PUBLICATIONS
Journal of Geophysical Research: Biogeosciences
RESEARCH ARTICLE
10.1002/2015JG002947
Key Points:
• The underlying WUE is superior to the
inherent WUE at the daily time scale
• The uWUE represents a nearly optimal
relationship among GPP, ET, and VPD
• The yearly uWUE is much better than
IWUE in predicting daily GPP for 34 sites
Supporting Information:
• Supporting Information S1
Correspondence to:
Y. Huang,
[email protected]
Citation:
Zhou, S., B. Yu, Y. Huang, and G. Wang
(2015), Daily underlying water use
efficiency for AmeriFlux sites, J. Geophys.
Res. Biogeosci., 120, 887–902,
doi:10.1002/2015JG002947.
Received 6 FEB 2015
Accepted 7 APR 2015
Accepted article online 10 APR 2015
Published online 18 MAY 2015
Daily underlying water use efficiency
for AmeriFlux sites
Sha Zhou1, Bofu Yu2, Yuefei Huang1, and Guangqian Wang1
1
State Key Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing,
China, 2School of Engineering, Griffith University, Nathan, Queensland, Australia
Abstract Water use efficiency (WUE) is a crucial parameter to describe the interrelationship between gross
primary production (GPP) and evapotranspiration (ET). Incorporating the nonlinear effect of vapor pressure
deficit (VPD), underlying WUE (uWUE = GPP · VPD0.5/ET) is better than inherent WUE (IWUE = GPP · VPD/ET) at
the half-hourly time scale. However, appropriateness of uWUE has not yet been evaluated at the daily time
scale. To determine whether uWUE is better than IWUE, daily data for seven vegetation types from 34 AmeriFlux
sites were used to validate uWUE at the daily time scale. First, daily mean VPD was shown to be a good
substitute for the effective VPD that was required to preserve daily GPP totals. Second, an optimal exponent, k*,
corresponding to the best linear relationship between GPP · VPDk* and ET, was about 0.55 both at half-hourly
and daily time scales. Third, correlation coefficient between GPP · VPDk and ET showed that uWUE (k = 0.5
and r = 0.85) was a better approximation of the optimal WUE (k = k* and r = 0.86) than IWUE (k = 1 and
r = 0.81) at the daily scale. Finally, when yearly uWUE was used to predict daily GPP from daily ET and mean
VPD, uWUE worked considerably better than IWUE. Comparing observed and predicted daily GPP, the
average correlation coefficient and Nash-Sutcliffe coefficient of efficiency were 0.81 and 0.59, respectively,
using yearly uWUE, and only 0.59 and 0.83 using yearly IWUE. As a nearly optimal WUE, uWUE consistently
outperformed IWUE and could be used to evaluate the effects of global warming and elevated atmosphere
CO2 on carbon assimilation and evapotranspiration.
1. Introduction
©2015. The Authors.
This is an open access article under the
terms of the Creative Commons
Attribution-NonCommercial-NoDerivs
License, which permits use and distribution in any medium, provided the
original work is properly cited, the use is
non-commercial and no modifications
or adaptations are made.
ZHOU ET AL.
Water use efficiency (WUE), defined as the ratio of carbon gain through photosynthesis to water loss through
transpiration, is a critical parameter to relate carbon assimilation and evapotranspiration at the ecosystem
scale. Knowledge of water use efficiency would help understand the interrelationship between carbon and
water cycles in terrestrial ecosystems, and provide valuable information on global carbon, water balance,
and vegetation growth. Several empirical models of water use efficiency have been developed, as water
use efficiency is correlated with some relatively stable environmental factors, such as water holding
capacity of the soil and leaf area index (LAI) [Beer et al., 2007, 2009; Yang et al., 2013]. These models have
been used to evaluate intersite variability of water use efficiency and predict regional gross primary
production (GPP) and/or evapotranspiration (ET). Water use efficiency has also been used to evaluate the
dynamic responses of ecosystems to climate change and elevated atmospheric CO2 [Guo et al., 2010; Niu
et al., 2011; Battipaglia et al., 2013; Keenan et al., 2013], and the responses have been simulated in several
process-based ecosystem models [Cramer et al., 2001; Mo et al., 2005; Tian et al., 2010; Zhu et al., 2011; Akihiko
and Motoko, 2012]. For example, Kauwe et al. [2013] used 11 ecosystem models such as GCM4, LPJ-GUESS,
SDGVM to predict the CO2 effect on water use efficiency. However, the impact of global change on terrestrial
carbon sequestration is uncertain, and explanations of the increasing water use efficiency and declining
vegetation growth with rising atmospheric CO2 concentrations are less than adequate [Peñuelas et al., 2008,
2011; Andreu-Hayles et al., 2011; Nock et al., 2011; Lévesque et al., 2014; Xu et al., 2014]. Thus, further researches
into water use efficiency should be conducted to address these questions under global change.
The eddy covariance technique has promoted and facilitated research of water use efficiency at different
time scales and among different vegetation types, and there are three different formulations of water use
efficiency to describe the relationship between GPP and ET at the ecosystem scale, with the effect of vapor
pressure deficit (VPD) incorporated in different ways (Table 1). Initially, water use efficiency (WUE) was
used to quantify the trade-off between carbon assimilation and water transpiration [Cowan and Farquhar,
1977], and WUE was calculated as the ratio of GPP over ET. Yang et al. [2013] showed that GPP relates to
DAILY UNDERLYING WUE
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a
Table 1. Various Formulations of Water Use Efficiency (WUE) at the Ecosystem Scale
WUE
Inherent WUE
Underlying WUE
Symbol
Formulation
Unit of Measurement
Time Scale
Reference
γ
γi
γu
GPP/ET
GPP · VPD/ET
0.5
GPP · VPD /ET
g C/kg H2O
g C hPa/kg H2O
0.5
g C hPa /kg H2O
Monthly
Daily
Half hourly
Yang et al. [2013]
Beer et al. [2009]
Zhou et al. [2014]
a
The validated time scale for each formulation of WUE is given with a reference. GPP, Gross Primary Production in
2 1
2 1
g C m d ; VPD, Vapor Pressure Deficit in hPa; ET, Evapotranspiration in kg H2O m d .
ET strongly and WUE remains generally invariant at the monthly time scale, whereas a large amount of
research has demonstrated that WUE is strongly dependent on VPD at daily or smaller time scales [Abbate
et al., 2004; Zhao et al., 2005; Hu et al., 2008]. Inherent water use efficiency (IWUE), derived from the
diffusion processes of carbon dioxide and water vapor through stomata between leaves and the
atmosphere, was proposed by Beer et al. [2009] to include the effect of VPD on WUE, and the IWUE was
validated using data from 43 FluxNet sites across a range of vegetation types. By comparison, the
relationship between GPP · VPD and ET is much stronger than that between GPP and ET in terms of the
linear correlation coefficient, and IWUE is much less variable than WUE at the daily time scale [Beer et al.,
2009]. However, IWUE is not entirely independent of VPD, and Zhou et al. [2014] showed that the
relationship between GPP · VPD and ET is in fact significantly nonlinear. Underlying water use efficiency
(uWUE), based on IWUE and a simple stomatal model of Lloyd and Farquhar [1994], is formulated to
represent the best linear relationship among GPP, ET, and VPD at the half-hourly time scale. The uWUE is
shown to be quite close to the optimal WUE by linear correlation analysis, and a linear relationship
between GPP · VPD0.5 and ET is further supported by a hysteresis model using half-hourly data from 42
AmeriFlux sites among seven vegetation types [Zhou et al., 2014]. The three different formulations of WUE
are proposed and validated at different time scales, namely WUE at the monthly time scale, IWUE at the
daily time scale, and uWUE at the half-hourly time scale (Table 1). An interesting question is whether there
is a superior formulation that is appropriate and consistent at varying time scales. As the uWUE is shown
to have a stronger linear relationship among GPP, ET, and VPD than WUE and IWUE at the half-hourly time
scale, would the uWUE be a suitable and superior formulation when applied to the daily time scale? Water
use efficiency at the daily time scale is of great importance and has been widely used in ecosystem
vegetation growth models and the remote sensing products. Daily water use efficiency is also the
foundation of annual water use efficiency, and the latter is crucial to evaluating the impact of global
change on ecosystem water use efficiency in the long term.
A generic model of water use efficiency proposed in Zhou et al. [2014] can be used to explore the optimal
relationship among GPP, ET, and VPD at different time scales.
γET ¼ GPP · VPDk
(1)
where γ stands for WUE (γ), uWUE (γu), and IWUE (γi), when k equals to 0, 0.5, and 1, respectively. At each time
scale, an optimal k, henceforth expressed as k*, is defined as the exponent value in equation (1) that would
result in the strongest linear relationship between GPP · VPDk and ET in terms of the correlation coefficient. It
is demonstrated that k* is quite close to 0.5 and a constant value of k is appropriate at the half-hourly time
scale [Zhou et al., 2014]. The question is whether k* is scale invariant and an exponent of 0.5 is also
suitable at the daily time scale. One of the most important issues with upscaling of water use efficiency is
the representativeness of VPD at different time scales. While GPP and ET can be accumulated from halfhourly to daily time scales, VPD cannot. VPD is affected by temperature and relative humidity, and it
remains relatively constant for each half hour but varies considerably during a day. Thus, it is important to
determine a daily effective VPD that would maintain the same value of uWUE when GPP and ET are
accumulated at the daily time scale. Such an effective VPD is required to interpret its effect on water use
efficiency at the daily time scale and to quantify the changes in the relationship among GPP, ET, and VPD
from half-hourly to daily time scales.
Another issue is how to assess the performance of different formulations of water use efficiency at the daily
time scale, and such an assessment should, in our view, consider at least three aspects: (1) linearity among
GPP, ET, and VPD; (2) variability of water use efficiency during a growth season; and (3) capacity to predict
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daily GPP or ET from a constant water use efficiency. Consistency in water use efficiency implies that WUE is
independent of a varying VPD to a large extent, and this is especially important for GPP or ET predictions. A
constant water use efficiency for each site has been modeled as a function of two relatively stable
environment properties, leaf area index (LAI) and water holding capacity of the soil, and such a constant
water use efficiency is shown to be effective in predicting monthly ET and yearly GPP at a regional scale
[Beer et al., 2007; Yang et al., 2013]. However, the performance of predicting daily GPP using constant
water use efficiency for each site has not yet been evaluated. As crops do change from year to year at
some sites, such as the mead-rainfed maize-soybean rotation site, it would be more appropriate to
predict daily GPP using constant water use efficiency for each site year instead of a constant value for all
years at the site.
The aim of this study was to determine whether the underlying water use efficiency, as defined in equation
(1) with k = 0.5, is superior and consistent at the daily time scale. Our specific objectives were (1) to test
whether the effective VPD at the daily time scale could be replaced by the daily mean VPD in calculating
water use efficiencies, (2) to evaluate the optimal water use efficiency formulation when applied to daily
time scales, (3) to test whether the underlying water use efficiency is a better approximation of the
optimal water use efficiency that relates GPP and VPD to ET in comparison of the inherent water use
efficiency in terms of linear correlation coefficient and parameter variability at the daily time scale, and (4)
to evaluate the prediction performance when the underlying water use efficiency at the annual time scale
combined with daily ET and the mean VPD were used to predict daily GPP values.
2. Materials and Methods
2.1. Data
This research was based on half-hourly data from 34 AmeriFlux sites (Table S1 in the supporting information).
There were seven vegetation types: cropland (CRO), deciduous broadleaf forest (DBF), grassland (GRA),
evergreen needleleaf forest (ENF), woody savanna (WSA), mixed forest (MF), and closed shrubland (CSH)
among the 34 sites. The record length for each site ranged from 1 to 13 years, and there were 123 site
years in total considered in this study. Data sets provided as Level 4 products (http://public.ornl.gov/
ameriflux) were used, including air temperature (°C), latent heat flux (W m2), VPD (hPa), and estimates of
GPP (g C m2 d1) derived from the CO2 flux measurements. Half-hourly values of ET (kg H2O m2 d1)
were calculated from air temperature and latent heat flux, using the method of Donatelli et al. [2006]. The
flux data measured using the eddy covariance technique were friction velocity (ustar) filtered, gap filled
using quality flags of four categories, namely, the original, most reliable, medium, and least reliable
[Reichstein et al., 2005].
The half-hourly data sets were processed and then aggregated to the daily time scale (midnight to midnight).
The data processing was performed following four steps. First, defective entries and data on the rainy days
and certain number of dry days after the rainy days were excluded. The number of dry days that were
excluded depended on the daily precipitation (P) and potential evapotranspiration (PET). Two dry days
following a rainy day were excluded when P was larger than twice of PET, otherwise one dry day excluded
when P was larger than PET. Only the rainy days were excluded when P was small than PET for the day.
PET was calculated using the Priestley-Taylor equation [Priestley and Taylor, 1972]. Second, the half-hourly
flux data were quality controlled, retaining only those entries with quality flags of the “original” and “most
reliable.” Third, only daylight data from 5 A.M. to 9 P.M. were selected, and data with negative net solar
radiation or negative GPP, ET, and VPD were excluded. Finally, the half-hourly data were used only for days
when there were at least 24 entries and when the average half-hourly GPP for the day was at least 10% of
the maximum half-hourly GPP for the site year. The half-hourly data of GPP and ET from available days
were then accumulated to daily totals. In order to achieve the four objectives of the paper, the selected
data were used as follows: (1) daily mean VPD and the effective VPD when k equal to 0.5 and 1 were
calculated to undertake the comparative analysis; (2) half-hourly and daily data on GPP, ET, and VPD were
used to analyze the scale effect on water use efficiency; (3) daily GPP, ET, and VPD were used to evaluate
the consistency of daily uWUE and IWUE values within a site year; and (4) yearly uWUE and IWUE values
were calculated from daily GPP, ET, and VPD to compare their performances in predicting daily GPP values.
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2.2. The Effective VPD From Half-Hourly to Daily Time Scales
2.2.1. Derivation of the Effective VPD
To derive a daily effective VPD, let ETi, GPPi, and VPDi be the half-hourly observations for time interval i, and
GPPd and ETd be the daily GPP and ET totals, respectively. That is
X
ETi
(2)
ETd ¼
X
GPPd ¼
GPPi
(3)
Applying equation (1) for each time interval and summing over all the time intervals in the day, we have
i
Xh
γETd ¼
GPPi ðVPDi Þk
(4)
Let VPDe be such an effective VPD at the daily time scale that VPDe satisfies equation (1) at the daily time
scale, i.e.,
γETd ¼ GPPd ðVPDe Þk
(5)
A comparison of equations (4) and (5) would lead to an expression for the effective VPD as follows:
"X
#1
GPPi ðVDPi Þk k
X
VPDe ¼
GPPi
(6)
Thus, an effective VPD should be derived from half-hourly GPP and VPD observations using equation (6), not
from the mean VPD directly.
2.2.2. Comparison of the Effective VPD and the Mean VPD
Diurnal variations in GPP, ET, and VPD are similar during days with clear skies. The three variables all increase
monotonically from sunrise to their peak values then decrease monotonically to sunset. However, a hysteresis
phenomenon exists among their diurnal variations, that is, they reach their peak values at different times,
which can be expressed by time lags [Mahecha et al., 2007; O’Grady et al., 2008; Pita et al., 2013]. In
general, ET would reach its diurnal peak value at noon, GPP before noon, and VPD after it. The diurnal
variations in the three variables and their time lags can be approximated by sinusoidal functions in a
hysteresis model below [Zhang et al., 2014; Zhou et al., 2014].
ET ¼ ET0 sinðωtÞ
(7)
GPP ¼ GPP0 sinðωt þ αÞ
(8)
VPD ¼ VPD0 sinðωt βÞ
h πi
β βþπ
;
; α; βϵ 0;
tϵ
ω ω
2
(9)
where ω is a constant diurnal frequency for ET, GPP, and VPD, and the peak values of the three variables are
ET0, GPP0, and VPD0, respectively. The time lag between ET and GPP is α/ω, while that between VPD and ET is
β/ω. The day time, t, in equations (7)–(9), applies to half of the period, i.e., π/ω. In this paper, we assume that t
starts at β/ω and ends at (β + π)/ω when VPD is zero to ensure that day time VPD is always nonnegative during
day time in the generic water use efficiency model (equation (1)).
Daily mean VPD, VPDd , can be derived from equation (9) in the hysteresis model.
VPDd
∫
¼
βþπ
ω
β
ω
VPD0 sinðωt βÞdt
π
ω
¼ VPD0
2
π
(10)
The effective VPD at the daily time scale, as defined in equation (6), can also be derived from the
hysteresis model.
VPDe ¼
ZHOU ET AL.
8
>
<
∫
>
:
βþπ
ω
β
ω
91k
=
GPP0 sinðωt þ αÞ½VPD0 sinðωt βÞk dt>
∫
βþπ
ω
β
ω
DAILY UNDERLYING WUE
GPP0 sinðωt þ αÞdt
>
;
(11)
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Let I1 be the numerator in equation (11), and I2 be the denominator. Define a new variable of integration
x as
x ¼ ½ sinðωt βÞk ; with k > 0
(12)
Note that as time, t, varies from β/ω to (β + π/2)/ω, and then to (β + π)/ω, x varies from 0 to 1 and then to 0
again. With trigonometric identities, evaluation of I1 with respect to x results in
I1 ¼
2cosðα þ βÞGPP0 ðVPD0 Þk
kω
I1 ¼
2cosðα þ βÞGPP0 ðVPD0 Þk
ω
2
∫
xk
pffiffiffiffiffiffiffiffiffiffiffiffi2ffi dx
0
1 xk
1
or simply
∫
1 pffiffiffiffiffiffiffiffiffiffiffiffi2ffi
0
1 x k dx
(13)
Evaluation of I2 is straightforward:
I2 ¼ GPP0
2 cosðα þ βÞ
ω
(14)
Combining equations (13) and (14), we can derive an analytic expression for the effective VPD in terms of its
peak value, VPD0, and the exponent k as follows:
VPDe ¼ VPD0
pffiffiffiffiffiffiffiffiffiffiffiffiffi 1k
1
2
1 x k dx
∫
0
(15)
The ratio of the effective over mean VPD from equations (15) and (10) is given as
VPDe π
¼
VPDd 2
pffiffiffiffiffiffiffiffiffiffiffiffiffi 1k
1
2
1 x k dx
∫
0
(16)
For k = 1, the ratio is exactly π 2/8 ≈ 1.23. In general, the ratio needs to be evaluated numerically. As the
exponent k varies from 0.001 to 1, the variation in the ratio is quite small, from 1.15 to 1.23, or <7.0%
only. When k = 0.5, as in the case of the underlying water use efficiency, the ratio is 1.20. Assuming the
hysteresis model, we have shown analytically that the ratio of VPDe over VPDd is a function of the
exponent k only, and the ratio is practically constant for most values of k. Thus, the effective VPD is
essentially proportional to the daily mean VPD. We sought empirical support from observed relationship
between the effective VPD and daily mean VPD, and proposed to use the daily mean VPD to predict GPP
at the daily time scale using the underlying water use efficiency. In particular, we used a linear
regression model through the origin:
VPDe ¼ λVPDd
(17)
to test whether the effective VPD and the daily mean VPD are well correlated and whether the daily mean
VPD can be used instead of the effective VPD for water use efficiency estimation and GPP predictions.
When the daily mean VPD is shown to be adequate for GPP predictions at the daily time scale, we can
define a daily underlying water use efficiency, uWUE, γu,d, as follows:
γu;d
0:5
GPPd VPDd
¼
ETd
(18)
2.3. Validation of the Underlying Water Use Efficiency at the Daily Time Scale
The daily uWUE formulation was validated for seven vegetation types using data from 123 AmeriFlux site
years, and a flow chart for the methodology is shown in Figure 1. First, daily mean VPD and the effective
VPD were calculated from half-hourly data, and the parameter, λ, was estimated as the slope of the
regression equation, i.e., equation (17) for each site year. Second, k* relating to the best linear
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Figure 1. Procedure adopted for data processing and analysis.
relationship between GPP · VPDk and ET was sought at the half-hourly and daily time scales, using the
method in Zhou et al. [2014], to test the scale invariance of k* and to validate uWUE at the daily time
scale. The paired t test and the test for homogeneity of variance were used to evaluate the consistency
of the mean and variance of the exponent k* at half-hourly and daily time scales. Third, three different
aspects were considered to compare uWUE and IWUE at the daily time scale: (1) the correlation
coefficient for the relationship of GPP · VPD0.5 versus ET and GPP · VPD versus ET at the daily time scale,
(2) the coefficient of variation, namely the ratio of standard deviation over the mean daily uWUE and
IWUE for each year at each site, (3) the discrepancy between daily and yearly water use efficiency in
terms of the mean and standard deviation. Finally, the performance of using yearly uWUE to predict
daily GPP values was evaluated and compared with yearly IWUE. Yearly uWUE, γu,y, and yearly IWUE, γi,y,
were calculated using daily data of GPP, ET, and VPD for each site year, the formulations are shown in
equations (19) and (20). Daily GPP, i.e., GPPu,d and GPPi,d, were predicted using equations (21) and (22)
and yearly uWUE and IWUE and daily ET and mean VPD for the site year.
Xh
0:5 i
GPPd VPDd
X
γu;y ¼
ETd
X
GPPd VPDd
X
γi;y ¼
ETd
(19)
(20)
γu;y ETd
GPPu;d ¼ 0:5
VPDd
GPPi;d ¼
(21)
γi;y ETd
(22)
VPDd
Table 2. Comparisons of the Effective VPD and Daily Mean VPD, Including the Average of the Coefficient of
2
Determination (R ), the Slope of the Linear Fit (λ) in Equation (17), and the Discrepancy (D) Between the Effective VPD
a
and Daily Mean VPD for the Seven Vegetation Types and the 123 Site Years
k = 0.5
CRO
DBF
GRA
ENF
WSA
MF
CSH
Average
2
k=1
2
Site Years
R
λ
D (%)
R
λ
D (%)
26
31
23
23
8
7
5
0.97
0.96
0.97
0.97
0.97
0.98
0.95
0.96
1.04
0.99
1.00
0.99
0.95
1.01
1.08
1.01
4.8
0.2
1.0
0.6
4.7
1.1
8.8
1.5
0.95
0.94
0.96
0.95
0.97
0.97
0.94
0.95
1.09
1.05
1.05
1.04
0.98
1.05
1.11
1.05
9.7
5.5
5.7
5.1
1.4
5.3
11.3
6.1
a
The effective VPD was calculated in equation (6) when k = 0.5 and k = 1, respectively.
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Prediction performance was assessed
using four widely used indicators: (1)
the bias, B (%), (2) the root-meansquare error, RMSE, (3) the correlation
coefficient, r, and (4) the Nash-Sutcliffe
coefficient of efficiency, Ec [Nash and
Sutcliffe, 1970].
X
!
^y
B ¼ 100 X 1
(23)
y
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
ð y y^Þ2
(24)
RMSE ¼
n
X
ð y y Þ ^y y^
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
r ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
X
2ffi (25)
ðy y Þ2
y^ y^
X
ð y y^Þ2
(26)
Ec ¼ 1 X
ð y y Þ2
where y represents the observed daily
GPP values, ŷ the predicted daily GPP
values, and n is the total number of
observations for the site year. The
mean of the observed and predicted
values are y and y^, respectively.
3. Results and Discussion
3.1. The Effectiveness of Daily
Mean VPD
The linear relationship between the
effective VPD and daily mean VPD was
evaluated using equation (17) for seven
vegetation types and 123 site years.
The effective VPD was computed using
equation (6) with k = 0.5 for uWUE and
k = 1 for IWUE. The average coefficient
of determination for equation (17)
ranged from 0.95 to 0.98 when k = 0.5
and from 0.94 to 0.97 when k = 1 for
the seven vegetation types, indicating a
strong linear relationship between the
effective VPD and daily mean VPD (Table 2). The strong linear relationship between VPDd and VPDe lent
empirical support for the proportional relationship derived from the hysteresis model in equation (16).
The mean and the distribution of the slope of the linear fit, i.e., λ for each vegetation type and all the
123 site years as a whole are shown in Table 2 and Figure 2. The slope λ ranged from 0.85 to 1.11 with
an average of 1.01 for k = 0.5 and from 0.91 to 1.17 with an average of 1.05 for k = 1. The estimated ratio
of λ is distributed evenly around the mean for all the site years for both k = 0.5 and k = 1, although the
distribution of λ varies slightly among the seven vegetation types (Figure 2). It is worth noting that
the mean of the ratio λ differed from the theoretical values based on the hysteresis model, and the
difference was about 0.19 for k = 0.5 and 0.18 for k = 1, and that the estimated ratio, i.e., λ of VPDe over
VPDd , was much closer to 1 than implied by the hysteresis model. Figure 3 shows as an example of the
relationship between the daily mean VPD and the effective VPD in 2006 at Station US-Goo (GRA), and it
is clear from Figure 3 that the scatters are around the 1:1 line for k = 0.5 and k = 1, and quite distinct
Figure 2. Frequency distribution of the slope of the linear fit, i.e., lambda
in equation (17) for (a) k = 0.5 and (b) k = 1 for the seven vegetation types
and the 123 site years (CRO = cropland, DBF = deciduous broadleaf forest,
GRA = grassland, ENF = evergreen needleleaf forest, WSA = woody
savanna, MF = mixed forest, and CSH = closed shrubland). The dashed
lines in the boxes refer to the average lambda values for the seven
vegetation types, and the solid lines refer to the median values. The
dotted lines outside the boxes are the mean of lambda values for the 123
site years, namely 1.01 for k = 0.5 and 1.06 for k = 1, as shown in Table 2.
The dashed lines outside the boxes are the theoretical lambda values
from equation (16), i.e., 1.20 for k = 0.5 and 1.23 for k = 1.
ZHOU ET AL.
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Journal of Geophysical Research: Biogeosciences
30
from the theoretical lines based on the
hysteresis model. The average discrepancy
between the effective VPD and the daily
mean VPD ranged from 4.7% to 8.8% for
k = 0.5 and from 1.4% to 11.3% for k = 1
for the seven vegetation types, and the
average discrepancy was only 1.5% for
k = 0.5, and 6.1% for k = 1 for all the site
years (Table 2). The systematic departures
from the theoretical values may have
resulted from the difference in the diurnal
processes of GPP, ET, and VPD and the
assumed sinusoidal functions in the
hysteresis model. Considering the small
variation in λ around unity among all the
site years, it would be sensible to assume
that λ = 1, and VPDe equals VPDd for
practical applications. Thus, the effective
VPD could be replaced by the daily mean
VPD for GPP predictions. We have shown
that the daily mean VPD can be used in the
generic water use efficiency model at the
daily time scale, and this daily mean VPD
was used henceforth for water use
efficiency calculation in this study.
The effective VPD (hPa)
25
20
15
10
k=0.5
k=1
VPDe=1.0092VPD
5
VPDe=1.0599VPD
0
0
5
10
15
20
25
10.1002/2015JG002947
30
Daily mean VPD (hPa)
Figure 3. Comparisons of the daily mean VPD and effective VPD
when k = 0.5 and k = 1 for station US-Goo (GRA) in 2006. The solid
line is the 1:1 line, and the dotted lines represent the linear fit
between the daily mean VPD and effective VPD. The dashed lines
are based on equation (16), and the slopes are 1.20 for k = 0.5 and
1.23 for k = 1.
3.2. The Optimal Water Use Efficiency From Half-Hourly to Daily Time Scales
The optimal exponent, i.e., k*, and the corresponding correlation coefficient for the relationship between
GPP · VPDk* and ET for each site year were calculated at both the half-hourly and daily time scales. Their
distributions and comparisons are shown in Table 3 and Figure 4a, and the difference in k* between halfhourly and daily time scales is shown in Figure 4b for different vegetation types. The average k* value was
about 0.55 using half-hourly and daily data for the 123 site years. There was no obvious difference
between the average k* at the half-hourly and daily time scales, both being close to 0.5, and their
difference was less than 0.01 (Table 3). However, the standard deviation of k* among the 123 site years
was larger at the daily time scale than that at the half-hourly time scale. As is shown in the paired t test,
the mean of k* was not significantly different at the 1% level (p value = 0.728). The test for homogeneity of
variance, however, showed that there was a significant difference between the variance of k* at the halfhourly and daily time scales (p value < 0.001). The average k* for all site years is scale invariant in a
k*
Table 3. Average ± 1 Standard Deviation of k* and the Correlation Coefficient (r) of GPP · VPD
a
Hourly and Daily Time Scales for the Seven Vegetation Types and the 123 Site Years
Half-Hourly Time Scale
CRO
DBF
GRA
ENF
WSA
MF
CSH
Average
Versus ET at the Half-
Daily Time Scale
Site Years
k*
r
k*
r
26
31
23
23
8
7
5
0.53 ± 0.08
0.55 ± 0.12
0.54 ± 0.13
0.57 ± 0.10
0.45 ± 0.16
0.61 ± 0.11
0.69 ± 0.14
0.55 ± 0.12
0.92 ± 0.05
0.86 ± 0.06
0.87 ± 0.08
0.87 ± 0.04
0.78 ± 0.06
0.85 ± 0.02
0.88 ± 0.04
0.87 ± 0.06
0.59 ± 0.17
0.51 ± 0.17
0.59 ± 0.18
0.56 ± 0.14
0.33 ± 0.12
0.72 ± 0.14
0.50 ± 0.24
0.55 ± 0.18
0.85 ± 0.10
0.85 ± 0.08
0.86 ± 0.12
0.88 ± 0.05
0.87 ± 0.04
0.86 ± 0.03
0.86 ± 0.04
0.86 ± 0.09
a
k
The term k* is the optimal exponent in equation (1) relating to the best linear relationship between GPP · VPD and ET
for each site year.
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Journal of Geophysical Research: Biogeosciences
1
CRO
DBF
GRA
0.8
ENF
Daily k*
WSA
MF
0.6
CSH
0.4
0.2
(a)
0
0
0.2
0.4
0.6
0.8
Half-hourly k*
1
10.1002/2015JG002947
statistical sense, although the changes in the average
k* from half-hourly to daily time scales are different
for different vegetation types. At the half-hourly
time scale, the average k* was around 0.5 and more
than half of the k* values lay between 0.4 and 0.6
for four of the seven vegetation types (cropland,
deciduous broadleaf forest, evergreen needleleaf
forest, and grassland) with the number of site years
greater than 20 (Table 3 and Figure 4a). From halfhourly to daily time scales, the change in the
average k* is the smallest for evergreen needle
forest and the largest for cropland among the four
vegetation types. The average k* for the other three
vegetation types (woody savanna, mixed forest, and
closed shrubland) with fewer site years shows
greater deviation from 0.5 at the half-hourly time
scale and also shows a greater change from halfhourly to daily time scales (Table 3 and Figure 4b).
The standard deviation and the range of k* become
larger for each vegetation type from half-hourly to
daily time scales, showing high variance at the daily
time scale (Table 3 and Figure 4b).
The linear relationship between GPP · VPDk* and ET
becomes weaker from half-hourly to daily time
scales on average (Table 3 and Figure 5). Largest
changes in the correlation coefficient are generally
associated with large changes in k*. The greatest
decrease in the average correlation coefficient was
Figure 4. A comparison of the optimal exponent k* at the 0.07 from 0.92 to 0.85 for cropland, with the
half-hourly and daily time scales (a) and the frequency
average k* increased from 0.53 to 0.59. The most
distribution of the difference in k* between the half-hourly
increase in the correlation coefficient was 0.09 from
and daily time scales (b). The dashed lines in the boxes
0.78 to 0.87 for woody savanna when the average
refer to the average k* values for the seven vegetation
k* was decreased from 0.45 to 0.33 (Table 3). The
types, and the solid lines in the boxes refer to the median
values. The optimal exponent was based on the best linear change in the average correlation coefficient for the
k*
relationship between GPP · VPD and ET for each site year. other five vegetation types was smaller than 0.02,
and the number of site years with an increased
correlation coefficient was close to that with a
decreased correlation coefficient (Table 3 and Figure 5). The average correlation coefficient was the largest
for cropland at the half-hourly time scale and one of the smallest at the daily time scale, the standard
deviation of the correlation coefficient at the daily time scale was as large as 0.10, indicating that the linear
relationship between GPP · VPDk* and ET varied considerably among the 26 site years for cropland at the
daily time scale. Although 0.5 is a good approximation for the optimal exponent at both half-hourly and
daily time scales, calculated k* values vary considerably at different time scales and among different
vegetation types. As the optimal exponent k* was derived by maximizing the correlation coefficient
between GPP · VPDk and ET, other environmental factors affecting the relationship among GPP, ET, and
VPD were not taken into account, resulting in errors in estimated k* values, especially at the daily time
scale. One of the most important factors is the composition of ET, and the major concern is the ratio of
canopy transpiration to ET [Beer et al., 2009; Zhou et al., 2014]. When a linear relationship between
GPP · VPDk and ET is sought within a year, we would expect that for days with low GPP, transpiration
contributes only a small portion of ET when the LAI is low. Additionally, the uncertainty in observations
may contribute to errors in the estimated k* as well, especially the uncertainty associated with GPP,
which was calculated from the net ecosystem exchange and ecosystem respiration using the Artificial
Neural Network method and the Marginal Distribution Sampling method [Papale and Valentini, 2003;
ZHOU ET AL.
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Journal of Geophysical Research: Biogeosciences
1
Reichstein et al., 2005]. Thus, the water
use efficiency would vary within a site
year, and a superior formulation for
water use efficiency would demand low
variance in the water use efficiency at
the daily time scale and minimum
difference between daily and yearly
water use efficiencies. Low variability in
the daily WUE and small discrepancy
between daily and yearly WUE can be
ascertained when the yearly WUE is
used to predict daily GPP values.
CRO
Daily r (GPP·VPDk* versus ET)
DBF
0.9
GRA
ENF
WSA
0.8
10.1002/2015JG002947
MF
CSH
0.7
0.6
3.3. Comparison of uWUE and IWUE at
the Daily Time Scale
Table 4 shows that the relationship
between GPP · VPD0.5 and ET is better
0.6
0.7
0.8
0.9
1
than that between GPP · VPD and ET for
Half-hourly r (GPP·VPDk* versus ET)
all the seven vegetation types at the
Figure 5. A comparison of the correlation coefficient for the relation- daily time scale, and the average
k*
ship between GPP · VPD and ET using the half-hourly and daily data
correlation coefficient for uWUE (r = 0.85)
for the seven vegetation types and the 123 site years.
is higher than that for IWUE (r = 0.81) for
the 123 site years. Figure 6 shows a
comparison of the correlation coefficient for IWUE and uWUE, and it is quite clear from Figure 6 that the
correlation coefficient is mostly high for uWUE than that for IWUE. The change in the correlation
coefficient from IWUE to uWUE ranged from 0.15 to 0.35 for all the 123 site years. The average increase
in the correlation coefficient was about 0.06 for 97 site years, and the average decrease was 0.02 for only
26 of all the site years, and the decrease in the correlation coefficient occurred when k* was relatively
large (>0.70). The difference in the average correlation coefficient between uWUE (r = 0.85) and the
optimal WUE (r = 0.86) was quite small for all the site years, indicating that uWUE would be a good
approximation of the optimal WUE, and the exponent k = 0.5 can be used in equation (1) because of the
strong linear relationship at the daily time scale. If the daily uWUE evaluated from daily GPP, ET, and VPD
observations is a constant during a growth season, there would be a perfect linear relationship between
GPP · VPD0.5 and ET for the year. A strong linear relationship among daily GPP, ET, and VPD for each site
year, as demonstrated with high-correlation coefficient in the paper, would therefore imply that the daily
uWUE is nearly constant or less variable for the year. Hence, the yearly uWUE, i.e., equation (19), could be
used to predict daily GPP with high accuracy for each site year.
0.5
0.5
a
Table 4. Comparisons of Daily and Yearly uWUE and IWUE for the Seven Vegetation Types and the 123 Site Years
uWUE
CRO
DBF
GRA
ENF
WSA
MF
CSH
Average
a
IWUE
Site Years
r
Cv
Mean Daily uWUE
Yearly uWUE
r
Cv
Mean Daily IWUE
Yearly IWUE
26
31
23
23
8
7
5
0.85
0.84
0.84
0.88
0.84
0.85
0.86
0.85
0.22
0.22
0.24
0.21
0.28
0.28
0.21
0.23
11.24 ± 2.90
9.55 ± 1.60
7.88 ± 1.78
9.96 ± 2.81
9.39 ± 1.35
9.07 ± 2.00
6.84 ± 1.44
9.52 ± 2.53
11.42 ± 3.03
9.36 ± 1.57
8.05 ± 1.84
9.90 ± 2.73
8.66 ± 1.14
8.99 ± 1.86
6.55 ± 1.32
9.47 ± 2.56
0.81
0.79
0.82
0.85
0.66
0.86
0.83
0.81
0.27
0.32
0.32
0.31
0.36
0.35
0.23
0.31
40.57 ± 11.66
28.54 ± 6.32
29.78 ± 7.55
34.49 ± 9.49
39.32 ± 3.25
29.49 ± 6.45
20.84 ± 8.28
32.87 ± 10.05
41.78 ± 12.42
28.92 ± 6.26
31.15 ± 8.10
35.81 ± 9.57
36.59 ± 2.58
30.93 ± 5.97
20.64 ± 8.19
33.62 ± 10.32
0.5
The average correlation coefficient (r) of GPP · VPD versus ET and GPP · VPD versus ET at the daily time scale, the mean coefficient of variation (Cv) of daily
uWUE and IWUE for a year was used to indicate consistency of the daily water use efficiency. Average ± 1 standard deviation of mean daily and yearly uWUE
0.5
(g C hPa /kg H2O) and IWUE (g C hPa/kg H2O) are presented.
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Journal of Geophysical Research: Biogeosciences
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1
r (GPP·VPD0.5 versus ET)
The difference between the mean daily
water use efficiency for a year and yearly
water use efficiency ranged from 0.61 to
0.9
1.56 g C hPa0.5/kg H2O for uWUE and from
3.80 to 4.95 g C hPa/kg H2O for IWUE for
the 123 site years. The largest difference
was no more than 17% for the yearly uWUE
0.8
and no more than 14% for the yearly IWUE
for these site years, and the difference
CRO
between the average daily and the average
0.7
DBF
yearly water use efficiency was less than
GRA
8% for the seven vegetation types using
ENF
uWUE and less than 7% using IWUE
0.6
WSA
(Table 4). As is shown in Figure 7, the mean
daily uWUE and IWUE are close to yearly
MF
uWUE and IWUE, respectively, and daily
CSH
0.5
uWUE values are distributed more tightly
0.5
0.6
0.7
0.8
0.9
1
around the yearly uWUE with small
r (GPP·VPD versus ET)
standard deviations than the IWUE for all
Figure 6. A comparison of the correlation coefficient of GPP · VPD the site years, indicating the daily uWUE is
0.5
versus ET and that of GPP · VPD versus ET for the seven vegetation
less variable in comparison to daily IWUE.
types and the 123 site years.
The coefficient of variation of the daily
uWUE in a year was much smaller than that
of daily IWUE, and the average coefficient of variation was 0.23 for daily uWUE and 0.31 for daily IWUE for
all the site years, and the average coefficient of variation of daily IWUE was 1.2 ~ 1.5 times larger than that
of daily uWUE for the seven vegetation types (Table 4). The variability of uWUE and IWUE in a year affects
the accuracy in predicted daily GPP values when daily uWUE and IWUE were replaced by constant uWUE
and IWUE for the year. Thus, we have shown that uWUE is not only more suitable than IWUE at the halfhourly time scale but also at the daily time scale, because of the stronger relationship between
GPP · VPD0.5 and ET and more consistent daily uWUE values within a year in comparison to IWUE.
3.4. Prediction of Daily GPP Values From Yearly uWUE and IWUE
A constant IWUE for individual site has been used to predict annual GPP using mean annual VPD and ET
values [Beer et al., 2007]. However, there is a lack of simple and effective model to predict GPP at the daily
time scale. Daily uWUE was shown to be more consistent with and closer to the yearly uWUE than IWUE;
thus, the yearly uWUE may be more effective in predicting daily GPP using daily ET and mean VPD values,
and the model performance can be contrasted with that using IWUE. Yearly uWUE values ranged from
3.50 to 15.83 g C hPa0.5/kg H2O for the 123 site years, about 25% of the yearly IWUE values, which ranged
from 5.32 to 62.31 g C hPa/kg H2O. The average yearly uWUE was 9.47 g C hPa0.5/kg H2O, and the average
yearly IWUE was 33.62 g C hPa/kg H2O (Table 4). Among all the seven vegetation types, cropland had the
highest yearly uWUE, 11.24 g C hPa0.5/kg H2O on average, followed by mixed forest, evergreen needleleaf
forest, deciduous broadleaf forest, and the lowest was for closed shrubland, about half of that for cropland
(Table 4). Apart from cropland and closed shrub forest, the variation in the mean yearly uWUE is quite
small, from 7.88 to 9.96 g C hPa0.5/kg H2O only (Table 4). The near constancy of the average yearly uWUE
indicates the potential to make a first-order prediction of the average GPP from VPD and ET for the five
remaining vegetation types. The standard deviation of the yearly uWUE among the 26 site yeas of
cropland was as large as 3.03 g C hPa0.5/kg H2O, indicating that yearly uWUE may vary considerably among
the same vegetation type, even at the same site. For example, US-Ne3 is a mead-rainfed maize-soybean
rotation site, the average yearly uWUE was 15.38 g C hPa0.5/kg H2O for maize and 8.68 g C hPa0.5/kg H2O for
soybean. The coefficient of variation was about 0.27 for the yearly uWUE and 0.31 for IWUE for all the 123
site years, indicating that the yearly uWUE is less variable among different site years (Table 4).
The bias in the predicted daily GPP values ranged from 3.6% to 5.5% with an average of 0.59% using the yearly
uWUE for all the 123 site years, and the average root-mean-square error was 2.88 g C m2 d1, indicating that the
ZHOU ET AL.
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Journal of Geophysical Research: Biogeosciences
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100
Mean daily IWUE (g C·hPa/kg H2O)
Mean daily uWUE (g C·hPa0.5/kg H2O)
yearly uWUE was effective as a predictor of
the daily GPP on average. In comparison,
(a)
the bias in predicted daily GPP using the
yearly IWUE was much larger, ranging from
1.4% to 31.9%, and the average bias was
about 3.2–12.5%, indicating a systematic
overprediction for all the seven vegetation
types (Table 5). The average root-mean10
CRO
square error using the yearly IWUE was
5.30 g C m2 d1, almost twice of that
DBF
using the yearly uWUE (Table 5). Although
GRA
the yearly IWUE is effective in predicting
ENF
yearly GPP [Beer et al., 2007], using the
WSA
yearly uWUE to predict daily GPP would
MF
have smaller bias and smaller root-meanCSH
square error than using the yearly IWUE.
1
average correlation coefficient
10
100 The
1
0.5
between
observed and predicted daily
Yearly uWUE (g C·hPa /kg H2O)
GPP values was larger than 0.7 for all the
100
seven vegetation types, and the average
(b)
Nash-Sutcliffe coefficient of efficiency was
almost 0.6 for all the site years (Table 5
and Figure 8). While the majority of the
correlation coefficient between the
observed and predicted daily GPP (95 out
of the 123 site years) was larger than 0.75
using uWUE, and there were only 32 site
10
years using IWUE with the correlation
CRO
coefficient above 0.75. The performance
DBF
using the IWUE varied much from site year
GRA
to site year, especially for deciduous
ENF
broadleaf forest with negative correlation
WSA
coefficients for 2 site years. Prediction
MF
performance was much improved using
CSH
the yearly uWUE, and none of the 31 site
years had a negative correlation coefficient
1
1
10
100
for deciduous broadleaf forest, and the
Yearly IWUE (g C·hPa/kg H2O)
correlation coefficient for the 2 site years
was larger than 0.7, as it can be seen from
Figure 7. Comparisons between (a) mean daily uWUE and yearly
Figure 8. In terms of the Nash-Sutcliffe
uWUE, and between the (b) mean daily IWUE and yearly IWUE for the
coefficient of efficiency, uWUE is much
seven vegetation types and the 123 site years. The error bar represents
1 standard deviation of the daily uWUE or IWUE for each site year.
better than IWUE at predicting the daily
GPP. The average Nash-Sutcliffe coefficient
of efficiency was 0.7 for cropland and 0.64 for grassland, and was 0.59 overall for the 123 site years (Table 5).
The average Nash-Sutcliffe coefficient of efficiency using the IWUE was less than zero for all vegetation types,
indicating IWUE is no better a predictor of the daily GPP than that predicted using the mean daily GPP as a
predictor. Inaccuracy of IWUE is attributed to the fact that the relationship between GPP · VPD and ET is largely
nonlinear, and that the daily IWUE is highly variable within a site year. As an example, Figure 9 shows a time
series of observed and predicted daily GPP in 2006 at station US-Goo (GRA). It is clear from Figure 9 that
the difference between daily and yearly IWUE is much greater than that between daily and yearly uWUE
for most days. Daily GPP predicted using IWUE is much larger than observed GPP when daily mean VPD
is small, and the yearly IWUE is much larger than the daily IWUE, such as the Julian days from 75 to 142,
and the difference between the observed and predicted GPP is much smaller using the uWUE for the
same period.
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Journal of Geophysical Research: Biogeosciences
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Table 5. Prediction Performances of the Daily GPP Derived From the Yearly uWUE and IWUE Using Equations (21)
a
and (22)
uWUE
IWUE
Site Years
B (%)
RMSE
r
Ec
B (%)
RMSE
r
Ec
26
31
23
23
8
7
5
0.3
0.5
0.4
0.8
1.9
0.7
0.2
0.6
4.04
3.28
2.38
2.08
1.80
2.67
2.28
2.88
0.84
0.79
0.81
0.80
0.88
0.72
0.79
0.81
0.70
0.54
0.64
0.57
0.60
0.47
0.41
0.59
6.1
11.5
8.7
11.4
12.5
10.3
3.2
9.5
6.28
7.52
3.83
4.02
3.63
4.42
2.86
5.30
0.68
0.53
0.60
0.51
0.80
0.41
0.68
0.59
0.26
2.52
0.09
1.09
0.55
0.47
0.08
0.83
CRO
DBF
GRA
ENF
WSA
MF
CSH
Average
a
Four indicators were used, namely the bias (B), the root-mean-square error (RMSE), the correlation coefficient (r), and
the Nash-Sutcliffe coefficient of efficiency (Ec), their definitions were given in relation to equations (23) to (26).
3.5. Discussion of the Two Water Use Efficiency Formulations
r (pred. GPP versus obs. GPP) with uWUE
IWUE was proposed and has been widely used to estimate regional and continental GPP and to evaluate the
responses of terrestrial ecosystems to global change at the yearly time scale [Beer et al., 2007, 2009; Keenan
et al., 2013]. IWUE has several important advantages to support its widespread application: (1) IWUE is derived
from the physical processes of carbon and water exchanges through stomata between terrestrial ecosystems
and the atmosphere; (2) the formulation is simple with only three variables; (3) the relationship among these
variables is consistent essentially under steady environmental conditions, and the relationship can respond
adaptively to a changing environment; (4) these variables, namely GPP, ET, and VPD, can be easily
observed by eddy covariance technique and meteorological instruments at a local scale, and estimated by
remote sensing techniques at a regional or global scale; and (5) the formulation could be upscaled to
larger time and spatial scales for widespread application. Comparing to IWUE, uWUE developed by Zhou
et al. [2014] presents a much stronger relationship among GPP, ET, and VPD at both half-hourly and daily
time scales, and is much less variable within a year, in addition to having the same five advantages
mentioned above. As such, daily uWUE is much more consistent with the yearly uWUE and is a superior
measure of water use efficiency. uWUE
1
could be readily adapted for global
change research, such as terrestrial
carbon and water cycles in a changing
0.8
environment. As a key component of the
terrestrial carbon balance, GPP plays an
important role in ecosystem services and
0.6
carbon sequestration. The improvement
CRO
in the accuracy of predicted GPP at the
DBF
daily time scale would make it possible to
0.4
GRA
predict daily GPP at a regional or global
scale combining the eddy covariance
ENF
technique with remote sensing products,
WSA
0.2
and these will contribute a great deal
MF
to the understanding and modeling of
CSH
global carbon cycle processes.
0
0
-0.2
0.2
0.4
0.6
0.8
1
-0.2
r (pred. GPP versus obs. GPP) with IWUE
Figure 8. A comparison of the correlation coefficient of predicted
versus observed daily GPP using the yearly IWUE and uWUE for the
seven vegetation types and the 123 site years.
ZHOU ET AL.
DAILY UNDERLYING WUE
There were several sources of uncertainties
in the analysis using the AmeriFlux data,
such as the effect of interception and soil
evaporation on ET and the effect of
predicted ecosystem respiration on GPP.
This analysis was focused on the growth
season with relatively high ET and GPP to
899
30
GPP (g C·m2·day-1)
(a)
24
10.1002/2015JG002947
Observed GPP
Predicted GPP
Yearly uWUE
Daily uWUE
25
20
18
15
12
10
6
5
0
70
100
130
160
190
220
250
uWUE(g C·hPa0.5/kg H2O)
Journal of Geophysical Research: Biogeosciences
0
280
Julian day
GPP (g C·m2·day-1)
(b)
24
Observed GPP
Predicted GPP
Yearly IWUE
Daily IWUE
100
80
18
60
12
40
6
20
0
70
100
130
160
190
220
250
IWUE(g C·hPa/kg H2O)
30
0
280
Julian day
0.5
Figure 9. The observed and predicted daily GPP using (a) yearly uWUE (8.92 g C hPa /kg H2O) and (b) yearly IWUE
(36.12 gC hPa/kg H2O) for station US-Goo (GRA) in 2006. Daily and yearly uWUE and IWUE are shown as dashed lines.
reduce these uncertainties. Data on the rainy days and some days following the rainy days were excluded to
avoid the effect of wet surface evaporation on ET. Cross-site evaluation of GPP and ecosystem respiration
showed that GPP uncertainty was low (less than 10%) based on the flux-partitioning method [Desai et al.,
2008], and the AmeriFlux data were processed using the standard data processing procedure which would
have constrained the expected uncertainty for GPP estimates. Moreover, all the analysis and comparison
between IWUE and uWUE were undertaken using the same data sets with the same amount of uncertainties
associated with the estimated ET and GPP. Thus, while uncertainties with the estimated ET and GPP no
doubt exist, their impact is likely to be negligibly small in relation to the main findings of this study, i.e., the
advantage of uWUE over IWUE.
4. Conclusions
The underlying water use efficiency was demonstrated to be superior and consistent at the daily time scale.
Detailed analysis for the seven vegetation types from 34 AmeriFlux sites shows that (1) the effective VPD
defined by equation (6) could be replaced by the daily mean VPD for water use efficiency estimation and
GPP predictions; (2) a constant exponent of 0.5 in equation (1) is nearly optimal for formulating water use
efficiency for all vegetation types both at the half-hourly and daily time scales; (3) the underlying water
use efficiency is a better approximation of the optimal water use efficiency than the inherent water use
efficiency at the daily time scale, because of the strong relationship between GPP · VPD0.5 and ET and the
quite consistent daily uWUE values within a site year; and (4) the yearly underlying water use efficiency can
be used to predict daily GPP values using daily ET and mean VPD, and the average correlation coefficient
was 0.81 and the average Nash-Sutcliffe coefficient of efficiency was 0.59. The underlying water use
efficiency could be used as an effective parameter to describe the interrelationship between the carbon and
ZHOU ET AL.
DAILY UNDERLYING WUE
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Journal of Geophysical Research: Biogeosciences
10.1002/2015JG002947
water coupling in terrestrial ecosystems, and the uWUE will contribute greatly to issues under global change,
including climate change impacts on the carbon assimilation and evapotranspiration and the ecosystem
responses to elevated atmosphere CO2 concentrations.
Acknowledgments
We acknowledge the following
AmeriFlux sites for their data records:
US-ARM, US-Bo1, US-IB1, US-Ne1,
US-Ne2, US-Ne3, US-Ha1, US-Moz,
US-UMB, US-WCr, US-Arb, US-Arc,
US-Bkg, US-FPe, US-Goo, US-IB2,
US-Var, US-Wkg, US-Wlr, CA-NS5,
CA-NS6, CA-NS7, US-Blo, US-Ho1,
US-NC1, US-NC2, US-Wi4, US-SRM,
US-Ton, US-FR2, US-Dix, US-Syv, US-KS2,
and US-Los. In addition, funding for
AmeriFlux data resources was provided
by the U.S. Department of Energy’s Office
of Science. This paper is financially
supported by the National Natural
Science Foundation of China (91125018),
National Key Science and Technology
Project Fund from the Ministry of Science
and Technology (MOST) during the
Twelfth 5 year Project (2013BAB05B03),
and the Research and Development
Special Fund for Public Welfare Industry
of the Ministry of Water Research in
China (201301081).
ZHOU ET AL.
References
Abbate, P. E., J. L. Dardanelli, M. G. Cantarero, M. Maturanoc, R. J. M. Melchiorid, and E. E. Sueroa (2004), Climatic and water availability effects
on water-use efficiency in wheat, Crop Sci., 44, 474–483.
Akihiko, I., and I. Motoko (2012), Water-use efficiency of the terrestrial biosphere: A model analysis focusing on interactions between the
global carbon and water cycles, J. Hydrometeorol., 13, 681-694, doi: doi:10.1175/JHM-D-10-05034.1.
Andreu-Hayles, L., O. Planells, E. Gutierrez, E. Muntan, G. Helle, K. J. Anchukaitis, and G. H. Schleser (2011), Long tree-ring chronologies reveal
20th century increases in water-use efficiency but no enhancement of tree growth at five Iberian pine forests, Global Change Biol., 17,
2095–2112.
Battipaglia, G., M. Saurer, P. Cherubini, C. Calfapietra, H. R. McCarthy, R. J. Norby, and M. F. Cotrufo (2013), Elevated CO2 increases tree-level
intrinsic water use efficiency: Insights from carbon and oxygen isotope analyses in tree rings across three forest FACE sites, New Phytol.,
197, 544–554, doi:10.1111/nph.12044.
Beer, C., M. Reichstein, P. Ciais, G. D. Farquhar, and D. Papale (2007), Mean annual GPP of Europe derived from its water balance, Geophys. Res.
Lett., 34, L05401, doi:10.1029/2006GL029006.
Beer, C., et al. (2009), Temporal and among-site variability of inherent water use efficiency at the ecosystem level, Global Biogeochem. Cycles,
23, GB2018, doi:10.1029/2008GB003233.
Cowan, I. R., and G. D. Farquhar (1977), Stomatal function in relation to leaf metabolism and environment: Stomatal function in the regulation
of gas exchange, Symp. Soc. Exp. Biol., 31, 471–505.
Cramer, W., et al. (2001), Global response of terrestrial ecosystem structure and function to CO2 and climate change: Results from six dynamic
global vegetation models, Global Change Biol., 7, 357–373.
Desai, A. R., et al. (2008), Cross-site evaluation of eddy covariance GPP and RE decomposition techniques, Agric. For. Meteorol., 148(6–7),
821–838.
Donatelli, M., G. Bellocchi, and L. Carlini (2006), Sharing knowledge via software components: Models on reference evapotranspiration, Eur. J.
Agron., 24, 186–192.
Guo, R., Z. Lin, X. Mo, and C. Yang (2010), Responses of crop yield and water use efficiency to climate change in the North China Plain, Agric.
Water Manage., 97, 1185–1194.
Hu, Z. M., G. R. Yu, Y. L. Fu, X. M. Sun, Y. N. Li, P. L. Shi, Y. F. Wang, and Z. M. Zheng (2008), Effects of vegetation control on ecosystem water use
efficiency within and among four grassland ecosystems in China, Global Change Biol., 14, 1609–1619, doi:10.1111/j.1365-2486.2008.01582.x.
Kauwe, M. G., et al. (2013), Forest water use and water use efficiency at elevated CO2: A model-data intercomparison at two contrasting
temperate forest FACE sites, Global Change Biol., 19, 1759–1779, doi:10.1111/gcb.12164.
Keenan, T. F., D. Y. Hollinger, G. Bohrer, D. Dragoni, J. W. Munger, H. P. Schmid, and A. D. Richardson (2013), Increase in forest water-use
efficiency as atmospheric carbon dioxide concentrations rise, Nature, 499, 324–327, doi:10.1038/nature12291.
Lévesque, M., R. Siegwolf, M. Saurer, B. Eilmann, and A. Rigling (2014), Increased water-use efficiency does not lead to enhanced tree growth
under xeric and mesic conditions, New Phytol., 203, 94–109.
13
Lloyd, J., and G. D. Farquhar (1994), C discrimination during CO2 assimilation by the terrestrial biosphere, Oecologia, 99, 201–215.
Mahecha, M. D., M. Reichstein, H. Lange, N. Carvalhais, C. Bernhofer, T. Grünwald, D. Papale, and G. Seufert (2007), Characterizing ecosystematmosphere interactions from short to interannual time scales, Biogeosciences, 4, 743–758.
Mo, X., S. Liu, Z. Lin, Y. Xu, Y. Xiang, and T. R. McVicar (2005), Prediction of crop yield, water consumption and water use efficiency with a SVATcrop growth model using remotely sensed data on the North China Plain, Ecol. Modell., 183, 301–322.
Nash, J. E., and J. V. Sutcliffe (1970), River flow forecasting through conceptual models, Part 1: A discussion of principles, J. Hydrol., 10,
282–290.
Niu, S., X. R. Xing, Z. Zhang, J. Y. Xia, X. H. Zhou, B. Song, L. H. Li, and S. Q. Wan (2011), Water-use efficiency in response to climate change:
From leaf to ecosystem in a temperate steppe, Global Change Biol., 17, 1073–1082, doi:10.1111/j.1365-2486.2010.02280.x.
Nock, C. A., P. J. Baker, W. Wanek, A. Leis, M. Grabner, S. Bunyavejchewin, and P. Hietz (2011), Long-term increases in intrinsic water-use
efficiency do not lead to increased stem growth in a tropical monsoon forest in western Thailand, Global Change Biol., 17, 1049–1063.
O’Grady, A. P., D. Worledge, and M. Battaglia (2008), Constraints on transpiration of Eucalyptus globulus in southern Tasmania, Australia,
Agric. For. Meteorol., 148, 453–465.
Papale, D., and R. Valentini (2003), A new assessment of European forests carbon exchanges by eddy fluxes and artificial neural network
spatialization, Global Change Biol., 9, 525–535.
13
Peñuelas, J., J. M. Hunt, R. Ogaya, and A. S. Jump (2008), Twentieth century changes of tree-ring δ C at the southern range-edge of Fagus
sylvatica: Increasing water-use efficiency does not avoid the growth decline induced by warming at low altitudes, Global Change Biol., 14,
1076–1088, doi:10.1111/j.1365-2486.2008.01563.x.
Peñuelas, J., J. G. Canadell, and R. Ogaya (2011), Increased water-use efficiency during the 20th century did not translate into enhanced tree
growth, Global Change Biol., 20, 597–608.
Pita, G., B. Gielen, D. Zona, A. Rodrigues, S. Rambal, I. A. Janssens, and R. Ceulemans (2013), Carbon and water vapor fluxes over four forests in
two contrasting climatic zones, Agric. For. Meteorol., 180, 211–224.
Priestley, G. H. B., and R. J. Taylor (1972), On the assessment of surface heat flux and evaporation using large-scale parameters, Mon. Weather
Rev., 100, 81-92, doi: doi:10.1175/1520-0493(1972)100<0081:OTAOSH>2.3.CO;2.
Reichstein, M., et al. (2005), On the separation of net ecosystem exchange into assimilation and ecosystem respiration: Review and improved
algorithm, Global Change Biol., 11, 1424–1439, doi:10.1111/j.1365-2486.2005.001002.x.
Tian, H., et al. (2010), Model estimates of net primary productivity, evapotranspiration, and water use efficiency in the terrestrial ecosystems
of the southern United States during 1895–2007, For. Ecol. Manage., 259, 1311–1327, doi:10.1016/j.foreco.2009.10.009.
Xu, Y., W. Li, X. Shao, Z. Xu, and P. Nugroho (2014), Long-term trends in intrinsic water-use efficiency and growth of subtropical Pinus
tabulaeformis Carr. and Pinus taiwanensis Hayata in central China, J. Soils Sediments, 14, 917–927.
Yang, Y. T., D. Long, and S. H. Shang (2013), Remote estimation of terrestrial evapotranspiration without using meteorological data, Geophys.
Res. Lett., 40, 3026–3030, doi:10.1002/grl.50450.
DAILY UNDERLYING WUE
901
Journal of Geophysical Research: Biogeosciences
10.1002/2015JG002947
Zhang, Q., S. Manzoni, G. Katul, A. Porporato, and D. Yang (2014), The hysteretic evapotranspiration-vapor pressure deficit relation,
J. Geophys. Res. Biogeosci., 119, 125–140, doi:10.1002/2013JG002484.
Zhao, L., Y. N. Li, S. Gu, X. Q. Zhao, S. X. Xu, and G. R. Yu (2005), Carbon dioxide exchange between the atmosphere and an alpine shrubland
meadow during the growing season on the Qinghai-Tibetan Plateau, J. Integr. Plant Biol., 47, 271–282, doi:10.1111/j.1744-7909.2005.00066.x.
Zhou, S., B. Yu, Y. Huang, and G. Wang (2014), The effect of vapor pressure deficit on water use efficiency at the subdaily time scale, Geophys.
Res. Lett., 41, 5005–5013, doi:10.1002/2014GL60741.
Zhu, Q., H. Jiang, C. Peng, J. Liu, X. Wei, X. Fang, S. Liu, G. Zhou, and S. Yu (2011), Evaluating the effects of future climate change and elevated
CO2 on the water use efficiency in terrestrial ecosystems of China, Ecol. Modell., 222, 2414–2429.
ZHOU ET AL.
DAILY UNDERLYING WUE
902