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Tropospheric ozone reduces carbon assimilation in trees: estimates from
analysis of continuous flux measurements
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SILVANO FARES1*, RODRIGO VARGAS2, MATTEO DETTO3, ALLEN H. GOLDSTEIN4,
JOHN KARLIK5, ELENA PAOLETTI6, MARCELLO VITALE7.
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1
Consiglio per la Ricerca e la sperimentazione in Agricoltura (CRA)- Research Centre for the Soil-Plant System, Rome,
Italy.
2
Department of Plant and Soil Sciences, Delaware Environmental Institute. University of Delaware, Newark, USA.
3
Smithsonian Tropical Research Institute, CTFS, USA.
4
Department of Environmental Science, Policy, and Management, University of California, Berkeley, USA.
5
University of California Cooperative Extension, Davis, United States.
6
National Research Council, Institute for Plant Protection, Firenze, Italy.
7
Department of Environmental Biology, “Sapienza” University of Rome, Rome, Italy.
*Corresponding author. Consiglio per la ricerca e la sperimentazione in agricoltura (CRA), Research Centre for the
Soil-Plant System, Via della Navicella, 2-4 00184 Rome, Italy. Tel.: +39 06 7005413 127. E-mail address:
silvano.fares@entecra.it (S. Fares).
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Supporting information
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Material and Methods
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Gas exchange measurements. For the Blogett and Castelporziano forests, in order to calculate
stomatal conductance to ozone (Gsto), we used measurements of latent heat flux (ET) to calculate its
resistance inverse (Rsto) using the Monteith equation. For Lindcove orchard, instead of ET, we used
canopy transpiration measured with sap flow sensors as described by Fares et al. (2012). The
inversion of Monteith equation is also called the Evaporative-Resistance method (Monteith and
Unsworth, 1990), and is commonly used in multiple studies (Kurpius and Goldstein 2003; Cieslik
2004; Gerosa et al. 2005; Fares et al. 2010, 2012). The calculation is:
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Rsto 
cp    VPD
 ( Ra  Rb )
    EL
(1)
where λ is the latent heat of vaporization in air (J kg-1), γ is the psychrometric constant (0.065 kPa
K-1), EL is the transpiration rate (kg H2O m-2 s-1), cp is the specific heat of air (J kg-1 K-1), ρ (kg m3
) is the density of dry air measured from a relative humidity and temperature sensor placed at
canopy level, VPD is the vapor pressure deficit at leaf level using leaf temperature (kPa), Ra and Rb
are aerodynamic and sublayer resistances for water vapor as calculated in Fares et al. (2010b).
Since soil evaporation can significantly contribute to water fluxes, in order to minimize soil
evaporation effect on total evapotranspiration (and therefore overestimation of Gsto), we did not use
measurements for three days after precipitation for the Blodgett and Castelporziano forests.
1
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Canopy-level stomatal conductance to ozone, hereon called also stomatal ozone deposition (GO3)
was calculated correcting Gsto for the difference in diffusivity between ozone and water vapor
(Massman, 1998).
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Random Forest Analysis (RFA). Random Forest module is a complete implementation of the RF
algorithm (Breiman, 2001). This technique can be used for regression-type problems (to predict a
continuous dependent variable) as well as classification problems (to predict a categorical
dependent variable). A RF consists of a collection (ensemble) of simple tree predictors, each
capable of producing a response when presented with a set of predictor values. For regression
problems, RFs are formed by growing simple trees, each capable of producing a numerical response
value. Here, too, the predictor set is randomly selected from the same distribution and for all trees.
For each tree, a different training set is created by randomly sampling samples from the data set
with replacement resulting in a training set, or ‘bootstrap’ set, containing about two-third of the
samples in the original data set. Trees are grown using binary partitioning (each parent node is split
into no more than two child nodes). During the building of each tree, for each split (that is for each
node), predictor statistics (i.e., sums of squares regression, since simple regression trees are built in
all cases) are computed for each predictor variable; the best predictor variable will then be chosen
for the actual split. The program also computes the average of the predictor statistics for all
variables over all splits and over all trees. The final predictor importance values are computed by
normalizing those averages so that the highest average is assigned the value of 1, and the
importance of all other predictors is expressed in terms of the relative magnitudes of the average
values of the predictor statistics, relative to the most important predictor. The advantages of the
approach used here is that it helps identify variables that may contain important predictive power
with respect to the outcome of interest. For this analysis, we used the same predictors at the same
time resolution used for the GRM analysis. All analyses were performed by STATISTICA 8.0
(StatSoft Inc., Tulsa, OK – USA).
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General Regression Model. Non-linear statistical models were generated through the application of
GRM based on the Response Surface Regression. Under this condition, the quadratic response
surface regression designs were a hybrid type of design with characteristics of both polynomial
regression designs and fractional factorial-regression designs. Quadratic response surface regression
designs contained all the same effects of polynomial regression designs to degree 2 and additionally
the 2-way interaction (i.e., combination) effects of the predictor variables. The regression equation
for a quadratic response surface regression design for three continuous predictor variables P, Q, and
R is (equation 2):
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Y = b0 + b1P + b2P2 + b3Q + b4Q2 + b5R + b6R2 + b7P×Q + b8P×R + b9Q×R
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The overall linear combinations of predictors allowed enhancing the predictive capacity of the
statistical model. The predictors among the four case studies here investigated were: PAR (umol m 2 -1
s ), air temperature (Ta, oC), Vapour Pressure Deficit (VPD, kPa), soil moisture (%), canopy
transpiration (ET, mmol m-2s-1), and stomatal ozone deposition (GO3, m s-1). Data averaged for 30-
(2)
2
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min time resolution were used in the model. The model was designed with 70% of the dataset and
then cross-validated with the remaining 30% of the data.
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Granger causality. The existence of correlation itself does not necessarily entail causation as
implied by an action and a subsequent reaction. G-causality explains phenomena by showing them
to be due to effects originating from prior causes in time as a signal processing technique. When
these prior causes are accounted for, predictions of the phenomenon are improved against a null
hypothesis that does not account for these prior causes. This is the statistical interpretation of
causality proposed by Granger (1969) and is commonly referred to as Granger or G-causality.
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This causality metric originated in econometrics but is now proliferating to a number of disciplines
including ecology (Detto et al., 2012).
In brief, let consider two discrete time random variables X and Y that admit autoregressive
representation in the form:
X t   j 1 a j X t  j   j 1 b jYt  j   t

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
Yt   j 1 c j X t  j   j 1 d jYt  j  t


(3)
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where  and  are white noise prediction errors with covariance matrix
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  2
cov( ,  )    xx


 cov( ,  )
 2    yx

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while a, b, c and d are coefficients describing the linear interactions between the variables, with
subscript j indicating time lags. When the above equation is compared with a univariate model
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X t   j 1 q j X t  j  t , and when the multivariate model outperforms the univariate case, (e.g.
 xy 
,
 yy 
(4)

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 2  2 ), Y is said to have a causal effect on X (and similarly for the effect of X on Y).
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G-causality is a measure of coupling with time directionality being explicit. For this reason, it is
based on prediction errors rather than on linear interactions among coefficients. Traditionally, it is
expressed as the ratio between the residual variance of the bivariate and the null model (i.e. the
univariate case) and is given as:
GY  X  ln
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 2
.
 2
(5)
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If the variables X and Y do not interact, there will be no improvement in using Y to predict X, i.e.
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   2 and GY  X  0 , even if the two variables are correlated. If otherwise Y has a causal
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influence on X,  2  2 so GY  X  0 .
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The spectral formulation of G-causality begins by applying a Fourier transform to both sides of Eq.
(6) and recasting the equations using the transfer function H():
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2
3
 X ( )   H xx ( ) H xy ( )  Ex ( ) 




 Y ( )   H yx ( ) H yy ( )  E y ( ) 
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From this representation it follows that the spectral matrix (the matrix of spectra and cospectra of X
and Y) is equal to:
S() = H()  H*()
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

S xx ( )
G( )Y  X  ln 

*
 H xx ( ) xx H xx ( ) 
(8)
where H( )  H( ) P-1 is the corrected transfer function matrix that separates the pure directional
interactions (Geweke, 1982). The rotation matrix P is a normalization matrix needed to recasts Eq.
(3) in the canonical form (with uncorrelated errors), that is:
1

P
  xy /  xx
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(7)
where * is the adjoint operator. The spectral Granger causality is defined as:
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(6)
0

1
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As in Eq. (5), if the variables X and Y are not interacting, the numerator and denominator of Eq. (8)
are equal and G( )Y  X  0 . If Y manifests a causal influence on X at a specific frequency  then
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G( )Y  X  0 .
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The adopted scheme can be extended to the multivariate case, which now involves k stochastic
variables (X, Y, Z3, …, Zk). In this extension, it becomes possible to compute the so-called
conditional G-causality G ( )Y  X |Z1 ,...,Z k , i.e. Y causes X, given that Z3, …, Zk cause X or Y. As above
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we define the following spectral matrices:
S( X , Y , Z3 ,..., Z k ,  )  H( )  H* ( )
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S( X , Z3 ,..., Z k ,  )  G( )  G* ( )
the conditional G-causality of Y on X given Z3, Z4, …, Zk is computed as (Chen et al., 2006):
G ( ) y  x| z3 ,..., zk  ln
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(9)
 xx
Q xx ( ) xx Q*xx ( )
(10)
where
 G XX

 0
Q=  G 31

 ...

 G k1
0
G XZ1
1
0
...
0
G 33
...
0
G k3
... G1k 

... 0 
... G 3k 

... ... 

... G kk 
-1
 H11

 H 21
 ...

 ...
H
 k1
H12
...
...
...
H k2
... ... H1k 

... ... ... 
... ... ...  ,

... ... ... 
... ... H kk 
4
H = H P1-1
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G = G P2-1
and P1 and P2 are the transformation matrix needed to make all noisy terms independent.
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Tables
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[O3]
Year
R2
p-value
Slope
Low [<50ppb]
2001
0.1
<0.001
0.25
2002
0.1
0.003
0.27
2003
0.05
0.04
0.2
2004
n.s.
0.145
n.s.
2005
0.06
0.006
0.16
2006
0.3
<0.001
0.35
2007
0.2
<0.001
0.29
2001
n.s.
0.135
n.s.
2002
0.13
<0.001
0.13
2003
0.32
<0.001
0.2
2004
0.1
<0.001
0.19
2005
0.1
<0.001
0.08
2006
0.22
<0.001
0.17
2007
0.41
<0.001
0.2
2001
n.s.
0.145
n.s.
2002
0.2
<0.001
0.2
2003
0.4
<0.001
0.12
2004
0.17
0.018
0.2
2005
n.s.
0.885
n.s.
2006
0.35
<0.001
0.54
2007
n.s.
0.714
n.s.
Medium [>50 & <75 ppb]
High [>75 ppb]
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141
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143
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Table S1. Results from regression analysis of residuals of gross primary productivity (residuals
GPP) and stomata ozone deposition (residuals GO3) divided by year of measurements in Blodgett
(2001-2007) for grouped episodes of atmospheric ozone concentrations. Data for this regression
analysis are shown in Figure S2. n.s. = not significant.
case 1
Predictors
Blodgett
Lindcove
case 2
CPZ
Blodgett
Lindcove
case 3
CPZ
Blodgett
Lindcove
case 4
CPZ
Blodgett
Lindcove
CPZ
5
Soil moisture
-24.09
13.49
-3.06
n.s.
42.07
n.s.
n.s.
41.85
-2.40
-25.51
44.59
n.s.
Soil moisture^2
53.77
n.s.
0.09
40.87
-55.83
n.s.
29.39
-45.49
0.07
61.68
-62.22
n.s.
PAR
-0.01
0.00
0.00
n.s.
0.00
n.s.
-0.01
0.00
n.s.
-0.01
-0.01
n.s.
PAR^2
0.00
0.00
0.00
n.s.
0.00
n.s.
0.00
0.00
0.00
n.s.
0.00
n.s.
Ta
1.12
n.s.
-0.54
3.63
n.s.
n.s.
0.50
n.s.
-0.29
0.51
-0.12
n.s.
Ta^2
0.05
n.s.
0.01
0.17
n.s.
0.01
0.04
0.01
0.01
0.03
n.s.
0.00
VPD
-0.05
-1.00
n.s.
-0.09
n.s.
n.s.
-0.03
n.s.
n.s.
-0.03
3.18
n.s.
VPD^2
n.s.
-0.32
n.s.
0.00
-0.39
n.s.
0.00
n.s.
n.s.
0.00
-0.25
n.s.
ET
-
-
-
n.s.
-1.50
-5.04
n.s.
-1.80
-4.93
n.s.
-3.80
n.s.
ET^2
-
-
-
-0.12
-0.26
0.21
n.s.
-0.26
n.s.
-0.10
n.s.
n.s.
[O3]
-
-
-
-
-
-
0.06
0.03
n.s.
-
-
-
[O3]^2
-
-
-
-
-
-
0.00
n.s.
n.s.
-
-
-
GO3
-
-
-
-
-
-
-
-
-
n.s.
1067.10
-1959.10
GO3^2
-
-
-
-
-
-
-
-
-
-
n.s.
n.s.
Soil moisture*PAR
0.00
-
n.s.
n.s.
n.s.
0.00
n.s.
0.00
0.00
n.s.
n.s.
0.00
Soil moisture*Ta
2.12
-0.58
n.s.
-0.93
-0.47
-0.02
1.03
-0.92
n.s.
0.90
n.s.
n.s.
PAR*Ta
0.00
n.s.
n.s.
0.00
n.s.
n.s.
0.00
n.s.
n.s.
0.00
0.00
n.s.
Soil moist. *[O3]
-
-
-
-
-
-
-0.17
n.s.
0.00
-
-
-
PAR*[O3]
-
-
-
-
-
-
n.s.
n.s.
0.00
-
-
-
Tair*[O3]
-
-
-
-
-
-
n.s.
n.s.
n.s.
-
-
-
Soil moist.*ET
-
-
-
n.s.
n.s.
0.15
n.s.
n.s.
0.15
n.s.
n.s.
n.s.
PAR*ET
-
-
-
0.00
n.s.
0.00
0.00
n.s.
0.00
0.00
0.00
0.00
Tair*ET
-
-
-
-0.09
0.05
n.s.
-0.09
0.06
n.s.
0.08
0.12
0.50
[O3]*ET
-
-
-
-
-
-
-0.01
n.s.
0.05
-
-
-
Soil moist.*VPD
-0.01
n.s.
n.s.
0.01
n.s.
n.s.
-0.01
1.28
n.s.
n.s.
-3.85
n.s.
PAR*VPD
0.00
n.s.
n.s.
n.s.
n.s.
n.s.
0.00
n.s.
n.s.
0.00
0.00
n.s.
Ta*VPD
0.00
0.10
n.s.
n.s.
0.08
n.s.
0.00
n.s.
n.s.
0.00
n.s.
n.s.
[O3]*VPD
-
-
-
-
-
-
n.s.
-0.01
n.s.
-
-
-
ET*VPD
-
-
-
n.s.
n.s.
n.s.
n.s.
n.s.
n.s.
0.00
n.s.
n.s.
Soil moist.*GO3
-
-
-
-
-
-
-
-
-
n.s.
n.s.
n.s.
PAR*GO3
-
-
-
-
-
-
-
-
-
n.s.
0.47
n.s.
Ta*GO3
-
-
-
-
-
-
-
-
-
n.s.
-56.50
n.s.
ET*GO3
-
-
-
-
-
-
-
-
-
128.62
n.s.
-358.20
VPD*GO3
-
-
-
-
-
-
-
-
-
n.s.
n.s.
n.s.
R2
0.58
0.19
0.37
0.51
0.27
0.34
0.64
0.27
0.40
0.61
0.28
0.36
slope
0.88
0.74
0.82
0.85
0.77
0.81
0.91
0.77
0.82
0.91
0.81
0.82
34179.00
4336.00
1349.00
19591.00
4333.00
1348.00
20251.00
4325.00
1343.00
16938.00
2927.00
13340.00
3306.72
154.70
134.10
1046.00
158.30
101.00
1317.37
124.00
76.30
992.15
70.64
109.00
Statistics
df
F
145
146
147
148
Table S2. Predictor's coefficients (beta) from the non-linear GRM model applied to the four case
studies in the three ecosystems: Blodgett pine forest, Lindcove orange plantation, and
Castelporziano mixed forest. Predictors in the model are evapotranspiration (ET), Photosynthetic
6
149
150
151
Active Radiation (PAR), Soil Moisture, Vapor Pressure Deficit (VPD), temperature of the air (Ta),
ozone concentration ([O3]), and stomatal ozone deposition (GO3). n.s.= not significant.
152
Figures
153
154
155
156
157
158
Figure S1: Wavelet coherence analysis to look the temporal correlations between the residuals of
gross primary productivity (GPP) and stomatal ozone deposition for the Blodgett site. The colors
for power values are from blue (low temporal correlations with GPP) to red (high temporal
correlations with GPP).
7
159
160
161
162
163
164
Figure S2: For each year in Blodgett site, relationship between the residuals of GPP at the 1-day
time period and the residuals of stomatal ozone deposition (GO3) at the 1-day time period for
grouped episodes of atmospheric ground-level ozone concentration: low (<50 ppb), medium (>50
and <75 ppb) and high (>75 ppb).
165
166
References not listed in the main paper
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168
169
Chen YH, Bressler, SL et al. (2006) Frequency decomposition of conditional Granger causality and
application to multivariate neural field potential data. Journal of Neuroscience Methods, 150, 228237.
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172
Cieslik, SA (2004) Ozone uptake by various surface types: a comparison between dose and
exposure. Atmospheric Environment, 38, 2409-2420.
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Gerosa G, Vitale M, Finco A, Manes F, Denti A, Cieslik S (2005) Ozone uptake by an evergreen
Mediterranean Forest in Italy. Part I: Micrometeorological flux measurements and flux partitioning.
Atmospheric Environment, 39, 3255–3266.
Geweke J (1982) Measurement of Linear-Dependence and Feedback between Multiple TimeSeries. Journal of the American Statistical Association 77, 304-313.
Kurpius MR, Goldstein AH (2003) Gas-phase chemistry dominates O 3 loss to a forest, implying a
source of aerosols and hydroxyl radicals to the atmosphere. Geophysical Research Letters, 30, 2-5.
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Arnold, E., New York, USA, 291 pp.
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