POLITECNICO DI MILANO EDDY COVARIANCE MEASUREMENTS IN THE PO VALLEY: REPRESENTATIVENESS AND ACCURACY

Transcription

1 POLITECNICO DI MILANO Department of Civil and Environmental Engineering PhD course in Environmental and Infrastructure Engineering EDDY COVARIANCE MEASUREMENTS IN THE PO VALLEY: REPRESENTATIVENESS AND ACCURACY Chair of the doctoral program: Prof. Fernando Sansò Tutor: Doctoral dissertation of: Daniele Masseroni Matr Year 213 Cicle XXV 1

2 2

3 Index General Abstract... 6 General Introduction... 8 Eddy covariance technique... 8 References... 1 (Chapter 1) - Impact of data corrections on turbulent flux measurements Abstract Introduction Data collection Preliminary processes for correction procedure Axis rotation for tilt correction Double rotation method Spike removal Time lag compensation Covariance maximization method Detrending Linear detrending Calculating fluxes Uncorrected fluxes level Spectral correction factors level Corrected fluxes level 2 and Results... 2 Effect of the preliminary processes on raw data... 2 Effect of the preliminary processes on uncorrected fluxes Effect of the spectral corrections on turbulent fluxes Flux loss in function of air temperature and relative humidity Flux loss in function of wind velocity and friction velocity Flux loss in function of stability parameter Daily and seasonal trend of flux losses Effect of the WPL and VD corrections on fluxes at level Quality of fluxes Energy balance closure Fluxes directly obtained from 3 minutes averaged data PEC software features PEC fluxes in comparison with Eddy Pro 4. fluxes Energy balance closure with PEC fluxes Conclusion References (Chapter 2) Energy balance closure of an eddy covariance station: limitations and improvements Abstract Introduction Instruments, data collection and site description The energy balance closure problem

4 Effect of data corrections Effect of storage terms Effect of time aggregation Effect of scale differences in fluxes measurement Effect of turbulent mixing Effect of vegetation Effect of seasonality Random error Conclusion... 6 References (Chapter 3) Experimental data about the spatial variability of scalar fluxes across maize field in Po Valley and comparison with theoretical footprint model predictions66 Abstract Introduction What is the importance of this experiment? Theoretical background Hsieh Model... 7 Kormann Model Study site, instruments and data Site characteristics Instruments Data corrections Fixed eddy covariance stations (A1 and A2) Experimental execution Results Flux measurements across the fields Experimental data compared with footprint model predictions Discussions... 8 Conclusion References General Conclusion Acknowledges

5 5

6 General Abstract This PhD work is mainly focused on researching utilities for increasing the micrometeorological flux reliabilities. Micrometeorological stations, which use the eddy covariance technique to estimate turbulent fluxes in the surface layer, are generally located in different agricultural fields to assess evapotranspiration and carbon dioxide fluxes between soil (or vegetation) and atmosphere. Evapotranspiration and carbon dioxide fluxes of the SVAT (Soil Vegetation Atmosphere) systems, have to be correctly estimated if a sustainable and parsimonious water resources management would be made. Moreover energy and mass balances model outputs (e.g. latent heat flux and soil moisture) can be compared with micrometeorological measurements, if and only if micrometeorological data are rigorously processed and their qualities are assessed. Micrometeorological technique was born about 3 years ago and, subsequently, a large contribution about data corrections was rapidly given by many scientists. However, many aspects about measurement proprieties and flux reliabilities are only now investigated. In the first part of this work, starting from high frequency measurements of the three wind components and carbon dioxide/water concentrations, eddy covariance data are processed using an open source program and the results are compared with those obtained by a simple software implemented at the Politecnico of Milan for averaged data for real time water management. Thanks to this comparison the main correction procedures which have to be necessarily implemented to obtain reliable turbulent fluxes from micrometeorological data, are shown. The reliability of the micrometeorological measurements is usually assessed with the energy balance closure. Moreover, the use of energy data to validate land surface models requires that the conservation of the energy balance closure is satisfied. However, the unbalance problem is an important issue which has not yet been resolved. In the second part of this work, many aspects which could cause underestimation in turbulent flux measurements are shown. The factors which could influence the energy balance colure are separately investigated and the energy balance closure improvements or worsening are shown in order to understand the number of factors which could play a fundament role into energy balance closure problem. One of these problems is represented by flux scale proprieties. In fact, net radiation, latent, sensible and ground heat fluxes (which represent the four components of the energy balance) have different representative source areas which covers different sectors of the field: from few centimeters for ground heat flux, to a hectare for latent and sensible heat fluxes. Therefore, several errors in energy balance closure can be related to the difficulty to match footprint area of eddy covariance fluxes with the source areas of the instruments which measure net radiation and ground heat flux. In the third part of this work, representative source area for turbulent fluxes measured by eddy covariance station is investigated through modeling and experimental campaigns in totally different field situations: bare and vegetated soils. A revisited simple method based on mobile and fixed eddy covariance stations is found to be helpful in intra-field spatial variability investigations of turbulent fluxes also over homogeneous canopy such us maize fields. The results of these experiments lead to interesting improvements about turbulent flux representative source area knowledge increasing literature results. This PhD thesis has been conceived as a collection of three strongly connected papers, which constitute the nucleus of the author research activities. One introduction, at the beginning of the 6

7 thesis, has been added to briefly explain eddy covariance technique and its mathematical basis. The PhD thesis is subdivided in three macro chapters which are independently built in order to simplify the comprehension of the text, giving to the reader the possibility to read each chapter separately from each others. Each chapter is built with a quite standard structure which is constituted by a synthetic abstract, an introduction which gives to the reader an overview about the problems which are developed in the chapter, a theoretical background which is widely referred to literature works, a site-instrument-data description, result discussions and finally a conclusion remark. Other author works, which have been developed during his PhD research period, are quoted in the text and they constitute parallel efforts which allowed completing this thesis. Here, only the papers which have already been published are shown, while other works which are in review or in press processes have not been quoted in the reference subparagraphs. Subparagraph, equation and figure enumerations restart at each chapter to improve the comprehension of the text. It is an author s choice to use, into the equations, symbols which are usually founded in literature articles also if they could be utilized several times into the text with different meanings which, however, are widely explained in order to prevent any misunderstanding. 7

8 General Introduction In this paragraph a theoretical background about the eddy correlation theory, with reference to three scientific works (Baldocchi et al. (1988), Verma (199) and Papale et al. (26)) is shown. It does not want to be an exhaustive dissertation about the micrometeorological method but only a general introduction about the mathematical basis which governs the turbulent flux calculus methodology focusing on limitations and problems connected to this approach. Eddy covariance technique Micrometeorological techniques provide for direct measurements of carbon dioxide, water and energy flux exchanges between biosphere and the atmosphere. Micrometeorological techniques have many advantages: 1) They are in situ and do not disturb the environment around the plant canopy. 2) These techniques allow continuous measurements. 3) Time averaged micrometeorological measurements at point provide an area-integrated, ensemble average of the exchange rates between the surface and the atmosphere. Defining as net ecosystem exchange the mass or energy quantity exchanged from ecosystem to atmosphere trough an imaginary surface of interface in a determinate range of time, the objectives of micrometeorological technique are: 1) To find a simple formulation about net ecosystem exchange which can be applied starting from measurements carry out using not many expensive instruments; 2) To find a net ecosystem exchange general formulation so that the results can be considered representative of the ecosystem behavior. The conservation equation provides the basis framework for measuring and interpreting micrometeorological flux measurements. In concept, the conservation equation states, which are represented by the variation at fixed point of a chemical constituent in time, are equal to the sum of the mean horizontal and vertical advection, mean horizontal and vertical divergence or convergence of the turbulent flux, molecular diffusion and any source or sink as described by Eq.1. t u c 2 c S c (1) Where c is the variation of the concentration (c) of a generic passive scalar in time; t u c is the turbulent transport of c generated by a wind field described by the vector u ; S is a source or sink of c in a fixed point in space; 2 c is the molecular diffusion and represents the gas diffusivity in air. While Eq. 1 represents the instantaneous transport equation, Eq. 2 describes the evolution in time of the mean concentration of the scalar c (Garrat, 1993). 8

9 t u c 2 c S c (2) Applying the Reynolds s decomposition (Foken, 28) which converts a generic instantaneous value as a sum of mean component and fluctuant component, in accordance with Reynolds s mean proprieties law, it is possible to obtain Eq. 3. c 2 t u c x v c y w c z c c c u' v' w' S c (3) x y z Where c c c u v w is the advection transport term generated by the mean wind flow; x y z u ' c x v' c y w' c z is the advection transport term generated by the turbulent flow. Eddy correlation theory is based on ideal conditions which permit to simplify Eq. 3 in accordance with technical objectives described before. Supposing that: 1) Molecular diffusion can be neglected in a turbulent flow; 2) Mean variation of the scalar quantity in horizontal directions can be neglected; 3) Mean vertical velocity can be neglected; 4) The turbulence is homogenous in horizontal directions; 5) The concentration of the constituent does not vary significantly with time; it is possible to obtain Eq. 4. c t S w' c' z (4) As described by Eq. 4, the variation of the mean concentration of gas in time is equal to the difference between what enters or leaves the controlled volume and turbulent vertical flux. Integrating Eq. 4 from surface to measurement height (z m ) and considering the sum of what enters or leaves the controlled volume as the net ecosystem exchange (F), it is possible to obtain Eq. 5. F z m c w' c' dz (5) t z Eq. 5 says that the net ecosystem exchange is the sum of turbulent vertical flux and storage term. The turbulent vertical flux is also called eddy covariance flux, while the storage term represents gas or energy quantities which are not carried by turbulent flow and remain stored under the 9

10 measurement point. In first approximation storage term can be neglected and Eq. 5 is simplified in Eq. 6. F w'c' (6) The equations of the turbulent fluxes can be summarized in: 1) Sensible heat flux (Eq. 7) H a Cp w't' (7) 2) Latent heat flux (Eq. 8) LE a w'q' (8) 3) Momentum flux (Eq. 9) a w'u' (9) Where is the air density, a C p is the specific heat capacity of air and is the vaporization latent heat of water. T represents air temperature while q water vapor turbulent concentration in the atmosphere. For other discussion on the conservation equation, as related to micrometeorological measurements, the reader should refer to the work of Kanemasu et al. (1979) and Businger (1986). References Baldocchi, D., Hincks, B., & Meyers, T. (1988). Measuring biosphere-atmosphere exchanges of biologically related gases with micrometeorological methods. Ecology, 69: Businger, J. (1986). Evaluation of the accuracy with which dry deposition can be measured with current micrometeorological techniques. Journal of Climate and Applied Meteorology, 25: Foken, T. (28). Micrometeorology. Berlin: Springer, pp. 36, ISBN Garratt, J. (1993). The atmospheric boundary layer. Cambridge: Cambridge university press, pp.316, ISBN Kanemasu, E., Wesely, M., Hicks, B., & Heilman, J. (1979). Techniques for calculating energy and mass fluxes. Michigan, USA: Pages in B.L. Barfield and J.F.Gerber editors. Papale, D., Reichstein, M., Aubinet, M., Canfora, E., Bernhofer, C., Kutsch, W., et al. (26). Towards a standardized processing of net ecosystem exchange measured with eddy covariance technique: algorithms and uncertainty estimation. Biogeosciences, 3 : Verma, S. (199). Micrometeorological methods for measuring surface fluxes of mass and energy. Remote Sensing Reviews, 5:

11 (Chapter 1) - Impact of data corrections on turbulent flux measurements Abstract Reliable estimation of evapotranspiration and carbon dioxide fluxes is based on a correction procedure due to eddy covariance methodology and instrumental characteristics. Literature standardized methods for data processing are defined for analyzing the quality of high frequency measurements. However, for operative applications, linked to real time irrigation water management, high frequency data are difficult to manage. So the objective of this paper is to verify the possibility of using eddy covariance data in an operative way in order to understand if averaged data at 3 minutes are still of good quality in relation to those obtained from high frequency measurements. Data have been collected by an eddy covariance station over a maize field at Livraga (Lodi, Italy) for the year 212. High frequency data (2 Hz) and averaged data (3 minutes) are collected separately in a PCMICA of 2Gb capacity and data logger memory respectively. High frequency data are analyzed with Eddy Pro 4. open source software. Effects of different types of corrections, from axis rotation to density fluctuations, are shown. Spectral correction factors have been calculated and flux losses are estimated. Quality of corrected fluxes and energy balance closure are also shown. Averaged data have been analyzed with Polimi Eddy Covariance software (PEC) which accounts only a portion of the correction procedures which can be applied to high frequency data, where the major difference is linked to the absence of the spectra correction. Evapotranspiration and carbon dioxide fluxes from high frequency and average data are then compared and cumulated trends over the growing season are assessed and a small difference is found. So these comparisons highlight the possibility of using averaged data for operative water management without drastically decreasing the quality of fluxes. Introduction Energy fluxes developed in a SVAT (Soil-Vegetation-ATmosphere) system are important for a wide range of applications at different spatial and temporal scales: from flood simulation at basin scale to water management in agricultural areas. Reliability of eddy covariance measurements has to be studied before using them in hydrological simulations (Aubinet et al., 2). Eddy covariance stations measure turbulent fluxes of sensible and latent heat, net radiation and heat flux in the soil at agricultural field-scale, having the objective to estimate the correct water requirement for a crop. The main instruments, which give the name to the eddy covariance technique, are gas analyzer and tridimensional sonic anemometer. They provide for estimate turbulent fluxes into surface layer (Stull, 1988), thanks to the covariance between vertical wind velocity and concentration of a scalar passive (for example: air/water, temperature or carbon dioxide). Flux estimations are obtained through complex series of steps starting from raw data acquired with high frequencies of about 1-2 Hz. The quality of these measurements is mainly influenced by problems of sensor configuration, place of the tower and stability of the 11

12 atmosphere (Baldocchi, 21; Foken and Wichura, 1996; Fuehrer and Friehe, 22). As described in Moncrieff at al. (1997), eddy covariance technique should be viewed as a 'system' of measurement, i.e. which includes not only the hardware but also the method of analysis, whether in real-time or off-line, and the algorithms used to filter or detrend the raw data and to apply calibrations and corrections. An example of the details and considerations which are necessary in a typical eddy covariance system is revealed in a series of papers (Shuttleworth et al., 1982, Shuttleworth et al., 1988 Moore, 1983, Moore, 1986; Lloyd et al., 1984; Shuttleworth, 1988) which describe not only the used instrumentation, including sensors and microcomputer control, but also the corrections required for real-time analysis. The problem of a correct implementation of data correction procedures is strongly connected with micrometeorological measurements which are often not able to close the surface energy balance equation (Foken, 28). Uncertainties in the post-field data processing of eddy covariance measurements of the turbulent fluxes are suspected to be crucial (Massman and Lee, 22). Lee et al. (24) formulate recommendations related to the eddy covariance technique for estimating turbulent mass and energy exchange, and give a comprehensive overview on the current state of the art regarding micrometeorological issues and methods. Eddy Pro 4. is an open source software used to calculate turbulent fluxes from high frequency measurements of wind velocity and gas concentrations. It can be founded at the WEB page and it has been implemented by University of Tuscia and Li-Cor industry. In recent decades, other softwares, implemented by different universities in the world, can be found in literature (TK3, EdiRe, EddySoft, Alteddy) with the main objective to standardize the correction procedure of eddy covariance measurements. These softwares have been widely validated and they are all based on five fundamental points: 1) Measured data are opportunely selected in function of quality tools; 2) Data are calibrated or corrected if necessary; 3) Data are aggregated in statistic tools as mean, variance or covariance; 4) Data are converted in averaged fluxes; 5) Reliability of fluxes is evaluated. To provide a complete data correction procedure high frequency data are needed because they can be used to find the reason for possible errors into flux measurements (Ueyama et al., 212). However, only averaged data are available sometimes (for example in real time application). High frequency data acquisition is not practical, considering that data loggers internal memories are not sufficient to store big quantities of data. Usually, a PCMCIA card allows expanding data logger memory capacity, so that, high frequency data are stored on this memory card while averaged data are stored on internal data logger memory. High frequency measurements could be directly downloaded trough Ethernet or Wi-Fi but in many case eddy covariance system location does not permit these types of connections. Typically through the use of GSM modem connection data logger memory could be downloaded on a personal computer which could be many kilometers away from the station, while the PCMCIA card has to download in situ using a personal computer and a compact flesh reader, leading to a non operative procedure. In order to overcome these complications, PEC software which uses directly averaged data to calculate turbulent fluxes has been implemented (Corbari et al., 212) and in this work comparison between Eddy Pro 4. and PEC software results are shown. 12

13 In the first part of this work, an overview of correction procedures which are necessary to obtain reliable turbulent fluxes is described in reference to Eddy Pro 4.. Only practical formulas are shown, while mathematical approaches are quoted in literature. In the second part, the impact of the various steps of post-field data processing on turbulent flux assesses is investigated. In the third part, fluxes performed by PEC are compared to the fluxes computed by Eddy Pro 4. in order to understand if reliable latent heat and carbon dioxide fluxes can still be obtained for an operative use of irrigation water management. Data collection Eddy covariance data are measured by a tridimensional sonic anemometer (Young 81) and open path gas analyzer (LICOR 75) located at the top of a tower 5 m high. The tower is placed in a maize field at the city of Livraga (LO) in the Po Valley. High frequency (2 Hz) measurements are stored in a compact flesh of 2 Gb connected with the data logger Campbell CR5 and downloaded in situ weekly. On compact flash only three wind velocity components, sonic temperature, vapor and carbon dioxide concentrations are stored (raw data). Data logger program is directly set to calculate averaged data over a time step of 3 minutes, and these data are collected into data logger internal memory. Contemporaneously, net radiation, measured by CNR1 Kipp&Zonen radiometer, soil heat flux, measured by HFP1 Campbell Scientific flux plate, and soil temperature measurements are stored on data logger in different memory tables. While high frequency data are directly used by Eddy Pro 4. software, 3 minutes averaged data are the starting point for the fluxes computation using PEC software. Experimental measurements were carried out from 21 May 212 to 7 September 212 but the dataset is composed by only 313 averaged data because some gaps due to malfunctioning of instrumentations or rainfall days are shown into the data sequences. From 131 to 241 Julian days the field is covered by vegetation, while the remaining days of the year, the field is characterized by bare soil. Preliminary processes for correction procedure Before calculating fluxes, high frequency data have to be adjusted and if necessary neglected. The different types of corrections are now analyzed. Axis rotation for tilt correction Each anemometer model adopts a customized convention for providing wind components in an orthogonal coordinate system, so that the user is able to retrieve the actual wind direction with respect to geographic north. Anemometer north is shown on Young 81, by an N on junction box. Wind components are indicated with u (positive if wind from East), v (positive if wind from North), and w (positive if wind from below) and they represent x,y,z directions respectively. Tilt correction algorithms are necessary to correct wind statistics for any misalignment of the sonic anemometer with respect to the local wind streamlines. In particular, this implies that 13

14 fluxes which are evaluated perpendicular to the local streamlines are affected by spurious contributions from the variance of along-streamlines components. Wilczak et al. (21), proposes three typologies of correction algorithms: double rotation, triple rotation, and the planar fit method. For Livraga 212 dataset a double rotation method has been used. Double rotation method With this method, the anemometer tilt is compensated by rotating raw wind components to nullify the average cross-stream and vertical wind components, evaluated on the time period defined by the flux averaging length (3 minutes). The rationale is that cross and perpendicular wind components are averaged to zero during such time period. In the first rotation, the measured wind vector is rotated about the z axis with objective to nullify v component. Successively, a second rotation is performed on a new y axis with the objective to nullify w component (for mathematical implementation of this method see Wilczak et al., 21). Spike removal The so called despiking procedure consists in detecting and eliminating short term outranged values in the time series. Following Vickers and Mahrt (1997), for each variable a spike is detected as up to three consecutive outliers with respect to a plausibility range defined within a certain time window, which moves throughout the time series. The rationale is that if more consecutive values are found to exceed the plausibility threshold, an unusual physical trend can be identified. The width of the moving window is defined as one sixth of the current flux averaging period and the plausibile range is quantified differently for each variable. Tab. 1 provides default values used in Eddy Pro 4.. The window moves forward half its length at a time. The procedure is repeated up to twenty times or until no more spikes are found for all variables. Detected spikes are counted and replaced by linear interpolation of neighboring values. Tab. 1. Plausibility range for spike detection for each sensitive variable. Variable Plausibility Range u,v Window mean +/- 3.5 standard deviation w Window mean +/- 5. standard deviation CO 2,H 2 O Window mean +/- 3.5 standard deviation Temperatures, Pressures Window mean +/- 3.5 standard deviation Time lag compensation In open path system the time lag between anemometric variables and variables measured by gas analyzer is due to the physical distance between the two instruments, which are usually placed several decimeters or less apart to avoid mutual disturbances. The wind field takes some time to 14

15 travel from one instrument to the other, resulting in a certain delay between the moments the same air parcel is sampled by the two instruments. It is a common practice to compensate for time lags before calculating covariances between anemometric variables and gas analyzer measurements. In literature four different alternative methods for detecting and compensating time lags exits: constant time lag, covariance maximization, covariance maximization with default and automatic time lag optimization (Runkle et al., 212; Fan et al., 199; Eddy Pro 4. manual, 212). For Livraga 212 dataset covariance maximization method has been used. Covariance maximization method The variability of wind regimes (in open path systems) suggests an automatic time lag detection procedure, normally performed for each flux averaging period. Typically the detection is accomplished via the covariance maximization procedure, consisting in the determination of the time lag that maximizes the covariance of two variables, within a window of plausible time lags (Fan et al., 199). Using the covariance maximization procedure a plausible time lag window has to be defined with the minimum and maximum time lags, which constitute the end points of the plausibility window. A too narrowed plausible window might lead to frequent use of the default (covariance maximization with default) or either endpoint (covariance maximization) time lag, because the actual time lag is often found to be outside the defined plausibility range. This situation leads to systematic flux underestimations. Conversely, imposing a too broad plausibility window, the possibility that unrealistic time lags are detected increases, especially when covariances are small and vary erratically with the lag time. These cases often result in flux overestimations. A tradeoff must be reached between the two contrasting needs. Detrending Eddy correlation method of calculating fluxes requires that the fluctuating components of the measured signals are derived by subtracting them from the mean signals. In steady-state conditions simple linear means would be adequate, but steady state conditions rarely exist in the atmosphere and it is necessary to remove the long term trends in the data which do not contribute to the flux (Gash and Culf, 1996). Different methods are described in literature for extracting turbulent fluctuations from time series data. The most commonly applied, in the context of eddy covariance, are the blockaveraging, linear detrending (Gash and Culf, 1996) and two types of high-pass filters, namely the moving average (Moncrieff et al., 24) and the exponentially weighted average (McMillen, 1988; Rannik and Vesala, 1999). For Livraga 212 data set the linear detrending is used. Linear detrending Gash and Culf (1996) show that it is possible to apply a linear detrend to eddy correlation data and calculate variances and fluxes in a single pass operation, accumulating an appropriate 15

16 combination of the sum of fluctuating variables and their cross products. Linear detrending method is generally done retrospectively using a two-pass method. The data are first divided into blocks each long normally 2-3 minutes, and a linear regression of the measured signal on time is then calculated. The fluctuations with respect to the regression line are then calculated during a second pass through the data. An alternative approach, proposed by Gash and Culf (1996), is to calculate the fluxes with respect to a filtered mean, which is derived by feeding the measured signal through a low-pass filter. Since this is a single pass method it can be used in real-time to calculate the fluxes as the data are collected. Calculating fluxes After completing the preliminary processes, it is possible to calculate turbulent fluxes, starting from uncorrected fluxes. Uncorrected fluxes represent gas, energy, and momentum fluxes which are obtained by merely adjusting units of relevant covariances, in order to match the desired output units. This operation may imply the inclusion of some previously calculated physical parameters described in Eddy Pro manual. These fluxes are uncorrected because some effects are not accounted in their calculation, notably the effects of air density fluctuations, of spectral losses, and effects of humidity on air temperature estimation through the sonic anemometer. Uncorrected fluxes level The uncorrected fluxes are calculated according to the following equations: 1) Sensible heat flux H c w' T ' (1) a p s 2) CO 2 flux, if CO 2 is measured as molar density with an open path analyzer 3 F, CO2 1 w' dco2' (2) 3) H2O flux, if H 2 O is measured as molar density with an open path analyzer F w d ' (3), H 2O ' H 2O 4) Latent heat flux LE F M 2 3 1, H 2O H O (4) 5) Evaporatranspiration flux 3 E F, H 2OM H 2O 1 (5) 6) Momentum flux 2 2 u' w' v' w' T a (6) Where H is the uncorrected sensible heat (W m -2 ). a is the air density (Kg m-3 ). cp is the air heat capacity at constant pressure (J Kg -1 K -1 ). 16

17 w' T ' s is the covariance between turbulent vertical wind velocity ( m s -1 ) and sonic temperature ( C). F is the uncorrected CO 2 flux (micromol m -2 s -1 ), CO2 w' d ' CO 2 is the covariance between turbulent vertical wind velocity ( m s -1 ) and moles of CO 2 per unit of volume (millimol m -3 ). F, H 2 O is the uncorrected H 2 O flux (millimol m -2 s -1 ). w ' d ' H 2O is the covariance between turbulent vertical wind velocity ( m s -1 ) and moles of H 2 O per unit of volume (millimol m -3 ). LE is the uncorrected latent heat (W m -2 ). is the latent heat of water vaporization (J Kg -1 ). M 2 is the molecular weight of H 2 O (Kg mol -1 ). H O E is the uncorrected evapotranspiration flux (Kg m -2 s -1 ). T is the uncorrected momentum flux (Kg m -2 s -1 ). u 'w' and v' w' is the covariance between horizontal turbulent wind velocities and vertical turbulent wind velocity, both calculated in m s -1. The subscript indicates the level of correction. Spectral correction factors level 1 Spectral corrections compensate flux underestimations due to two distinct effects. The first is referred to the fluxes which are calculated on a finite averaging time, implying that longer-term turbulent contributions are under-sampled at some extent, or completely. The correction for these flux losses is referred to as high-pass filtering correction because the detrending method acts similarly to a high-pass filter, by attenuating flux contributions in the frequency range close to the flux averaging interval. The second is connected with instrument and setup limitations that do not allow sampling the full spatiotemporal turbulence fluctuations and necessarily imply some space or time averaging of smaller eddies, as well as actual dampening of the small-scale turbulent fluctuations. The correction for these flux losses is referred to as low-pass filtering correction. Mathematical approach to calculate spectral corrections can be found in Moncrieff et al. (1997). For any given flux, the spectral correction procedure requires a series of conceptual steps which can be found in Ibrom et al. (27) and Massman (24) works: 1) Calculation or estimation of a reference flux cospectrum, representing the true spectral content of the investigated flux as it would be measured by a perfect system. 2) Estimation of the high-pass and low-pass filtering properties implied by the actual measuring system and the chosen averaging period and detrending method. 3) Estimation of flux attenuation. 4) Calculation of the spectral correction factor (SCF) and application of the correction. Spectral corrections are implemented on Livraga 212 dataset. High-pass filtering correction is applied following Moncrieff et al. (24) while for low-pass filtering correction a fully analytic method described in Moncrieff et al. (1997) is applied. 17

18 SCF is defined as the ratio between the integral of theoretical cospectrum model and the integral of measured co spectrum (Moncrieff et al., 1997). Measured co spectrum can be obtained starting from theoretical co spectrum multiplied for a transfer function which describes the proprieties of the measurement system (Eq. 7). SCF i Co Co Theo i Theo i ( f ) df ( f ) T ( f ) df F (7) Theo Where Coi is the theoretical co spectrum of the flux i, TF is the transfer function and f is the frequency. SCF is always major of 1 because it has to compensate flux underestimations caused by the problems described in section 4.2. The most widely used theoretical co spectral models are those from Kaimal et al. (1972). Moore (1986) proposes a scheme whereby a series of transfer functions could be defined for each of the correction terms required in an eddy covariance system. The transfer function defines the system reliance on different factors as digital recursive running mean, dynamic frequency response of the sensors, sensors response mismatch, scalar path averaging and so on, each connected with the typology of anemometer and gas analyzer used on the eddy covariance tower (Massman, 2). Starting from SCF, it is possible to calculate the fractional error on the measured flux as Eq.8 (Moncrieff et al., 1997). 1 Flux lossi (%) 1 1 (8) SCF i Where Flux loss defines the whole system flux losses. Spectral corrections are applied first to open path fluxes. This is because sensible and latent heat fluxes used in the Webb-Pearman-Leuning (WPL) correction (Webb et al., 198) are the environmental ones, those actually present in the atmosphere and affecting measurements of molar densities in open path analyzer. Marking as 1 the fluxes obtained after spectral corrections, CO 2, H 2 O latent heat and evapotranspiration fluxes are described by Eq. 9, Eq. 1, Eq. 11 and Eq.12 respectively. F F SCF (9) 1, CO2, CO2 w, CO2 F, H 2O F, CO2SCFw, H 2O 1 (1) LE LE SCF w H 2 1, O (11) E ESCF w, H 2O 1 (12) SCF and SCFw, H 2 O are the spectral correction factors calculated for CO 2 and H 2 O Where w,co2 respectively. Furthermore, uncorrected momentum flux is corrected using the relevant spectral correction factor SCF, (Eq. 13). u w 18

19 T TSCF u, w 1 (13) Corrected fluxes level 2 and 3 After the spectral correction, evapotranspiration flux is at first corrected with the WPL term, following the formulation proposed in Webb et al. (198) (Eq.14). H w E2 ( 1 ) E1 (1 ) (14) ac pta Where is the ratio between molar density of dry air and molar density of the water ( non dimensional). is the water to dry air density ratio (non dimensional). Ta is the ambient air temperature ( C). w is the water density (Kg m-3 ). Sonic temperature and sensible heat flux are corrected for humidity effects following van Dijk et al. (24), revising Schotanus et al. (1983) (Eq. 15). In next sections, this correction is simply called VD. E2 H H c T Qw' T ' (15) 2 a p s s a Where is a constant equals to.51 and Q is the specific humidity (non dimensional). H 2 is then spectrally corrected to get the first fully corrected flux (Eq. 16). H H2SCF w, Ts 3 (16) Where SCF w, Ts is the spectral correction factor calculated for sonic temperature. When CO 2 and H 2 O molar densities are measured with an open path gas analyzer in cold environmental (with low temperature below -1 C) H has to be corrected to account for the additional instrumentrelated sensible heat flux, due to instrument surface heating/cooling. This correction is fully described and tested in literature (Burba et al., 28). Now that sensible heat is fully corrected, evapotranspiration flux is corrected again, adding the WPL terms with the revised H (Eq. 17). H 3 w E3 ( 1 ) E1 (1 ) (17) ac pta Water vapor and latent heat fluxes are easily determined: 19

20 Wind velocity (m s -1 ) Gas concentration (millimol m -3 ) 3 F, H 2O E3M H 2O 3 1 (18) LE 3 E 3 (19) Now that evapotranspiration and sensible heat fluxes are fully corrected, fluxes of other gases such as carbon dioxide can be corrected for air density fluctuations, according to Webb et al. (198). For carbon dioxide we get the Eq. 2. d H d 2 1 (2) CO2 3 CO2 F, CO2 A F1, CO2 B E1 C d acpta Where A, B and C are multipliers described in Webb et al. (198). Finally, corrected fluxes of CO 2 (F 3,CO2 ) in a system with open path instrument, coincide with fluxes at level 2. Results As shown in the previous paragraphs, correction procedures can be summarized in three groups: preliminary processes, spectral corrections, WPL and VD corrections. In this section the impact of correction procedures in half-hourly measurements is quantified. With the expectation of the corrected fluxes calculation, results of the standardized processing procedure described above are performed. In general, to quantify the impact of each correction procedure, the slope and intercept values between the post-processed fluxes and pre-processed fluxes from a regression analysis on half hourly basis, have been calculated. The slope represents a difference in proportion to flux magnitude, and the intercept represents a constant difference on all flux range. Effect of the preliminary processes on raw data Preliminary processes should be applied on raw data measurements to prepare the dataset for fluxing calculation. In Fig.1 the effect of different correction methods on each u, v, w, H 2 O and CO 2 averaged component is shown. 6 A 14 B Julian day u (raw data) u (raw data+despiking+double rotation+time lag+detrending) H2O (raw data) 2 H2O (raw data+despiking+double rotation+time lag+detrending) Julian day 2

21 Wind velocity (m s -1 ) Wind velocity (m s -1 ) Gas concentration (millimol m -3 ) 6 C 3 D Julian day v (raw data) v (raw data+despiking+double rotation+time lag+detrending).1 E 15 CO2 (raw data) 1 CO2 (raw data+despiking+double rotation+time lag+detrending) Julian day Julian day w (raw data) w (raw data+despiking+double rotation+time lag+detrending) Fig. 1. Effects of the preliminary correction methods on wind velocities (A, C, E) and gas concentrations (B, D). Double rotation method produces a modification of the anemometer coordinate system (x,y,z) in respect to the local wind streamlines. The consequence of these rotations is that v and w wind components are led to zero (Fig. 1C and E) while u turns out to be characterized only by positive terms (Fig. 1A). This effect is also shown Fig. 2A where the dots, which represent modulus of u after double correction, take place only in first and fourth sectors. The effect of double rotation is major in correspondence of weak wind intensity. The modulus of u is subject to slight variations in a range of wind velocity between -3 m s -1 and 3 m s -1 ; while no variation are present for high values of modulus of u, and the dots stay on bisectors of first and fourth sectors (grey line). CO 2 and H 2 O concentrations are not particularly affected by preliminary corrections procedures (Fig. 2B and C), and only in correspondence of the raw data peaks, data corrections are relevant (Fig. 1B and D). This behavior could be a good indicator of the reliability of the gas analyzer measurements. In fact, calculating over the experimental period the mean differences between CO 2 and H 2 O raw data concentrations and CO 2 and H 2 O corrected concentrations (after the application of the preliminary processes), the results are quite similar and equal to millimol m -3 and.118 millimol m -3 respectively. 21

22 Slope (-) R 2 (-) CO 2 corrected concentration (millimol m -3 ) u - wind corrected velocity (m s -1 ) H 2 O corrected concentration (millimol m -3 ) A B u - wind raw data velocity (m s -1 ) C CO 2 raw data concnetration (millimol m -3 ) H 2 O raw data concentration (millimol m -3 ) Fig. 2. Comparison between mean raw data of u (A), H 2 O (B) and CO 2 (C) concentrations before and after preliminary correction procedures. Effect of the preliminary processes on uncorrected fluxes When fluxes directly obtained by raw data covariances and those calculated after preliminary processes (uncorrected level ) are compared, slight differences are found, and in Fig.3 the results are shown. The differences are quantified as slope between uncorrected fluxes and raw data fluxes from a regression analysis on half-hourly basis. The (1-slope) and intercepts quantities measure the difference in flux magnitude after the application of correction procedure while R 2 represents the dots dispersion around the regression line which describes the amplification of the random error (Ueyama et al., 212) Slope R2 A FH2O FCO2 LE H.2 22

23 CO 2 flux (micromol m -2 s -1 ) H 2 O flux (millimol m -2 s -1 ) Intercept (millimol m -2 s -1 ) Intercept (W m -2 ) B C FH2O FCO2* -6. LE H Fig. 3. A. Slope and R 2 determined by regression of half-hourly fluxes before and after preliminary corrections. B and C. Intercepts of the regression lines. In FCO2* the intercept is represented as (millimol m -2 s -1 )1 3. As shown in Fig. 3A, preliminary corrections produce a decrease of flux intensities which varies from 8% for latent heat and H 2 O to 36% for CO 2. Only sensible heat has a slight increase of about 6%. For momentum flux (not shown in figure) slope is equal to.86 while intercept is about -.1 Kg m -2 s -1, therefore preliminary processes produce a decrease of about 14% in its flux magnitude. Evaluating mean slope performed over the whole preferable fluxes (from vapor to momentum), the preliminary corrections produce a decrease of turbulent flux intensities of about 12%. R 2 deviates from 1 of about 18% on all fluxes, except for CO 2 where R 2 is equal to.47, indicating that, for this flux, application of preliminary processes create random error amplification. Moderated shifts of turbulent flux mean intensities are shown Fig.3B and C, where the range of intercept values vary from -5 W m -2 for sensible heat to 1.71 W m -2 for latent heat. For CO 2 flux the intercept is equal to -2.3 micromol m -2 s -1 while for H 2 O flux preliminary processes do not play a substantial role in the alteration of its mean intensity. As shown in Fig. 4, where the trend of fluxes over an experimental day is shown, spike removal correction leads to the elimination of some peaks of data. However, the remaining peaks in the flux series may be due to particular physical phenomena related with atmospheric or field events A Julian day Fo,CO2 (from raw data) Fo,CO2 (uncorrected) B Fo,H2O (from raw data) -2 Fo,H2O (uncorrected) -3 Julian day 23

24 Intercept (millimol m -2 s -1 ) Intercept (W m -2 ) Slope (-) R 2 (-) Sensible heat flux (W m -2 ) Latent heat flux (W m -2 ) C D Julian day Ho (from raw data) Ho (uncorrected) Julian day LEo (from raw data) Fig. 4. Comparison between mean raw data fluxes before and after preliminary correction procedures. Effect of the spectral corrections on turbulent fluxes n Fig.5, spectral correction impact over uncorrected turbulent fluxes is shown. In this case, slope represents the ratio between fluxes at level 1 and fluxes at level. Only for sensible heat the ratio is calculated between H 3 and H 2 because the spectral correction is applied after the WPL and VD equations. Spectral correction factor is a value always greater than 1, and this produce, on all turbulent fluxes (including momentum flux), a systematic growth in slope of about 1% (Fig.5A). The regression coefficient (R 2 ) is closed at about.99 on all fluxes. The maximum intercept values are in correspondence with CO 2 and latent heat fluxes where the difference before and after the application of the spectral correction is equal to.61 micromol m -2 s -1 and.6 W m -2 respectively (Fig. 5B and C), while H 2 O and sensible heat intercepts are near to zero. A Slope R B.6 FH2O FCO2 LE H.8 C FH2O FCO2* LE H Fig. 5. A. Slope and R 2 calculated by regression of half-hourly fluxes before and after the application of SCF on uncorrected fluxes. B and C. Intercepts of the regression lines. In FCO2* the intercept is represented as (millimol m -2 s -1 )

25 In the next sessions flux losses for the whole range of turbulent fluxes are investigated with the objective to understand if some atmospheric or turbulent characteristics could influence the spectra or cospectra information losses. In Fig. 6 the flux losses (for water vapor, carbon dioxide, latent heat, sensible heat and momentum fluxes), in function of the main atmospheric proprieties, are shown. Flux loss in function of air temperature and relative humidity Minimum value of flux loss for momentum and sensible heat is about.7% while maximum value of flux loss is about 3%. For latent heat, CO 2 and H 2 O minimum flux loss is about 7% while the maximum flux loss is about 87%. This is probably due to the proprieties of transfer function ( T F ) which is calculated as a product of different transfer functions connected with characteristics of the systems used to measure eddy covariance variables (Moore, 1986). Sensible heat and momentum fluxes can be calculated starting only from data measured by sonic anemometer instrument, so that transfer function has to take into account only anemometer signal losses. Instead, latent heat, H 2 O and CO 2 fluxes are calculated using sonic anemometer and gas analyzer contemporaneously. In this case, the transfer function has to take into account flux information losses derived by anemometer and gas analyzer with a consequent rising in the turbulent flux loss. For all fluxes, the flux loss is not particularly influenced by air temperature. In general, a random distribution of the dots is shown in correspondence with a range of temperature which varies from 1 C to 3 C. Major dispersion of dots is shown in association with latent heat, CO 2 and H 2 O fluxes with a standard deviation in flux loss of about 9%. Air humidity plays a modest role on flux loss. For high values of relative humidity, dispersion of dots and flux loss tend to increase up to maximum values of 3% (for sensible heat and momentum fluxes) and 87% (for latent heat, H 2 O and CO 2 fluxes). As shown in Runkle et al. (212), relative humidity plays a fundamental role on time lag of close-path gas analyzers, where the time lag is a parameter included in the transfer function implementation (Massman, 2). Fig. 6 results show that high air humidity concentrations (also in an open path gas analyzer) could influence transfer function with a consequent increase in flux loss. 25

26 Friction velocity Fig. 6. Flux loss in function of atmospheric characteristics. Flux loss (%) Flux loss (%) Flux loss (%) Flux loss (%) Flux loss (%) Stability parameter (-).5 1 Friction velocity (m s-1) Wind velocity (m s-1) Realtive humidity (%) Air temperature ( C) H2O flux Flux loss (%) Flux loss (%) Flux loss (%) Flux loss (%) Flux loss (%) Stability parameter (-).5 1 Friction velocity (m s-1) Wind velocity (m s-1) Realtive humidity (%) Air temperature ( C) CO2 flux Flux loss (%) Stability parameter (-) Friction velocity (m s-1) Wind velocity (m s-1) Realtive humidity (%) Air temperature ( C) Latent heat Flux loss (%) Flux loss (%) Flux loss (%) Flux loss (%) Flux loss (%) Flux loss (%) Flux loss (%) Flux loss (%) Wind velocity Flux loss (%) Stability parameter (-) Friction velocity (m s-1).5 Wind velocity (m s-1) Realtive humidity (%) Air temperature ( C) Sensible heat Flux loss (%) Flux loss (%) Flux loss (%) Flux loss (%) 26 Relative humidity Flux loss (%) Air Temperature Stability parameter Stability parameter (-) Friction velocity (m s-1).5 Wind velocity (m s-1) Realtive humidity (%) Air temperature ( C) Momentum flux

27 Flux loss in function of wind velocity and friction velocity In Po Valley wind velocity intensities are not particularly elevated. During unfavorable weather conditions maximum velocities can be up to about 1 m s -1. As shown in Moncrieff et al. (1997), low wind speed, which favors a greater proportion of large eddies, produces a flux underestimation. In Fig. 6 graphs of flux loss in function of wind velocity and friction velocity are shown in a semi logarithmic Cartesian plane to highlight the negative effect of slow wind velocities. For wind velocities of about 2.5 m s -1, flux loss tends to be stabilized at about 1%. Analyzing the trend with wind velocities higher than 4 m s -1, flux underestimation tends to increase slightly in a linear way. However, the experimental design for a limited range of wind intensity does not permit to understand if also high velocities could add flux losses. Moncrieff et al. (1997) show that in a close-path gas analyzer, errors occur with high wind speed and when the instruments are near the ground leading to a flux loss up to 4% with a wind velocity of about 8 m s -1. Even if an open path anlyzer is a completely different instrument in respect to a close path, it is constituted as well by an optical window which should modify wind flow during its passage through it with a consequent slight increase of information loss. Friction velocity is a characteristic parameter of mechanical turbulence (Foken, 28). Turbulence is an important issue connected with the correct measurement obtained by eddy covariance stations. Eddy covariance technique is based on measurement of wind and gas concentrations turbulent variables in atmospheric surface layer (Foken, 28; Garrat, 1993). Laminar flows or advection conditions represents negative situations where the eddy covariance station is not able to measure correctly fluxes. As shown in Fig.6, for small values of friction velocity, flux loss increases drastically. In many different literature works (Aubinet et al., 2; Falge et al., 21), friction velocity is used as a threshold which indicates the level of turbulence in a site. Reichstein et al. (22) assumes that all eddy covariance data with u* <.2 m s -1 should be excluded from the analysis, as it is likely that under these conditions storage and advection can reduce gas fluxes through the boundary layer. However, as shown in Barr et al. (26),.2 m s -1 can not be used as a universal threshold value, but it has to be estimated starting from micrometeorological parameters measured by the tower at each site. From results shown in Fig. 6, optimal u* threshold definition could not be individuated. To provide the u* threshold, Papale et al. (26) method should be applied but, it is not an objective of this work. Flux loss in function of stability parameter Stability parameter is defined as the ratio between measurement height (taking into account about displacement height) and Monin-Obukhov length (Obukhov, 1946). It is a dimensionless parameter that characterizes turbulent processes in the surface layer, and it is described by Eq.21. (z d) L (21) Where is the stability parameter (non dimensional). z is the measurement height (m) 27

28 d is the displacement height described in Foken (28) (m). L Monin-Obukhov length (m). Monin-Obukhov length is defined as the ratio between mechanical and convective forces as shown in Eq. 22. kgw'* 3 L T u a T ' (22) Where T a is the main air temperature (K). u* is the friction velocity (m s -1 ). k is the Von Karman constant (.4) (non dimensionaless). g is the gravity acceleration (m s -2 ). Starting from Monin-Obukhov length, it is possible to define if the atmosphere is in convective, stable or adiabatic conditions (Foken, 28). When L< ( w 'T ' > and ) atmosphere is in a convective condition, L> ( w 'T ' < and ) atmosphere is in a stable condition and L = ( w't ' and tend to ) atmosphere is in adiabatic condition. Spectral and co spectral theoretical models are described with different formulations respect to the stability characteristics of the atmosphere (Kaimal et al., 1972) and, as a consequence of this reason, stability parameter plays an important role on flux loss with a substantial difference between stable or convective conditions. As shown in Fig. 6, during convective conditions flux loss is constant (about 8%), while in stable conditions flux loss tends to increase rapidly (up to 8%). That being so, turbulence generated by convective and mechanical forces contemporaneously is necessary to guarantee a minimum flux loss. Starting from all experimental data set, assuming that convective conditions is verified when. 1, stable conditions when. 1and near adiabatic conditions when.1. 1 (Foken, 28), 43% of data is in convective conditions, 33% in stable conditions and 25% is in adiabatic conditions. Daily and seasonal trend of flux losses In Fig. 7 daily and seasonal trend of flux losses are shown. During daytime the averaged flux losses are smaller than night time of about 1% (Fig. 7A). From 6 A.M. to 18 P.M. for latent heat, carbon dioxide and air vapor fluxes, flux loss is about 8%. Form 18 P.M. to 6 A.M. the flux loss is about 17%. Considering the effect of stability conditions on flux losses, these results are in accordance with those obtained in many literature works and in Masseroni et al. (211) which, starting from eddy covariance data sets measured in Landriano and Livraga in the year 211, shows that convective situations are prevalent during day time while in the night time the stable conditions are dominant. Sensible heat and momentum fluxes are characterized by a small flux loss of about 2% for the entire day. This marked difference in flux loss between latent heat, carbon dioxide, air vapor fluxes and sensible heat, momentum fluxes is probably due to the proprieties of the transfer functions. Combination of several instruments to measure a flux give a contribute to increase flux loss. 28

29 Slope(-) R 2 (-) Flux loss (%) Flux loss (%) A peak of flux loss (of about 15% for latent heat, CO 2 and H 2 O fluxes) is located at July but, as shown in Fig. 7B, a seasonal trend is not definable. A B Time (h) Momentum flux Sensible heat flux Latent heat flux Carbon dioxide flux Water vapour flux Momentum flux Sensible heat flux Latent heat flux Carbon dioxide flux Water vapour flux Fig. 7. Daily (A) and seasonal (B) trends of flux losses. Effect of the WPL and VD corrections on fluxes at level 3 After the application of the preliminary processes and spectral corrections, turbulent fluxes need to be corrected for density fluctuation and humidity effects trough the WPL and VD algorithms (Leuning, 24). VD correction impact on sensible heat (Eq. 15) produces a decrease in its uncorrected value (H ) as a consequence of the humidity effect on sonic temperature, while WPL correction is an additive terms for the uncorrected fluxes of latent, vapor and carbon dioxide as shown by Eq. 14 and Eq. 2. All flux estimations, with the exception of momentum flux, change in magnitude after the application of these corrections (as shown in Fig. 8A). The slope is calculated as the ratio between corrected fluxes at level 3 and fluxes at level 1 (after the spectral corrections), while for sensible heat the ratio is performed between H 2 and H. From H 2 O flux to latent heat, an important increase in magnitude of fluxes is caused by WPL correction, while for sensible heat VD correction produces a decrease of the mean intensity. Magnitude of the differences is about 2% for H 2 O, CO 2 and latent heat, while for sensible heat the examined difference is about - 15%. A constant increase of flux is presented in CO 2 terms where the intercept is 2.2 micromol m -2 s -1 (Fig. 8B). On the contrary, sensible heat is subjected to a decreasing of flux of about -4 W m -2 (Fig. 8C). A FH2O FCO2 LE H.8 29

30 Evapotranspiration (mm) CO 2 cumulated flux (g m -2 ) Intercept (millimol m -2 s -1 ) Intercept (W m -2 ) B C FH2O FCO2* -5.6 LE H Fig.8. A. Slope and R 2 calculated by regression of half-hourly fluxes before and after the application of WPL and VD corrections on fluxes at level 1. B and C. Intercepts of the regression lines. In FCO2* the intercept is represented as (millimol m -2 s -1 ) 1 3. To quantify the impact of WPL and VD corrections over the whole experimental days, cumulated evapotranspiration and carbon dioxide fluxes are calculated, and the results are shown in Fig. 9. Impact of correction procedures, which permit to obtain reliable values of turbulent fluxes, is shown taking into account the divergence between fluxes at level 1 and the corrected fluxes. At the end of the growing season, uncorrected evapotranspiration results are underestimated with respect to corrected fluxes with a difference of about 34 mm (Fig. 9A). After a brief period of time where CO 2 cumulated flux is positive, due to the absence of vegetation in the field, plant photosynthesis effects play an essential role in the reduction of CO 2 concentration in the air (Fig. 9B). Correction procedures permit to estimate correctly CO 2 cumulated flux which is distant from uncorrected flux of about 443 g m -2. If the WPL and VD corrections are not applied, CO 2 sequestration is overestimated. Another important issue connected with the necessity to apply the WPL and VD corrections for the correct estimation of CO 2 flux, is shown in reference with the first period of growing season which come from 14 to 16 Julian days. This period of time, which is characterized by a heterogeneous surface, fluxes between soil and atmosphere are exchanged. When the vegetation is sufficiently high to cover completely the soil, respiration effects, characteristics of a bare soil, are substituted by photosynthesis processes produced by the vegetation. If WPL and VD corrections are not applied, physical process of respiration that occurs in the first part of growing season is not evidenced with a drastic consequence over the physical interpretation of the flux measurements. A B ET_uncorrected ET_corrected Julian day 3.E+2.E E+2-6.E+2-9.E+2-1.2E+3-1.5E+3-1.8E+3 CO2_uncorrected CO2_corrected Julian day Fig. 9. Evapotranspiration (A) and carbon dioxide (B) cumulated fluxes over growing season.

31 Frequency (%) Frequency (%) Quality of fluxes Quality of fluxes is evaluated through two different automatic tests implemented in Eddy Pro 4.: statistical tests applied directly on high frequency measurements (Vickers and Mahrt, 1997) and micrometeorological tests (Foken et al., 24; Mauder and Foken, 24). Statistical screen for high frequency data is obtained applying six statistical tests described in the work of Vickers and Mahrt (1997): spike, amplitude resolution, drop-out, absolute limits, discontinuities, skewness and kurtosis. Family of micrometeorological tests is constituted by two tests which are known as steady state test and developed turbulent conditions test (Foken et al. 24; Foken and Wichura, 1996; Gockede et al., 28). As described in Foken and Wichura (1996) stationary test and developed turbulence test are summarized in a classification scheme defined above 9 levels of averaged data quality. 1 corresponds to good quality, 9 bad quality of data which should be discarded from the dataset. In Mauder and Foken (24), quality of fluxes is based on a flag which can be, 1 or 2 from best quality to worst quality respectively. quality flag corresponds with a range of steady state and developed turbulence test levels which vary from 1 to 2; 1 quality flag corresponds with a range which is up to 5 and 2 quality flag corresponds with a range from 6 to 7. Eddy Pro 4. shows these flags in association with each flux value (latent, sensible heat, momentum and carbon dioxide flux) in order that the user can decide if the flux should be discarded from results dataset. Steady state test is based on idea to compare covariances determined for an averaging period with the same parameters evaluated in short intervals within this period, using the method explained in Gurjanov et al. (1984). A time series is considered to be in steady state if the difference between both covariances (that are the covariance calculated over whole period and the mean of covariances obtained in short intervals within this period) is lower 3% (Foken and Wichura, 1996). In Fig. 1A, frequency of w u', w' Ts ', w' CO ' and w ' H ' ' 2 2 O covariance data for each degree of quality, are shown. About 45% of data are included in 1 degree of quality highlighting the good agreement of quality of measurements in respect to the stationary condition control. From class 2 to 6 there are about 1% of data (for each class) and from class 7 to 9 about 5% of data. A B 6 5 Stationary test (Foken and Wichura, 1996) 6 5 Developed turbulence test (Foken and Wichura, 1996) w/u w/ts w/co2 2 1 u w w/h2o Ts Degree of quality Degree of quality Fig. 1. Percentage of data for each degree of quality using two different tests: stationary test (A) and developed turbulent test (B). 31

32 Sensible heat flux (W m -2 ) Latent heat flux (W m -2 ) Frequency (%) The so called flux variance similarity, which is explained in many textbooks as Foken (28), is a good measure to test the development of turbulent conditions. This similarity means that the ratio of standard deviation of a turbulent parameter and its turbulent flux is nearly constant or function of the stability conditions of atmosphere through Monin-Obukov length parameter and measurement height. This ratio called integral turbulence characteristic (ITC) is the basic parameter to describe atmospheric turbulence. Foken (1991) classify ITC functions in three groups related to u, w and T s parameters, and a well developed turbulence can be assumed if the modulus of relative error between modeled ITC and measured ITC is lower than 3%. In Fig. 1B frequency of ITC u, ITC w and ITC Ts values for each degree of quality are shown. The results evidence a discrete percentage of data (about 15%) which stay in class 9 of quality, showing that well developed turbulence is not always guarantee. Assuming the Mauder and Foken (24) classification of data quality (Fig. 11) about 25% of turbulent fluxes over the total data set should be neglected because they are included in the class 2 of quality sectors. This is probably due to the fact that, in general, nighttime data are flagged because developed turbulence test is failed while during dawn and dusk the steady test fails. 6 5 Quality test (Mauder and Foken, 24) Degree of quality H LE CO2_flux Fig. 11. Percentage of data for each quality class using Mauder and Foken (24) quality test. In Fig. 12, turbulent fluxes are shown using dots with different shape in relation with their quality class. Bad quality of data is shown mainly during night time, while during day time the fluxes measured by eddy station can be considered of good quality. Dawn and dusk represent intermediate conditions where it is not always possible to define the good or bad quality of data. A B 2 15 _(good quality) 1_(sufficient quality) 2_(bad quality) 5 4 _(good quality) 1_(sufficient quality) 2_(bad quality) Julian day Julian day 32

33 Frequency (%) Frequency (%) Frequency (%) CO 2 flux (micromol m -2 s -1 ) 4 2 _(good quality) 1_(sufficient quality) 2_(bad quality) C Julian day Fig. 12. Turbulent fluxes representation in function of their quality class. (A) Sensible heat. (B) Latent heat. (C) Carbon dioxide flux. Quality of data is strongly connected with atmospheric stability as shown in Fig. 13. Data are subdivided in convective, adiabatic and stable conditions and their quality flag has been examined. The results shown in Fig. 13 indicate that the bad quality of fluxes is mainly concentrated during stable condition of the atmosphere while for adiabatic and convective situations quality of fluxes is often guaranteed. However, it is not possible to eliminate completely fluxes in stable conditions because it should cause a loss of data of about 1%, calculated as the sum of stable fluxes which belong to and 1 quality classes. A B 4 Quality test for sensible heat flux 4 Quality test for latent heat flux Degree of quality 2 Convective Adiabatic Stable 1 1 Degree of quality 2 Convective Adiabatic Stable C Quality test for CO 2 flux Convective 1 Degree of quality 2 Adiabatic Stable Fig. 13. Quality test for data subdivision in convective, adiabatic and stable conditions. (A) Quality test for sensible heat. (B) Quality test for latent heat. (C) Quality test for carbon dioxide flux. 33

34 Rn-LE-H-G (W m -2 ) Fluxes (W m -2 ) Fluxes (W m -2 ) Energy balance closure The turbulent fluxes of sensible and latent heat, net radiation, ground heat flux and energy balance closure are calculated before and after the whole correction procedures. In Fig. 14A and B, ensemble means of diurnal variations of turbulent fluxes over the whole experimental period are shown. Correction procedures play an important role on all turbulent fluxes of latent and sensible heat, and also ground heat has to be corrected for storage term to obtain a reliable flux estimation. For ground heat flux the correction procedure (not described in this work) is required to account for the heat storage that occurs in the layer between the soil surface and the heat flux plate (Kustas and Daughtry, 199). As shown in Fig.14A, if correction procedures are not applied, during daytime, latent, sensible and ground heat fluxes collapsed to zero, while in nighttime overestimations of latent and sensible heat leads to an unsatisfactory flux interpretations. In Fig.14B, corrected fluxes have a typical trend described in literature, with latent heat greater then sensible heat because the field is covered by the vegetation for a wide range of the experimental period. In Fig. 14C, residual flux calculated as R n -LE-H-G is shown. Residual magnitude for uncorrected fluxes is characterized by peaks in daytime and nighttime, with maximum values of about 4 W m -2 at 12 A.M and -3 W m -2 at 2 A.M.. Residual trend for corrected fluxes is close to zero with the exception of some hours in the morning, where the mean residual value is about 5 W m -2. A B Rn LE_uncorrected H_uncorrected G_uncorrected Rn LE_corrected H_corrected G_corrected Hours 6 C Residual_uncorrected fluxes Resudual_corrected fluxes Hours Hours Fig. 14. Ensemble means of diurnal variation of turbulent (A, B) and residual (C) fluxes for the whole period of the experimental campaign. 34

35 LE+H (W m -2 ) LE+H (W m -2 ) The energy balance closure using all corrected fluxes (Fig. 15A) or only fluxes related to and 1 quality classes (Fig. 15B), is shown. Even if the increase in energy balance closure is only of about 4%, quality check permits to eliminate data which could be cause of major dispersion of dots in respect 1:1 ideal line with R 2 which comes from.75 to.8. Energy budget is typically not closed when measuring energy fluxes with an eddy covariance station, available energy is usually bigger than the sum of turbulent vertical heat fluxes with a ratio that varies between 7 and 98% (Jacobs et al., 28; Meyers and Hollinger, 24; Wilson et al., 22; Foken et al., 26). As shown in Fig. 15A the slope of linear regression is.81 which is included in the range of values which are usually described in literature. However, there are several aspects which could give a relevant improvement in energy balance closure: the contribution of additional storage fluxes such as photosynthesis flux, crop, air enthalpy changes (Jacobs at al., 28; Meyers and Hollinger, 24), footprint shape and the representativeness of measured fluxes as a function of scale (Shmid, 1997) to make mention of some problems. Usually for homogeneous area it is considered valid the assumption that source areas are the same for all fluxes. However these areas can be significantly different, if the footprint of turbulent fluxes is compared to the source area of ground heat flux. So a portion of the error in energy balance closure can be related to the difficulty to match footprint area of eddy covariance fluxes with the source areas of the net radiation and heat flux plate instruments (Wilson et al., 22). A B 8 6 y =.81x R² = y =.85x R² = Rn-G (W m -2 ) -2 Rn-G (W m -2 ) Fig. 15. Energy balance closure with all data set (A) and only with and 1 quality fluxes (B). Fluxes directly obtained from 3 minutes averaged data As explained in Ueyama et al. (212), in literature, it is unstill clear which data processing steps are influential in the calculation of half-hourly and annual fluxes. According to results shown in previous sections, WPL and VD corrections provide for a substantial fluxes modification, influencing drastically cumulated evapotranspiration and carbon dioxide flux annual budgets. These corrections are the heart of PEC software (Corbari et al., 212), which is designed to answer question of real time data management. With the objective to verify the possibility of using eddy covariance station in an operative way for water irrigation management, so to understand if averaged data at 3 minutes are still of good quality in respect to high frequency data, the results obtained by PEC software are compared with those obtained by Eddy Pro

36 PEC software features Data logger program has to be compiled to convert electrical signals, originated from sensors, in physical measurements. Moreover, choosing an appropriated averaged interval, it can be set to perform some elementary mathematical operations as mean, variance or covariance among different measured variables. High frequency data will be lost but on the data logger memory aggregated data which are at 3 minutes will be stored. Time step (averaged time) has been chosen in accordance with results shown in different literature works as Lumley and Panofsky (1964), Lenschow et al. (1994) and Gluhovsky and Agee (1994). According to these authors, averaged time can not be less than 3-6 minutes if means, variances and covariance have to be assessed with an accuracy of about 5-15%. The complete procedure implemented in PEC for real time data management is reported in Corbari et al. (212). Steps which describe the procedure for turbulent fluxes calculation, can be summarized in four points: 1) Starting from averaged data, uncorrected fluxes (level ) are calculated; 2) WPL and VD corrections are implemented; 3) Rainfall days are discarded; 4) Elimination of spikes is applied. While points 1 and 2 are implemented with a programming language, points 3 and 4 are performed manually by the operator. During rainfall periods the data are completely discarded and if the rain falls during night time the data until the net radiation is greater than W m -2 are discarded. Despiking is applied on turbulent fluxes of latent, sensible heat and carbon dioxide in accordance with the experience of the operator. Deep knowledge of site, cultivation typology and literature data are the basic information which give to the operator the possibility to exclude, for the analysis, turbulent fluxes which are not representative of the physical phenomena in the field. In Tab. 2 the plausibility ranges for latent, sensible heat and carbon dioxide are shown. Preliminary processes and spectral corrections have not been applied. Tab. 2. Plausibility range for turbulent fluxes of latent, sensible heat and carbon dioxide Min Max Latent heat (W m -2 ) Sensible heat (W m -2 ) Carbon dioxide (millimol m -2 s -1 ) -8 5 PEC fluxes in comparison with Eddy Pro 4. fluxes In Fig. 16 two simple schemes which describe the levels of flux intensities applying the sequences of correction procedures for Eddy Pro 4. and PEC software, are shown. Starting from raw flux of latent heat (LE ), spectral correction factor is multiplied for LE obtaining LE 1 and subsequently WPL correction is added for the calculation of the definitive corrected flux LE 3. Using PEC software, LE 3 is directly calculated applying only the WPL correction, and a flux loss is shown as a consequence of spectral information losses. VD correction algorithm produces a decrease of the raw flux of sensible heat from H to H 2. Subsequently, it is multiplied for the 36

37 Evapotranspiration (mm) CO 2 cumulated flux (g m -2 ) Intensity of latent heat (W m -2 ) Intensity of sensible heat (W m -2 ) spectral correction factor for sonic temperature, to obtain H 3. Also in this case, using PEC software, the data has not been opportunely corrected for spectral losses. A B Eddy Pro 4. Averaged dataset Eddy Pro 4. Averaged dataset LE 3 Flux loss LE 3 H H LE 1 LE LE H 3 H 2 Flux loss H 3 Fig. 16. Intensities of latent(a) and sensible(b) heat fluxes before and after the application of the correction procedures using Eddy Pro 4. and PEC softwares. The consequences of the spectral losses are remarked in the slope of linear regression between PEC and Eddy Pro fluxes. Flux losses, for latent and sensible heat, produce a mean decrease in flux magnitude of about 8%, with slopes equal to.95 for latent heat and.9 for sensible heat. Intercepts are near closed to zero while R 2 is about.9 for both fluxes. Usually, engineering applications need to know evapotranspiration flux overall growing season. Cumulated evapotranspiration flux and carbon dioxide trend could be used to define the characteristics of canopy comportment from sowing to reaping time. In Fig.17, cumulated evapotranspiration flux and carbon dioxide trend over growing season of maize field are shown. In black, the fluxes calculated using Eddy Pro 4., and in grey the fluxes obtained by PEC software are shown. As shown in Fig. 17A, the divergence among two fluxes starts at the beginning of the growing season and it remains constant on all experimental period. As shown in Fig. 17B, the divergence begins more or less at 2 Julian day and increases until the end of the cultivated season. At the end of growing season the difference among the fluxes is about 1 mm for the cumulated evapotranspiration and 9 g m -2 for CO A ET_from_averaged_data ET_from_EddyPro B 3.E+2.E E+2-6.E Julian day -9.E+2-1.2E+3 CO2_from_averaged_data CO2_EddyPro Julian day Fig. 17. Comparison between cumulated evapotranspiration (A) and carbon dioxide (B) fluxes obtained by PEC and Eddy Pro 4. softwares. 37

38 LE+H (W m -2 ) Energy balance closure with PEC fluxes In order to complete the analysis over fluxes obtained by PEC software, energy balance closure is shown in Fig. 18. The slope of the linear regression is quite differenced by that shown in Fig. 15A (obtained by Eddy Pro 4.). In this case the slope is equal to.74, while the dispersion of the dots is reduced and R 2 value is about.89. This result is probably due to the moderated influence of preliminary processes and spectral losses which have not been considered into the PEC software corrections. 8 6 y =.74x R² = Rn-G (W m -2 ) Fig. 18. Energy balance closure using latent and sensible heat fluxes calculated by PEC software. Conclusion In this work the impact of different correction procedures on turbulent flux measurements collected by an eddy covariance station, are described. Starting from high frequency data a complex series of processes have to be implemented to extract reliable turbulent fluxes of latent, sensible heat, carbon dioxide and water vapor from raw data measurements. In the preliminary processes, the double correction procedure play a fundamental role to adjust the orientation of the Cartesian system of axis respect to streamlines. Spectral corrections are necessary to define flux losses due to the specific transfer functions which characterize the measurement system. Turbulent fluxes need to be corrected for density fluctuation and humidity effect on sonic temperature using WPL and VD corrections. These corrections should not be considered as corrections, but a normal step to calculate turbulent fluxes. In fact, if the WPL and VD corrections are not applied, turbulent fluxes do not reproduce correctly the physical aspects of the experimental site. A final control based on micrometeorological tests of steady state and developed turbulence permits to highlight the quality of calculated fluxes advising the operator if flux data should be neglected. High frequency (1-2 Hz) measurements of the three components of wind velocity and gas concentrations have to be stored to obtain reliable turbulent fluxes at different scale. It is widely known in literature, but in some cases, impossibility to have high frequency data do not permit to apply the whole categories of correction procedures. Moreover, some engineering applications which for example refer to the possibility to estimate evapotranspiration fluxes over a growing season could not require for the accuracy developed in the previous analysis. For these problems, a simple method which permits to the operator the possibility to calculate turbulent fluxes from 38

39 an averaged dataset has been shown. In fact, in PEC software only WPL and VD corrections are implemented and these corrections could be defined as essential ingredients to covert measurements in reliable fluxes. As shown in Fig. 17A the difference between PEC software results and Eddy Pro 4. fluxes is small and PEC fluxes underestimates Eddy Pro evapotranspiration fluxes only for 1 mm. Reducing the number of corrections, the algorithm implementations in a programming language appear to be of easy application also for operators which are not expert in software engineering. In general it is possible to conclude that turbulent fluxes could be approximately assessed starting from averaged data, but if the flux accuracies are rigorously required, the whole range of corrections should be taken into account. References Aubinet, M., Grelle, A., Ibrom, A., Rannik, U., Moncrieff J., Foken, T., et al. (2). Estimates of the annual net carbon and water exchange of forests: the euroflux methodology. Advanced in Ecological Research, 3: Baldocchi, D., Falge, E., Gu, L., Olsen, R., Hollinger, D., Running, S., et al. (21). FLUXNET: a new tool to study the temporal and spatial variability of ecosystem scale carbon dioxide, water vapor, and energy flux densities. Bulletin of American Meteorological Society, 82: Barr, A., Morgenstern, K., Black, T., McCaughey, J., and Nesic, Z. (26). Surface energy balance closure by the eddy-covariance method above three boreal forest stands and implications for the measurement of CO2 flux. Agricultural and Forest Meteorology, 14: Burba, G., McDermitt, D., Grelle, D., Anderson, D., and Xu, L. (28). Addressing the influence of instrument surface heat exchange on the measurements of CO2 flux from open path gas analyzer. Global Change Biology, 14: Corbari C., Masseroni,D.,Mancini, M., (212). Effetto delle correzioni dei dati misurati da stazioni eddy covariance sulla stima dei flussi evapotraspirativi. Italian Journal of Agrometeorology,1: Fan, S., Wofsy, S., Bakwin, P., Jacob, D., and Fitzjarrald, D. (199). Atmosphere-biosphere exchange of CO2 and O3 in the Central Amazon Forest. Journal of Geophysical Research, 95: Foken, T. (1991). Informationen uber das internationale experiment TARTEX-9, torevere bei tartu, estland, 28.5 bis Zeitschrift fur Meteorologie, 41: 227. Foken, T. (28). Micrometeorology. Berlin: Springer, pp. 36, ISBN Foken, T., and Wichura, B. (1996). Tools for quality assessment of surface-based flux measurements. Agricultural and Forest Meteorology., 78: Foken, T., Gockede, M., Mauder, M., Mahrt, L., Amiro, B., and Muger, J. (24). A guide for surface flux measurements. Kluwer Academic, Dordrecht Foken, T., Wimmer, F., Mauder, M., Thomas, C., and Liebhetal, C. (26). Some aspects of the energy balance closure problem. Atmospheric Chemistry and Physics, 6: Fuehrer, P.L. and Friehe, C.A. (22) Flux correction revised. Boundary Layer Meteorology, 12: Garratt, J. (1993). The atmospheric boundary layer. Cambridge: Cambridge university press, pp.316, ISBN

40 Gash, J., and Culf, A. (1996). Applying linear de-trend to eddy correlation data in real time. Boundary Layer Meteorology, 79: Gluhovsky A. and Agee E. (1994): A definitive approach to turbulence statistical studies in Planetary Boundary Layer. Journal of Atmospheric Sciences, 51: Gockede, M., Foken, T., Aubinet, M., Aurela, M., and Banza, J. (28). Quality control of CarboEurope flux data - Part1: Coupling footprint analysis with flux data quality assesment to evaluate sites in forest ecosystems. Biogeosciences, 5: Gurjanov AE, Zubkovskij SL and Fedorov MM (1984) Mnogokanalnaja avtomatizirovannaja sistema obrabotki signalov na baze EVM (Automatic multi-channel system for signal analysis with electronic data processing). Geod Geophys Veröff, R II. 26:17-2. Ibrom, A., Dellwik, E., Larse, E., and Pilegaard, K. (27). On the use of the Webb-Pearman_Leuning theory for closed-path eddy correlation measurements. Tellus Series B-Chemical and Physiscal Meteorology, 59: Jacobs, A., Heusinlveld, B., and Holtslag, A. (28). Towards closing the energy surface budget of a mid-latitude grassland. Boundary Layer Meteorology,126: Kaimal, J., Wyngaard, J., Izumi, Y., and Cotè, O. (1972). Spectral characteristics of surface-layer turbolence. Quarterly Journal of the Royal Meteorological Society, 98: Kustas, W., and Daughtry, C. (199). Estimation of the soil heat fluxnet radiation ratio from spectral data. Agricultural and Forest Meteorology: 49: Lee, X., Massman, W., and Law, B. (24). Handbook of Micrometeorology: A Guide for Surface Flux Measurement and Analysis. Kluwer Academic Press, Dordrecht, 25 pp. Lenschow D.H., Mann,J., and Kristensen, L. (1994): How long is long enough when measuring fluxes and other turbulence statistics? Journal of Atmospheric and Oceanic Technology, 11: Leuning, R. (24). Measurements of trace gas fluxes in the atmosphere using eddy covariance : WPL correction revisited. Kluwer, Dordrecht, pp Lloyd, C., Shuttleworth, W., and Gash, J. T. (1984). A microprocessor system for eddy-correlation. Agricultural and Forest Meteorology, 33: Lumley, H.H., and Panofsky, H.A. (1964): The structure of atmospheric turbulence. John Wiley&Sons. Masseroni, D., Ravazzani, G., Corbari, C., and Mancini, M. (211). Correlazione tra la dimensione del footrpint e le variabili esogene misurate da stazioni eddy covariance in Pinura Padana, Italia. Italian Journal of Agrometeorology, 1: Massman, W. (2). A simple method for estimating frequency responce corrections for eddy covariance systems. Agricoltural and Forest Meteorology, 14: Massman, W. (24). Concerning the measurement of atmospheric trace gas fluxes with open and closed path eddy covariance system: The WPL terms and spectral attenuation, in Handbook of micrometeorology: a guide for surfacem flux measurements. Kluwer Academic, Netherlands, Massman, W., and Lee, X. (22). Eddy covariance flux corrections and uncertainties in long-term studies of carbon and energy exchanges. Agricultural Forest Meteorology, 113:

41 Mauder, M. and Foken, T. (24). Documentation and instruction manual of the eddy covariance software package TK2. Arbeitsergebn, Univ Bayreuth, Abt Mikrometeorol, ISSN : 42 pp. Mauder, M., and Foken, T. (26). Impact of post field data processing on eddy covariance flux estimates and energy balance closure. Meteorologische Zeitschrift, 15: McMillen, R. (1988). An eddy correlation technique with extended applicability to non-simple terrein. Boundary Layer Meteorology, 43: Moncrieff, J., Clement, R., Finnigan, J., and Meyers, T. (24). Averanging and filtering of eddy covariance time series, in Handbook of micrometeorology: a guide for surface flux measurements. Kluwer Academic, Dordrecht, Moncrieff, J., Massheder, J., De Bruin, H., Ebers, J., Friborg, T., Heusinkveld, B., et al. (1997). A system to measure surface fluxes of momentum, sensible heat, water vapor and carbon dioxide. Journal of Hydrology, : Moore, C. (1983). On the calibration and temperature behaviour of single-beam infrared hygrometer. Boundary Layer Meteorology, 25: Moore, C. (1986). Frequency response corrections for eddy correlation systems. Boundary Layer Meteorology, 37: Obukov, A. (1946). Turbolance in an atmosphere with a non-uniform temperature. Trudy Ins. Theor. Geofiz. AN SSSR, 1: Rannik, U., and Vesala, T. (1999). Autoregressive filtering versus linear detrending estimation of fluxes by the eddy covariance method. Boundary Layer Meteorology, 91: Reichstein, M., Tenhunen, J., Roupsard O., Orcival, J., Rambal, S., Dore S., and Valentini R. (22). Ecosystem respiration in two Mediterranean evergreen holm oak forests: drought effects and decomposition dynamic. Functional Ecology, 16: Runkle, B., Wille, C., Gazovic, M., and Kutzbach, L. (212). Attenuation correction procedures for water vapor fluxes from closed-path eddy covariance systems. Boundary Layer Meteorology, 142: Schmid HP (1997) Experimental design for flux measurements: matching scales of observations and fluxes. Agricultural and Forest Meteorology. 87: Schotanus, P., Nieuwstadt, F., and De Bruin, H. (1983). Temperature meaurement with a sonic anemometer and its application to heat and moisture fluxes. Boundary Layer Meteorology, 26: Shuttleworth, W. (1988). Corrections for the effect of background concentrations change and sensor drift in real time eddy correlation systems. Boundary Layer Meteorology, 42: Shuttleworth, W., Gash, J., Lloyd, C., McNeil, D., Moore, C., and Wallance, J. (1988). An integrated micrometeorological system for evaporation measurement. Agricultural and Forest Meteorology, 43: Shuttleworth, W., McNeil, D., and Moore, C. (1982). A switched continuous-wave sonic anemometer for measuring surface heat fluxes. Boundary Layer Meteorology, 23: Stull, R. (1988). An introduction to boundary layer meteorology. Dordrecht, Boston, London, 666: Kluwer Academic Publisher. 41

42 Treviño G., E.L. Andreas (2): Averaging interval for spectral analysis of non stationary turbulence - Bound. Layer Meteor., 95: Ueyama, M., Hirata, R., Mano, M., Hamotani, K., Harazono, Y., Hirano, T., Miyata, A., Takagi, K., and Takahashi, Y., (212). Influences of various calculation options on heat, water and carbon fluxes determined by open- and closed path eddy covariance methods. Tellus B, 64: Van Dijk, A., Kohsiek, W., and De Bruin, H. (23). Oxygen sensitivity of krypton and Lyman-alfa Hygrometer. Journal of Atmospheric and Oceanic Technology, 2: Vickers, D., and Mahrt, L. (1997). Quality control and flux sampling problems for tower and aircraft data. Journal of Atmospheric and Oceanic Technology, 14: Webb, E., Pearman, G., and Leuning, R. (198). Correction of the flux measurements for density effects due to heat and water vapour transfer. Boundary Layer Meteorology, 23: Wilczak, J., Oncley, S., and Stage, S. (21). Sonic anemometer tilt correction algorithms. Boundary Layer Meteorology, 99: Wilson, K., Goldstein, A., Falge, E., Aubinet, M., Baldocchi, D., Berbigier, P., et al. (22). Energy balance closure at FLUXNET sites. Agricultural and Forest Meteorology, 113:

43 (Chapter 2) Energy balance closure of an eddy covariance station: limitations and improvements Abstract The use of energy fluxes data to validate land surface models requires that the conservation of the energy balance closure is satisfied; but usually this condition is not verified when, measuring energy components with an eddy covariance station, available energy is bigger than the sum of turbulent vertical fluxes. In this work, a comprehensive evaluation of the energy balance closure problems is performed on Livraga 212 data set which is obtained by a micrometeorological eddy covariance station located in a maize field in Po Valley. Energy balance closure is calculated by statistical regression of turbulent energy fluxes and soil heat flux against available energy. Generally, the results indicate a lack of closure with a mean imbalance in the order of 2%. Storage terms are the main reason for the unclosed energy balance but also the turbulent mixing conditions play a fundamental role in the reliable turbulent flux estimations. Recently introduced in literature, the energy balance problem has been studied as a scale problem. Representative source area for each flux of the energy balance has been analyzed and the closure has been performed in function of turbulent flux footprint areas. Surface heterogeneity and seasonality effects have been studied with objective to understand the influence of canopy growth on energy balance closure. High frequency data have been used to calculate co-spectral and ogive functions which suggest if averaging period of 3 minutes may miss temporal scales that contribute to the turbulent fluxes. Finally, latent and sensible heat random error estimations are computed to give information about measurement system and turbulence transport deficiencies. Introduction Surface energy fluxes are important for a huge range of application over different spatial and temporal scales: from flash flood simulation at basin scale to water management in agricultural area. It is then important to understand the quality of measured fluxes before using them for land atmosphere simulations. The quality of eddy covariance measurements is influenced not only by possible deviations from the theoretical assumptions but also by problems of sensor configurations and meteorological conditions (Foken and Wichura, 1996). However, it is difficult to isolate the causes of measurements errors. Instrumental errors, uncorrected sensor configurations, problem of heterogeneities in the area and atmospheric conditions are the main problems that afflict the data quality (Jacobs et al., 28; Wilson et al., 22; Foken et al., 26; Foken, 28a). Eddy covariance method produces reliable results when the theoretical assumptions in the surface layer are respected (Baldocchi et a. 21; Foken and Wichura, 1996; Fisher et al., 26). In particular, the theoretical requirements, such as steady-state condition, horizontal homogeneity of the field, validity of the mass conservation equation, negligible vertical density flux, turbulent 43

44 fluxes constant with height and flat topography, should be satisfied. Moreover, sensors configuration should be analyzed in relation to the sampling duration and frequency, separation of sonic anemometer and gas analyzer, sensor placement within the constant flux layer, but out of the roughness sub-layer. Meteorological conditions, such as precipitation events and low turbulence, especially at night time, can lead to errors in fluxes measurement. The unbalance of the energy budget has been widely studied in the last decade due to the fact that the use of energy fluxes to validate land surface models requires that the closure of the energy balance is satisfied. Energy budget is typically not closed when, measuring energy fluxes with an eddy covariance station, available energy is usually bigger than the sum of turbulent vertical heat fluxes with a ratio that varies between 7 and 9% (Jacobs et al., 28; Wilson et al., 22; Foken et al., 26; Ma et al., 29). Thus, it is important to understand the different factors that can lead to an improvement of the energy balance closure. The first cause of the lack of energy balance closure is liked to an uncorrected implementation of a complete set of instrumental and flux corrections as described in Aubinet et al. (2). Axis rotation, spike removal, time lag compensation and detrending are the preliminary correction processes which should be applied on high frequency raw data set measured by sonic anemometer and gas analyzer. Subsequently, spectral information losses, air density fluctuations and humidity effects have to be taken into account to obtain reliable fluxes of latent and sensible heat (Moncrieff et al. 1997,Webb et al. 198; Van Dijk et al. 24). However, later studies discuss unbalance problem as an effect of the fractional coverage of vegetation and the influence of the soil storage (Foken, 28b). Additional storage terms, like the ones linked to the photosynthesis processes or vegetation canopy, give a relevant improvement in energy balance closure (Meyers and Hollinger, 24). Different time aggregation could reduce the effect of storage terms because they have an opposite behavior during day time and night time (Papale et al., 26). Some recent works (Finnigan et al., 23; Oncley et al., 1993) have suggested that averaged time (generally 3 minutes) which is chosen to calculate covariances could be inadequate for assessing turbulent fluxes. Ogive function for each half hour data set can be a good indicator for measurement errors associated to such energy balance problems (Oncley et al., 1993). Moreover, energy balance closure can be seen as a scale problem, because the representativeness of a measured flux is a function of scale. Usually, for homogeneous areas, the assumption that source areas are the same for all fluxes is considered valid. However, these areas can be significantly different if the footprint of turbulent fluxes is compared to the source area of ground heat flux. So a portion of the error in energy balance closure can be related to the difficulty to match footprint area of eddy covariance fluxes with the source areas of the instruments which measure net radiation and ground heat flux (Wilson et al., 22; Schmid, 1997; Hsieh et al 2). Eddy flux measurements can be underestimated during periods with low turbulence and air mixing. This underestimation acts as a selective systematic error and it generally occurs during the night time. Massman and Lee (22) listed the possible causes of the night-time flux error. There is now a large consensus to recognize that the most probable cause of error is the presence of small scale movements associated with drainage flows or land breezes that take place in low turbulence conditions and create a decoupling between the soil surface and the canopy top. In these conditions, advection becomes an important term in the flux balance and cannot be neglected anymore. It has been recently suggested (Finnigan et al., 26) that, contrary to what 44

45 was thought before, advection probably affects most of the sites, including also flat and homogeneous ones. Direct advection fluxes measurements are difficult to measure as they require several measurement towers at the same site. Attempts are notably made by Aubinet et al. (23), Feigenwinter et al. (24), Staebler and Fitzjarrald (24) and Marcolla et al. (25). They find that advection fluxes are usually significant during calm weather conditions. However, in most cases, the measurement uncertainty is too large to allow their precise estimation. In addition, such direct measurements require a too complicated set up to allow routine measurements at each site. In practice, flux problem is by-passed by discarding the data corresponding to low mixed periods. The friction velocity is currently used as a criterion to discriminate low and high mixed periods. This approach is generally known as the u correction. Although being currently the best and most widely used method to circumvent the problem, the u correction is affected by several drawbacks and must be applied with care. Factors connected with growing vegetation and seasonality have been investigated. As shown in Panin et al. (1998) the unbalance could be attributed to the influence of the surface heterogeneity and vegetation height in respect to sensors position. Different sources of uncertainties in flux measurements can be sometimes difficult to assess. Random measurement errors in flux data, including errors due to measurement system and turbulence transport, have been assessed by Hollinger and Richardson (25), comparing the measurements from two towers with the same flux source area ( footprint ) and by Richardson et al. (26), comparing pair of measurements made on two successive days from the same tower under equivalent environmental conditions. A simple method described in Moncrieff et al. (1996) can be used to quantify the influence of random error on momentum, latent and sensible heat calculating a degree of uncertainty for each turbulent flux. In this work relevant findings on energy balance closure problem over maize field in Po Valley are summarized mainly on the basis of recent investigation works as Foken (28b), Oncley et al. (27) and Wilson et al. (22). Turbulent fluxes from a raw data set of high frequency measurements, are obtained using Eddy Pro 4. software with the main objective to standardize the correction procedure of eddy covariance measurements. Impacts of each investigated factor is quantified by the slope and intercept values between turbulent vertical heat fluxes (latent heat, sensible heat and ground heat fluxes) and available energy (net radiation) from a regression analysis of half hourly basis. Each examined factor is separately studied to each other to improve understanding of its impact on energy balance closure. Theoretical backgrounds are not summarized in a separate chapter but they are included in each sub-paragraph to improve the description of the exanimate problems. Only practical formulas are shown, while mathematical approaches are quoted in literature. Instruments, data collection and site description Experimental campaign was carried out over a maize field at Livraga (LO) in Po Valley during the year 212. The field is about 1 hectare large and the local overall topography is flat. In the middle of the field an island of about 5 m 2 is designed to include agro-micrometeorological instruments and devices. Eddy covariance data are measured by a tridimensional sonic anemometer (Young 81) and open path gas analyzer (LICOR 75) located at the top of a tower at an height of about 5 m. 45

46 High frequency (2 Hz) measurements are stored in a compact flesh of 2 Gb connected with the data logger Campbell CR5 and downloaded in situ weekly. On compact flash only three wind velocity components, sonic temperature, vapor and carbon dioxide concentrations are stored (raw data). Contemporaneously net radiation, measured by CNR1 Kipp&Zonen radiometer (4.5 m high), soil heat flux, measured by HFP1 Campbell Scientific flux plate, and soil temperature measurements are stored on data logger in different memory tables. Into the island also soil moisture at different levels and rain are measured. Averaged fluxes are calculated over a time step of 3 minutes. Experimental measurements were carried out from 21 May to 7 September but the dataset is composed by only 313 averaged data because some gaps due to malfunctioning of instrumentations or rainfall days are shown into the data sequences. From 131 to 241 Julian day the field is covered by vegetation, while the remaining days of the year, the field is characterized by bare soil. Vegetation height varies from zero to 32 cm and the canopy grew during the project can be spatially considered homogeneous across the field. Wind direction is quite steady, generally from West during day time and East during night time but in some days this convention is not always respected. Considering each wind direction, the eddy tower position is compatible with the constant flux layer (CFL) (Elliot, 1958). CFL is defined as 1-15% of internal boundary layer (Baldocchi and Rao, 1995), and it represents a space area where measured fluxes by the eddy tower are constant. Applying Elliot s (1958) formula in unfavourable conditions of bare soil, with a calculated aerodynamic roughness of about.4 m (Garrat, 1993), the CFL depth at the tower is about 6 meters ensuring that the eddy covariance instruments (tridimentional sonic anemometer and gas analyser) are included into the CFL. During the summer period the site is typically characterized by a cloud-free sky in association with a quit high evapotranspiration and net radiation values of about 6 and 7 W m -2 respectively. Cumulated rain over the experimental period is about 2 mm, while soil moisture measured at a depth of 1 cm varies between maximum and minimum peaks of about.4 and.15 respectively. The energy balance closure problem Energy balance closure, a formulation of the first law of thermodynamic, requires that the sum of the estimated latent (LE) and sensible (H) heat and ground heat flux (G) has to be equivalent to all other energy sink or source (Eq. 1). LE H G (1) R n Where R n is the net radiation. Generally, fluxes are typically integrated over periods of half hour building the basis to calculate energy balance to annual time scales. The slope (defined as (LE+H+G)R n -1 ) and intercept values of the regression line quantify the reliability of the energy balance closure which is close to 1 in an ideal case. In the following sections the relevant findings on the energy balance closure are summarized and data processing results using the experimental measurements are shown. 46

47 Effect of data corrections In this paragraph the procedures necessary to obtain reliable fluxes starting from high frequency raw data set are briefly described (see Chapter 1). Eddy covariance measurements have to be corrected to obtain reliable turbulent fluxes of latent and sensible heat. Before calculating fluxes, two groups of corrections should be implemented: instrumental and physical corrections. Instrumental corrections can be considered as preliminary processes which have to be directly applied on high frequency measurements to prepare the data set for fluxes calculation. Axis rotation for tilt correction. Tilt correction algorithms are necessary to correct wind statistics for any misalignment of the sonic anemometer with respect to the local wind streamlines. Wilczak et al. (21), proposes three typologies of correction algorithms, and for Livraga 212 dataset a double rotation method has been used. Using this method, the anemometer tilt is compensated by rotating raw wind components to nullify the average cross-stream and vertical wind components. Spike removal. The so called despiking procedure consists in detecting and eliminating short term outranged values in the time series. Following Vickers and Mahrt (1997), for each variable a spike is detected as up to three consecutive outliers with respect to a plausibility range defined within a certain time window, which moves throughout the time series. Time lag compensation. In open path system the time lag between anemometric variables and variables measured by gas analyzer is due to the physical distance between the two instruments, which are usually placed several decimeters or less apart to avoid mutual disturbances. The wind field takes some time to travel from one instrument to the other, resulting in a certain delay between the moments the same air parcel is sampled by the two instruments (Runkle et al., 212). Detrending. Eddy correlation method of calculating fluxes requires that the fluctuating components of the measured signals are derived by subtracting them from the mean signals. In steady-state conditions simple linear means would be adequate, but steady state conditions rarely exist in the atmosphere and it is necessary to remove the long term trends in the data which do not contribute to the flux (Gash and Culf, 1996). After completing the preliminary processes, physical corrections have to be implemented. Spectral information losses, air density fluctuation and humidity effects on sonic temperature are taken into account in accordance with the procedure described in Ueyama et al. (212). Spectral correction. Spectral corrections compensate flux underestimations due to two distinct effects. The first is referred to the fluxes which are calculated on a finite averaging time, implying that longer-term turbulent contributions are under-sampled at some extent, or completely. The correction for these flux losses is referred to as high-pass filtering correction because the detrending method acts similarly to a high-pass filter, by attenuating flux contributions in the frequency range close to the flux averaging interval. The second is connected with instrument and setup limitations that do not allow sampling the full spatiotemporal turbulence fluctuations and necessarily imply some space or time averaging of smaller eddies, as well as actual dampening of the small-scale turbulent fluctuations (Moncrieff et al., 1997). WPL correction. The open-path gas analyzer does not measure nondimensional carbon dioxide and water vapor concentrations as mixing ratios but it measures carbon dioxide and water vapor densities. For this reason, the trace gas flux using this analyzer needs to correct for the mean 47

48 vertical flow due to air density fluctuation. Webb et al. (198) suggested that the flux due to the mean vertical flow cannot be neglected for trace gases such as water vapor and carbon dioxide. To evaluate the magnitude of the influence by the mean vertical flow, Webb et al. (198) assumed that the vertical flux of dry air should be zero. Practically, sensible and latent heat fluxes evaluated by the eddy covariance technique are used to calculate water vapor and carbon dioxide fluxes by the mean vertical flow (WPL correction). VD correction. Sonic anemometer measures wind velocity components and sonic temperature. Sonic temperature, which is the basis of the sensible heat calculation, is affected by both humidity and velocity fluctuations. Van Dijk et al. (24), revising the experiment carried out by Schotanus et al. (1983), defines a correction term to apply on sensible heat formula to obtain reliable flux (VD correction). Corrections impact on turbulent fluxes as a consequence of the procedure described above, can be founded in the work of Ueyama et al. (212) and also in Chapter 1 of this thesis. As shown in Chapter 1, where ensemble means of diurnal variations of turbulent fluxes over the whole experimental period are computed, if correction procedures are not applied, during daytime, latent, sensible and ground heat fluxes collapsed to zero, while in nighttime overestimations of latent and sensible heat brings to an unsatisfactory flux interpretations. The energy balance closure calculated after the correction procedures only applied on latent and sensible heat flux components is equal to.75 with a correlation coefficient (R 2 ) of about.8 and intercept of about 1 W m -2. Effect of storage terms Eddy covariance measurements are based on turbulent air mixing and vertical flux exchanges. Sometimes, portion of latent and sensible heat could be stored below measurement point and these concentrations are not measured by anemometer and gas analyzer devices. Usually, when the canopy covers the field, the effect of the canopy heat storage and photosynthesis flux increase drastically. The best way to compute storage flux is to deduce it from a concentration profile method inside the canopy (Papale et al, 26). However, at many sites, a discrete estimation based only on concentration at the tower top is used (Meyer and Hollinger, 24). Moreover, a correction is required to account for the heat storage that occurs in the layer between the soil surface and the heat flux plate (Mayocchi and Bristow, 1995), so Eq. 1 can be rewritten adding the storage terms (Eq. 2). LE H G S S S R (2) g c p n Where S p is the energy flux for photosynthesis, S c is the canopy heat storage in biomass and water content and S g is the ground heat storage above the soil heat plate. The heat storage terms for the local surface energy balance are calculated by computing the total enthalpy change over a given time interval ( t ) which is 3 minutes. For the canopy, the rate change in enthalpy is described by Eq.3. mwcw mbcb Sc (3) t 48

49 Where is the temperature exchange over the canopy directly measured by radiometer. In fact, CNR1 Kipp & Zonen radiometer permits to measure directly long wave and short wave radiation incoming and outgoing the surface. Starting from long wave radiation outgoing the surface, considering the surface as a bleakbody, temperature can be calculated inverting Stefan- Boltzmann law. Plant water mass (m w ), biomass (m b ) density, specific heat for plant water (c w ) and biomass (c b ) are directly estimated by Meyers and Hollinger (24) work, where the maize plant were weighed, dried, and weighed again in order to assess the plant water content and biomass density. A similar procedure for heat storage in the soil surface is followed (Eq. 4). T wcwmsw scs z S g (4) t Where T is the temperature exchange in the soil, m sw is the density of water, w is the measured volumetric content measured by soil moisture probe at 1 cm depth, z is the depth above the soil heat plate to the ground surface, is the soil bulk density and c s s is the specific heat capacity of soil (Kustas and Daughtry, 199). The light energy transformed in the photosynthetic process to carbon bond energy in biomass has long been ignored when compared to the other terms in the surface energy balance. However, as researchers continue to be plagued by a lack of closure in the surface energy balance (Meyer and Hollinger, 24) all of the data processing methods and terms should be reevaluated. Analyzing the formation of glucose in its chemical reaction (Eq.5), an estimate of the energy used in photosynthesis is obtained from the net sum of the energy that is required to break the bonds of the reactants and those in forming glucose and oxygen. 6H 2 O + 6CO 2 6O 2 + C 6 H 12 O 6 (5) This is the solar energy that is now stored in the bonds of carbohydrate and is 422 kj of energy per mole of CO 2 fixed by photosynthesis (Nobel, 1974). A canopy assimilation rate of 2.5 mg CO 2 m 2 s 1 equates to an energy flux of 28 W m 2. This conversion factor is used to compute the measured photosynthesis rates from the eddy covariance measurements to an equivalent energy flux. In accordance with Meyers and Hollinger (24) procedure, storage terms are computed for the daytime period only and the data are grouped into 2 hours bins beginning at 6: and ending to 18:. The averaged daytime storage fluxes for the whole experimental period are shown in Fig. 1. As shown in Fig.1A, heat storage in the soil is grater then the other storage fluxes. Its trend is characterized by a peak of about 34 W m -2 in correspondence with the midday. During the morning, heat storage in the soil increases while in the afternoon it decreases up to 1 W m -2. Photosynthesis storage term have a similar behavior with a peak of about 1 W m -2, while the canopy heat storage term tend to decrease during the day. In Fig. 1B the ratio between the sum of storage terms (Total storage) and net radiation, which represents the available energy in the ecosystem, is shown. The storage fluxes constitute a significant fraction of the available energy 49

50 Slope and R 2 (-) Intercept ( W m -2 ) Energy flux ( W m -2 ) Total storage/r n (%) with a ratio of about 1% which is quite constant from 8: to 14:, while it tends to decrease in the late afternoon. A B 4 Sc 15 3 Sp Sg Hours Hours Fig. 1. A. The average daytime cycle for each storage term for the whole experimental perid. B. Fraction of net radiation that is portioned to storage for maize plants. The effect of storage terms on surface energy balance is examined by comparing the sum of H, LE and G with and without each storage flux against R n for the daytime periods over the whole experimental campaign. For the maize filed, without including the storage terms, the slope from simple linear regression is.75 with an R 2 of about.8 (Fig. 2). When the storage terms, in the surface energy balance, are included the slope of the linear regression tends to increase up to.86 with a R 2 of about.8 and an intercept of about 1.8 W m -2. If in the energy balance closure storage terms are included, the systematic error in fluxes, described by linear regression intercept, is characterized by a drastic decreasing from 1 W m -2 to 1.8 W m -2. As explained in Foken (28a), the ground heat storage has to be added into soil heat flux to obtain reliable G flux estimation. In fact, as shown in Fig. 2, ground storage term plays a fundament role into the energy balance closure improvement having a positive influence of about 6% which is equal to about 54% over the total energy balance improvement if the whole storage terms are considered Slope R2 Intercept Fig. 2. Energy balance closure adding storage terms. Although the daytime energy balance with total storage terms is on average closed within 14%, closure deficit may be a consequence of an inaccurate G flux estimation which is extremely different in the spatial contest as described in Wilson et al. (22). Moreover, storage fluxes 5

51 obtained by a single point measurement can be underestimated in respect to the more complicated profile methods. In the common practice, heat soil flux (measured by heat soil plate) is usually corrected with ground storage term, so that, in the following paragraphs, in G flux the ground heat storage term is already included. Effect of time aggregation As described in Foken (28b), an energy transport with large eddies which cannot be measured with the eddy covariance method is assumed as one of the main reasons of the closure problems. In literature, several methods are discussed to investigate this problem (Sakai et al. 21, Finnigan et al. 23, Foken et al. 26). About 15 years ago, the ogive function was introduced into the investigation of turbulent fluxes (Oncley et al. 199, Friehe 1991). This function was proposed as a test to check if all low frequency parts are included in the turbulent flux measured with the eddy covariance method (Foken et al. 1995). The ogive function is the cumulative integral of the co-spectrum starting with the highest frequencies as described by Eq.6. f Og ( f ) Co ( f ) df (6) wx wx where Co wx is the co-spectrum of a turbulent flux, w is the vertical wind component, x is the horizontal wind component or scalar, and f is the frequency. In Fig. 3 sensible and latent heat flux cospectrums and their ogive functions are respectively shown. In Fig. 3A example of a ogive function and co-spectrum for of a ogive function and co-spectrum for w't ' in 2 July at 14: is shown, while in Fig. 3B example w ' H 2 O ' in 11 August at 3:3 is shown. A B Og WT Ogive (WT) Cospectrum (WT) Co WT 2 Og WH2O Ogive (WH2O) Cospectrum (WH2O) Co WH2O Frequency (Hz) Frequency (Hz) Fig. 3. Example of a ogive function and cospectrum for w 'T ' (A) and w ' H ' (B) in 2 July at 14: and 11 August at 3:3 respectively. 2 O In the convergent case (Fig.3A), the ogive function increases during the integration from high frequencies to low frequencies until a certain value is reached and remains on a more or less constant plateau before a 3 minutes integration time. If this condition is full-filled, the 3 51

52 Slope and R 2 (-) Intercept (W m -2 ) minutes covariance is a reliable estimate for the turbulent flux, because it is possible to assume that the whole turbulent spectrum is covered within that interval and that there are only negligible flux contributions from longer wavelengths (Case 1). But it can also occur that the ogive function shows an extreme value and decreases again afterwards (Case 2- Fig.3B) or that the ogive function doesn t show a plateau but increases throughout (Case 3). Ogive functions corresponding to Case 2 or 3 indicate that a 3 minutes flux estimate is possibly inadequate. Foken et al. (26) define thresholds about ogive characteristic behaviors in order to prescribe if a ogive belongs to Case 1, 2 or 3. From the ogive analysis performed for latent and sensible heat fluxes over the whole experimental period, 3 minutes averaging interval appears to be sufficient to cover all relevant flux contributions with about 8% of cases included in the Case 1, while only 2% of cases belongs to Case 2 and 3. Finnigam et al. (23) propose a site specific extension of the averaging time up to several hours to close the energy balance. In Fig. 4 energy balance closures with reference to energy flux aggregations at different temporal scales, are shown Slope R2 Intercept hour 6 hour 24 hour -5 Fig. 4. Energy balance closure with different aggregation times. The slope tends to increase if large size of averaging time are considered, but if an aggregation period of 6 hours is examined, the linear regression (.76) is quite similar to that calculated with half-hourly data (.75). Instead, with an aggregation time period equal to 24 hours, the slope has a large improvement (.83). This is probably due to the effect of storage terms which can be considered negligible at daily scale as shown in Foken (28b). Effect of scale differences in fluxes measurement The energy balance closure can also be seen as a scale problem, because each flux is representative of an area (Fig.5). In fact net radiometer source area is the field of view of the instrument at nadir related to sensor height and it doesn t change with time. In Fig.5A the net radiometer source area described by Schmid s (1997) equation using the radiometer configuration on the tower for this experimental campaign, is shown. Radiometer is located on a arm (b) of about 2.5m long, attached on the tower at the height of about 4.5 m (z r ). Its orientation is from North to South to receive the whole solar radiation during the daily hours. Its source area has a circular shape with a maximum radius of about 4 m, and the major representativeness of 52

53 the short and long wave measurement, which are coming from the surface, are in correspondence with the projection of the radiometer on the ground (red zones). The flux footprint of turbulent fluxes varies in space and time depending mainly on wind velocity and direction, surface roughness, stability condition of the atmosphere and measurement height (Hsieh et al., 2). According to Hsieh et al. (2) definition, the footprint represents a weight function (for unit of length) of different contribution that is coming from the surface area at a certain distance away for the instruments (anemometer and gas analyzer - EC station). This function change in space and in time and it is different for each 3 minutes measurement. In Fig. 5B footprint source area of the eddy covariance station considering the whole experimental data from May to September, is shown. Bi-dimensional footprint is computed using Hsieh et al. (2) and Detto et al. (26) models for the longitudinal and lateral spreads respectively. The mathematical approach to match Hsieh et al. (2) and Detto et al. (26) models is not described in this work but it is widely discussed in the recent article of van de Boer et al. (213). The footprint area obtained for each half-hourly data has been oriented in respect to the wind directions, and performing this procedure on the whole experimental data set, the footprint shape represented in Fig. 5B has been obtained. In general, the major representativeness of the latent and sensible heat flux measurements is confined in an area of about 45m 2 on the right of the tower (West direction). This is probably due to the limited magnitude of the wind intensities in Po Valley which are not exceeded 1 m s -1. A Radiometer footprint (m -2 ) B EC station footprint (m -1 ) b EC station z r projection of the radiometer center z m Fig. 5. A. Radiometer source area. B. Footprint source area for eddy covariance instruments. (b) arm length, (z r ) radiometer height, (EC station) eddy covariance instruments (gas analyzer and sonic anemometer), (z m ) eddy covariance instrument heights. The effect of flux spatial scales on energy balance closure is evaluated considering the peak location of the footprint function inside the field. As shown in Fig. 6, the peak data have been subdivided into four percentile groups (each with 25% of the data) so that turbulent fluxes of latent and sensible heat connected to each peak are used to compute the energy balance closure. 53

54 Slope and R 2 (-) Intercept ( W m -2 ) % 1-5% 22-75% 628-1% x peak (m) - percentile Slope R2 Intercept Fig. 6. Energy balance closure for four 25 percentile groups of footprint function peak location (x peak ). The energy balance closure tends to increase when the peak location is far from the eddy covariance station up to 22 m. The maximum value of the linear regression slope is.88 in correspondence with 75 percentile group, i.e. with the footprint peak far from the tower which varies between 1 and 22 meters. However, when the peak exceeds 22 m the slope tends to decrease probably because representative source area of eddy covariance measurements exceed the field dimension. Instead, when the peak location is near the station the heterogeneity of the island surface (which is sown by hand) and devices influence could create alteration in turbulent flux measurements. The systematic error defined by intercept, increases linearly with the percentile groups up to 9.7 W m -2. Ground heat flux is usually very small in respect to the other energy fluxes, ranging from 5 to 4 % of net radiation but this flux is the one with the highest uncertainty in its estimate that can reach an error up to 5% (Foken, 28a). Moreover, it is measured with an instrument with the smallest source area that can be up to two orders of magnitude lower than latent and sensible heat fluxes footprints. So that it can be very changeable in a field due to different soil characteristics or soil moisture conditions as shown in Kustas et al. (2), where they found that, measuring G with 2 instruments in a small site, mean differences in soil heat flux are of about 4 W m -2 but they can deviate in some occasion also of 1 Wm -2. Investigation of variation of heat soil flux across the field and its influences on energy balance closure, is an important issue which has been studied by many scientists. In the current state, G is assumed uniform on the field and its strong variability across the field is in first approximation neglected. Effect of turbulent mixing The effect of turbulent mixing is evaluated in respect to friction velocity (u*). Friction velocity typically changes with stability of atmosphere and time of day as explained in Wilson et al. (22). The change in energy balance closure could also be the direct result of changes in friction velocity. In accordance with Wilson et al. (22), a simple method used to isolate the effects of friction velocity on energy balance improvement, is shown. Data are separated into four 25 percentile groups, and each group contains data when the friction velocity is included among two consecutive friction velocity percentile values. Slope of the linear regression, R 2 and intercept are also evaluated during daytime and night time as shown in Fig.7. As explained in 54

55 Slope and R 2 (-) Intercept (W m -2 ) Slope and R 2 (-) Intercept (W m -2 ) Slope and R 2 (-) Intercept (W m -2 ) Fig. 7A, during daytime the slope increases from.73 to.85 and the intercept varies from -1 to 2 W m -2. Only when friction velocity is included between.28 and.83 m s -1, intercept collapsed on a value of about.7 W m -2. During nighttime (Fig. 7B) energy balance closure is drastically worsen with a mean slope of about.6. Intercept is quite closed to W m -2 while R 2 considerably varies among the percentile groups. This is probably due to low wind velocities which, during nighttime, prevent the well turbulent mixed conditions of the atmosphere increasing the advection transport of scalar fluxes and worsening the eddy covariance measurements. A B Slope R2 Intercept %.21-5%.28-75%.83-1% u* (m s -1 ) - percentile Slope R2 Intercept %.9-5%.15-75%.69-1% u* (m s -1 ) - percentile Fig. 7. Energy balance closure for four 25 percentile groups of u* friction velocities. A. Daytime. B. Nighttime In Fig. 8, friction velocity influence on energy balance closure globally evaluated for the whole experimental data set, is shown. The slope constantly increases up to.82 when the data are included in a friction velocity range between.24 and.83 m s -1. The systematic errors defined by the intercept values tend to decrease, and in correspondence with a closure of.82 the intercept value is about 4.3 W m -2. Literature results (Wilson et al., 22; Barr et al., 26) are also confirmed from the analysis performed at Livraga station, given that with the increase of friction velocity the closure of the energy budget tends to increase as well. In fact when the friction velocity is low, the turbulence is softened and the fluxes are usually underestimated. The problem related to the use of friction velocity as an indicator of good measured data is linked to a u* threshold definition. In Alavi et al. (26) a value of.1 m s -1 is considered, while Oliphant et al. (24) use.3 m s -1 and Barr et al. (26).35 m s -1, showing that the choice of this limit on u* seems to be site dependent Slope R2 Intercept.8-25%.15-5%.24-75%.83-1% u* (m s -1 ) - percentile Fig. 8. Energy balance closure for four 25 percentile groups of u* friction velocities for the whole experimental dataset. 2 55

56 Effect of vegetation Many experimental results about energy balance problems above low and tall vegetations are available in literature (Wilson et al., 22; Aubinet et al., 2; Panin et al., 1998). Here, the influence of the vegetation height and heterogeneity on energy balance closure is studied subdividing the experimental data set into five classes from C1 to C5. Each class contains data with different vegetation height (Tab. 1) in function of canopy growth. Tab. 1. Vegetation height classis. Class Vegetation height (cm) C1 From to 3 C2 From 3 to 6 C3 From 6 to 9 C4 From 9 to 15 C5 From 15 to 32 For each class the energy balance closure is calculated and the results are shown in Fig. 9A. The slope tends to decrease, with an increase of vegetation height, up to.76 for a canopy height between 15 and 32 cm. The maximum slope value is about.98 in correspondence with C1 class when the surface heterogeneity is particularly accentuated. Intercept changes its plus sign in correspondence with C5 class, where the intercept value is about -3.4 W m -2. To better understand how these results are possible, the storage terms should be taken into account. In Fig. 9B, the slopes of the linear regression is compared with the percentage storage weights defined by Eq.7. Storage weight is the ratio between the averaged storage fluxes for each class and the sum of these averages on the whole class subdivisions. N 1 Sxi N i 1 Storage weight x 1 (7) 5 N 1 Sxi N j 1 i 1 j Where S is the storage term for the x flux (soil heat ground, photosynthesis or canopy storages), N is the number of data for each class and j is a class indicator so that when it is equal to 1 it represents C1 class, when it is equal to 2 it represents C2 class, and so on. As shown in Fig. 9B, the slope trend is opposite to canopy and photosynthesis storage weight terms. In fact, when the canopy is tall the weights of Sc and Sp are particularly relevant reaching the value of about 35% in correspondence with C5 class. Instead, the soil heat ground storage weight term drastically decreases when the vegetation is tall, moving it from 25% to 5% when the class changes from C4 to C5. The presence of vegetation which covers the field play a fundamental role in energy balance closure. In particular way, during the canopy growth, the Sp and Sc storage terms increase their influence on energy balance closure and if they are not considered the energy unbalance is accentuated. When the vegetation is lowed Sp and Sc effects can be neglected while Sg becomes relevant reaching the weight value of about 3% (C1 class). 56

57 Slope and R 2 (-) Intercept (W m -2 ) Slope (-) Storage weight (%) A B Slope R2 Intercept C1 C2 C3 C4 C Slope Sg Sc Sp C1 C2 C3 C4 C Fig. 9. A. Energy balance closure for five class of vegetation height. B. Slope and storage weight terms in function of vegetation height classes. Effect of seasonality To clearly describe the partition of energy balance components during different seasons, the daily patterns of the 3 minutes averages of Rn, LE, H and G in May, June, July and August are plotted in Fig.1. Net radiation maximum peak is quite constant from May to August oscillating between 5 and 6 W m -2. Latent and sensible heat have a strong variability trough the months, showing a quite similar trend from May to June while in July and August latent heat is about 3 times greater than sensible heat. The soil heat flux accounts for a small proportion of the available energy, in particular way, when the vegetation covers the field surface. In fact, in May at 12: it can also reach the maximum value of about 1 W m -2, while in July and August the soil heat flux is equal to few tens of watt to meter square. The partitioning of net radiation into sensible heat and latent heat fluxes is strongly influenced by change in vegetative characteristics. Specifically, when the vegetation is tall, the dominant component of the energy budget is represented by latent heat with a peak in July of about 45 W m -2. Sensible heat is the main energy component when the vegetation is absented. It tends to decrease during the canopy growth but, as shown in August, when the vegetation is fully developed, it returns to be similar to values shown in May. One special phenomenon, called the oasis effect can be noted in July when latent heat is the main component which takes the largest portion of R n and sensible heat is very small. In the case of optimum conditions for evaporation, i.e. high soil moisture and well turbulent conditions (Foken, 28a), the evaporation process will be greater than the sensible heat flux. In such cases, sensible heat changes its sign 1-3 hours before sunset and sometimes in the shortly afternoon, occurring in the atmosphere a temperature gradient inversion and a downwarded sensible heat transfer. 57

58 Fluxes ( W m -2 ) Fluxes ( W m -2 ) Fluxes ( W m -2 ) Fluxes ( W m -2 ) Rn LE H G A Hours Rn LE H G C Hours Rn LE H G B Hours Rn LE H G D Hours Fig. 1. Seasonal variation of energy fluxes. A. May. B. June. C. July. D. August. Energy balance closure for each month is shown in Fig. 11. The slope of the linear regression is particularly influenced by the canopy growth. When the field is completely covered by the vegetation and it can be considered as an homogenous surface, energy balance closure decreases up to.77 with an intercept value of about -1.4 W m -2. This is probably due to the effect of canopy and photosynthetic storage terms which become important when the vegetation is tall and the surface is homogenously covered by the plants. Analyzing each flux of the energy balance over the whole experimental period (Fig. 1) it is possible to realize that over a field covered by dense vegetation, latent heat is the main dominant component of the energy budget (respect to sensible heat and soil heat ground) and a lack of the energy balance closure corresponds to an underestimation of the canopy evapotranspiration fluxes. In water management practices this problem assumes a dominant role in irrigation procedure given that a correct estimation of the evapotranspiration fluxes corresponds to an efficacious and sustainable management of the water resource. 58

59 Random uncertainity (W m -2 ) Random uncertainity (W m -2 ) Slope and R 2 (-) Intercept (W m -2 ) Slope R2 Intercept May June July August Fig. 11. Energy balance closure evaluated for each month. Random error Reliability of turbulent fluxes can be obtained only if theoretical assumption of the eddy covariance technique, described in Moncrieff et al. (1996), are followed. Non steady-state conditions, random noise of the signal, inadequate length of sampling interval, size variation of flux footprint and surface heterogeneity, single point measurement of turbulence and inadequate sensor response could cause random uncertainty in fluxes measurements. Random errors have been mainly studied by Hollinger and Richardson (25) comparing flux measurements obtained by two identical micrometeorological stations located in the same place with the same flux footprint, or by Richardson et al. (26) comparing pair of measurements made on two successive days from the same tower under equivalent environmental conditions. Using Lenschow et al. (1994) method to detect random uncertainty in sensible and latent heat fluxes, it is possible to realize that errors in estimated means, variances and co-variances diminish increasing the size of data set (as long as the data set is not enlarged that, for example, seasonal trends become important) and the random uncertainty magnitude proportionally increases with the growth of sensible and latent heat flux intensities (Fig. 12). 5 A 1 B Sensible heat ( W m -2 ) Latent heat ( W m -2 ) Fig. 12. Random uncertainty in function of sensible (A) and latent (B) heat flux magnitudes. Some authors as Bernardes and Dias (21) include error bars when reporting measured values of turbulent fluxes. It is not a common micrometeorological practice but to realize how random 59

60 Sensible heat (W m -2 ) Latent heat (W m -2 ) errors affects latent and sensible heat fluxes, in Fig. 13 the mean daily turbulent flux intensities jointed with their range of confidence, are shown. The maximum uncertainty is associated with daytime when maximum latent and sensible heat magnitudes are shown. During daytime, the maximum range of confidence is about 4 W m -2 for sensible heat and 8 W m -2 for latent heat, while during the nighttime it tends to zero. A B 13 1 H Random uncertainity 38 3 LE Random uncertainity Hours Hours Fig. 13. Range of confidence obtained from random error estimation for sensible (A) and latent (B) heat fluxes. Generally, some random error sources could be solved trying to apply rigorously practical rules described in many literature works which have been written starting from the birth of the eddy covariance technique (Foken, 28a; Schmid, 1997). However, the energy balance closure is affected by these errors which can not be completely eliminated. Filtering methods based on a spatially decomposition of turbulent fluxes (Salesky et al., 212) tries to quantify rigorously the random errors with the objective, in the common practice for the authors, to include an estimate of random errors magnitude when micrometeorological measurements are shown. Conclusion Livraga 212 measurements have been an excellent data set for evaluating the surface energy balance problems. All findings about the flux error sources cannot completely explain the problem of the unclosed surface energy balance. It is founded that crucial attention to calibration, maintenance and software correction of data is essential to obtain half-hourly reliable fluxes. Despite this effort, data set contains an unbalance of about 25% which has been studied taking into account different turbulent flux problems. Storage terms play a fundamental role to improve the energy balance closure and they are about 1% of the daily available radiation energy. Photosynthesis and canopy storage terms are prevalent in the field when the vegetation covers the soil surface and the canopy is fully developed. Ground heat storage is greater than the other storage terms and it can reach up to 5% of the soil heat flux. Canopy growth and seasonality effects are strongly connected with storage terms. When the vegetation is lowed the energy balance closure is almost equal to 1 because only ground heat storage term exists with a percentage weight of about 3%. From class C1 to class C5 the energy balance closure decreases if the vegetation storage terms (canopy and 6

61 photosynthesis terms) are not considered. Similarly, energy balance closure decreases from May to August in accordance with the increasing of the vegetation storage terms. Energy balance flux partitioning highline how the available energy (net radiation) is subdivided in latent, sensible and soil heat fluxes, detecting the flux which could mainly contribute to the unbalance problem. During experimental campaign the results show that latent heat is the main component of the energy budget, and, in some months, it is grater then 4% of the available energy. Atmospheric turbulence characteristics play a fundamental role in flux reliable estimations. In some cases, half-hourly averaged time is not sufficiently longed to take into account the longwave terms of the turbulent flux measurements. Studying the ogive functions, the results show that about 2% of data are partially corrected because their aggregation time covers only a portion of turbulent eddies which stay in the surface layer (Garrat, 1993). Some authors (Lenschow et al., 1994) suggests to change the averaged aggregation time of the eddy covariance flux measurements in function of the atmospheric turbulence characteristics, but increasing drastically the complexity of the common practice measurements. State of turbulent mixing is an important aspect against to the advection phenomenon. One of the theoretical assumption of the eddy covariance technique is that advection terms can be neglected. Friction velocity is used to give a threshold which discerns the existing probability of the advection transport. Energy balance closure in developed turbulent mixing conditions is greater than the cases with low turbulence, and the closure is about.8 if friction velocity is confined between.24 and.83 m s -1. In the past the researches on the energy balance closure problems was mainly directed on measuring errors, and only a few results underline the scale hypothesis. The results shown in this work underline the complexity of the source area footprint definition for each flux of the energy budget. Atmospheric stability conditions, measurement height, surface roughness and wind velocity are some common parameters which govern the footprint models. In Po Valley, the weak wind velocities and strong convective forces during summer months provoke the movement of footprint peak in direction of the tower, so that the major representativeness of source area is certainly confined inside the field. Site specific new experiments should be made to understand how the representative source area for eddy covariance measurements change in function of atmospheric, physical and geometrical characteristics of the field. It should be a subject of further researches to recalculate eddy covariance experimental results again using a new experimental plan and a specialized measuring setup calibrated for the scale problem. LES modeling studies could be used to support these researches. Despite this overview cannot be a final work, this paper shows important results about the energy balance closure problem. Moreover, this work is one of the few researches on maize field in Po Valley which are presented in literature, increasing the knowledge on the energy balance problems at international scale. References Alavi, N., Warland, J., and Berg, A. (26). Filling gaps in evapotranspiration measurements for water budget studies: Evalutation of a Kalman filtering approach. Agricultural and Forest Meteorology, 141: Aubinet, M., Grelle, A., Ibrom, A., et al. (2). Estimates of the annual net carbon and water exchange of forests: the euroflux methodology. Advanced in Ecological Research, 3:

62 Aubinet, M., Heinesch, B., and Yernaux, M. (23). Horizontal and vertical CO2 advection in a sloping forest. Boundary Layer Meteorology, 18: Baldocchi, D., Falge, E., Gu, L., Olsen, R., Hollinger, D., Running, S., et al. (21). FLUXNET: a new tool to study the temporal and spatial variability of ecosystem scale carbon dioxide, water vapor, and energy flux densities. Bullettin of the American Meteorological Society, 82: Baldocchi, D. and Rao K.S. (1995). Intra field variability of scalar flux densities across a transition between a desert and an irrigated potato field. Boundary Layer Meteorology, 76: Barr, A., Morgenstern, K., Black, T., McCaughey, J.,and Nesic, Z. (26). Surface energy balance closure by the eddy-covariance method above three boreal forest stands and implications for the measurement of CO2 flux. Agricultural and Forest Meteorology, 14: Bernardes, M., and Dias, N. (21). The alignment of the mean wind and stress vectors in the unstable surface layer. Boundary Layer Meteorology, 134: Detto, M., Montaldo, N., Alberston, J., Mancini, M., and Katul, G. (26). Soil moisture and vegetation controls on evapotranspiration in a eterogeneus Mediteranean ecosystem on Sardinia,Italy. Water Resources Research, 42: Elliot, W. (1958). The growth of the atmospheric internal boundary layer. Transaction American Geophysic Union, 5: Feigenwinter, C., Bernhofer, C., and Vogt, R. (24). The influence of advection on the short term CO2- budget in and above a forest canopy. Boundary Layer Meteorology, 113: Finnigan, J., Clement, R., Malhi, Y., Leuning, R., and Cleugh, H. (23). A re-evaluation of long term flux measurement techniques part I: averaging and coordinate rotation. Boundary Layer Meteorology, 17: Finningam, J., Aubinet, M., Katul, G., Leuning, R., and Schimel, D. (26). Report of a specialist workshop on "Flux measurements in difficult conditions",26-28 January, Boulder Colorado. Bullettin of the American Meteorological Society, in press. Fisher, J., Baldocchi, D., Misson, L., Dawson, T., and Goldstein, A. (27). What the towers don't see at night: nocturnal sap flow in trees and shrubs at two AmeriFlux sites in California. Tree Physiology, 27: Foken, T. (28a). Micrometeorology. Berlin: Springer, pp. 36, ISBN Foken, T. (28b). The energy balance closure problem:an overview. Ecological Applicatons, 18: Foken, T., and Wichura, B. (1996). Tools for quality assessment of surface-based flux measurements. Agricultural and Forest Meteorology, 78: Foken, T., Dlugi, R., and Kramm, G. (1995). On the determination of dry deposition and emission og gaseous compounds at biosphere-atmosphere interface. Meterologische Zeitschrift, 4: Foken, T., Wimmer, F., Mauder, M., Thomas, C., and Liebhetal, C. (26). Some aspects of the energy balance closure problem. Atmososperich and Chemistry Physics, 6, Friehe, C. (1991). Air-sea fluxes and surface layer turbulence around a sea surface temperature front. Journal of Geophysical Research, C96:

63 Garratt, J. (1993). The atmospheric boundary layer. Cambridge: Cambridge university press, pp.316, ISBN Gash, J., and Culf, A. (1996). Applying linear de-trend to eddy correlation data in real time. Boundary Layer Meteorol., 79: Hollinger, D., and Richardson, A. (25). Uncertainity in eddy covariance measurements and its application to physiological models. Tree Physiology, 25: Hsieh, C., Katul, G., and Chi, T. (2). An approximate analytical model for footprint estimation of scalar fluxes in thermally stratified atmospheric flows. Advanced Water Resource, 23: Jacobs, A., Heusinlveld, B., and Holtslag, A. (28). Towards closing the energy surface budget of a mid-latitude grassland. Boundary Layer Meteorology, 126: Kustas, W.,and Daughtry, C. (199). Estimation of the soil heat fluxnet radiation ratio from spectral data. Agricultural and Forest Meteorology, 49: Kustas, W., Prueger, J., Hatfieldb, J., Ramalingamc, K., and Hippsc, L. (2). Variability in soil heat flux from a mesquite dune site. Agricultural and Forest Meteorology, 13: Lenschow, D., Mann, J., and Kristensen, L. (1994). How long is long enough when measuring fluxes and other turbulence statistics? Journal of Atmospheric and Oceanic Technology, 11: Ma, Y., Wang, Y., Wu, R., Hu, Z., Yang, K., Ma, W., et al. (29). Recent advances on the study of atmosphereland interaction observations on the Tibetan Plateau. Hydrology Earth System Sciences, 13: Marcolla, B., Cescatti, A., Montagnani, L., Manca, G., Kerschbaumer, G., and Minerbi, S. (25). Importance of advection in atmospheric CO2 exchanges of an alpine forest. Agricultural and Forest Meteorology, 13: Massman, W., and Lee, X. (22). Eddy covariance flux corrections and uncertainties in long-term studies of carbon and energy exchanges. Agricultural and Forest Meteorology, 113: Mayocchi, C., and Bristow, K. (1995). Soil surface heat flux: some general questions and comments on measurements. Agricultural and Forest Meteorology, 75: Meyers, T., and Hollinger, S. (24). An assessment of storage terms in the surface energy balance of maize and soybean. Agricultural and Forest Meteorology, 125: Moncrieff, J., Malhi, Y., and Leuning, R. (1996). The propagation of errors in long term measurements of land atmosphere fluxes of carbon and water. Global Change Biology, 2: Moncrieff, J., Massheder, J., De Bruin, H., Ebers, J., Friborg, T., Heusinkveld, B., et al. (1997). A system to measure surface fluxes of momentum, sensible heat, water vapor and carbon dioxide. Journal of Hydrology, 188: Nobel, P. (1974). Introduction to biophysical physiology. New York: Freeman. Oliphant, A., Grimmond, C., Zutter, H., Schmid, H., H.B., S., Scott, S., et al. (24). Heat storage and energy balance fluxes for a temperate deciduos forest. Agricultural and Forest Meteorology, 126: Oncley, S., Businger, J., Itsweire, C., Friehe, J., LaRue, J., and Chang, S. (199). Surface layer profiles and turbulence measurements over uniform land under near-neutral conditions. American Meteorological Society Washinton D.C., USA, Pages in 9th Symposium on Boundary Layer and Turbulence. 63

64 Oncley, S., Delany, A., Horst, T., and Tans, P. (1993). Verification of flux measurement using relaxed eddy accumulation. Atmospheric Environment, 27: Oncley, S., Foken, T., Vogt, R., Kohsiek, W., DeBruin, H., Bernhofer, C., et al. (27). The energy balance experiment EBEX-2. Part I: overview and energy balance. Boundary Layer Meteorology, 123: Panin, G., Tetzlaff, G., and Raabe, A. (1998). Inhomogeneity of the land surface and problems in the parameterization of surface fluxes in natural conditions. Theoretical and Applied Climatology, 6: Papale, D., Reichstein, M., Aubinet, M., Canfora, E., Bernhofer, C., Kutsch, W., et al. (26). Towards a standardized processing of net ecosystem exchange measured with eddy covariance technique: algorithms and uncertainty estimation. Biogeosciences, 3: Richardson, A., Hollinger, D., Burba, G., Davd, K., Flanagan, L., Katul, G., et al. (26). A multi site analysis of random error in tower-based measurements of carbon and energy fluxes. Agricultural and Forest Meteorology, 136: Runkle, B., Wille, C., Gazovic, M., and Kutzbach, L. (212). Attenuation correction procedures for water vapor fluxes from closed-path eddy covariance systems. Boundary-Layer Meteorology, 142: Sakai, R., Fitzjarrald, D., and Moore, K. (21). Importance of low frequency contributions to eddy fluxes observed over rough surface. Journal of Applied Meteorology, 4: Salesky, S., Chamecki, M., and Dias, N. (21). Estimating the random error in eddy covariance based fluxes and other turbulence statistics: the filtering method. Boundary Layer Meteorology, 144: Savelyev, S., and Taylor, P. (25). Internal Boundary Layer: I. Height formulae for neutral and diabatic flows. Boundary Layer Meteorology, 115: Schmid, H. (1997). Experimental design for flux measurements: matching scales of observations and fluxes. Agricultural and Foest Meteorology, 87: Schotanus, P., Nieuwstadt, F., and De Bruin, H. (1983). Temperature meaurement with a sonic anemometer and its application to heat and moisture fluxes. Boundary Layer Meteorology, 26: Staebler, R., and Fitzjarrald, D. (26). Observing subcanopy CO2 advection. Agricultural and Forest Meteorology, 122: Ueyama, M., Hirata, R., Mano, M., Hamotani, K., Harazono, Y., Hirano, T., Miyata, A., Takagi, K., and Takahashi, Y., (212). Influences of various calculation options on heat, water and carbon fluxes determined by open- and closed path eddy covariance methods. Tellus B, 64: Van de Boer A., A.F. Moene, D. Schuttemeyer, A. Graf (213). Sesnitivity and uncertainity of analytical footprint models according to a combined natural tracer and ensemble. Agricultural and Forest Meteorology, 169: Van DijK, A., Kohsiek, W., and De Bruin, H. (23). Oxygen sensitivity of krypton and Lyman-alfa Hygrometer. Journal of Atmospheric and Oceanic Technology, 2: Vickers, D and Mahrt, L. (1997). Quality control and flux sampling problems for tower and aircraft data. Journal of Atmospheric and Oceanic Technology, 14: Webb, E., Pearman, G., and Leuning, R. (198). Correction of the flux measurements for density effects due to heat and water vapour transfer. Boundary Layer Meteorology, 23:

65 Wilczak, J., Oncley, S., and Stage, S. (21). Sonic anemometer tilt correction algorithms. Boundary Layer Meteorology, 99: Wilson, K., Goldstein, A., Falge, E., Aubinet, M., Baldocchi, D., Berbigier, P., et al. (22). Energy balance closure at FLUXNET sites. Agricultural and Forest Meteorology, 113:

66 (Chapter 3) Experimental data about the spatial variability of scalar fluxes across maize field in Po Valley and comparison with theoretical footprint model predictions Abstract Representative source area for turbulent flux measurements by eddy covariance stations is an important issue which has not yet been fully investigated. In particular way, the validation of the analytical footprint models is generally based on the comparison with Lagrangian model predictions, while experimental results are not largely diffused in literature. In this work, latent, sensible heat and carbon dioxide flux measurements across two experimental fields in Po Valley are shown, and two totally different scenarios at bare and vegetated soils are analyzed. Experiments are performed using two eddy covariance systems: one fixed station which is located about in the middle of the field and a mobile station which is placed at various distances from the field edge to investigate the horizontal variation of the vertical scalar fluxes. The measured fluxes of latent, sensible heat and carbon dioxide are compared with the predictions of two analytical footprint models. There is a good agreement between measurements and one of the two analyzed model predictions. The results have also shown that the spatial distribution of turbulent fluxes is strongly influenced by the presence of vegetation in the field. Moreover, each turbulent flux is characterized by its own representative source area which could be extremely different from the others increasing the complexity of the footprint problem determinations for eddy covariance measurements. Introduction Eddy covariance measurements are widely applied to continuously monitor turbulent exchange of mass and energy at the vegetation-atmosphere interface (Aubinet et al., 2). Moreover, the eddy covariance method is one of the most accurate and direct approaches available in literature to measure turbulent exchanges over field areas with different sizes (Baldocchi et al., 21). The eddy covariance method is a statistical tool which, stating from high-frequency data of wind components and scalar densities, provides to assess latent, sensible heat and carbon dioxide turbulent fluxes (Baldocchi, 23). The fluxes are calculated as a covariance among turbulent components of vertical wind velocity and scalar concentration (vapor, air temperature or carbon dioxide). The main micrometeorological instruments which give the name to the eddy covariance technique are the tridimensional sonic anemometer and gas analyzer respectively. The reliability of flux measurements depend on certain theoretical assumptions of the eddy covariance technique (Kaimal and Finnigan, 1994; Foken and Wichura, 1996), the most important of which are horizontal homogeneity, stationarity and mean vertical wind speed equal to zero during the averaging period. Eddy covariance method was used in micrometeorology for over 3 years, and now, modern instruments and software make this method easily available and widely used in 66

67 different research fields, such as in ecology, hydrology, environmental and industrial monitoring (Baldocchi et al., 1988; Papale et al., 26). In the past years a global network of micrometeorological tower sites which use eddy covariance methods to measure carbon dioxide, water vapor and energy exchanges between soil-vegetation and atmosphere systems was constituted. Its name is Fluxnet and as of January 29, there are over 5 tower sites in continuous long-term operation ( Wilson et. al., 22; Sanchez et. al., 21). The proliferation of eddy covariance flux systems in a variety of conditions and ecosystems, often violating some the theoretical requirements of the methodology, has created an increasing interest in footprint analysis (Schmid, 1997; Rannik et al., 2). Schuepp et al. (199) specify the term footprint as the relative contribution from each element of the upwind source area to the measured concentration or vertical flux. It can be interpreted as the probability that a trace gas, emitted from a given elemental source, reaches the measurement point. Mathematically, flux and footprint are related by Eq. 1 as explained in Hsieh et al. (2). m x F ( x, z ) S( x) f ( x, z ) dx (1) m Where F is the scalar flux, f is the footprint function, S is the source strength, z m is the measurement height and x represents the horizontal coordinate along wind direction. As described in Vesala et al. (28), the determination of the footprint function is not a straightforward task and several theoretical approaches have been derived over the previous decades. They can be classified into four categories: (i) analytical models, (ii) Lagrangian stochastic particle dispersion models, (iii) large eddy simulations, and (iv) ensemble-averaged closure models. Additionally, parameterizations of some of these approaches have been developed, simplifying the original algorithms for use in practical applications (e.g., Horst and Weil, 1992; Schmid, 1994). The criterion of a 1:1 fetch to measurement height ratio was long held as the golden rule guiding internal boundary layer (IBL) estimation and nowadays is still used as a rule-of- thumb to crudely approximate the source area of flux measurements over short canopies in daytime conditions. However, the unsatisfactory nature of the 1:1 ratio and the related footprint predictions were explicitly discussed by Leclerc and Thurtell (199). The dramatic increase of publications that address footprint modeling, applications or related issues of fetch and spatial representativeness for flux measurements in recent years, demonstrates the growing need for practical footprint models. The development of a growing number of longterm trace gas exchange studies over complex forest canopies and in often topographically challenged terrain, underlines the fact that the requirements for future footprint models are divergent: on the one hand, practical footprint models must be easy to use, if ever possible in the field, where the availability of computer resources (and time) is limited. The recent developments in analytical footprint models satisfy this need, but these models are limited to homogeneous surface layer similarity conditions (Horst and Weil, 1992; Schuepp et al., 199; Hsieh et al. 2; Kormann and Meixner, 21). On the other hand, footprint models should produce realistic results in real-world situations for measurements over (or below) tall canopies, spatially heterogeneous turbulence, stability conditions from extremely stable to free-convective, and instationarity. Backward Lagrangian models and the large eddy simulation-based footprint 67

68 studies provide for the analysis of the representativeness source area in real-world situations but also if they are considered promising, computational time and extreme complexity restrict their application field (Kljun et al., 22; Rodean, 1996; Wilson and Sawford, 1996; Thomson, 1987). There is a general need for footprint model validations. According to Foken and Leclerc (24) only a few experimental data set are available for validation proposes. Lagrangian dispersion models are tested against dispersion experiments of artificial traces for different turbulence regimes (Thomson, 1987; Kurbanmuradov and Sabelfeld, 2; Kljun et al., 22; Leclerc et al., 23). Measurements in complex flow fields, as dispersion inside and above high vegetation canopy, may not be ideal for evaluation and validation of footprint models. Kljun et al. (24) suggest the validation under ideally controlled conditions that can be reproduced in wind tunnels. Generally, analytical footprint predictions are often evaluated using results of Lagrangian footprint models. Nowadays, only sites with short vegetation and an accurate selection of measured data, according to the quality check criteria by Foken and Wichura (1996), allow the in situ validation of analytical footprint models in nearly ideal conditions. In Marcolla and Cescatti (25) a new approach for the determination of the relative contribution of a source area to the measured turbulent flux is shown. In their study areas at different distances from the measuring point are cut at different times, thus generating spatial and temporal variability in the sink strength. Light response curves at three different time periods, characterized by homogenous or heterogeneous surface coverage, are used to quantify the contribution of the area within a certain distance from the measuring system to the total flux. Gockede et al. (25) approach is constituted by two flux stations over bare soil and a meadow. A third station, with a footprint area covering both surfaces, is used to validate the footprint model, because the contributions of both surfaces changed with the stability and wind velocity. Earlier investigations used a similar approach: Soegaard et al. (23) operated five ground-level eddy covariance systems over five different crop fields together with a sixth set-up on top of a higher mast to enable landscape-wide flux measurements. The agreement between high-level values and those integrated from ground-level using a re-formulated version of the models of Gash (1986) and Schuepp et al. (199) is good. Van de Boen et al. (213) use a data set obtained by three eddy covariance stations located in landscape with different land use typologies, to test the performance of the Hsieh et al. (2) and Kormann and Meixner (21) footprint models using an experimental methodology widely described in Neftel et al. (28). In literature, only one experiment which investigates the horizontal variation of the vertical turbulent fluxes over a potato field is shown (Baldocchi and Rao, 1995). The experiment is performed by placing a mobile eddy covariance station at various distances from the upwind field edge versus a fixed eddy covariance station located in the middle of the field. The results are used by Hsieh et al. (2) to validate their footprint model starting from natural traces. In this paper Baldocchi and Rao (1995) methodology to validate Hsieh et al. (2) and Kormann and Meixner (21) footprint models has been proposed again but, for the first time, it is applied over two experimental fields located in Po Valley: one characterized by bare soil and another one covered by maize plants. Particular wind condition regimes, atmospheric turbulence characteristics and field geometrical shapes, which occur in Po Valley, make of this experiment an interesting footprint model validation proof. This paper describes experimental set up and its execution, furthermore, the results about intra-field spatial variability of latent, sensible and carbon dioxide fluxes are compared with Hsieh et al. (2) and Kormann and Meixner (21) 68

69 footprint models to verify their reliability also for eddy covariance station placed over Padana region cultivations. What is the importance of this experiment? In this paragraph many different improvement connected with a correct definition of the representative source area for turbulent flux measurements are briefly summarized. 1) Representative source area for turbulent fluxes has to be confined inside the field if the eddy covariance flux measurements are used to characterize water management practices or canopy phenological growth. In Po Valley, where the field shapes are quite small (in the order of ten hectares), rigorous footprint modeling predictions are necessary to reduce uncertainty over the evapotranspiration flux representative source areas. Footprint model validations could also contribute to improve the reliability of turbulent flux measurements by eddy covariance stations decreasing the uncertainty about evapotranspiration annual budget over cultivated fields. 2) This experiment actively contributes to improve literature results about footprint model validation experiments with a scenario totally different by the other presented nowadays in literature. Moreover, as highlighted by Foken and Leclerc (24), many experimental campaigns to validate footprint models are expensive, and hence prohibitive for the vast majority of university researches. Increasing literature experimental results, which try to resolve this problem, a common database could be developed so that it can be consulted by the researcher for their experiments. 3) Flux spatial distribution results above the canopy or on bare soil can be used in some mathematical models, from Lagrangian stochastic dispersion to large eddy simulation, to describe in an accurate way the field-domain turbulent real conditions, comparing output model results with the experimental measurements. 4) The knowledge about representative source areas for latent and sensible heat fluxes could contribute to resolve the energy unbalance problem which can be seen as a scale problem about sensor measurements as widely discussed in Foken (28). 5) Another practical implication about footprint model validations is connected with the correct definition of the eddy covariance tower position in the field. In fact, it has to be located sufficiently far from the field edge to avoid the influence of the neighbor fields. However, eddy covariance measurements which are performed in fields where the heterogeneity is particularly accentuated, need to known the footprint shape and its size to understand the weight of fluxes which come from the neighbor fields. These points explain five macro-areas which could be affected by the results of this experiment, making a list about the problems which many scientists met in their researches. Theoretical background Estimation of flux footprint from experimental data is compared with predictions of two analytical footprint models proposed by Hsieh et al. (2) (called Hsieh model) and Kormann and Meixner (21) (called Kormann Model). The choice of these footprint models is a 69

70 compromise between reliability and simplicity, following the suggestion by Foken and Leclerc (24) on the necessity of easy-to-use footprint models. Hsieh et al. (2) model is constituted by a combination of Lagrangian stochastic model results and dimensional analysis. It analytically relates atmospheric stability, measurement height and surface roughness length to obtain an approximated analytical expression which accurately describes the footprint function. The results are organized in non-dimensional groups and related to the input variables by regression analysis. The advantages of this model are evident: the hybrid model can be expressed by a set of explicit algebraic equations, while some of the complexity and skill of the full model is retained through the regression. However, the pitfall of any approximation or parameterization is that its validity is strictly limited to the range of conditions over which it is developed. Kormann and Meixner (21) model belongs to the class of the Eulerian analytic flux footprint models which explore several approaches to approximately resolve the advection-diffusion equation. Schuepp et al. (199) are the first scientists that have taken a purely analytical approach, based on an approximate solution of the diffusion equation given by Calder (1952) for thermally neutral stratification and a constant wind velocity profile. As stated by the authors, it suffers from the restriction to neutral stratification. Their suggestion, to correct the wind velocity in the footprint calculation based on thermal stability, has no mathematical basis. Instead, Kormann and Meixner (21) model includes parameterizations of power law for wind velocity and eddy diffusivity extending the applicability of their footprint model to the whole atmospheric stability range. However, some model limitations are present, such as its usage in areas where wind velocity and eddy diffusivity profiles are horizontally homogeneous, and at heights where the effects of a finite mixing depth are negligible. In addition, this model assumes that turbulent diffusion in streamwise direction is small compared to advection, a form of Taylor s hypothesis, and are thus confined to flow situations with relatively small turbulence intensities. Hsieh Model Hsieh et al. (2) develops an approximate analytical model to estimate the flux footprint in thermally stratified flows. This is a hybrid approach combining elements from Calder s analytical solution (1952) with the results of Thompson s Lagrangian model (1987). In the analysis of their results, they scaled Gash (1986) effective fetch with the Obukhov length and accounted for the effect of stability introducing two similarity parameters D and P, obtaining the Eq. 2. x 1 D z P u (2) 2 L k ln( F / S) L Where z u is a length scale, function of measurement height and surface roughness. k is the Von Karman constant, L the Obukhov length and D and P depends on stability conditions of the atmosphere. F/S is the ratio between scalar flux and source strength always confined between and 1 (Hsieh et al., 2). The footprint function is expressed by Eq. 3. 7

71 1 Dz P u k x L 2 1 P 1 P 1 P f ( x, zm ) Dzu L e (3) 2 2 k x Kormann Model The Kormann Model is based on a modification of the analytical solution of the advectiondiffusion equation of Van Ulden (1978) and Horst and Weil (1992) for power low profiles of the mean wind velocity and the eddy diffusivity. To allow for the analytical treatment, the model assumes homogenous and stationary flow conditions over homogeneous terrain, it represents the vertical turbulent transport as a gradient diffusion process and it considers only advection in along wind direction. Assuming that vertical and crosswind dispersion are independent, the continuity equation reduces to a two-dimensional advection-diffusion equation. In the Kormann Model the footprint function is expressed by Eq m r r r 1 u zm u zm f ( x, zm) exp (4) m r K x r K x x r Where is the gamma function, r the shape parameter related to the exponents of the power laws as r=2+m-n (Van Ulden, 1978) and u, K are proportionally constants determined by fitting the power laws for u ( u ) and K ( n K ) to Monin-Obukhov similarity theory (Garrat, 1993). z m u K z Study site, instruments and data In this paragraph, filed characteristics, instruments necessary to perform the experiments and data corrections are briefly shown. Site characteristics The experiments are carried out in two fields destined for maize cultivations at Landriano (Pavia, Italy) and Livraga (Lodi, Italy) respectively. Fields geographic coordinates are (45.19 N, 9.16 E, 87 m a.s.l.) and (45.11 N, 9.34 E, 61 m a.s.l.) for Landriano (Field 1) and Livraga (Field 2) respectively. The experiments are performed in two different situations: after reaping time (Field 1) and during maximum phenological development of the homogenous maize canopy (Field 2). Both fields have a polygonal shape with a flat area of about ten hectares large. Field 1 is completely surrounded by tall row plants which generate a strong discontinuity with the neighbouring fields, while Field 2 is surrounded on three sites by other maize fields and in South-West direction it forms a border with an uncultivated zone. 71

72 Instruments With objective to investigate evapotranspiration and carbon dioxide fluxes over maize cultivation in Po Valley, in the middle of Field 1 and 2, fixed eddy covariance towers A1 (for the Field 1) and A2 (for the Field 2) are installed, and here, instruments are briefly summarised. The stations are equipped with the following sensors: one three-dimensional sonic anemometer (Young 81), which measures sonic temperature and three components of wind speed at the height of 5 m; one open-path gas analyzer (LICOR 75) which measures water vapour and carbon dioxide concentrations at the height of 5 m too. Both these instruments have been set with an acquisition frequency of 1 Hz, so that the data can be used to calculate latent, sensible heat and carbon dioxide fluxes trough eddy covariance method. One net radiometer (CNR1 by Kipp & Zonen) is located on an arm (2.5 m long) attached on the tower at the height of 4 m. One thermo-hygrometer (HMP45C Campbell Scientific) is located at the height of 3.5 m to measure air humidity and temperature. In the soil, two thermocouples (by ELSI) and a heat flux plate (HFP1 by Hukseflux) are placed at a depth of about 1 cm. Contemporaneously, soil moisture is detected by three humidity probes (CS616 by Campbell Scientific) at different depths. Finally, one rain gauge (AGR1 by Campbell Scientific) is separately located by the tower and, at the height of about 1.5 m, it measures the precipitation intensity. Data logger CR5 (Cambpell Scientific) is used to store all data with an averaged time step of 5 minutes. This averaged time is designed to ensure that the eddy flux measurement system captures most of the flux-containing eddies. This goal was accomplished by sampling anemometer and gas analyzer sensors rapidly and averaging data over a time step of 5 minutes. This averaged time is also justified by the results obtained by Masseroni et al. (212) which, studying surface layer turbulent characteristics over the Field 1, show that eddy integral lengths in convective situations tends to be stationary for a time major of 3 s (about 5 minutes). Data corrections Energy fluxes have been corrected applying the whole range of correction procedures described in many different literature works (Aubinet et al., 2; Foken et al., 24; Mauder and Foken, 24). Before calculating fluxes, two groups of correction have been applied: instrumental and physical corrections. Axis rotation for tilt corrections, spike removal, time lag compensation and detrending represent preliminary processes which have to be directly applied on high frequency measurements to prepare the data set for fluxes calculation. Spectral information losses as a consequence of measurement system typologies trough transfer function characteristics and sampling errors, have to be opportunely corrected to compensate the underestimation of the turbulent fluxes (Moncrieff et al., 1997). Moreover, air density fluctuations and air humidity effects on sonic temperature have to be necessarily corrected trough Webb et al. (198) and Van Dijk et al. (24) procedures respectively. These instrumental and physical corrections are automatically implemented in a PEC (Polimi Eddy Covariance) software which has been opportunely developed for this experiment by Corbari et al. (212). The core of software is based on four substantial points: a) Data stored into the data logger are sent on specific computer at the Politecnico of Milan using a GSM modem; 72

73 Slope and R 2 (-) Intercept (W m -2 ) b) Automatically, correction algorithms are activated and turbulent fluxes are calculated; c) Some statistic indexes are generated to control the micrometeorological variables; d) Turbulent flux and micrometeorological variable graphics are plotted at the web page Fixed eddy covariance stations (A1 and A2) Energy flux measurements are proper to the cultivation if eddy covariance station is correctly positioned inside the field. It has to be opportunely located far from the field edges, so that flux measurements do not belong to the neighboring fields. Moreover, anemometer and gas analyzer have to be compatible with the constant flux layer (Savelyev and Taylor, 25). The constant flux layer represents a space area where eddy covariance station measurements are constant, and it is defined as 1-15% of internal boundary layer (Baldocchi and Rao, 1995). Considering the whole wind direction ranges and analyzing the bare soil unfavourable conditions where aerodynamic roughness for both fields is about.41 m, the constant flux layer depth at the towers A1 and A2, calculated trough Elliot (1958) s formula, is about 6 m ensuring that anemometer and gas analyser are included into the constant flux layer. Moreover, several conditions should be met before eddy correlation method can be applied to measure the fluxes of mass and over an experimental field. First, the site should be flat. Second, vertical velocity should be measured normal to the surface streamlines. Third, the crop should be homogeneous and sufficiently extensive. Finally, no intermediate or advective sources or sinks should be exist for the scalar under inverstigation (Baldocchi et al., 1988). A method which is generally used to confirm the reliability of turbulent flux measurements of an eddy covariance station is the energy balance closure (Foken et al., 26). However, energy balance issue is still unresolved problem and the closures which are present in literature generally vary from.5 to.98 (Foken, 28). The slope of the regression line between latent and sensible heat turbulent fluxes and ground heat flux against available energy (net radiation) is performed over Field 1 and 2 and the results are shown in Fig Slope R2 Intercept A1 A Fig. 1 Energy balance closure for fixed eddy covariance stations A1 and A2. Intercept and correlation coefficient (R 2 ) are also included in Fig. 1, to highlight the presence of systematic or random errors. The energy balance closure for A1 and A2 stations is about equal to.8 with a low dots dispersion around the regression line and a negligible systematic error of about 1 W m

74 Experimental execution Experimental campaigns were carried out in two consecutive years: 211 and 212 respectively. For the Field 1 the experiment was performed over a range of nine days, from 15 September to 23 September in the year 211, while for the Field 2 the experiment was performed over a range of six days, from 2 August to 8 August in the year 212. In Tab.1 and 2 four daily averaged atmospheric parameters measured by the eddy covariance stations over the experimental periods, are shown. The fields, which are at a distance of about 5 Km, are characterized by similar atmospheric turbulent conditions. Weak wind velocities, which are typical in Po Valley, have a range which vary between.7 and 3 m s -1. Friction velocities are quite constant at a value of about.1 m s -1. Air temperatures are greater than 2 C in accordance with the seasonal mean temperatures. Net radiations are grater then 2 W m -2 except for 261 and 262 Julian days of the year 211 where the sky were particularly covered by clouds. Tab. 1. Meteorological conditions measured by A1 eddy covariance station in the year 211. Julian day Mean velocity (m s -1 ) Friction velocity (m s -1 ) Air Temperature ( C) Wind direction ( ) Net radiation (W m -2 ) Tab. 2. Meteorological conditions measured by A2 eddy covariance station in the year 212. Julian day Mean velocity (m s -1 ) Friction velocity (m s -1 ) Air Temperature ( C) Wind direction ( ) Net radiation (W m -2 ) To investigate the horizontal variation of turbulent fluxes across the fields, the experiments are performed by placing a mobile eddy covariance station (B1 for the Field 1 and B2 for the Field 74

75 2) at various distances from the field edge, moving it versus the fixed stations (A1 or A2) placed about in the middle of the fields. The mobile stations (Fig. 2A and B) are equipped by a sonic anemometer (Young 81) as well as the open-path gas analyzer (LICOR 75) which are attached at the top of an extensible tripod. To verify if mobile station measurements are equal to those obtained by fixed stations, both stations have been placed close together for some days before the experiments. Moreover, the clock among two data loggers (CR5 for B1 and CR23X for B2) has been set to obtain measurements at the same time. A B Fig. 2. Mobile stations in the Field 1 (A) and in Field 2 (B). In (A) fixed tower A1 is also shown. In the Field 1, the mobile system (B1) is placed at nominal distances of (P1_1), 15 (P2_1) and 65 (P3_1) meters from the field edge along a reference line inclined of about 191 in respect to North. In the Field 2, the mobile system (B2) is placed at nominal distances of (P1_2), 14 (P2_2) and 5 (P3_2) meters from the field edge along a reference line inclined of about 236 in respect to North. The fixed towers (A1 and A2) are placed at a distance of the field edge of about 184 and 188 meters respectively (Fig. 3). 75