Part 2: Elementary..?

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

Let me present the reader with some features of interest concerning the case and my thoughts. I have certainly struggled with the case as it is a vast area so any deductions from yourselves would be greatly appreciated. So please have a whiskey and pipe handy as you review my case notes:

Feature of interest no. 1: Soil Heterogeneity 

The Richard' equation assumes the soil to be homogeneous in its pore size; which it rarely is.

Feature of interest no. 2: Preferential Flow

Preferential flows are important regarding recharge as they can suddenly raise groundwater levels regardless of current soil moisture. The Richard's equation does not hold for preferential flows and further adaptations to the equation have to be made, almost warping the physical principles and in turn making it a more conceptual than physical equation.

Feature of interest no 3: Number of Parameters

The number of parameters needed for models using Darcy-Richard's equations is greater. Especially when modelling preferential flows. Cuthbert et al., (2013) found for their study site that to model water flow using a dual-porosity approach they would need between 18 to 48 parameters.

The reason this is not ideal involves delving into the meaning of uncertainty. Uncertainty in the model is how much our model differs from the physical truth.

There will be uncertainty with input data: human error in collecting, recording equipment error, spatial/temporal resolution, interpolation of data. Uncertainty with the model structure; a key process might be absent or the model could be biased. If it is based on solving Darcy-Richard's equations then there will be uncertainty with the best method used to do this: finite difference vs finite element (I have written more on this, so post in the comments if you want to know more.). More relevant to this debate is that there will be uncertainty with the parameters generated because the values are unknown to us and found using optimisation methods. Starting ranges are often gauged from laboratory experiments; obtaining values from the field for Darcy-Richard's equations is nigh on impossible.

In some cases by using Darcy-Richard's equations do we increase the complexity without getting significant rewards in return, only additional uncertainty?

Feature of interest no 4: Horizontal Flow

If horizontal flows in the unsaturated zone contribute to recharge then the SWMB method is not complex enough. Darcy-Richard's equations - or simplifications of them - need to be employed, and they have captured groundwater recharge of the system under study as can be seen in Doumar et al., (2012)

Thoughts: 

Source: Tv Tropes

Hmmmm.... it seems there is no clear solution to this case! Neither method has 100% success rate and both are limited in different ways. For a simple recharge model I am initially inclined towards the SMWB method, as yes you can get a better spatial discretization with Darcey-Richard's but the number of parameters is significantly increased. Almost complexity for complexity's sake. But there is no denying that horizontal flows in the unsaturated zone are important for many aquifers, and Darcy-Richard's equations are the predominant option available to capture this. Therefore, I understand their incorporation into a larger catchment models; processes can be combined in a model (as seen in Liu et al.,(2007)), soil can be spatially discretized (not possible to such a fine scale with the SMWB method), and sometimes we need that level of complexity to discover new aspects of system. i.e. what parameter the model is most sensitive too can give insight into the physical system it is describing.

Therefore we cannot close the case completely. Both methods have their uses, and I deem the success of the method dependent on the dominant processes driving recharge and the extent of soil homogeneity.

We need to accurately capture recharge patterns in order to see how groundwater may be affected by climate change and prevent groundwater depletion. With no perfect method available at the moment, to model recharge I would try first an adaption of the SMWB method. If this failed to capture groundwater recharge patterns and incorporate the hydrological processes I wanted to include, then I would try a model based on Darcy-Richard's equations.

 Do you agree with my solution?