a depth and soil type, vertical and horizontal hydraulic conductivity of the soil type is assigned, boundary conditions need to be specified, as well as hydraulic head (if using full Richard's equation).

Preferential Flows

A hurdle for both types of modelling is preferential flows. Preferential flows are difficult to model as they can take place regardless of the soil moisture content and do not conform to Richard's equation which assumes equilibrium conditions and a steady-state.

One way SMWB models handle this is by adding a bypass mechanism: when the rainfall is above a certain limit, x% of the rainfall become preferential flow. Alternatively a source-responsive model, where lower layers of soil respond to inputs, can be coupled with a SMWB model. See Cutherbert et al., (2013) for a detailed description.

Models using the Richard's Equation model preferential flows using a 'dual' approaches, where the soil is split into two different domains: one domain consists of the micropores (domain 1) and the other consists of the macropore / fracture system (domain 2). Some water is exchanged between the two domains but dual-porosity models assume that water flows only in domain 2, whereas dual-permeability models allow for flow in both domains. Water flow in each domain is governed by different equations. Dual-permeability approaches are preferred yet implementing them requires a large number of parameters. Physically based model codes commercially available explain which method they employ and the governing equations for the different domains, i,e,: MODFLOW (dual-porosity), HYDRUS (dual porosity or dual-permeability), MACRO (dual-permeability)


That wraps up our brief introduction to groundwater modelling. Happy New Year and in the next post I'll investigate the case!

Source: www.bbc.co.uk