Tree Physiology 35, 425–438
doi:10.1093/treephys/tpu113
Research paper
Simulating nectarine tree transpiration and dynamic water
storage from responses of leaf conductance to light and sap
flow to stem water potential and vapor pressure deficit
Indira Paudel1,2, Amos Naor3, Yoni Gal4 and Shabtai Cohen1,5
1Department
of Environmental Physics and Irrigation, Institute of Soil, Water and Environmental Sciences, ARO Volcani Center, PO Box 6, Bet Dagan 50250, Israel;
Soil and Water Sciences, The R.H. Smith Faculty of Agriculture Food and Environment, The Hebrew University of Jerusalem, Rehovot, Israel; 3Golan Research
Institute, PO Box 97, Kazrin 12900, Israel; 4Ministry of Agriculture and Rural Development, 10200 Kiryat Shmona, Israel; 5Corresponding author ([email protected])
2Department of
Received July 6, 2014; accepted November 21, 2014; published online January 24, 2015; handling Editor Maurizio Mencuccini
For isohydric trees mid-day water uptake is stable and depends on soil water status, reflected in pre-dawn leaf water potential
(Ψpd) and mid-day stem water potential (Ψmd), tree hydraulic conductance and a more-or-less constant leaf water potential
(Ψl) for much of the day, maintained by the stomata. Stabilization of Ψl can be represented by a linear relationship between
canopy resistance (Rc) and vapor pressure deficit (D), and the slope (BD) is proportional to the steady-state water uptake. By
analyzing sap flow (SF), meteorological and Ψmd measurements during a series of wetting and drying (D/W) cycles in a nectarine orchard, we found that for the range of Ψmd relevant for irrigated orchards the slope of the relationship of Rc to D, BD
is a linear function of Ψmd. Rc was simulated using the above relationships, and its changes in the morning and evening were
simulated using a rectangular hyperbolic relationship between leaf conductance and photosynthetic irradiance, fitted to leaflevel measurements. The latter was integrated with one-leaf, two-leaf and integrative radiation models, and the latter gave the
best results. Simulated Rc was used in the Penman–Monteith equation to simulate tree transpiration, which was validated by
comparing with SF from a separate data set. The model gave accurate estimates of diurnal and daily total tree transpiration for
the range of Ψmds used in regular and deficit irrigation. Diurnal changes in tree water content were determined from the difference between simulated transpiration and measured SF. Changes in water content caused a time lag of 90–105 min between
transpiration and SF for Ψmd between −0.8 and −1.55 MPa, and water depletion reached 3 l h−1 before noon. Estimated mean
diurnal changes in water content were 5.5 l day−1 tree−1 at Ψmd of −0.9 MPa and increased to 12.5 l day−1 tree−1 at −1.45 MPa,
equivalent to 6.5 and 16.5% of daily tree water use, respectively. Sixteen percent of the dynamic water volume was in the
leaves. Inversion of the model shows that Ψmd can be predicted from D and Rc, which may have some importance for irrigation
management to maintain target values of Ψmd. That relationship will be explored in future research.
Keywords: capacitance, isohydric behavior.
Introduction
Use of sap flow (SF) sensors in the past few decades has
resulted in an improved understanding of the responses of
plant water relations to environment on the whole-plant level.
Early on, it was found that under high-light conditions canopy
conductance (Gc) is negatively related to the vapor pressure
deficit of ambient air (D) (e.g., Granier et al. 1996b, Oren et al.
1998, Li et al. 2002), a response that stabilizes transpiration
and mid-day leaf water potential as D increases (Monteith and
Unsworth 1990, Cohen and Naor 2002, David et al. 2004).
Stabilization of leaf water potential is typical isohydric behavior
© The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected]
426 Paudel et al.
of many tree species (Tardieu and Simonneau 1998). The relationship of Gc to D is similar, but not identical, to the response
of leaf-level conductance to D. At the whole-plant level, the
response is related to the tendency of whole plants to coordinate water use with internal constraints on water transport, like
the hydraulic capacity of the stem and roots (Solari et al. 2006,
Cohen et al. 2007) and the negative water potential at which the
stomata are observed to close (Buckley et al. 2012). Those plant
traits are in turn related to the structural properties and physical
limits of the water transport system, as demonstrated by many
studies showing the correspondence between water potential
at which the stomata are observed to close and that at which
hydraulic capacity is impaired (Kocher et al. 2013). However,
water potential in the plant is not fixed and depends on soil
water content (David et al. 2004, Meinzer et al. 2004).
The relationship of canopy conductance to D has been fitted empirically to an exponential function (Jones 1992, Granier
et al. 1996a, 1996b, Oren et al. 1998, 1999a, Ewers et al.
2002, Orgaz et al. 2007, Katul et al. 2012), and parameters of
that function for many species have been reviewed (Oren et al.
1999b, Katul et al. 2012). A simpler option is an inverse relationship, i.e., a linear relationship between canopy resistance
and D (Cohen and Naor 2002, David et al. 2004). Villalobos
et al. (2013) showed that the linear relationship could be
derived from the Ball–Berry model of leaf photosynthesis
(Dewar 2002). These models have dealt with forests and irrigated orchards, but how the relationship changes when soil
water content decreases has not been addressed.
Models of the response of daily plant water use to soil and
climate provide basic information necessary for irrigation management. Currently, the most widely used is the Penman–
Monteith model (Penman 1948, Monteith 1965) applied to a
well-irrigated cut-grass surface (the FAO56 model, Allen et al.
1998), which has been validated by lysimeter measurements
(e.g., Sumner and Jacobs 2005). Application of the model to
other crops involves the use of an empirical crop factor, which
can also be adjusted for deficit irrigation conditions (Allen et al.
1998, Naor 2006, Katul et al. 2012, Villalobos et al. 2013).
Canopy conductance of the grass (or other) crop is fixed and
therefore reference crop evapotranspiration (ET0) increases
with the atmospheric demand for evaporation, i.e., as a wet surface. Models that include the response of canopy conductance
to D may be a useful extension of the standard ET0 calculation,
since for many crops the resulting ET0 would be more realistic in
predicting actual crop water use (Goldstein et al. 1998, Phillips
et al. 2003, Testi et al. 2006, Orgaz et al. 2007, Katul et al.
2012, Villalobos et al. 2013). Another possible advance might
be the introduction of models that predict daily water use accurately using only D and radiation (e.g., Testi et al. 2006, Orgaz
et al. 2007, Buckley et al. 2012, Villalobos et al. 2013), which
would preclude the need for measurement of wind speed in
agro-meteorological stations.
Tree Physiology Volume 35, 2015
More detailed models predict instantaneous rates of water
use. These can be used to gain insight into plant processes
(Meinzer et al. 2009, Manzoni et al. 2012), for example
determining the difference between transpiration from the
leaves and uptake of water from the soil, or the hydraulic
capacitance of the plant (Sperry et al. 2002, Manzoni et al.
2012). Sometimes changes in water content can be determined from direct measurements, e.g., where eddy covariance measurements or SF measurements in the upper
branches are made simultaneously with monitoring of soil
water balance and trunk SF (Moore et al. 2008, Richards et
al. 2013). Capacitance is an important feature of plant water
relations since the leaves draw on stored water, water content declines along with water potential and thus water is
drawn from the soil. Capacitance introduces a significant time
lag between trunk SF and transpiration (Phillips et al. 1997,
Goldstein et al. 1998, Ford et al. 2005, Kumagai et al. 2009).
Time constants associated with the lag can be estimated as
the product of hydraulic resistance and hydraulic capacitance
between the soil and the reference point within the plant,
and especially in the leaves (Meinzer et al. 2004, Cermak et
al. 2007). Detailed models of plant capacitances have been
developed and some of these include descriptions of daily
stem contractions (e.g., Zweifel et al. 2001, Steppe et al.
2006), which is important because stem contractions can
be measured with dendrometers and are useful for irrigation
control (e.g., Naor and Cohen 2003, Fernandez and Cuevas
2010). Here, we use a combination of SF measurements and
a model of tree transpiration to determine the dynamics of
water storage in the plant.
The hypothesis of our study is that nectarine water use for
different levels of soil water content can be determined from
a model of climate demand for transpiration and the response
of canopy conductance to D, mid-day stem water potential
(Ψmd) and radiation. In order to study the ability of the model
to predict diurnal changes, plant water storage, which plays a
significant role in the daily cycle of water uptake and loss from
the plant, was quantified as the difference between simulated
transpiration and SF.
Our objectives were to (i) develop a model of canopy conductance based on experimentally derived relations under nonstress and water stress conditions, (ii) validate the model and
compare alternatives for modeling radiation and (iii) explore
the use of the model to predict changes in tree water content
resulting from temporal differences between model transpiration and water uptake.
Theory: model description
Canopy conductance from SF measurements
Canopy conductance (Gc, m s−1) was computed with an inversion of the Penman–Monteith equation as
Simulating nectarine tree transpiration and dynamic water storage 427
Gc =
F λGa
,
∆(Rn − G ) + ρ Cp DGa − F λ (∆ + γ )
(1)
where F is canopy water use measured with the SF sensors (kg m−2 s −1), Δ is the slope of the relationship between
water vapor pressure and temperature [KPa °C −1], ρ is the
density of dry air (kg m−3)], Cp is specific heat of dry air
at constant pressure (J kg −1 C −1), D is vapor pressure deficit (KPa), γ is the psychrometric constant (KPa °C −1) and
λ is the latent heat of vaporization of water (J kg−1). Net
radiation (R n, MJ m−2 s −1) and soil heat flux (G, MJ m−2 s −1)
were estimated as recommended by Allen et al. (1998) for
cases where only short wave solar radiation is available
(Allen et al. 1998, Eqs 38, 39, 45 and 46). Aerodynamic
resistance (G a , m s −1) was calculated from the wind speed
measured above the orchard, u (after Granier et al. 1996b,
Damour et al. 2010) as
Ga = 0.1 × u. (2)
The canopy conductance Gc ′ model
Relationships to D and Ψmd Canopy conductance was simulated based on relationships found between canopy conductance Gc and other parameters, where Gc was computed from
SF using Eq. (1). The influence of D on simulated canopy resistance (Rc,D) was expressed as
1/ Gc′ = Rc,D = AD + BD × D,
(3)
where G c ′ is simulated canopy conductance; AD is the
resistance when D = 0 and B D is the slope, which should
be proportional to a steady-state rate of transpiration and
sap flux maintained by the plant as D varies. Here the linear
relationship Eq. (3) was found to apply for mid-day conditions and a wide range of Ψmds measured in the wetting and
drying cycles (Figure 2a). The constant AD was not found
to change significantly with Ψmd and its average value was
0.045 ± 0.001 (Figure 2c; Table 1). B D was linearly related
to Ψmd, i.e.,
BD = AΨ + BΨ × Ψmd , (4)
where AΨ and BΨ were 0.0362 and −0.116, respectively
(Figure 2b; R2 = 0.89; P < 0.05).
Equations (3) and (4) cover mid-day clear-sky conditions.
Relationships of leaf conductance to PPFD
In order to simulate the influence of solar radiation on Gc′, which
causes increases and decreases in morning and evening,
respectively, a rectangular-hyperbola relationship of relative
leaf conductance Gc,rel to photosynthetic photon flux density
(PPFD) on the leaf surfaces, Sl, was applied (Thornley 1976),
with parameters fitted to leaf conductance measurements, i.e.,
Gc,rel = s × Sl /(1 + s × Sl ).
(5)
For this equation the asymptotic value of Gc′ when Sl is
large is 1 and when Sl approaches zero, the slope of the equation is s. Regression of measurements of leaf conductance
for low D (i.e., <1 KPa) on PPFD yielded a value of 0.220
(mmol m−2 s−1)−1 for s.
Finally, canopy conductance (mm/s) was simulated as
Gc′ = Gc,rel /Rc,D .
(6)
Model parameters are listed in Table 1 along with symbols
and units.
Mean leaf irradiance from a one-leaf model
In our first method to apply the leaf-level model of leaf conductance to a whole canopy, we took Sr as the average radiation
incident on the leaves. Intercepted short wave radiation was
calculated from the light interception coefficients of our nectarine row canopy, using a simple model of hedgerow canopies
(Fuchs and Stanhill 1980) as shown below.
Ray interception by a hedgerow, which is a good estimate
of absorption of radiation in the photosynthetic waveband
where leaf absorptance is high, is the relative shadow area
projected on the ground surface by direct radiation. For an
array of long parallel solid rows with rectangular cross sections, height h, width w and spacing d, the interception P is
described by
P = w /d + (h/d )tanθ | sinΦ |; θ < θ w ,
P = 1; θ > θ w ,
(7)
where θ is the zenith angle of the solar beam and Φ is the difference between the solar azimuth and the row direction. θw is
the zenith angle at which the shadows cast by adjacent rows
overlap:
θ w = tan−1[(d − w )/(h | sinΦ |)].
(8)
Sl is then obtained as
Sl = P × Sg / L,
(9)
where L is leaf area index and Sg is global PPFD derived from
global radiation based on the mean PPFD in global radiation (in
W m−2), taken as 49% for Israeli conditions (after Stanhill and
Fuchs 1977) and translated to moles based on the energy of
a mole of quanta at the average wavelength of photosynthetic
radiation (Campbell and Norman 1998).
Tree Physiology Online at http://www.treephys.oxfordjournals.org
428 Paudel et al.
Figure 1. Seasonal courses of SF, Ψmd, ET0, D and solar radiation for the irrigation season of 2011 and 2012. Sap flow (a), solar radiation (e), D (d)
and ET0 (c) were measured continuously and Ψmd (b) was measured weekly. SF is plotted as weekly averages. Vertical bars indicate two standard
errors of the mean.
Mean leaf irradiance from a two-leaf model
The second method was a two-leaf model that considered conductance to be the sum of the conductance of the sunlit and
shaded parts of the canopy, whose portions, L sun and L shade,
Tree Physiology Volume 35, 2015
are calculated from the canopy geometry (see Appendix). We
assumed that the sunlit portion receives global radiation, while
the shaded portion receives only diffuse radiation, so relative conductance, Gsun and Gshade, for the two portions can be
Simulating nectarine tree transpiration and dynamic water storage 429
Figure 2. Relationship of canopy resistance (Rc) to D for four values of Ψmd (a), slope of the Rc to D relationship (BD in Eqs (3) and (4)) plotted against
Ψmd (b) and the intercept of the Rc to D relationship (AD in Eq. (3)) plotted against Ψmd (c). First, second and third refer to the order of the D/W cycles.
Table 1. Model parameter, symbol, value and units of the canopy conductance model for nectarine trees.
Model parameter
Equation
Symbol
Value
Units
Intercept of ΔRc/ΔD on Ψmd
Slope of ΔRc/ΔD on Ψmd
Intercept of Rc on D
Slope dGc/dSr when Sr is 0
6
6
5
7
A
B
AD
S
0.0362
−0.116
0.0451 ± 0.001
0.220
s mm−1 kPa−1
s mm−1 kPa−1 MPa−1
s mm−1
(mmol m−2 s−1)−1
computed from the light-response curve Eq. (5) using their
appropriate radiation values, Sg/SLAI and Sd/(LAIshade), respectively, where SLAI is the sunlit LAI and Sd is diffuse PPFD above
the canopy. Relative canopy conductance is the weighted average of the two parts, i.e.,
Gc,rel = (Gsun × Lsun + Gshade × Lshade ).
(10)
Gc,rel =
1
L
∫
L
0
sSgexp(−GL/ cosθ )
dL,
1 + sSgexp(−GL/ cosθ )
(11)
where L is leaf area index and G is the leaf area shape factor whose value is 0.5 for a random canopy. The integral was
solved by numerical quadrature using L steps of 0.1 and measured leaf area index L.
Simulated canopy transpiration
Integrated leaf conductance from extinction of irradiance
in the canopy
A third method integrated leaf conductance for all leaf area to
get canopy conductance. In this case, the rectangular hyperbola describing the leaf-level response was integrated using
a model of extinction of radiation in a canopy with randomly
distributed leaves, i.e.,
The Penman–Monteith equation (Monteith 1965) was used to
calculate canopy transpiration Tc (Granier et al. 1996a, 1996b)
using climate data and simulated canopy conductance Gc′, i.e.,
Tc =
∆(Rn − G ) + pCpDGa
.
λ[∆ + γ (1 + (Ga /Gc′ ))] (12)
Tree Physiology Online at http://www.treephys.oxfordjournals.org
430 Paudel et al.
Tree water storage and the contribution of leaf water
The difference between measured SF in the trunk and
model-derived canopy transpiration (Eq. (12)) was used to
quantify the change in water content of the tree (Cermak
et al. 2007, Kumagai et al. 2009, Phillips et al. 2009, Kocher
et al. 2013).
Leaf water release curves were used to estimate the change
in leaf water content for a given change in tree water potential.
This was then multiplied by the total leaf area of a tree and
compared with changes in tree water content in order to estimate the portion of change in total tree water content that can
be attributed to leaves.
Model inversion to compute Ψmd
Analysis of the relationship of Rc to D (Eq. (3)) and of BD to
Ψmd (Eq. (4)) yields the relationship of Ψmd to climate parameters and Rc, i.e.,
Ψmd
R − AD − AΨ D
= c
.
BΨ D
(13)
Equation (13) can be solved using measurements of SF or
crop transpiration and standard meteorological variables.
Materials and methods
The study site
The experimental site was a 10-year-old commercial orchard
of a late variety (Arctic Mist) of nectarine (Prunus persica var.
nectarina) at Kfar Haruv in Northern Israel (33°44′N, 35°41′E,
340 m above mean sea level). The experiment was conducted
during the irrigation seasons (May–October) of 2011 and
2012; and the measurement periods were from 20 May to
September 2011 and 15 April to 18 September 2012. The climate is semi-arid with rainless summers and annual precipitation (October–April) of ∼600 mm. Tree spacing was 3 × 5 m.
Irrigation was with two drip lines per row and 1.6 l h−1 emitters at 0.5 m spacing. Tree height was 3–4 m and rows were
planted in the north–south direction.
Irrigation
The commercial orchard was used for an experiment on irrigation control using various soil- and plant-based sensors (Cohen
et al. 2013, Paudel et al. 2013b). That experiment was conducted in 20 plots with more or less the same ‘normal’ irrigation and therefore those plots were considered well irrigated.
Each plot contained three rows with five trees per row (i.e.,
a total of 15 trees), so that three trees could be measured.
‘Normal’ irrigation was applied every 1–3 days according to a
pre-set irrigation table based on long-term average pan evaporation from a nearby climate station and standard crop coefficients for the region. Irrigation crop coefficients were adjusted
Tree Physiology Volume 35, 2015
once a week in order to maintain a pre-set range of Ψmd (−0.8
to −1.0 MPa in 2011 and −0.9 to −1.1 MPa in 2012) in the ‘normal’ irrigation plots. Results of the irrigation control experiment
are presented elsewhere (Cohen et al. 2013).
Two additional plots with a total of six experimental trees
were used for experimental drying and wetting cycles (D/W)
in different parts of the irrigation season. In the cycles Ψmd
began close to that of the ‘normal’ irrigation plots and then irrigation was stopped until Ψmd reached a pre-set value (−1.4 to
−1.8 MPa) after which the plot was irrigated with supplemental
water in order to bring Ψmd back to the initial values. Normal
irrigation continued for a few weeks before the next cycle was
run. Wetting and drying cycles were run in each of the three
nectarine fruit development stages (cell division, pit hardening
and cell expansion) in the summers of 2011 and 2012.
Meteorological data and reference evapotranspiration (ET0)
A meteorological station consisting of a solarimeter (Kipp and
Zonen type CM11), temperature and relative humidity sensor
(Campbell Scientific, Model HMP45C, Logan, UT, USA) and
anemometer (Met One, Campbell Scientific) was installed in
the middle of the experimental orchard with the anemometer
∼2 m above the tree tops and connected to a CR1000 datalogger (Campbell Scientific). Climate data were logged every
15 min, and reference ET0 (in mm day−1) was computed using
the standard FAO56 Penman–Monteith equation (Allen et al.
1998) using air temperature and relative humidity, wind speed
and solar radiation (Sr) measured in the orchard. ET0 values
compared favorably with those from a nearby meteorological
station at Avnei Eitan (32°49′N 35°46′E; 380 m above sea
level). Global radiation and calculated extraterrestrial radiation
were used to determine atmospheric turbidity and then to partition global radiation into direct and diffuse components using
models from Campbell and Norman (1998).
Sap flow
Sap flow was monitored continuously with 2-cm long thermal dissipation (TD) probes (Granier 1985, 1987) in two
trees in each normally irrigated plot, i.e., in 42 trees. In the
drying and wetting plots, SF was measured in all six trees.
Thermal dissipation sensors were manufactured in our laboratory and connected to a multiplexer (Campbell Scientific,
Model AM16/32) and a datalogger (CR1000). For details of
construction, calibration and corrections for the radial distribution of sap flux density and radial depths not measured, see
Paudel et al. (2013a). Radial depth for zero flow was taken as
4.9 cm (ibid). In 2011, all probes were heated continuously
from the time of their installation in March until the end of
May, after which discontinuous heating (15 min on and 15 min
off; Do and Rocheteau 2002, Isarangkool et al. 2010, Paudel
et al. 2013a) was used for half of the probes, so that approximately half of the probes were operated continuously and half
Simulating nectarine tree transpiration and dynamic water storage 431
discontinuously at any specific time. Continuous and discontinuous heating was alternated among trees every other day.
In 2012, the two methods of heating continued. Comparison
between the two heating methods in the same trees was used
to determine the relative quality of the two methods as well as
calibration factors (Paudel et al. 2013a). Following the current
study, we have implemented discontinuous heating in our other
remote field studies in order to save power.
Trunk circumference, measured once in each season, was
used to determine trunk diameter.
Azimuthal variation of SF in the stem was measured with
additional TD sensors installed in six more well-irrigated trees
at four different directions during the irrigation season of
2012, i.e., 24 sensors. Differences in SF for different azimuthal
directions were measured on four trees on warm days in the
summer of 2012 when the climate was uniform and skies
cloudless. Differences were not consistent from tree to tree
and did not exceed 20% (not shown). Relative SF in different
azimuths was similar in the morning and afternoon, indicating
that the solar direction accounts for little of the variation. Since
all other measurements in this study were made with probes
inserted from the south and differences between directions
were not consistent, we assume that there was no bias due to
azimuthal variation.
Mid-day stem water potential
Mid-day stem water potential (Ψmd) was measured with a pressure chamber (ARIMAD, MRC Ltd, Holon, Israel) at weekly
intervals during the experimental period. A total of 40 leaves
(two from each plot) were measured for Ψmd of the ‘normally’
irrigated plots, and 12 additional leaves (two per tree) in the
D/W plot. Leaves, sampled from the shaded section of the
canopy near main branches, were covered for at least 1.5 h
with aluminum foil zip-lock bags (PMS Instruments, Albany,
OR, USA), cut with a sharp blade, transported to the pressure
chamber in plastic bags and measured immediately. The measurements were made between 12:00 and 13:30 standard
time, when stem water potential is very stable and changes
due to time differences are negligible. During wetting and drying cycles, measurements in the D/W plot were more frequent.
Leaf area
Plant area index (PAI), assumed to be equal to leaf area index,
was measured in May and July 2011 and every 2 weeks during
the irrigation season in 2012. Measurements were made with a
‘Sunlink’ linear PPFD (in µmol m−2 s−1) sensor array (Decagon
Devices, Inc., Pullman, WA, USA) containing 80 sensors.
Measurements were made at 20-cm intervals below a representative area of the orchard using the protocol described
by Cohen et al. (1997) and Li et al. (2002). Accuracy of LAI
measurements is ∼20% (Welles and Cohen 1996, Cohen et al.
1997). Measurements at different solar angles were used to
estimate leaf angle distribution, and these showed that the
­distribution was not significantly different from random.
Leaf gas exchange and light-response curves
Light-response curves for leaf conductance and photosynthesis were measured three times (July, August and September
of 2012) on fully developed leaves using a portable photosynthesis system (Model 6400XT, LI-COR, Inc., Lincoln, NE, USA).
Measurements were made in both water-stressed (W/D) and
normally irrigated plots.
Leaf water release curves
Water released from nectarine leaves as a function of applied
pressure was measured in the laboratory in August and
September 2012 using a pressure chamber. Data collected in
this way are used to derive pressure–volume curves. Branches
from well-irrigated plots were collected in the field, covered
with plastic bags and cut branch tips were immersed in water
during transportation to the laboratory. Leaves were pressurized in a pressure chamber and water exuded from the leaves
was collected at pressure steps of ∼0.5 MPa from 0.15 to 2.5
or 3.0 MPa.
Model validation
Sap flow measured with the continuous heating mode in the
D/W plot was used for determining model parameters during
the irrigation season of 2011. The model was validated using
SF measured in the well-irrigated plots in 2011 and 2012 and
with the discontinuous method in the D/W plot during D/W
cycles in 2011 and 2012. The validation data were used to
compute Gc using Eq. (1) and compared with model outputs.
Results
Seasonal trends of water use in the orchard
Figure 1 shows the seasonal course of daily total SF (a), Ψmd
(b), daily reference evapotranspiration (ET0, c), daily average
vapor pressure deficit (D, d) and solar radiation (Sr, e) in 2011
and 2012. Sap flow rates were highly variable in spring and
autumn and relatively constant during the summer season
(June until the end of September), with small variations apparently caused by variations in soil water availability and Ψmd
(Figure 1). Maximum values of SF were 6–7 mm day−1 in both
years. Ψmd under normal irrigation was relatively high in spring,
almost constant during the summer and declined in the fall. Sap
flow and Ψmd varied with soil moisture in the D/W plots during
the drying and wetting cycles in both seasons as expected.
Minimum Ψmd was −1.55 MPa in 2011 and −2.3 MPa in 2012,
at which times SF decreased to 3.5 and 3.3 mm day−1, respectively. We note that for good yields Ψmd is generally maintained
at values above −1.1 MPa (Naor 2006), so the low values during the drying cycles represent significant stress for the trees
Tree Physiology Online at http://www.treephys.oxfordjournals.org
432 Paudel et al.
and did reduce the yield of those trees. The general seasonal
course of SF was most similar to that of ET0, and was significantly correlated with ET0, Sr and D (in that order), especially for normal irrigation (Table 2). Low mid-day Ψmd led to
reduced SF.
Empirical relationships between Rc and climate
Rc was linearly related to D for mid-day conditions and a wide
range of Ψmd. Relationships for four values of Ψmd are shown
in Figure 2a. When Ψmd changed, the slope of the Rc to D relationship (i.e., ΔRc/ΔD from linear regression) changed proportionately and a linear relationship was found between the slope
and Ψmd (Figure 2b). The intercept of the Rc to D relationship
was not significantly related to Ψmd (Figure 2c). Thus as the
soil becomes drier, the sensitivity of Rc to D increases. These
empirical relationships are summarized in Eqs (3) and (4).
Typical light-response curves for the relationship of leaf
conductance to PPFD were obtained from the leaf-level measurements, and the average curve was used to determine the
parameter s in Eq. (5) (see above). The above relationships,
summarized in Eqs (3)–(5), were used to model the response
of canopy resistance to D and PPFD as described in the
‘Theory: model description’ section.
Diurnal and seasonal ET0, SF and modeled transpiration Figure 3 shows the diurnal courses of SF, ET0 and transpiration from the model using the three approaches for dealing
with radiation distribution in the canopy and scaling from leaf
to canopy conductance, for the fully developed canopy in wellirrigated plots in July 2012. Early in the morning and late in the
afternoon canopy water use is higher than ET0 because tree
LAI and conductance exceed that of a reference grass surface,
while at mid-day reduced canopy conductance resulting from
the high D depresses canopy water use. Differences between
the daily courses of SF and model transpiration are discussed
below. Overall, the radiation sub-models gave similar results,
and daily totals differed by <10%. However, the one- and twoleaf models both gave afternoon transpiration exceeding SF,
while the integrative model predicted afternoon transpiration
to be less than SF. The latter is expected, since trees normally
recharge morning water deficits in the afternoon and evening.
In addition, the integrative model was more successful in predicting the decline in transpiration (observed in daily SF) late
in the season (shown in Figure 4a). Therefore, we used the
integrative model for the continuation. Figure 4a shows the
seasonal course of SF, model transpiration and reference ET0
in well-irrigated plots in 2011. Simulated values were more
similar to measured SF than ET0. Similar results were obtained
Figure 3. Diurnal courses of SF, model transpiration from the three
models and ET0 averaged for six trees measured in well-irrigated plots
on a typical day, 22 July 2011.
Table 2. Regressions of meteorological parameters on SF for data from 2011 and 2012 during the irrigation season when the canopy was fully
developed. Sap flow and ET0 were in mm day−1, D in kPa, temperature in °C, Sr in W m−2, wind in m s−1 and relative humidity (RH) in %. *, ** and
*** indicate significance at P < 0.05, 0.01 and 0.001, respectively.
Year
2011
Relation
R2
Slope
Intercept
R2
Slope
Intercept
0.47***
0.18**
0.14*
0.29***
0.011
0.016
0.78
1.59
0.24
0.013
0.08
0.018
0.35
2.8
−1.4
0.76
4.17
2.85
0.39***
0.19**
0.138*
0.29***
0.011
0.014
0.65
1.59
0.23
0.013
0.078
0.017
0.25
2.8
−1.6
0.76
3.17
2.85
0.40***
0.11**
0.012
0.23***
0.167*
0.016
0.728
1.075
0.0375
0.0085
0.945
0.0205
0.32***
0.13**
0.02
0.24***
0.167*
0.012
0.67
0.98
0.0375
0.008
0.845
0.01805
Normal irrigation
SF vs ET0
SF vs D
SF vs temperature
SF vs Sr
SF vs wind
SF vs RH
Drying plots
SF vs ET0
SF vs D
SF vs temperature
SF vs Sr
SF vs wind
SF vs RH
Tree Physiology Volume 35, 2015
2012
0.5
3.85
3.952
2.269
2.81
3.17
0.5
3.59
3.9
2.24
2.91
3.47
Simulating nectarine tree transpiration and dynamic water storage 433
Figure 4. Seasonal course of daily total ET0, SF and model transpiration in the well-irrigated treatments (a) and the absolute difference
between ET0 and SF, and simulated transpiration and SF (i.e., the prediction ‘error’) for the main part of the season, when the canopy was
fully developed in 2011 (b).
for 2012 (not shown). ET0 and model transpiration were compared by calculating the absolute difference between them
and measured SF (Figure 4b). This demonstrated that ET0 was
less able to predict the magnitude as well as the character of
the tree water use. Differences between measured SF and
model transpiration in the normally irrigated trees may be due
to small day-to-day differences in Ψmd during the season and/
or changes in canopy development not covered by the model.
Figure 5 shows the diurnal course of simulated and calculated Gc, measured SF, simulated transpiration and the difference between SF and transpiration (i.e., change in tree water
content) for three values of Ψmd (5b), along with wind speed
(5c), solar radiation and D (5d). Data are obtained from the
wetting and drying plot measured in 2011 using the discontinuous heating mode, which were not used for model fitting.
These figures show that when Ψmd was high (−0.87 MPa)
simulated and calculated Gc, SF and transpiration were high,
and low Ψmd (−1.27 to −1.45 MPa) reduced them all.
Time lags between SF measured at the base of the trunk and
simulated transpiration from the leaves were estimated using
a matched-paired sample t-test. Data were not significantly
related for time lags <75 min and >120 min (Table 3), and
90 min was taken as an estimate of the average time lag.
Linear regressions between simulated and calculated midday Gc adjusted temporally according to the average time lag
are shown in Figure 6 (P < 0.01). Regression of simulated on
Figure 5. Simulated and calculated diurnal courses of canopy conductance (Gc, dashed and solid lines, respectively) (a), and model transpiration
(dashed line), measured SF (dashed line) and change in water content (Δ water content, solid line with solid symbols) (b), for 3 days in 2011 with
different Ψmd. Vertical bars indicate standard error of the means. All means of SF are for at least four trees. Wind speed (c), solar radiation and
vapor pressure deficit (D) are also given (d).
Tree Physiology Online at http://www.treephys.oxfordjournals.org
434 Paudel et al.
Table 3. P values for the time lag of calculated Gc (from SF) behind that simulated from meterological data, and for the lag of SF behind transpiration simulated from climate data. Analysis is from a matched paired sample t-test. * and ** indicate significance at P < 0.05 and 0.01, respectively.
Lag (min)
15
30
45
60
75
90
105
120
Simulated and calculated Gc
Transpiration and SF
0.222
0.645
0.115
0.652
0.128
0.272
0.092
0.197
0.0518
0.0498
0.0061**
0.008**
0.011*
0.016*
0.098
0.067
Figure 6. Relationship between simulated and calculated mid-day
canopy conductance, adjusted for time lags. Regression line is Gc calculated = 1.06 Gc simulated. R2 = 0.85 (P < 0.05).
calculated Gc gave a slope of 1.06 (r2 = 0.85). Thus, the model
overestimated Gc by only 6%, and otherwise it accurately predicted canopy conductance for different soil water conditions.
Tree and leaf water storage
Using measured SF and simulated tree transpiration, the diurnal
course of the cumulative change in water storage was quantified for a range of Ψmd (Figure 5b). Water was released in the
morning and recharged in the afternoon. Assuming that there is
no net change in tree water content over a 24-h period (Phillips
et al. 2009), we averaged the sum of water lost in the morning
with that recharged in the afternoon, and consider that to be the
dynamic daily volume of water for our summer conditions. The
dynamic volume increased as Ψmd decreased (Figure 7; R2 = 0.64;
P < 0.01). The minimum dynamic volume was 5.5 l tree−1 when
Ψmd was −0.9 and its maximum was 12 l, found on 3 days
when Ψmd was between −1.3 and −1.5 MPa. These values corresponded to 6.5 and 16.5% of the total daily transpiration,
respectively. The slope of the linear regression lines indicates that
for a change of −0.1 MPa in Ψmd, the dynamic volume increases
by 0.83 l or 1.4% of the total daily transpiration.
Water release curves for nectarine leaves (Figure 8) show
that less water was released in September than in August, which
might be related to changes in the leaves as they approach
senescence. In August, 27.6 ± 0.5 g m−2 was released when
leaf Ψ declined from −0.1 to −1.5 MPa. If that represents the
Tree Physiology Volume 35, 2015
Figure 7. Average volume of water released in the morning and
recharged in the afternoon as related to Ψmd. Data are presented in
water volume (a) and as a percentage of total daily SF (b). Slopes
of the linear relationships in (a) and (b) are −8.3l and −14% MPa−1,
respectively.
daily change in water content of the leaves, then multiplying by
LAI and tree spacing gives 1860 g released per tree. This is
equivalent to ∼2% of the total daily transpiration (6 mm day−1)
and 16% of the maximum dynamic volume of water.
Discussion
The linear relationship between Rc and Ψmd and the
isohydric concept
The response of leaf and canopy conductance to D is an
important determinant of tree water use (Leuning et al. 1991,
Roberts and Rosier 1994). A high D leads to decreased conductivity, which stabilizes SF (David et al. 2004). A similar
response of canopy conductance to D was reported for tropical rainforest (Granier et al. 1996a, 1996b) and several forest species (Roberts et al. 1990). Alarcon et al. (2000) and
Tognetti et al. (2004) showed that for olive trees at high D (1.5
to 2.5 kPa) the daily course of SF is plateau shaped.
Simulating nectarine tree transpiration and dynamic water storage 435
(Microsoft Excel), so this is a practical option for improving
model accuracy. After comparing the three models, we continued with the integrative model.
Comparing calculated and simulated Gc and transpiration
Figure 8. Relationship between increasing applied pressure (in the
pressure chamber) and cumulative water released from leaves taken
from well-irrigated trees in August (n = 3) and September (n = 4)
2012.
The linear relationship between Rc and D (Figure 2a) stabilizes SF, which tends to reach a constant value during midday hours. We consider this stabilization of mid-day leaf water
potential and SF to be isohydric behavior, since it leads to relatively constant leaf water potential for several hours. Mid-day
Rc increased as Ψmd decreased and a second linear relationship was found between the slope of the Rc to D relationship
(ΔRc/ΔD) and Ψmd, which was obtained from SF measurements
at different times in the drying cycle (Figure 2b). We are not
familiar with previous reports of this latter linear relationship.
Thus, as Ψmd declined Rc increased, and the mid-day constant
value of SF also declined, which would follow from the fact that
less soil water was available to the plant. This demonstrates
the strong interaction between stomatal control and environment, which is modulated by soil water availability.
Scaling leaf-level radiation response to canopy level
The response of leaf conductance to solar radiation was
scaled up to simulate the corresponding canopy conductance response. This allowed simulation of the daily and seasonal courses of transpiration, which are highly dependent
on changes in solar radiation, solar angles and radiation distribution in the canopy (Wang and Leuning 1998). Previous
modeling studies have shown that a one-leaf model gives
poor results and that a two-leaf model, which deals separately
with sunlit and shaded portions of the canopy, is necessary to
obtain accurate results (Wang and Leuning 1998, Wang 2000,
see Ding et al. 2014 for a review). In our study, a one-leaf
model was found to give similar results to the two-leaf model
but both overestimated transpiration in the afternoon, and only
the multiple layer integrative model was found to give afternoon transpiration less than SF. The more calculation-intensive
integrative model was implemented as a normal spreadsheet
The diurnal courses of calculated and simulated Gc and transpiration and SF, compared for three values of Ψmd, were similar
(Figure 5). This demonstrates that the hourly variations in Gc
and transpiration are caused mainly by the changes in solar
radiation and D (Figure 5), and the model was able to capture
even small variations.
Early morning transpiration draws water from internal storage compartments, resulting in lags between transpiration and
SF at the base of the tree. We found time lags of 90–105 min.
Similar lags have been reported in many tree species including deciduous trees (Kumagai et al. 2009), while time lags of
45 min were observed in bananas (Liu et al. 2008). Phillips
et al. (1997, 1999) and Meinzer et al. (2004) reported 0.5–
0.7 h time lags in forest species. It appears that time lags are
species specific or dependent on tree size and wood anatomy,
and possibly soil properties.
Tree water storage and changes in leaf water content
Description of dynamic water storage in trees is complicated by
resistances and storage in different parts of stems and capacitance of different plant tissues. Models (e.g., Zweifel et al.
2001, Steppe et al. 2006) have been developed to describe
these processes, allowing additional measurements of stem
contraction to be used to provide insight into water storage
and release. The daily discharge and recharge of water from
internal tissues depends on daily replacement of transpirational
losses, which can be determined from SF and simulated transpiration (Cermak et al. 2007). Stored water used in the morning and the complementary water recharge in the afternoon,
estimated from the difference between predicted transpiration
and SF (Figure 7), which we refer to as the dynamic water
volume, was highly correlated with Ψmd and increased as Ψmd
decreased. We were not able to find estimates of this relationship in the literature to compare with. Meinzer et al. (2004)
measured differences in SF between the base and the crown.
Their measurements, which do not include water released from
the leaves, showed that sapwood capacitance of branches
decreases with representative branch Ψ for a number of species in the range of values that we investigated. If sapwood
capacitance decreases with Ψmd then less water should
be available from the sapwood as Ψmd decreases because
the corresponding branch Ψ should be lower, as shown by
Meinzer et al. (2004). However, as Ψmd decreases water from
other storage pools may become available. In fact, canopy
desorption curves modeled by Steppe et al. (2006) are nonlinear and show that large amounts of water may be available
from associated pools at low and high values of Ψ, while in
Tree Physiology Online at http://www.treephys.oxfordjournals.org
436 Paudel et al.
the middle of the range the relationship between the available
water and Ψ is linear. The additional water drawn at low Ψ may
come from non-sapwood tissues. Further evidence for this is
the well-known increase in stem contraction as Ψmd decreases
(Fernandez and Cuevas 2010). We also observed increasing
stem contraction as Ψmd decreased in the range studied here
(Cohen et al. 2013). Thus, the relationship found here between
dynamic water volume and Ψmd (Figure 7) is both possible and
novel, and awaits confirmation from other studies.
Roberts (1976) and Tyree and Yang (1990) concluded that
stored water is not a significant source of water for transpiration
in most woody plants. However, Ladefoged (1963), Hinckley
and Bruckerhoff (1975) and Cermák et al. (1982) suggested
that internal water storage may be important in supporting
diurnal and seasonal transpiration of woody plants. The model
indicates that morning discharge (i.e., the dynamic volume) was
∼6.5–10.5% of daily sap flow at −0.9 MPa and increased up
to 16.5% at −1.45 MPa (Figure 7), which is a significant part
(P = 0.05). A similar but relatively larger amount (20–25%) was
observed by Cermak et al. (2007) in forest species and by Ford
et al. (2004) in Pinus species. Tyree and Yang (1990) estimated
that water withdrawn from living cells in stems of Thuja occidentalis contributed ∼6% to the total daily transpirational water loss.
On the other hand, Schulze et al. (1985) suggested that there
was little water available in the main trunk of a Larix decidua tree,
while stored water in branches contributed 24% to the total daily
transpiration. Thus, the contribution of the internal water storage to daily transpirational losses apparently is not fixed. Our
measurements are for a deciduous fruit species which may have
lower water storage capacity because of high wood density (we
found 0.74 g cm−3) compared with evergreen trees. This storage represents a buffering capacity, allowing trees to overcome
afternoon and short periods of soil water deficit. Analysis based
on water release curves for nectarine leaves (Figure 8) showed
that water released from leaves comprises ∼16% of the dynamic
changes in water content.
Prediction of Ψmd
Accuracy in irrigation requires feedback from monitoring of actual
crop water status. Ψmd is considered the best parameter for that
(Naor 2006), but usually requires manual measurement. Equation
(13) provides an opportunity to determine Ψmd from measurements of mid-day crop water use (e.g., from SF measurements)
and the climate variables needed to solve Eq. (1) for Rc. Use of
Eq. (13) to predict Ψmd will be explored in future research.
Summary and conclusions
Sap flow measurements in a nectarine orchard showed that
canopy resistance is linearly related to D during the summer
irrigation season. When trees dried during drying and wetting
cycles the slope of the linear relationship increased linearly
Tree Physiology Volume 35, 2015
as Ψmd decreased, but the intercept, which is the minimum
canopy resistance for low D, did not change significantly. That
relationship, along with a leaf-level light-response curve scaled
to the canopy level, was used to model transpiration from the
trees. Coupling the simple canopy resistance model with the
Penman–Monteith equation yielded accurate estimates of daily
total water use, which were more accurate than standard reference evapotranspiration which is computed using climatic data
and parameters of a well-irrigated cut grass surface.
The model, along with SF measurements, was used to estimate the use of water stored in the canopy during the day. This
analysis showed that the trees can use up to ∼12 l day−1 tree−1
of stored water and the analysis based on leaf water release
curves showed that ∼16% was from water stored in the leaves.
This dynamic water volume was found to increase as Ψmd
decreased.
In conclusion, use of the relatively simple model proved to
be robust for a range of soil water contents, gave better results
than the standard reference evapotranspiration model and
­provided some useful physiological insight.
Acknowledgments
The authors thank Dr Josef Tanny and Amit K. Jaiswal for useful
discussions; Avraham Grava, Victor Lukyanov, Moti Peres and
Eyal Nevo for technical assistance; and Avi Ben-Aroya for access
to his orchard. I.P. wishes to thank the UK Pears Foundation for
its support during the time that this research was done and
she was a Pears scholar at the Hebrew University's Faculty of
Agriculture in Rehovot, Israel. This is contribution No. 608/13
from the Agricultural Research Organization, Institute of Soil,
Water and Environmental Sciences, Bet Dagan, Israel.
Conflict of interest
None declared.
Funding
This study was funded by grants from the Chief Scientist’s
Fund of the Israeli Ministry of Agriculture, nos. 596-0415 and
304-0496.
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Appendix
Computation of sunlit and shaded leaf area index, after
Campbell and Norman (1998)
For an ellipsoidal leaf angle distribution extinction coefficient
Kbe(Z) for parallel rays traversing the canopy can be expressed
as (Campbell 1986)
K be( Z ) =
x 2 + tan2( Z )
,
x + 1.774( x + 1.182)-0.733 (i)
where Z is the zenith angle and x is the ellipsoidal leaf angle
distribution parameter, which is 1 for a random (or hemispherical) leaf angle distribution (as in our case).
Once we have determined the value of the extinction coefficient for our canopy and LAI, the fraction of the sunlit (SLAI)
and shaded leaf area (LAIshade) were calculated as follows:
SLAI =
1 − exp(− K be( Z ) × LAI)
.
K be( Z )
(ii)
Shaded LAI is then computed from
LAIshade = LAI − SLAI. (iii)