Author's note

As the case of groundwater modelling cannot be closed with my knowledge so far - I have found that groundwater modelling methods have been playing on my mind. Espeically if you want to model contamination and other global changes. Is SMWB too limited? As all models are abstractions of reality, can we consider it okay that the Richard's equation is not physically correct for preferential flows and heterogenous media? What modelling method do we 'interfere' with the most to fit our data?

I am studying about groundwater modelling this term and so as I learn more about this area I will continue to summarise my findings for this blog. I will decrease in blogging for a while as the module for which this blog was for is over (and coursework for other modules has already begun) but if this is an area you find interesting then follow me on twitter, @_alicefitch, where I will provide a link for when I post. I also hope to set up a permaculture blog when I get planting again, which would follow on from this blog as permaculture is an ecologically friendly way of food production.

Anyway, I hope you found the posts interesting =)

Over and out for now!  

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?

A break from the case - floods, groundwater, and a rant!

I came across this article in The Guardian that is very interesting in relation to groundwater but really angered me so much I had to bring it to your attention.

The interesting stuff is that the Northerners rely on surface waters for their freshwater while the Southerners mostly rely on groundwater aquifers. Though we have had extensive rainfall, because this has been in the North and not the South, the South faces a risk of drought if we don't get enough rainfall before the summer.

The second half of the article is where I got annoyed, specifically with Allen Jenkins as his tone in this article is very dismissive of natural flood defenses:

“..... we have not come across hard evidence that [Lord Krebs] is right. Restoring upland peat bogs is not necessarily going to protect [places such as Tewkesbury],

“There is little evidence that changes in the way we maintain the uplands would have helped reduce the impact of the [rainfall of] the last few weeks. There is little documentation that shows that planting trees or blocking drains or removing sheep would or would not have reduced flooding. "

 “It is probably true that there is an impact in the run-off. But rewilding is beneficial, [so] why not [do it]? But it needs to be done carefully and with evidence.”

I do understand what he is getting at when he says we need more research, but I don't agree with his sentiment that changes in how we maintain and manage the uplands will have little to no effect! I think restoring peat bogs will be effective, Exeter University have found that peat bogs reduce water leaving Exmoor during heavy rains! So I don't understand why he says the evidence is not there. Because, albeit preliminary, it is. 

Also I feel a bit of common sense is needed: we have dramatically altered our upland and lowland landscape - England was once completely forested, we have dredged and straightened river channels, drained marshland, built on floodplains, purposefully kept areas altered (for an example see George Monbiot's article here). Of course we are going to be seeing it exacerbate climatic situations.

I would like to draw your attention to the town of Pickering:

To prevent flooding the town of Pickering implemented in the hills above the town 167 leaky dams made of logs and branches, and added 187 smaller obstructions made of bales of heather that would allow normal flow but slow down high flows. They also planted 29 hectares of woodland and built a bund (embankment) to store and slowly release floodwater. For the grand total of £2 million as opposed to a £20 million concrete wall running through the center of town. Their defenses held, and the town which had previously suffered huge devastation from flooding remained dry.

A leaky dam above Pickering. Source: Pickeringblog

Here is Pickering's website with a video on their flood defences.

I feel Allan Jenkins should have said that more research is needed on an area to area basis to determine which combination of strategies would reduce flooding. For some areas we may find that no environmental measures would have reduced the impact, because of their location. I strongly believe we need to work with nature rather than continue to blindly construct flood defenses around urban areas without a thought to what is happening/ has happened to the wider environment.

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

Water for Thought...

While writing my next post I came across this article for Eva-Lotta Jannson's new book An Acid River Runs Through It which shows the effect of mining on South Africa's rivers.

The blue and yellow-green colour of this pond is where acid mine drainage has created such a low pH. This low pH value means fish and birds cannot survive here.  Source: www.theguardian.com

Untreated water from mining has been allowed to mix with local rivers, making the water highly toxic and devastating local wildlife and communities. As well as affecting surface waters, polluted water will have entered groundwater aquifers. Much like dryland salinity but with perhaps more deadly effects, I think we are going to see the land and local communities experience the consequences of this for a while. 

This is Robinson Lake in Randfontein. It was once rich with wildlife but is now a 'no-go' area as it is filled with dried uranium oxide sediment. Source www.theguardian.com

Sea Under the Land

Unlike river discharge or snow cover groundwater is harder to quantify and monitor, precisely because it is under the ground. Yet it is our largest accessible store of freshwater. therefore, we need to understand how agricultural practices are affecting it.

Bumpiness shows variation in gravity.
GRACE satellites are those in the top right hand corner
 Image source: CEOS EO handbook

We can retrieve information about groundwater levels using piezometers, which will provide information concerning one aquifer or part of an aquifer. Alternatively, to obtain a wider picture we can use the satellites of GRACE (NASA's Gravity Recovery and Climate Experiment mission). From GRACE we get an estimate of terrestrial water storage (TWS) which consists of snow, ice, permafrost, surface water, soil water and groundwater. In order to obtain an estimate of groundwater we first calculate the quantities of the other components using remote sensing, models, and ground based measurements THEN subtract these from the TWS. Here is a really clear document to read explaining more about how GRACE satellites work and how groundwater data can be retrieved.

So how can agriculture impact globally upon groundwater? This will be a bit longer than my average post so have a cup of tea and a mince pie handy!

Thirsty Crops:

Roughly 70% of groundwater abstracted is used for irrigation. When abstraction exceeds recharge then groundwater depletion, the permanent loss of groundwater, can occur. 

The risk of groundwater depletion occurring is especially high during periods of drought. Castle et al., (2014) studied the changes in surface water storage and groundwater storage in the Colorado Basin during drought from December 2004 to November 2013 using GRACE data for TWS, Land Surface Models for soil moisture estimates, SNOWDAS data for snow water equivalent, and reservoir storage data from U.S. Bureau of Reclamation. This period was one of the driest that the area has seen. 

Monthly volume anomalies (changes in volume) for groundwater storage (black line) and surface water storage (green line) with errors (shading) for A) the whole basin and Lake Powell and Lake Mead combined  B)  the upper basin and Lake Powell C) the lower basin and Lake Mead. Source: Castle et al., 2014

The results show that the groundwater store of the Colorado basin risks becoming depleted. Groundwater levels have been decreasing as a consequence of successive droughts reducing recharge and driving higher levels of groundwater abstraction due to drought surfacewater allocations not meeting water demands. The Colorado basin the world's most over allocated catchment and with potential increases in drought severity and occurrence due to climate change we are going to see higher levels of groundwater abstraction in the Colorado basin. Joodaki et al., (2014) using the same method highlighted a similar groundwater situation occurring in the Middle East, which indicates this is a situation we are likely to see happening across the globe as climate becomes more variable.

Land Change:  

Source: http://www.sciencemag.org/site/feature/misc/
webfeat/soilmap/soil_austral_links.html

One of the most dramatic situations illustrating the complex relationship between land use and groundwater can be seen in Australia. In parts of Australia groundwater is very saline and the original vegetation, which was deep rooted trees, kept groundwater levels low and in equilibrium. Deforestation of the land and replacement with agricultural crops (that are shallow rooted) led to a huge rise in the level of the water table, bringing all the dissolved salts to the surface, the consequence of which was the salinisation of large swathes of land rendering it unusable. No vegetation can tolerate the salinity; this situation is known as dryland salinity and is still a major problem for Australia.

Another example is the type of crop grown on the land as different crops have different water requirements. Esnault et al., (2014) have undertaken detailed study to determine which groundwater irrigated crops could 'stress' an aquifer system further by looking at the 'groundwater footprint'. The groundwater footprint is the area needed to sustain groundwater use.

The results for the Central Valley and High Plains aquifer systems in the USA are:

The contribution of each crop type to the regions to groundwater footprint.
The colours for the High Plains aquifers (f, g, and h) are different. Source: Esnault et al., 2014

The pie charts shows each crop type's contribution to the region's groundwater footprint to area ratio. For the Central Valley system hay has the largest ratio and for the High Plains system it is corn gain and cotton. Such information can be highly useful in terms of managing groundwater resources by understanding the consequences of growing a particular crop in a certain region. 
Another point worth noting is that the corn grain and hay grown in the regions of study are mainly for the meat industry.... which makes me think more on the issue of whether you can reconcile being an environmentalist and eating meat brought up in the blog Sown on Stony Ground.

With modelling I don't want to present the results without showing a bit of what's going on 'behind the scenes'. 

Esnault et al., (2014) 's study is complex  requiring data on:

•  irrigated and harvested crop areas
• proportion of crop irrigated by groundwater
• efficiency of irrigation system
• management of surface and groundwater
• groundwater abstraction rates

as well as using global and local hydrological models to:

• obtain recharge estimates
• obtain environmental flow requirements 
• obtain net surface water (called blue water) requirements 

The margin for error grows with each parameter added in, however, to certain extents this cannot be avoided as all the information and processes listed above are needed to calculate groundwater footprint. To be aware of the uncertainty in their approach the authors quantified the amount of uncertainty that each parameter contributed:

The actual value and relative contribution to total uncertainty for each parameter for (a) Central Valley and (b) High Plains aquifer systems. Source: Esnault et al., 2014

By doing this the authors clarified where the largest proportion of uncertainty in their estimates of groundwater footprint lay. For this study it is concerning the quantification of irrigation system efficiency and in estimating groundwater recharge using models. 

This leads me onto my next post which will be about groundwater modelling and what we mean by uncertainty.  

Before I go i'll leave you with this interesting conversational tidbit for Christmas dinner:  in the tropics it is not the duration of rainfall but the intensity that is important for groundwater recharge. As such, we might see groundwater playing an important role in human adaption to climate change. 

With that food for thought have a very MERRY CHRISTMAS! 

Source: https://bongous.com/merry-christmas/

Water, water, everywhere .... ?

As my next post is on agriculture and groundwater, before we get started I thought I'd share this map from Taylor et al., (2012) showing locations of aquifer systems:

As well as Aqueduct's Water Risk Atlas; a really cool interactive map showing inter-annual variability, drought severity, flood occurrence etc across the globe.

Two maps I have picked out for you from the site are: 

Drought severity, red areas are those that have the most extreme droughts:

Groundwater stress, which is the ratio of consumption to withdrawal, red areas indicate potentially unsustainable use of groundwater.

BUT we still need a bit of caution: when studying these maps it is important to take note of the source of the data. These maps are based on data from 1901 - 2008  and 1958 - 2000 respectively. Another two important things to be aware of when looking at groundwater stress is recharge was modelled, and we don't have the full picture concerning groundwater withdrawals and rates. We don't actually know how many wells there are and how much water is being abstracted, especially in developing countries.This point is illustrated in this news article from 2010 (also an interesting tidbit for all those Christmas dinners you are going to) about groundwater withdrawals in Siem Reap, Cambodia which are endangering the future of Angkor Wat.


On another groundwater note ....

I love the history and culture of past civilisations like the Maya, Incas and Khmer Empire. Why such societies 'disappeared' is intriguing; usually attributed to conflict and/or the introduction of disease from explorers - access to water during drought could have played a part. For the Maya, settlements in the north of Yucatá who had natural and easier access to groundwater stores were the ones that appear to have been abandoned last.... interesting eh..... but could drought be the main cause for the disappearance of the Maya.....hmmmmm...... what do you think?