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.


A wild bunch of references

  • Aroca, R., Porcel, R., & Ruiz-Lozano, J. M. (2011). Regulation of root water uptake under abiotic stress conditions. Journal of Experimental Botany, 63(1), 43–57.
  • 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.
  • 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.
  • Couvrer, V. (2017, October 30). Emergent properties of plants hydraulic architecture: a modelling study. 
  • Debenedetti, P. G. (2012). Stretched to the limit. Nature Physics, 1–2. 
  • 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.
  • Fiscus, E. L. (1975). The Interaction between osmotic- and pressure-induced water flow in plats roots, 55, 917–922. 
  • Fisher, J. C. (1948). The Fracture of Liquids. Journal of Applied Physics, 19(11), 1062–1067.
  • Hartvig, K. (2016). Osmotically driven flows and maximal transport rates in systems of long, linear, porous pipes. arXivfluid, 1–18. 
  • Hildebrandt, A., Kleidon, A., & Bechmann, M. (2016). A thermodynamic formulation of root water uptake. Hydrology and Earth System Sciences, 20(8), 3441–3454.
  • Hodge, A., Berta, G., Doussan, C., Merchan, F., & Crespi, M. (2009). Plant root growth, architecture and function. Plant and Soil, 321(1-2), 153–187.
  • Holbrook, N. M., Burns, M. J., & Field, C. B. (1995). Negative Xylem Pressures in Plants: A Test of the Balancing Pressure Technique. Science, 270(5239), 1–3. 
  • Huber, K., Vanderborght, J., Javaux, M., & Vereecken, H. (2015). Simulating transpiration and leaf water relations in response to heterogeneous soil moisture and different stomatal control mechanisms. Plant and Soil, 394(1-2), 1–18.
  • Huber, K., Vanderborght, J., Javaux, M., Schröder, N., Dodd, I. C., & Vereecken, H. (2014). Modelling the impact of heterogeneous rootzone water distribution on the regulation of transpiration by hormone transport and/or hydraulic pressures. Plant and Soil, 384(1-2), 93–112.
  • Iversen, C. M., McCormack, M. L., Powell, A. S., Blackwood, C. B., Freschet, G. T., Kattge, J., et al. (2017). A global Fine-Root Ecology Database to address below-ground challenges in plant ecology. New Phytologist, 215(1), 15–26.
  • Janbek, B., & Stokie, J. (2017). Asymptotic and numerical analysis of a porous medium model for transpiration-driven sap flow in trees. arXivfluid, 1–24. 
  • Javaux, M., Couvreur, V., Vanderborght, J., & Vereecken, H. (2013). Root Water Uptake: From Three-Dimensional Biophysical Processes to Macroscopic Modeling Approaches. Vadose Zone Journal, 12(4), 0–16.
  • Javaux, M., Schröder, T., Vanderborght, J., & Vereecken, H. (2008). Use of a Three-Dimensional Detailed Modeling Approach for Predicting Root Water Uptake. Vadose Zone Journal, 7(3), 1079–1088.
  • Jensen, K. H., Berg-Sørensen, K., Bruus, H., Holbrook, N. M., Liesche, J., Schulz, A., et al. (2016). Sap flow and sugar transport in plants. Reviews of Modern Physics, 88(3), 320–63.
  • Jorda, H., Perelman, A., Lazarovitch, N., & Vanderborght, J. (2017). Exploring Osmotic Stress and Differences between Soil–Root Interface and Bulk Salinities. Vadose Zone Journal, 0(0), 0–13.
  • Kalbacher, T., Delfs, J.-O., Shao, H., Wang, W., Walther, M., Samaniego, L., et al. (2011). The IWAS-ToolBox: Software coupling for an integrated water resources management. Environ Earth Sci, 65(5), 1367–1380.
  • KALDENHOFF, R., RIBAS-CARBO, M., SANS, J. F., LOVISOLO, C., HECKWOLF, M., & UEHLEIN, N. (2008). Aquaporins and plant water balance. Plant, Cell and Environment, 31(5), 658–666.
  • Kuhlmann, A. (2011, November 14). Influence of soil structure and root water uptake on flow in the unsaturated zone. (I. Neuweiler, Ed.). Stuttgart University. 
  • Ma, L., Chen, H., Li, X., He, X., & Liang, X. (2016). Root system growth biomimicry for global optimization models and emergent behaviors. Soft Computing, 21(24), 1–18.
  • Maherali, H. (2017). The evolutionary ecology of roots. New Phytologist, 215(4), 1295–1297.
  • Medlyn, B. E., De Kauwe, M. G., Lin, Y.-S., Knauer, J., Duursma, R. A., Williams, C. A., et al. (2017). How do leaf and ecosystem measures of water-use efficiency compare? New Phytologist, 216(3), 758–770.
  • Nelson, P. (2002). Biological Physics: Energy, Information, Life (pp. 1–532).
  • Nobel, P. (2017). Physicochemical and environmental plant physiosology (pp. 1–8).
  • Pickard, W. F. (1981). The ascent of sap in plants. Progr. Biophys. Molec. Biol., 37, 181–229. 
  • PITTERMANN, J. (2010). The evolution of water transport in plants: an integrated approach. Geobiology, 8(2), 112–139.
  • Rand, R. H. (1983). Fluid Mechanics of Green Plants. Annu. Rev. Fluid Mech., 15(1), 29–45.
  • Rockwell, F. E., Holbrook, N. M., & Stroock, A. D. (2014). The Competition between Liquid and Vapor Transport in Transpiring Leaves. Plant Physiology, 164(4), 1741–1758.
  • Sack, L., Ball, M. C., Brodersen, C., Davis, S. D., Marais, Des, D. L., Donovan, L. A., et al. (2016). Plant hydraulics as a central hub integrating plant and ecosystem function: meeting report for “Emerging Frontiers in Plant Hydraulics” (Washington, DC, May 2015). Plant, Cell and Environment, 39(9), 2085–2094.
  • Sane, S. P., & Singh, A. K. (2011). Water movement in vascular plants: a primer. Journal of the Indian Institute of Science, 91(3), 233–243. 
  • Schlüter, S., Vogel, H. J., Ippisch, O., & Vanderborght, J. (2013). Combined Impact of Soil Heterogeneity and Vegetation Ty e on the Annual Water Balance at the Field Scale. Vadose Zone Journal, 12(4), 0–17.
  • Schneider, C. L., Attinger, S., Delfs, J. O., & Hildebrandt, A. (2010). Implementing small scale processes at the soil-plant interface - the role of root architectures for calculating root water uptake profiles. Hess, 279–290. 
  • Schröder, N. (2013, November 14). Three-dimensional Solute Transport Modeling in Coupled Soil and Plant Root Systems. 
  • Schwartz, N., Carminati, A., & Javaux, M. (2016). The impact of mucilage on root water uptake-A numerical study. Water Resources Research, 52(1), 264–277.
  • Severino, G., & Tartakovsky, D. M. (2014). A boundary-layer solution for flow at the soil-root interface. Journal of Mathematical Biology, 70(7), 1645–1668.
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  • Sperry, J. S., Hacke, U. G., Oren, R., & Comstock, J. P. (2002). Water deficits and hydraulic limits to leaf water supply. Plant, Cell and Environment, 25(2), 251–263.
  • Steudle, E. (2000a). Water uptake by roots: effects of water deficit. Journal of Experimental Botany, 51(350), 1351–1542. 
  • Steudle, E. (2000b). Watter uptake by plant roots: an integration of views. Plant and Soil, 226, 45–56. 
  • Steudle, E., & Henzler, T. (2005). Water channels in plants: do basic concepts of water transport change ? Journal of Experimental Botany, 46(290), 1067–1076. 
  • Steudle, E., & Peterson, C. A. (1998). How does water get through roots ? Journal of Experimental Botany, 49(322), 775–788. 
  • Stroock, A. D., Pagay, V. V., Zwieniecki, M. A., & Michele Holbrook, N. (2014). The Physicochemical Hydrodynamics of Vascular Plants. Annu. Rev. Fluid Mech., 46(1), 615–642.
  • THOMPSON, M. V., & Holbrook, N. M. (2003). Application of a Single-solute Non-steady-state Phloem Model to the Study of Long-distance Assimilate Transport. Journal of Theoretical Biology, 220(4), 419–455.
  • Thompson, M. V., & Holbrook, N. M. (2003). Scaling phloem transport: water potential equilibrium and osmoregulatory flow, 1–17.
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  • Tyree, M. T. (2003). The ascent of water. Nature, 423(26 June 2003), 923. 
  • Vadez, V., Kholova, J., Medina, S., Kakkera, A., & Anderberg, H. (2014). Transpiration efficiency: new insights into an old story. Journal of Experimental Botany, 65(21), 6141–6153.
  • Vrugt, J. A., Hopmans, J. W., & Simunek, J. (2001). Calibration of a two-dimenional root water uptake model. Soil Science Society of America Journal, 1–11. 
  • WINDT, C. W., VERGELDT, F. J., DE JAGER, P. A., & van AS, H. (2006). MRI of long-distance water transport: a comparison of the phloem and xylem flow characteristics and dynamics in poplar, castor bean, tomato and tobacco. Plant, Cell and Environment, 29(9), 1715–1729.
  • Zarebanadkouki, M., Meunier, F., Couvreur, V., Cesar, J., Javaux, M., & Carminati, A. (2016). Estimation of the hydraulic conductivities of lupine roots by inverse modelling of high-resolution measurements of root water uptake. Annals of Botany, 118(4), 853–864.

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