Water transport through tall trees: A vertically explicit, analytical model of xylem hydraulic conductance in stems

Abstract

Trees grow by vertically extending their stems, so accurate stem hydraulic models are fundamental to understanding the hydraulic challenges faced by tall trees. Using a literature survey, we showed that many tree species exhibit continuous vertical variation in hydraulic traits. To examine the effects of this variation on hydraulic function, we developed a spatially explicit, analytical water transport model for stems. Our model allows Huber ratio, stem-saturated conductivity, pressure at 50% loss of conductivity, leaf area, and transpiration rate to vary continuously along the hydraulic path. Predictions from our model differ from a matric flux potential model parameterized with uniform traits. Analyses show that cavitation is a whole-stem emergent property resulting from non-linear pressure-conductivity feedbacks that, with gravity, cause impaired water transport to accumulate along the path. Because of the compounding effects of vertical trait variation on hydraulic function, growing proportionally more sapwood and building tapered xylem with height, as well as reducing xylem vulnerability only at branch tips while maintaining transport capacity at the stem base, can compensate for these effects. We therefore conclude that the adaptive significance of vertical variation in stem hydraulic traits is to allow trees to grow tall and tolerate operating near their hydraulic limits.

Modelling water fluxes in plants: from tissues to biosphere

“…Procedures to scale up curves of vulnerability to embolism within plants are not well established. Modelling (Hölttä et al ., ) analyses suggest that a vertically varying profile of ψ X,50 (more negative ψ X,50 values attained towards the top of the tree) may be realistic, consistent with the hypothesis of hydraulic vulnerability segmentation (see review of available data and theory in Couvreur et al ., ). However, some empirical reports contradict this hypothesis (Wason et al ., ), despite general trends for narrower conduits in leaves vs stems/roots.…”

“…Moreover, xylem hydraulic properties and their variation with branch order constrain metabolic scaling laws emerging from fractal tree models (West et al, 1999;Savage et al, 2010). As process understanding improved, mathematical approaches to solve the water transport problem also developed, from the first models based on series of point conductances (electrical analogy) (van den Honert, 1948), to those employing the matrix flux potential approach (Kirchhoff transform) to account for continuous variations in water potential along homogenous stem segments (Sperry et al, 1998;Sperry & Love, 2015), to more sophisticated numerical (Bohrer et al, 2005;Janott et al, 2011) and analytical (Couvreur et al, 2018) solutions.…”

“…This minimal representation of water transport in plants allows for full analytical tractability, but rests on the assumptions that plant water storage, the effect of gravity, and the temporal variability of environmental conditions other than rainfall and soil moisture can be neglected. The first assumption is reasonable especially at the daily time scale and under moist conditions, while the second one especially so for relatively short plants, but even in that case the progressive development of cavitation along the hydraulic pathway cannot be captured (Couvreur et al, 2018). Xylem vulnerability and stomatal closure curves are assumed static and piecewise linear functions of leaf water potential.…”

Beyond isohydricity: The role of environmental variability in determining plant drought responses

“…Given the potentially intractably large number of traits and environmental variables that could be relevant for drought vulnerability in different biomes (O'Brien et al, ), the challenge of effective plant response classification will lie in the identification of a minimal set of key parameters that drive plant water relations. We have shown recently that simple plant hydraulics models—in the spirit of those adopted by Couvreur et al (), Feng, Dawson, Ackerly, Santiago, and Thompson (), Manzoni, Vico, Katul, Palmroth, and Porporato (), and Sperry et al ()—can embed the interplay of plant phenotypic traits and environmental variations in plant response dynamics and suggest a promising way forward for systematically exploring this multidimensional space (Feng et al, ). More complex computational models (Mackay et al, ; Mirfenderesgi et al, ) complement these simple approaches by providing more process‐based descriptions that point to limitations in the simpler models (albeit at the cost of additional data requirements).…”

Relationship between foliar δ13C and sapwood area indicates different water use patterns across 236 Salix genotypes

“…c a = 400 μmol/mol, Δ = 1 MPa, D = 0.01 mol/mol, g SL = 25 mol/ (m 2 s MPa), k = 0.05 mol/(m 2 s) (baseline constant; to model changes with TLA, the baseline k value is multiplied by TLA/1.5), SA = 750 mm 2 (baseline constant; to model changes with TLA, the SA/TLA ratio was assumed equal to 500 mm 2 /m 2 ) "Relationship between sapwood area and foliar carbon isotope values as indicator of water use patterns". As our model neglects vertical variations in hydraulic traits and pressure, it is not adequate as a general model for larger trees (Couvreur et al 2018), but it is suitable for short trees such as willows in short-rotation coppices, as in our case. The highly variable effects of sapwood area (and total leaf area) on leaf carbon isotope values (Fig.…”