Introduction
Plant water-use efficiency (WUE) is the ratio of the CO2 assimilated
through photosynthesis (gross primary productivity, GPP), to the water used
by plants as the flux of transpiration (ET):
WUE=GPPET.
Carbon dioxide may affect plants through increases in photosynthesis
(Ainsworth and Rogers, 2007; Franks et al., 2013) and possible reductions in
transpiration associated with the partial closure of leaf stomatal pores
under elevated CO2 (Field et al., 1995; Gedney et al., 2006;
Betts et al., 2007). Both of these effects are uncertain though.
CO2 fertilization of photosynthesis is often found to be limited by
nutrient availability (Norby et al., 2010), and large-scale transpiration may
not reduce even with CO2-induced stomatal closure, if plant leaf area
index increases enough to counteract reduced transpiration from each leaf
(Piao et al., 2007). WUE does however appear to be increasing more robustly
with CO2, according to both tree-ring (Franks et al., 2013) and
eddy covariance flux measurements (Keenan et al., 2013).
Plant photosynthesis and transpiration are coupled through the behaviour of
leaf stomatal pores, through which CO2 must diffuse to be fixed during
photosynthesis, and through which the transpiration flux escapes to the
atmosphere. The combined behaviour of the leaf stomata leads to an
environmentally dependent “canopy conductance” that controls both the water
and carbon fluxes. As a consequence, both GPP and ET can be
written as the product of a canopy conductance and a concentration gradient,
which is sometimes described as an electrical analogue (Cowan, 1972). For
GPP, the concentration gradient is the difference between the atmospheric
CO2 concentration at the leaf surface (Ca) and the internal
CO2 concentration within plant leaves (Ci):
GPP=gc(Ca-Ci),
where gc is the canopy conductance for CO2.
For ET, the concentration gradient is the difference between the
specific humidity of the atmosphere at the leaf surface (qa) and
the specific humidity inside the plant leaves, which is saturated at the leaf
temperature (qsat). The canopy conductances for GPP and ET both arise from diffusion through leaf stomatal pores, and therefore only
differ by a constant factor of 1.6 (the square root of the ratio of the
molecular masses of CO2 and H2O).
ET=1.6gc(qsat-qa).
Changes in stomatal opening in response to changes in sunlight, atmospheric
temperature and humidity, soil moisture, and CO2, are complex and
uncertain (Berry et al., 2010), as are the scaling of these leaf-level
responses up to the canopy and beyond (Piao et al., 2007; Jarvis and
McNaughton, 1986; Jarvis, 1995). However, since stomatal behaviour affects
transpiration and photosynthesis similarly, WUE is relatively insensitive to
these uncertainties:
WUE=(Ca-Ci)1.6(qsat-qa)=(Ca-Ci)1.6D=Ca(1-f)1.6D,
where D is the atmospheric humidity deficit (qsat-qa) and f is the ratio of the internal to the external CO2
concentration (Ci / Ca). This equation therefore
expresses WUE in terms of atmospheric variables, Ca and D (which
itself depends on relative humidity and temperature), along with the factor
f. The remaining uncertainty associated with plant physiology is therefore
contained in f.
In the absence of water limitations, there is good evidence that f is
approximately independent of Ca, so that Ci remains
proportional to Ca, unless D changes (Jacobs, 1994; Katul et
al., 2010; Leuning, 1995; Morison et al., 1983). Even during drought, f
will vary with D, due in part to correlations between D and soil moisture
(Brodribb, 1996).
Stomatal optimization theories, which assume that stomata act so as to
maximize photosynthesis for a given amount of available water (Cowan and
Farquhar, 1977), also suggest that f should depend predominantly on
Ca and D (Katul et al., 2010; Medlyn et al., 2011). Absolute
values of WUE will depend on the nature of the vegetation and soil, such as
the plant and soil hydraulics, but these optimization theories imply that
there will be a near universal sensitivity of fractional changes in WUE to
fractional changes in Ca and D (see Supplement):
WUEWUE(0)=CaCa(0)aDD(0)b,
where the subscript (0) denotes the initial state of each variable, and a
and b are dimensionless coefficients. For given a and b values this
equation describes how the fractional change in WUE at each location varies
with fractional changes in Ca and D. Although they differ in
their underlying assumptions and detailed conclusions, it is interesting to
note that the latest stomatal optimization theories (Katul et al., 2010;
Medlyn et al., 2011) both imply a=1 and b=-0.5 (see the
Supplement).
We focus in this study on fractional changes in WUE, which are more likely to
be independent of these complex factors. Therefore, we use two very different
datasets of WUE, derived from tree-ring measurements and eddy covariance
fluxes and aim to model the fractional changes in plant WUE by using
atmospheric data alone. The longer-term climate signals are derived from the
tree rings, spanning at least the last 100 years. Monthly WUE values are
derived from eddy covariance observations between 1995 and 2006. We do not
assume the applicability of stomatal optimization theories, but instead adopt
equation 5 as a parsimonious empirical model for the fractional changes in
WUE observed at each measurement site, given suitable fitting parameters a
and b. Tests using more elaborate statistical models, with additional
environmental variables or vegetation-specific parameters, were not found to
produce significant improvements in the fit to the observed changes in WUE
despite the introduction of extra fitting parameters. Finally, we have
compared our reconstruction of the fractional change in plant WUE to Earth
System Models (ESMs) simulations, focussing on regional variations in the WUE
changes and how these compare to the long-term tree-ring observations.
Locations of the eddy covariance flux sites and tree-ring sites used
(see Table S2 and S3 in the Supplement for a list of the sites). Tropical
tree-ring sites are used as independent data sources for comparison.
Materials and methods
We estimate the sensitivity of WUE to Ca and D by fitting to observed WUE
changes inferred from both eddy covariance fluxes (relatively short records
with high-temporal resolution) and carbon isotope records from tree rings
(longer-term records with annual resolution). We use observations from 28
eddy covariance and 31 tree-ring sites (see Fig. 1 and the Supplement
Tables S1 and S2).
Eddy covariance observations
The carbon and water flux observations were taken from the Free
Fair-use Fluxnet database (www.fluxdata.org) (Baldocchi, 2008; Papale
et al., 2006; Reichstein et al., 2005). We selected a total of 28 sites based
on data availability (Table S1 in the Supplement). Monthly WUE was estimated
from Eq. (1) with GPP used directly from the database (Reichstein et al.,
2005). In general the total latent heat flux (LE) has contributions from
interception loss, soil evaporation and transpiration. We follow previous
studies (Dekker et al., 2001; Groenendijk et al., 2011; Keenan et al., 2013;
Law et al., 2002) in assuming that the latent heat flux is dominated by
transpiration during periods with no rain in the preceding 2 days, when the
interception loss and soil evaporation are assumed small. Monthly average
values of GPP, ET, Ca, D and T were calculated from
half-hourly observations (not gap-filled) during dry periods (i.e. no rain in
the preceding 2 days) when GPP was larger than zero. To exclude periods
with unrealistic WUE values due to the division by very small ET
values, we used only months during the growing season. Annual average growing
season values were calculated from the months with an average temperature
above 10 ∘C. Only sites with at least six annual values were used,
resulting in a dataset of 222 annual growing season values of WUE, Ca and D. Data are used between 1995 and 2006. Fractional changes were
calculated relative to the mean over the observational period for each of the
sites, to enable comparison between sites.
Tree-ring observations
To derive a longer-term relationship between the fractional change in WUE and
variations in Ca and D, we used Δ13C tree-ring
observations from 31 locations (Fig. 1), ranging from 1900 to current, as
described in two previous studies (Franks et al., 2013; Hemming et al., 1998)
(see the Supplement, Table S2). The discrimination of 12C against
13C (Δ13C) is estimated from the tree-ring samples (Hemming et
al., 1998; van der Sleen et al., 2015). The Δ13C measurements can
be used to estimate the ratio of the internal to the external CO2
concentration (f=Ci / Ca) using the relationship
f = (Δ13C–4.4) / (27–4.4), where Δ13C is in
parts per thousand (‰), and Ca is taken from the Mauna Loa
atmospheric CO2 record (Farquhar et al., 1989; Franks et al., 2013;
Keeling et al., 1976). WUE is estimated with Eq. (4) using annual average
growing season values of D from the CRU dataset, taking the nearest pixel
to each site (Harris et al., 2013). This large-scale dataset for D ensures
consistency among the sites, but may underestimate the finer spatial
variation in D. As for the eddy covariance sites, we estimated the
fractional changes relative to the mean over the observational period at each
of the sites. For this analysis we have 1007 observations of WUE derived from
tree-ring observations of Δ13C.
Fractional WUE
To estimate a and b with a linear regression model we rewrite Eq. (5) in
a logarithmic form:
ln1+ΔWUEWUE(0)=aln1+ΔCaCa(0)+bln1+ΔDD(0).
Here the second term in each bracket represents the fractional change in WUE,
Ca and D, respectively. These fractional change variables are
used in all our subsequent statistical analyses and modelling. We set out to
fit the fractional change in WUE at each observation site (Fig. 1) from the
fractional change in Ca and the fractional change in D. For
comparison and fitting we therefore need to calculate WUE(0), Ca(0) and D(0) for the observational data, which we take as the mean
over the entire observational record available at each site.
Global fractional change of WUE
The dependence of fractional changes in WUE on Ca and D allows
us to use these relationships to estimate changes in WUE at large scales
using global climate data. The fractional change in D can be further
partitioned into a change in temperature (T) and relative humidity (RH),
which makes it possible to separate the effect of changes in these variables
on WUE (see the Supplement). To do this, we used the CRU climate dataset
(Harris et al., 2013) at a 0.5∘ × 0.5∘
latitude/longitude grid and the annual CO2 concentration at Mauna-Loa
(Keeling et al., 1976) to derive the global and local variation in WUE. We
only used months during the growing season when photosynthesis occurs,
assumed to be above a monthly average temperature threshold of
10 ∘C, where we assemed photosynthesis to be above a monthly.
For the period 1900–1930 the average temperature was
calculated for each month from which a spatial mask was generated (see
Supplement Fig. S4). This mask was then used to calculate annual
time-evolving values of WUE from the growing season values of temperature and
humidity for each year between 1901 and 2010.
Water-use efficiency (WUE) from tree-ring and eddy covariance
observations. The relationship between the observed fractional change in WUE
and the fractional change in (a) CO2 concentration and
(b) humidity deficit of both datasets is fitted to Eq. (3),with
best-fit values for a (1.51 ± 0.57) and b (-0.72 ± 0.16).
(c) The colours show the root mean square error (RMSE) of the
simulated vs. observed fractional change in WUE as a function of a and b,
with the black area representing the best parameters within 5 % of the
RMSE of the best fit (white star). The black star represents the values
according to the optimality hypothesis.
Other independent data sources
For three locations, western North America, western Europe and East Asia, we
have compared our simulated fractional change in plant WUE with remote-sensing (RS) products of GPP and ET (Jung et al., 2011). This
dataset covers the period 1982–2006; we use the period 1986–1990 as a
reference period for both our estimate and the fractional change in WUE from
the RS product. As the RS data do not cover a response to changes in
Ca, we estimated the fractional change in WUE with and without the
Ca response.
At the global scale, we have compared our simulated fractional change in
plant WUE with simulations of Earth System Models (ESMs). Most of the latest
ESMs calculate changes in both GPP and ET. This allows a
comparable change in WUE to be calculated for 28 CMIP5 models (Taylor et al.,
2012) based-on their historical simulations. Finally, regional differences in
responses are compared to the 31 tree-ring observation sites.
Results and discussion
Figure 2 summarizes the derivation of the a and b parameters, which are
the sensitivity of WUE to Ca and D, for the tree-ring and
eddy covariance observations. In general, eddy covariance data alone are
unable to fully constrain the CO2 sensitivity of the WUE (Keenan et al.,
2013), because the data records are too short to sample significant changes
in CO2, resulting in a value of a of 0.79 ± 0.79 for all
eddy covariance sites (see Supplement Fig. S1 and Table S3). However, the
longer tree-ring records overall yield a good constraint on a of
1.61 ± 0.54. The annual data points for the two datasets can be
combined into a single dataset. Fitting against this more complete dataset
gives generic sensitivity coefficients of a=1.51 ± 0.57 and
b=-0.72 ± 0.16. These values are mainly constrained by the tree-ring
observations for which the fits to Eq. (6) are more tightly defined (Fig. 2a
and Supplement Fig. S1 top row).
A value of a larger then 1, suggests that WUE has been increasing even
faster than the atmospheric CO2 concentration (Fig. 2c). This is
qualitatively consistent with conclusions from a previous study, which was
based purely on eddy covariance data (Keenan et al., 2013), but is more
robustly demonstrated here due to the much longer tree-ring records.
It is interesting to note that our overall values of a=1.51 ± 0.57
and b=-0.72 ± 0.16 are larger by about 50 % than the values
derived from stomatal optimization theories: a=1.0, b=-0.5 (Cowan and
Farquhar, 1977; Katul et al., 2010; Palmroth et al., 2013), indicating a
stronger response to changes in both CO2 and climate. Such theoretical
sensitivities are common to variants of stomatal optimization theory,
including those that assume either electron transport-limited or
Rubisco-limited photosynthesis, and even when additional nitrogen limitations
are accounted for Prentice et al. (2014). The differences between the optimization theory and our
empirically derived WUE sensitivities may arise from differences between
leaf-surface and atmospheric values of CO2 and humidity, but they may
also be indicative of missing constraints and feedbacks in the optimization
theories (Lin et al., 2015; Prentice et al., 2014; de Boer et al., 2011,
2016).
Testing more elaborate statistical models
Equation (6) is motivated by empirical evidence and theory suggesting that
WUE should vary predominantly with Ca and D. However, it is
conceivable that the fractional change in WUE could also depend on other
environmental conditions or the detailed vegetation type. In order to test
for this, we carried out two additional sets of fits against the
observational data. In the first test we extended our statistical model
(Eq. 6) to include other environmental variables that had been measured at
the Fluxnet sites, most notably solar radiation, air temperature,
and soil water content. Including these additional predictor variables does
not significantly improve the fit to the observed changes in WUE (as measured
by r2), and typically results in less robust predictions (as measured by
the adjusted r2), because of the introduction of extra fitting
parameters (see the Supplement, Table S4). In the second test, we carried out
separate statistical fits for each of the sites listed in the
Fluxnet dataset. Clustering of these values by vegetation type would
indicate that a and b parameters are dependent on vegetation type, but we
find no evidence of such clustering (Fig. 3).
Comparison of best-fit a and b parameters (see Eq. 5) by plant
functional type (PFT). Here the sites are organized by dominant PFT, using
classifications used for the FluxNet sites: evergreen broadleaf forest (EBF),
evergreen needleleaf forest (ENF), grassland (GRA), mixed forest (MF),
wetland (WET) and woody savannah (WSA).
Comparison of estimated water-use efficiency trends to independent
observations. Simulated fractional change in WUE (orange) compared to
observations for three tropical tree-ring sites in Bolivia (a),
Cameroon (b) and Thailand (c) (blue, van der Sleen 2015).
Simulated fractional change in WUE for (d) western North America,
(E) western Europe and (F) East Asia, with (dark red) and without (orange)
CO2 effect, compared to the WUE trend derived from a remote sensing
product of carbon uptake and water loss (Jung et al., 2011). The location of
the tree-ring sites is presented in Fig. S1 and the regions
(d)–(f) are as in Fig. 5.
Comparison to independent WUE estimates.
Our best-fit generic a and b parameters are able to reasonably reproduce
the fractional changes in WUE due to fractional changes in both Ca
and D across the 59 tree-ring and eddy covariance sites (see Supplement
Fig. S2). However, it is important to evaluate the estimated response of WUE
to Ca and D against independent data. We compared the change in
WUE estimated with the best-fit parameters to observations at three tropical
tree-ring sites from a recent study (van der Sleen et al., 2015). At these
sites a range of species of both trees and under-storey were sampled. Our
estimate for these three locations passes close to the mean of the observed
WUE fractional changes (Fig. 4a–c). Because the RS data do not include a
response to changes in Ca, we estimated a fractional change in WUE
with and without this response (Fig. 4d–f) for three regions, which show
distinct changes in WUE: western North America, western Europe and East Asia.
The RS fluxes show little inter-annual variability, and much less variability
than we estimate. For the three regions in Fig. 4d–f our estimates with and
without CO2 effects sit on either side of the RS estimates. In the
Amazon, South Africa and South-East Asia (see Supplement Fig. S3), our
estimates excluding CO2 effects are similar to the RS estimates; whilst
the inclusion of CO2 effects leads to significant increases in WUE (see
Supplement Fig. S3) that appear to be inconsistent with the RS estimates
(which do not account for CO2 changes), but are more consistent with the
tree-ring (Franks et al., 2013) and eddy covariance data (Keenan et al.,
2013).
20th century fractional change of water-use efficiency (WUE).
(a) Time series of the estimated global fractional change in WUE
(orange, relative to the average over 1901–1930) partitioned into the
effects of changes in CO2, relative humidity and temperature.
(b) Spatial pattern of the estimated fractional change in WUE
between 1901–1930 and 2001–2010. These calculations use observed monthly
surface air temperature and vapour pressure (Harris et al., 2013) during the
growing season, and annual atmospheric CO2 concentrations at Mauna Loa
(Keeling et al., 1976).
Comparison of measured and modelled fractional changes in WUE from
1860 to 2010. Estimates from tree-rings and eddy covariance data are shown by
the black and blue points respectively, with the bars in each case showing
±1 standard deviation about the mean response. The results from complex
coupled Earth System Models are shown by the black continuous line and the
green plume (with dark green showing 1 standard deviation and light green
showing 2 standard deviations). The algorithm presented in this paper,
which estimates fractional WUE changes from changes in CO2 concentration
and humidity deficit alone (Eq. 6), is shown by the orange lines. To enable
the comparison between these different estimates, we normalized over common
overlapping periods (for the tree-ring data and model simulations –
1900–1930; for the tree-ring and eddy covariance data – the period of
overlap when at least three eddy covariance sites are available).
Changes in WUE arising from climate variables. Spatial patterns of
the fractional changes in WUE arising from changes in (a) climate,
i.e. both temperature and relative humidity (RH) together,
(b) temperature alone, and (c) RH alone, between 1901–1930
and 2001–2010. Time-series are as in Fig. 5 for (d) western North
America, (e) western Europe and (f) East Asia, which show
the large regional and temporal variations in these climate-driven changes in
WUE.
Global fractional change of WUE
Globally, we estimate that WUE has increased by 48 ± 22 % since
1900 (Fig. 5a), with the CO2 increase contributing
+47 ± 21 % and relative humidity contributing
+3.6 ± 1.3 %, counteracted by a much smaller reduction in WUE due
to a warming of -2.3 ± 0.8 %. Estimated fractional changes in WUE
between 1901–1930 and 2001–2010 differ regionally between 0.1 and 0.6
(Fig. 5b). Uncertainties in global WUE changes were derived from the range of
the parameters a and b within 5 % of the RMSE of our best fit
(Fig. 2c).
Comparison to simulations with complex Earth System Models (ESMs)
The CMIP5 models simulate an increase in WUE of between 2 % and 28 %
to 2005, with an ensemble mean of 14 % (see the Supplement, Table S5).
For comparison, our overall fit against the tree-ring and eddy covariance
data indicates an approximately 40 % increase in WUE over the same
period. Figure 6 compares the annual time series of the fractional changes in
WUE from the CMIP5 models (black line and green uncertainty plumes), our
statistical fit (orange lines), and the mean changes observed for the
tree-ring (black marks and grey uncertainty bars) and eddy covariance sites
(dark blue marks and light blue uncertainty bars). This comparison suggests
that the latest ESMs significantly underestimate the historical increase in
WUE.
Regional changes in WUE
Our global average change in WUE hides substantial regional differences
(Fig. 5b). This is a result of the spatially and temporally varying impact of
climate change on WUE (Fig. 7a and animation in the Supplement), driven by
the heterogeneity of the warming (Fig. 7b) and the large variation in changes
in near-surface RH (Fig. 7c). In many regions the overall impact is a
significant increase in WUE, such as western North America (Fig. 7d).
However, the recent rate of increase has declined substantially in several
heavily populated regions. For example, WUE shows a slower increase in
western Europe since the 1980s, as a result of increases in T, which has
counteracted the WUE increase due to increasing CO2 (Fig. 7e). This is
also observed in WUE trends derived from isotopic tree-ring observations in
Spain (Linares and Camarero, 2012). Our analysis indicates that
East Asia has suffered an even more significant suppressions of WUE since
about 1990, due predominantly to reductions in RH (Wang et al., 2012)
(Fig. 7f). This pattern of changing RH is comparable with the trends in
precipitation and drought since 1950 (Dai, 2011).
For the 31 tree-ring observation sites, we have plotted the ensemble mean
regional ESM model results against the individual observed tree-ring data
(Fig. S5 in the Supplement). For 10 out of 31 observation sites, the
simulated fractional WUE increases between 5 and 10 %. For 3 out of the 31
sites, the fractional WUE increases by more than 50 %, and for 14 out of
the 31 observation sites the WUE change inferred from the tree-ring data is
significantly higher than that simulated by the ESMs.