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1 2 3 4 Tropospheric ozone reduces carbon assimilation in trees: estimates from analysis of continuous flux measurements 5 6 SILVANO FARES1*, RODRIGO VARGAS2, MATTEO DETTO3, ALLEN H. GOLDSTEIN4, JOHN KARLIK5, ELENA PAOLETTI6, MARCELLO VITALE7. 7 8 9 10 11 12 13 14 15 16 17 18 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). 19 Supporting information 20 21 22 Material and Methods 23 24 25 26 27 28 29 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: 30 31 32 33 34 35 36 37 38 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 39 40 41 42 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). 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 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). 66 67 68 69 70 71 72 73 74 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): 75 Y = b0 + b1P + b2P2 + b3Q + b4Q2 + b5R + b6R2 + b7P×Q + b8P×R + b9Q×R 76 77 78 79 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 80 81 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. 82 83 84 85 86 87 88 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. 89 90 91 92 93 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 94 Yt j 1 c j X t j j 1 d jYt j t (3) 95 where and are white noise prediction errors with covariance matrix 96 2 cov( , ) xx cov( , ) 2 yx 97 98 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 99 X t j 1 q j X t j t , and when the multivariate model outperforms the univariate case, (e.g. xy , yy (4) 100 2 2 ), Y is said to have a causal effect on X (and similarly for the effect of X on Y). 101 102 103 104 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 105 2 . 2 (5) 106 If the variables X and Y do not interact, there will be no improvement in using Y to predict X, i.e. 107 2 and GY X 0 , even if the two variables are correlated. If otherwise Y has a causal 108 influence on X, 2 2 so GY X 0 . 109 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(): 110 2 3 X ( ) H xx ( ) H xy ( ) Ex ( ) Y ( ) H yx ( ) H yy ( ) E y ( ) 111 112 113 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*() 114 115 118 119 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 120 121 (7) where * is the adjoint operator. The spectral Granger causality is defined as: 116 117 (6) 0 1 122 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 123 G( )Y X 0 . 124 125 126 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 127 we define the following spectral matrices: S( X , Y , Z3 ,..., Z k , ) H( ) H* ( ) 128 129 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 130 131 132 (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 P1-1 133 134 G = G P2-1 and P1 and P2 are the transformation matrix needed to make all noisy terms independent. 135 136 137 Tables 138 [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] 139 140 141 142 143 144 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 167 168 169 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. 170 171 172 Cieslik, SA (2004) Ozone uptake by various surface types: a comparison between dose and exposure. 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