Wednesday, December 13, 2017

Monday's discussion on evapotranspiration - Part II - The soil-plants fluxes

The first post treated transpiration from the point of view of the atmosphere control volume. There is a “below” though. Below is composed by leaves, trunks/stems, roots. Roots, in turn, are being inserted in soil from where they sip water and nutrients.
Water in soil is understood to be moved by Richards equation (with all the possible variations or extensions), essentially a Stokesian flow (therefore laminar) in the bundle of soil pores.
Plants do not have a pumping heart and therefore has been since long time argued how they can move water up until the tallest leaves that, can be as high as 150 m above soil level. Some plants do not have either a real “vascular” system in the sense we mean for animals, with arteries and veins. They have indeed specialised interconnected cells to move water up, called collectively xylem, and specialised interconnected cells to move around sucrose and the products of photosynthesis (especially to fruits and roots) called phloem.

So the xylem is the place were to look for ascending water. But how water moves in it ? Since Hales (1727), reported in Holbrook and Zwieniecki (2005), the theory invoked was the cohesion-tension one, which is well illustrated in the introduction of e.g. Holbrook and Zwieniecki (2005), which is open (on Amanazon). Other references include Tyree (2003), which is satisfying from the conceptual point of view but not from the point of view of equations. From this side, possibly Steudle (2001) and Strook et al., (2014) are better. Also Pickard (1981) remains a good reference.
The problems to be understood in xylem water movement is how cohesion-tension works. Under normal conditions, atmosphere is very arid and, for instance at normal temperatures, assuming a 50% of specific humidity of air, it correspond to a pressure of -100MPa (e.g. Jensen at al, 2016), while at roots is usual conditions, water is at much higher pressure, ~ -1.5MPa, meaning, that the gradient of pressure along a plant of ten can be as high are 10 MPa/m (see also Nobel, 2009).
Therefore water is “pulled” and we have to face with the counterintuitive idea that water resist to a tension. For liquids to resist to tensile forces, it is necessary that no bubble is nucleated inside the liquid that disrupt the liquid continuity (creating emboli, e.g. Fsher, 1948). Eventually mechanisms for refilling the vessels have also to be required for understanding the real functioning of plants. This is actually matter of research.
Very much attention to the physics of the process, is also paid in the recent review by Jensen et al, (2016). There also the phloem flux is covered with quite detail and reference therein is large and up-to date. Reading the papers I cited, that are just a few in my collection, can be a starting point for understanding the problem, and this is an advise that I am experimenting myself.
Personally, being highly ignorant of plants physiology, I also require to study it overall. A reference I am following is a classic textbook, Taiz and Zeiger (2002), but a more physical-chemical-mathematical approach ca be found in Nobel (2009).
My first look at the above papers make me remain with the idea that too details hide a possible, more integrated and macroscopic treatment of the matter, at level of single tree, without having necessarily to cope with each cellular movements of water. In fact a look to plants functioning as a whole, is what we, hydrologists are looking for.
Concentrating on plants does not mean we have the whole picture, since soil-plant(s) interactions must be accounted for. We already said that, especially in this case, Richards equation is considered the equation describing water flow in soil. Richards equation, however, is a partial differential equation, ideally written at the Darcy scale, while soil-water-plant interactions happen at the smallest scale of roots. Pickard (1981) gives a description of roots structure but this is therefore not enough to understand well what happens. Soil scientists are bold, and therefore they use a sort of brute-force attack to the problem, where the Darcy scale is ignored and Richards equation is used at small scale where one root link can be associated “mechanistically” to an elementary control volume. A good and up-to-date illustration of this approach is given, for instance in Schröder (2013) Ph.D. Thesis. The only trick used to differentiate the usual approach for adapting it to root interactions is to add two type of conductivities. But please read Schröder (2013) and Huber et al. (2014) to have full and detailed account of it. Companion to this approach is the use of some root model, for instance as Root Typ (Pagès et al., 2004). The latter model are useful also alone, cause the information they contain of roots architecture and density, factors that certainly any theory cannot neglect.


So, I hope to have indicated some initial lectures of which you find the reference below. Below below you also find a bunch of other references, some from the same Authors, that could probably be a good second lecture.

References

A wild bunch of references

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  • Bouda, M., & Saiers, J. E. (2017). Dynamic effects of root system architecture improve root water uptake in 1-D process-based soil-root hydrodynamics. Advances in Water Resources, 1–53. http://doi.org/10.1016/j.advwatres.2017.10.018
  • Carminati, A., Moradi, A. B., Vetterlein, D., Vontobel, P., Lehmann, E., Weller, U., et al. (2010). Dynamics of soil water content in the rhizosphere. Plant and Soil, 332(1-2), 163–176. http://doi.org/10.1007/s11104-010-0283-8
  • Couvrer, V. (2017, October 30). Emergent properties of plants hydraulic architecture: a modelling study. 
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  • Delory, B. M., Baudson, C., Brostaux, Y., Lobet, G., Jarden, du, P., Pagès, L., & Delaplace, P. (2015). archiDART: an R package for the automated computation of plant root architectural traits, 1–20.
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  • Hildebrandt, A., Kleidon, A., & Bechmann, M. (2016). A thermodynamic formulation of root water uptake. Hydrology and Earth System Sciences, 20(8), 3441–3454. http://doi.org/10.5194/hess-20-3441-2016
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