Analysis of short-term closure of the surface energy balance above short vegetation

Analysis of short-term closure of the surface energy balance above short vegetation

agricultural and forest meteorology 148 (2008) 82–93 available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/agrformet Analysi...

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agricultural and forest meteorology 148 (2008) 82–93

available at www.sciencedirect.com

journal homepage: www.elsevier.com/locate/agrformet

Analysis of short-term closure of the surface energy balance above short vegetation D. Cava *, D. Contini, A. Donateo, P. Martano CNR - Institute of Atmospheric Sciences and Climate, U. O. of Lecce, Strada Prov. Lecce-Monteroni km 1,2, Polo Scientifico dell’Universita`, 73100 Lecce, Italy

article info

abstract

Article history:

A detailed study of the surface energy balance was performed at a Mediterranean site in

Received 20 April 2007

southern Italy. Two data sets of measurements of surface heat fluxes taken in the spring and

Received in revised form

autumn were tested with emphasis on the short-term (h) closure of the surface energy

6 September 2007

budget. The analysis shows that correction of the wind speed measurement sonic anem-

Accepted 19 September 2007

ometer error at large angles of attack has influence on the energy budget closure; an important contribution also comes from heat storage between the soil flux sensor and the ground surface, not only for the amplitude but also for the relative phases of the

Keywords:

measured fluxes. An analysis of the time series stationarity did not show appreciable effects

Surface energy balance

on the energy budget. Instead, it appeared to be sensitive to the length of the averaging

Ground heat storage

period for the coordinate rotation system. The use of a ‘long term coordinate system’,

Large-scale transport

together with spectral analysis indicated that the usual 30-min averaging time is too short to

Turbulent flux measurements

include the entire contribution of the turbulent heat fluxes and that a 2-h averaging period is more suitable if larger scale motion effects are to be included. # 2007 Elsevier B.V. All rights reserved.

1.

Introduction

The problem of energy imbalance at the earth surface has been widely investigated in the last few decades. Several experimental and numerical studies (Tsvang et al., 1991; Kanemasu et al., 1992; Aubinet et al., 2000; Wilson et al., 2002; Kanda et al., 2004) indicated a surface imbalance ranging from about 10–30%, typically related to an underestimation of surface energy fluxes measured by the eddy-covariance technique at a single measurement point. Moreover, the energy imbalance generally appears strongly dependent on the characteristics of the measurement sites, being more pronounced in complex terrain, but often present also in quasi-ideal conditions for the application of eddy-covariance methods, i.e. nearly flat and homogeneous surfaces covered by short vegetation.

The understanding of the factors that mainly affect the closure of the surface energy balance (hereinafter SEB) has strong implications on the interpretation of energy flux measurements and in their comparison with model simulations. As a matter of fact, SEB has been historically accepted as a fundamental validation of data quality, particularly for the accuracy of eddy-covariance data, with important implications for the estimates of CO2 flux (Twine et al., 2000; Wilson et al., 2002). Moreover, a good comprehension of the mass and energy exchange between the earth’s surface and the atmosphere is fundamental for improving regional weather and global climate models. Over an ideal (non-vegetated) horizontal surface the SEB is written as: Rnet  Q H  Q E  Q G ¼ 0

* Corresponding author. Tel.: +39 0832 298721; fax: +39 0832 298716. E-mail address: [email protected] (D. Cava). 0168-1923/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.agrformet.2007.09.003

(1)

agricultural and forest meteorology 148 (2008) 82–93

where Rnet is the net radiation flux, QH the sensible heat flux, QE the latent heat flux and QG is the ground heat flux. In this paper the fluxes are always expressed in W m2. The observed systematic imbalance of energy cannot be imputable only to the effect of random measuring errors associated to SEB components. In the scientific literature different hypotheses have been proposed to explain SEB imbalance, and they can be classified into three main categories: (i) Errors associated with measurement processes that include: systematic errors related to eddy-covariance (EC) technique; systematic errors produced by instrumental bias; errors induced by alignment problems, by sensor separation, or by flow distortion; errors dependent on the ultrasonic anemometer angle of attack (Nakai et al., 2006); errors induced by non-stationarity of the measured time series over the typical 30 min averaging periods, often caused by diurnal trend, mesoscale motions, or passage of clouds (Mahrt, 1998); errors related to the coordinate system in which the SEB is represented and to the averaging operations applied to the instantaneous variables (Finnigan et al., 2003; Finnigan, 2004); errors related to the limitation of single tower measurements. In particular Kanda et al. (2004) demonstrated through numerical experiments using a large-eddy simulation that horizontally-averaged turbulent fluxes based on point measurements systematically underestimate real flux producing a negative imbalance, due to the temporal and spatial change of turbulent organized structures that causes low-frequency trends in time-series and a large horizontal scatter in flux estimates. (ii) Errors associated with different scales or layers influencing the measurement of SEB components that include: the footprint effect, which is the lack of coincidence of the source area among the terms of SEB measured using different instruments and techniques (Schmid, 1997); the heterogeneity in the distribution of energy sinks; energy storage in the canopy and in the soil. Typically the canopy heat storage can be neglected for quasi-steady state situations where there is no significant change in the mean air temperature between the soil surface and the level of measurements. This is the case for nearly flat and barren surfaces or surfaces covered by short vegetation (see Stull, 1988, pp. 254–255). On the other hand the heat storage that occurs in the layer between the soil surface and the heat flux plates cannot be neglected and a correction is required to account for this effect (Kukharets et al., 2000). (iii) Errors produced by the loss of low and/or high frequency contributions to the energy transport. They include the loss or distortion of high-frequency contributions to the turbulent spectra due to the finite sampling frequency. Although the loss of high-frequency contribution can be neglected because of the very small effect on the energy imbalance (Foken et al., 2006), this is not the case for the loss of low frequency contributions to the turbulent spectra. These losses are associated with the largest convective eddies, comparable in scale to the thickness of the convective boundary layer (CBL) and advected past to the sensors by the mean horizontal wind. In fact, the

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typical 30 min averaging period appears often insufficient to include a sufficient number of these eddies to statistically resolve them (Sakai et al., 2001). The consequent underestimation of the turbulent fluxes is particularly evident in low or moderate wind conditions. Moreover, the loss of low frequency contributions to energy transport can be associated with local circulations driven by the interplay of thermal forcing and topographical heterogeneity. These organized circulations often produce mesoscale stationary eddies that may have a preferred location (attached to the surface), producing a mean vertical velocity systematically different from zero at the sensor location and giving rise to a vertical advective flux (Lee, 1998; Mahrt, 1998). Finally, significant contribution to the energy imbalance can arise from the advection produced by nocturnal drainage flow on undulating terrain, in particular because micrometeorological sites are rarely flat (Lee, 1998; Baldocchi et al., 1997). The objective of this study is to investigate the effect of the correction of the main potential causes of SEB imbalance by analysing data collected over a nearly-flat field covered by short vegetation, in two different seasons. The importance of different correction terms in the achievement of SEB closure has been investigated; moreover, the effects that mainly influence energy balance on a daily basis (hereinafter ‘global energy balance’) as well as on short time scales (hereinafter ‘short-time energy balance’) have been highlighted. As a matter of fact, the daily energy balance (that has been subject of several scientific studies) can give an unrealistically good assessment and tends to mask deficiencies in the EC method because energy storage terms and erratic fluctuations can cancel, leaving the daytime energy imbalance partially compensated by the night-time imbalance (often of opposite sign). On the other hand, individual 30-min observations can produce energy imbalances as large as 150 W m2 (around 30% of the available energy flux). The difficulty in closing the energy imbalance at short time scales is still an open challenge and efforts have to be made to detect and to correct main error sources for obtaining reliable estimates of all terms of SEB.

2.

Data and instrumentation

2.1.

Instrumental set-up and measurement site

Measurements have been carried out at a site placed in the Salentum peninsula in the SE part of Italy (Apulia region). The measurement site (Lecce) is the experimental field of the Lecce Operative Unit of ISAC-CNR placed inside the University Campus (N408200 10.800 , E188070 21.000 WGSA) located about 3.5 km SW of the town. The site is a rectangular field with a major side of about 200 m characterised by short vegetation, with two contiguous sides surrounded by small trees. The urban-background area is characterised by at least 1 km in all directions by the presence of patches of trees (5–10 m tall) and small two-story buildings. Therefore, it is possible that they may have possible effects on the measured turbulence parameters, due to the wakes of the buildings when the wind

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is blowing from the southern sector. The roughness length z0 of the site is about 0.5 m and the displacement height is 7.5 m (Martano, 2000). Two field measurement campaigns were performed: the first from 22 April 2005 to 10 June 2005 (46 days, hereinafter summer campaign) and the last between 9 October and 17 November 2006 (39 days, hereinafter autumn campaign). In this instrumental set-up there are two types of platforms: a fast response system and a slow response system. The first is to measure the variables needed to compute the turbulent transfer of CO2, H2O, sensible and latent heat flux, and momentum flux. The system is based on two sensors, the ultrasonic anemometer Gill R3 operating at 100 Hz in calibrated mode (Gill Instruments, 1999) and a CO2–H2O infrared gas analyser LI-7500 (Licor Inc., 2000). This anemometer incorporates six analogue input differential channels that can digitize signals between 5 V with 14-bit resolution. Data from the anemometer (wind speed components, sonic temperature, and analogue inputs) are output as a single serial stream on an RS232 port at the selected sampling rate (100 Hz). Additional instruments have their outputs sampled and digitized by the anemometer itself synchronously with velocity measurements. A LiCor LI-7500 open-path CO2–H2O analyser (Zeller and Nikolov, 2000; Anderson and Farrar, 2001; Anthoni et al., 2002; Obrist et al., 2003) was chosen to make density measurements of CO2 and water vapour. The calibrated CO2 and H2O densities are output as analogue voltages and are connected at the signal box collector to the sonic anemometer analogue inputs. In particular the LI-7500 was set up to sample in a range 0–50 mmol/m3 for CO2 and 0–1500 mmol/m3 for H2O. The fast-response instruments were mounted on a horizontal bar placed at the top of a telescopic mast (Clark Mast SQT9/M) 9.6 m above the ground. The lateral separation between the two sensors was fixed at about 20 cm. To minimize flux loss and flow distortion, a gas analyser was mounted few centimetres below the anemometer volume centre (Kristensen et al., 1997). As recommended in the LiCor LI-7500 manual, this instrument was tipped about 508 from vertical to facilitate drainage of condensation and rain from the optical windows. The anemometer was slightly off-axis with respect to the mast in order to limit flow distortions. In all campaigns, the anemometer was fitted with a bi-axial inclinometer (MicroStrain FAS-A) used to measure the alignment of the anemometer with respect to the gravity vector. The fast-response data collection program was homemade and was implemented in Labview1 environment. The central function of the program was to read the serial data stream from the anemometer and store it in binary form on a hard disk at regular time intervals (1 h), fixed by the operator. The slow-response system, mounted on a 3 m height mast, was equipped with standard meteorological surface instrumentation (wind speed and direction, air temperature, humidity and surface pressure, cumulative rain), plus a set of instruments to complete the energy balance analysis. It consisted of a net radiometer (Rebs Q*7.1), two heat flux plates (Huxeflux HFP01SC) and two soil temperature sensors (Campbell 107 Thermistor) for two-level soil measurements (2 and 5 cm depth) and a soil moisture sensor (Decagon EC-20) averaging moisture between the surface and 5 cm depth. Data were collected as 30 min averages.

2.2.

Data selection and preliminary data-processing

In order to investigate SEB closure, 18 days relative to the summer campaign and 8 days relative to the autumn campaign were selected. Entire days that clearly exhibited persistent noisy behaviour due to instrumental problems or adverse meteorological conditions (for example rainy days, or foggy days that are quite frequent in autumn at the experimental site) were discarded. Selected days were characterized by sunny or partially cloudy meteorological conditions with light or moderate winds. During the summer campaign the wind velocity reached a maximum mean value of about 3 (1) m s1 in the central part of the day and was reduced to very low values during the night (1  0.7 m s1); daily mean temperature reached a maximum value of 26 (2) 8C and a minimum value of 18 (3) 8C. In the autumn campaign the maximum mean value of wind velocity was 3.5 (1.4) m s1 and the minimum value was 0.7 (0.4) m s1; daily mean temperature reached a maximum value of 20 (5) 8C and a minimum value of 14 (6) 8C. In order to compute turbulent fluxes, the wind velocity components were rotated in a streamline coordinate system according to McMillen (1988). The statistics obtained by the 3rotation method ðv¯ ¼ 0; w¯ ¼ 0; v0 w0 ¼ 0Þ and by the tworotation method ðv¯ ¼ 0; w¯ ¼ 0Þ were compared in order to check the effect of the choice of the reference system on the flux computations and on energy imbalance. The two methods produced very similar results in the analysed experimental campaigns; therefore, the three-rotation method was applied in the performed analysis. The McMillen (1988) rotation procedure was applied to the period P (=30 min) commonly used in literature as the averaging interval for the computation of mean turbulent statistics. Moreover, in Section 3.4 the same rotation procedure was applied to the different periods NP (=1, 2, 4, and 8 h) in order to compute the same statistics in ‘long-term coordinates’ and to evaluate the contribution of transport by ‘large-scale’ motions (see Section 3.4 for details). Fluctuations of sonic temperature were converted into fluctuations of the actual temperature according to Schotanus et al. (1983) and scalar flux of water vapour was corrected for the density effect following Webb et al. (1980). Finally, detrending or filtering operation was not applied to measured time series in order to investigate the role of largescale motions on energy transfer (see Section 3.4). Other important corrections and their effect on the SEB closure are discussed in the following sections.

3.

Results and discussions

Experimental estimate of the surface energy balance computed on the pre-elaborated statistics exhibit a similar behaviour in both summer and autumn data sets (Fig. 1). The global closure rate (derived from the slope of the linear fit of (QH + QE) vs. (Rnet  QG)) is 0.82 for summer campaign (Fig. 1a) and 0.76 for autumn campaign (Fig. 1c). Furthermore, the mean ‘residual’ energy (Rnet  (QH + QE + QG)) was computed every 30 min in order to focus on the short-time energy balance. The residual energy exhibits a daily pattern characterised by positive values during the first part of the day, and

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Fig. 1 – (a and c) Scatter plot of the global closure of the SEB (QH + QE vs. Rnet S QG) based on 30 min averages computed on the measured data pre-elaborated as in Section 2.2 for summer campaign (a) and autumn campaign (c). Dashed black line represents the linear fit of the data (summer: (QH + QE) = 0.82 (Rnet S QG) + 2.3, R2 = 0.86; autumn: (QH + QE) = 0.76 (Rnet S QG) S 6.7, R2 = 0.86). For reference, the 1:1 line is also shown (solid black line). (b and d) Average diurnal variation of the residual energy (Rnet S (QG + QH + QE)) based on 30 min averages computed on the measured data pre-elaborated as in Section 2.2 for the summer campaign (b) and the autumn campaign (d). Bars represent the standard deviation of the mean.

by an inversion of sign after 14:00 both in the summer (Fig. 1b) and autumn campaigns (Fig. 1d). During the summer season the residual energy assumes greater values than in autumn, both as positive and negative values, because of higher incoming radiation energy. The observed daily patterns confirm that the global energy balance tends to be more easily balanced because the contributions of different signs tend to cancel out. In the following sections the impact of different potential sources of error on both the global and the short-term SEB closure were investigated.

3.1.

Attack angle calibration

Recently the impact of the attack angle calibration on the closure of the surface energy balance has been investigated (Gash and Dolman, 2003; van der Molen et al., 2004; Nakai et al., 2006). The angle of attack (a) is the angle between the wind vector and the anemometer plane. According to manufacturer’s specifications the optimal range for the Gill R3 ultrasonic anemometer is jaj < 208. For larger values the performance of the anemometer tends to degrade because of self-sheltering by the transducers or because of flow distortion induced by the frame of the instrument itself. As a consequence, the measured wind components differ from the true values and the corresponding turbulent fluxes tend to be underestimated. The impact of this error on the energy balance closure problem can be important; in fact, Gash and

Dolman (2003) found that eddies associated to rare, but large values of a could carry a large portion of daytime fluxes (from 20% above short vegetation to 50% above forest). The distortion associated with this effect depends on the anemometer model and it is known as the (co)sine error, a general term referring to both sine error in the vertical wind component and cosine error in the horizontal one. By using results obtained from wind tunnel experiments, van der Molen et al. (2004) proposed a calibration methodology to correct this effect through non-linear relationships between a and the wind components measured by two types (the R2- and R3-type) of Gill ultrasonic anemometers, frequently used in micrometeorological experiments. Subsequently, Nakai et al. (2006) improved that calibration method and obtained closer fit to the calibration data with less computation time (see van der Molen et al., 2004 and Nakai et al., 2006 for further details). Fig. 2 shows the mean frequency of occurrence of a during the day (between 13:00 and 14:00) and during the night (between 01:00 and 02:00). In both experimental campaigns jaj > 208 occurs more frequently during daytime, whereas a attains smaller values during the night. Moreover, the distributions of a frequencies are negatively skewed during daytime, probably because of a more frequent occurrence of weak downdrafts and less occurrence of strong thermal updrafts in convective conditions. After applying the calibration method of Nakai et al. (2006), QH increased by 6.9% in the summer campaign and by 5.9% in

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Fig. 2 – Mean occurrence of a between 13:00 and 14:00 and between 01:00 and 02:00 for the summer campaign (a and c, respectively) and the autumn campaign (b and d, respectively). Vertical dashed lines indicate the optimal range for the Gill R3 ultrasonic anemometer.

the autumn campaign; moreover, QE increased by 8.3% in the summer campaign and by 6.4% in the autumn campaign. The increases in turbulent fluxes are similar to those found by Nakai et al. (2006) and their effect on the surface energy balance is an improvement of the global closure rate from 0.82 to 0.88 in the summer campaign and from 0.76 to 0.86 in the autumn campaign (see Table 1). Nonetheless the correction does not greatly reduce the daily pattern of energy residuals (Fig. 3). This is true even if the effect of the calibration appears more evident during daytime, according to a correspondingly greater frequency of large angles of attack in convective conditions.

3.2.

Non-stationarity

Non-stationarity is one of the most critical problems in assessing turbulent statistics. In fact nearly all atmospheric motions are non-stationary and inhomogeneous to some degree. Non-stationarity may be driven by changes of measured quantities during the day (i.e. diurnal trends) or by changes in weather patterns at meso- and synoptic scales. The standard procedure frequently used to reduce the effect of non-stationarity is linear detrending. However, it adequately removes non-stationarity only if non-turbulent and turbulent motions are completely separated. This is the case for synoptic

Table 1 – Global closure of the SEB (QH + QE vs. Rnet S QG) based on: (uncorrected) 30 min averages computed on the measured data pre-elaborated as in Section 2.2; (a correction) 30 min averages corrected for the errors dependent on the ultrasonic anemometer angle of attack; (NS correction) 30 min averages corrected for non-stationarity; (S correction) 30 min averages corrected for the ground heat storage; (LS correction) 2 h averages to include the contribution of large scales to the main transport Global closure rate (Rnet  QG) vs. (QH + QE) Slope Intercept R2

Uncorrected

a correction

+NS correction

+S correction

+LS correction

Summer

Autumn

Summer

Autumn

Summer

Autumn

Summer

Autumn

Summer

0.82 +2.3 0.86

0.76 6.7 0.86

0.88 +2.6 0.87

0.86 7.3 0.86

0.87 +2.0 0.88

0.84 7.2 0.86

1.02 17 0.91

0.96 13 0.88

1.01 11 0.88

The described corrections are superimposed to each other.

Autumn 1.01 8.4 0.81

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Fig. 3 – Comparison between the average diurnal variation of the residual energy computed on the uncorrected data (black lines and symbols) and on the data calibrated for errors dependent by the ultrasonic anemometer angle of attack a (grey lines and symbols), for the summer campaign (a) and the autumn campaign (b). Bars represent the standard deviation of the mean.

motions, but is not the case for mesoscale motions. As a consequence, linear detrending can be ineffective or sometimes may even lead to bias and may distort important contributions to transport by scales longer than the averaging period (see Section 3.4). Therefore other procedures have been proposed in the literature to remove non-stationarity. In this work the effect of non-stationarity on turbulent flux computations has been investigated using two different tests proposed in the literature (for details see Foken and Wichura, 1996; Mahrt, 1998). Both methods compare the variability of a chosen quantity (i.e. w0 T0 or w0 q0 ) in the full time series (i.e. 30 min) and the mean value of the variability in shorter intervals (i.e. 5 min). Nonetheless they use slightly different methodologies to make this comparison. The non-stationarity index (NSFoken) in Foken and Wichura (1996) is obtained by comparing the covariance for the full period of 30 min (x0 y0 ) and the mean covariance in I(=6) shorter P intervals of 5 min (hx0 y0 i ¼ ð1=IÞ Ii¼1 ½x0 y0 i ). If the difference between the two covariances is less than 30%, then the time series is considered to be stationary. In the Mahrt test each time series has been divided into non-overlapping 5 min records (i = 1, . . ., I(=6)); moreover, each record has been divided into non-overlapping 50-s subrecords (j = 1, . . ., J(=6)). The non-stationarity index (NSMahrt, called non-stationarity ratio in Mahrt, 1998) is obtained by comparing the variability of the chosen quantity (x0 y0 ) between qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 2 the different records (s between ¼ ð1=ðI  1Þ Ii¼1 ð½x0 y0 i  x0 y0 Þ ) and the average of variability within each record (s within ðiÞ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 2 ð1=ðJ  1Þ Jj¼1 ð½x0 y0 i; j  ½x0 y0 i Þ ). For stationary conditions pffiffi NSMahrt ð¼ s between =ðs within = JÞÞ is approximately 1, because the standard error of the record average due to the variability within the record predicts the variability between record averages (Bendat and Piersol, 1986). The performance of both methods has been evaluated by comparing the non-stationarity indexes (NSFoken and NSMahrt) obtained by applying the tests to the kinematic heat and water vapour fluxes computed on 30 min time series (Fig. 4).

Noteworthy is the non-univocal identification of the nonstationary time series not only between different tests (Fig. 4c and d), but also between the same test applied to different time variables (Fig. 4a and b). For example, Fig. 4a clearly shows that the non-stationary time series identified by applying the Foken method to w0 T0 do not correspond to the non-stationary time series identified by applying the same method to w0 q0 . On the other hand, the scatter plot of NSMahrt applied to the two kinematic fluxes better collapses on the 1:1 line shown for reference in Fig. 4b. On the base of this comparison, strong non-stationarity was discarded by using the Mahrt method (NSMahrt > 2), because it identifies in a more univocal way nonstationarity in the w0 T0 and in w0 q0 time series. Mahrt (1998) found that excluding strong non-stationary time series greatly improves the energy imbalance. However, in the present study, non-stationarity identified by excluding time series relative to NSMahrt > 2 (about 17% in the summer campaign, and 16% in the autumn campaign) did not have a great influence on SEB closure. The global closure appears unchanged (not shown), as well as the diurnal pattern of the residual energy (Fig. 5). Similar results were obtained by reducing the NS threshold from 2 to 1.5, or by applying the method proposed by Foken and Wichura (1996). The reason of the negligible impact of non-stationarity on SEB closure may be due to the small stationarity violation in the analysed time series (not shown).

3.3.

Near-surface heat storage

Ground heat flux is a significant component of surface energy balance, in particular over arid land surfaces, or during lowlevel turbulence conditions. Therefore, an accurate measurement of this term is fundamental to improve the closure of the surface energy balance (Liebethal et al., 2005). Heat flux plates have to be placed at a certain depth in the soil to avoid disturbances, such as the loss of contact with the underlying soil or the accumulation of water below the plates (Mayocchi and Bristow, 1995). As a consequence, to obtain the real surface values of the soil heat flux (QG), heat storage between

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Fig. 4 – Comparison between the non-stationarity indexes computed by the test proposed by Foken and Wichura (1996) (NSFoken) and by the test proposed by Mahrt (1998) (NSMahrt), applied to the 30 min time series of kinematic heat (w0 T0 ) and water vapour (w0 q0 ) fluxes. Black stars refer to the summer campaign and grey circles refer to the autumn campaign. Dashed lines represent the thresholds indicating non-stationary time series (NSFoken > 30%; NSMahrt > 2). For reference, in (b) the 1:1 line is also shown (solid black line).

the ground and the depth of the plate (S) has to be added to the measured flux (QGm): Q G ¼ Q Gm þ S:

(2)

The ground heat storage is expressed by the simple equation: Z z¼zD @T (3) S¼ cv dz @t z¼0 where cv is the volumetric heat capacity of the soil and zD is the depth of the buried plate. The integration between the surface

(z = 0) and zD is computed by dividing the layer into sub-layers depending on the available temperature measurement levels. Moreover, cv has been estimated from a table of soil heat capacity (for clay soil) with variable moisture content (Pielke, 2002), by interpolating the reported heat capacity values with the measured soil moisture content between a depth of 0 and 5 cm (Section 2.1). Fig. 6 shows the effect of the storage correction on the ground heat flux measured by the plates buried at 2 cm and 5 cm depths. Note as the maxima of net radiation and of uncorrected ground heat fluxes (QGm) are shifted by about 45–

Fig. 5 – Comparison between the average diurnal variation of the residual energy computed on all selected time series (black lines and symbols) and on stationary data only (grey lines and symbols), for the summer campaign (a) and the autumn campaign (b). Bars represent the standard deviation of the mean.

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Fig. 6 – Comparison between the average diurnal variation of the ground heat flux (sign reversed) measured at 2 cm (solid lines) and 5 cm depth (dashed lines), before (black lines) and after (grey lines) the correction for the ground heat storage (S), for the summer campaign (a) and the autumn campaign (b). For comparison the average diurnal variation of Rnet is also shown (dot-dashed black lines).

60 min, both in the summer and in the autumn campaigns. The storage correction removes that shift and it greatly reduces the differences between the data collected at the two available measurement levels, with the uncorrected measurements at 5 cm are more damped because of the larger heat storage. Storage correction reduces those differences from 40% to about 17% in the summer campaign and from 15 to 2% in the autumn campaign. The effect of the storage correction on the surface energy balance confirms the importance of an accurate estimate of QG (Fig. 7). Global closure rate has a clear improvement from 0.88 to 1.02 in the summer campaign, and from 0.86 to 0.96 in the autumn campaign (see Table 1). Also, the daily pattern of the short-term SEB is greatly damped in particular in the negative part of the residual curve. This is due to the improvement of the estimate of QG, and to the consequent removal of the phase shift with respect to the Rnet curve. However, the energy residual still appears not to be negligible, in particular during the first part of the day. The performed analysis highlighted the equivalence of QG estimates at the two levels, after a correction for ground heat storage. In the following, the highest (2 cm) has been chosen as the reference depth.

3.4.

Contribution to the transport of ‘large-scale’ motions

In the past decades micrometeorologists have used time periods of about 15–30 min as the averaging interval for the computation of mean turbulence statistics. The choice of this period was derived from the assumption of a spectral gap between turbulent time-scales of flux transport and longerscale atmospheric motions. However, it is dubious if this gap really exists, and if 30 min is sufficient to adequately sample all motions that contribute to transport. Recent studies (Sakai

et al., 2001; Finnigan et al., 2003; Foken et al., 2006) highlighted that the optimum period for time averaging may be longer than 30 min. These studies suggest that averaging periods of 2–4 h are often needed to statistically resolve the largest convective turbulent eddies or also non-stationary mesoscale motions that sometimes can modulate turbulent fluxes (Mahrt, 1998). A method used to ensure if an adequate number of the larger eddies have been sampled in the chosen period P is to look at the empirical cospectra or, in particular, at the ogive functions. The ogive function describes the cumulative contribution to total transport by eddies of increasing period: Z f0 Coxy ð f Þ d f (4) Ogxy ð f 0 Þ ¼ 1

where Coxy is the cospectrum of the turbulent variables x and y, and f is the frequency. When the ogive function reaches an asymptote at some period it indicates that time scales larger than that period do not contribute to the transport. Analysis of ogive and cospectrum functions computed on the selected data sets highlights the role of large-scale motions in the transport of the sensible and latent heat fluxes. Fig. 8 shows an example of ogives and cospectra of the kinematic heat flux computed in one of the selected days in the summer campaign. Each line represents a 2-h sample period. Note that often the ogive function does not reach the asymptote in 30 min, but tends to increase or decrease depending on the time of the day, indicating the presence of large-scale structures that contribute to the main transport. In particular this effect is evident in the central part of the day, when the cospectra also do not approach zero at 30 min, but can be significantly different from zero at longer time scales. This behaviour has been observed in both experimental campaigns.

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Fig. 7 – (a and c) Scatter plot of the global closure of the SEB (QH + QE vs. Rnet S QG) based on 30 min averages computed by using the ground heat flux measured at 2 cm, before (black symbols) and after (grey symbols) the storage correction (S), for summer campaign (a) and autumn campaign (c). Dashed black line represents the linear fit of the uncorrected data (summer: (QH + QE) = 0.88 (Rnet S QG) + 2.6, R2 = 0.87; autumn: (QH + QE) = 0.86 (Rnet S QG) S 7.3, R2 = 0.86); Dashed grey line represents the linear fit of the data corrected for storage (summer: (QH + QE) = 1.02 (Rnet S QG) S 17, R2 = 0.91; autumn: (QH + QE) = 0.96 (Rnet S QG) S 13, R2 = 0.88). For reference, the 1:1 line is also shown (solid black line). (b and d) Comparison between the average diurnal variation of the residual energy computed by using the ground heat flux measured at 2 cm depth, before (black lines) and after (grey lines) the storage correction for the ground heat storage (S), for the summer campaign (b) and the autumn campaign (d). Bars represent the standard deviation of the mean.

Fig. 8 – Ogives (a) and cospectra (b) of the kinematic heat flux computed on 14 May 2005. Each line represents a 2-h sample period in the selected day. Grey lines correspond to ogives and cospectra computed between 8:00 and 10:00 (dashed lines), 10:00 and 12:00 (solid lines) and 12:00 and 14:00 (dot-dashed lines). Vertical black dashed lines correspond to 30 min, 1 h and 2 h time scales.

agricultural and forest meteorology 148 (2008) 82–93

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Fig. 9 – Comparison between the average diurnal variation of the residual energy computed on the uncorrected data (black stars and lines) and after the described corrections superimposed each other in the following order: correction for errors dependent by the ultrasonic anemometer angle of attack and for the ground heat storage (a + S: light grey circles and lines— 30 min averages); and corrections for the effect of the ‘large-scale’ motions (LS: dark grey pentagrams and lines—2 h averages). Bars represent the standard deviation of the mean.

In order to include the contribution of these large scales to the estimate of total transport, the ‘block-ensemble’ averaging procedure proposed by Finnigan et al. (2003) was followed. They demonstrated that the effect of the ‘classical’ coordinate rotation in a streamline coordinate system (McMillen, 1988) that imposes w¯ P ¼ 0 over a ‘short’ averaging period P (for example P = 30 min) is equivalent to a high-pass filter applied to the covariance wcP that removes contributions from atmospheric motions with periods longer than P, but also distorts the portion of the cospectrum relative to scales of shorter periods. The degree of underestimation depends mainly on the magnitude of the rotation angles applied to each period and to the actual spectral content of the covariance at periods longer than P. As a consequence a longer averaging and coordinate rotation period is needed to obtain a reliable evaluation of the fluxes. In the ‘long-term coordinates’ rotations are defined by imposing mean vertical velocity to zero over the longer period NP, but not in any single period P: hw¯ P iNP ¼ 0, but w¯ P 6¼ 0; moreover, the total covariance hwcP iNP over the period NP is the ensemble average of the sum of w¯ 0P c¯0P (the vertical advection term in the period P) and w0 c0 P (the eddy flux in the period P): D 0 0 E hwcP iNP ¼ wP cP þ w0 c0 P

NP

(5)

Finnigan et al. (2003) showed that in each period the vertical advection term w¯ 0P c¯0P carries the low frequency part of the covariance wcP , but it also balances any transient and unmeasured horizontal advection events. This last contribution of the vertical advection term actually does not contribute to the vertical flux, but its values in each period can be very noisy. As a consequence many periods must be averaged to ensure the cancelling out of the transient vertical and horizontal advection terms but also to ensure the inclusion of all important low frequency contributions. In order to find the optimal averaging period, the blockensemble averaging procedure has been applied by choosing

long term averaging periods NP that were multiples of the basic 30 min period P. Finnigan et al. (2003) demonstrated that ‘the block-ensemble average covariance (hwcP iNP ) computed from the N period P is precisely equal to the simple block-averaged eddy-covariance (w0 c0 NP ) that can be computed by changing the averaging time from the short period P to the total period NP. On the basis of this equivalence the fluxes on the ‘long-term coordinate’ periods have been computed by applying the McMillen (1988) rotation procedure to the total periods NP (1, 2, 4, and 8 h). The comparison (not shown) of the fluxes computed over 30 min and the fluxes computed on the ‘long-term coordinate’ periods showed that time scales until 2 h continue to add covariance; in particular the sensible and latent heat fluxes globally increase by 9% in the summer campaign and by 18% in the autumn campaign. Conversely, when the averaging period is extended to 4 or 8 h, fluxes tend to decrease and be very noisy, suggesting that the corresponding scales of motions deteriorate the flux estimates, probably due to the introduction of trend and non-stationarity connected to synoptic scale motions. On the basis of the obtained results, the effect of large-scale motions on daily and short-term energy balance has been checked by moving the averaging period from 30 min to 2 h. The large-scale correction (LS) did not significantly affect the global closure rate in summer campaign, that was already improved by accounting for the energy storage correction in both experimental campaigns (see Table 1). On the other hand, the global closure rate in the autumn campaign improved from 0.96 to 1.01. The LS correction had the strongest impact on the shortterm energy balance: in fact the daily pattern of the residual energy appeared strongly attenuated, in particular in the central part of the day, in both experimental campaigns (Fig. 9). This is probably because ‘large scale’ transport is associated with the largest turbulent eddies during convective conditions, as evidenced by the analysis of the ogive and cospectrum functions.

92 4.

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Conclusions

The aim of this study was to investigate the main causes of surface energy imbalance over a nearly-flat field covered by short vegetation. In the last few decades most surface experiments and carbon dioxide flux networks found a global closure of SEB of about 80%. However, the daily energy budget is more easily balanced than the hourly energy budget, because of the cancellation of energy residuals of opposite sign. What distinguishes this study is the effort to close the ‘short-term’ energy budget, and to explore the factors that mainly affect the energy imbalance throughout the day. The analysis has been performed on data collected in two different seasons in order to ensure the validity of the obtained results, or to observe possible differences deriving from different atmospheric conditions. Before applying the investigated correction terms, global closure rates of SEB (derived from the slope of the linear fit of (QH + QE) vs. (Rnet  QG)) equal to 0.82 in the summer campaign and 0.76 in the autumn campaign were observed. Moreover, the mean residual energy computed every 30 min exhibited a daily pattern, common to both seasons, characterised by positive values during the first part of the day, and by an inversion of sign in the afternoon. The residual energy values observed during the summer were greater than those observed in autumn because of higher incoming radiation energy. The application of the correction terms has highlighted the following results: (1) Global energy closure improves after corrections for errors dependent on the ultrasonic anemometer angle of attack. That calibration produces an appreciable increase in the turbulent sensible and latent heat fluxes in both seasons and a consequent improvement of the global closure rates (from 0.82 to 0.88 in the summer campaign and from 0.76 to 0.86 in the autumn campaign). However, the daily pattern of ‘short-term’ energy residual is not greatly affected by this calibration; a modest effect is only evident during daytime, according to a greater frequency of large angles of attack in convective conditions. (2) The ground heat flux plays an important role in the energy transformation processes in the analysed time series because of the low moisture content inside the ground, in particular during the summer season. After correction for heat storage into the soil, the global closure rate significantly improves to 1.02 in the summer and to 0.96 in the autumn. The most interesting result is the partial attenuation of the daily pattern of the short-term energy residual; this effect is particularly evident in the afternoon when the negative residual is greatly attenuated, and also because the storage correction removes the original phase displacement between QG and Rnet maxima. Moreover, the storage correction has a greater effect in the attenuation of the daily SEB pattern during the summer. (3) The standard procedure of linear detrending frequently used to reduce the non-stationarity effect can be ineffective because turbulent and non-turbulent motions (i.e. mesoscale motions) cannot be completely separated. Therefore one may wish to avoid detrending or filtering

and different methods have been proposed in the literature to identify and remove non-stationary records. However, the performed analysis has highlighted the difficulty of identifying non-stationarity in time series. Two different methods often used in the literature have been compared and their effect on the energy balance closure has been checked. Results indicate that discarding non-stationary time series does not have any influence either on the global or short-term energy balance. (4) Another critical aspect in the evaluation of eddy fluxes is the choice of the optimal averaging time in order to adequately sample any motions that can contribute to the transport. According to other recent theoretical and experimental studies, the performed analysis confirms that the SEB cannot be closed on very short time scales (e.g. 30 min) and the shortest time scale that is appropriate for use in SEB analysis may be on the order of a few hours, even with near ideal sites. The application of a long-term averaging and coordinate rotation on a period of 2 h allows a further reduction in the energy residual pattern. Moreover, after all the corrections described above the absolute value of the residual assumes very low values, often much lower than 50 W m2 during day phases, being compatible with random error combinations associated with measurement procedures. The ‘large-scale’ correction is particularly relevant between 05:00 and 12:00 when the residual of energy remaining after storage correction is still significant. On the contrary the effect during night is low. As a consequence, the large-scale contribution to eddy fluxes may derive from the larger convective eddies probably insufficiently sampled using the classical average period of 30 min. This result confirms a need indicated in recent studies (Foken et al., 2006; Finnigan et al., 2003; Sakai et al., 2001) to properly assess the contribution to the mass and energy transport by large-scale motions caused by the landscape of the measurement area. (5) None of the corrections discussed above influenced the closure of the SEB during the night. Even if the energy residual assumes very low values during the night (lower than 20 W m2), these values are not unimportant because of the typical low values of net radiation during the night. However, the comprehension of the mechanisms creating the energy imbalance at night remains a problem and more efforts have to be made in order to progress the closure of the nocturnal energy budget. An improvement of the quality of the estimation of heat fluxes by the eddy correlation method can also affect the improvements of understanding of ecosystem respiration, considerably influenced by the defective evaluation of the nocturnal CO2 fluxes, often comparable to their daytime counterpart.

Acknowledgements This work has been carried out in the framework of the Italian MIUR Project: ‘Sviluppo di un Sistema Integrato Modellistica Numerica-Strumentazione e Tecnologie Avanzate per lo Studio e le Previsioni del Trasporto e della Diffusione di Inquinanti in Atmosfera’, grant ‘‘Bando 1105/2002 project no. 245’’.

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