Original Research A Simple Representation of Plant Water Storage Effects in Coupled Soil Water Flow and Transpiration Stream Modeling Tomas Vogel,* Jana Votrubova, Michal Dohnal, Core Ideas and Jaromir Dusek • A previous soil water flow model was extended to allow simulation of ​When describing the movement of water in a variably saturated plant root transient plant water storage. zone, most existing hydrological models use the assumption of quasi-steady- • Comparison with measured Nor- state flow to relate root water uptake to canopy transpiration, thereby way spruce sap flow data indicates neglecting the effect of changing plant water storage. This approach improved model performance. is known to be problematic, especially when considering relatively large • The proposed algorithm can be easily incorporated into existing soil volumes of water stored in the tissues of tall trees. We propose a simple algo- water flow models. rithm, based on the concept of whole-plant hydraulic capacitance, to deal with the problem. The algorithm is implemented in a one-dimensional soil water flow model involving vertically distributed macroscopic root water uptake. In this study, the proposed transient storage approach was com- pared with the quasi-steady-state approach. Both approaches were used to simulate soil water flow and diurnal variations of transpiration at a forest site covered with Norway spruce [Picea abies (L.) H. Karst.]. The key param- eter of the transient storage approach, the plant hydraulic capacitance, is estimated by comparing the variations in the potential transpiration rate, derived from micrometeorological measurements, with observed sap flow intensities. The application of the proposed algorithm leads to more realistic predictions of root water uptake rates at the site of interest. The inclusion of the plant water storage effects improved the ability of the model to capture the anticipated diurnal variations in actual transpiration rates. The algorithm can be easily implemented into existing soil water flow models and used to simulate transpiration stream responses to varying atmospheric and soil moisture conditions including isohydric and partly also anisohydric plant responses to drought stress.

Abbreviations: RWU, root water uptake.

T. Vogel, J. Votrubova, M. Dohnal, and J. Dusek, Faculty of Civil Enginee- ring, Czech Technical Univ. in Prague, The role of plant water storage in soil–plant–atmosphere systems has been Thakurova 7, 166 29 Prague, Czech Republic. *Corresponding author given increasing attention in recent plant physiology studies (e.g., Borchert and Pockman, ([email protected]). 2005; Cermak et al., 2007; Meinzer et al., 2008; Carrasco et al., 2015; Pfautsch et al., 2015). These studies have shown that water can be stored intracellularly or extracellularly in plant Received 12 Dec. 2016. tissues. Stored water can be released from plant tissues due to their elasticity or by cavita- Accepted 1 Mar. 2017. tion. According to Cermak et al. (2007), the amount of water released from water storage compartments inside mature trees can account for up to one third of daily water loss by Citation: Vogel, T., J. Votrubova, M. transpiration. Stem water storage effects result in significant buffering of xylem water Dohnal, and J. Dusek. 2017. A simple potential fluctuations, which helps to preserve the integrity of the xylem water system representation of plant water storage effects in coupled soil water flow and during water stress periods (Meinzer et al., 2003; Scholz et al., 2007). transpiration stream modeling. Vadose Zone J. 16(5). doi:10.2136/vzj2016.12.0128 To minimize the risk of xylem embolism, caused by cavitation, plants need to keep their xylem water potential above a certain threshold value specific for different plant tissues and plant species (Cochard, 1992; Lu et al., 1996). For plants exposed to water stress, the Vol. 16, Iss. 5, 2017 © Soil Science Society of America. range of xylem water potential between the daily minimum potential and the potential This is an open access article distributed corresponding to the onset of cavitation can be interpreted as a safety margin (Sperry, under the CC BY-NC-ND license (http://creativecommons.org/licenses/ 2000; Meinzer et al., 2009; Carrasco et al., 2015). It is assumed that there are two possible by-nc-nd/4.0/).

Vadose Zone Journal | Advancing Critical Zone Science

Downloaded from http://pubs.geoscienceworld.org/vzj/article-pdf/16/5/1/4020615/vzj2016.12.0128.pdf by guest on 27 September 2021 regulation strategies in dealing with water stress—referred to as simulation results obtained with the transient plant water storage isohydric and anisohydric behaviors (Tardieu and Simonneau, approach with those based on the quasi-steady-state assumption 1998; McDowell et al., 2008; Pretzsch et al., 2013). Isohydric and by comparing both approaches with observed Norway spruce plants maintain their midday xylem water potential at a relatively sap flow data. constant level by closing their stomata and thus reducing transpira- tion. By contrast, anisohydric plants allow the midday xylem water potential to decline and maintain transpiration until the transpira- 66Materials and Methods tion stream is disrupted by cavitation. Study Site An increasing number of soil–plant–atmosphere continuum The Norway spruce sap flow data were acquired in a small moun- models include a capacitance term to account for the water storage tainous watershed (the Liz catchment), situated in the Bohemian in plant tissues. Among the more recent ones, for example, are the Forest, Czech Republic. The catchment outlet is located 830 m models of Lhomme et al. (2001), Zhuang et al. (2014), and Tardieu above sea level. The average annual precipitation is 861 mm, and et al. (2015). While these models pay a great deal of attention to the average annual temperature is 6.5°C. The prevailing soil type hydraulic resistances and capacitances of plant tissues along the is oligotrophic forest Eutric Cambisol developed on biotite parag- transpiration stream (Lhomme et al., 2001); capacitance, induc- neiss bedrock. The catchment is mostly covered with Norway tance, and fuse effects associated with plant xylem water storages, spruce and European beech (Fagus sylvatica L.). The majority of hydraulic architecture of leaf system and imperfections in soil–root spruce trees are 94 yr old, with a height of about 28 m and a diame- contact (Zhuang et al., 2014); and coordination of stomatal con- ter of about 40 cm. Data used in the present study were recorded at trols, transpiration forcing, leaf growth, and abscisic acid signaling two monitoring stations—at the spruce forest floor and at a nearby (Tardieu et al., 2015), they neglect the effects of distributed soil meadow (Tesar et al., 2006). Variables measured at the forest water status and treat the soil compartment as a zero-dimensional station included sap flow, air and soil temperatures, soil water system, characterized by effective values of soil water potential and pressure, soil water content, and precipitation. Complementary soil water content. micrometeorological variables (Fig. 1) were monitored at the meadow station. Sap flow in the stem xylem of four Norway spruce Plant responses to water stress are reflected in variations of tran- trees was monitored at breast height using the heat field deforma- spiration and root water uptake intensities, which are important tion method with multipoint sensors (Nadezhdina et al., 2012). hydrological variables. It is essential, therefore, that these responses are adequately parameterized and properly incorporated in hydro- Soil Water Flow Model logical models. In the context of vadose zone hydrology, root To describe the vertical flow of water in a soil profile, we use the water uptake (RWU) is usually represented as a spatially distrib- one-dimensional Richards’ equation (Richards, 1931): uted macroscopic sink of soil water. Most existing soil water flow æö models apply the assumption of quasi-steady-state flow in plant ¶q ¶ç ¶H ÷ = ç K÷ - S, H =+ h z [1] xylem to relate the RWU intensity to the actual transpiration rate, ¶¶tzèøç ¶ z neglecting transient water storage effects in plant tissues (Raats, 2007; Šimůnek and Hopmans, 2009; Jarvis, 2011; de Willigen et where q is the volumetric soil water content (m3 m−3), K is the al., 2012; Guswa, 2012; Javaux et al., 2013; de Jong van Lier et al., unsaturated hydraulic conductivity of the soil (m s−1), S is a sink 2013; Couvreur et al., 2014; Manoli et al., 2014). A few models term representing the intensity of root water uptake (s−1), H is the combine soil water and plant xylem flow in a coupled system in soil water potential (m), h is the soil water pressure head (m), and which both the soil and the xylem are treated as porous media with z is the vertical coordinate, considered positive upward (m). The distributed hydraulic properties (Janott et al., 2011; Rings et al., intensity of root water uptake varies with depth and time accord- 2013). Such an approach is, in principle, much more realistic, but ing to the transpiration demand of the atmosphere, the soil water the resulting models are complex and computationally demanding. availability, and the plant water status. The algorithm used to evaluate the RWU intensity is often referred to as the macroscopic In this study, we combined the concept of lumped hydraulic capac- RWU model (e.g., Raats, 2007). itance, representing the hydraulic effect of variable whole-plant water storage, with the concept of spatially distributed macroscopic Root Water Uptake Model root water uptake to obtain an algorithmically simple transpira- The uptake of soil water by plant roots is described by a macroscopic tion stream model that could be easily implemented into existing RWU model based on the traditional water-potential-gradient soil water flow models. The proposed approach allows simulation approach (van den Honert, 1948; Hillel et al., 1976; and many others). of basic plant responses to varying atmospheric and soil mois- It is assumed that the RWU intensity is directly proportional to the ture conditions, including isohydric–anisohydric adjustments to difference between water potentials of the soil and the root xylem water stress. The suggested approach was tested by comparing the and indirectly proportional to the respective hydraulic resistances:

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Downloaded from http://pubs.geoscienceworld.org/vzj/article-pdf/16/5/1/4020615/vzj2016.12.0128.pdf by guest on 27 September 2021 Fig. 1. Seasonal variations of (a) selected meteorological variables affecting plant transpiration—hourly averages of vapor pressure deficit and net radia- tion (the latter expressed in units of equivalent evaporation, i.e., energy divided by the density of water and the latent heat of vaporization) and (b) variables defining the soil moisture conditions—daily precipitation totals and soil water pressure head variations observed at two depths.

s( ) 1 z éù s( ) =p2,( ) ( )= Sz( )=- ëûHrx- H soil ( z) [2] z rR01 z r z [4] rroot+ rz soil ( ) pRz( )

−1 where s is the specific active root surface (m ), rroot is the root and, finally, the characteristic length l can be expressed as a frac- radial resistance (s), rsoil is the effective hydraulic resistance of the tion of r1: soil matrix (s), Hrx is the root xylem water potential and Hsoil is the soil water potential. In this study, we assumed that Hrx varies with r0 l(z) = ar1 ( z),1 <£ a [5] time but is constant within the root system. This is consistent with r1 the observation that the axial resistance to water flow in roots is one to several orders of magnitude lower than the radial resistance where a is the dimensionless fraction coefficient. (e.g., Steudle and Peterson, 1998). Plant Water Balance We assumed that the effective soil hydraulic resistance can be Under the assumption of quasi-steady-state flow of water through expressed as the soil–plant–atmosphere continuum, the RWU intensity, inte- grated over the depth of the root zone, is equal to the actual l( ) −1 z transpiration rate Ta (m s ): rzsoil ( )= [3] Kz( )

z0 Tra==ò Sz( )d z T [6] where l(z) is the characteristic length associated with the transport zR of water from the bulk soil to the root surface, derived from the −1 active root system geometry (e.g., Vogel et al., 2013, 2016). where Tr is the whole-plant root water uptake (m s ) and zR and z0 are the coordinates of the lower and upper boundary of the root The active root system geometry is characterized by the active root zone, respectively (m). length density R (m−2), the specific active root surface s, the aver- age active root radius r0 (m), and the rhizosphere radius r1 (m). In A more realistic form of the whole-plant water balance equation this study, the spatial variability of R and s was limited to the verti- can be obtained by adding a transient storage term to Eq. [6]: cal direction and r0 was spatially invariant. Furthermore, assuming the cylindrical character of the root system geometry, the vertical dW z0 =-Sz( )d z Ta [7] òz distributions of R, s, and r1 can be related through simple formulas: dt R

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Downloaded from http://pubs.geoscienceworld.org/vzj/article-pdf/16/5/1/4020615/vzj2016.12.0128.pdf by guest on 27 September 2021 where W is the whole-plant water storage (m). Assuming that W the observed course of potential transpiration has a nearly semi- can be expressed as a single-valued function of Hrx, we obtain sinusoidal shape, reaching zero at sunset, while the trunk xylem sap flow exhibits an after-dusk tailing shape (Fig. 2). We assumed that ddWWddHH H increases overnight from its pre-dusk value to the value that ==rx C rx [8] rx ddtHtrx d d t is close to equilibrium with the average soil water potential. The C estimate can be obtained by dividing the cumulative nocturnal where C is the whole-plant hydraulic capacitance. Because both root water uptake (interpreted as DW) by the corresponding dif- W and Hrx are expressed in units of length, C is here defined as ference in Hrx. Because the pre-dusk value of Hrx was not measured dimensionless. at our study site, we used the combined soil water flow and tran- D spiration stream model iteratively to estimate both C and Hrx Substitution of Eq. [8] into Eq. [7] yields the final form of the (setting C = 0 as an initial estimate). whole-plant water balance equation: Isohydric Control

dH rx z0 In isohydric plants, the xylem water potential is limited to values C=- Sz( )d z Ta [9] òz dt R above a certain threshold value, here denoted as Hcrit. The plants maintain a distinct safety margin between this value and another Determination of Plant threshold value associated with the onset of cavitation, Hcav, by Hydraulic Capacitance means of stomatal control (e.g., Meinzer et al., 2009). A variety of methods have been used to determine the hydrau- lic capacitance of plants. The capacitance of sapwood can be To simulate isohydric behavior, we used a simple procedure that estimated directly from measurements of sapwood water release ensures that the root xylem water potential, Hrx, is kept greater curves (e.g., Meinzer et al., 2003; Scholz et al., 2007). Vergeynst than or equal to the threshold value Hcrit. The procedure con- et al. (2014) estimated whole-branch capacitance by combining sists of two alternative stages: (i) under favorable atmospheric measurements of acoustic emissions caused by cavitation, supple- and soil moisture conditions, the actual transpiration equals the mented with branch diameter shrinkage and gravimetric water loss atmospheric demand, i.e., Ta = Tp (where Tp is the potential tran- measurements. Whole-tree capacitance can be determined from spiration rate [m s−1]), and the root xylem potential is greater than observations of the time lag between evaporative demand and stem the critical value, i.e., Hrx > Hcrit; and (ii) when the atmospheric sap flow (e.g., Phillips et al., 1997; Kumagai et al., 2009) or the demand is too high or the soil profile too dry, the xylem water time lag between sap flow signals measured at different heights of potential reaches the critical value (Hrx = Hcrit) and the actual a tree stem (e.g., Cermak et al., 2007). transpiration becomes a fraction of its potential value (Ta < Tp).

Sapwood capacitance has been defined as the slope of a line fitted Transpiration Stream Model to the initial phase of the sapwood water release curve (Meinzer et The proposed transpiration stream model requires a simultaneous al., 2003, 2008; Vergeynst et al., 2014). According to Meinzer et solution of soil water flow Eq. [1], root water uptake Eq. [2], and al. (2003), the measured water release curves are nearly linear in a plant water balance Eq. [9]. This is achieved by a simple sequential relatively broad range of xylem water potentials, changing the slope coupling procedure. as the water potential approaches the point of cavitation. Thus, in the linear range of water release curves, the sapwood capacitance The time derivative on the left-hand side of Eq. [9] is discretized can be approximated by a constant value. The capacitance value is using a finite difference formula: expected to significantly increase at the onset of cavitation. dH HH- ¢ CCrx» rx rx [11] When simultaneous estimates of stem water storage and root xylem dttD water potentials are available, it is possible to determine the effec- tive whole-plant hydraulic capacitance directly from the definition By substituting Eq. [2] and [11] into Eq. [9], we obtain of Eq. [8]: HHrx- rx¢ z0 s C =-ò (Hrx-- H soil)d zT a [12] dWWD D+tzR rr C =» [10] root soil dHHrxD rx This equation is then used to derive an explicit formula for the In this study, we estimated the whole-tree hydraulic capacitance root xylem water potential as a function of transpiration, as well of Norway spruce by comparing the potential transpiration rate as the inverse relationship, i.e., transpiration as a function of root (determined from micrometeorological measurements) with the xylem water potential (for a given vertical distribution of the soil observed time series of stem sap flow data. On clear summer days, water potential Hsoil):

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Downloaded from http://pubs.geoscienceworld.org/vzj/article-pdf/16/5/1/4020615/vzj2016.12.0128.pdf by guest on 27 September 2021 Fig. 2. The results of transpiration stream modeling based on (a) a quasi-steady-state assumption and (b) a constant whole-plant capacitance approach (transient storage model), and (c) the simulated variations of root xylem water potential, Hrx, and the vertically averaged soil water potential, Hsoil. The secondary vertical axis relates Hrx, predicted with the transient storage model, to the plant water storage depletion (no storage change is assumed in the quasi-steady-state model).

z0 D¢ +séù + - rroot is constant, the root geometry is time invariant, and C is con- (C tH) rx ò ëû( rroot r soil) H soild z T a zR stant. However, these assumptions, unlike the one about the spatial H rx = [13] z0 éù invariance of , can be easily relaxed. CtD+ò ëû s( rroot + r soil ) d z Hrx zR At each time step of the numerical solution of Richards’ Eq. [1], ¢ z0 s HHrx- rx the root xylem water potential, Hrx, is first evaluated from Eq. [13], Ta =- (Hrx-- H soil )d zC [14] òz R rrroot+D soil t assuming Ta = Tp. If Hrx falls below Hcrit for a given potential tran- spiration rate, Hrx is set equal to Hcrit and Ta is calculated using The derivation of Eq. [13] and [14] requires that Hrx is constant Eq. [14], yielding Ta < Tp. The resulting Hrx value is then used to within the root system and changes only with time. In this study, calculate the RWU intensity S(z) (from Eq. [2]) and to update the we used several additional simplifying assumptions, such as that value of the sink term in Eq. [1].

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Downloaded from http://pubs.geoscienceworld.org/vzj/article-pdf/16/5/1/4020615/vzj2016.12.0128.pdf by guest on 27 September 2021 Quasi-Steady-State Flow Assumption on site, were used to define the upper boundary condition. The The quasi-steady state flow condition can be invoked by setting observed soil water pressure was applied as a time-dependent C equal to zero in Eq. [13] and [14]. This leads to an algorithm Dirichlet type boundary condition at the lower boundary of the that is similar to the one suggested by Hillel et al. (1976) and later soil column. Potential transpiration of spruce trees was estimated implemented in several RWU models (e.g., de Jong van Lier et by means of the Penman–Monteith equation (Monteith, 1981) al., 2008; de Willigen et al., 2012; Vogel et al., 2013; to name the based on the micrometeorological data observed at Liz. This more recent ones). was done by applying the standard FAO procedure for reference evapotranspiration (Allen et al., 1998), using hourly data from Anisohydric Control the nearby meteostation (located at the meadow site). The actual To simulate anisohydric behavior, Hcrit in the above algorithm transpiration rate was assumed to drop to zero overnight as well can be set equal to Hcav, and the plant hydraulic capacitance at as during rainfall events. Hcav modified to represent a partly embolized xylem. For short periods, partial cavitation could be a reversible process. However, The values of plant-related parameters (with the exception of if unfavorable weather conditions induce irreversible changes in the whole-plant hydraulic capacitance) were adopted from our plant tissues, hydraulic capacitance becomes a complex function of previous study (Vogel et al., 2016). The parameter values are sum- related plant physiological processes. In such a case, a more elabo- marized in Table 2. We assumed that water is taken up mostly by rate transpiration stream model would have to be considered. fine roots (commonly defined as roots with a diameter <0.2 cm). Based on values reported in the literature for spruce trees (e.g., Model Application at the Study Site Ruess et al., 2006; Kucbel et al., 2011), the mean radius of active The proposed transpiration stream algorithm was implemented roots, r0, was set equal to 0.01 cm and the maximum root length in the numerical code S1D (Vogel et al., 2010, 2013), which is density to 0.2 cm−2. The shape of the root length density func- designed to simulate soil water flow in a vertical soil profile tion, R(z), was estimated based on information found in the containing preferential pathways (solving a dual set of Richards’ literature and a limited survey performed at the site of interest. equations for a two-domain flow system). The soil profile at the We assumed a constant value of R(z) equal to the estimated maxi- study site was assumed to consist of two hydraulically connected mum root length density for depths 1 to 20 cm, followed by a flow domains—the soil matrix domain and the preferential flow linear decrease, with R(z) equal to zero at the lower boundary of domain. By partly diverting storm water from the root zone, the root zone at the depth of 70 cm. No roots were assumed in preferential flow significantly affects the soil water balance at the uppermost 1 cm of organic soil. Furthermore, we estimated the macroscopic scale; therefore it could not be neglected. It was that the coefficient a in Eq. [5] was equal to 0.05. This value was assumed that roots take water up from the soil matrix, i.e., the S(z) determined using the mesoscopic analysis of radial flow toward function was evaluated in the soil matrix domain only. roots (Vogel et al., 2016).

The S1D code was used to simulate soil water flow and spruce To facilitate the comparison with simulated actual transpiration tree transpiration at the Liz site from April to September 2010. rates (m s−1), the time series of the sap flow densities (kg m−2 The soil profile was schematized as a vertical one-dimensional s−1) obtained for the individual Norway spruce tree specimen 70-cm-deep soil column. The soil matrix flow domain was were upscaled to the forest stand using a procedure explained divided into two layers—an organic soil layer and a mineral soil in our previous study (Vogel et al., 2016). The threshold value layer—distinguished by different soil hydraulic properties (Table at the onset of cavitation, Hcav, was reported around −250 m 1). The initial condition for the simulations was derived from for Norway spruce (estimated from the leaf water potential by the observed variations in soil water pressure at the beginning Cochard [1992] and Lu et al. [1996]). Assuming a safety margin of the simulated period. Precipitation data, measured directly of about 50 m (Bréda et al., 2006) and the difference between

Table 1. Parameters characterizing soil hydraulic properties of individual soil layers at the Liz forest site (adopted from Vogel et al. [2013] and simpli- fied); qr and qs are the residual and saturated soil water contents, Ks is the saturated hydraulic conductivity, hs is the air-entry value, and aVG and nVG are empirical parameters determining the shape of the water retention and unsaturated hydraulic conductivity functions (van Genuchten, 1980; Vogel et al., 2000). The soil profile is conceptualized as a dual-continuum system represented by two flow domains: the soil matrix domain (SM) and the preferential flow domain (PF).

Domain Layer Depth qr qs aVG nVG Ks hs cm cm−1 cm d−1 cm SM 1 0–8 0.001 0.630 0.030 2.00 1000 0.00 2 8–70 0.001 0.503–0.267† 0.042 1.45 150–1† −2.00 PF 0–70 0.010 0.600 0.020 3.00 5000 0.00

† In the SM second layer, Ks and qs are varied linearly between the given limits.

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Downloaded from http://pubs.geoscienceworld.org/vzj/article-pdf/16/5/1/4020615/vzj2016.12.0128.pdf by guest on 27 September 2021 Table 2. Plant-related parameters assumed for Norway spruce. change causes separation of the actual transpiration rate from the actual RWU rate. The predicted sunny-day transpiration Parameter Value stream variations can be divided into three stages. Starting in the Depth of the root zone ( – ), cm 70 z0 zR morning, the plant actual transpiration fully meets the poten- Active root radius (r0), cm 0.01 tial transpiration demand while the root water uptake rate lags Radial hydraulic resistance of active roots (rroot), d 10 000 behind and the plant water storage decreases. When the root Critical root-xylem water potential (H ), m −150 crit xylem water potential reaches the critical value, Hcrit, the plant Maximum root length density (max{R(z)}), cm−2 0.2 water storage becomes fixed and the plant transpiration becomes Whole-plant hydraulic capacitance (C) 9 ´ 10−6 limited by the plant RWU. After the potential transpiration rate reduces below the limiting RWU rate, the actual transpiration follows the potential transpiration demand, while the RWU rate leaf and root water potentials, the Hcrit value can be expected reduces gradually, allowing the nocturnal replenishment of the to be in the range of about −200 to −150 m. In this study, we plant water storage. assumed Hcrit = −150 m. In Fig. 2c, the simulated root xylem water potential variations, The whole-tree hydraulic capacitance was set equal to 9 ´ 10−6. assuming either constant or transient plant water storage, are pre- The value was chosen to produce a reasonable agreement between sented. The value of Hrx fluctuates between the soil water potential the simulated variation of Tr and the observed sap flow. Expressed (depicted by dashed lines) and the critical xylem potential main- in units of water mass per unit pressure change, it corresponds to tained by the plant (set to −150 m). Considering nonzero hydraulic 12 kg MPa−1 per tree (assuming 13 m2 of ground area per tree, as capacitance helps to smooth the xylem potential variations and to determined for the study site), or 7 kg MPa−1 m−3 of sapwood delay or even eliminate the critical state at which the transpiration (assuming 1.6 m3 of sapwood per tree). becomes reduced.

Our model assumes a linear relationship between the root xylem 6 6Results and Discussion water potential, Hrx, and the whole-plant water storage, W. Thus the Hrx variations directly reflect the development of plant water Effects of Plant Water Storage storage depletion (note the secondary vertical axis on the right- Precipitation data, together with the key micrometeorological vari- hand side of Fig. 2c). Assuming that W is full at Hrx equal to zero, ables affecting the magnitude of spruce tree transpiration (Fig. 1a), the maximum possible depletion of W is determined by the critical indicate that the soil was well supplied with water throughout the value of the root xylem water potential, Hcrit, and by the value of season studied, with two drier periods in the first half of July and plant hydraulic capacitance. In our case, the maximum reduction the second half of August. That is also reflected in the soil water is about 1.4 mm. Considering 13 m2 of ground area per tree, the pressure (Fig. 1b) and soil water content data (not shown). maximum possible reduction in the xylem water storage is 18 L per tree. Cermak et al. (2007) detected a maximum daily variation The effects of two different approaches to plant water storage of 53 L for a 56-m-high Douglas-fir tree [Pseudotsuga menziesii in coupled soil-water-flow and root-water-uptake modeling are (Mirb.) Franco]; Zweifel and Häsler (2001) reported a maximum presented in Fig. 2. A 12-d period with intensive transpiration daily water depletion of 5 L for a mature Norway spruce tree; demand, interrupted by a rainy day, was selected to illustrate the Waring and Running (1978) evaluated the daily depletion of the functioning of the model. xylem water storage of a mature Douglas-fir stand to be 1.7 mm. On a sunny day with high transpiration demand, the maximum In Fig. 2a, the actual transpiration rate, Ta, calculated assuming amount of water that can be taken from the plant water storage is quasi-steady-state flow through the transpiration stream, is pre- determined by the difference between the pre-dawn value of Hrx sented together with the applied potential transpiration, Tp, and and Hcrit. the observed sap flow in a selected spruce tree specimen. Under the quasi-steady-state assumption, the whole-plant RWU rate equals Considering the predicted actual transpiration, the nonzero the actual transpiration rate (the plant water storage is constant) plant hydraulic capacitance approach allows the system to and both are nonzero only when nonzero potential transpiration satisfy a higher transpiration demand. Estimated actual transpi- is applied (i.e., during the daytime in our simulation). In contrast, ration amounts during the simulated season (Fig. 3) increased the sap flow measurements indicate nonzero nocturnal fluxes in from 301 mm, assuming zero capacitance, to 330 mm assuming the stem xylem. a capacitance of 9 ´ 10−6. The change represents 8% of the cumulative potential transpiration. The average daily contribu- Simulation results obtained assuming transient plant water stor- tion to the transpiration due to the elastic plant water storage age are presented in Fig. 2b. Allowing the plant water storage to is 0.2 mm d−1.

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Downloaded from http://pubs.geoscienceworld.org/vzj/article-pdf/16/5/1/4020615/vzj2016.12.0128.pdf by guest on 27 September 2021 Fig. 5. The sensitivity of the transpiration stream model to the value of whole-plant hydraulic capacitance, C, reflected in the different predictions of whole-plant root water uptake, Tr, and the actual tran- spiration rate, Ta.

Fig. 3. Simulated cumulative actual transpiration rates, Ta, for quasi- steady-state and transient plant storage approaches compared with the Isohydric vs. Anisohydric Control cumulative potential transpiration rate, T . p To a first approximation, an anisohydric plant strategy can be simulated by setting the critical value of the xylem water poten- Assuming a nonzero hydraulic capacitance significantly reduces tial, Hcrit, equal to Hcav, which marks conditions under which the simulated soil water redistribution via roots (Fig. 4). The zero- the plant becomes susceptible to xylem embolism. Figure 6 com- capacitance simulations predict regular nightly redistribution of pares the results of simulations performed assuming isohydric the soil water demonstrated by negative root water uptake intensi- and anisohydric strategies of two different transpiring plants— ties (Fig. 4c). If a nonzero plant capacitance is assumed, the water Norway spruce vs. a hypothetical anisohydric tree under the redistribution via roots is predicted only occasionally during major same environmental conditions. The value of Hcrit = Hcav was rainfall events (Fig. 4d). set equal to −250 m for the anisohydric species, while Hcrit was fixed at −150 m for the isohydric species. In our example, the As expected, the transpiration stream model is quite sensitive to Hrx value, resulting from the simulation of an anisohydric strat- the magnitude of the whole-plant hydraulic capacitance. Figure 5 egy, did not reach the value of Hcav, thus the effect of increased shows differences in predictions of root water uptake and actual hydraulic capacitance due to cavitation need not be considered. transpiration rates obtained with different values of C, ranging That, however, would not be true under the conditions of more from 0 to 2 ´ 10−5. pronounced drought stress.

Fig. 4. Simulated temporal variations in the vertical distribution of root water uptake, S: (a,c) quasi-steady-state flow assumption, and (b,d) transient plant storage approach; (c) and (d) show negative values of root water uptake, indicating root-mediated hydraulic redistribution.

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Downloaded from http://pubs.geoscienceworld.org/vzj/article-pdf/16/5/1/4020615/vzj2016.12.0128.pdf by guest on 27 September 2021 Fig. 6. Comparison of isohydric and anisohydric behavior (Norway spruce vs. a hypothetical anisohydric species under the same environmental condi- tions): (a) whole-plant root water uptake rates, Tr, and (b) root xylem water potential, Hrx, and vertically averaged soil water potential, Hsoil.

To simulate the effects of xylem embolism under severe long-lasting The suggested transpiration stream model is based on an explicit drought stress, the hydraulic capacitance would need to be varied evaluation of the root xylem water potential as a function of the based on not only the Hrx value but also the history of Hrx develop- actual transpiration rate and therefore can be easily incorporated ment. Such a description would require a quantitative evaluation into existing models of soil water flow to facilitate more realistic of the related plant physiological processes (e.g., the cavitation- simulations of plant root water uptake and transpiration. induced loss of hydraulically active tissues, decrease of xylem axial conductance, and the subsequent process of regeneration). Acknowledgments The research was funded by the Czech Science Foundation, Project no. 16-05665S. Sap flow and meteorological data from the Liz experimental site were available through the courtesy of the Institute of Hydrodynamics of the Czech Academy of Sciences. 66Summary and Conclusions A previously developed one-dimensional numerical model of soil References water flow, involving macroscopic vertically distributed plant root Allen, R.G., L.S. Pereira, D. Raes, and M. Smith 1998. Crop evapotranspiration: Guidelines for computing crop water requirements. Irrig. Drain. Pap. 56. water uptake, was extended to allow simulations of transient plant FAO, Rome. water storage effects. The resulting model predicted reasonably Borchert, R., and W.T. Pockman. 2005. Water storage capacitance and xy- lem tension in isolated branches of temperate and tropical trees. Tree well the evening recharge of plant water storage by root water Physiol. 25:457–466. doi:10.1093/treephys/25.4.457 uptake as well as morning discharge to the atmosphere. The pro- Bréda, N., R. Huc, A. Granier, and E. Dreyer. 2006. Temperate forest trees posed approach can be used to simulate plant responses to water and stands under severe drought: A review of ecophysiological respons- es, adaptation processes and long-term consequences. Ann. For. Sci. stress caused by high midday potential transpiration demand and/ 63:625–644. doi:10.1051/forest:2006042 or by soil drought. Carrasco, L.O., S.J. Bucci, D. Di Francescantonio, O.A. Lezcano, P.I. Campan- ello, F.G. Scholz, et al. 2015. Water storage dynamics in the main stem of subtropical tree species differing in wood density, growth rate and life The comparison of transpiration stream fluxes with sap flow history traits. Tree Physiol. 35:354–365. doi:10.1093/treephys/tpu087 Cermak, J., J. Kucera, W.L. Bauerle, N. Phillips, and T.M. Hinckley. 2007. Tree observations revealed improved model performance when the water storage and its diurnal dynamics related to sap flow and changes conventional assumption of quasi-steady-state flow along the tran- in stem volume in old-growth Douglas-fir trees. Tree Physiol. 27:181–198. doi:10.1093/treephys/27.2.181 spiration stream was replaced by the more realistic transient plant Cochard, H. 1992. Vulnerability of several conifers to air embolism. Tree water storage assumption. Physiol. 11:73–83. doi:10.1093/treephys/11.1.73

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