Karsts exist and cover approximately 15% of the Earth surface. Therefore it can happen very easily that in your hydrological analysis you across a Karst catchment. A general knowledge of karst environment can be gained by reading the White, 2002 paper but, online you can find also the book by Ford and Williamson, 2007.They are quite comprehensive readings, not necessarily focused on the hydrology of the karst systems and how they can be modeled.
White (2000) propose a conceptual map of karst hydrology that is better represented later in Hartmann et al., Figure 4 (see below).
Precipitation falling into a karstic system can be divided into:
- Allogenic recharge: precipitation that falls on non-carbonatic portion of the catchment and enter the carbonate aquifer to the swallets
- Disperse-diffuse infiltration directly happening on the karst surface and from there through the soil or the fractures
- Internal runoff, falling into sinkholes drains
- Flow from perched aquifers. Rainfall is collected by there aquifer and subsequently captured by vertical shaft or widen fractures in the vadose zone.
One important point for hydrologists is to be able to recognize the karst geomorphology, e.g. Waele 2011, to be able to automatically detect it and to treat differently from the rest of the catchment. Hofierka et al., 2018 offers a modern view (and very nice maps) on how to detect the areas presenting sink-holes (dolines) and so from IDAR topographic data. The topic of sinkholes detection, actually is sufficiently covered in literature, see, for instance, other recent references are Pardo-Igúzquiza, 2013, Wu et al., 2016, Zunpanoi et al., 2019. It i s not clear to me at present if sinkholes are the only detectable manifestation of karst, but what I believe is that the decrease superficial erosion in karst area should also be recognizable, together with a disconnected or absent river network but on these specific topics, I did not find suitable references.
Where you have karst, you also have springs. Even if they are not usually detectable by objective methods to find them (e.g.
Geology Stack Exchange), many of them are already known from geological surveys and therefore a smart use of geological maps can help. It is self evident but hydrologist often rush to extract catchment and network characteristics without taking care of them in advance, as they should.
Karst formation are usually mapped, geologists do their work since long time ago, and we should use appropriately their information.
Coming to us, hydrologists measure rainfall and discharges and observe that the spring discharges of catchments affected by karst may look quite insensitive to rainfall variations. The direct way to investigate the response of these catchment is to make leverage on tracer and tracers theory, as for instance reviewed in Hartmann et al., 2014, and shown in Zhang et al., 2021, or Nanni et al., 2020. These techniques, however, are well consolidated and known. For the desktop hydrologist, something can be tried out with techniques of analysis of correlation between rainfall and discharge. Two notable contributions are Fiorillo and Doglioni, 2010 and Jukic and Denic-Jukic, 2015. And another, more hydrological-hydrological, oriented to the determination of some characteristics time of catchments (not necessarily karst) is Giani et al., 2021. More techniques for analyzing these time series, can be found in
one previous post of this blog.
From a practical point of view, what said so far would them urge the astute hydrologist to look for karst when delineating the catchments and subsequently do a careful time series analysis.
Finally, one like me wants to model the water budget. Even this case there exist a quite developed literature. The paper by White (2000) let us envision the typer of models which can be more process-based-groundwater oriented (Rooji, 2007, Hartmann et al, 2014) or lumped, i.e. built
on reservoir type of models (also Hartmann et al., 2014).
In the more process-based type of models, the issue is put properly at work together the Darcian flow and the turbulent flow whose path is unknown and buried, hidden to our eyes which both contribute to the final flow. Because of the structure of the karst network, which is three-dimensional, threshold type of functioning can happen make the modelling more complex (Hartmann et al., 2014).
Lumped, ordinary differential equation (ODEs) type of modelling is simpler but to be not too simple, much heuristic has to be used to implement models that return reasonable behavior. The high heterogeneity of the medium sometimes could help in simplifying the picture but just the real cases applications can discern what is acceptable. In both cases, obviously, the problem of parameter identification is the more important one. There are several good examples of lumped model, well summarized by the paper of Hartmann et al, 2014 or, from a more practical point of view by the KarstMod model, Mazzilli et al., 2019 (
please find its manual here). A careful reading of Hartmann et al 2014, can bring easily to a general conceptual model of karst in term of reservoirs. Rimmer et al, 2012, gives a few use case example of simple working models. Butscher and Huggenberger, 2008 and Tritz et al, 2011 are some deployments of these models that can give some general guidance.
The high heterogeneity of the medium sometimes could help in simplifying the picture but just the real cases applications can discern what is acceptable.
In both cases, of using process-based modelling or lumped models, obviously, the problem of parameter identification is an important one. Worldwide Karst data were made available by Olarinoye et al.,
If you do not have enough time, the best is to read White (2000), De Waele, 2011 and Hartmann et al, 2014 papers first. If you have time for reading just one paper, read Hartmann et al. 2020.
References
Mazzilli, N., V. Guinot, H. Jourde, N. Lecoq, D. Labat, B. Arfib, C. Baudement, C. Danquigny, L. Dal Soglio, and D. Bertin. 2019. “
KarstMod: A Modelling Platform for Rainfall - Discharge Analysis and Modelling Dedicated to Karst Systems.”
Environmental Modelling and Software[R] 122 (103927): 103927.
