Performance of eddy-covariance measurements in fetch-limited applications

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Performance of eddy-covariance measurements in fetch-limited applications Nicolini G. a,b,*, Fratini G. c, Avilov V. d, Kurbatova J.A. d, Vasenev I. e, Valentini R.

1 Performance of eddy-covariance measurements in fetch-limited applications Nicolini G. a,b,*, Fratini G. c, Avilov V. d, Kurbatova J.A. d, Vasenev I. e, Valentini R. a,b a University of Tuscia, DIBAF, Viterbo, Italy b Euro-Mediterranean Center on Climate Change, IAFENT Division, Viterbo, Italy c LI-COR Biosciences Inc., Lincoln, NE, USA d Russian Academy of Sciences, Moscow, Russia e K.A. Timiryazev Russian State Agrarian University - MTAA, Moscow, Russian Federation * Corresponding author: CMCC Euro Mediterranean Centre on Climate Change, IAFENT Impacts on Agriculture, Forest, and Natural Ecosystems Division. Via A. Pacinotti 5, I Viterbo, Italy. Phone: giacomo.nicolini@cmcc.it SUPPLEMENTARY INFORMATIONS Experiment set-up The experiment was carried out at the K.A. Timiryazev Russian State Agrarian University (MTAA, Moscow) experimental crop fields (55 50'12.87" N; 37 33'48.71" E; 160 m a.s.l.) from July 31 to August 4, Figure S1 shows (a) a landscape view of the field, (b) a close-up of the measuring system and (c) the positioning of the release line (50 m) on the canopy top. The field was cultivated with potatoes (Solanum tuberosum) that, during the experiment period, were at the end of the cultural cycle. In the rightmost picture (c), the ploughing ripples characterizing the surface and its anisotropy in roughness properties are also visible. The two identical EC systems, superimposed on the mast, were composed of a CSAT-3 sonic anemometer (Campbell Scientific Inc., Logan, UA, USA) and a LI-7200 enclosedpath gas analyser (LI-COR Biosciences Inc., Lincoln, NE, USA). The gas inlet was placed 0.18 m apart from the anemometer and the systems were spaced by 0.60 m. Pure CO 2 was released at a steady rate from the source line (polyurethane tube, internal diameter of 4.0 mm) through 10 equidistant orifices of 1.0 mm (interspaced by 5 m). The flow rate was kept stable ensuring a constant line pressure (at 0.3 MPa). Monitored with a flow-meter at the beginning and at the end of each sampling, it exhibited an average a b c Fig. S1 Timiryazev Russian State Agrarian University experimental crop fields and experiment set-up

variation of 0.5-1.2% between the releasing orifices as it can be seen in Fig. S2. Each bar is the average flow in the source line (of the 10 orifices) and the error bars are the standard deviations.

manuscript we summarize mean atmospheric conditions during the experiment in Table 1. In Fig.

Statistics are referred to the 6 minutes runs. The conditions during the two runs used in the original manuscript as exemplary comparison of experimental and modeled footprint (Fig.

2 variation of % between the releasing orifices as it can be seen in Fig. S2. Each bar is the average flow in the source line (of the 10 orifices) and the error bars are the standard deviations. Fig S2 Comparison of tracer flow measurements between each source orifices at the beginning and end of each sampling Variability of atmospheric conditions during the releases In the original manuscript we summarize mean atmospheric conditions during the experiment in Table 1. In Fig. S4 we report an overview of the distribution of meteorological and turbulence variables throughout the experiment as measured by the HI (blue) and LO (red) systems. Statistics are referred to the 6 minutes runs. The conditions during the two runs used in the original manuscript as exemplary comparison of experimental and modeled footprint (Fig. 4) are highlighted with a grey shadowing.. Fig S3 Schematic representation of the release timeline and meaning of some terms used in the manuscript Release design The tracer was progressively released from 6 distances upwind from the EC mast (Fig S3). Each release, from each distance, lasted 15 min but was effectively sampled for 12 min (first 3 min to allow the tracer plume to fully develop). A series of six releases is named run. We determined 6 min to be the optimal flux averaging period (see original manuscript) thus we split each release into 2 sub-periods. Finally, we used such 6 min runs (i.e. a set of 6 flux values averaged over 6 minutes, N=12) for the analysis. Stationarity during the tracer releases We only selected runs, for which stationary conditions held. We evaluated it by means of the Foken s stationarity test (e.g. Foken et al. 2004), applied to the whole runs. Fig. S5 shows the results of this test for all runs. The deviation from perfect stationarity is virtually always well below the 30% threshold which Foken and co-authors set as the maximum for the definition of highquality data, suitable for fundamental research.

3 Fig S4 Distribution of meteorological and turbulence variables throughout the experiment as measured by the HI (in blue) and LO (in red) systems. Note that wind directions are in the range of Each couple refers to the 6 minutes runs, sub-period of a 12 minutes run Fig S5 Results of the steady state test for all runs, made on the covariances of vertical wind speed (w) and horizontal wind speed (w/u), sonic temperature (w/ts) and CO 2 (w/co 2 )

4 Comparison of flux measurements The short vertical distance between the two systems (e.g. 60 cm between the centers of the anemometers measurement volumes) may raise concerns of potential cross-interference. It is worth nothing that such distance is larger than the typical horizontal displacement of e.g. open-path instruments and anemometers in eddy covariance setups (i.e cm). Considering that instantaneous vertical wind components are typically much smaller than horizontal wind components (and tend to average to zero over minutes-scale periods), we do not suspected a significant mutual interference between the systems. This a priori assumption was substantiated by the analysis of sensible heat (H, W m -2 ) and latent heat (LE, W m -2 ) fluxes for 10 days before and during the experiment, as well as of CO 2 fluxes (μmol m -2 s -1 ) before the experiment (Fig. S6). If any significant mutual interference existed we would expect it to have opposite effects on the measurement of e.g. the vertical wind component between both anemometers, and lead to a significant systematic flux divergence. However, the plot shows that systematic and random differences were as low as 1-3%, well within the overall uncertainty of the EC method itself (see, e.g., Finkelstein and Sims 2001; Billesbach 2011; Mauder et al. 2013). We could thus conclude that, if any interference existed at all, main results have not been significantly affected. To further test the agreement between the systems and evaluate the uncertainty related to surrounding surface heterogeneities, we compared the daily courses of CO 2 fluxes (notracer) during 10 days before the experiment. Assuming the vegetation within the footprints of both levels to be the same, the measurements of natural CO 2 fluxes should be very similar. Fig. S6 Comparison of sensible heat (H), latent heat (LE) and no-tracer CO 2 fluxes before and during the experiment

x p = u(z d) 2ku (Eq. S2) where k is the von Karman constant. Eq. (S1) is a 1D representation of the footprint (along the x-z plane), assuming an infinite crosswind area source.

5 x p = u(z d) 2ku (Eq. S2) where k is the von Karman constant. Eq. (S1) is a 1D representation of the footprint (along the x-z plane), assuming an infinite crosswind area source. To get a 2D representation it is possible to incorporate the cross-wind contribution into the equation, normally assumed to be Gaussian (Soegaard et al. 2003). Fig. S7 Daily courses of CO 2 fluxes (no-tracer) during 10 days before the experiment as measured by the Lo (in red) and Hi (in blue) systems As it can be seen in Fig. S7, after that QA/QC and despiking has been applied to measured fluxes, the agreement was very high, with R 2 = 0.9 (RSE = 0.55). During the hours corresponding to the experimental period (highlighted with a grey band in the figure) the average CO 2 flux was ± 0.23 μmol m -2 s -1 and ± 0.24 μmol m -2 s -1 as measured by the LO and HI systems respectively. Analytical footprint models Schuepp model (SH90) In the formulation proposed by Schuepp et al. (1990) the crosswind integrated footprint function is reported as f cwi (x, z) = 2x pφ x 2 exp ( 2x pφ ) (Eq. S1) x where x p is the distance at which the source strength has its maximum (function peak) and ϕ is the momentum correction for stability (Dyer 1963) which is expressed as ϕ = [1-16 (z-d)/l]^(-1/4) where L is the Monin- Obukhov length. The peak distance x p is computed from the mean wind speed u and the friction velocity u * Hsieh model (HS00) Hsieh et al. (2000) proposed an approximate analytical model derived from Lagrangian dispersion model results and dimensional analysis. Their footprint function has the form: f cwi (x, z) = 1 k 2 x 2 Dz u P L 1 P exp ( 1 k 2 x Dz u P L 1 P ) (Eq. S3) where D and P are similarity constants which change according to stability conditions (unstable, neutral and stable) and z u is a length scale derived from z and z 0 as z u = z[ln(z z 0 ) 1 + z 0 z]. The footprint peak location is expressed as a function of Monin- Obukhov length and z u by x p = Dz u P L 1 P 2k 2 (Eq. S4) Like SH90, Eq. (S3) can be combined with a crosswind distribution model to get a 2D footprint (Detto et al. 2006; van de Boer et al. 2013). Korman and Meixner model (KM01) The analytical model proposed by Kormann and Meixner (2001) results from an enhancement of the more general solution of the diffusion equation (e.g. van Ulden, 1978). It allows to account for thermal stability by

6 using power laws for the wind velocity (u) and the eddy diffusivity (K). Their crosswind integrated footprint function takes the form: f(x, z) = 1 Γ(μ) ξ μ exp ( ξ )(Eq. S5) x 1+μ x Here Γ(x) is the Gamma function, μ = (1 + m)/r with r (shape factor) related to the exponents m and n of the power laws for u and K by r = 2 + m n, and ξ(z) = Uz r /r 2 κ, a length scale related to the constants U and κ, determined by respectively fitting the u and K power laws profiles to Monin Obukhov similarity functions. The maximum of the function can be found at (peak location): x p = ξ 1+μ (Eq. S6) Combining Eq. S5 with the Gaussian crosswind distribution function (Pasquill 1974), the authors furthermore provide a 2D representation. Footprint models' performance at different averaging periods As outlined in the original manuscript, we considered different flux averaging interval. Looking for an optimal compromise between measurement reliability and numbers of replicates we performed an analysis of the ogive convergence to determinate the minimal averaging time (see Fig. 2 in the original manuscript). We found that averaging intervals shorter than 6 minutes should be ignored as significant flux contributions would be lost in many instances. We thus experimented with 2 averaging intervals, namely 6 and 12 minutes (the latter being the longest possible). In Fig. S8 we report NMSE calculated for SH90, HS00 and KM01 against experimental data for 6 and 12 minutes flux averages. Then we used an estimator of prediction accuracy, the normalized mean square error (NMSE) (Finn et al. 1996; Metzger et al. 2012) to quantify footprint models performances against observed fluxes (see next Section) at these two time scales. We found that results are not statistically different between NMSE calculated at 6 and 12 minutes averaging intervals (Wilcoxon rank sum test, α = 0.05). In Fig. S9 and S10 we report models' performance at different averaging period. In particular, on the left of each figure there are the modeled and experimental crosswind integrated footprint comparison considering 12 minutes averages, while on the right the corresponding estimations for 6 minutes averages. 12 minutes data reported in the Fig S8 Comparison of 12' and 6' flux averages normalized mean square error (NMSE) calculated for SH90, HS00 and KM01 over the whole footprints' extension

7 original manuscript came from the averaging of the two 6 minutes sub-periods. Their difference with the genuine 12 minutes fluxes was not significant. Footprint models' performance evaluation We used the experimental footprint contributions (f exp ) as reference to evaluate models predictions, and quantify model performances by means of median absolute deviation (MAD) and normalized mean squared error (NMSE) estimators. MAD is sensitive to the error distribution while is not affected by outliers and sample size and indicated how close predictions are to the observations, NMSE is an estimator of the overall deviations between predicted and measured values (residuals). It is more sensitive to largest deviations in the dataset yet it is not biased towards over or under predictions. We firstly verified if there was a statically significant difference between different models' predictions by analysing the residuals around the peak and the tail of the footprint separately (Wilcoxon rank sum test, α = 0.05). Then, according to Metzger et al. (2012) we evaluated the models' prediction accuracy by considering different sections of the footprint separately. In particular we evaluated NMSE around the peak and MAD at the tail. For both systems the performance of HS00 and KM01 are similar and generally better that of SH90. Especially for the higher system, as it is also noticeable from Fig. S9 and S10, the peak prediction of SH90 considerably deviates from both experimental data and other models' predictions. Though, at longer distances SH90 approaches other models. In conclusion, according to all estimators KM01 (after the correction for upwind contributions overestimation, see Sect. 2.5 in the original manuscript) and HS00, demonstrated their consistency in flux footprint prediction even at low measurement height. Table S1 Performance of the footprint predictions of SH90, HS00 and KM01 for LO and HI systems. Summary measures of the prediction accuracy normalized mean squared error (NMSE, here expressed in percent 0 100) are calculated around the peak and reported as median ± standard deviation over each runs. Median absolute deviation (MAD) considered at the footprint tail is reported in relative values and calculated over the whole dataset (each releasing distances of each run) LO system HI system SH90 HS00 KM01 SH90 HS00 KM01 NMSE [%] 1.74 ± ± ± ± ± ± 0.85 MAD

8 Fig. S9 left: Comparisons between modeled and experimental crosswind integrated footprint from system HI (z = 1.8 m) considering 12' tracer flux averages for the whole experimental runs (by rows). right: corresponding comparisons considering 6' tracer flux averages. Error bars represent tracer flux random uncertainty

9 Fig. S10 left: Comparisons between modeled and experimental crosswind integrated footprint from system LO (z = 1.2 m) considering 12' tracer flux averages for the whole experimental runs (by rows). right: corresponding comparisons considering 6' tracer flux averages. Error bars represent tracer flux random uncertainty

10 References Billesbach DP (2011) Estimating uncertainties in individual eddy covariance flux measurements: A comparison of methods and a proposed new method. Agric For Meteorol 151: doi: /j.agrformet Detto M, Montaldo N, Albertson JD, et al (2006) Soil moisture and vegetation controls on evapotranspiration in a heterogeneous Mediterranean ecosystem on Sardinia, Italy. Water Resour Res 42:n/a n/a. doi: /2005WR using eddy correlation and footprint modelling. Agric For Meteorol 114: Van de Boer A, Moene AF, Schüttemeyer D, Graf A (2013) Sensitivity and uncertainty of analytical footprint models according to a combined natural tracer and ensemble approach. Agric For Meteorol 169:1 11. doi: /j.agrformet Van Ulden AP (1978) Simple Estimates for Vertical Diffusion from Sources near the Ground. Atmos Environ 12: Dyer AJ (1963) The adjustment of profiles and eddy fluxes. Q J R Meteorol Soc 89: Finkelstein PL, Sims PF (2001) Sampling error in eddy correlation flux measurements. J Geophys Res 106: Finn D, Lamb B, Leclerc M, Horst TW (1996) Experimental evaluation of analytical and lagrangian surface-layer flux footprint models. Boundary-Layer Meteorol 80: Foken T, Göckede M, Mauder M, et al (2004) Postfield data quality control. In: Lee X, Massman WJ, Law BE (eds) Handbook of micrometeorology: a guide for surface flux measurements and analysis. Kluwer Academic Publishers, Dordrecht, pp Kormann R, Meixner FX (2001) An analytical footprint model for non-neutral stratification. Boundary-Layer Meteorol 99: Mauder M, Cuntz M, Drüe C, et al (2013) A strategy for quality and uncertainty assessment of longterm eddy-covariance measurements. Agric For Meteorol 169: doi: /j.agrformet Metzger S, Junkermann W, Mauder M, et al (2012) Eddy-covariance flux measurements with a weight-shift microlight aircraft. Atmos Meas Tech 5: doi: /amt Pasquill F (1974) Atmospheric Diffusion. New York Schuepp P, Leclerc M, MacPherson J (1990) Footprint prediction of scalar fluxes from analytical solutions of the diffusion equation. Boundary- Layer Meteorol 50: Soegaard H, Jensen NO, Boegh E, et al (2003) Carbon dioxide exchange over agricultural landscape

Footprints: outline Üllar Rannik University of Helsinki

Footprints: outline Üllar Rannik University of Helsinki -Concept of footprint and definitions -Analytical footprint models -Model by Korman and Meixner -Footprints for fluxes vs. concentrations -Footprints