A dynamic model for studying flow of water in single trees

Modeling Xylem Functionality Aspects

Depending on the questions to be answered, water flow in the xylem can be modelled following different approaches with varying spatial and temporal resolution. When focussing on the influence of hydraulic architecture upon flow dynamics, distribution of water potentials in a tree crown or questions of vulnerability of the hydraulic system, functional-structural plant models, which link representations of morphological structure with simulated processes and with a virtual environment, can be a promising tool. Such a model will then include a network of idealized xylem segments, each representing the conducting part of a stem or branch segment, and a numerical machinery suitable for solving a system of differential equations on it reflecting the hydrodynamic laws, which are the basis of the broadly accepted cohesion-tension theory of water flow in plants. We will discuss functional-structural plant models, the simplifications that are useful for hydraulic simulations within this framework, the deduction of the used differential equations from basic physical conservation laws, and their numerical solution, as well as additional necessary models of radiation, photosynthesis, and stomatal conductance. In some supplementary notes, we are shortly addressing some related questions, for example, about root systems or about the relation between macro-scale hydraulic parameters and fine-grained (anatomical) xylem structure.

The dynamics of stem water storage in the tops of Earth's largest trees-Sequoiadendron giganteum

Water stored in tree stems (i.e., trunks and branches) is an important contributor to transpiration that can improve photosynthetic carbon gain and reduce the probability of cavitation. However, in tall trees, the capacity to store water may decline with height because of chronically low water potentials associated with the gravitational potential gradient. We quantified the importance of elastic stem water storage in the top 5-6 m of large (4.2-5.0 m diameter at breast height, 82.1-86.3 m tall) Sequoiadendron giganteum (Lindley) J. Buchholz (giant sequoia) trees using a combination of architectural measurements and automated sensors that monitored summertime diel rhythms in sap flow, stem diameter and water potential. Stem water storage contributed 1.5-1.8% of water transpired at the tree tops, and hydraulic capacitance ranged from 2.6 to 4.1 l MPa-1 m-3. These values, which are considerably smaller than reported for shorter trees, may be associated with persistently low water potentials imposed by gravity and could indicate a trend of decreasing water storage dynamics with height in tree. Branch diameter contraction and expansion consistently and substantially lagged behind fluxes in water potential and sap flow, which occurred in sync. This lag suggests that the inner bark, which consists mostly of live secondary phloem tissue, was an important hydraulic capacitor, and that hydraulic resistance between xylem and phloem retards water transfer between these tissues. We also measured tree-base sap flux, which lagged behind that measured in trunks near the tree tops, indicating additional storage in the large trunks between these measurement positions. Whole-tree sap flow ranged from 2227 to 3752 l day-1, corroborating previous records for similar-sized giant sequoia and representing the largest yet reported for any individual tree. Despite such extraordinarily high daily water use, we estimate that water stored in tree-top stems contributes minimally to transpiration on typical summer days.

Modelling water fluxes in plants: from tissues to biosphere

Contents Summary 1207 I. Introduction 1207 II. A brief history of modelling plant water fluxes 1208 III. Main components of plant water transport models 1208 IV. Stand-scale water fluxes and coupling to climate and soil 1213 V. Water fluxes in terrestrial biosphere models and feedbacks to community dynamics 1215 VI. Outstanding challenges in modelling water fluxes in the soil-plant-atmosphere continuum 1217 Acknowledgements 1218 References 1218 SUMMARY: Models of plant water fluxes have evolved from studies focussed on understanding the detailed structure and functioning of specific components of the soil-plant-atmosphere (SPA) continuum to architectures often incorporated inside eco-hydrological and terrestrial biosphere (TB) model schemes. We review here the historical evolution of this field, examine the basic structure of a simplified individual-based model of plant water transport, highlight selected applications for specific ecological problems and conclude by examining outstanding issues requiring further improvements in modelling vegetation water fluxes. We particularly emphasise issues related to the scaling from tissue-level traits to individual-based predictions of water transport, the representation of nonlinear and hysteretic behaviour in soil-xylem hydraulics and the need to incorporate knowledge of hydraulics within broader frameworks of plant ecological strategies and their consequences for predicting community demography and dynamics.

Leaf water maintains daytime transpiration in young Cryptomeria japonica trees

Compared with stem water storage, leaf water storage is understudied although it may be important for alleviating water stress by contributing quickly and directly to transpiration demand. To quantify the relative contribution of stem versus leaf water storage to daily water deficit, we measured diurnal changes in transpiration rate, sap-flow velocity and stem radius of 10-year-old Cryptomeria japonica D. Don trees. We assumed that the duration of time lags between transpiration rate and sap-flow velocity reflected stored water in the stem and leaf, and that stem volume change represented water content of elastic tissue. The relationship between fresh mass and water potential of the whole tree indicated that the study trees had capacity to store, on average, 91.4 ml of water per kg fresh mass at turgor loss. Leaves, sapwood and elastic tissue contributed around 51%, 29% and 20% of stored water, respectively. During morning, transpiration rates were higher than sap-flow velocity suggesting depletion of stored water. During the first 2 h after onset of transpiration, stored water contributed more than 100% of whole-tree transpiration. Depletion of leaf water (PLeaf) and sapwood water (PSap) coincided with the onset of transpiration and became maximum around 15:00 h. Depletion of elastic tissue water (PElastic) lagged behind that of PLeaf and PSap by 1-2 h, indicating that replenishment of stored water occurs late in the day when low leaf water potentials resulting from daytime transpiration drive water uptake. Maximum depletion of PLeaf was about 1-3 times and 5-10 times that of PSap and PElastic, respectively. The contribution of PLeaf to total daily transpiration was 5-8%, while those of PSap and PElastic were 3-4% and 0.7-1%, respectively. Our results suggest the importance of leaf water storage in maintaining daily transpiration in young C. japonica trees.

The effect of plant water storage on water fluxes within the coupled soil-plant system

In addition to buffering plants from water stress during severe droughts, plant water storage (PWS) alters many features of the spatio-temporal dynamics of water movement in the soil-plant system. How PWS impacts water dynamics and drought resilience is explored using a multi-layer porous media model. The model numerically resolves soil-plant hydrodynamics by coupling them to leaf-level gas exchange and soil-root interfacial layers. Novel features of the model are the considerations of a coordinated relationship between stomatal aperture variation and whole-system hydraulics and of the effects of PWS and nocturnal transpiration (Fe,night) on hydraulic redistribution (HR) in the soil. The model results suggest that daytime PWS usage and Fe,night generate a residual water potential gradient (Δψp,night) along the plant vascular system overnight. This Δψp,night represents a non-negligible competing sink strength that diminishes the significance of HR. Considering the co-occurrence of PWS usage and HR during a single extended dry-down, a wide range of plant attributes and environmental/soil conditions selected to enhance or suppress plant drought resilience is discussed. When compared with HR, model calculations suggest that increased root water influx into plant conducting-tissues overnight maintains a more favorable water status at the leaf, thereby delaying the onset of drought stress.

A series RCL circuit theory for analyzing non-steady-state water uptake of maize plants

Understanding water uptake and transport through the soil-plant continuum is vital for ecosystem management and agricultural water use. Plant water uptake under natural conditions is a non-steady transient flow controlled by root distribution, plant configuration, soil hydraulics, and climatic conditions. Despite significant progress in model development, a mechanistic description of transient water uptake has not been developed or remains incomplete. Here, based on advanced electrical network theory (RLC circuit theory), we developed a non-steady state biophysical model to mechanistically analyze the fluctuations of uptake rates in response to water stress. We found that the non-steady-state model captures the nature of instantaneity and hysteresis of plant water uptake due to the considerations of water storage in plant xylem and coarse roots (capacitance effect), hydraulic architecture of leaf system (inductance effect), and soil-root contact (fuse effect). The model provides insights into the important role of plant configuration and hydraulic heterogeneity in helping plants survive an adverse environment. Our tests against field data suggest that the non-steady-state model has great potential for being used to interpret the smart water strategy of plants, which is intrinsically determined by stem size, leaf size/thickness and distribution, root system architecture, and the ratio of fine-to-coarse root lengths.

Investigating xylem embolism formation, refilling and water storage in tree trunks using frequency domain reflectometry

Trunks of large trees play an important role in whole-plant water balance but technical difficulties have limited most hydraulic research to small stems, leaves, and roots. To investigate the dynamics of water-related processes in tree trunks, such as winter embolism refilling, xylem hydraulic vulnerability, and water storage, volumetric water content (VWC) in the main stem was monitored continuously using frequency domain moisture sensors in adult Betula papyrifera trees from early spring through the beginning of winter. An air injection technique was developed to estimate hydraulic vulnerability of the trunk xylem. Trunk VWC increased in early spring and again in autumn, concurrently with root pressure during both seasons. Diurnal fluctuations and a gradual decrease in trunk VWC through the growing season were observed, which, in combination with VWC increase after significant rainfall events and depletion during periods of high water demand, indicate the importance of stem water storage in both short- and long-term water balance. Comparisons between the trunk air injection results and conventional branch hydraulic vulnerability curves showed no evidence of 'vulnerability segmentation' between the main stem and small branches in B. papyrifera. Measurements of VWC following air injection, together with evidence from air injection and xylem dye perfusion, indicate that embolized vessels can be refilled by active root pressure but not in the absence of root pressure. The precise, continuous, and non-destructive measurement of wood water content using frequency domain sensors provides an ideal way to probe many hydraulic processes in large tree trunks that are otherwise difficult to investigate.

Transient response of sap flow to wind speed

Transient responses of sap flow to step changes in wind speed were experimentally investigated in a wind tunnel. A Granier-type sap flow sensor was calibrated and tested in a cylindrical tube for analysis of its transient time response. Then the sensor was used to measure the transient response of a well-watered Pachira macrocarpa plant to wind speed variations. The transient response of sap flow was described using the resistance-capacitance model. The steady sap flow rate increased as the wind speed increased at low wind speeds. Once the wind speed exceeded 8.0 m s(-1), the steady sap flow rate did not increase further. The transpiration rate, measured gravimetrically, showed a similar trend. The response of nocturnal sap flow to wind speed variation was also measured and compared with the results in the daytime. Under the same wind speed, the steady sap flow rate was smaller than that in the daytime, indicating differences between diurnal and nocturnal hydraulic function, and incomplete stomatal closure at night. In addition, it was found that the temporal response of the Granier sensor is fast enough to resolve the transient behaviour of water flux in plant tissue.

Comparison between gradient-dependent hydraulic conductivities of roots using the root pressure probe: the role of pressure propagations and implications for the relative roles of parallel radial pathways

Hydrostatic pressure relaxations with the root pressure probe are commonly used for measuring the hydraulic conductivity (Lp(r)) of roots. We compared the Lp(r) of roots from species with different root hydraulic properties (Lupinus angustifolius L. 'Merrit', Lupinus luteus L. 'Wodjil', Triticum aestivum L. 'Kulin' and Zea mays L. 'Pacific DK 477') using pressure relaxations, a pressure clamp and osmotic gradients to induce water flow across the root. Only the pressure clamp measures water flow under steady-state conditions. Lp(r) determined by pressure relaxations was two- to threefold greater than Lp(r) from pressure clamps and was independent of the direction of water flow. Lp(r) (pressure clamp) was two- to fourfold higher than for Lp(r) (osmotic) for all species except Triticum aestivum where Lp(r) (pressure clamp) and Lp(r) (osmotic) were not significantly different. A novel technique was developed to measure the propagation of pressure through roots to investigate the cause of the differences in Lp(r). Root segments were connected between two pressure probes so that when root pressure (P(r)) was manipulated by one probe, the other probe recorded changes in P(r). Pressure relaxations did not induce the expected kinetics in pressure in the probe at the other end of the root when axial hydraulic conductance, and probe and root capacitances were accounted for. An electric circuit model of the root was constructed that included an additional capacitance in the root loaded by a series of resistances. This accounted for the double exponential kinetics for intact roots in pressure relaxation experiments as well as the reduced response observed with the double probe experiments. Although there were potential errors with all the techniques, we considered that the measurement of Lp(r) using the pressure clamp was the most unambiguous for small pressure changes, and provided that sufficient time was allowed for pressure propagation through the root. The differences in Lp(r) from different methods of measurement have implications for the models describing water transport through roots and the potential role of aquaporins.

Biophysical properties and functional significance of stem water storage tissues in Neotropical savanna trees

Biophysical characteristics of sapwood and outer parenchyma water storage compartments were studied in stems of eight dominant Brazilian Cerrado tree species to assess the impact of differences in tissue capacitance on whole-plant water relations. The rate of decline in tissue water potential with relative water content (RWC) was greater in the outer parenchyma than in the sapwood for most of the species, resulting in tissue-and species-specific differences in capacitance. Sapwood capacitance on a tissue volume basis ranged from 40 to 160 kg m-3 MPa-1, whereas outer parenchyma capacitance ranged from 25 to only 60 kg m-3 MPa-1. In addition, osmotic potentials at full turgor and at the turgor loss point were more negative for the outer parenchyma compared with the sapwood, and the maximum bulk elastic modulus was higher for the outer parenchyma than for the sapwood. Sapwood capacitance decreased linearly with increasing sapwood density across species, but there was no significant correlation between outer parenchyma capacitance and tissue density. Midday leaf water potential, the total hydraulic conductance of the soil/leaf pathway and stomatal conductance to water vapour (gs) all increased with stem volumetric capacitance, or with the relative contribution of stored water to total daily transpiration. However, the difference between the pre-dawn water potential of non-transpiring leaves and the weighted average soil water potential, a measure of the water potential disequilibrium between the plant and soil, increased asymptotically with total stem capacitance across species, implying that overnight recharge of water storage compartments was incomplete in species with greater capacitance. Overall, stem capacitance contributes to homeostasis in the diurnal and seasonal water balance of Cerrado trees.

Modeling tree water flow as an unsaturated flow through a porous medium

The electric circuit analogy has had a profound influence on how tree physiologists measure, model and think about tree water flow. For example, previous models that attempt to account for changes in saturation use the electric circuit analogy to define capacitance as the change in saturation per change in pressure. Given that capacitance is constant, this relationship implies that subjecting a block of wood to a pressure of -2.5 MPa for 2 min results in the same change in saturation as subjecting the same block to the same pressure for 2 days. Given the definition of capacitance, it is unclear how the electric circuit analogy could be used to predict changes in saturation separately from changes in pressure. The inadequacies in the electric circuit analogy discussed in this paper necessitate a new theory of tree water flow that recognizes the sapwood as being a porous medium and explicitly deals with the full implications of the unsaturated flow occurring in the sapwood. The theory proposed in this paper combines the Cohesion theory with a mathematical theory of multiphase flow through porous media. Based on this theory, both saturated and unsaturated tree water flow models are presented. Previous partial differential equation models of tree water flow based on the electric circuit analogy are shown to be mathematically equivalent to the model of saturated porous flow. The unsaturated model of tree water flow explicitly models the pressure profile and the rates of change in saturation and specific interfacial area (a measure of how the water in the unsaturated sapwood is partitioned between mobile and immobile components). The unsaturated model highlights the differences between saturated and unsaturated flow and the need to measure the variables governing tree water flow at higher spatial and temporal resolutions.

Compression wood has little impact on the water relations of Douglas-fir (Pseudotsuga menziesii) seedlings despite a large effect on shoot hydraulic properties

• Compression wood has been shown to reduce stem permeability, but it is not known to what extent it affects leaf-level processes. Here, we report whole-plant hydraulic properties of Douglas-fir (Pseudotsuga menziesii) seedlings induced to form varying amounts of compression wood. • Seedlings were grown under three bending treatments to assess the impact of compression wood on hydraulic properties, including stomatal conductance (g_s ), above-ground shoot conductance (K_l(abg) ), and both specific and leaf area-specific conductivity (k_s and k_l , respectively). • K_l(abg) was significantly lower (50% reduction) in severely bent seedlings than in controls. Similarly, both k_s and k_l of the main axis were significantly reduced (by 52% and 46%, respectively) in severely bent seedlings relative to controls. Seedlings in the moderate bending treatments had k_s and k_l that were intermediate between controls and severe bending. • Despite clear differences in above-ground shoot hydraulic properties, severely bent seedlings maintained the same water potentials as controls and had similar diurnal patterns of g_s . This suggests that when the entire soil-plant-atmosphere continuum is considered, even a severe reduction in stem k_s caused by compression wood has little impact on leaf-level processes.

The hydraulic system of trees: theoretical framework and numerical simulation

Empirical studies pose the problem of the physiological integration of the tree organism, which is also important on the scale of ecosystems. Recently, spatially distributed models emerged, which approach this problem by reflecting the close linkage between physiological processes and the structures of trees and tree stands. In the case of water flow, the tree organism can be regarded as hydraulic system and the branched tree architecture as hydraulic network. Previous models of the hydraulic system either did not take into account the network structure, or they had shortcomings regarding the translation of the underlying physiological assumptions by the discrete computation method. We have developed a theoretical framework which takes the form of a numerical simulation model of tree water flow. A discrete initial boundary value problem (IBVP) combines the phenomena of Darcy flow, water storage and conductivity losses in the hydraulic network. The software HYDRA computes the solution of the IBVP. The theoretical derivation and model tests corroborate the consistent translation of the physiological assumptions by the computational method. Simulation studies enabled us to formulate hypotheses on the following points: (1) differences in the hydraulic segmentation between Picea abies and Thuja occidentalis, (2) responses of the hydraulic system to rapid transpiration changes and to a scenario of drought stress, and (3) how these responses depend on architectural quantities of the trees. The simulation studies demonstrated our possibilities of deriving theoretically well-founded hypotheses about the functioning of the hydraulic system and its relation to system structure. The numerical simulation model is designed as a tool for structure-function studies, which is able to treat tree architecture as independent variable. The model supports the integration of data on tree level, and it can be used for computer experiments which quantify the dynamics of the hydraulic system according to the concepts of system theory. Copyright 1999 Academic Press.

Water-storage capacity ofThuja, Tsuga andAcer stems measured by dehydration isotherms : The contribution of capillary water and cavitation

Water-storage capacity was measured inThuja occidentalis L.,Tsuga canadensis (L.) Carr., andAcer saccharum Marsh. during the dehydration of stem segments 1.5-2.5 cm in diameter. Stem water potential was measured with a temperature-corrected stem hygrometer and cavitations were detected acoustically. Water loss was measured by weight change. Dehydration isotherms consistently displayed three phases. The first phase, from water potential (Ψ) 0 to about -0.2 MPa, had a high capacitance (C>0.4kg water lost· (1 of tissue)(-1)· MPa(-1)) and we have attributed this high C to capillary water as defined by Zimmermann (1983, Xylem structure and the ascent of sap, Springer-Verlag). The second phase from Ψ=-0.5 to about -2.0 had the lowest C values (<0.02 kg·l(-1)·MPa(-1)) and was accompanied by a few cavitation events. This phase may have been a transition zone between capillary storage and water released by cavitation events as well as water drawn from living cells of the bark. The third phase also had a high C (about 0.07-0.22kg·l(-1)·MPa(-1)) and was associated with many cavitation events while Ψ declined below about -2.5 MPa; we presume the high capacitance was the consequence of water released by cavitation events. We discuss the ecological adaptive advantage of these three phases of water-storage in trees. In moist environments, water withdrawn from capillary storage may be an important fraction of transpiration, but may be of little adaptive advantage. For most of the growth season trees draw mainly on elastic storage, but stem elastic storage is less than leaf elastic storage and therefore unlikely to be important. In very dry environments, water relased by cavitation events might be important to the short-term survival of trees.