Supplementary information
Model
Tree allometry
The individual tree structure is similar to the one described in Farrior et al. (2013). The
structure of individual tress is governed by species-specific allometric relationships based
on field measurements:
Z = HDg -1 ,
(S1)
W = a w Dg .
(S2)
Tree height (Z) (in m) and the cross-sectional area of the crown of the tree (W) (in m2) are
all functions of the stem diameter (D) (in cm). The allometric constants are species
specific. The exponent g is shared by all allometric relationships and is assumed to be
equal to 1.644 for Piñons and 1.518 for Junipers based on fit to observational dataset.
Those exponents are the same order of magnitude as the 1.5 value used by Farrior et al.
(2013). Those values are based on fit to observations over 65 Junipers and 75 Piñons.
Sapwood has been shown to be described by an allometry: the sapwood area
scales with stem diameter and leaf area index l (Kumagai et al., 2005) and sapwood
width is relatively constant within a tree (Longuetaud et al., 2006). The total sapwood
volume is thus proportional to sapwood area times height: sapwood volume = a sw Dg l
(Farrior et al., 2013).
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The total leaf area and fine-root surface area scale with the crown area. l is the leaf area
per unit crown area (LAI: leaf area index) and r is the fine-root surface area per unit
crown (RAI: root area index). The total leaf area is lW and the total fine-root surface area
is rW . The root:shoot ratio is r/l. The model parameters are thus H, a s ,a w ,l and r.
Tree-level carbon assimilation
The model assumes that water is the only limiting resource and that nutrients do not limit
the assimilation. For given atmospheric conditions (radiation, temperature, humidity,
wind) the maximum assimilation per unit leaf area (kg m-2 s-1) is obtained under
conditions of soil saturation. Carbon assimilation at the tree-level is obtained by
integration of the leaf assimilation over the entire leaf area. The attenuation of light
throughout the canopy is obtained using Beer's law, L = L0 exp(-knl) , with L0 the light at
the top of the canopy. The total tree-level assimilation is simply:
Al = min(Vl, L0exp(-knl))
(S3)
with V the maximum light-saturated photosynthetic rate.
Water transport in the tree
The main difference of our model with the model of Farrior et al. (2013) is related to the
representation of the water transport in the tree. The tree water transport includes a stem
water capacitance Cw , which can be a key factor to regulate the leaf water potential and
mitigate hydraulic safety margins avoiding diurnal desiccation during the peak diurnal
atmospheric demand (Goldstein et al., 1998; Meinzer et al., 2001; 2008). We also
account for stomatal controls and changes in the hydraulic xylem conductivity
vulnerability curves (Linton et al., 1998; Pockman & Sperry, 2000; Cruiziat et al., 2002;
2
Johnson et al., 2011). With the capacitance, stomata control and xylem vulnerability
curve we can represent different types of plant water regulation mechanisms from
isohydric to anisohydric (Meinzer et al., 2009; Meinzer & McCulloh, 2013).
The water uptake U per unit crown area by the roots is proportional to the water potential
gradient between the soil and the xylem accounting for the gravity potential rw gZ , with
rw the density of water, g gravity:
U = rgroot-xylem (y s - y x - rw gZ) = Gtotal Dy
(S4)
where Gtotal is the whole plant conductance per unit crown area, groot-xylem is the rootxylem hydraulic conductance (in kg m-2 s-1 Pa-1) and is proportional to LAI and depends
inversely on the vegetation height Z as groot-xylem = kleaf_specificl / Z . kleaf _ specific is the leafspecific hydraulic conductivity (Bucci 2004), i.e. the conductivity per unit leaf area (in kg
m-1 s-1 Pa-1).
kleaf _ specific and groot-xylem depends on the xylem water potential assuming that the
percentage loss of conductivity (PLC) vulnerability curve follows a Weibull function
(Pammenter & Van der Willigen, 1998; Cai et al., 2013):
PLC
= 1- e
100
æy ö
-ç x ÷
èy k ø
ck
(S5)
with y k the reference potential drop, corresponding to 63% loss of conductivity, and ck
the shape factor of the Weibull function. The leaf specific conductivity is thus related to
the maximum leaf specific conductivity kleaf _ specific,max through the loss of conductivity
induced by embolism/cavitation:
3
kleaf specific
æ æ y ö ck ö
= kleaf specific,max exp ç - ç x ÷ ÷
è è y 50 ø ø .
(S6)
with kleaf_specific,max = kspecific,max Asw / Aleaf = kspecific,max Asw / (lW ) where kspecific is the specific
maximum hydraulic conductivity (Bucci 2004), i.e. the conductivity per unit sapwood
area (in kg m-1 s-1 Pa-1), Asw the sapwood area and Aleaf the total leaf area. We also define
the maximum root-xylem hydraulic conductance groot-xylem,max as the conductance at
saturation.
The maximum water capacitance in the tree Cw,max (m3 Pa-1) is assumed to be described
by an allometry and is linearly related to the sapwood volume (Bohrer et al., 2005):
Cw,max = cwVsw
(S7)
with cw a species specific capacitance parameter and Vsw the sapwood volume.
Vegetation water content is usually exponentially decaying as a function of xylem
potential (Edwards & Jarvis, 1982) so that the capacitance dependence to xylem water
potential is written:
æ æ y ö ck +1 ö
dv
= Cw,max exp ç ç - x ÷ ÷
dy x
èè yc ø ø
(S8)
with y c the potential defining the e-folding potential of vegetation water content. The
exponent ck+1 in the exponential is used to insure that the time constant of the RC circuit
goes to zero when the water potential is infinite in agreement with recent observations
(Ward et al., 2013) as seen in Figure 1. Omission of this factor and use of a typical
exponential decrease without the exponent leads to unrealistically large time constant at
low potential.
4
Figure 1: Normalized dependence of the product of the bulk tissue capacitance Cw times the inverse of the
conductivity k. Saturation value is used as the reference for the normalization.
Stomata closure under water stress reduces assimilation and transpiration rates (Tuzet et
al., 2003). The regulation of stomata is more related to xylem water potential than to leaf
water potential (Zhang et al., 2012). Stomata closure is assumed to limit the
photosynthesis rate through the same Weibull function as in the xylem, even though we
are aware that the shape of the regulation can change slightly from the root to xylem to
leaves (Tsuda & Tyree, 1997; Linton et al., 1998). We use a single Weibull curve for
model tractability. The limitation of assimilation by water stress is related to the
maximum (non-water limited) assimilation and xylem potential y x :
5
æ æ y ö ck ö
A = Al exp ç - ç x ÷ ÷
è è y 50 ø ø
(S9)
To compute the tree water demand (i.e. transpirational losses) per unit crown area, T, we
assume a constant intrinsic water-use efficiency wue linking the CO2 demand to water
losses through stomata (Farrior et al., 2013):
æ A
ö
T = min ç
, Ep ÷
è wue
ø,
(S10)
with E p the potential evaporation (Lhomme, 1997), which depends on the atmospheric
conditions (radiation, temperature, humidity, wind).
The water ( Wns ) budget accessible by the roots thus reads:
rw
d(zrWns)
= W (P -U - E - L)
dt
(S11)
with n the soil porosity, zr the effective rooting depth, s the relative soil moisture content
of the soil, P the precipitation rate per unit crown area entering the soil , U the root water
uptake, E the bare soil evaporation, and Le the leakage term corresponding to saturation
runoff and percolation to the water table (Gentine et al. 2012). We here neglect the water
table recharge.
Since soil moisture variations are much faster (order of a few days to few weeks) than
changes in biomass and roots, equation (S11) can be simplified into:
rw zr n
ds
= P -U - E - Le
dt
(S12)
dv
= W (U - T )
dt
(S13)
The water budget in the tree reads:
Cw,max
6
with v the relative vegetation water content, with a maximum value of 1. This can be
rewritten in terms of difference between xylem and soil water potential:
æ y ö dy
Cw,max exp ç - x ÷ x = W (U - T )
è y c ø dt
(S14)
The light level received by the ground per unit crown area is composed of the soil shaded
by all the leaves exp(-knl) :
fbare = exp(-knl)
(S15)
The soil evaporation E per unit crown area (in kg m-2 s-1) is related to the soil water
content (Laio et al., 2001; Porporato et al., 2001) and depends on the illuminated area f
(Gentine et al., 2012; Chen 2005):
E = E p exp(-knl) f (s)
(S16)
with f (y ) = min æç max æ y s - y h ,0ö ,1ö÷ the soil moisture limitation (between 0 and 1), y h
s
s
ç y -y
÷
è
è
fc
h
ø ø
hygroscopic point (-10MPa), and y fc the field capacity (Laio et al., 2001; Porporato et
al., 2001).
Carbon allocation
We here consider only drydowns and therefore neglect the allocation of carbon to replace
dropped leaves, dead fine roots or to bulks additional leaves and fine roots or to produce
offspring, and to grow the stem biomass (Sala et al., 2012). Future work will investigate
this. We instead assume that in the period of intense droughts most of the carbon is lost
through the different components of respiration (all in kg s-1) fine root respiration:
Rroot = pr rW ,
(S17)
leaf respiration:
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Rleaves = pl lW ,
(S18)
sapwood respiration:
Rsapwood = pswa sw Dg l
.
(S19)
pl, pr, and psw are the respiration rates of leaves, fine roots, and sapwood, respectively.
Because respiration rates are functions of temperature in nature, pl, pr, and psw should be
thought of as time averages in a constant climate.
The tree carbon balance is:
W
dC
= WA - Rroot - Rleaves - Rsapwood
dt
.
(S20)
During a drydown we assume that carbon C is mostly withdrawn from the non structural
carbon (NSC) pool CNSC , which increases with plant biomass and environmental stresses
(Sala et al., 2012). It has been shown that two (slow and fast) carbon pools better
represent the NSC balance (Hoch et al., 2003). We here only account for a single carbon
pool which is assumed proportional to the plant biomass and is mostly located in the
roots and the leaves (Sala et al., 2012). We therefore assume that the initial NSC pool
linearly scales with the sum of the root and leaf biomass NSC = a NSC (l LMA + r RMA)
with a NSC is of the order of a few percent of the total biomass.
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