## Wednesday, September 4, 2019

### Stomatal resistance and Transpiration

There are several factor influencing water vapor availability in the leaves’ viscous layer and we can start from the water availability in soil. To get into the root, water of some capillaries must be close to roots. Experimental studies about soil tend to say that flux (to the atmosphere) is sustained at the maximum rate to a critical point of soil suction. Does roots cease to sip water when water is not anymore a connected phase ? Or can roots extract water from vapor ? Or what else ? I do not feel that these questions were answered properly in literature, but I also confess I missed some reading so far of the papers where the coupling soil-roots has been treated explicitly.

The other big topic is the physiological reaction to water scarcity. Plants in fact can close stoma: they are like a tap which is being closed with an effect in literature is known as “stomatal resistance”. It cuts the evaporative flux to oppose to the evaporation demand and the reduction is usually represented as a multiplicative factor, the stomatal conductance (actually the inverse of a resistance) which multiply the driving force, which is given as a different of water vapor concentration between the zone very close to the available liquid water and a zone in the viscous boundary layer (VBL) a little apart, such that:
$$Tr = g_l (c(z_0) - c(z))$$
where $T_r$ is transpiration, $g_l$ the stomatal conductance, $c(z_0)$ is the water vapor concentration close to the leaves surface and $c(z)$ is is the vapor concentration at distance $z$.
There is a variety of plants actions that regulate the stomatal resistance which are summarised in the isohydric and anisohydric behavior (Martinéz-Vilalta and Garcia-Forner, 2016). In the first case, the plant progressively closes the stoma as reaction to water stress to maintain as much as possible a balanced water content. In the other case the plant delays stoma closure in the measure it can resist to manifestation of cavitation and produces in its interior a very uneven water distribution. Actually the stomatal resistance $g_s$ is not the only one affecting plants. Plants have roots and a steam that convey water fluxes and also the flux there is traditionally treated as a viscous flow with some resistance. In that cases though, the driving force is the gradient of water potential or, if we prefer the Nobel (1999) view, of the chemical potential (of which the water potential is a particular expression).
Assuming an almost stationary situation along the root-stem-leaves system, the connection between plants compartments can be manipulated within the electric circuitry analogy (resistances sums to obtain a total resistance, as $g_v = 1/g_r+1/g_s+1/g_l$).
This model allows to obtain the suction in leaves, which, in turn, controls the quantity of water vapor in stomatal cavities.
The resistances are further unknown in the coupled water-energy-momentum system that determines evaporation, heat transfer and the water budget, however $g_l$ has been found to be connected to carbon cycle productivity trough the so called Ball-Berry formula (1987, BB). BB (see also Collatz et al, 1991) has been built out of empirical bases and it was subsequently modified (e.g Verhoef and Egea, 2014) to include physiological reactions and the production of abscisic acid, ABA (Buckley, 2017).
To obtain the final result of transpiration, (besides the determination of roots and stem resistances), there is the further problem of the coupling of stoma with the VBL. Again the tradition assume quasi-stationarity of the fluxes and therefore uses the resistance metaphor, assigning to the VBL a resistance according to an integrated Fick’s law. Also in this case, resistances are summed to obtain the comprehensive flux law that regulates the water ascending.
New questions arise: which is the dominant between the two resistances ? Is the resistance metaphor really applicable ?

A couple of papers, in particular, Manzoni et al., 2013 and Bonan et al. 2014 offer two remarkable points of view of the matter. Manzoni is more interested to processes, equations and general issues with plants hydraulics. Bonan et al. goal is the implementation of a model of the soil-plant-atmosphre continuum and therefore its appendixes can be useful to understand some of the details that can be perceived as ambiguous by the beginners in the field. Bonan's treatment is “traditional” being based on the set of assumptions all literature use which give you back an already well packaged simplification of the physics involved. Manzoni et al. put more emphasis on the biophysical aspects and their connections with plants physiology and use partial differential equations to illustrate the concepts. Both of them have a large list of references and, together with the recent work of Verohef and Egea (2016, VE) and the work of Dewar, 2002, can be a solid start for any study of the subject. VE in particular, compare various approaches to modelling the water stress and discuss their ability to reproduce experimental data. One of its main interest is to clarify if either water content or the water pressure explains better plant’s transpiration behavior. VE approach is very practical, since it does not discuss the rational behind the different approaches but just use and test them. The final verdict that pressure explain more properly: this is not so clear indeed until the end. Apparently the result is counter-intuitive with respect the organization of the paper that starts from empirical observation that transpiration follow a two-stage behavior (similar to the one seen in soils) when actual (daily) relative transpiration is plotted against the water available. Therefore there is no better that read it to get the vision clear.

References
• Ball, J. T., Woodrow, J. B., & Berry, J. A. (1987). A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions. Progress in Photosynthesys Research, 4, 221–224. http://doi.org/10.1007/978-94-017-0519-6_48
• Bonan, G. B., Williams, M., Fisher, R. A., & Oleson, K. W. (2014). Modeling stomatal conductance in the earth system: linking leaf water-use efficiency and water transport along the soil–plant–atmosphere continuum. Geoscientific Model Development, 7(5), 2193–2222. http://doi.org/10.5194/gmd-7-2193-2014
• Buckley, T. N. (2017). Modeling Stomatal Conductance. Plant Physiology, 174(2), 572–582. http://doi.org/10.1104/pp.16.01772
• Collatz, G. J., Ball, J. T., Grivet, C., & Berry, J. A. (1991). Physiological and environmental regulation of stomatal conductance, photosynthesis and transpiration: a model that includes a laminar boundary layer,. Agricultural and Forest Meteorology, 54, 107–136.
• Dewar, R. C. (2002). The Ball-Berry-Leunning and Trdieu-Davis stomata models: synthesis and extension with a spatially ggregated picture of guard cell function, 25, 1383–1398. http://doi.org/10.1046/j.1365-3040.2002.00909.x
• Martínez-Vilalta, J., & Garcia-Forner, N. (2016). Water potential regulation, stomatal behaviour and hydraulic transport under drought: deconstructing the iso/anisohydric concept. Plant, Cell and Environment, 40(6), 962–976. http://doi.org/10.1111/pce.12846
• Manzoni, S., Vico, G., Porporato, A., & Katul, G. (2013). Biological constraints on water transport in the soil-plant-atmosphere system. Advances in Water Resources, 51(C), 292–304. http://doi.org/10.1016/j.advwatres.2012.03.016
• Nobel, P. (1991). Pysicochemical and environmental plant physiology (pp. 1–637). S.Diego (CA): Academic Press, Inv.
• Verhoef, A., & Egea, G. (2014). Modeling plant transpiration under limited soil water: Comparison of different plant and soil hydraulic parameterizations and preliminary implications for their use in land surface models. Agricultural and Forest Meteorology, 191, 22–32. http://doi.org/10.1016/j.agrformet.2014.02.009