Carbon dioxide and energy fluxes over a small ... - Wiley Online Library

PUBLICATIONS Journal of Geophysical Research: Biogeosciences RESEARCH ARTICLE 10.1002/2014JG002873 Key Points: • Dynamics of CO2 and energy exchange over a boreal lake are studied • The lake acted as net source of carbon dioxide • Nighttime cooling of surface water enhances the gas transfer efficiency

Carbon dioxide and energy fluxes over a small boreal lake in Southern Finland Ivan Mammarella1, Annika Nordbo1, Üllar Rannik1, Sami Haapanala1, Janne Levula2, Heikki Laakso2, Anne Ojala3,4, Olli Peltola1, Jouni Heiskanen1, Jukka Pumpanen3, and Timo Vesala1 1

Department of Physics, University of Helsinki, Helsinki, Finland, 2Hyytiälä Forestry Field Station, University of Helsinki, Korkeakoski, Finland, 3Department of Forest Sciences, University of Helsinki, Helsinki, Finland, 4Department of Environmental Sciences, University of Helsinki, Lahti, Finland

Abstract Dynamics of carbon dioxide and energy exchange over a small boreal lake were investigated. Correspondence to: I. Mammarella, ivan.mammarella@helsinki.fi

Citation: Mammarella, I., et al. (2015), Carbon dioxide and energy fluxes over a small boreal lake in Southern Finland, J. Geophys. Res. Biogeosci., 120, 1296–1314, doi:10.1002/2014JG002873. Received 26 NOV 2014 Accepted 2 JUN 2015 Accepted article online 5 JUN 2015 Published online 23 JUL 2015

Flux measurements have been carried out by the eddy covariance technique during two open-water periods (June–October) at Lake Kuivajärvi in Finland. Sensible heat (H) flux peaked in the early morning, and upward sensible heat flux at night results in unstable stratification over the lake. Minimum H was measured in the late afternoon, often resulting in adiabatic conditions or slightly stable stratification over the lake. The latent heat flux (LE) showed a different pattern, peaking in the afternoon and having a minimum at night. High correlation (r2 = 0.75) between H and water-air temperature difference multiplied by wind speed (U) was found, while LE strongly correlated with the water vapor pressure deficit multiplied by U (r2 = 0.78). Monthly average values of energy balance closure ranged between 70 and 99%. The lake acted as net source of carbon dioxide, and the measured flux (FCO2) averaged over the two open-water periods (0.7 μmol m2 s1) was up to 3 times higher than those reported in other studies. Furthermore, it was found that during period of high wind speed (>3 m s1) shear-induced water turbulence controls the water-air gas transfer efficiency. However, under calm nighttime conditions, FCO2 was poorly correlated with the difference between the water and the equilibrium CO2 concentrations multiplied by U. Nighttime cooling of surface water enhances the gas transfer efficiency through buoyancy-driven turbulent mixing, and simple wind speed-based transfer velocity models strongly underestimate FCO2.

1. Introduction Advancing our understanding on physical processes controlling turbulent exchange of energy, carbon dioxide, and other trace gases over lacustrine systems is crucial in order to improve climate and weather forecast models. Lakes have different albedo, lower surface roughness, and greater effective heat capacity than surrounding land areas [Beyrich et al., 2006]. These properties affect climate and weather through changes in surface energy budgets at different spatiotemporal scales [Dutra et al., 2010; Balsamo et al., 2012]. Moreover, lakes are able to process large amounts of organic carbon of terrestrial origin, and their importance in landscape carbon cycle and climate change issues is well recognized [Battin et al., 2009; Williamson et al., 2009; Regnier et al., 2013]. Nevertheless, the amount of carbon dioxide (CO2) and methane (CH4) released into the atmosphere is still uncertain [Bastviken et al., 2011; Raymond et al., 2013].

©2015. American Geophysical Union. All Rights Reserved.

MAMMARELLA ET AL.

The eddy covariance (EC) technique is widely used for continuous and long-term monitoring of energy and gas exchange between land ecosystems (forest, wetland, arable land, and grassland) and atmosphere [Baldocchi, 2003]. The method has been applied only recently to inland aquatic ecosystems, and at the moment there is no comprehensive network of long-term lacustrine EC sites covering different latitude and climatic zones and lake characteristics. Most of the previous studies have focused on water-atmosphere energy exchange, and only few studies have reported direct EC fluxes of CO2 and CH4 (see Table 1). The first study on CO2 exchange was carried out by Anderson et al. [1999], who reported 5 weeks of EC measurements at Williams Lake in the U.S. The longest data set is from Huotari et al. [2011], who measured CO2 fluxes for five consecutive open-water periods (May–November) at Lake Valkea-Kotinen in Southern Finland. EC measurements have to undergo laborious analyses for evaluating the EC system performance and calculating turbulent fluxes. In addition, data quality control, filtering criteria, and flux random uncertainty may depend on site characteristics and atmospheric turbulence characteristics [Vickers et al., 2010; Nordbo et al., 2012]. So far, none of the lake studies have reported the random errors associated with the EC fluxes. CO2 AND ENERGY FLUXES OVER LAKE

1296

Journal of Geophysical Research: Biogeosciences Table 1. List of Published Lake Eddy Covariance Flux Measurements Lake Name

2

10.1002/2014JG002873

a

Location

Area (km )

Mean Depth (m)

Max Depth (m)

EC Fluxes

Reference

Thermokarst Lakes Valkea-Kotinen

72°22′N, 126°30′E 61.14°N, 25.03°E

0.041

2.5

5 6.5

H, LE, CO2 H, LE, CO2

Soppensee Williams Eshkol Reservoir Rotsee Kuivajärvi Toolik Kossenblatter Wohlen Reservoir Merasjärvi Scharmützelsee Tämnaren

47.06°N, 9.05°E 46.57°N, 94.40°E 32.46°N, 35.14°E 47°04′N, 8°18′E 61°50′N, 24°17′E 68.37°N, 149.36°W 52.08°N, 14.06°E 46°57′N, 7°18′W

60.09°N, 17.20°E

0.25 0.341 0.36 0.5 0.63 1.5 1.86 2.5 3.8 12.1 34

12 5.2 3.5 9 6.4 7 2.1 9 5.1 9.8 1.2

27 9.3 16 13.2 25 4 18 17 31 2

Thau Lagoon Ross Barnett Reservoir Alqueva Reservoir Geneva Taihu Great Slave Great Bear Superior

43°24′N, 3°36′E 32°26′N, 90°02′W 38.22°N, 7.46°W 46.27°N, 6.25°E 31°24′N, 120°13′E 61.92°N, 113.73°W 65.8°N, 120.8°W 47°18′N, 87°23′W

75 133 250 582 2,400 27,000 31,000 82,100

4 5 16.5 3 1.9 41 72 148

11 11 65 2.6 614 413 406

H, LE, CO2 CO2 H, LE CH4 H, LE, CO2 H, LE, CO2 H, LE CH4 H, LE, CO2 H, LE H, LE CH4 H, LE H, LE H, LE H, LE H, LE H, LE H, LE H, LE

Abnizova et al. [2012] Vesala et al. [2006], Nordbo et al. [2011], and Huotari et al. [2011] Eugster et al. [2003] Anderson et al. [1999] Assouline et al. [2008] Schubert et al. [2012] This study and Heiskanen et al. [2014] Eugster et al. [2003] Panin et al. [2006] Eugster et al. [2011] Jonsson et al. [2008] Beyrich et al. [2006] Venäläinen et al. [1998] Podgrajsek et al. [2014] Bouin et al. [2012] Liu et al. [2011] Salgado and Le Moigne [2010] Assouline et al. [2008] Vercauteren et al. [2008] Deng et al. [2013] and Xiao et al. [2013] Blanken et al. [2000] Rouse et al. [2008] Blanken et al. [2011]

a

The table is an update of the one reported in Nordbo et al. [2011].

Common methods for estimating lake-atmosphere gas exchange are based on noncontinuous and/or indirect measurements, e.g., floating chamber [Duchemin et al., 1999] and boundary layer [Cole and Caraco, 1998] techniques. The former may cause disturbances in the air-water interface producing a bias in the flux measurements [Vachon et al., 2010], whereas the major source of uncertainty of the latter approach is in the parameterization used for the physical rate of exchange between the water and the air, usually expressed as a piston velocity [Cole and Caraco, 1998]. Recently, EC measurements have been used also to develop new empirical models of gas transfer velocity k [e.g., Jonsson et al., 2008; Heiskanen et al., 2014; Podgrajsek et al., 2015], using simultaneous measurements of CO2 partial pressure at the water surface. Similar to previous EC-based ocean studies [McGillis et al., 2004], these studies have reported higher CO2 emissions relative to those estimated from k models derived from other approaches (e.g., SF6 in Cole and Caraco [1998]). High-resolution EC measurements allow relating air-water gas exchange rate variability not only to wind speed but also to other physical factors. Some studies [Eugster et al., 2003; MacIntyre et al., 2010; Heiskanen et al., 2014] have stressed the importance of nighttime thermal cooling of the lake, generating convective mixing and turbulence in the water, which can lead to an increase of CO2 exchange at the water-air interface. Thermally induced water turbulence is particularly important in small windsheltered lakes [Read et al., 2012]. In this study we report 2 years of EC flux measurements of CO2, as well as sensible and latent heat, during the open-water period (June–October) collected at a small boreal lake in Southern Finland. The aims are (i) to provide new insights on EC methodology applied to lake ecosystems, including data processing, quality control, and flux random errors; (ii) to determine the energy balance closure, as well as the diurnal variation of energy exchange and related driving factors; (iii) to quantify CO2 release during the openwater period; and (iv) to assess the relative contribution of shear- and buoyancy-induced water turbulence on CO2 exchange.

2. Materials 2.1. Site Description Since June 2010, energy and CO2 exchange has been measured at Lake Kuivajärvi (61°50′N, 24°17′E), located close to the Hyytiälä Forestry Field Station and SMEAR II Station [Hari and Kulmala, 2005]. Lake Kuivajärvi is a

MAMMARELLA ET AL.

CO2 AND ENERGY FLUXES OVER LAKE

1297

Journal of Geophysical Research: Biogeosciences

10.1002/2014JG002873

Table 2. Eddy Covariance Setup in 2010 and 2011 2010 Sonic anemometer

2011 Metek USA-1

Inclinometer

SCA121T D07 (VTI Technologies Oy, Finland)

IRGA Inlet height Horizontal separation between sonic probe and air sampling inlet Vertical separation between sonic probe and air sampling inlet Sampling line material Sampling line length

Licor LI-7000

Licor LI-7200 1.7 m 0.03 m 0.12 m PTFE

3.5 m

Sampling line diameter Flow rate Sampling frequency

0.7 m 0.004 m

8 LPM

12 LPM 10 Hz

small humic boreal lake extending about 2.6 km in northwest to southeast direction, and it is a few hundred meters wide (surface area is 0.63 km2). The measurement platform is located approximately 1.8 km and 0.8 km from the northern end and southern end, respectively. The moored platform, firmly anchored from all the four corners, has a size of about 3.1 × 6.2 m being big enough to be stable and small enough to minimize distortion effects on the turbulence measurements. The lake has a maximum depth of 13.2 m, and the depth at the location of the platform is 12.5 m. Lake Kuivajärvi is mainly surrounded by managed coniferous forest (average height of the trees is 15 m), but also, small open wetland areas are present mainly in southwest and west directions. Except the surroundings around the outlet in the southern end of the lake, the littoral zone fringing the lake is small and sparsely vegetated. 2.2. Eddy Covariance Measurements Turbulent fluxes of momentum, heat, CO2, and H2O were measured using the EC technique. The system, located on the above mentioned platform, includes an ultrasonic anemometer (Metek USA-1, GmbH, Elmshorn, Germany) to measure the three wind velocity components and sonic temperature and a closedpath infrared gas analyzer (IRGA) that measures CO2 and H2O concentrations. The data were sampled at 10 Hz, and the gas inlet was at 1.7 m above the water surface close to the sonic anemometer (horizontal and vertical separation were about 3 and 12 cm, respectively). Until June 2011, the Li-7000 (LI-COR Inc., Lincoln, NE, USA) was used. The polytetrafluoroethylene (PTFE) sampling line was 3.5 m long, and the inside diameter was 4 mm. The flow rate inside the sampling line was 8 L min1. On 9 June 2011, the system was renewed and the LI-7000 was replaced with the enclosed path gas analyzer LI-7200 (LI-COR Inc., Lincoln, NE, USA). In the new setup, the sampling line is similar to the previous one, but as the gas analyzer was mounted on the mast below the anemometer, the length of the sampling line is only 0.7 m. The flow rate inside the sampling line is 12 L min1. Fast measurements of the platform tilt angles were performed using a dual-axis inclinometer (SCA121T-D07, VTI Technologies Oy, Vantaa, Finland, now Murata Electronics Oy), in order to assess the platform oscillation caused by waves. The EC setup details are summarized in Table 2. 2.3. Ancillary Measurements Continuous measurements of the water temperature were performed by a string of Pt-100 temperature sensors installed at the depths of 0.2, 0.5, 1.0, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 6.0, 8.0, 10.0, and 12.0 m. The sampling frequency was 0.2 Hz, and the probe resolution and accuracy were 0.1 and ±0.5°C, respectively. The short- and long-wave radiation components were measured with a CNR-1 net radiometer (Kipp & Zonen B.V., Delft, Netherland), mounted at 1 m above the water surface on a horizontal boom extending 1.2 m from the platform. The LI-193 Spherical Quantum Sensor (LI-COR Inc., Lincoln, NE, USA) was used for measuring the photosynthetic active radiation (PAR) in the water at 0.2 m depth. The ambient relative humidity and air temperature were measured by using the Rotronic MP106A sensor (Rotronic AG, Bassersdorf, Switzerland) installed inside a naturally ventilated radiation shield at 1.5 m height. For the continuous measurements of the water column concentrations of CO2 at the depths of 0.2 m, 0.5 m, 1.0 m, and 3.0 m, we used a measuring system (consisting of gas-impermeable tubing (stainless steel and Teflon),

MAMMARELLA ET AL.


1298


10.1002/2014JG002873

a CO2 analyzer (CARBOCAP® MP343; Vaisala Oyj, Vantaa, Finland), and semipermeable silicone rubber tubing with 1.5 mm wall thickness (Rotilabo 9572.1, Carl Roth GmbH, Germany) for gas collection), where a continuous airstream was circulated with a diaphragm pump (KNF Neuberger Micro gas pump, KNF Neuberger AB, Stockholm, Sweden) in a closed loop (see Heiskanen et al. [2014] for more details). All ancillary measurements were averaged to 30 min resolution consistently with the EC fluxes.

3. Methods 3.1. Raw Data Postprocessing The EC fluxes were calculated as 30 min block-averaged covariances between the scalars and the vertical wind velocity according to commonly accepted procedures [Aubinet et al., 2012]. The postprocessing software EddyUH (http://www.atm.helsinki.fi/Eddy_Covariance/EddyUHsoftware.php) was used. In order to eliminate outliers, the 10 Hz EC raw data were automatically despiked according to standard methods [Vickers and Mahrt, 1997]. Since no effect of the platform oscillation was found in the power spectra of wind velocities (see section 4.3.2), the measured two axes angles from the inclinometer were not used for correcting the sonic anemometer wind components. Furthermore, the wind velocity components were rotated into a natural coordinate system, by performing a two-step rotation [Kaimal and Finnigan, 1994] to each 30 min interval, which sets the x axis along the mean wind direction and the mean vertical wind velocity to zero. The CO2 mole fraction data were converted to dry mole fraction values by performing a point-by-point dilution correction [Burba et al., 2012]. The cross-wind correction was applied point by point to the sonic temperature data according to Liu et al. [2001]. The time delay between the vertical wind speed w and the scalar (CO2 or H2O) is derived for each 30 min interval by maximizing the difference between their respective cross-correlation function and the linear curve connecting the values of cross correlation found at the lag window boundaries [Clement, 2004]. This approach gives the same time delay values as found by simply maximizing the cross-correlation function in case of high flux signal. However, during periods with low flux and nonstationarity in the time series, the former approach is more reliable, avoiding cases where the estimated delay is located exactly on the window boundaries. A constant search window is used through the whole measurement period for CO2 time delay estimation, whereas for H2O the lag window boundaries vary as a function of relative humidity [Clement, 2004; Nordbo et al., 2012]. Such dependence was first determined by allowing the H2O signal to have a longer lag than CO2. Hence, a variable and narrower search window was determined and the H2O time delay estimated again. Fluxes were corrected for high- and low-frequency losses, due to the limited frequency response of the EC system and the finite time averaging period used for calculating the fluxes, respectively [Foken et al., 2012]. Assuming that the normalized cospectrum of all scalars has the same form (scalar similarity) and that the cospectrum CwT(f) of the potential temperature flux w′T′ can be measured with adequate accuracy, the flux correction factor CF was determined as ∞

CF ¼

∞

∫0 CmwT df

∫0 TFLF TFHF CmwT df

;

(1)

where f is the natural frequency, TFLF is the transfer function of high-pass filtering associated with block averaging [Rannik and Vesala, 1999], TFHF is the low-pass filtering transfer function, and C m wT is the site-adapted scalar cospectral model, whose functional form is similar to the one proposed by Kristensen et al. [1997] Cm wT ¼

f C^ m β1 n wT ¼ 2π h i7=6β3 ; w′T′ 1 þ ð2πβ nÞ2β3

(2)

2

where n = fz/U is the normalized frequency, z the measurement height, and U the mean wind speed. The w′T′ cospectra were fitted to equation (2) by nonlinear regression obtaining the parameters β1, β2, and β3. The results are discussed in section 4.3.2. High-frequency response correction for the momentum and sensible heat fluxes was performed using a theoretical formulation for the transfer function TFHF, according to Aubinet et al. [2000]. Instead, the CO2 and H2O fluxes were corrected using experimentally estimated cospectral transfer functions.

MAMMARELLA ET AL.


1299


10.1002/2014JG002873

The transfer function TFHF was experimentally estimated as the ratio of the measured cospectrum C of the scalar (CO2 or H2O) and temperature flux. A first-order Lorentzian function [Eugster and Senn, 1995] was fitted to the measured TFHF in order to retrieve the low-pass filter time constant. To account for sorption/desorption effects on the sampling line internal walls [Nordbo et al., 2014], the TFHF for water vapor was calculated for different classes of relative humidity. More details on the procedure to estimate TFHF can be found in Mammarella et al. [2009]. 3.2. Flux Random Uncertainty and Footprint The total random error δF associated with each 30 min covariance value is generally due to the instrumental noise and the stochastic nature of turbulence (one-point sampling uncertainty). The uncertainty due to instrumental noise was estimated by the method proposed by Lenschow et al. [2000] and recently applied to EC measurements [Mauder et al., 2013; Peltola et al., 2014]. Instead, the total random uncertainty δF associated with each 30 min run is presented as standard deviation of the covariance and was evaluated according to Finkelstein and Sims [2001] v" ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi # u m m X u X 1=2 t δF ¼ n (3) Rs;s ðpÞRw;w ðpÞ þ Rw;s ðpÞRs;w ðpÞ ; p¼m

p¼m

where n = 18,000 is the number of samples in the chosen 30 min averaging period, Rs,s and Rw,w are the autocovariance functions of scalar s and vertical velocity w time series, and Rw,s and Rs,w are their cross-covariance functions. As suggested by [Finkelstein and Sims, 2001], m was chosen equal to 200, which corresponds to ±20 s integration limits for the covariance functions. Since δF typically depends (increases) on the magnitude of turbulent flux F, the random flux uncertainty is further discussed in terms of relative flux error ΔF = δF/F. Flux footprint distribution functions were estimated using the Kormann and Meixner [2001] model. For the calculation, a constant value of 0.001 m for the roughness length was used, whereas wind speed, Obukhov length, and standard deviation of lateral wind velocity component were acquired from the EC data. The footprint was calculated for each 30 min flux value, rotated toward the prevailing wind direction and then aggregated with the previously calculated footprints. With this procedure a cumulative footprint, i.e., footprint climatology, was obtained. The aggregation of footprints was done separately for different stability conditions. 3.3. Energy Balance The energy balance closure (EBC) and the energy residual (Res) of the lake are defined as EBC ¼

H þ LE 100% Rn ΔQs

Res ¼ Rn ΔQs H LE;

(4) (5)

where H and LE are the sensible and latent heat fluxes, Rn the net radiation, and ΔQs the heat storage change in the water. All the fluxes have units of W m2. H and LE are defined positive when directed upward from the lake surface to the atmosphere, Rn is positive when directed toward the lake surface, and ΔQs is positive when the lake is gaining heat. ΔQs was calculated using the water temperature profile data, measured at 12 depths, according to Nordbo et al. [2011]. The monthly values of EBC and Res were estimated by summing the mean daily courses of the energy balance components for each month [Nordbo et al., 2011]. That is, in order to close the lake energy balance, the daily sum of turbulent fluxes (H + LE) has to be equal to the daily sum of available energy (Rn ΔQs). This method is justified by an analysis showing that the energy balance at half-hourly time scales is unclosed due to phase lags in the energy storage [Leuning et al., 2012]. This effect is particularly important in lake ecosystems, where the heat storage change term represents a substantial large fraction of the lake energy balance. 3.4. Estimation of the Waterside Turbulent Velocities u* w and w* w The waterside turbulent velocities u* w and w* w were estimated from the available atmospheric measurements. In particular, the waterside friction velocity was calculated as uw ¼ u

MAMMARELLA ET AL.

ρair

=ρw


0:5 (6)

1300


10.1002/2014JG002873

where u* (m s1) is the friction velocity derived from EC measurements, ρw (kg m3) the water density, and ρair (kg m3) the air density [Deacon, 1977]. The waterside convective velocity w* w was defined as in Imberger [1985] 1=

w w ¼ ½F b zML 3 ;

(7)

where the actively mixing layer depth zML (m) was estimated from the water temperature profile and calculated as the first depth where the temperature difference relative to the surface temperature (at 0.2 m) was larger than 0.1°C (corresponding to the maximum precision of our temperature probes). The buoyancy flux Fb (m2 s3) was calculated according to Imberger [1985] as Fb ¼

gαQeff ; cpw ρw

(8)

where cpw (J kg1 K1) is the specific heat of water at constant pressure, g (m s2) is the gravity acceleration, α the water thermal expansion coefficient, and Qeff the effective heat flux (W m2), defined as Qeff ¼ QSnet þ QSW ð0Þ þ QSW ðzML Þ

2 zML

∫z

0 ML

QSW ðz Þdz:

(9)

Here QSnet = QLWnet H LE is the net surface heat flux (W m2), QLWnet the net long-wave radiation, and QSW the short-wave radiation [Kim, 1976; Imberger, 1985]. The penetration of solar radiation into the water column was parameterized by the Beer-Lambert’s law. The diffuse light extinction coefficient was estimated by simultaneous measurements of underwater PAR (at 0.2 m depth) and incoming PAR (measured at the SMEAR II station 750 m away from the raft), and typically, values ranged between 0.5 and 2.5 m1 during the analyzed period. A constant value of 2 m1 was used in this study. The measured PAR was used for estimating the third and fourth terms of the right-hand side of equation (9), assuming that all the penetrating solar radiation is in the visible wavelength range. The effective heat flux, as defined in equation (9), represents the actual heating of the actively mixing layer. When the effective heat flux is greater than zero, the uppermost part of the water column will stratify; when it is less than zero, cooling occurs and turbulence can be induced not only by shear but also by heat loss (convective mixing). Note also from equation (9) that, in the absence of solar radiation (nighttime), the effective heat flux equals the net surface heat flux. 3.5. Bulk Estimation of Air-Water CO2 Exchange The CO2 flux over a lake can be parameterized with the gas transfer velocity (k) as F c ¼ βk C w C eq ;

(10)

where Cw is the dissolved CO2 concentration in the surface water and Ceq is concentration of the dissolved CO2 at equilibrium with the air concentration. The chemical enhancement factor β was assumed to be 1, which is a common practice in studies in circumneutral or acidic lakes in comparison to marine systems with high pH where chemical enhancement must be taken into account [Bolin, 1960]. Ceq was estimated from the measured CO2 air concentration using the Henry’s law with in situ surface water temperature. Two commonly used parameterizations for k were considered: the model by Cole and Caraco [1998] is based purely on wind speed k cc ¼ 2:07 þ 0:215U1:7 10 ;

(11)

where the 10 m wind velocity U10 was derived from the measured wind velocity at 1.7 m using the surface layer logarithmic profile accounting for the stability correction function [Kaimal and Finnigan, 1994], and the surface renewal model kSR = 0.5(ευ)0.25Sc0.5, where υ is the kinematic viscosity of water, Sc the Schmidt number for CO2, and ε the dissipation rate of turbulent kinetic energy taken as recently proposed by Tedford et al. [2014], including the effect of friction velocity and buoyancy fluxes, e.g., 8 u3 > > < 0:56 w 0:77F b ; when F b < 0 κz ε¼ ; (12) > u3w > : 0:6 ; when F b > 0 κz with the von Karman constant κ = 0.4 and a constant depth z = 0.15 m [Tedford et al., 2014]. All models were fit to the in situ surface water temperature with the Schmidt number correction [Jahne et al., 1987]. The model fluxes were then compared to the measured fluxes (section 4.5). MAMMARELLA ET AL.


1301


10.1002/2014JG002873

Figure 1. Bathymetric map of the lake. The location of the raft is indicated by a white dot. Contour lines represent the 80% flux footprint for different atmospheric stability and all wind direction. Red line (z/L < 0.0625), green line (0.0625 < z/L 2 and the kurtosis smaller than 1 or larger than 8 [Vickers and Mahrt, 1997]. These criteria removed 10%, 7%, and 2% of CO2, H and LE flux data, respectively. Furthermore, the flux steady state test (FST) was applied [Foken and Wichura, 1996]. Data were flagged according to two threshold values, FST < 0.3 (flag = 0) and FST < 1 (flag = 1), which omitted 7% and 2% of H and 5% and 1% of LE. The stationarity criteria were more effective in removing the CO2 flux, the fraction of omitted data being 35% and 13% for FST < 0.3 and FST < 1, respectively. Unless otherwise stated, flux data flagged with FST < 1 were used for further analysis. In addition, 15% of the flux data were excluded from the analysis, when the wind was not blowing along the lake (345°–135° and 170°–290°). Finally, the overall data coverage for CO2, sensible, and latent heat fluxes during the selected period was 37%, 63%, and 53%, respectively. Available data were equally distributed between day and night (being the nighttime data 43% of the available data). No gap filling was attempted. Although the fraction of accepted data is quite low, it is comparable with earlier studies reporting EC measurements over lakes [Vesala et al., 2006; Jonsson et al., 2008; Nordbo et al., 2011]. The average source area contributing to 80% of the flux ranges from 100 m in slightly unstable conditions up to about 300 m in near-neutral slightly stable conditions (Figure 1). All wind directions retained after quality screening were included in the footprint analysis. Such a simple model may overestimate the footprint, because it does not account for the extra turbulence generated by the surrounding forest, which would

MAMMARELLA ET AL.


1302


10.1002/2014JG002873

Figure 2. Time series of (a) wind speed; (b) air temperature Tair (black) and surface water temperature Tw (grey); (c) air vapor pressure e (black) and saturated vapor pressure esat (grey); and (d) air (black) and surface water (grey) CO2 partial pressure. Data are shown as 5 day running mean.

result in a smaller source area [Vesala et al., 2006]. On the other hand, this result gives us confidence that selecting only periods when the wind is blowing along the lake ensures that the source area of the measured fluxes is on the water surface. 4.2. Meteorological Conditions and Thermal Structure of the Lake Five days running mean values of several meteorological and within lake parameters are shown in Figure 2. The wind speed ranged between 1 and 5 m s1, with an average value of about 2 m s1 (Figure 2a), being slightly higher than the value reported in another small Finnish lake mainly due to a longer fetch [e.g., Nordbo et al., 2011]. Air temperature had its maximum value of 22°C in July 2010 and minimum value of 4°C at the end of October 2010, being most of the time below the surface water temperature, which ranged between 2°C and 23°C (Figure 2b). The vapor pressure at water surface esat (i.e., saturation value at the water surface temperature) and the air vapor pressure e, measured at 1.7 m, are presented in Figure 2c. The water-air vapor pressure gradient shows a typical seasonal pattern, being larger during summer and decreasing during fall. During the analyzed period, the surface water CO2 partial pressure (measured at 20 cm depth) was always larger than the CO2 partial pressure in the air, and its variation strongly depended on the water column stratification, on average varying from 500 μatm in the summer when the lake was thermally stratified up to 1600 μatm during the fall, when the mixing depth increased and the accumulated CO2 was supplied from the hypolimnion to the surface (Figure 2d). The wind direction distributions are very similar for both years (Figure 3), meaning that the lake-induced tunneling was the main reason. The wind direction distributions are also quite similar for day and night. During daytime (positive sun elevation angle) the wind blew 53% of the time from south (135°–170°) and 31% from north (290°–345°) and during nighttime (negative sun elevation angle) 61% of the time from south and 26% from north. The wind speed was lower at night (mean value for 2011 equals to 1.8 m s1) than at daytime (2.6 m s1). Typical of boreal humic lakes [e.g., Huotari et al., 2011; Ojala et al., 2011], the lake is thermally stratified during summer and a thermocline, which typically develops in June, deepens through the summer months, reaching a depth of 8 m at the end of September. At the beginning of October, the lake turns over, resulting in a mixing of the whole water column (data not shown). 4.3. EC System Performance 4.3.1. Power Spectra/Cospectra and EC System Low-Pass Filtering Spectral analysis was applied to the measured turbulent fluctuations in order to assess the EC system performance and evaluate flux attenuation at high frequencies. The w and T power spectra follow the MAMMARELLA ET AL.


1303


10.1002/2014JG002873

Figure 3. Wind direction distribution for the years 2010 and 2011 and for daytime and nighttime. The data sets are classified also according to the wind speed.

surface layer similarity scaling, showing a 2/3 power law in the inertial subrange and spectral peaks at n ≈ 0.2 and n ≈ 0.02, respectively (Figure 4a). The w power spectrum does not display any secondary peak, caused by the rocking of the raft, as found in previous studies [e.g., Eugster et al., 2003]. This gives us confidence that the measurement platform is very stable, and a tilting correction of the sonic wind components is unnecessary for such small lakes [Nordbo et al., 2011], where the wind speed is usually low and surface waves very small. The power spectra curves of CO2 and H2O are clearly damped at high frequencies, where they decreased faster than the T power spectrum. In closed-path measurements, the sampling line and filters are the main reasons for the turbulent signal low-pass filtering [Aubinet et al., 2012]. Some of the power spectra (especially CO2) are affected by white noise at the high-frequency end. When the fluxes are very small, the small fluctuations of turbulent signals are covered by white noise, which shows as +1 slope in the power spectrum. Although the noise increases the flux random uncertainty, it does not correlate with w and thus does not systematically affect the measured flux. The w′T′ cospectrum follows the expected slope (n4/3) in the inertial subrange and peaks at the frequency n = 0.044 (Figure 4b). For the range of the analyzed open-water period stability conditions (from unstable to near neutral), the cospectral peak frequency does not depend on stability, similar to what was found for Lake Valkea-Kotinen [Nordbo et al., 2011]. The site-specific cospectral model was estimated by a nonlinear fit of equation (2) to the measured w′T′ cospectrum, which was corrected for the sonic path averaging effect [Kaimal et al., 1968]. Figure 4b shows the difference between the original and corrected w′T′ cospectra at high frequencies. The effect is particularly important for low measurement height and high wind speed. Alternatively, unbiased site-specific cospectral models can be estimated by performing the fitting on a frequency range unaffected by low-pass filtering [Nordbo et al., 2011]. A larger high-frequency damping is evident in the CO2 and H2O cospectra, showing a 10/3 slope in the inertial subrange. The overall low-pass filtering effect on CO2 and H2O flux was estimated using the experimental method (section 3.1). The estimated time constants for CO2 were 0.25 and 0.1 s for 2010 and MAMMARELLA ET AL.


1304


10.1002/2014JG002873

Figure 4. (a) Normalized frequency-weighted power spectra of vertical wind velocity (w), sonic temperature (T), LI-7000 IRGA CO2, and H2O signals (c and q) as a function of normalized frequency (n). (b) Normalized frequency-weighted cospectra for the same variables as a function of normalized frequency (n). The model fit curve is the cospectral model obtained by fitting the equation (2) to the measured temperature cospectrum. The obtained coefficients are β1 = 4.86, β2 = 2.26, and β3 = 0.36.

2011 setups. For water vapor, relative humidity dependency of the time constants was estimated separately for the two measurement setups. At low relative humidity (30% to 40%), the time constant values were 0.3 and 0.15 s in 2010 and 2011, while they respectively increased up to 0.85 and 0.63 s during high relative humidity conditions. The fluxes were corrected using the correction factors estimated according to equation (1). The CO2 flux correction ranged between 5% and 15% depending on the EC setup and wind speed. For the H2O flux, the correction range was larger (from 8% to 35%) depending also on the ambient relative humidity. 4.3.2. Flux Random Uncertainty Estimates of random uncertainty of EC fluxes have not been reported for lakes before. The total random uncertainty of 30 min fluxes is dominated by the one-point sampling error originating from the stochastic nature of turbulent signals. The relative error due to instrumental noise, estimated according to section 3.2, was around 1% for both EC setups used and being in line with other estimates reported for CO2 and H2O sensors [Mauder et al., 2013]. On average the total relative random error for FCO2 was about twice that estimated for energy fluxes (Figure 5). Median value of δF for CO2 was 0.14 μmol m2 s1, corresponding to 26% (interquartile range (IQR) = 32%) of the observed flux. If only 30 min periods with the best quality (flag = 0) are included, median values of δF and ΔF were 0.11 μmol m2 s1 and 20% (IQR = 21%), respectively, showing that, on average, more conservative flux quality criteria lead to lower flux random uncertainty. The estimated values of ΔF are close to the ones reported in other ecosystems [e.g., Finkelstein and Sims, 2001]. Fluxes of H and LE were characterized by smaller random uncertainty and narrower error distributions, the median

MAMMARELLA ET AL.


1305


10.1002/2014JG002873

Figure 5. Median values of the absolute value of relative flux random error for (a) sensible heat, (b) CO2 and (c) latent heat fluxes as estimated for 2010 and 2011. White boxes correspond to flux with quality flag = 0, and grey boxes to flux with flag = 1. Error bars are the lower and upper quartiles.

values of δF and ΔF being equal to 2.0 W m2 and 10% (IQR = 6%) for H and 3.3 W m2 and 11% (IQR = 4%) for LE, respectively. In this case, including only flux runs with flag = 0 did not produce any change in the random error statistics, because the criteria used for flagging the data had a very low impact on energy fluxes (see section 4.1). The values of ΔF for H and LE are smaller than those observed at vegetated [Finkelstein and Sims, 2001; Vickers et al., 2010] and urban [Nordbo et al., 2012] sites. Using data sets from two forests, Vickers et al. [2010] found that ΔF for energy fluxes strongly increases for stable conditions, when the turbulent signals are typically nonstationary and intermittent, and the flux footprint may extend to more heterogeneous surfaces. Strong stable conditions did not occur over Lake Kuivajärvi, and typically, the thermal stratification was unstable during the night and near-neutral or slightly stable in the afternoon. For energy fluxes, no dependence of ΔF on stability and/or time of the day was found. Other reasons for the small values of ΔF are possibly due to less heterogeneity in the surface temperature and humidity with respect to forests and cities, as well as due to the low measurement height used in this study. 4.4. Energy Exchange 4.4.1. Flux Diurnal Cycle and Driving Forces The diurnal variation of energy fluxes in Lake Kuivajärvi showed a typical pattern (Figure 6) previously found in other lake studies [e.g., Liu et al., 2009; Nordbo et al., 2011]. The energy fluxes have larger amplitude in summer (June–August) than in autumn, following the seasonal variation of incoming solar radiation. Net radiation (Rn) peaked around noon (UTC + 2 h), having the maximum daily value of 498 W m2 in June 2010 and the lowest (50 W m2) in October 2010. Nighttime values of Rn ranged between 75 W m2 (June 2010) and 32 W m2 (October 2010). The net radiation was the main driving factor for the water heat storage change flux ΔQs, which shows monthly diurnal cycles in close correspondence with those of Rn. On average, heat is accumulated in the lake water column during summer, and it is released starting from August. Later in September, when the epilimnion reaches its maximum depth, followed by fall turnover, the loss of stored heat is enhanced and accelerated. Maximum daytime values of ΔQs ranged between 250 W m2 (June 2011) and 37 W m2 (October 2011), while minimum nighttime values were between 180 W m2 (August 2010) and 57 W m2 (October 2011). Turbulent fluxes of H and LE have a diurnal cycle, with a phase and amplitude clearly different from those typically found over land. Early in the morning, at the time of large water-air temperature difference,

MAMMARELLA ET AL.


1306


10.1002/2014JG002873

Figure 6. Mean diurnal course of net radiation (Rn), heat storage (ΔQs), sensible heat flux (H), latent heat flux (LE), water-air temperature difference (Tw Ta), and water-air vapor pressure difference (esat eair) for different months and years. The time on the x axis is in UTC + 2 h. Measurements of ΔQs and LE were not available for June–July 2010.

H reaches maximum values, and upward sensible heat flux at night results in unstable stratification over the lake. Minimum H was measured in the late afternoon, often resulting in adiabatic conditions or very weak stratification over the lake. During the analyzed period, the amplitude of H has its maximum value in June (40 W m2), decreasing to 20 W m2 in October. The diurnal variation of LE shows a different pattern, peaking in the afternoon (around 15:00 UTC + 2) and having a minimum at night. Daytime flux magnitude correlates with the magnitude of Rn, being larger during the summer months than in September–October. Nighttime evaporation ranges between 15 W m2 (October) and 45 W m2 (June–July), and it is larger than the evapotranspiration rate over the surrounding forest, which is typically near zero [Launiainen, 2010]. Differences in vapor pressure gradients explain the large values of LE found in August and October 2010 compared to the same months in 2011. Generally, H is lower over the lake compared with typical values found over land [Wilson et al., 2002], because more available energy is directed to evaporation (Table 3). On average, the observed summer values of Bowen ratio were 0.2 and 0.8 for the lake and the surrounding forest, respectively. Compared to previous lake studies, differences in the magnitudes of H and LE can be found. Nordbo et al. [2011] reported smaller average values of LE (up to 100 W m2) during summer daytime at Lake ValkeaKotinen, where the mean wind speed is only half of that measured in this study. On the other hand, EC measurements over a midlatitude lake (Ross Barnett Reservoir) show summer evaporation rates 2 (day) to 3 (night) times higher than in this study [Liu et al., 2012]. The reason is probably due to different lake sizes and different diurnal courses in wind speed between the two lakes. At summer nights, average U is

Table 3. Energy Partitioning, Balance Closure (EBC), and Residual (Res) Values for Different Months in 2010 and 2011 LE/Rn

H/Rn

June July August September October

MAMMARELLA ET AL.

dQ/Rn

2

EBC (%)

Res (W m

)

2010

2011

2010

2011

2010

2011

2010

2011

2010

2011

0.11 0.05 0.21 0.43 2.20

0.09 0.13 0.27 1.12 2.51

0.82 0.91 5.49

0.53 0.56 0.63 1.81 2.91

0.26 0.94 6.94

0.37 0.28 3.08 6.21

82 71 97

99 70 71 75

19.60 22.03 1.76

0.85 26.86 21.54 12.29


1307


10.1002/2014JG002873

Figure 7. (a) Sensible heat flux as a function of water-air temperature difference multiplied by wind speed U for the openwater periods (June–October). (b) Latent heat flux as a function of vapor pressure difference multiplied by wind speed U for the same period. The solid lines represent the linear fit. Only the best data with the quality flag equal zero (FST < 0.3) were used in the figure.

much higher at Ross Barnett Reservoir (3.63 m s1 in June–July) than the value measured at Lake Kuivajärvi in June–July 2011 (1.4 m s1). Daytime U difference is smaller, although still significant (3.06 m s1 at Ross Barnett Reservoir versus 2.2 m s1 over Kuivajärvi). High correlation (r2 = 0.75) was found between H and the water-air temperature difference multiplied by wind speed (Figure 7a). The slope b of the fitting curve is related to the bulk transfer coefficient for heat (e.g., CH ≈ b/(ρaCp), where Cp is the specific heat capacity of air) for all wind speeds and atmospheric stabilities. Assuming typical values for air density and specific heat capacity, an average estimate of CH was 1.6 · 103 ± 3 · 105. This value of CH can be seen as an effective transfer coefficient, and it is a function of measurement height and atmospheric stability, and thus, it cannot be compared directly with other sites. Following the approach of Xiao et al. [2013], we estimated the effective transfer coefficient at the reference height of 10 m, that is, CH10m = 1.2 · 103 ± 2 · 105, which is in the range of values reported in other lakes [see Xiao et al., 2013, Table 1]. LE shows a good correlation (r2 = 0.78) with the vapor pressure gradient (esat eair) multiplied by wind speed (Figure 7b), similar to the one reported in other lakes [e.g., Blanken et al., 2000; Nordbo et al., 2011]. Following the same approach used for estimating CH, the corresponding values for the effective transfer coefficient for water vapor were Cq = 1.9 · 103 ± 3 · 105 and Cq10m = 1.45 · 103 ± 2 · 105, being very close to the ones found for heat and previously reported [Xiao et al., 2013]. 4.4.2. Energy Balance Closure and Residual Monthly estimates of the energy balance closure (EBC) and residual (Res) are reported in Table 3. The EBC ranges from 70% in August 2011, when the difference between available energy and the turbulent fluxes was 26.86 W m2, to 99% in July 2011, when Res was only 0.84 W m2. The averaged values of EBC were 83% and 79% for 2010 and 2011, respectively. The observed EBC and Res values are very close to those found in other lake studies. Liu et al. [2012] reported monthly estimates of EBC, measured at Ross Barnett Reservoir (Mississippi, USA) during 2008, ranging from 85 to 117%. Available energy was smaller than the sum of turbulent fluxes during February–June and larger for the rest of the months. However, the reason for this systematic behavior was not further investigated. Nordbo et al. [2011] reported long-term EC measurements of energy fluxes for a small and shallow boreal lake and found monthly EBC and Res values ranging from 57% to 112% and 7 to 40 W m2, respectively. The averaged values of EBC measured at Lake Kuivajärvi are also comparable with the 84% reported for 173 terrestrial ecosystems in the FLUXNET network [Stoy et al., 2013]. Although, recently, new corrections and methods for EC flux calculations have been proposed [Aubinet et al., 2012], the energy imbalance problem MAMMARELLA ET AL.


1308


10.1002/2014JG002873

Figure 8. Daily mean values of CO2 fluxes for the two analyzed periods: (top) June–October 2010 and (bottom) June– October 2011. Data are not gap filled. Bars denote the standard deviations. Data with the quality flag equal one (FST < 1) were used.

is still under debate in the flux community. Wilson et al. [2002] suggested that EBC improves with turbulence intensity, or friction velocity, which has been further corroborated by Stoy et al. [2013]. However, such dependence was not found in our study. Foken et al. [2006] concluded that buoyancy-driven large-scale circulations caused by surface heterogeneity are responsible for the imbalance. Shephard [2005] showed that 45% of the FLUXNET sites reached energy balance closure when daily averages were used to take into account the hysteresis effect. 4.5. Carbon Dioxide Flux On average, the lake acted as a net CO2 source, and the measured flux (FCO2) averaged over the two openwater periods was 0.7 μmol m2 s1 (Figure 8). The monthly mean values range between 0.53 and 0.88 μmol m2 s1 during the analyzed period (Table 4). Monthly values were also conditionally averaged for daytime and nighttime, but no clear diurnal variation was found. The CO2 emission values are larger than the EC flux magnitudes reported in other studies [Jonsson et al., 2008] but similar to those measured in 2011–2012 in Lake Kuivajärvi using the boundary layer method [Miettinen et al., 2015]. Huotari et al. [2011] reported the longest time series (5 years) of CO2 flux measured during open-water periods over Lake Valkea-Kotinen: the CO2 flux was 8 times smaller in summer (June–July) and about 30% smaller in August–October. One possible explanation for this difference is that Lake Valkea-Kotinen is very productive; i.e., photosynthetic rate is high and the lake can be regarded as hypereutrophic [Peltomaa et al., 2013]. This results in a net CO2 uptake during summer months as measured by EC [Huotari et al., 2011]. Since boreal lakes also emit and process carbon of terrestrial origin, it is possible that the

Table 4. Monthly Mean Values (±SD) of CO2 Fluxes for All Data, Only Daytime (Sun Elevation Angle > 0), and Only a Nighttime (Sun Elevation Angle < 0) 2 1

FCO2 (μmol m June July August September October All a

MAMMARELLA ET AL.

0.88 ± 0.72 0.87 ± 0.60 0.72 ± 0.61 0.80 ± 0.71 0.53 ± 0.72 0.69 ± 0.66

s

)

FCO2 (μmol m

2 1

s

) Day

0.90 ± 0.69 0.87 ± 0.61 0.71 ± 0.64 0.83 ± 0.69 0.53 ± 0.71 0.73 ± 0.68

2 1

FCO2 (μmol m

s

) Night

0.73 ± 0.76 0.79 ± 0.44 0.74 ± 0.48 0.75 ± 0.72 0.54 ± 0.62 0.63 ± 0.60

Data are not gap filled. Data with the quality flag equal one (FST < 1) were used.


1309


10.1002/2014JG002873

Figure 9. The CO2 flux as a function of CO2 partial pressure difference multiplied by wind speed U. The data points are marked according to the magnitude of (a) the wind speed (U), (b) the logarithm of absolute values of relative flux error (log(|ΔF|), and (c) the ratio u* w/w* w. Only the best quality data with flag equal zero (FST < 0.3) were used.

differences in surrounding forests are behind the large difference in fluxes in lakes Valkea-Kotinen and Kuivajärvi; the first is surrounded by pristine old-growth forest, whereas the latter has a catchment dominated by managed forests. Weak correlation was found between CO2 flux and CO2 partial pressure difference multiplied by wind speed (ΔPCO2U, r2 = 0.078). In particular, for low wind speed (U < 3 m s1), the data show larger scatter, meaning that other explaining factors than ΔPCO2 and U may control the CO2 flux (Figure 9a). Furthermore, the relative random error ΔF does not explain the large scatter found for wind speed less than 3 m s1 (Figure 9b), being larger for small fluxes. Finally, the high CO2 emission values found for ΔPCO2U < 2 · 103 atm m s1 are clearly correlated with periods when the relative contribution of the buoyancy-driven water mixing increases, as indicated by low values of the ratio between the waterside friction velocity u* w and the waterside convective velocity w* w (Figure 9c). This result is in line with previous studies [Eugster et al., 2003; Jeffery et al., 2007; MacIntyre et al., 2010; Podgrajsek et al., 2015] addressing the importance of penetrative convective mixing in lakes. During summer, the nighttime cooling of surface water may weaken the water column stratification and temporally enhance the water-air gas transfer efficiency at night, when typically low wind conditions occur. The ratio u* w/w* w is used here as an indicator of periods when the wind shear-driven turbulence in the water dominates over the buoyancy-driven turbulence (large u* w/w* w values) or vice versa (small u* w/w* w values). Furthermore, the measured fluxes were compared to those obtained from transfer velocity models [Cole and Caraco, 1998; Tedford et al., 2014] as a function of buoyancy flux Fb (Figure 10). While kcc is purely a windbased model, kSR includes also the effect of buoyancy fluxes by differentiation of the negative and positive buoyancies. For the positive buoyancy flux side, very good agreement is found between the measured and kSR model fluxes. Instead, kcc model underestimates on average the CO2 flux by 47%, corresponding to a systematic absolute bias of 0.33 μmol m2 s1. The systematic absolute bias does not show any clear dependence on Fb. Conversely, a dependency on Fb is seen during periods of heat loss (Fb < 0): the difference between the measured and kcc model fluxes stays around 0.45 μmol m2 s1 and further increases to 0.75 μmol m2 s1 for larger negative values of buoyancy fluxes (average relative bias 95%). kSR performed much better when Fb < 0, giving on average smaller CO2 flux underestimation of 0.15 μmol m2 s1, with no clear dependence on Fb. MAMMARELLA ET AL.


1310


10.1002/2014JG002873

Figure 10. Difference between the measured and modeled 30 min CO2 fluxes as a function of buoyancy flux Fb. The modeled fluxes were calculated using the boundary layer model with transfer velocity parameterizations according to Cole and Caraco [1998] and Tedford et al. [2014]. Bin average values are shown with square symbols (black for Cole and Caraco [1998] and grey for Tedford et al. [2014].

We hypothesize that several reasons may explain this systematic difference. Other studies have also shown that gas transfer velocity models including other factors besides wind lead to better estimation of the gas fluxes. McGillis et al. [2004] reported enhanced fluxes in the ocean during nighttime at low wind speeds, and they attributed such increase to strong surface turbulent energy driven by diurnal heating cycle. Using a shorter period data set (August–November 2011) from Lake Kuivajärvi, Heiskanen et al. [2014] showed that the measured values of gas transfer velocity during summer stratification at low wind speed were of similar magnitude (6–9 cm h1) to those reported in McGillis et al. [2004]. Gas exchange physical processes may also be affected by lake characteristics (surface area and fetch), and system-specific empirical regression models for k may be not valid for lakes with different characteristics [Read et al., 2012; Vachon and Prairie, 2013]. In our study, however, only wind directions along the lake were selected, for which the fetch is either 0.8 km (southern end) or 1.8 km (northern end). No fetch dependency of the measured fluxes was found. Another explanation for the differences between EC measurements and model estimates might be that the CO2 surface concentration (caq used in equation (10)) measured at one location close to the measurement platform is not representative of the EC flux source area. Wind-induced thermocline deflection may cause upwelling of CO2 and consequent spatial variability of caq within the EC footprint. In order to account for this effect, Heiskanen et al. [2014] proposed a simple model for retrieving the enhanced caq due to the tilting thermocline, based on calculations of the Wedderburn number and the depth of the actively mixing layer. Generally, this simple approach improved the estimated k from the EC measurements at Lake Kuivajärvi, and it is easy to use also in other lakes. However, they concluded that, in order to reduce the uncertainty of new EC-based parameterizations of k, multiple location measurements are needed for resolving the spatial variability of caq. Finally, considering the coupling between a small lake and the surrounding forest, variations in surface cover and topography may introduce perturbations in scalar concentration and flux fields. By using a modeling approach, Sogachev et al. [2004] have shown that the perturbations in carbon dioxide fluxes are caused by modified wind speed and turbulence fields, resulting in significant variation of scalar fluxes over the forested areas surrounding the lake. The study, however, relied on the simplified assumption that the uptake and emissions of carbon dioxide did not depend on turbulence conditions. The coupling of lake-forest system is much more complex, and the modeling efforts usually capture only certain, limited aspects of the interactions. Furthermore, based on airborne measurements over a small lake surrounded by forest, Sun et al. [1998] have shown how the local nocturnal drainage flows bringing terrestrial CO2 over the lake may enhance MAMMARELLA ET AL.


1311


10.1002/2014JG002873

the vertical flux. Using data from Valkea-Kotinen, Vesala et al. [2006] found that an averaging time much shorter than 30 min was effective in removing very large CO2 flux values especially during early morning when the measured CO2 may have been affected by the signal from the land. In our study, shorter averaging time did not produce any significant difference in the calculated CO2 fluxes (not shown). Instead, the used quality criteria based on steady state test were very effective in removing nonstationary flux records, assuring high quality of the final data set (section 4.1).

5. Summary and Conclusions Dynamics of EC fluxes of energy and CO2, measured during two consecutive open-water periods (June–October) at Lake Kuivajärvi in Southern Finland, was analyzed. For the first time, we report estimates of short-timescale random uncertainty for lake EC fluxes. The relative random errors associated to CO2 fluxes (average value equals to 26%) are larger than those for H and LE fluxes (10% and 11%, respectively). We suggest that the main reason may be the larger spatial variability in CO2 surface water partial pressure comparing to the surface temperature. The magnitude and the diurnal changes of H and LE fluxes were in good agreement with previous studies. Diurnal flux amplitudes were larger during summer (40 W m2 and 75 W m2 for H and LE, respectively) comparing to the fall (20 W m2 and 30 W m2 for H and LE, respectively). During nighttime, in contrast to what is typically found over land, upward sensible heat flux results in unstable stratification over the lake and the evaporation ranged between 10 and 40 W m2. The observed energy fluxes followed very well the bulk transfer relationships used in numerical models, and the resulting effective values for the Stanton number (CH10 = 1.2 · 103) and Dalton number (Cq10 = 1.45 · 103) were in good agreement with those reported in previous lake studies. Further, monthly average values of energy balance closure ranged between 70% and 99%. The lake acted as net source of CO2, and the measured flux (FCO2) averaged over the two open-water periods (0.7 μmol m2 s1) was up to 3 times higher than those reported in other studies. Furthermore, it was found that nighttime cooling of surface water enhances the water-air gas transfer efficiency, and simple wind speed-based transfer velocity models strongly underestimate FCO2. We also evaluated a new model which includes the buoyancy-driven turbulent mixing [Tedford et al., 2014], and although the modeled fluxes agreed better with the EC fluxes, a small systematic average bias still remains during strong cooling periods (0.15 μmol m2 s1). This result highlights the need for more studies using long-term EC measurements in lakes of different types and sizes in order to improve gas transfer velocity models and reduce the uncertainty when the fluxes are upscaled at regional and global levels. Acknowledgments The study was supported by EU projects InGOS and GHG-LAKE (project 612642), Nordic Centre of Excellence DEFROST, and National Centre of Excellence (272041), ICOS (271878), ICOS-FINLAND (281255), ICOS-ERIC (281250), CarLAC (281196), PACE (139291), and project 256082 (Flux measurements of greenhouse gases for agricultural, lake and wetland ecosystems and process modeling of wetland methane production) funded by Academy of Finland. The data presented in this study are available upon request from the author.

MAMMARELLA ET AL.

References Abnizova, A., J. Siemens, M. Langer, and J. Boike (2012), Small ponds with major impact: The relevance of ponds and lakes in permafrost landscapes to carbon dioxide emissions, Global Biogeochem. Cycles, 26, GB2041, doi:10.1029/2011GB004237. Anderson, D. E., R. G. Striegl, D. I. Stannard, C. M. Michmerhuizen, T. A. McConnaughey, and J. W. LaBaugh (1999), Estimating lake-atmosphere CO2 exchange, Limnol. Oceanogr., 44(4), 988–1001. Assouline, S., S. W. Tyler, J. Tanny, S. Cohen, E. Bou-Zeid, M. B. Parlange, and G. G. Katul (2008), Evaporation from three water bodies of different sizes and climates: Measurements and scaling analysis, Adv. Water Resour., 31(1), 160–172, doi:10.1016/j.advwatres.2007.07.003ER. Aubinet, M., et al. (2000), Estimates of the annual net carbon and water exchange of forests: The EUROFLUX methodology, Adv. Ecol. Res., 30, 113–175, doi:10.1016/s0065-2504(08)60018-5. Aubinet, M., T. Vesala, and D. Papale (2012), Eddy Covariance: A Practical Guide to Measurement and Data Analysis, Springer, Netherlands. Baldocchi, D. (2003), Assessing the eddy covariance technique for evaluating carbon dioxide exchange rates of ecosystems: Past, present and future, Global Change Biol., 9(4), 479–492, doi:10.1046/j.1365-2486.2003.00629.x. Balsamo, G., R. Salgado, E. Dutra, S. Boussetta, T. Stockdale, and M. Potes (2012), On the contribution of lakes in predicting near-surface temperature in a global weather forecasting model, Tellus Ser. A Dyn. Meteorol. Oceanogr., 64, 15829, doi:10.3402/tellusa.v64i0.15829. Bastviken, D., L. J. Tranvik, J. A. Downing, P. M. Crill, and A. Enrich-Prast (2011), Freshwater methane emissions offset the continental carbon sink, Science, 331(6013), 50, doi:10.1126/science.1196808. Battin, T. J., S. Luyssaert, L. A. Kaplan, A. K. Aufdenkampe, A. Richter, and L. J. Tranvik (2009), The boundless carbon cycle, Nat. Geosci., 2(9), 598–600, doi:10.1038/ngeo618. Beyrich, F., et al. (2006), Area-averaged surface fluxes over the litfass region based on eddy-covariance measurements, Boundary Layer Meteorol., 121(1), 33–65, doi:10.1007/s10546-006-9052-xER. Blanken, P. D., W. R. Rouse, A. D. Culf, C. Spence, L. D. Boudreau, J. N. Jasper, B. Kochtubajda, W. M. Schertzer, P. Marsh, and D. Verseghy (2000), Eddy covariance measurements of evaporation from Great Slave Lake, Northwest Territories, Canada, Water Resour. Res., 36(4), 1069–1077, doi:10.1029/1999WR900338. Blanken, P. D., C. Spence, N. Hedstrorn, and J. D. Lenters (2011), Evaporation from Lake Superior: 1. Physical controls and processes, J. Great Lakes Res., 37(4), 707–716, doi:10.1016/j.jglr.2011.08.009.


1312


10.1002/2014JG002873

Bolin, B. (1960), On the exchange of carbon dioxide between the atmosphere and the sea, Tellus, 12(3), 274–281. Bouin, M., G. Caniaux, O. Traulle, D. Legain, and P. Le Moigne (2012), Long-term heat exchanges over a Mediterranean lagoon, J. Geophys. Res., 117, D23104, doi:10.1029/2012JD017857. Burba, G., et al. (2012), Calculating CO2 and H2O eddy covariance fluxes from an enclosed gas analyzer using an instantaneous mixing ratio, Global Change Biol., 18(1), 385–399, doi:10.1111/j.1365-2486.2011.02536.x. Clement, R. (2004), Mass and energy exchange of a plantation forest in Scotland using micrometeorological methods, chap. 5, PhD dissertation, Univ. of Edinburgh, U. K. Cole, J., and N. Caraco (1998), Atmospheric exchange of carbon dioxide in a low-wind oligotrophic lake measured by the addition of SF6, Limnol. Oceanogr., 43(4), 647–656. Deacon, E. L. (1977), Gas transfer to and across an air-water interface, Tellus, 29(4), 363–374. Deng, B., S. Liu, W. Xiao, W. Wang, J. Jin, and X. Lee (2013), Evaluation of the CLM4 lake model at a large and shallow freshwater lake, J. Hydrometeorol., 14(2), 636–649, doi:10.1175/JHM-D-12-067.1. Duchemin, E., M. Lucotte, and R. Canuel (1999), Comparison of static chamber and thin boundary layer equation methods for measuring greenhouse gas emissions from large water bodies, Environ. Sci. Technol., 33(2), 350–357, doi:10.1021/es9800840. Dutra, E., V. M. Stepanenko, G. Balsamo, P. Viterbo, P. M. A. Miranda, D. Mironov, and S. Schär (2010), An offline study of the impact of lakes on the performance of the ECMWF surface scheme, Boreal Environ. Res., 15(2), 100–112. Eugster, W., and W. Senn (1995), A cospectral correction model for measurement of turbulent NO2 flux, Boundary Layer Meteorol., 74(4), 321–340. Eugster, W., G. Kling, T. Jonas, J. McFadden, A. Wuest, S. MacIntyre, and F. Chapin (2003), CO2 exchange between air and water in an Arctic Alaskan and midlatitude Swiss lake: Importance of convective mixing, J. Geophys. Res., 108(D12), 4362, doi:10.1029/2002JD002653. Eugster, W., T. DelSontro, and S. Sobek (2011), Eddy covariance flux measurements confirm extreme CH4 emissions from a Swiss hydropower reservoir and resolve their short-term variability, Biogeosciences, 8(9), 2815–2831, doi:10.5194/bg-8-2815-2011. Finkelstein, P. L., and P. F. Sims (2001), Sampling error in eddy correlation flux measurements, J. Geophys. Res., 106(D4), 3503–3509, doi:10.1029/2000JD900731. Foken, T., and B. Wichura (1996), Tools for quality assessment of surface-based flux measurements, Agric. For. Meteorol., 78(1–2), 83–105. Foken, T., F. Wimmer, M. Mauder, C. Thomas, and C. Liebethal (2006), Some aspects of the energy balance closure problem, Atmos. Chem. Phys., 6, 4395–4402. Foken, T., M. Aubinet, and R. Leuning (2012), The Eddy Covariance Method, in Eddy Covariance—A Practical Guide to Measurement and Data Analysis, vol. 1, edited by M. Aubinet et al., pp. 1–19, Springer atmospheric sciences, Netherlands. Hari, P., and M. Kulmala (2005), Station for measuring ecosystem-atmosphere relations (SMEAR II), Boreal Environ. Res., 10(5), 315–322. Heiskanen, J. J., I. Mammarella, S. Haapanala, J. Pumpanen, T. Vesala, S. Macintyre, and A. Ojala (2014), Effects of cooling and internal wave motions on gas transfer coefficients in a boreal lake, Tellus Ser. B Chem. Phys. Meteorol., 66, 22827, doi:10.3402/tellusb.v66.22827. Huotari, J., A. Ojala, E. Peltomaa, A. Nordbo, S. Launiainen, J. Pumpanen, T. Rasilo, P. Hari, and T. Vesala (2011), Long-term direct CO2 flux measurements over a boreal lake: Five years of eddy covariance data, Geophys. Res. Lett., 38, L18401, doi:10.1029/2011GL048753. Imberger, J. (1985), The diurnal mixed layer, Limnol. Oceanogr., 30(4), 737–770. Jahne, B., K. O. Munnich, R. Bosinger, A. Dutzi, W. Huber, and P. Libner (1987), On the parameters influencing air-water gas exchange, J. Geophys. Res., 92(C2), 1937–1949, doi:10.1029/JC092iC02p01937. Jeffery, C. D., D. K. Woolf, I. S. Robinson, and C. J. Donlon (2007), One-dimensional modelling of convective CO2 exchange in the Tropical Atlantic, Ocean Modelling, 19(3–4), 161–182, doi:10.1016/j.ocemod.2007.07.003. Jonsson, A., J. Aberg, A. Lindroth, and M. Jansson (2008), Gas transfer rate and CO2 flux between an unproductive lake and the atmosphere in northern Sweden, J. Geophys. Res., 113, G04006, doi:10.1029/2008JG000688. Kaimal, J. C., and J. J. Finnigan (1994), Atmospheric Boundary Layer Flows, Their Structure and Measurements, Oxford Univ. Press, New York. Kaimal, J. C., J. C. Wyngaard, and D. H. Haugen (1968), Deriving power spectra from a three component sonic anemometer, J. Appl. Meteorol., 7, 827–834. Kormann, R., and F. Meixner (2001), An analytical footprint model for non-neutral stratification, Boundary Layer Meteorol., 99(2), 207–224, doi:10.1023/A:1018991015119. Kristensen, L., J. Mann, S. Oncley, and J. Wyngaard (1997), How close is close enough when measuring scalar fluxes with displaced sensors?, J. Atmos. Oceanic Technol., 14(4), 814–821, doi:10.1175/1520-0426(1997)0142.0.CO;2. Launiainen, S. (2010), Seasonal and inter-annual variability of energy exchange above a boreal Scots pine forest, Biogeosciences, 7, 1–20. Lenschow, D. H., V. Wulfmeyer, and C. Senff (2000), Measuring second- through fourth-order moments in noisy data, J. Atmos. Oceanic Technol., 17(10), 1330–1347, doi:10.1175/1520-0426(2000)0172.0.CO;2. Leuning, R., E. van Gorsel, W. J. Massman, and P. R. Isaac (2012), Reflections on the surface energy imbalance problem, Agric. For. Meteorol., 156, 65–74, doi:10.1016/j.agrformet.2011.12.002. Liu, H., G. Peters, and T. Foken (2001), New equations for sonic temperature variance and buoyancy heat flux with an omnidirectional sonic anemometer, Boundary Layer Meteorol., 100(3), 459–468. Liu, H., Y. Zhang, S. Liu, H. Jiang, L. Sheng, and Q. L. Williams (2009), Eddy covariance measurements of surface energy budget and evaporation in a cool season over southern open water in Mississippi, J. Geophys. Res., 114, D04110, doi:10.1029/2008JD010891. Liu, H., P. D. Blanken, T. Weidinger, A. Nordbo, and T. Vesala (2011), Variability in cold front activities modulating cool-season evaporation from a southern inland water in the USA, Environ. Res. Lett., 6(2), 024022, doi:10.1088/1748-9326/6/2/024022. Liu, H., Q. Zhang, and G. Dowler (2012), Environmental controls on the surface energy budget over a large southern inland water in the United States: An analysis of one-year eddy covariance flux data, J. Hydrometeorol., 13(6), 1893–1910, doi:10.1175/JHM-D-12-020.1. MacIntyre, S., A. Jonsson, M. Jansson, J. Aberg, D. E. Turney, and S. D. Miller (2010), Buoyancy flux, turbulence, and the gas transfer coefficient in a stratified lake, Geophys. Res. Lett., 37, L24604, doi:10.1029/2010GL044164. Mammarella, I., S. Launiainen, T. Gronholm, P. Keronen, J. Pumpanen, Ü. Rannik, and T. Vesala (2009), Relative humidity effect on the high-frequency attenuation of water vapor flux measured by a closed-path eddy covariance system, J. Atmos. Oceanic Technol., 26(9), 1856–1866, doi:10.1175/2009JTECHA1179.1ER. Mauder, M., M. Cuntz, C. Druee, A. Graf, C. Rebmann, H. P. Schmid, M. Schmidt, and R. Steinbrecher (2013), A strategy for quality and uncertainty assessment of long-term eddy-covariance measurements, Agric. For. Meteorol., 169, 122–135, doi:10.1016/j.agrformet.2012.09.006. McGillis, W. R., et al. (2004), Air-sea CO2 exchange in the equatorial Pacific, J. Geophys. Res., 109, C08S02, doi:10.1029/2003JC002256. Miettinen, H., J. Pumpanen, J. J. Heiskanen, H. Aaltonen, I. Mammarella, A. Ojala, J. Levula, and M. Rantakari (2015), Towards a more comprehensive understanding of lacustrine greenhouse gas dynamics —Two-year measurements of concentrations and fluxes of CO2, CH4 and N2O in a typical boreal lake surrounded by managed forests, Boreal Environ. Res., 20, 75–89.

MAMMARELLA ET AL.


1313


10.1002/2014JG002873

Nordbo, A., S. Launiainen, I. Mammarella, M. Leppäranta, J. Huotari, A. Ojala, and T. Vesala (2011), Long-term energy flux measurements and energy balance over a small boreal lake using eddy covariance technique, J. Geophys. Res., 116, D02119, doi:10.1029/2010JD014542. Nordbo, A., L. Järvi, and T. Vesala (2012), Revised eddy covariance flux calculation methodologies—Effect on urban energy balance, Tellus Ser. B Chem. Phys. Meteorol., 64, 18184, doi:10.3402/tellusb.v64i0.18184. Nordbo, A., P. Kekäläinen, E. Siivola, I. Mammarella, J. Timonen, and T. Vesala (2014), Sorption-caused attenuation and delay of water vapor signals in eddy-covariance sampling tubes and filters, J. Atmos. Oceanic Technol., 31, 2629–2649. Ojala, A., J. L. Bellido, T. Tulonen, P. Kankaala, and J. Huotari (2011), Carbon gas fluxes from a brown-water and a clear-water lake in the boreal zone during a summer with extreme rain events, Limnol. Oceanogr., 56(1), 61–76, doi:10.4319/lo.2011.56.1.0061. Panin, G. N., A. E. Nasonov, T. Foken, and H. Lohse (2006), On the parameterisation of evaporation and sensible heat exchange for shallow lakes, Theor. Appl. Climatol., 85(3–4), 123–129, doi:10.1007/s00704-005-0185-5. Peltola, O., et al. (2014), Evaluating the performance of commonly used gas analysers for methane eddy covariance flux measurements: The InGOS inter-comparison field experiment, Biogeosciences, 11(12), 3163–3186, doi:10.5194/bg-11-3163-2014. Peltomaa, E., P. Zingel, and A. Ojala (2013), Weak response of the microbial food web of a boreal humic lake to hypolimnetic anoxia, Aquat. Microb. Ecol., 68(2), 91–105, doi:10.3354/ame01602. Podgrajsek, E., E. Sahlee, and A. Rutgersson (2014), Diurnal cycle of lake methane flux, J. Geophys. Res. Biogeosci., 119, 236–248, doi:10.1002/ 2013JG002327. Podgrajsek, E., E. Sahlée, and A. Rutgersson (2015), Diel cycle of lake-air CO2 flux from a shallow lake and the impact of waterside convection on the transfer velocity, J. Geophys. Res. Biogeosci., 120, 29–38, doi:10.1002/2014JG002781. Rannik, Ü., and T. Vesala (1999), Autoregressive filtering versus linear detrending in estimation of fluxes by the eddy covariance method, Boundary Layer Meteorol., 91(2), 259–280. Raymond, P. A., et al. (2013), Global carbon dioxide emissions from inland waters, Nature, 503(7476), 355–359, doi:10.1038/nature12760. Read, J. S., et al. (2012), Lake-size dependency of wind shear and convection as controls on gas exchange, Geophys. Res. Lett., 39, L09405, doi:10.1029/2012GL051886. Regnier, P., et al. (2013), Anthropogenic perturbation of the carbon fluxes from land to ocean, Nat. Geosci., 6(8), 597–607, doi:10.1038/ NGEO1830. Rouse, W. R., P. D. Blanken, N. Bussieres, C. J. Oswald, W. M. Schertzer, C. Spence, and A. E. Walker (2008), Investigation of the thermal and energy balance regimes of Great Slave and Great Bear Lakes, J. Hydrometeorol., 9(6), 1318–1333, doi:10.1175/2008JHM977.1ER. Salgado, R., and P. Le Moigne (2010), Coupling of the FLake model to the Surfex externalized surface model, Boreal Environ. Res., 15(2), 231–244. Schubert, C. J., T. Diem, and W. Eugster (2012), Methane emissions from a small wind shielded lake determined by eddy covariance, flux chambers, anchored funnels, and boundary model calculations: A comparison, Environ. Sci. Technol., 46(8), 4515–4522, doi:10.1021/ es203465x. Shephard, J. M. (2005), A review of current investigations of urban-induced rainfall and recommendations for the future, Earth Interact., 9, 12, doi:10.1175/EI156.1. Sogachev, A., Ü. Rannik, and Y. Vesala (2004), On flux footprints over the complex terrain covered by a heterogeneous forest, Agric. Forest Meteorol., 127, 143–158. Stoy, P. C., et al. (2013), A data-driven analysis of energy balance closure across FLUXNET research sites: The role of landscape scale heterogeneity, Agric. For. Meteorol., 171, 137–152, doi:10.1016/j.agrformet.2012.11.004. Sun, J., R. Desjardins, L. Mahrt, and I. MacPherson (1998), Transport of carbon dioxide, water vapor, and ozone by turbulence and local circulations, J. Geophys. Res., 103(D20), 25,873–25,885, doi:10.1029/98JD02439. Tedford, E., S. MacIntyre, S. Miller, and M. Czikowsky (2014), Similarity scaling of turbulence in a temperate lake during fall cooling, J. Geophys. Res. Oceans, 119, 4689–5584, doi:10.1002/2014JC010135. Vachon, D., and Y. T. Prairie (2013), The ecosystem size and shape dependence of gas transfer velocity versus wind speed relationships in lakes, Can. J. Fish. Aquat. Sci., 70(12), 1757–1764, doi:10.1139/cjfas-2013-0241. Vachon, D., Y. T. Prairie, and J. J. Cole (2010), The relationship between near-surface turbulence and gas transfer velocity in freshwater systems and its implications for floating chamber measurements of gas exchange, Limnol. Oceanogr., 55(4), 1723–1732, doi:10.4319/ lo.2010.55.4.1723. Venäläinen, A., M. Heikinheimo, and T. Tourula (1998), Latent heat flux from small sheltered lakes, Boundary Layer Meteorol., 86(3), 355–377. Vercauteren, N., E. Bou-Zeid, M. B. Parlange, U. Lemmin, H. Huwald, J. Selker, and C. Meneveau (2008), Subgrid-scale dynamics of water vapour, heat, and momentum over a lake, Boundary Layer Meteorol., 128(2), 205–228, doi:10.1007/s10546-008-9287-9ER. Vesala, T., J. Huotari, Ü. Rannik, T. Suni, S. Smolander, A. Sogachev, S. Launiainen, and A. Ojala (2006), Eddy covariance measurements of carbon exchange and latent and sensible heat fluxes over a boreal lake for a full open-water period, J. Geophys. Res., 111, D11101, doi:10.1029/2005JD006365. Vickers, D., and L. Mahrt (1997), Quality control and flux sampling problems for tower and aircraft data, J. Atmos. Oceanic Technol., 14(3), 512–526. Vickers, D., M. Gockede, and B. E. Law (2010), Uncertainty estimates for 1-h averaged turbulence fluxes of carbon dioxide, latent heat and sensible heat, Tellus Ser. B Chem. Phys. Meteorol., 62(2), 87–99, doi:10.1111/j.1600-0889.2009.00449.x. Williamson, C. E., J. E. Saros, and D. W. Schindler (2009), Sentinels of change, Science, 323(5916), 887–888, doi:10.1126/science.1169443. Wilson, K., et al. (2002), Energy balance closure at FLUXNET sites, Agric. For. Meteorol., 113, 223–243. Xiao, W., S. Liu, W. Wang, D. Yang, J. Xu, C. Cao, H. Li, and X. Lee (2013), Transfer coefficients of momentum, heat and water vapour in the atmospheric surface layer of a large freshwater lake, Boundary Layer Meteorol., 148(3), 479–494, doi:10.1007/s10546-013-9827-9.

MAMMARELLA ET AL.


1314