EGU Blogs


Guest Post: Jeremy Bennett – Approaches to modelling heterogeneity in sedimentary deposits

Hello everyone. Great that you could make it out to my blog post. I would like to introduce you to some ideas about environmental modelling that I have recently discovered during my work. These ideas are from this paper by Christine Koltermann and Steven Gorelick back in 1996. Whilst the primary focus of their paper is on modelling hydrogeological properties such as hydraulic conductivity, I think there is crossover with other modelling too.

What I find the most interesting about this work are the words they used to describe modelling approaches, meaning the way the modeller sees the world. They break down modelling into three different approaches: structure-imitating, process-imitating, and descriptive methods. Over the next few mousewheel-scrolls I hope I can explain these ideas in simple terms so that they are easy to understand.

This paper discusses models that are spatially distributed – this means that we are trying to estimate values at different locations in space. In the following diagrams I have simplified things to one dimension to hopefully make things a bit clearer. It is also important to note that many models will combine elements of one or more of the following model approaches – often at different scales.

Descriptive methods

Descriptive modelling approaches are primarily conceptual – kind of like joining the data dots in Figure 1 to produce the circle. There might be no hard and fast rules here, although models may be based on years of experience and observation in the field. These models may not be so rigorous and possibly difficult to replicate in different environments.


Fig.1. Descriptive diagram

A good example of descriptive modelling are geological cross sections. They are constructed using borehole data and similar lithologies at similar depths are assumed to be part of the same geological formation. More experienced practitioners will have better intuition for connecting the dots and interpreting the stratigraphic record. In many cases thes cross sections are a suitable model. However in some hydrogeological applications this level of modelling is insufficient as more information is required about the geometry of the formation, and perhaps variations in its hydraulic properties – something that is difficult to derive solely from descriptive methods.

Structure-imitating methods

Structure-imitating modelling approaches quantify observations of the thing to be modelled and use these rules to produce something that looks similar. The structure that is imitated could be the actual shape of the object to be modelled, or it could be something more abstract, such as the geostatistical structure of the observations. To demonstrate: In Figure 2 we have some data shown with black lines. We can then derive information about this data, say in this case the distance of each data point from the centre. From this structural information we can model the rest of the circle.


Fig.2. Structure-imitating diagram

A well-known structure-imitating method is kriging. This method uses the geostatistical structure (i.e. mean and covariance) of a set of observations to estimate values of a variable at other locations. A typical criticism of kriging and other geostatistical methods is that defined boundaries between facies become indistinct and don’t look so geologically plausible. Many other methods have been developed, such as multiple-point statistics, to address these arguments.

Process-imitating methods

Process-imitating modelling approaches rely on the governing equations of a process to produce a plausible model. Governing equations describe the physical principles underlying processes such as fluid motion or sediment transport. This type of approach can occur both as forward or inverse modelling. Forward models require setting key parameters in the model (such as hydraulic conductivity) and then predicting an outcome, such as the distribution of groundwater levels. Inverse models start with the observations and try to fit the hydrogeological parameters to the data.

Our final circle model is in Figure 3. In this particular case we know the equation that gives us the circle. As with all process-imitating modelling approaches there is some kind of parameter input required (or forcing). Here we have assumed that the circle is centred about the origin, and our parameter input is the radius of the circle (4) on the right hand side of the equation. Thus we can model the circle based on the equation and a parameter input.


Fig.3. Process-imitating diagram

The classic process-imitating model approach in hydrogeology is aquifer model calibration. This is a relatively simple, but widely used, application where zones of hydraulic conductivity are created and adjusted to reproduce measured groundwater levels (hydraulic heads). Often these zones are tweaked using a trial-and-error process to get a better match (or reduce the error). Aquifer model calibration is considered a process-imitating approach because it attempts to replicate the governing equations of fluid flow within porous media. MODFLOW is a model from USGS that is often used in this type of modelling.

Thanks for making it all the way down here. My aim was to provide you with a couple of new words to describe modelling approaches in geosciences and beyond. If you are working in hydrogeology then this paper by Koltermann and Gorelick is definitely worth a read – it gives an excellent foot-in-the-door to hydrogeological modelling.


Koltermann, C. E., and Gorelick, S. M. (1996). Heterogeneity in Sedimentary Deposits: A Review of Structure-Imitating, Process-Imitating, and Descriptive Approaches. Water Resources Research, 32(9), pp.2617-2658.

About Jeremy CVpic

Jeremy Bennett is conducting doctoral research at the University of Tübingen, Germany. He is researching flow and transport modelling in heterogeneous porous media. Prior to his post-graduate studies in Germany he worked in environmental consultancies in Australia and New Zealand. Jeremy figures there is no better way to understand a concept than to explain it to others – hopefully this hypothesis proves true. Tweets as @driftingtides and blogs here.

Geology Photo of the Week #46

This week’s photo brings us back to the world of geochemistry. I don’t have much information on this photo beyond that it was taken in Italy.  However, if I may speculate a little it looks like these crystals may possibly be volcanic in origin and the fact that it was taken in Italy, which is famous for its volcanic sulphur deposits. I say this because such crystals are often found near active volcanoes and form from the degassing of sulphur dioxide (SO2) and hydrogen sulphide (H2S) gas from vents known as fumaroles. Groundwater dissolves gases and mineral rich in sulphur at high temperatures however, once the water reaches the low pressure atmosphere of the Earth’s surface these gases are released from the water and native sulphur precipitates.

Close-up of sulphur crystals with condensation drop by Ulrich Kueppers

Close-up of sulphur crystals with condensation drop by Ulrich Kueppers. Source


As you may have gathered from my enthusiastic title I just submitted my thesis! After 6 years of hard work it’s been passed in. To celebrate I decided to make this really cool word cloud showing the most frequently occurring words in the thesis, which currently contains a total of 55,713 words. The bigger the font the more common the word. As you may notice 129I occurs a lot, 1,220 times to be exact, since it is the topic of the entire thing. WordCloud

Here is a pic of the whole thing ready to turn in to the grad studies office. Now that this thing is done hopefully I’ll be able to get back to blogging a little more frequently. Actually, I have ideas for several posts saved up including summaries of a few of my thesis chapters.


By the way, I lied above. I’m going to get a beer to celebrate. Cheers!

Geology Photo of the Week #45

This weeks photo is once again related to permafrost and the Arctic….something tells me I miss being there.

Anyway, the gorgeous photo below shows a terrific example of polygonal patterned ground from Siberia. Patterned ground is a phenomenon that occurs frequently in cold regions and is caused by the seasonal freeze-thaw of the active layer/soil. This process can produce a phenomenon called ice wedges that extend deep into the permafrost (see my photo of a large ice wedge below) as water infiltrates into a crack freezing it and expanding it. This repeats annually as the ice cracks due to the extreme cold and is then filled by new meltwater from the active layer, which freezes.

Ice wedges have excellent potential as a climate research tool as they can be very old and preserve the isotopic signature of each new year’s water. In fact, my research group has an MSc. student working on this exact thing.

Sorting of sediments by the freeze thaw of groundwater also creates patterned ground as the process forces larger sediments upward and lets smaller sediment settle eventually creating little piles of rocks on the ground surface. However, in the case of the photo below, which is in a poorly drained peatland, there are likely lots of ice wedges.

Wet Sedge Polygons on Samoylov Island with Stolb Island in the background - Samoylov Island - Lena River Delta - 20.08.2010 - Sebastian Zubrzycki

Wet Sedge Polygons on Samoylov Island with Stolb Island in the background – Samoylov Island – Lena River Delta – 20.08.2010 – Sebastian Zubrzycki

Ice wedge along the Dempster Hwy. in the Yukon.

Partially collapsed ice wedge in cross section along the Dempster Hwy. in the Yukon. (Photo: Matt Herod)