JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, G04006, doi:10.1029/2008JG000688, 2008
Gas transfer rate and CO2 flux between an unproductive lake and the
atmosphere in northern Sweden
A. Jonsson,1 J. Åberg,1 A. Lindroth,2 and M. Jansson1
Received 11 January 2008; revised 10 July 2008; accepted 25 July 2008; published 11 October 2008.
[1] Measurements of the gas transfer rate of CO2 between lake water and the atmosphere
present a critical problem for the understanding of lake ecosystem carbon balances and
landscape carbon budgets. We present calculations of the gas transfer rate of CO2 from
direct measurements of the CO2 flux using an eddy covariance system and concurrent
measurements of the concentration of CO2 in the surface water in a lake in boreal zone of
northern Sweden. The measured gas transfer rate was different, and in general larger than,
rates obtained with the most commonly used models for prediction of the gas transfer rate
in lakes. The normalized gas transfer rate (k600EC) was well predicted from the wind
speed at 10 m height if data were bin classed into wind classes of 1 m/s for winds above
1 m/s. Unbinned data were also correlated to wind speed but also to water temperature,
water temperature/air temperature ratio and to incoming photosynthetic active radiation
(PAR). These relationships could reflect effects of both physico-chemical reactions and
biological activity.
Citation: Jonsson, A., J. Åberg, 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.
1. Introduction
[2] The lack of quantitative data on respiration in aquatic
systems constitutes a large gap in the understanding of the
global carbon cycle [del Giorgio and Williams, 2005].
Lakes represent a small share of the global aquatic environments but probably play a disproportionately large role in
the global carbon balance [Cole et al., 2007]. Most of the
world’s lakes are unproductive and net heterotrophic [Cole
et al., 1994]. Net heterotrophy is caused by respiration of
allochthonous organic carbon which turns lakes into net
sources of carbon dioxide (CO2) to the atmosphere [Cole et
al., 1994; Duarte and Prairie, 2005]. Lake respiration of
organic carbon fixed by terrestrial photosynthesis represents
a return flux of CO2 to the atmosphere which is seldom
accounted for in global modeling but which may be
quantitatively important for large scale carbon balances
[Cole et al., 2007]. The total release of CO2 from lakes in
the world has been estimated to correspond to ca 0.15 Gt C/
a [Cole et al., 1994]. However, recent estimates of the
global lake area [Downing et al., 2006] show that this area
may be twice as large as the value used by Cole et al.
[1994]. The CO2 contribution from lakes to the atmosphere
may, therefore, be considerably higher than 0.15 Gt C/a.
[3] The uncertainties linked to large scale estimates of
CO2 release from lakes are not only related to uncertain
measures of global lake area, but above all to the problem of
1
Department of Ecology and Environmental Science, Umeå University,
Umeå, Sweden.
2
Department of Physical Geography and Ecosystems Analysis, Lund
University, Lund, Sweden.
Copyright 2008 by the American Geophysical Union.
0148-0227/08/2008JG000688
obtaining accurate measurements, or estimates, of the net
CO2 evasion from lake surfaces. This flux has seldom been
measured. CO2 emissions have mostly been calculated with
the boundary layer technique where evasion is modeled
from the CO2 concentration in the surface water [e.g., Cole
and Caraco, 1998; Crusius and Wannikhof, 2003]. Several
attempts have been made to determine gas transfer rates in
lakes for this type of calculations. Most of them include
addition of an inert gas (e.g., sulfur hexafluoride, SF6) to the
lake water and the concentration decline over time of this
gas is used as measure of gas transfer rates between water
and atmosphere. The gas transfer is influenced by a number
of processes [Jähne et al., 1987] but wind speed has been
shown to be the variable which best explains the variation in
gas transfer rates [Jähne et al., 1987]. Different models give
different gas transfer rates, especially at higher wind speeds
[e.g., Cole and Caraco, 1998; Crusius and Wannikhof,
2003]. Gas transfer rate – wind speed models are also
general in the sense that they can be applied to any gas of
interest for which the Schmidt numbers are known [e.g.,
Cole and Caraco, 1998; Wannikhof, 1992].
[4] The eddy covariance (EC) technique is, in contrast to
the boundary layer technique, a means for direct measurement of turbulent scalar flows such as CO2 emission from a
lake. In principle, the vertical movement of the air is
correlated with the concentration of a scalar (e.g., CO2)
that occurs across a virtual surface at a certain distance
above the lake surface [Baldocchi, 2003], with a resulting
output as a flux from a specific (but often difficult to decide)
area upwind of the measuring sensors (often named ‘footprint’ or ‘source area’).
[5] There are two major types of ground based ECsystems commonly in use today: one in which the path of
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transfer rate of CO2 from the lake to the atmosphere and to
compare these with estimates of the gas transfer rate
obtained by calculations using the boundary layer technique. Fluxes obtained with the different techniques were
evaluated against measurements of the dissolved inorganic
carbon (DIC) production in the lake and a whole lake
carbon balance calculation.
2. Methods
Figure 1. The morphology of Lake Merasjärvi with 3 m
depth contours, and the location of the eddy covariance
(EC) system. The 100 m and the 350 m radius from the ECsystem are indicated.
the scalar sensor is closed and connected to the atmosphere
via tubes, and one where the path is open and placed where
free air can flow with minimum disturbance. Song et al.
[2005] showed that an open path system captured about
20% more of the flux than a corresponding closed path
system, which suggest that the open path can better capture
the small fluctuations of the scalar. However, since the
closed path systems are much more resilient to disturbances
from harsh weather, the choice of system cannot only be
dependent on its accuracy in optimal conditions.
[6] Measurements of the emission using EC technique
have been performed in terrestrial systems for several years
but are scarce over lakes. Anderson et al. [1999] carried out
measurements for five weeks over a three year period in
Williams Lake, Minnesota, USA. Eugster et al. [2003]
made measurements in Toolik Lake Alaska, USA, for five
days and in Lake Soppense in Switzerland for three days.
The longest measurement period is from the humic lake
Valkea-Kotinen in Finland [Vesala et al., 2006], where the
CO2 flux was measured for the period May – November.
One of these few studies indicated that emission values
obtained with the boundary layer technique may have been
underestimated by as much as 2.5 times [Anderson et al.,
1999] while the study of Vesala et al. [2006] showed good
agreement between fluxes measured with the EC and the
boundary layer techniques.
[7] It is obvious that there still are considerable uncertainties involved when estimating the CO2 emission from
lakes. Consequently, attempts to integrate lake CO2 fluxes
in landscape carbon balances are limited by these methodological uncertainties. It is essential to be able to evaluate the
accuracy of fluxes obtained with the boundary layer technique relative to those obtained from EC-measurements. One
reason is that large-scale estimates of CO2 flux from many
individual lakes are likely to use the boundary layer technique because it allows simple and rapid analyses of a great
number of lakes in contrast to EC-measurements which can
only be applied on a very limited number of lakes.
[8] We present EC-measurements for a moderately humic
lake with the aim of acquiring correct estimates of the gas
2.1. Site Description
[9] Lake Merasjärvi is located in northern Sweden, approximately 150 km north of the Arctic Circle in the
northern boreal forest zone. The catchment area covers
65 km2 and consists mainly of forest (51.5%) composed
of Scotch pine (Pinus sylvestris) and Norwegian Spruce
(Picea abies). Mires (fens) cover 31.5% and lakes cover
16.5% of the catchment area. Only minor areas (0.9%) are
cultivated. The lake has a surface area of 3.8 km2, a mean
depth of 5.1 m and a maximum depth of 17 m. In 2005, the
lake became ice-free on 6 June, and froze over on 23 October.
2.2. Sampling
[10] Water samples were taken in the major inlet at
northwest and in the outlet (Figure 1) on six occasions
between 16 June and 13 October 2005 using a Ruttner
sampler. Water was analyzed for DIC and dissolved organic
carbon (DOC) (see below). The water level was measured
during this period in the outlet using a data logger and a
pressure transducer registering every 10 min. Discharge was
calculated using a manually derived discharge curve.
[11] Lake water was sampled at a central location in the
lake on five occasions between 10 June and 12 October
2005. Water was sampled at 0, 1, 2, 3, 4, 5, 8 and 15 m
depth using a Ruttner sampler. Water was analyzed for
DOC, chlorophyll a and bacterial numbers (see below).
Additionally the CO2 concentration of the surface water
nearby the EC-system raft (see below) was measured
approximately once a week using a headspace technique.
For this purpose, three 1 L bottles were filled with surface
water using a Ruttner sampler. The surface water CO2
concentration was also measured every 10 min with a logger
system (see below). Conductivity of the water was measured with a field probe (WTW, TA 197LF) from the water
surface to the lake bottom. On 22 September, we collected
water for total nitrogen (TN) and total phosphorous (TP)
determination. These samples were taken in middle of the
lake from 1, 3 and 5 m depths.
[12] EC-measurements, climate, and CO2 surface water
concentration measurements were made between 17 June
and 15 October. The water temperature was also measured
every 10 min between 10 June and 13 October with
TinyTag loggers (Gemini Ltd.). These were placed at a
central location in the lake at every meter between the water
surface and 11 m depth plus one at 14 m depth.
2.3. Incubations
[13] The net production of DIC in the water column and
in the sediment was measured using in situ incubations
under ambient light and dark cycles [Åberg et al., 2007].
The difference in DIC concentration between start and end
of the in situ incubations was used as a measure of the net
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DIC production. Incubations with pelagic water (approximately 0.65 L) were made on five occasions; on 10 and
29 June, 19 July, 24 August and 21 September, and lasted
for 48 h except for the September incubation, which lasted
for 72 h. Sampling and incubations were made at 0, 1, 2, 3,
4, 5, 8 and 14 m. Duplicate incubations were made in
transparent acrylic thin-walled (2 mm) tubes except for the
incubation made on 10 June, which was made using one set
of tubes only.
[14] Incubations of sediment (0.0035 m2) with a small
volume (approximately 0.35 L) of overlying water were
made during three sampling periods: 7 – 14 July, 1 – 4
August, and 2– 16 September. During these three periods
37, 28 and 42 (a total of 107) incubations were made, using
transparent PVC tubes. Samples were taken at the following
depths: 0.5, 1, 3.5, 7.5 and 12.5 m. Each incubation depth
was represented by three sampling sites distributed over the
lake, except for incubations made at 12.5 m which were
sampled from two sites only. Three samples were incubated
at each site. Incubations lasted for 24 h.
2.4. Analyses
[15] DIC and CO2 concentrations were analyzed using an
infrared gas analyzer (EGM-4, PP-Systems Inc.) with a
headspace technique [Åberg et al., 2007]. A known volume
(20 or 50 mL) of chemically pure nitrogen gas was added to
a known volume (40 mL or 1 L) of sample water using
syringes. The gas-water mixture was shaken for 1 min and
the gas was extracted and analyzed. For DIC measurements
a small volume of 10% HCl was added to the water prior to
shaking. DOC was analyzed on GF/F (Whatman) filtered
samples. Filters were ignited at 500°C for 3 h prior to use.
DOC samples were acidified with 100 mL 1.2M HCl/10 mL
sample water. Analyses were made at Umeå Marine Science
Centre with a Schimadzu 5000-TOC analyzer. TN and TP
were analyzed at the department of Limnology, EBC,
Uppsala University as described by Bergström and Jansson
[2000].
[16] Extraction and analyses of chlorophyll a and determination of bacterial numbers were made as described by
Jonsson et al. [2003]. In short: For chlorophyll a, approximately 200 mL of sample water was filtered through a
0.45 mm filter (Durapore HVLP) in the dark. Chlorophyll
a was extracted from the filter with ethanol for 24 h in the
dark and analyzed using a Perkin Elmer LS-55 luminescence spectrophotometer. Bacterial numbers were obtained
by filtering 2 mL of sample water through black 0.22 mm
polycarbonate filters. Bacteria were stained with acridine
orange and counted using an epifluorescence microscope.
2.5. EC-System Instrumental Setup
[17] The EC system was composed of four parts; a
system-raft, a pole with sensors and two solar panel rafts.
The system-raft (3 m 3 m) was placed approximately
350 m from the nearest shoreline (Figure 1). The following
instrumentation/systems were placed on this raft: (1) a
computer for EC-data processing and data storage; (2) a
logger system (Campbell, CR 10X with the multiplexer
AM16/23), which collected meteorological data from: a rain
gauge (tipping bucket, ARG100, Campbell), an air temperature probe (107, Campbell), a relative humidity probe, RH,
(HMP45C, Campbell) and five thermocouples (Copper and
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Constantan) for collecting water temperature data from 0.1,
0.5, 1, 2 and 3 m water depths. The surface water concentration of CO2 was measured using a CO2 permeable
membrane and an infrared gas analyzer (IRGA), LI-820
(LI-COR), which was connected to the logger. The logger
system recorded the surface water concentration of CO2
every 10 min. A more detailed description of the logger
CO2 system was made by Jonsson et al. [2007].
[18] A pole was fixed in the sediments approximately 5 m
from the system-raft in a northeast direction (toward open
water). The EC-sensors; an open path IRGA (LI-7500, LICOR) and a sonic anemometer (R3, Gill Inc.) were mounted
on a vertical metal bar fixed on the pole. These sensors were
mounted 2.6 m above the lake surface between 17 June and
6 July, and 1.6 m above the surface during the period from 7
July to 15 October. The sensor height varied with the lake
surface level, which resulted in a variation of the sensor
height with approximately ± 17 cm. Control boxes for the
IRGA and the anemometer were also mounted on the pole.
Additional instrumentation on the pole included an air
pressure sensor (PTB101B, Vaisala), a net radiation (Rn)
meter (NR Lite, Kipp & Zonen), a wave height gauge (WG50, Richard Brancker Research Ltd.) and two photosynthetic
active radiation (PAR) sensors (LI-190SZ, LI-COR), which
measured incoming and reflected radiation. The Rn and PAR
sensors were mounted horizontally 1.5 m above the lake.
[19] Except for the wave height gauge which logged the
average, the minimum and maximum water levels every
minute from readings every 0.5 s, all meteorological data
were logged as 10 min averages of readings every 10 s. The
open path IRGA and the sonic anemometer data were
logged 20 times per second (20 Hz).
[20] The energy for the systems and sensors were supplied by eight 0.5 m2 solar panels with a theoretical effect of
620 W, charging a battery pack with a theoretical capacity
of 720Ah (4x180). The practical capacity that could be used
before low voltage fault on the system computer was about
140 Ah, which was enough for approximately 24 h of data
logging without charge.
2.6. Online and Postprocessing of EC-Data
[21] Raw EC-data were collected by the system computer
on the raft, with the software EcoFlux 1.4 (Insitu Flux AB,
Ockelbo, Sweden). The software which is partly described
by Grelle and Lindroth [1996] performed the following
processing of the IRGA and anemometer data: (1) coordinate rotation. Each average interval was rotated individually.
(2) covariance optimization by cross correlation. This correction for sensor separation due to sensor lag in IRGA and
physical separation between the sensors was done by letting
the software find the optimum covariance within 900 ms
(±18 samples) from the response lag (300 ms, 6 samples) of
the IRGA. (3) Calculations of covariances and statistical
parameters of the wind and CO2 signals. (4) Spikes during
measurements were automatically removed by the software.
[22] Since the need for detrending has been questioned
[Baldocchi, 2003], the effect of the recursive filter for
detrending in Ecoflux was tested. It was concluded that
the effect of the filter was a negligible loss of flux.
Detrending was, therefore, not applied prior to calculation
of the flux.
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[23] The average interval for the covariance variables
such as the turbulent flux of CO2 was set to 30 min, which
was determined from ogive analysis of the low frequency
contribution to the cospectrum of the vertical wind and CO2
signal [Moncrieff et al., 2004]. For accurate performance of
the fast fourier transformation (FFT) in the low frequency
domain the time series were linear detrended prior to this
analysis. The ogive analysis showed that most of the
relevant low frequency turbulence at 1.6 m was captured
within 5 min.
[24] Raw EC data were recalculated in order to get one
additional database with corresponding 5 min averages. A
steady state test [Foken et al., 2004] was run with the 5 min
and 30 min database using the flux of CO2 as tested
covariance variable. Only fluxes in steady state with a
difference <30% were kept.
[25] The flux of CO2 was corrected for air density
fluctuations by using the Webb correction [Webb et al.,
1980]. Values of Webb-corrected fluxes of CO2 outside 3
standard deviations of the original database were also
removed, as were values during rain and values with
positive momentum flux indicating that fluxes were not a
direct effect of local surface exchange processes.
[26] In order to check the bandwidth limitation of the
system at the high frequencies, a cross spectrum analysis of
the vertical wind and CO2 signals was performed for
controlling that the sampling frequency was high enough
to capture all turbulence contributing to the flux [see Wolf
and Laca, 2007]. Data with both high shear (high wind) and
normal atmospheric (low wind) conditions were selected.
Detrending was not applied, and coordinate rotation was not
needed. Since no detrending was applied the FFT performed
badly in the lowest frequencies and were not used in the
analysis. The high frequencies, however, were probably
slightly better captured without detrending. The cospectra
were then multiplied with their corresponding frequencies
and averaged into bins of the log of frequency. For the
comparison, the cospectra from each half hour were normalized with their corresponding integrated cospectrum.
The frequencies were not normalized to sensor height and
wind speed.
2.7. Energy Balance
[27] The heat budget comprises the latent heat flow (LE),
the sensible heat flow (H) and the rate of change of storage
of heat in the lake water (S). LE and H were measured with
the EC-system. Heat storage was calculated as the difference in heat content in the water column over time. The
following calculations were made: The content of heat in
the lake water was calculated by letting the temperature
(measured with the thermocouples) measurements at the
water surface represent the volume 0 – 0.25 m; measurements at 0.5 m the volume 0.25 – 0.75 m; measurements at
1 m the volume 0.75 –1.5 m; measurements at 2 m the
volume 1.5– 2.5 m; measurements at 3 m the volume 2.5–
5.5 m. Before calculating the amount of heat stored in the
different volumes, the temperatures at the specific depths
were filtered by calculating the running average temperature
filtered (±3 h) for each 10 min case. A 30 min average was
calculated from these values to be used together with
measured 30 min averages of LE and H.
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[28] The energy balance closure was assessed by comparing the Rn with the sum of LE, H and S. Rn should equal this
sum when the heat budget has been accurately determined.
2.8. Footprint Analysis
[29] The radius of open water around the system was
always more than 500 m (up to >1600 m) in the directions
from southeast to southwest (accounting for 270 degrees),
and 350 – 700 m in the remaining 90 degrees sector around
south (Figure 1). Data with the shortest fetch (155 to
210 degrees) were not used in any calculations. The
footprint area of the EC-system was estimated via Kljun’s
web-based footprint calculator (http://footprint.kljun.net).
We estimated the footprint for 1000 cases for which the
close to 100% footprint radius ranged between 115 and
480 m, with an average of 255 m. Thus the expected footprint
was less than the fetch, and the impact from surrounding
forest on the flux estimations is expected to be minimal.
2.9. Estimates of the Flux Using the Boundary Layer
Model
[30] From our measurements of the surface water CO2
concentration using the logger system we estimated the
emission of CO2 by applying a gas transfer velocity (k). The
k600 was modeled using the formula given by Cole and
Caraco [1998].
k600 ¼ 2:07 þ 0:215 U1:7
10
ð1Þ
where k600 is the gas transfer velocity (cm h1) for a gastemperature combination that has a Schmidt number of 600,
for example, CO2 at 20°C and U10 is wind speed at 10 m
height.
[31] The k600 was used to calculate k for the actual
temperature in the surface water according to equation (2)
[Jähne et al., 1987], using the Schmidt number (Sc) for the
measured water temperature [Wannikhof, 1992] and assuming that the Schmidt number exponent n = 0.5 [Jähne et
al., 1987].
kgas1
¼
kgas2
Scgas1
Scgas2
n
ð2Þ
We estimated the flux of CO2 [Cole and Caraco, 1998]
from the estimated k and the measured supersaturation of
CO2 in the surface water.
Flux ¼ k CO2water CO2equ
ð3Þ
where CO2water is measured concentration in the surface
water and CO2equ is air water equilibrium concentration.
[32] The CO2 concentration of the surface water was
measured with the logger system and concurrent measurements of the concentrations of CO2 of the air were taken
from measurements using the EC-system IRGA. Wind data
for 10 m heights were obtained by correcting the sonic wind
speed (of the EC-system) for sensor height and surface
roughness in a logarithmic wind profile:
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U10 ¼ UZs lnð10=z0 Þ
lnðzs =z0 Þ
ð4Þ
JONSSON ET AL.: CO2 EMISSION IN AN UNPRODUCTIVE LAKE
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where zs is sensor height and where the roughness
parameter z0 was calculated as
z0 ¼
Z
s
ð5Þ
KUzs
exp
*
u
where K is von Karman constant (0.4), exp is equal to
2.7183, zs is height of the anemometer (m), Uzs is wind
speed at zs (m/s), and u* is the friction velocity calculated
by the EC-system (m/s).
2.10. Calculation of the Gas Transfer Rate
[33] The gas transfer rate was calculated by combining
data from measurements of the surface water concentration
of CO2 with concurrent measurements of the flux measured
with the EC-system:
kEC ¼
EC
CO2water CO2equ
ð6Þ
where kEC is gas transfer rate obtained from the ECmeasurements, EC is flux of CO2 measured with the
EC-system, CO2water is measured concentration in the
surface water, and CO2equ is air water equilibrium
concentration.
[34] Negative values of kEC were obtained in some cases,
These might be artifacts caused by noise in the EC-measurements or erroneous surface water CO2 values. Negative
values were kept, since noise in the EC-values probably
produced both too large and erroneous negative flux values.
Combining the measurements above gave 928 individual
estimates of the gas transfer rate of CO2. Outliers, including
values with a gas transfer rate above 50 cm/h and below
50 cm/h, were excluded reducing the number of data
points by 5%. The remaining 877 individual gas transfer
rates were used in a stepwise forward regression analysis to
find the best predictive variables among the measured
climatic variables (surface water temperature, wave height,
wind speed at tower height, wind speed at 10 m height,
relative humidity, air temperature, ratio between water and
air temperature, air pressure, net radiation, incoming and
reflected PAR).
[35] The gas transfer rates (kEC) were normalized to a
Schmidt number of 600 [Wannikhof, 1992], by equation (2),
and we obtained k600EC values which were structured into
10 bin classes of 1 m/s from 0 to 1 m/s up to 9 m/s plus one
for wind speeds above 10 m/s. Median values within these
wind classes were then used in a linear regression analysis
with U10 as the independent variable. Raw data were always
visually inspected before regression analysis. If raw data
were skewed they were log transformed. Bin-classed data
were normally distributed.
2.11. Organic Carbon Balance Calculations
[36] An organic carbon balance was calculated to estimate
the CO2 emission for the period 29 June to 26 August,
during which period we have the most complete EC-data.
Emission was calculated as: Emission = input (via inlets) ±
change in lake pool (this was in this case a positive term in
the budget) sediment burial output (via outlet).
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[37] Input of organic carbon was estimated from measurements of the DOC concentration in the major inlet at the
northwest end of the lake. The concentration in this inlet
was assumed to be representative for the input from all other
inlets including diffuse inlets. To obtain TOC input we
assumed that POC added another 10% to the DOC concentration [Hope et al., 1994; A. Jonsson, unpublished data,
2002].
[38] The change in the lake water DOC pool was calculated by the difference in the lake water pool between the
start and the end of the budget period taking into account
that the water level decreased with 0.16 m during the budget
period (from water level measurements at the outlet). The
average DOC concentration on the two occasions was used
to estimate the pool of DOC in the whole lake.
[39] Mass balance calculations for boreal lakes have
shown that net sedimentation (permanent burial) of organic
carbon is small compared to other carbon fluxes. Algesten et
al. [2004] thus found that annual net sedimentation of
organic carbon was less than 6% of the TOC input as a
mean for a large number of lakes in northern Sweden, and
Jonsson et al. [2001] reported a net sedimentation for the
summer in the humic Lake Örträsket to be approximately
6% of the total input. We therefore assumed that net
sedimentation of organic carbon in Lake Merasjärvi during
summer was 6% of calculated input of TOC. Output of
organic carbon via the outlet was calculated from the
measured DOC concentration.
[40] The input of water was assumed to equal the measured output of water via the outlet plus the amount of water
estimated to evaporate from the lake surface. Evaporation
was estimated to 0.1 m3/s from measurements of the water
vapor flux with the EC-system. Daily concentrations in
inflowing and outflowing waters were obtained by linear
interpolation between measurements. Daily input and output
of organic carbon were estimated by multiplying daily
concentrations with the daily input and output of water.
[41] Uncertainties of different terms in the mass balance
were estimated as follows: Uncertainties of the DOC
concentration in the inlet and outlet water were obtained
by adding or subtracting the seasonal confidence interval
(CI, 95%) of the six samples taken during the period 16
June to 13 October to/from the daily concentration. Uncertainties in the POC input varied with changes in the DOC
concentration as the POC was assumed to be 10% of the
DOC. Sediment burial of organic carbon varied similar to
the DOC + POC input change. The uncertainty in the lake
water pool of DOC in the beginning and at the end of the
budget period was estimated by adding or subtracting the CI
of the eight samples taken on each occasion to/from the
mean concentration. Uncertainty of the emission of CO2
measured with the eddy covariance system was estimated
by adding or subtracting the CI of the emission during the
flux period to/from the median emission.
3. Results
3.1. Lake Characteristics
[42] The lake was moderately humic, with a mean DOC
of 6.2 mg/L, and unproductive with mean chlorophyll a
concentration of 1.9 mg/L. The average number of bacteria
in the lake water was 1.5 106/mL during the summer. The
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highest chlorophyll concentration was found in the beginning of July and the highest bacterial numbers in the middle
of August. The total nitrogen (113 mg N/L) and total
phosphorous (6.6 mg P/L) concentrations were low. The
lake had soft water with a specific conductivity of approximately 24 mS/cm (25°C), and a pH of approximately 7.0.
3.2. Data Coverage
[43] During the period 17 June and 15 October the logger
system measuring climate variables had a better data cover
compared to the EC-system, mainly due to technical and
power supply problems. Water temperature measured with
the thermocouples, Rn, PAR, air temperature, relative humidity, precipitation and wave height had a data cover
between 89 and 94% of possible measurements. The logger
registration of the surface water concentration of CO2
measured 68% of all possible occasions. The EC-system
data cover was 34% of the possible occasions, of which
54% did not fulfill the quality criteria (see Methods).
3.3. Hydrological and Meteorological Data
[44] The input of water was high at the start of the study
period due to snowmelt. As a result the water level in the
lake was high in the beginning of the study and progressively decreased as runoff decreased. The water level of the
lake decreased by approximately 0.18 m over the whole
study period. The theoretical water exchange of the lake
volume was approximately 77% between June and October
and approximately 33% for the period 29 June and 26
August. The average wave height was 3.2 cm, and waves up
to 37 cm were registered.
[45] The total amount of rain measured with the logger
system was 286 mm over the whole study period. The
average air temperature was 11.3°C (Figure 2). The average
wind speed was 3.1 m/s at tower height and 3.9 m/s at 10 m
height calculated according to equation (3) (see Methods).
3.4. Surface Water CO2 Concentration
[46] Measurements of the surface water CO2 concentration with both the manual headspace technique and the
automated IRGA-measurements showed large diel variation. During the summer when there were large variations,
these two methods did not match very well (average
difference equal to 19% of IRGA concentration, n = 7).
Later in the season when the daily variation in surface water
CO2 concentration became low, the two methods compared
well (average difference equal to 3% of IRGA concentration, n = 7). The difference during summer was probably
due to the low diffusivity of the membrane resulting in slow
response time of the IRGA compared to the registration
time of 10 min. Previous measurements with the system
showed that the system could need a 3 h response time for
reaching equilibrium with the water when the system
switched between measuring in the air and water [Jonsson
et al., 2007]. On a few occasions, the 10-min logger data
were close to atmospheric equilibrium, so it is possible that
the surface water was undersaturated with CO2 on these
occasions.
3.5. Performance of the EC-System
[47] The cross spectrum analysis showed that during
normal atmospheric conditions the cospectrum tapered off
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to near zero before the Nyquist frequency (10 Hz) [Diniz et
al., 2002], which indicated no limitation to capture the
relevant frequencies in the high frequency end of the
spectrum (Figure 3, gray line). During conditions of high
shear, the cospectrum showed a larger proportion of flux in
the high frequency end as expected (Figure 3, black line).
However, the cospectrum still tapered off to near zero at the
Nyquist frequency.
3.6. Energy Balance
[48] During the period shown in Figure 4a the average
latent heat flux was 58 W/m2, the average sensible heat flux
22 W/m2 and the rate of change of storage 26 W/m2. During
the period 29 July until 2 August the net radiation was
similar to the calculated heat budget (Figure 4b) and there
was a good closure of the energy balance (r2 = 0.76, p <
0.001, intercept set to 0, slope = 0.80). On most other
occasions (here exemplified by the period 3 – 8 August) the
energy balance closure was very poor. During the period
with good energy balance closure the lake was not thermally
stratified and also showed clear day/nighttime differences in
water temperature (Figure 5). During periods of poor energy
balance closure the lake was often stratified and did not
show a clear variation in temperature between day and night
(Figure 5).
3.7. Gas Transfer Rates of CO2
[49] The gas transfer rates (kEC) varied between 24 cm/h to
48 cm/h. The median gas transfer rate was 7.0 ± 0.6 cm/h (±95%
confidence interval) for the period of 17 June and 15
October. Data on the calculated normalized (to 20°C) gas
transfer rate (k600EC) in 1 m/s bin classes of the wind speed
at 10 m height are shown in Table 1.
[50] Variables that best explained the variation in kEC
were wind speed at tower height (delta r2 = 0.12), water
temperature (delta r2 = 0.06), the ratio between water and air
temperature (delta r2 = 0.05) and incoming PAR (delta r2 =
0.01) (Table 2). However, these variables together explained
only approximately 24% of the variation, and, thus, a large
fraction of the variation was unexplained. The k600EC was
strongly correlated to wind speed at 10 m height, which
explained approximately 96% of the variation between wind
classes (Figure 6). In this comparison the wind class
between 0 and 1 m/s was excluded since the gas transfer
rate was negative. The low number of observations and the
large CI in this class (Table 1) indicates that the median gas
transfer rate was uncertain.
3.8. Quantitative Estimates of the CO2 Flux
[51] The median flux of CO2 measured with the ECsystem during the period of 17 June and 15 October was
221 ± 20 mg C/m2/d (±95% CI) (the seasonal average was
233 mg C/m2/d), with invasion in June, high emission in
July and a low emission in October (Figure 7). The daily
median emission in July and August was 238 ± 29 and 221
± 49 mg C/m2/d (±95% CI), respectively. The high emission
in the beginning of September occurred during autumn
circulation when the lake was completely thermally isothermal (Figure 2).
[52] The temporal variation of the emission, calculated
using the boundary layer model (equations (1), (2), and (3)),
was much less than the EC-measurements (Figure 7). The
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Figure 2. Climatic variables measured with the logger system; daily sum of precipitation, and daily
averages of air temperature and incoming PAR. The 1/2 h average wind speed at tower height measured
with the EC-system is shown.
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Figure 3. The cospectra of the vertical wind and the CO2
signals during two atmospheric conditions; slightly unstable
conditions (z/L is 0.5) with a mean friction velocity
equal to 0.1 m/s and mean wind speed equal to 2.6 m/s, and
neutral conditions (z/L is 0) with a mean friction velocity
equal to 0.4 m/s and mean wind speed equal to 5.7 m/s.
Data represent averages of three 1/2 h averages during
unstable conditions and four 1/2 h averages during neutral
conditions.
median emission during the study period June – October
was 82 ± 3 mg C/m2/d (the seasonal average was 102 mg C/
m2/d). Median emission in July and August was 101 ± 5 and
135 ± 5 mg C/m2/d (±95% CI), respectively.
3.9. Net DIC-Production
[53] The whole lake net DIC production was calculated as
the sum of net DIC production from the pelagic and benthic
incubations. The median net production was 274 ± 226 mg
C/m2/d (±95% CI), and varied between 29 to 688 mg C/
m2/d (Figure 7). The net DIC production was dominated by
the pelagic DIC production, with a median of 184 ± 202
(±95% CI) mg C/m2/d, which accounted for 69% of the
total (pelagic plus benthic). The production rates varied
considerably over the season from negative values in the
beginning of June (119 mg C/m2/d) to positive values on
all later occasions (124– 598 mg C/m2/d). Benthic net DIC
production varied little over the season with an average of
90 ± 9 mg C/m2/d (±95%CI).
3.10. Carbon Balance
[54] The CO2 emission calculated from the carbon balance for the lake during the period 29 June until 26 August
showed a good agreement with the EC-system emission.
CO2-emission based on the model by Cole and Caraco
[1998] was approximately 60% of the emission based on the
carbon balance (Table 3).
4. Discussion
4.1. Quality and Robustness of the Eddy Covariance
Measurements
[55] Owing to the fact that the EC-sensors were mounted
close to the water surface (1.6 m most of the time), there
was a risk to not detect the small (fast) eddies [Wolf and
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Laca, 2007] since there is a decreasing eddy size toward the
surface [Monteith, 1975]. To test if the bandwidth of the
EC-system was wide enough to capture both the lowest and
highest frequencies of the relevant turbulence, both ends of
the cross spectra of the vertical wind and CO2 signals were
analyzed. In the low frequencies most of the flux was
captured within 5 min which indicated that 30 min averaging interval should be sufficient in all cases. The analysis of
the highest frequencies indicated good performance of the
EC-system, especially for the most common situations of a
slightly unstable atmosphere (Figure 3), but also during near
neutral conditions (high shear) with high friction velocities.
In the latter cases a large proportion of the flux did indeed
occur in high frequencies, but the contribution was near
zero at 10 Hz. The closing to zero at the upper detection
limit of the system (which was 10 Hz, or half of the
sampling rate) lead to the conclusion that the highest
frequencies were resolved by the system independent of
the atmospheric conditions during the study period. This
conclusion was supported by the fact that there was no
significant change in the daily patterns of the absolute flux
when the sensors were lowered from 2.6 to 1.6 m (data not
shown).
[56] For the EC data to be considered of good quality the
energy balance should be closed [Baldocchi, 2003], i.e.,
there should be a strong correlation between the measured
net radiation and the calculated sum of the heat budget. We
had a good energy balance closure (Figure 4b) when the
water column was mixed and all storage changes contributed to the heat budget measured with the Rn-meter, i.e.,
there was a dominant vertical heat exchange as indicated by
a clear daily pattern in the water temperature (Figure 5).
However, in most situations the energy balance closure was
very poor. This is not a result of the eddy covariance
measurements performing poorly, but that a large part of
the energy flux was due to variations in heat storage in the
lake water (Figure 4a), which did not contribute to energy
fluxes measured with the net radiation sensor. During the
period with good energy balance closure the storage term
(S) was approximately 52% of the heat budget, and energy
fluxes measured with the EC-system were only 48%. The
latent and sensible heat fluxes were comparable to those
measured over other lakes [Heikinheimo et al., 1999]. The
poor closure of the heat budget in most situations was thus
probably because heat storage was strongly affected by
transport processes other than exchange with the atmosphere, such as horizontal exchange by underwater currents.
4.2. Variation and Controlling Factors for the Gas
Transfer Rate
[57] Equations (7) and (8) (Table 2) revealed that the gas
transfer rate was higher at higher wind speeds, as shown in
other studies [McGillis et al., 2001], which probably is a
result of the decreased boundary layer thickness at higher
turbulence of the water, as well as release of bubbles and
spray from breaking waves [Deacon, 1977; Merlivat and
Memery, 1983]. The gas transfer rate was also higher when
the water temperature was high and when the water temperature was higher than the air temperature (T-ratio). We
cannot explain the reason for these temperature couplings. It
may be a physiochemical relationship or an indirect biological effect.
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Figure 4. (a) The heat flux from the sensible heat (H), the latent heat (LE) and the change in heat
storage in the water (S) during a period with good energy balance closure and one period of poor energy
balance closure. Included is also the net radiation (Rn). (b) Comparison of the calculated heat budget
(H+LE+S) with the net radiation (Rn) during a period with good energy balance closure and one period
with poor energy balance closure.
[58] In theory, the increasing gas transfer rate with increasing water temperature may be affected by the dissolution of CO 2 , which decreases with increasing water
temperature, and by the fact that we measured the surface
water temperature approximately 10 cm below the water
surface where the temperature probably was lower than in
the surface boundary layer, at least during warm and sunny
periods. The effect of such temperature differences on the
gas transfer rate are difficult to assess but should be
proportional to the difference in temperature [cf. Deacon,
1977; McGillis and Wannikhof, 2006]. The positive relationship with the temperature ratio indicates that the gas
transfer rate is higher when the water is warmer than the air,
and vice versa. The water temperature is typically higher
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Figure 5. The water temperature at the water surface, 0.5, 1, 2, and 3 m depth measured with the
thermocouples during a period with good energy balance closure and one period with poor energy
balance closure. Temperatures are smoothened by filtering over ± 3 h.
than the air temperature at night but similar during the day.
Higher emission rates during night could be connected to
daily variations in photosynthesis/respiration ratios [cf.
Eugster et al., 2003]. An alternative explanation is that high
fluxes occurs during periods of convective mixing of the
water column, which should occur mostly at night when
cooling of the surface water can induce vertical water
movement. Convective mixing and entrainment, and upwelling of deep CO2-rich water were important for increasing CO2 fluxes in the study by Eugster et al. [2003].
Another illustration of the influence of a heat difference
between water and air on the gas transfer is that the factor
T-ratio in equation (7) (Table 2) can be interchanged by
the sensible heat flux (H) measured with the eddy covariance system. The resultant equation (equation (7)) would
not change, and the r2 and the standard error of the equation
would be the same. This effect of heat flux on the gas
transfer rate was also seen by MacIntyre et al. [2001] in
Toolik Lake, USA. The inclusion of the T-ratio in the
equation could in turn only be a reflection of the importance
of atmospheric heat flux (H) for the convective mixing of
water and CO2 in the water column and thus for the gas
transfer between water and air. The negative relationship
with PAR possibly indicates that photosynthetic consumption of CO2 reduces the gas transfer rate even though this
effect is not a very strong (delta r2 only 1%) parameter in
equation (7) (Table 2), probably because light is not the
limiting factor for photosynthesis in this nutrient poor
system.
[59] The low explanatory power of equation (7) is probably an indication of a complex regulation of the gas
transfer across the air water interface in a natural environment that cannot be fully assessed with the simple relationships or factors measured here. Part of the explanation for
the poor correlation was probably also scatter in the gas
transfer rate due to noise in the measurements. However, a
fairly good approximate value of the gas transfer rate can be
given by the median gas transfer rate calculated from the
wind speed at 10 m height as shown in Figure 6 and by the
equation (8) (Table 2). The low confidence interval for wind
speeds below 7 m/s (Figure 6) should make it possible to
use this relationship for the studied lake.
4.3. Comparison With Indirect Methods to Estimate k
and Large-Scale Implications
[60] The measured gas transfer rates were different from
rates estimated with commonly used boundary layer models
[i.e., Cole and Caraco, 1998; Wannikhof, 1992]. These
differences are illustrated in Figure 6 where gas transfer
rates are plotted against wind speed. The model of Cole and
Caraco [1998] gave lower gas transfer rates compared to
the measured except at wind speeds <2 m/s. The Wannikhof
[1992] model gave lower estimates below 6 m/s and higher
Table 1. Median Values of the Wind Speed at 10 m Height (U10)
and the Normalized Gas Transfer Velocity (k600EC), Including the
95% Confidence Interval and Number of Observations (n) for Bin
Classes of 1 m/s Over the Wind Spectra Measured
Median
Bin Class
U10
(m/s)
k600EC
(cm/h)
±95% CI k600EC
(cm/h)
n
0–1
1–2
2–3
3–4
4–5
5–6
6–7
7–8
8–9
9 – 10
>10
0.7
1.5
2.5
3.5
4.4
5.4
6.5
7.3
8.3
9.2
11.2
4.4a
1.8
5.5
6.8
8.2
7.5
10.3
13.6
15.9
17.9
23.2
6.2
2.6
1.4
1.6
1.4
1.7
1.9
2.9
3.1
6.3
6.1
12
53
101
152
193
142
82
57
43
19
22
a
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Negative values are considered to be calculation artifacts, see Methods.
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Table 2. Results of the Stepwise Forward Regression Analysis Between k and k600EC and Climatic Variablesa
k = a (±SE) + b (±SE) [var1] + c (±SE) [var2] + d (±SE) [var3] + e (±SE) [var4]
k = 3.663 (±2.070) + 2.630 (±0.199) [U] + 0.611 (±0.076)
[Twat] + 15.284 (±2.519) Log[Tratio] 3.086 (±0.820) Log[PAR + 100]
k600EC = 1.318 (±0.967) + 2.067 (±0.145) [U10]
r2
SE
F
n
Equation
0.24
8.2
67
877
(7)
0.96
1.3
203
10
(8)
a
For both regressions p < 0.001. [U] is the wind speed at tower height, [Twat] is the surface water temperature, [Tratio] is the ratio between surface water
temperature and the air temperature, Log[PAR + 100] is the logarithm of the photosynthetic active radiation + 100 (to avoid negative values), and [U10] is
the wind speed at 10 m height.
estimates above 6 m/s. There may be several reasons for the
deviations between measured and calculated gas transfer
rates. One factor influencing the gas transfer rate is the
fetch. An increasing fetch seems to increase the gas transfer
[Wannikhof, 1992; Borges et al., 2004], probably because
the same wind speed produces larger waves (more turbulent
water) if the fetch is larger. Indications that fetch could be
important can be seen from that similar fluxes were
obtained with EC-measurements and Cole and Caraco
[1998] model in the small (4 ha) Lake Valkea-Kotinen
[Vesala et al., 2006], but much larger fluxes obtained with
the EC-technique in the somewhat larger (37 ha) Williams
Lake [Anderson et al., 1999]. In our study, the fetch varied
from approximately 370 – 2100 m dependent on wind
direction, with most data (95%) representing a fetch of over
500 m. No effect on the gas transfer rate could be seen from
the length of the fetch. However, it is possible that we had too
few data representing a short fetch. Marine studies comparing
EC-measurements with boundary layer models also give
much higher gas transfer rates from EC-measurements
[Jacobs et al., 2002; Kondo and Tsukamoto, 2007]. Typically, the difference increased at higher wind speeds
[McGillis et al., 2001], which was also evident when
comparing EC-measurements and estimated values in
Lake Merasjärvi (Figure 6). Thus, our equation (8) would
give the same result as the Cole and Caraco [1998] model
(equation (1)) in the study by Vesala et al. [2006] (see
above), where the average wind speed was only approximately 2 m/s (Figure 6). Another explanation for the
differences between EC-measurements and boundary layer
estimates might be that the boundary layer technique
models a gas transfer rate via conversion factors, of which
several are temperature dependent. One such conversion is
from the measured gas transfer rate of SF6 (or some other
gas) to the gas transfer rate of CO2. This conversion is
obviously not straight-forward since the temperature dependent conversion for both SF6 and CO2 has to be known. The
temperature dependent conversion of the gas transfer rate
(as calculated by the Schmidt number) of SF6 also differs
between different equations [Wannikhof, 1992; King and
Saltzman, 1995]. No comparison for CO2 has been found in
the literature. Whether or not uncertainties in conversion
factors contribute to the different gas transfer values of
measured and modeled data are therefore unclear. Further,
Figure 6. The normalized (to 20°C) median gas transfer rate of CO2 (k600) as a function of the wind
speed at 10 m height (U10). Data were structured into bin classes of 1 m/s. The black circle represents the
k600 at wind speed less than 1 m/s and was not accounted for in the regression analyses (equation (8) and
Table 2). Error bars represent the 95% confidence interval. Data are compared with boundary layer
estimates based on the models presented by Cole and Caraco [1998] and Wannikhof [1992].
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Table 3. An Organic Carbon Balance for the Period 29 June to 26
August (59 Days) 2005 in Lake Merasjärvia
g C/m2
Compartment
Flux
Inlet streams
Change in lake water pool
Sediment burial
Outlet streams
Carbon balance based CO2 emission
Measured CO2 emission
Modeled CO2 emission
19.3
3.9
1.2
10.3
11.7
13.3
7.0
Range
18.1
3.1
1.1
10.0
–
–
–
–
20.6
5.5
1.2
10.6
11.9 – 14.8
a
The carbon balance based CO2 emission was calculated as described in
the Methods section. Measured emission was based on EC-measurements.
Modeled emission was calculated according to Cole and Caraco [1998]. A
positive emission signifies a loss from the lake to the atmosphere. Ranges
were calculated from the uncertainty estimates of the concentrations
of DOC in the different compartments and of the measured emission
(see Methods).
the difference between gas transfer rates obtained with the
EC-technique and SF6 amendments could be due to the
timescale of the calculations. EC-measurements operate on
a timescale of seconds/minutes, while SF6 amendments can
only detect concentration changes over several days. Therefore, the gas transfer rate of the SF amendments represents a
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much different timescale than that over which wind speed
changes occur.
[61] Our measurements using the EC-technique gave
more accurate estimates of the emission of CO2 to the
atmosphere than the indirect estimates with the boundary
layer technique in Lake Merasjärvi. Both the organic carbon
balance derived emission (Table 3) and the amount of DIC
produced in the incubation experiments compared well with
the EC-measurements (Figure 7), but not with values
obtained with the boundary layer technique. Moreover, the
net DIC production rates indicated CO2 invasion in June
when the EC-method measured an invasion, and high DICproduction occurred simultaneous with high emission
shown by the EC-measurements in the middle of July.
Consequently, we consider that the EC-measurements better
reflected actual exchange of CO2 between lake water and
the atmosphere in Lake Merasjärvi than did the boundary
layer estimates.
[62] EC-measurements should therefore be superior for
detailed studies of the CO2 exchange between lakes and
atmosphere when there is, e.g., a need for high temporal
solution or detailed understanding of the processes which
regulate the CO2 exchange. On the other hand, large scale
estimates of lake- CO2-fluxes comprising a large number of
Figure 7. The flux of CO2 measured with the EC-system and estimated from the boundary layer model
[Cole and Caraco, 1998]. Included is also the net DIC-production in the lake. The flux measured with the
EC-system is presented both as 1/2 h values and as a 3 h running mean.
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JONSSON ET AL.: CO2 EMISSION IN AN UNPRODUCTIVE LAKE
lakes cannot be based on EC-measurements because of the
fact that each lake is unique, so CO2-fluxes vary considerably between lakes. However, this study stresses the need to
carry out more EC-measurements in different types and
sizes of lakes to enable a more detailed comparison between
different techniques and facilitate a calibration of different
boundary layer models.
[63] Acknowledgments. We wish to thank Klockar Jenny Nääs,
Thomas Westin and Ingemar Bergström for technical assistance. Financial
support was provided by the Swedish Research Council, Kempestiftelserna,
Ebba and Sven Schwartz stiftelse and Stiftelsen Längmanska Kulturfonden.
This work was also a collaboration within the Nordic Centre for Studies of
Ecosystem Carbon Exchange and its Interaction with the Climate System
(NECC).
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J. Åberg, M. Jansson, and A. Jonsson, Department of Ecology and
Environmental Science, Umeå University, SE-901 87 Umeå, Sweden.
([email protected])
A. Lindroth, Department of Physical Geography and Ecosystems
Analysis, Lund University, SE-223 62 Lund, Sweden.
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