Ohm's Law Analogy Research Articles

Conceptualizing Biogeochemical Reactions With an Ohm's Law Analogy

AbstractIn studying problems like plant‐soil‐microbe interactions in environmental biogeochemistry and ecology, one usually has to quantify and model how substrates control the growth of, and interaction among, biological organisms (and abiotic factors, e.g., adsorptive mineral soil surfaces). To address these substrate‐consumer relationships, many substrate kinetics and growth rules have been developed, including the famous Monod kinetics for single‐substrate‐based growth and Liebig's law of the minimum for multiple‐nutrient‐colimited growth. However, the mechanistic basis that leads to these various concepts and mathematical formulations and the implications of their parameters are often quite uncertain. Here, we show that an analogy based on Ohm's law in electric circuit theory is able to unify many of these different concepts and mathematical formulations. In this Ohm's law analogy, a resistor is defined by a combination of consumers’ and substrates’ kinetic traits. In particular, the resistance is equal to the mean first passage time that has been used to derive the Michaelis‐Menten kinetics under substrate replete conditions for a single substrate as well as the predation rate of individual organisms. We further show that this analogy leads to important insights on various biogeochemical problems, such as (a) multiple‐nutrient‐colimited biological growth, (b) denitrification, (c) fermentation under aerobic conditions, (d) metabolic temperature sensitivity, and (e) the legitimacy of Monod kinetics for describing bacterial growth. We expect that our approach will help both modelers and nonmodelers to better understand and formulate hypotheses when studying certain aspects of environmental biogeochemistry and ecology.

La arquitectura hidráulica de las plantas vasculares terrestres, una revisión

El transporte de agua en las plantas vasculares terrestres es pasivo y está determinado por la transpiración o pérdida de agua a través de las hojas. La teoría de la cohesión-tensión es la más aceptada para explicar este proceso, y se complementa con la analogía de la ley de Ohm, que analiza el flujo del agua como un proceso catenario. La resistencia al estrés hídrico y a la cavitación está fuertemente asociada con las características anatómicas del xilema, de las punteaduras intervasculares y de sus membranas, estas últimas se alteran en función de las propiedades químicas de la solución acuosa que fluye a través de ellas. Con base en estas premisas, esta revisión aborda el fenómeno del ascenso del agua en las plantas vasculares terrestres y analiza los conceptos, las teorías y los métodos más usados en el estudio de la arquitectura hidráulica. Además, señala las diferencias en la estructura del xilema y el transporte del agua entre dicotiledóneas y monocotiledóneas.

VIC+ for water‐limited conditions: A study of biological and hydrological processes and their interactions in soil‐plant‐atmosphere continuum

The Three‐Layer Variable Infiltration Capacity (VIC‐3L) land surface model is extended to include biological and hydrological processes important to water, energy, and carbon budgets under water‐limited climatic conditions: (1) movement of soil water from wet to dry regions through hydraulic redistribution (HR); (2) groundwater dynamics; (3) plant water storage; and (4) photosynthetic process. HR is represented with a process‐based scheme and the interaction between HR and groundwater dynamics is explicitly considered. The impact of frozen soil on HR in the cold season is also represented. Transpiration is calculated by combining an Ohm's law analogy, where flow from the soil to leaves is buffered by plant water storage, with the Penman‐Monteith method, where stomatal conductance is linked with photosynthesis. In this extended model (referred to as VIC+), water flow in plants and in the unsaturated and saturated zones, transpiration and photosynthesis are closely coupled, and multiple constraints are simultaneously applied to the transpiration process. VIC+ is evaluated with an analytical solution under simple conditions and with observed data at two AmeriFlux sites. Scenario simulations demonstrate the following results: (1) HR has significant impacts on water, energy, and carbon budgets during the dry season; (2) Rise of groundwater table, increase of root depth, HR, and plant water storage are favorable to dry‐season latent heat flux; (3) Plant water storage can weaken the intensity of upward HR; (4) Frozen soil can restrict downward HR in the wet winter and reduce the soil water reserves for the dry season.

Leaf hydraulics II: Vascularized tissues

Current models of leaf hydration employ an Ohm's law analogy of the leaf as an ideal capacitor, neglecting the resistance to flow between cells, or treat the leaf as a plane sheet with a source of water at fixed potential filling the mid-plane, neglecting the discrete placement of veins as well as their resistance. We develop a model of leaf hydration that considers the average conductance of the vascular network to a representative areole (region bounded by the vascular network), and represent the volume of tissue within the areole as a poroelastic composite of cells and air spaces. Solutions to the 3D flow problem are found by numerical simulation, and these results are then compared to 1D models with exact solutions for a range of leaf geometries, based on a survey of temperate woody plants. We then show that the hydration times given by these solutions are well approximated by a sum of the ideal capacitor and plane sheet times, representing the time for transport through the vasculature and tissue respectively. We then develop scaling factors relating this approximate solution to the 3D model, and examine the dependence of these scaling factors on leaf geometry. Finally, we apply a similar strategy to reduce the dimensions of the steady state problem, in the context of peristomatal transpiration, and consider the relation of transpirational gradients to equilibrium leaf water potential measurements.

Analysis of Scaling‐Up Resistances from Leaf to Canopy Using Numerical Simulations

A multi‐layer model, combining Lagrangian dispersion at the canopy level with Ohm's Law analogy at the leaf level, was used in numerical simulations to assess the leaf‐to‐canopy scale translation of surface resistances. The model produced unique profiles of fluxes and scalar concentrations that satisfied both the dispersion and leaf models. Environmental factors and canopy architecture were varied, and stomatal conductance was simulated using either a simple relationship with net radiation or the Ball and Berry model to account for feedback mechanisms. Results showed that, when the assumptions of the Penman–Monteith equation were met, scaled‐up leaf conductance closely matched the bulk canopy conductance. However, as the scenarios modeled departed from the ideal conditions of Penman–Monteith, the agreement decreased. In particular, correct estimation of the aerodynamic resistance, through correct parameterization of the roughness length for sensible heat, was identified as a key issue.

Plant size, not age, regulates growth and gas exchange in grafted Scots pine trees

We studied the effect of scion donor-tree age on the physiology and growth of 6- to 7-year-old grafted Scots pine (Pinus sylvestris L.) trees (4 and 5 years after grafting). Physiological measurements included photosynthethetic rate, stomatal conductance, transpiration, whole plant hydraulic conductance, needle nitrogen concentration and carbon isotope composition. Growth measurements included total and component biomasses, relative growth rates and growth efficiency. Scion donor trees ranged in age from 36 to 269 years at the time of grafting. Hydraulic conductance was measured gravimetrically, applying the Ohm's law analogy, and directly, with a high-pressure flow meter. We found no effect of scion donor-tree age on any of the variables measured. There was, however, great variation within scion donor-tree age groups, which was related to the size of the grafted trees. Differences in size may have been caused by variable initial grafting success, but there was no indication that grafting success and age were related. At the stem level, hydraulic conductance scaled with total leaf area so that total conductance per unit leaf area did not vary with crown size. However, leaf specific hydraulic conductance (gravimetric), transpiration, photosynthesis and stomatal conductance declined with increasing total tree leaf area and needle width. We hypothesize that needle width is inversely related to mesophyll conductance. We conclude that canopy and needle size and not scion donor-tree age determined gas exchange in our grafted trees.

Hydraulic characteristics and water relations of net house-grown bell pepper as affected by irrigation regimes in a Mediterranean climate

Trends in hydraulic architecture and water relation parameters of bell pepper ( Capiscum annuum, L.) as affected by fertigated drip irrigation regimes (well-watered and water-stressed conditions) in a Mediterranean climate were investigated. The aim were to evaluate the coupling of xylem conductance and stomatal conductance, the regulation of water use of bell pepper by xylem hydraulics and whether the functionality of xylem hydraulic conductance changes under different fertigation regimes. Fertigation (simultaneous application of irrigation water and fertilizers) consisted of daily fertigation rates of 1.2, 1.0 and 0.7 PET delivered using 8, 2 and 0.4 l/h drippers. Emitter discharge rates determine amount of time required to deliver a known quantity of water and hence soil water availability per unit time. Hydraulic conductance was monitored by the evaporative flux (EF) method from the slope of the water potential difference (Δ ψ) versus transpiration flux ( Q) using the Ohm's law analogy. Water potential gradient was estimated as the difference between pre-dawn and midday leaf water potential. Day time courses of leaf (lwp) and stem (swp) water potentials and stomatal conductance ( g s) were monitored at pre-dawn, 1000, 1200 and 1400 h. Values of midday stomatal conductance and leaf water potentials, water uptake rates (sap flow) and hydraulic conductance through the plant to the canopy (soil–plant–atmosphere (SPAC)) were affected by irrigation regimes. Plant water potential (pre-dawn and midday) ranged from 0.95 to −0.41 MPa for well-watered and water-stressed pepper. Plant hydraulic conductance ranged from 6.57 × 10 −01 to 2.27 × 10 −03 (g s −1 MPa −1) for well-watered and water-stressed plants. The estimated value of whole plant hydraulic conductance ( K T) confirmed increased hydraulic and stomatal resistance under deficit irrigation condition while well-watered pepper plants had greater water uptake rate and remarkably higher within plant (hydraulic) and stomatal conductance. The components of the resistance elements in the SPAC changed as a function of irrigation regimes (root zone water status). Hydraulic characteristics optimize water uptake from the soil, the stomatal respond to changes in leaf water status and the leaf system and sapwood area adjust as necessary to maximize water uptake and avoid loss of hydraulic contact with the soil. The hydraulic non-isolation of the shoot processes to root zone conditions are important attributes of bell pepper grown under variable irrigation regimes.

A long drink of water: how xylem changes with depth.

A long drink of water: how xylem changes with depth.

Developmental changes in plant resistance to water flow in Pisum sativum (L.)

Soil and plant resistance to water flow under field conditions in pea (Pisum sativum L.) plants were measured at six ages. Transpiration flux, leaf and soil water potentials were used to calculate the total resistance to water flow using the Ohm's law analogy. Plant resistance was estimated from the slope of the water potential difference (ΔΨ) vs. transpiration (Q) relationship. Plant growth, root density and soil water content distribution were measured. Leaf area and root length both increased until the end of seed filling and decreased during seed maturation. Total resistance decreased with the transpiration flux in a non-linear relationship. Plant resistance estimated as the slope of the ΔΨ vs. Q regression line increased until pod filling and then decreased. The increased resistance to water flow during pod filling was associated with a 10% increase in cell wall thickness.

AN ELECTRICAL-CIRCUIT MODEL FOR PREDICTING MENTAL WORKLOAD IN COMPUTER-BASED TASKS

ABSTRACT With the increased use of computer-based technology, the work of the human has become more cognitive. As a result, the objective measurement of mental workload has become vital in the design of jobs and the development of adaptive interfaces. This research focused on developing and validating an Ohm's law analogy for mental workload based on individuality and the human's ability to process information. In this model, current was defined as the rate of information transmission (in bit/s); voltage was the mental workload per unit of processed information; resistance was a function of task type and individual factors. To test the hypothesis, the analog voltage-current relationship was evaluated in 24 senior nursing students operating a computer-based system. All subjects performed three different, rule-based, self-paced tasks varying in complexity (low, moderate, and high). Regression analysis across all three tasks showed that a linear relationship existed between the analogs of voltage and current (t (1,69) = −5.97, p = 0.0001), indicating that a negative differential resistance was present. Cognitive ability, fatigue, stress, anxiety, computer skill, and content skill were measured as possible components of resistance. Using stepwise regression analysis, cognitive ability was identified as a significant component of resistance (F(1,22) = 14.2, p = 0.0011). A model relating voltage to current and cognitive ability produced an R 2 = 0.66 for the moderate and high complexity task sets. Similar results were also obtained from a more pragmatic model in which the voltage analog was the mental workload per decision and the current analog was the decision rate (R 2 = 0.63). This electrical-curcuit model could be refined and applied in the workplace for on-line, mental-workload monitoring and in the control of adaptive computer interfaces.

Stomatal conductance and photosynthesis vary linearly with plant hydraulic conductance in ponderosa pine

AbstractRecent work has shown that stomatal conductance (gs) and assimilation (A) are responsive to changes in the hydraulic conductance of the soil to leaf pathway (KL), but no study has quantitatively described this relationship under controlled conditions where steady‐state flow is promoted. Under steady‐state conditions, the relationship between gs, water potential (Ψ) and KL can be assumed to follow the Ohm's law analogy for fluid flow. When boundary layer conductance is large relative to gs, the Ohm's law analogy leads to gs = KL (Ψsoil−Ψleaf)/D, where D is the vapour pressure deficit. Consequently, if stomata regulate Ψleaf and limit A, a reduction in KL will cause gs and A to decline. We evaluated the regulation of Ψleaf and A in response to changes in KL in well‐watered ponderosa pine seedlings (Pinus ponderosa). To vary KL, we systematically reduced stem hydraulic conductivity (k) using an air injection technique to induce cavitation while simultaneously measuring Ψleaf and canopy gas exchange in the laboratory under constant light and D. Short‐statured seedlings (< 1 m tall) and hour‐long equilibration times promoted steady‐state flow conditions. We found that Ψleaf remained constant near − 1·5 MPa except at the extreme 99% reduction of k when Ψleaf fell to − 2·1 MPa. Transpiration, gs, A and KL all declined with decreasing k (P < 0·001). As a result of the near homeostasis in bulk Ψleaf, gs and A were directly proportional to KL (R2 > 0·90), indicating that changes in KL may affect plant carbon gain.

Hydraulic Resistance of Sorghum (C4) and Sunflower (C3)

Summary It is well known that C4 crops have a lower water requirement than C3 crops. Reasons for the difference are not well understood. Therefore, hydraulic resistance of sorghum [Sorghum bicolor (L.) Moench] (C4) and sunflower (Helianthus annuus L.) (C3) was determined to see if it might be one explanation for the lower water use of crops with the C4 photosynthetic pathway. Plants were grown under greenhouse conditions in pots with soil, which was well watered (soil matric potential of ∼0 MPa) or allowed to dry (soil matric potential of −0.038 MPa and −0.065 MPa for sorghum and sunflower, respectively). Hydraulic resistance was calculated in two ways: (1) using the classic Ohm's law analogue, which assumes that the relation between flux (transpiration) and difference in water potentials of the soil and plant is linear and (2) using an equation that considers diurnal changes in leaf water content along with transpiration and difference in water potentials. Because change in leaf-water content during a da...

Plant and soil resistance to water flow in faba bean (Vicia faba L. major Harz.)

An experiment was conducted to determine soil and plant resistance to water flow in faba bean under field conditions during the growing season. During each sampling period transpiration flux and leaf water potential measured hourly were used with daily measurements of root and soil water potential to calculate total resistance using Ohm's law analogy. Plant growth, root density and soil water content distributions with depth were measured. Leaf area and root length per plant reached their maximum value during flowering and pod setting (0.31 m2 and 2200 m, respectively), then decreasing until the end of the growing period. Root distribution decreased with depth ranging, on average, between 34.2% (in the 0–0.25 m soil layer) and 18.1% (in the 0.75–1.0 m soil layer). Mean root diameter was 0.6 mm but most of the roots were less than 0.7 mm in diameter. Changes in plant and soil water potentials reflected plant growth characteristics and climatic patterns. The overall relationship between the difference in water potential between soil and leaf and transpiration was linear, with the slope equal to average plant resistance (0.0165 MPa/(cm3 m-1 h-1 10-3). Different regression parameters were obtained for the various measurement days. The water potential difference was inversely related to transpiration at high leaf stomatal resistance and at high values of VPD. Total resistance decreased with transpiration flux in a linear relationship (r=−0.68). Different slope values were obtained for the different measurement days. Estimated soil resistance was much lower than the observed total resistance to water flow. The change from vegetative growth to pod filling was accompanied by an increase in plant resistance. The experimental results support previous findings that resistance to water flow through plants is not constant but is influenced by plant age, growth stage and environmental conditions. A more complex model than Ohm's law analogy may be necessary for describing the dynamic flow system under field conditions.

Formulation of root water uptake in a multi-layer soil-plant model: does van den Honert's equation hold?

Abstract. The withdrawal of water from soil by vegetation, which in steady state conditions is equivalent to the transpiration rate, can be written in terms of water potential in the form of an Ohm's law analogy, known as van den Honert's equation: The difference between an effective soil water potential and the bulk canopy water potential is divided by an effective soil-plant resistance. This equation is commonly used, but little is known about the precise definition of its parameters. The issue of this paper is to bridge the gap between the bulk approach and a multi-layer description of soil-plant water transfer by interpreting the bulk parameters in terms of the characteristics of the multi-layer approach. Water flow through an elementary path within the soil or the root is assumed to follow an Ohm's law analogy, and the soil and root characterisics are allowed to vary with depth. Starting from the basic equations of the multi-layer approach, it is proved that the total rate of transpiration can also be expressed in the form of an Ohm's law analogy. This means that van den Honert's equation holds at canopy scale, insofar as the assumptions made on the physics of root water uptake hold. In the bulk formulation derived, the effective soil-plant resistance appears as a combination of the elementary resistances making up the multi-layer model; and the effective soil water potential is a weighted mean of the water potentials in each soil layer, the weighting system involving the complete set of elementary resistances. Simpler representations of soil-plant interaction leading to Ohm's law type formulations are also examined: a simplified multi-layer model, in which xylem (root axial) resistance is neglected, and a bulk approach, in which soil-root interaction is represented by only one layer. Numerical simulations performed in different standard conditions show that these simpler representations do not provide accurate estimates of the transpiration rate, when compared to the values obtained by the complete algorithm.

Growth dynamics of root and shoot hydraulic conductance in seedlings of five neotropical tree species: scaling to show possible adaptation to differing light regimes.

The dynamics of growth (shoot and root dry weights, surface areas, hydraulic conductances, and root length) were measured in seedlings of five neotropical tree species aged 4-16 months. The species studied included two light-demanding pioneers (Miconia argentea and Apeiba membranacea) and three shade-tolerant young- or old-forest species (Pouteria reticulata, Gustavia superba, and Trichilia tuberculata). Growth analysis revealed that shoot and root dry weights and hydraulic conductances and leaf area all increased exponentially with time. Alternative methods of scaling measured parameters to reveal differences that might explain adaptations to microsites are discussed. Scaling root conductance to root surface area or root length revealed a few species differences but nothing that correlated with adaptation to light regimes. Scaling of root surface area or root length to root dry weight revealed that pioneers produced significantly more root area and length per gram dry weight investment than shade-tolerant species. Scaling of root and shoot hydraulic conductances to leaf area and scaling of root conductance to root dry weight and shoot conductance to shoot dry weight also revealed that pioneers were significantly more conductive to water than shade-tolerant species. The advantages of scaling hydraulic parameters to leaf surface area are discussed in terms of the Ohm's law analogue of water flow in plants.

Daily transpiration of field soybeans as related to hydraulic conductance, root distribution, soil potential and midday leaf potential

The present study aims at characterizing plant water status under field conditions on a daily basis, in order to improve operational predictions of plant water stress. Ohm's law analog serves as a basis for establishing daily soil-plant relationships, using experimental data from a water-limited soybean crop: 227-1. The daily transpiration flux, T, is estimated from experimental evapotranspiration data and simulated soil evaporation values. The difference, 227-2, named the effective potential gradient, is derived from i) the midday leaf potential of the uppermost expanded leaves and ii) an effective soil potential accounting for soil potential profile and an effectiveness factor of roots competing for water uptake. This factor is experimentally estimated from field observation of roots. G is an apparent hydraulic conductance of water flow from the soil to the leaves. The value of the lower potential limit for water extraction, required to assess the effective soil potential, is calculated with respect to the plant using the predawn leaf potential. It is found to be equal to −1.2 MPa. It appears that over the range of soil and climatic conditions experienced, the daily effective potential gradient remains constant (1.2 MPa), implying that, on a daily basis, transpiration only depends on the hydraulic conductance. The authors explain this behaviour by diurnal variation of osmotic potential, relying on Morgan's theory (1984). Possible generalization of the results to other crop species is suggested, providing a framework for reasoning plant water behaviour at a daily time step.

The kinetics of stomatal responses to VPD in Vicia faba: electrophysiological and water relations models

Abstract. An Ohm's law analogy is frequently employed to calculate parameters of leaf gas exchange. For example, resistance to water vapour loss is calculated as the quotient of vapour pressure difference (VPD) and vapour loss by transpiration. In the present research, this electrical analogy was extended. Steady‐state transpiration as a function of VPD, assayed in leaflets of Vicia faba using gas exchange techniques, was compared with steady‐state K+ current magnitude as a function of voltage in isolated guard cell protoplasts of Vicia faba, assayed using the patch clamping technique in the whole cell configuration. An electrophysiological model originally developed to explain the kinetics of current changes following step changes in voltage across a cell membrane was used to fit the kinetics of transpiration changes following step changes in VPD applied to leaflets of Vicia faba. Following step increases in VPD, transpiration exhibited an initial increase, reflecting the increased driving force for water loss and, for large step increases in VPD, a transient decrease in stomatal resistance. Transpiration subsequently declined, reflecting stomatal closure. By analogy to electrophysiological responses, it is hypothesized that the humidity parameter that is sensed by guard cells is VPD. Two models based on epidermal water relations were also applied to transpiration kinetics. In the first model, the transient increase in transpiration following a step increase in VPD was attributed partially to an increase in the Physical driving force (VPD) and partially to a transient decrease in stomatal resistance resulting from reduced epidermal backpressure. In the second model, the transient decrease in stomatal resistance was attributed to a direct response of the guard cells to VPD. Both models based on water relations gave good fits of the data, emphasizing the need for further study regarding the metabolic nature of the guard cell response to humidity.

Estimation of Root Hydraulic Conductivity on Intact Peach and Citrus Rootstock

Estimates of root hydraulic conductivity (Lp) were obtained on intact peach (Prunus persica × P. davidiana `Nemaguard') and sour orange (Citrus aurantium L.) rootstock over a broad range of transpiration rates. Within a species, Lp was lower when estimated using the Ohm's law analog than the reciprocal of the slope of the linear regression between transpiration (E) and stem xylem water potential (Ψ). Nonzero y-intercepts in linear regressions of Ψ vs. E resulted in the lack of agreement between Lp estimates. Removal of the root system caused xylem Ψ to rapidly approach zero in both species when E ≈ 0, suggesting that factors responsible for nonzero y intercepts resided within roots. Lp was 2.2 and 3.5 times lower for sour orange than peach when calculated by the Ohm's law and regression methods, respectively.

Diurnal Variation of Crop Hydraulic Resistance: A New Analysis

AbstractSeveral explanations have been advanced to account for the apparent diurnal variation in crop hydraulic resistance (Rp) calculated from a simple Ohm's Law analog. In this paper, we suggest that Rp, calculated in this way, may vary because of spatial variation in soil water potential (Ψs). We propose that whenever transpiration rate (Q) is small and leaf water potential (Ψl) is relatively high, roots extract water mainly from those regions of the soil profile where Ψs is also high (usually deep in the profile). As Q increases and Ψl becomes more negative, roots begin removing water from regions of the profile where Ψs is more negative. Hence the length of roots actually taking up water at a particular time, and therefore Rp, may vary diurnally. Also, variations in Ψ3 and rooting density often make the relation between Ψl and water uptake rate unique for each soil region. So, even when all roots are taking up water, Ψl and the aggregated uptake rate may be nonlinearly related, and Rp will vary diurnally with Ψl. This theory is illustrated with exploratory calculations of Rp for hypothetical temperate cereal crops grown in three different soils (a clay, a silt loam, and a sandy loam), with various combinations of root system properties and evapotranspiration rates. Crop water content and root radial resistivity were assumed constant. Although Ψs was initially distributed uniformly in these simulations, heterogeneity in root distribution soon caused spatial variation in Ψs, and Rp showed marked diurnal variations. Variation in Rp increased with the predicted variation in Ψs. Detailed field experiments and simulation analyses are needed to quantitatively compare this and other hypotheses to explain diurnal variation in Rp.

Evaluating water fluxes of field-grown alfalfa from diurnal observations of natural isotope concentrations, energy budget and ecophysiological parameters

In this work, the isotopic composition of water in soil, plant and atmospheric vapour has been used to investigate the flow processes in an alfalfa canopy during a typical summer day under Mediterranean climate. In addition to the stable isotopes of water, energy budget, leaf water potential and stomatal conductance were used in an integrated approach to a better understanding of the mechanisms of water transfer. The daily enrichment cycle of 18O and 2H in the leaves can be described by a physical model assuming that one of the important factors influencing the daily variation of 18O and 2H content is the daily humidity cycle. The isotopic composition of the input water can be either determined by the collar water or by the water of the soil layers supplying water to the active roots. There is no fractionation during water uptake by the roots. Total resistance to water flow in alfalfa calculated using an Ohm's law analogue was similar to other reported values. However, alfalfa contains internal stores of water. Differences between transpiration and root water uptake can be interpreted as indicating that these internal stores contribute substantially to transpiration during the day. Upshifts and downshifts in the isotopic composition of leaves are due to contributions from these internal stores and can probably result from a modification of the values of the kinetic fractionation factor in relation to the changes in the aerodynamical regime and the stomatal opening.