2.4 | Transpiration estimate
We used the canopy transpiration model of Tor-Ngern et al. (2017) to
avoid the need to repeat their scaling from trees to canopy. The model
was originally derived using the measurements at the two plots in
Rosinedal. Per-tree transpiration rates were derived from sap flux
measured with Granier thermal dissipation probes (Granier, 1985, 1987;)
set in five to eight mature trees at varying depths in both the R and F
plots (data and methods in Tor-Ngern et al. (2017)). Tree daily
transpiration (Ecd, mm d-1tree-1) was then upscaled to stand level.
The stand-level transpiration estimates were modeled from
VPDZ and relative extractable water (REW).
VPDZ is the integral of daytime mean atmospheric vapour
pressure deficit. To estimate it, we first defined daytime as the period
when PPFD exceeded a threshold of 10 µmol m-2s-1 (Hultine et al., 2008). VPDD was
then calculated (Murray, 1967; Ngao, Adam, & Saudreau, 2017) for the
daylight period, as follows:
\(\text{VPD}_{D}=(0.6108\ \times\ e^{\frac{17.27\times T_{a}}{T_{a}+237.3}})\times(1-\frac{\text{RH}}{100})\)Eqn. 1
Second, VPDD (kPa) was integrated over the number of
daylight hours (Oren, Zimmermann, & Terbough, 1996):
\(\text{VPD}_{Z}=\text{VPD}_{D}\times\frac{n_{D}}{24}\) Eqn. 2
with nD being the number of daylight hours.
VPDZ thus combines daytime VPD and daylength in a single
variable.
REW was calculated at 15 cm depth as follows (Granier, Loustau, &
Bréda, 2000):
\(REW=\frac{{\overset{\overline{}}{\text{SWC}}}_{t}-\text{SWC}_{\text{WP}}}{\text{SWC}_{\text{FC}}-\text{SWC}_{\text{WP}}}\)Eqn. 3
where \(\overset{\overline{}}{\text{SWC}_{t}}\) is the mean volumetric
soil water content (m3 m-3) per day.
SWC was measured with reflectometric soil moisture probes (SM300,
Delta-T Devices, Cambridge, UK) at 15cm depth. SWCWP and
SWCFC are the soil water content at wilting point and
field capacity, respectively. They were estimated from the annual
minimum and maximum SWC, respectively, at our sites. For the F plot,
SWCWP and SWCFC were 0.052 and 0.306
m3 m-3, respectively, and for the R
plot, the values were 0.052 and 0.218 m3m-3. The F plot had a higher SWCFCvalue because the soil organic layer was deeper than in the R plot
(Hasegawa et al., personal communication).
Using the parameters above, the model of stand-level transpiration rate
begins with an estimate of the maximal transpiration rate
(Ecdmax). It then adjusts the maximum rate downward for
REW, as follows:
\(E_{\text{cdmax}}=1.812\times(1-e^{\left(-3.121\times\text{VPD}_{Z}\right)})\)Eqn. 4
\(E_{\text{cd}}=E_{\text{cdmax}}\times(1-e^{\left(-18.342\times\text{REW}\right)})\)Eqn. 5
Eqn. 4 means that the maximal Ecdmax is 1.812 mm
d-1 at high VPDZ.
Canopy conductance to H2O was then inferred from
corresponding Ecd and VPDD as:
\(g_{C}=\frac{\frac{E_{\text{cd}}}{M_{H2O}}\times 1000}{\frac{\text{VPD}_{D}}{P_{145}}}\)Eqn. 6
in mol H2O m-2 ground area
d-1 with MH2O the molar mass of water
(18 g mol-1) and P145, the atmospheric
pressure at 145 m a.s.l (99.6 kPa).
We applied two filters and one correction to these conductance data.
First, we accounted for the acclimation of photosynthetic capacity to
air temperature (Mäkelä, Hari, Berninger, Hänninen, & Nikinmaa, 2004).
We did this because of the tight coupling of photosynthesis and stomatal
opening (Farquhar & Wong, 1984; Medlyn et al., 2011; Tuzet, Perrier, &
Leuning, 2003), which allows us to account for the low stomatal
conductance during the wintertime. Photosynthetic capacity\(\hat{\alpha},\ \)(Mäkelä et al., 2004) was estimated as follows:
\(\hat{\alpha}=max\{c_{1}\times S\left(t\right)-S_{0},0\}\) Eqn.
7
where c1 a coefficient of proportionality (0.0367
m3 mol-1 °C), S(t) is the state of
photosynthetic acclimation (°C) at time t, and S0 a
threshold value of the state of acclimation (-5.33 °C). S(t) was
obtained on daily time scale in two steps:
\(\text{ΔS}(t)=\frac{T_{a}(t)-\ S_{t}}{\tau}\) Eqn.8
Where Ta(t) is daily mean temperature on day t and τ the
time constant (8.23 days)
\(S\left(t+1\right)=S\left(t\right)+\Delta S(t)\ \) Eqn. 9
This model describes the linear increase in photosynthetic capacity with
temperature in boreal conifers. We corrected our gCvalues as follows (Mäkelä et al., 2008):
\(g_{c\hat{\alpha}}=\ \frac{\hat{\alpha}}{{\hat{\alpha}}_{\max}}\times\ g_{C}\)Eqn. 10
with \(\hat{\alpha}\)max the mean value of\(\hat{\alpha}\) when photosynthetic capacity was maximal. For\(\hat{\alpha}\)max, we used the averages from July of
2012 and 2013. July was chosen because temperatures and PPFD were both
high and the canopy was presumably near its photosynthetic capacity
throughout this period.
Recall that gc was estimated from VPDD(Eqn. 6). Because VPDD was in the denominator and
approached zero in early spring, the estimates of gCwere often noisy at that time. Therefore, we filtered and removed all
VPDD values < 0.1 kPa. During the summer time
(June-August) the filter threshold was increased to 0.25 kPa. The higher
transpiration rate and a longer day-light period during summer created
uncertainty in the gC calculation (Emberson, Wieser, &
Ashmore, 2000; Tarvainen, Räntfors, & Wallin, 2015), but we reduced the
summer filter threshold to the minimum that would allow us to keep as
many data as possible. We filled the resulting GPP gaps using a
predictive model (gC = a × \(\hat{\alpha}\) +b) with a
and b determined for each combination of treatments. We replaced the
GPPiso/SF outliers and filtered values by the predicted
functions only during the thermal growing season. We did this because
the common gapfill functions are based on EC data and we wished to
maintain our independence from EC data. The gaps were much larger
outside the thermal growing season than within it; because tree
photosynthesis is reduced during that time we chose not to fill these
gaps.
Using the phloem samples collected between October 2011 and September
2012, we estimated isotopic discrimination against 13C
(Δ, ‰). It was calculated as follows:
\(\Delta=\ \frac{\delta^{13}{C_{a}-\ \delta^{13}C_{p}}}{1+(\frac{\delta^{13}{C_{p})}}{1000})}\)Eqn. 11
We fitted linear interpolations (Figure S1) to determine a daily value
of Δ. This step allowed us to estimate GPPiso/SF at a
daily time scale.
The intrinsic water use efficiency for the stand (WUEi)
was then inferred from the following equation (Seibt et al., 2008), in
each plot:
\(\text{WUE}_{i}=\frac{C_{a}}{r}\times\ \left[\frac{b-\Delta-f\times(\frac{\Gamma^{*}}{C_{a}})}{b-a_{a}+(b-a_{i})\times\frac{g_{C\hat{\alpha}}}{r\times g_{m}}}\right]\)Eqn. 12
where Ca is the atmospheric CO2concentration (µmol mol-1), r the ratio of
diffusivities of water vapour relative to CO2 in air
(1.6), b the fractionation during carboxylation (29‰), f the
fractionation during photorespiration (16.2‰, Evans & Caemmerer, 2013),
aa and ai the fractionations of the
diffusion through air (4.4‰) and the fractionation of diffusion and
dissolution in water (1.8‰), respectively, and gm the
mesophyll conductance (mol CO2 m-2d-1). The resulting value has units of µmol
CO2 mol air-1 The CO2compensation point (Γ*, μmol mol-1), was calculated
according to the following formula (Medlyn et al., 2002):
\(\Gamma^{*}=42.75\times e^{\frac{37830\ \times(T_{K}-298)}{298\times T_{K}\times R}}\)Eqn. 13
with TK the ambient temperature (K) and R the universal
gas constant (8.314 J mol-1 K-1).
We also used the
δ13Cpfrom 2012 to estimate WUEi for the same dates in 2013,
assuming that WUEi was mainly affected by\(g_{C\hat{\alpha}}\) and its link with VPDD and not by
the absolute values of δ13Cp.
Similarly, we estimated Δ in October and November 2012 and 2013 based on
the 2011 measurements of δ13Cp.
WUEi was then calculated on a daily time scale, based on
the daily-modeled values of Δ.