Lakes and reservoirs contribute to regional carbon budgets via significant
emissions of climate forcing trace gases. Here, for improved modelling, we
use 8 years of floating chamber measurements from three small, shallow
subarctic lakes (2010–2017, n=1306) to separate the contribution of
physical and biogeochemical processes to the turbulence-driven,
diffusion-limited flux of methane (CH4) on daily to multi-year
timescales. Correlative data include surface water concentration
measurements (2009–2017, n=606), total water column storage (2010–2017,
n=237), and in situ meteorological observations. We used the last to
compute near-surface turbulence based on similarity scaling and then applied
the surface renewal model to compute gas transfer velocities. Chamber fluxes
averaged 6.9±0.3 mg CH4 m-2 d-1 and gas transfer
velocities (k600) averaged 4.0±0.1 cm h-1. Chamber-derived
gas transfer velocities tracked the power-law wind speed relation of the
model. Coefficients for the model and dissipation rates depended on shear
production of turbulence, atmospheric stability, and exposure to wind.
Fluxes increased with wind speed until daily average values exceeded 6.5 m s-1, at which point emissions were suppressed due to rapid water column
degassing reducing the water–air concentration gradient. Arrhenius-type
temperature functions of the CH4 flux (Ea′=0.90±0.14 eV) were robust (R2≥0.93, p<0.01) and also applied to
the surface CH4 concentration (Ea′=0.88±0.09 eV). These
results imply that emissions were strongly coupled to production and supply
to the water column. Spectral analysis indicated that on timescales shorter
than a month, emissions were driven by wind shear whereas on longer
timescales variations in water temperature governed the flux. Long-term
monitoring efforts are essential to identify distinct functional relations
that govern flux variability on timescales of weather and climate change.
Introduction
Inland waters are an important source of the radiatively active trace gas
methane (CH4) to the atmosphere
(Bastviken
et al., 2011; Cole et al., 2007). On regional to global scales, an estimated
21 %–46 % of ice-free season CH4 emissions from lakes, ponds, and
reservoirs occur via turbulence-driven diffusion-limited gas exchange
(Bastviken
et al., 2011; DelSontro et al., 2018; Wik et al., 2016b) (hereafter
abbreviated to “diffusive fluxes”). Diffusive fluxes are often measured with
floating chambers (Bastviken et al., 2004), but gas
transfer models are increasingly used, for example in regional emission
budgets
(Holgerson
and Raymond, 2016; Weyhenmeyer et al., 2015). Fluxes computed with modelled
gas transfer velocities agree to a certain extent with floating chambers and
the eddy covariance technique in short-term intercomparison campaigns
(Bartosiewicz
et al., 2015; Crill et al., 1988; Erkkilä et al., 2018). However,
long-term comparisons are needed to identify weather- and climate-related
controls on the flux that are appropriate for seasonal assessments.
Considering the increased use of process-based approaches in regional
emission estimates (Tan and Zhuang, 2015), understanding the
mechanisms that drive the components of the diffusive flux is imperative for
improving emission estimates.
Drivers of diffusive CH4 emissions
Diffusive fluxes at the air–water interface are estimated with a two-layer
model (Liss and Slater, 1974):
F=kCaq-Cair,eq.
The flux F (mg CH4 m-2 d-1, hereafter abbreviated mg m-2 d-1) depends on the concentration difference across a thin
layer immediately below the air–water interface (Δ[CH4], mg m-3), of which the upper boundary is in equilibrium with the atmosphere
(Cair,eq) and the base represents the bulk liquid (Caq) and is
limited by the gas transfer velocity k (m d-1). k has been conceptualized
as characterizing transfer across the diffusive boundary layer. Other models
envision exchange as driven by parcels of water intermittently in contact
with the atmosphere. In these surface renewal models, k depends on the
frequency of the renewal events (Csanady, 2001; Lamont
and Scott, 1970). The resulting calculation for k is based on the Kolmogorov
velocity scale uη=(εν)1/4, where
ε is dissipation rate of turbulent kinetic energy (TKE) and
ν is kinematic viscosity (Tennekes and Lumley, 1972).
Progress has been made in understanding how to compute ε and
gas transfer rates as a function of wind speed and the heating and cooling
at the lake's surface (Tedford et al., 2014).
Comparisons between models and other flux estimation methods, such as the
eddy covariance technique, illustrate the improved accuracy when computing
gas transfer velocities using turbulence-based as opposed to wind-based
models
(Czikowsky
et al., 2018; Heiskanen et al., 2014; Mammarella et al., 2015).
The supply of sparingly soluble trace gases to the air–water interface
moderates fluxes when concentrations are higher within the water column than
in the atmosphere. Trace gases such as CH4 are produced in the
sediments and diffuse into the overlying water. During stratification, these
gases may accumulate if the density gradient restricts the efficacy of wind
mixing. Thermal convection associated with surface cooling can deepen the
mixed layer and transfer stored gas to the surface, enhancing emissions
(Crill
et al., 1988; Eugster et al., 2003). Temporal patterns of stratification and
mixing contribute to variability in diffusive CH4 fluxes
(López
Bellido et al., 2009; Podgrajsek et al., 2016) and concentrations
(Loken et al., 2019; Natchimuthu
et al., 2016). Periodic emissions from storage at depth have been
particularly difficult to resolve in lake emission budgets
(Bastviken et al., 2004; Wik et
al., 2016b).
CH4 emissions to the atmosphere also depend on the rates of methane
metabolism regulated by substrate availability and temperature-dependent
shifts in enzyme activity and microbial community structure
(Borrel
et al., 2011; McCalley et al., 2014; Tveit et al., 2015). Arrhenius-type
relationships of CH4 fluxes have emerged from field studies
(DelSontro et
al., 2018; Natchimuthu et al., 2016; Wik et al., 2014) and across latitudes
and aquatic ecosystem types in synthesis reports
(Rasilo
et al., 2015; Yvon-Durocher et al., 2014). However, the temperature
sensitivity is modulated by biogeochemical factors that differ between lake
ecosystems, such as nutrient content
(Davidson et
al., 2018; Sepulveda-Jauregui et al., 2015), methanotrophic activity
(Duc et al., 2010;
Lofton et al., 2014), predominant emission pathway
(DelSontro
et al., 2016; Jansen et al., 2019), and warming history
(Yvon-Durocher et al., 2017). In lakes, the
air–water concentration difference driving the flux (Eq. 1) is further
affected by factors that dissociate production from emission rates. These
include biotic factors, such as aerobic and anaerobic methanotrophy, and
abiotic factors such as hydrologic inputs of terrestrially produced CH4
(Miettinen et al., 2015;
Paytan et al., 2015) and storage-and-release cycles associated with
transient stratification
(Czikowsky
et al., 2018; Jammet et al., 2017; Vachon et al., 2019). Given these
interacting functional dependencies, the magnitude of fluxes has complex
patterns of temporal variability.
Disentangling the physical and biogeochemical drivers of the diffusive
CH4 flux remains a challenge. The component drivers respond differently
to slow and fast changes in meteorological covariates
(Baldocchi et al., 2001;
Koebsch et al., 2015) such that different mechanisms may explain the diel
and seasonal variability of the flux. For example, temperature affects
emissions through convective mixing on short timescales and through the rate
of sediment methanogenesis on longer timescales; the diurnal cycle of
insolation may have a limited effect on production because the heat capacity
of the water buffers the temperature signal (Fang and
Stefan, 1996). Similar phase lags and amplifications may lead to hysteretic
flux patterns, such as cold season emission peaks due to release of gases
from the hypolimnion in dimictic lakes
(Encinas Fernández et
al., 2014; López Bellido et al., 2009) or thermal inertia of lake
sediments (Zimov et al., 1997).
Spectral analysis of the flux and its components can improve our
understanding of the flux variability by quantifying how much power is
associated with key periodicities (Baldocchi et al., 2001).
Here we present a high-resolution, long-term dataset (2010–2017) of
diffusive CH4 fluxes from three subarctic lakes estimated with floating
chambers (n=1306) and fluxes obtained by modelling using in situ
meteorological observations and surface water concentrations (n=535). The
surface renewal model is used to compute gas transfer velocities. Arrhenius
relationships of Δ[CH4] and fluxes of CH4 are also
calculated. Using spectral analysis of our time series data, we distinguish
the temporal dependency of abiotic and biotic controls on the flux. The
effects of lake size and wind exposure are illustrated by comparing results
from the three different lakes.
Materials and methodsField site
CH4 emissions were measured from three subarctic lakes of postglacial
origin (Kokfelt et al., 2010), located
around the Stordalen Mire in northern Sweden (68∘21′ N,
19∘02′ E, Fig. 1), a palsa mire complex underlain by
discontinuous permafrost (Malmer et al.,
2005). The Mire (350 m a.s.l.) is part of a catchment that connects Mt.
Vuoskoåiveh (920 m a.s.l.) in the south to Lake Torneträsk (341 m a.s.l.) in the north
(Lundin et
al., 2016; Olefeldt and Roulet, 2012). Villasjön is the largest and
shallowest of the lakes (0.17 km2, 1.3 m max. depth) and drains through
fens into a stream feeding Mellersta Harrsjön and Inre Harrsjön,
which are 0.011 and 0.022 km2 in size and have maximum depths of 6.7 m
and 5.2 m, respectively (Wik et al., 2011).
The lakes are normally ice-free from the beginning of May through the end of
October. Manual observations were generally conducted between mid-June and
the end of September. Diffusion accounts for 17 %, 52 %, and 34 % of
the ice-free CH4 flux in Villasjön, Inre, and Mellersta
Harrsjön, respectively, with the remainder emitted via ebullition
(2010–2017; Jansen et al., 2019).
We used floating chambers to directly measure the turbulence-driven
diffusive CH4 flux across the air–water interface (Fig. 1). They
consisted of plastic tubs covered with aluminium tape to reflect incoming
radiation and were equipped with polyurethane floats and flexible sampling
tubes capped at one end with three-way stopcocks
(Bastviken et al., 2004). Depending on flotation
depth, each chamber covered an area between 610 and 660 cm2 and
contained a headspace of 4 to 5 L. Chambers were deployed in pairs with
a plastic shield mounted 30 cm below one chamber of each pair to deflect
methane bubbles rising from the sediment. Every 1–2 weeks during the
ice-free seasons of 2010 to 2017, two to four chamber pairs were deployed in
Villasjön and four to seven chamber pairs were deployed in Inre and Mellersta Harrsjön in
different depth zones (Fig. 1). The number of chambers and deployment
intervals exceeded the minimum needed to resolve the spatio-temporal
variability of the flux (Wik et al., 2016a). Over a 24 h
period, two to four 60 mL headspace samples were collected from each chamber using
polypropylene syringes, and the flotation depth and air temperature were
noted in order to calculate the headspace volume. The 24 h deployment
period integrates diel variations in the gas transfer velocity
(Bastviken et al., 2004).
The fluxes reported here are from the shielded chambers only. To check that
the shields were not reducing fluxes from turbulent processes such as
convection, we compared fluxes from shielded and unshielded chambers on days
when the lake mean bubble flux was < 1 % of the lake mean
diffusive flux (bubble traps, 2009–2017;
Jansen et al., 2019; Wik
et al., 2013). Averaged over the three lakes, the difference was
statistically significant (0.20±0.16 mg m-2 d-1, n=58,
mean ±95 % CI), but small in relative terms (6 % of the mean
flux). Conversely, some types of floating chambers can enhance gas transfer
by creating artificial turbulence when dragging through the water
(Matthews
et al., 2003; Vachon et al., 2010; Wang et al., 2015).
Ribas-Ribas et al. (2018), Banko-Kubis et al. (2019), and
Gålfalk et al. (2013) assessed gas transfer velocities in floating
chambers of similar design, size, and flotation depth as those used in this
study. Ribas-Ribas et al. (2018) and Banko-Kubis et al. (2019) measured TKE
dissipation rates with acoustic Doppler velocimetry (ADV) inside and outside
the chamber perimeter and concluded that the chambers did not cause
artificial turbulence. Gålfalk et al. (2013) similarly found good
agreement between k600 derived from free-floating chamber observations
with a CH4 tracer and k600 computed independently from nearby ADV
measurements and an infrared (IR) imaging technique.
Water samples
Surface water samples were collected 0.2–0.4 m below the surface at two to three
different locations in each lake, at 1- to 2-week intervals from June to
October (Fig. 1). Samples were collected from the shore with a 4 m Tygon tube
attached to a float to avoid disturbing the sediments (2009–2014) and from
a rowboat over the deepest points of Inre and Mellersta Harrsjön
(2010–2017) and at shallows (< 1 m water depth) on either end of
the lakes (2015–2017) using a 1.2 mL × 3.2 mm i.d. Tygon tube. In addition,
water samples were collected at the deepest point of Inre and Mellersta
Harrsjön at 1 m intervals down to 0.1 m from the sediment surface with a 7.5 mL × 6.4 mm i.d. fluorinated ethylene propylene (FEP) tube. Subsequently,
60 mL polypropylene syringes were rinsed thrice with sample water before
duplicate bubble-free samples were collected and were capped with airtight
three-way stopcocks. The 30 mL samples were equilibrated with 30 mL headspace and
shaken vigorously by hand for 2 min (2009–2014) or on a mechanical
shaker at 300 rpm for 10 min (2015–2017). Prior to 2015, outside air –
with a measured CH4 content – was used as headspace. From 2015 on we
used an N2 5.0 headspace (Air Liquide). Water sample conductivity was
measured over the ice-free season of 2017 (n=323) (S230, Mettler-Toledo)
and converted to specific conductance using a temperature-based approach.
Concentration measurements
Gas samples were analysed within 24 h after collection at the Abisko
Scientific Research Station, 10 km from the Stordalen Mire. Sample CH4
contents were measured on a Shimadzu GC-2014 gas chromatograph which was
equipped with a flame ionization detector (GC–FID) and a 2.0 m long, 3 mm i.d.
stainless-steel column packed with 80/100 mesh HayeSep Q and used N2 > 5.0 as a carrier gas (Air Liquide). For calibration we used
standards of 2.059 ppm CH4 in N2 (Air Liquide). A total of 10 standard
measurements were made before and after each run. After removing the highest
and lowest values, relative standard deviations of the standard runs were
generally less than 0.25 %.
Water temperature, pressure, density, and mixed-layer depth
Water temperature was measured every 15 min from 2009 to 2018 with
temperature loggers (HOBO Water Temp Pro v2, Onset Computer) in
Villasjön and at the deepest locations within Inre and Mellersta
Harrsjön. Sensors were deployed at 0.1, 0.3, 0.5, and 1.0 m depth in all
lakes, with additional sensors at 3.0, 5.0 m (IH and MH), and 6.7 m (MH).
Sensors were intercalibrated prior to deployment in a well-mixed water tank
and by comparing readouts just before and during the onset of freezing when the water
column was isothermal. In this way a precision of < 0.05 ∘C was achieved. The bottom sensors were buried in the surface sediment and
were excluded from in situ intercalibration. Water pressure was measured in
Mellersta Harrsjön (5.5 m) with a HOBO U20 water level logger (Onset
Computer). Water density was computed from temperature and salinity
(Chen and Millero, 1977), using lake-averaged specific
conductivity and a salinity factor (mS cm-1) × (g kg-1)-1 of 0.57. The
salinity factor was based on a linear regression of simultaneous
measurements of conductivity and dissolved solids (R2=0.99, n=7) in five lakes in the Torneträsk catchment (Miljödata-MVM, 2017).
We defined the depth of the surface mixing layer (zmix) at a density
gradient threshold (dρ/ dz) of 0.03 kg m-3 m-1
(Rueda et al., 2007).
Meteorology
Meteorological data were collected from four different masts on the Mire and
collectively covered a period from June 2009 to October 2018 with
half-hourly measurements of wind speed, air temperature, relative humidity,
air pressure, and irradiance (Fig. 1, Table 1). Wind speed was measured with
3D sonic anemometers at the Palsa tower (z=2.0 m), the Villasjön
shore tower (z=2.9 m), the InterAct Lake tower (z=2.0 m), and
the Integrated Carbon Observation System (ICOS) site (z=4.0 m). Air
temperature and relative humidity were measured at the Palsa tower, at the
Villasjön shore tower (Rotronic MP100a (2012–2015)/Vaisala HMP155
(2015–2017)), and at the InterAct lake tower. Incoming and outgoing
shortwave and long-wave radiation were monitored with net radiometers at the
Palsa tower (Kipp & Zonen CNR1) and at the InterAct lake tower (Kipp &
Zonen CNR4). Precipitation data were collected with a WeatherHawk 500 at the
ICOS site. Overlapping measurements were cross-validated and averaged to
form a single time series.
Location and instrumentation of meteorological observations on
the Stordalen Mire, 2009–2018.
IdentifierPeriodLocationWindAir temp. and humidityRadiationReferencePalsa tower2009–201168∘21′19.68′′ N 19∘2′52.44′′ EC-SAT 3 Campbell ScientificHMP-45C Campbell ScientificCNR-1 Kipp & ZonenOlefeldt et al. (2012)Villasjön shore tower2012–201868∘ 21′14.58′′ N 19∘ 3′1.07′′ ER3-50 GillMP100a, Rotronic HMP155, VaisalaREBS Q7.1 Campbell Sci.Jammet et al. (2015)InterAct Lake tower2012–201868∘21′16.22′′ N 19∘3′14.98′′ EuSonic-3 Scientific MetekCS215 Campbell ScientificCNR-4 Kipp & Zonen–ICOS site2013–201868∘21′20.59′′ NWeatherHawk 500 –19∘2′42.08′′ ECampbell Scientific Computation of CH4 storage and residence time
The amount of CH4 stored in the water column (g CH4 m-2) was
computed by weighting and then adding each concentration measurement by the
volume of the 1 m depth interval within which it was collected. For the
upper 2 m of the two deeper lakes, we separately computed storage in the
vegetated littoral zone from nearshore concentration measurements, as these
values could be different from those further from shore due to outgassing
and oxidation during horizontal transport (DelSontro et al.,
2017). We computed the average residence time of CH4 in the lake by
dividing the amount stored by the lake mean surface flux. Residence times
computed with this approach should be considered upper limits, because in
this calculation we assumed that removal processes other than surface
emissions, such as microbial oxidation, were negligible or took place at the
sediment–water interface with minimal effect on water column CH4.
Flux calculations
In order to calculate the chamber flux with Eq. (1), we estimated the gas
transfer velocity, kch (cm h-1), from the time-dependent
equilibrium chamber headspace concentration Ch,eq(t) (mg m-3)
(Bastviken et al., 2004):
Caq-Ch,eq(t)=Caq-Ch,eq(t0)e-KHRTwaterAVkcht,
where KH is Henry's law constant for CH4 (mg m-3 Pa-1)
(Wiesenburg and Guinasso, 1979), R is the universal gas
constant (m3 Pa mg-1 K-1), Twater is the surface water
temperature (K), and V and A are the chamber volume (m3) and area
(m2), respectively. This method accounts for gas accumulation in the
chamber headspace, which reduces the concentration gradient and limits the
flux (Eq. 1) (Fig. 2). For a subset of chamber measurements where
simultaneous water concentration measurements were unavailable (n=949) we
computed the flux from the headspace concentrations alone:
F=c1M∂xh∂tPVRTairA.∂xh/∂t is the headspace CH4 mole fraction change
(mol mol-1 d-1) computed with ordinary least-squares (OLS) linear
regression (Fig. 2), M is the molar mass of CH4 (0.016 mg mol-1), P is the air pressure (Pa), and Tair is the air temperature (K).
Scalar c1 corrects for the accumulation of CH4 gas in the chamber
headspace and increases over the deployment time. Comparing both chamber
flux calculation methods, we find c1=1.21 for 24 h deployments
(OLS, R2=0.85, n=357). Chambers were sampled up to four times
during their 24 h deployment (at 10 min, 1–5 h, and 24 h),
which allowed us to compute fluxes at time intervals of 1 and 24 h.
P and Tair were averaged over the relevant time interval.
Figure 2 shows that the headspace correction is necessary to avoid
underestimating fluxes. The headspace-corrected flux (dashed red line)
equals the initial slope of Eq. (2) (solid red line) and is about 21 %
higher than the non-corrected flux (lower dashed black line in Fig. 2).
However, both Eq. (2) (solid red line) and Eq. (3) with c1=1 (dashed
black lines) fit the concentration data (R2≥0.98 for 94 % of
24 h flux measurements). This similarity results partly because the
fluxes were low enough to keep headspace concentrations well below
equilibrium with the water column. Short-term measurements (upper dashed
black line) may omit the need for headspace correction
(Bastviken et al., 2004). Because concentration
measurements were not available for all chamber observations, we used
multi-year mean values of Δ[CH4] and kch to compute
c1 as a function of chamber deployment time. For 24 h chamber
deployments, c1=1.21.
Example of chamber headspace CH4 concentrations versus
deployment time. Measured concentrations (dots) are averages from 2015 to 2017
(0.1 h) and 2011 (1–24 h); error bars represent the 95 % confidence
intervals. Linear regressions (dashed black lines) show the rate increase
over 1 h (two measurements) and over 24 h (five measurements). The
solid red line represents chamber concentrations computed with Eq. (2). The
rate increase associated with the mean 24 h flux corrected for headspace
accumulation is shown as a dashed red line (Eq. 1 with kch from Eq. 2,
or Eq. 3 with c1=1.21). Labels denote fluxes calculated from the linear regression slopes (Eq. 3,
black) and from Eq. (2) (red).
Computing gas transfer velocities with the surface renewal model
We used the surface renewal model (Lamont and Scott, 1970)
formulated for small eddies at Reynolds numbers > 500
(MacIntyre et al., 1995; Theofanous et al.,
1976) to estimate k:
kmod=αεν14Sc-12,
where the hydrodynamic and thermodynamic forces driving gas transfer are
expressed, respectively, as the TKE dissipation rate ε (m2 s-3) and the dimensionless Schmidt number Sc, defined as the ratio of
the kinematic viscosity v (m2 s-1) to the free solution diffusion
coefficient D0 (m2 s-1)
(Jähne et al., 1987; Wanninkhof,
2014). The scaling parameter α has a theoretical value of 0.37
(Katul et al., 2018) but is often estimated empirically
(α′) to calibrate the model
(e.g. Wang et al., 2015). To allow for
a qualitative comparison between model and chamber fluxes, we took ratios of
kch (floating chambers) and (εν)14Sc-12 (surface renewal model,
half-hourly values of kmod averaged over each chamber deployment
period) and determined α′=0.23±0.02 for all lakes (mean
±95 % CI, n=334) (Fig. 3), α′=0.31±0.06
(n=67) for Villasjön, α′=0.25±0.03 (n=136) for
Inre Harrsjön, and α′=0.17±0.02 (n=131) for
Mellersta Harrsjön (Supplement Fig. S1). Calibrating the model in this
way allowed us to assess whether chamber flux relationships with wind speed
and temperature were reproduced by the model. For similar comparative
purposes, k values were normalized to a Schmidt number of 600 (CO2 at 20 ∘C) (Wanninkhof, 1992): k600=600/Sc-0.5k. The wind speed at 10 m (U10) was computed from
measured wind speed following Smith (1988), assuming a neutral
atmosphere.
Determination of the model scaling parameter α′ via
comparison between gas transfer velocities from floating chambers (Eq. 2)
and the surface renewal model (Eq. 4 with α′=1 and Sc= 600,
half-hourly values averaged over each chamber's 24 h deployment period)
for all three lakes. Dots represent individual chamber deployments (grey)
and multi-chamber means for each weekly deployment in 2016 and 2017, when
concentration measurements were taken simultaneously with, and in close
proximity to, the chamber measurements (black). Mean ratios, and therefore
α′, are represented by the slopes of the dotted lines. Error bars
represent 95 % confidence intervals of the means.
We used a parametrization by Tedford et
al. (2014) based on Monin–Obukhov similarity theory to estimate the TKE
dissipation rate at half-hourly time intervals:
ε=0.56u∗w3/κz+0.77βifβ>0(cooling)0.6u∗w3/κzifβ≤0(heating),
where u∗w is the water friction velocity (m s-1), κ is
the von Kármán constant, and z is depth below the water surface (0.15 m, the depth for which Eq. 5 was calibrated). We determined u∗w
from the air friction velocity u∗a assuming equal shear stresses
(τ) on both sides of the air–water interface, τ=ρau∗a2=ρwu∗w2, and taking into account
atmospheric stability
(MacIntyre et al.,
2014; Tedford et al., 2014). β is the buoyancy flux (m2 s-3), which accounts for turbulence generated by convection
(Imberger, 1985):
β=αTgQeff/cpwρw.
Here, αT is the thermal expansion coefficient (m3 K-1) (Kell, 1975), g is the standard gravity
(m s-2), cpw (J kg-1 K-1) is the water specific heat, and
ρw (kg m-3) is the water density. Qeff (W m-2)
represents the net heat flux into the mixing layer and is the sum of net
shortwave and long-wave radiation and sensible and latent heat fluxes.
Penetration of radiation into the water column was evaluated across seven
wavelength bands via Beer's law (Jellison
and Melack, 1993). An attenuation coefficient of 0.74 was computed for the
visible portion of the spectrum from Secchi depth
(2.3 m; Karlsson et al., 2010)
following Idso and Gilbert (1974). Net long-wave radiation
(LWnet= LWout- LWin) was computed via measurements of
LWin (Table 1) and LWout=σT4, where σ is the
Stefan–Boltzmann constant (5.67×10-8 W m-2 K-4)
and T is the surface water temperature in kelvin. LWnet time series were
gap-filled with ice-free mean values for each lake. Sensible and latent heat
fluxes were computed with the bulk aerodynamic formula
(MacIntyre et al., 2002). Both Qeff
and β are here defined as positive when the heat flux is directed out
of the water, for example when the surface water cools.
Direct measurements of ε in an Arctic pond (1 m depth, 0.005 km2 surface area) demonstrate that Eq. (5) can characterize
near-surface turbulence in small, sheltered water bodies similar to the
lakes studied here (MacIntyre et al., 2018). When the near
surface was strongly stratified at instrument depth (buoyancy frequencies
(N=g/ρw×dρw/dz)
> 25 cycles per hour, cph), the required assumption of
homogeneous isotropic turbulence was not met and Eq. (5) could not be
evaluated. We observed cases with N>25 cph < 3 % of the
time.
Calculation of binned means
We binned data to assess correlations between the flux and environmental
covariates. Half-hourly values of water temperature and wind speed were
averaged over the deployment period of each chamber (fluxes) and over 24 h prior to the collection of each water sample (concentrations),
reflecting the mean residence time of CH4 in the water column. Fluxes,
concentrations, and k values were then binned in 10 d, 1 ∘C, and
0.5 m s-1 bins to obtain relationships with time, water temperature, and
wind speed, respectively. The 10 d bins typically contained at least 1
sampling day for each overlapping year and enabled representative averaging
across years. Lake-dependent variables (e.g. flux) were normalized by lake
to obtain a single time series (divided by the lake mean, multiplied by the
overall mean).
Calculation of the empirical activation energy
Chamber and modelled fluxes as well as concentrations were fitted to an
Arrhenius-type temperature function
(e.g. Wik et al.,
2014; Yvon-Durocher et al., 2014):
F=e-Ea′/kBT+b,
where kB is the Boltzmann constant (8.62×10-5 eV K-1) and T is the water temperature in kelvin. The empirical activation
energy (Ea′, in electron volts (eV), 1 eV = 96 kJ mol-1) was
computed with a linear regression of the natural logarithm of the fluxes and
concentrations onto the inverse temperature (K-1), of which b is the
intercept.
Timescale analysis: power spectra and climacogram
We computed power spectra for near-continuous time series of the surface
sediment, water and air temperature, and wind speed according to Welch's
method (pwelch in MATLAB 2018a), which splits the signal into overlapping
sections and applies a cosine tapering window to each section
(Hamming, 1989). Data gaps were filled by linear interpolation.
We removed the linear trend from the original time series to reduce red noise,
and we block-averaged spectra (eight segments with 50 % overlap) to suppress
aliasing at higher frequencies. We normalized the spectral densities by
multiplying by the frequency and dividing by the variance of the original
time series (Baldocchi et al., 2001).
We evaluated our discontinuous (fluxes, concentrations) and continuous
(meteorology) time series with a climacogram, an intuitive way to visualize a
continuum of variability (Dimitriadis and
Koutsoyiannis, 2015). It displays the change of the standard deviation
(σ) with averaging timescale (tavg). Variables were normalized
by lake to create a single time series at half-hourly resolution (e.g. 48
entries for each 24 h chamber flux). To compute each standard deviation
(σ(tavg)) data were binned according to averaging timescale,
which ranged from 30 min to 1 year. Because of the discontinuous nature
of the datasets, n bins were distributed randomly across the time series. We
chose n=100000 to ensure that the 95 % confidence interval of the
standard deviation at the smallest bin size was less than 1 % of the value
of σ (Sheskin, 2007). To allow for comparison between
variables, we normalized each σ series by its initial smallest-bin
value: σnorm=σ/σinit. For timescales
< 1 week we used 1 h chamber observations, noting that sparse
daytime-only observations of concentrations and 1 h fluxes may
underestimate short-term variability (σinit). We use the
climacogram to test whether the variability of the diffusive CH4 flux
is contained within meteorological variability, as for terrestrial ecosystem
processes (Pappas et al., 2017).
Statistics
We used analysis of variance (ANOVA) and the t test to compare means of
different groups. The use of means, rather than medians, was necessary
because annual emissions can be determined by rare high-magnitude emission
events. Parametric tests were justified because of the large number of
samples in each analysis, in accordance with the central limit theorem.
Linear regressions were performed with the ordinary least-squares method
(OLS): reported p values refer to the significance of the regression slope.
Non-linear regressions were optimized with the Levenberg–Marquardt algorithm
for non-linear least squares with confidence intervals based on bootstrap
replicates (n=1999). Computations were carried out in MATLAB 2018a and in PAST
v3.25 (Paleontological Statistics software package)
(Hammer et al., 2001).
ResultsMeasurements and models
Chamber fluxes averaged 6.9 mg m-2 d-1 (range 0.2–32.2, n=1306) and closely tracked the temporal evolution of the surface water
concentrations (mean 11.9 mg m-3, range 0.3–120.8, n=606), with the
higher values in each lake measured in the warmest months (July and August,
Fig. 4a, e). Diffusive fluxes increased with wind speed and water temperature
(Fig. 4b,c). Reduced emissions were measured in the shoulder months (June and
September) and were associated with lower water temperatures. We also
observed abrupt reductions of the flux at wind speeds lower than 2 m s-1 and higher than 6.5 m s-1. Surface water concentrations
generally increased with temperature and peaked in the summer months, but
unlike the chamber fluxes they decreased with increasing wind speed (Fig. 4f, g). Relationships with wind speed were approximately linear, while
relationships with temperature fitted an Arrhenius-type exponential function
(Eq. 7). Activation energies were not significantly different when using
either surface water or sediment temperature (Ea′=0.90±0.14 eV, R2=0.93 and Ea′=1.00±0.17,
R2=0.93, respectively, mean ±95 % CI). The fluxes,
concentrations, and wind speed were non-normally distributed (Fig. 4d, h, o). Surface water temperatures (0.1–0.5 m) were normally distributed
around the mean of each individual month of the ice-free season (Fig. 4n),
but the composite distribution was bimodal.
Fluxes computed with the surface renewal model (Eq. 1 using kmod)
closely resembled the chamber fluxes (Eq. 3) in terms of temporal evolution
(Fig. 4a) and correlation with environmental drivers (Fig. 4b, c). Mean model
fluxes were slightly higher than the chamber fluxes in Villasjön and
Inre Harrsjön and slightly lower in Mellersta Harrsjön (Table 2).
Model fluxes were significantly different between littoral and pelagic zones
in Inre and Mellersta Harrsjön (paired t tests, p≤0.02),
reflecting spatial differences in the surface water concentration (Table 2).
Similar to the chamber fluxes, the air–water concentration difference
(Δ[CH4]) explained most of the temporal variability of the
modelled emissions; both kmod (Eq. 4) and kch (Eq. 2) were functions
of U10 (Fig. 4k) and did not display a distinctive seasonal pattern
(Fig. 4i). Modelled fluxes decreased at higher wind speeds when surface
concentrations decreased and displayed a cut-off at daily mean U10≥6.5 m s-1, similar to the chamber fluxes, but not at U10<2.0 m s-1. The temperature sensitivity of the modelled fluxes
(Ea′=0.97±0.12 eV, mean ±95 % CI, R2=0.94) did not differ significantly from that of the chamber fluxes.
CH4 fluxes from floating chambers and the surface renewal
model as well as surface CH4 concentrations. Data from 2014 were excluded from
the model flux means because of a substantial bias in the timing of sample
collection. Model fluxes for each lake were computed with lake-specific
scaling parameter values (Fig. S1).
Scatter plots of the CH4 flux (a–c), CH4 air–water
concentration difference (e–g), and gas transfer velocity (i–k) versus time,
surface water temperature, and wind speed, as well as the histograms of the
aforementioned variables (d, h, l, m, n, o). In each scatter plot binned means of
the flux (squares, a–c), concentrations (triangles, e–g), and gas transfer
velocities (rhombuses, i–k) are represented by large symbols with 95 %
confidence intervals (error bars). Orange and light blue symbols reflect
chamber-derived and model-derived binned values, respectively. Model k was
computed with α′=0.23. Bin sizes were 10 d, 1 ∘C,
and 0.5 m s-1 for time, surface water temperature, and U10,
respectively. Small green, blue, and red dots represent individual
measurements in Villasjön, Inre Harrsjön, and Mellersta Harrsjön,
respectively. Open rhombus symbols in panels (i–k) represent the buoyancy
component of the gas transfer velocity; closed rhombus symbols include both
the wind-driven and buoyancy-driven components. Dashed lines in panels (b) and
(f) represent fitted Arrhenius functions (Eq. 7). Histograms of modelled
(light blue) and measured (light orange) quantities (d, h, l) overlap.
Histograms of the surface water temperature (m) and U10(o) are stacked
by month, from June (darkest shade) to October (lightest shade).
Meteorology and mixing regime
Throughout the ice-free season the lakes were weakly stratified (Table 3).
Figure 5 shows a time series of the mixed-layer depth and water temperature
in the deeper lakes, along with wind speed, air temperature, and
precipitation for the ice-free period of 2017. The ice-free period consisted
of two phases. In the first, air and surface water temperatures were higher
and the two deeper lakes were stratified. Wind speeds increased to mean values
approaching 5 m s-1 for a few days at a time and then decreased for a
day or two. Deep mixing events followed surface cooling and heavy rainfall.
Water level maxima and surface temperature minima were observed 2–3 d
after rainfall events, for example between 15 and 18 July 2017 (Fig. 5e). In
the second phase, wind speeds were persistently higher (U10 >5 m s-1), air and surface water temperatures declined, and all lakes were
mixed to the bottom. Strong nocturnal cooling on 16 August 2017 broke up
stratification and the lakes remained well-mixed until ice formation (20 October).
Throughout the ice-free seasons from 2009 to 2018, stratified periods
(zmix≤1 m) lasted for 7 h on average and were common (31 %
and 45 % of the time in Inre and Mellersta Harrsjön, respectively),
but were frequently disrupted by deeper mixing events. Shallow mixing
(zmix≤zmean) occurred on diel timescales. Deeper mixing
occurred at longer intervals (days to weeks) and more frequently toward the
end of the ice-free season (Fig. 5g, h) in association with higher wind
speeds.
Lake morphometry, temperature of the surface mixing layer,
buoyancy frequency, and CH4 residence time. Mean values were calculated
over the ice-free seasons of 2009–2017.
Fluxes and near-surface concentrations also varied within these periods.
CH4 concentrations and fluxes were higher in the warmer, stratified
period and lower in the colder, mixed periods. In 2017, the highest
concentrations and fluxes occurred earlier in the season, with the initial
high values in the two deeper lakes indicative of residual CH4 that had
not escaped to the atmosphere immediately after ice melt, around 1 June 2017 (Fig. 5c, d). As
residual CH4 was emitted, near-surface concentrations declined and
then in the first half of the stratified period (July 2017, Fig. 5d),
particularly in Mellersta Harrsjön, increased with increased rainfall
and with temperature. During this period, kch and kmod were similar.
Decreases in kch were coupled to increases in thermal energy input via two mechanisms: (1) when the air temperature increased above the surface water temperature in the day, leading to a stable atmosphere over the lakes, and (2) when the near-surface temperature was warmer and the water column was stratified to the surface. Thus, lower fluxes occurred during the second part of the
stratified period (August 2017, Fig. 5c) when surface concentrations
increased during warming periods when winds were light, the atmosphere was
stable during the day, and the upper water column was strongly stratified.
Fluxes and concentrations were lower in the autumn mixed periods, by which
time the lakes had degassed, and with the colder surface sediment
temperatures rates of production had decreased.
The modelled gas transfer velocity generally followed the temporal pattern
of the wind speed (Fig. 4b). Due to model calibration, the modelled gas
transfer velocities (Fig. 4b, blue line) tracked those derived from chamber
observations (Fig. 4b, orange rhombuses). Discrepancies pointed to a
mismatch between 24 h integrated chamber fluxes and surface
concentrations measured at a single point in time. For example, measuring a
low surface concentration in the de-gassed water column after a windy period
during which the surface flux was high led to an overestimated kch on 21 September 2017. Contrastingly, kch was lower than kmod on 3 August 2017 due to elevated surface concentrations and a low chamber flux
associated with a warm and stratified period preceding water sampling.
The temperature of the surface mixed layer exceeded the air temperature by
1.6 ∘C on average (Fig. 5a), such that the atmospheric boundary
layer over the lakes was often unstable, particularly at night during warm
periods as well as during the many cold fronts. We computed an unstable
atmosphere over the lakes (z/LMO,a < 0, where z is the measurement
height and LMO,a is the air-side Monin–Obukhov length;
Foken, 2006) ∼76 % of the time during ice-free
seasons. Atmospheric instability increases sensible and latent heat fluxes
(Brutsaert, 1982), enhancing the cooling rate. Thus, buoyancy
fluxes were positive at night and during cold fronts throughout the ice-free
season (Figs. 5b, 4i–k). The magnitude of buoyancy flux during cooling
periods tended to range from 10-8 to 10-7 m2 s-3 in the
stratified period and decreased as water temperatures cooled in autumn (Fig. 4i, j). TKE dissipation rates at 0.15 m were high, with values often between
10-6 and 10-5 m2 s-3, although values did fall as low as
10-8 m2 s-3 when winds were light. Comparison of these two
terms indicated that buoyancy flux during cooling was typically 2 orders
of magnitude less than ε and was only equal to it during the
lightest winds (Fig. 4k). Consequently, its contribution to the gas transfer
coefficient was minor (Fig. 7). Averaged over all ice-free seasons
(2009–2017), the buoyancy flux contributed only 8 % to the TKE dissipation
rate, but up to 90 % during rare, very calm periods (U10≤0.5 m s-1, Fig. 4k) and up to 25 % during the warmest periods
(Tsurf≥18∘C, Fig. 4j).
Time series of air and surface mixed-layer temperature
(three-lake mean) (a), wind speed, gas transfer velocity from the surface
renewal model (kmod and its buoyancy component, kmod,β) and
from chamber observations (kch) (three-lake mean values, error bars
represent 95 % confidence intervals) (b), chamber CH4 flux (c),
air–water CH4 concentration difference (d), precipitation and changes
in water level in Mellersta Harrsjön (e), and the water temperature in
Villasjön (f), Inre Harrsjön (g), and Mellersta Harrsjön (h)
during the ice-free season of 2017 (1 June to 20 October). The white lines
in panels (f–h) represent the depth of the surface mixed layer. Thin and thick
lines in panels (a) and (b) represent half-hourly and daily means, respectively.
In panel (a) only the half-hourly time series of Twater was plotted.
CH4 storage and residence times
Residence times of stored CH4 varied between 12 h and 7 d and
were inversely correlated with wind speed in all three lakes (OLS: R2≥0.57, Fig. 6). The mean residence time was shortest in the shallowest
lake and was not significantly different between the two deeper lakes
(paired t test, p<0.01, Table 3). We did not find a statistically
significant linear correlation between the residence time and day of year or
the water temperature. CH4 storage was greatest in the deeper lakes and
displayed patterns similar to the surface concentrations, increasing in the
warmest months with water temperature and decreasing with wind speed.
Scatter plots of the CH4 residence time (a–c) and storage
(d–f) versus time, surface water temperature, and wind speed. Symbol colours
represent the different lakes. Large symbols represent binned means, and small
symbols represent individual estimates. Bin sizes were 10 d, 1 ∘C, and 0.5 m s-1 for time, water temperature, and U10,
respectively. Each storage observation was paired with T and U10 averaged
over the 24 h (Villasjön) and 72 h (Inre and Mellersta Harrsjön) prior
to water sampling, reflecting average conditions during CH4 residence
times. The linear regressions of the residence time onto time (a) and
temperature (b) were not statistically significant (p=0.07–0.10). Linear
relations of binned quantities and U10 were statistically significant
(c: p≤0.002; f: p≤0.04). Arrhenius-type functions (Eq. 7)
adequately described the storage-temperature relation in each lake (e:
R2≥0.70, p<0.001).
Variability
Chamber fluxes and surface water concentrations differed significantly
between lakes (ANOVA, p<0.001, n=287, n=365) (Table 2). Both
quantities were inversely correlated with lake surface area. CH4
concentrations in the stream feeding the Mire (22.2±5.1 mg m-3,
n=29, mean ±95 % CI) were significantly higher than those in
the lakes (Table 2). Surface water concentrations over the deep parts of the
deeper lakes (≥2 m water depth) were lower than those in the shallows
(< 2 m) by 21 % to 26 % for Inre and Mellersta Harrsjön,
respectively. However, the diffusive CH4 flux did not differ
significantly between depth zones in either Inre Harrsjön (ANOVA, p=0.27, n=290) or Mellersta Harrsjön (ANOVA, p=0.90, n=293) or
between zones of high and low CH4 ebullition in Villasjön (paired
t test, p=0.27, n=89). The similar fluxes inshore and offshore present
a contrast with ebullition, for which the highest fluxes were consistently
observed in the shallow lake and littoral areas of the deeper lakes
(Jansen et al., 2019; Wik
et al., 2013).
Relations between the flux and its drivers – temperature, wind speed, and
the surface concentration – manifested on different timescales (Fig. 7).
Over the ice-free season both the CH4 fluxes and surface water
concentrations tracked changes in the water temperature. The wind speed
(U10) showed less variability over seasonal (CV = 7 %, n=17) than
over diel timescales (CV = 12 %, n=24) and displayed a clear diurnal
maximum. The surface water and sediment temperature varied primarily on a
seasonal timescale (CV = 52 % and 45 %, n=17) and less on diel
timescales (CV = 3 % and 2 %, n=24). Similar to the wind speed the gas
transfer velocity varied primarily on diel timescales (Fig. 7), albeit with
a lower amplitude. This was in part because kmod∝u3/4
(Eq. 4) and because the drag coefficient, used to compute the water-side
friction velocity in Eq. 5, increases at lower wind speeds and under an
unstable atmosphere, which was typically the case. The surface concentration
was correlated with wind speed and temperature (Fig. 4f, g) and showed both
seasonal and diel variability. On diel timescales Δ[CH4] and
kmod were out of phase; Δ[CH4] peaked just before noon,
when the gas transfer velocity reached its maximum value (Fig. 7b, d).
However, binned means of the 1 h chamber fluxes (Fch (1 h)) were not
significantly different at the 95 % confidence level (error bars) and did
not show a clear diel pattern (Fig. 7b). Temporal patterns of fluxes and
concentrations were very similar between the lakes (Figs. S2 and
S3).
Temporal patterns of CH4 chamber fluxes, concentrations (a, b), gas transfer velocity, air and surface water temperature, and wind
speed (c, d). Bin sizes are 10 d (a, c) and 1 h (b, d). Error bars
represent 95 % confidence intervals of the binned means. Temporal patterns
in each individual lake are shown in Figs. S2 and S3.
Timescale analysis
The spectral density plot (Fig. 8a) disentangles dominant timescales of
variability of the drivers of the flux. The power spectra of wind speed and
temperature peaked at periods of 1 d and 1 year, following well-known diel
and annual cycles of insolation and seasonal variations in climate
(Baldocchi et al., 2001). The diel spectral peak was subdued
for the surface sediment temperature. For U10, the overall spectral
density maximum between 1 d and 1 week, and somewhat longer in spectra for
the ice-free period only (Fig. S4), corresponds to
synoptic-scale weather variability, such as the passage of fronts
(MacIntyre et al., 2009). U10 and
Tair also exhibit spectral density peaks at 1–3 weeks, which could be
associated with persistent atmospheric blocking typical of the Scandinavian
region (Tyrlis and Hoskins, 2008). While the
temperature variability was concentrated at annual timescales, the wind
speed varied primarily on timescales shorter than about a month and often
shorter than a week.
The climacogram (Fig. 8b) reveals that the variability of the chamber flux
and the gas transfer velocity were enveloped by that of the water temperature
and the wind speed, as was the surface concentration difference for
timescales < 5 months. The distribution of variability over the
different timescales is similar to that shown in the spectral density plot
(Fig. 8a). The standard deviation of the water temperature did not change
from its initial value (σ/σinit=1) until timescales
of about 1 month, following the 1-year harmonic. In contrast, most of the
variability of the wind speed was concentrated at timescales shorter than 1 month. The variability of the chamber and modelled fluxes first tracked that
of the wind speed, but for timescales longer than about 1 month the decrease
in variability resembled that of water temperature. The variability of the
modelled fluxes followed that of the surface concentration difference rather
than the gas transfer velocity. However, the coarse sampling resolution of
the fluxes and concentrations may have led to an underestimation of both the
variability at < 1-week timescales (Fig. 7b) and the value of
σinit. Finally, the climacogram shows that kmod retains
about 72 % of its variability at 24 h timescales, which justifies our
averaging over chamber deployment periods for comparison with kch and
the computation of the model scaling parameter α′ (Fig. 3).
Timescale analysis of the diffusive CH4 flux and its
drivers. (a) Normalized spectral density of whole-year near-continuous
time series of the air temperature (Tair), temperature of the surface
water and ice (0.1–0.5 m, Twater), temperature of the surface sediment
in Mellersta Harrsjön (Tsed), and wind speed (U10). (b) Climacogram of the measured and modelled CH4 flux (Fch,
Fmod), air and surface water temperature (Tair, Twater),
water–air concentration difference (Δ[CH4]), modelled gas
transfer velocity (kmod), and wind speed (U10) during the
ice-free seasons of 2009–2017. Dashed, light-grey curves represent
(combinations of) trigonometric functions of mean 0 and amplitude 1 with a
specified period. The 24 h and 1-year harmonic functions were continuous over the
dataset period while the 24 h + 1-year harmonic was limited to periods when
chamber flux data were available. Panel (a) is based on continuous time series
that include the ice-cover seasons: Fig. S4 shows spectral
density plots for individual ice-free seasons.
DiscussionMagnitudes of fluxes and gas transfer velocities
Overall, diffusive CH4 emissions from the Stordalen Mire lakes (6.9±0.3 mg m-2 d-1, mean ±95 % CI) were lower than
the average of postglacial lakes north of 50∘ N, but within the
interquartile range (mean 12.5, IQR 3.0–17.9 mg m-2 d-1;
Wik et al., 2016b). Emissions are also at the
lower end of the range for northern lakes of similar size (0.01–0.2 km2) (1–100 mg m-2 d-1; Wik et
al., 2016b). As emissions of the Stordalen Mire lakes do not appear to be
limited by substrate quality or quantity (Wik et al.,
2018), but strongly depend on temperature (Fig. 4b), the difference is
likely because a majority of flux measurements from other postglacial lakes
were conducted in the warmer, subarctic boreal zone. Boreal lake CH4
emissions are generally higher for lakes of similar size: 20–40 mg m-2 d-1 (binned means), n=91
(Rasilo et al., 2015) and ∼12 mg m-2 d-1, n=72 (Juutinen
et al., 2009).
The gas transfer velocity in the Stordalen Mire lakes was similar to that
predicted from wind-based models of
Cole and Caraco (1998)
and Crusius and Wanninkhof (2003) at low wind speeds (Fig. 9). Both were
based on tracer experiments with sampling over several days and thus, like
our approach, are integrative measures. The slope of the linear
wind–kch relation (OLS: 0.81±0.21, slope ±95 % CI,
R2=0.20 and p<0.01 for the individual kch estimates
(small orange rhombuses in Fig. 9)) was similar to that reported by
Soumis et al. (2008) (0.78 for
a 0.06 km2 lake), who also used a mass balance approach, and
Vachon and Prairie (2013) (0.70–1.16 for lakes
0.01–0.15 km2). Part of the difference with the models of Vachon and
Prairie (2013), Cole and Caraco (1998) and Soumis et al. (2008) was caused
by the offset at 0 wind speed, which may stem from a larger contribution of
the buoyancy flux in their lakes than we computed for our lakes with the
surface renewal model
(Crill et al., 1988; Read
et al., 2012). The offset could also be caused by remnant wind shear
turbulence (MacIntyre et al., 2018). While fetch limitation
can reduce gas transfer at high wind speeds in small lakes
(Vachon and Prairie, 2013; Wanninkhof, 1992),
and the lakes studied here are at the low end of the size spectrum of water
bodies in which the gas transfer models in Fig. 9 were developed (Table S1 in the Supplement),
there are a number of other explanations for the low values we obtained. We
further discuss these in Sect. 4.5 after evaluating drivers of flux.
Drivers of flux
Methane emitted from lakes in wetland environments can be produced in situ
or be transported in from the surrounding landscape
(Paytan et al., 2015). The
distinction is important because some controls on terrestrial methane
production, such as water table depth (Brown et al.,
2014), are irrelevant in lakes. In the Stordalen Mire lakes, the
Arrhenius-type relation of CH4 fluxes and concentrations (Fig. 4b, f)
together with short CH4 residence times (Fig. 6) suggest that efficient
redistribution of dissolved CH4 strongly coupled emissions to sediment
methane production. High CH4 concentrations in the stream (Sect. 3.4)
further suggest that external inputs of CH4 – produced in the fens
and transported into the stream with surface runoff, or produced in stream
sediments – may have elevated emissions in Mellersta Harrsjön
(Lundin et al., 2013). However, although
the Mire exports substantial quantities of dissolved organic carbon (DOC) and presumably CH4 from
the waterlogged fens to the lakes
(Olefeldt and Roulet, 2012), after
rainy periods we observed either no significant change in Δ[CH4] (3–6 July and 21–27 August 2017, Fig. 5) or a decrease (13–19 July 2017, Fig. 5). It remains unclear whether such reduced storage resulted
from lower methanogenesis rates associated with the temperature drop after
rainfall, convection-induced degassing, or lake water displacement or
dilution by surface runoff.
Turbulent transfer was dominated by wind shear, and we computed a minor
contribution (∼8 %) of the buoyancy-controlled fraction of k. Our
result differs from that in
Read et al. (2012), who found
that buoyancy flux dominated turbulence production in temperate lakes 0.1 km2 in size and smaller. For the Stordalen Mire lakes we computed
higher ice-free season mean values of u∗w, as well as lower values
of the water-side vertical friction velocity, w∗w=(βzmix)1/3, (1.2–1.8 mm s-1) than they report
(2.0–7.5 mm s-1, n=40 lakes). The difference results from high wind
speeds and often colder surface waters here compared to many temperate
lakes. Therefore, values of sensible and latent heat fluxes are lower in our
lakes than in lakes in warmer regions. Consequently, the temperate lakes
surveyed in Read et al. (2012), will have a larger contribution of buoyancy flux to the gas transfer
coefficient at night, when wind speeds are low
(MacIntyre and Melack, 2009). The contribution of
convection also depends on the wind-sheltering properties of the landscape
surrounding the lake (Kankaala et al., 2013;
Markfort et al., 2010). Depending on the turbulence environment, the
buoyancy flux is thus weighed differently in different parameterizations of
ε
(Heiskanen
et al., 2014; Tedford et al., 2014) and in wind-based models (offsets at
U10=0 in Fig. 9), contributing to significant divergence among model
realizations of k
(Dugan
et al., 2016; Erkkilä et al., 2018; Schilder et al., 2016).
The distinct spectral peaks of temperature and U10 (Fig. 8a) indicate
that flux dependencies on these parameters (Fig. 4b, c) acted on different
timescales. This difference has implications for the choice of models or
proxies of the flux in predictive analyses. For lakes that mix frequently
and have a climatology similar to that of the Stordalen Mire
(Malmer et al., 2005), temperature-based
proxies (e.g. Thornton et al., 2015) would
resolve most of the variability of the ice-free diffusive CH4 flux at
timescales longer than a month. Advanced gas transfer models that account
for atmospheric stability and rapid variations in wind shear, such as we
have used here, allowed us to resolve variability in flux at timescales
shorter than about a month. Our results are representative of small,
wind-exposed lakes in cold environments, where, as a result of considerable
wind driven mixing, fluxes are lower than would be predicted in lakes where
buoyancy fluxes during heating and cooling are higher.
Storage and stability
The robust temperature sensitivity of lake methane emissions (Fig. 4b,f)
(Wik et al., 2014;
Yvon-Durocher et al., 2014) is driven by biotic and abiotic mechanisms. Lake
mixing can modulate temperature relations by periodically decoupling
production from emission rates (Engle
and Melack, 2000). Here, enhanced CH4 accumulation during periods of
stratification may have contributed to concentration and storage maxima in
July and August (Figs. 4e, 6d). However, as the CH4 residence time was
invariant over the season and with temperature (Fig. 6a, b), the
storage–temperature relation (Fig. 6e) likely reflects rate changes in
sediment methanogenesis rather than inhibited mixing. For example, the
highest CH4 concentrations in our dataset (59.1±26.4 mg m-3, n=37) were measured during a period with exceptionally high
surface water temperatures (Twater=18.5±3.6∘C)
that lasted from 23 June to 30 July 2014. Emissions during this period
comprised 29 %–56 % (depending on the lake) of the 2014 ice-free diffusive
flux, while the peak quantity of accumulated CH4 comprised < 5 %. Two mechanisms may explain the lack of CH4 accumulation. First,
stratification was frequently disrupted by vertical mixing (Fig. 5g–h), and
concurrent hypolimnetic CH4 concentrations were not significantly
different from (Inre Harrsjön, 2010–2017, paired t test, p=0.12, n=32) or lower than (Mellersta Harrsjön, 2010–2017, paired t test,
p<0.01, n=35) those in the surface mixed layer. Second,
stratification often was not strong enough to affect gas transfer
velocities. Even when assuming ε was suppressed by an order of
magnitude for N>25 and by 2 orders of magnitude for
N>40 (MacIntyre et al., 2018), kmod was only
slightly lower (2.8 cm h-1) than the multi-year mean (3.0 cm h-1).
Thus, in weakly stratified lakes with strong wind mixing, the temperature
sensitivity of diffusive CH4 emissions may be observed without
significant modulation by stratification.
Degassing (Fig. 4c, g) prevented an unlimited increase in the emission rate
with the gas transfer velocity. In this way, Δ[CH4] acted as a
negative feedback that maintained a quasi-steady state between CH4
production and removal processes throughout the ice-free season. In all
three lakes CH4 residence times were inversely proportional to the wind
speed (Fig. 6c), indicating an imbalance between production and removal
processes. We hypothesize that the imbalance exists because the variability
of wind speed peaked on shorter timescales than that of the water
temperature (Fig. 8a). Changes in wind shear periodically pushed the system
out of production–emission equilibrium, allowing for transient degassing and
accumulation of dissolved CH4. The temporal variability of dissolved
gas concentrations is likely higher in shallow wind-exposed systems with
limited buffer capacity (Natchimuthu et
al., 2016, 2017) and should be taken into account when applying gas
transfer models to small lakes and ponds.
Rapid degassing occurred at U10≥6.5 m s-1 (Fig. 4c). Gas
fluxes at high wind speeds may have been enhanced by the kinetic action of
breaking waves (Terray et al., 1996) or
through microbubble-mediated transfer. Wave breaking was observed on the
Stordalen lakes at wind speeds ≥7 m s-1. Microbubbles of
atmospheric gas (diameter < 1 mm) can form due to photosynthesis,
rain, or wave breaking (Woolf and Thorpe, 1991) and remain
entrained for several days (Turner, 1961). Due to their
relatively large surface area, they quickly equilibrate with sparingly
soluble gases in the water column, providing an efficient emission pathway
to the atmosphere when the bubbles rise to the surface
(Merlivat and Memery, 1983). In inland
waters microbubble emissions of CH4 have only been indirectly inferred
from differences in CO2 and CH4 gas transfer velocities
(McGinnis et al.,
2015; Prairie and del Giorgio, 2013), and more work is needed to evaluate
their significance in relatively sheltered systems.
Normalized gas transfer velocities (k600) versus the wind
speed at 10 m (U10). Binned values (large rhombuses, kch and
kmod, bin size = 0.5 m s-1) and individual observations (small
rhombuses, kch) from floating chambers (kch) and the surface renewal
model (kmod with α′=0.23). Error bars represent 95 %
confidence intervals of the binned means. Solid lines represent models from
the literature:
Cole
and Caraco (1998) (CC98), Crusius and Wanninkhof (2003) (bilinear and power-law models) (CW03), Soumis et al. (2008) (S08) and Vachon and Prairie (2013)
(VP13) for lake surface areas of 0.01 and 0.15 km2. Supplement Table S1 lists the model equations and calibration ranges. A power-law regression
model is shown for the individual kch datapoints (n=334):
k600=0.77×U101.02+0.62 (dashed yellow line).
Timescales of variability
Overall, the short-term variability of the flux due to wind speed (1.1–13.2 mg m-2 d-1) was similar to the long-term variability due to
temperature (0.7–12.2 mg m-2 d-1) (ranges of the binned means,
Fig. 4b–c). The diel patterns in the mixed-layer depth (Fig. 5) and the gas
transfer velocity (Fig. 7d) and daytime variation in the surface
concentration (Fig. 7b) were indicative of daily storage-and-release cycles,
resulting in a flux difference of about 5 mg m-2 d-1 between
morning and afternoon, about half the mean seasonal range (Fig. 7a). Diel
variability of lake methane fluxes has been observed at Villasjön (eddy
covariance, Jammet et al., 2017)
and elsewhere
(Bastviken
et al., 2004, 2010; Crill et al., 1988; Erkkilä et al., 2018; Eugster et
al., 2011; Hamilton et al., 1994; Podgrajsek et al., 2014). Similarly, diel
patterns in the gas transfer velocity have been inferred from eddy
covariance observations (Podgrajsek et al., 2015) and in
model studies (Erkkilä et al.,
2018). Apparent offsets between the diurnal peaks of the flux, surface
concentrations, and drivers (Fig. 7b, d) have been noted previously
(Koebsch et al., 2015), but have
yet to be explained. Continuous eddy covariance measurements in lakes where
the dominant emission pathway is turbulence-driven diffusion could help
characterize flux variability on short timescales (e.g.
Bartosiewicz et al., 2015).
The CH4 residence times (1–3 d) were not much longer than the diel
timescale of vertical mixing (Fig. 5g, h). As a result, horizontal
concentration gradients developed in the deeper lakes (Table 2). The 23±11 % concentration difference between depth zones in the deeper
lakes (mean ±95 % Cl) fits transport model predictions of
DelSontro et al. (2017) for small lakes (< 1 km2) that highlight the role of outgassing and oxidation during
transport from production zones in the shallow littoral zones or the deeper
sediments (Hofmann, 2013). Concentration gradients may
also have been caused by physical processes, such as upwelling due to
thermocline tilting
(Heiskanen et al.,
2014). Higher-resolution measurements, for example with automated
equilibration systems
(Erkkilä
et al., 2018; Natchimuthu et al., 2016), are needed to assess how much of
the spatial and diel patterns of the CH4 concentration can be explained
by physical drivers such as gas transfer and mixed-layer deepening
(Eugster
et al., 2003; Vachon et al., 2019), or by biological processes such as
methanogenesis and microbial oxidation
(Ford et al., 2002).
Gas transfer models can only deliver accurate fluxes if they are combined
with measurements that capture the full spatio-temporal variability of the
surface concentration
(Erkkilä
et al., 2018; Hofmann, 2013; Natchimuthu et al., 2016; Schilder et al.,
2016). The short CH4 residence times and diel pattern of Δ[CH4] suggest that weekly sampling did not capture the full temporal
variability of the surface concentrations. Especially after episodes of high
wind speeds and lake degassing (Fig. 4c, g), concentrations may not have been
representative of the 24 h chamber deployment period.
Model–chamber comparison
It is fundamental to our understanding of controls on fluxes to determine
why empirically derived values of the model scaling parameter α′ are
relatively low in this study (0.17–0.31) compared to the theoretical value
of 2/15≅0.37 (Katul et
al., 2018) and why they were different among the three lakes. kmod did
not differ significantly between lakes (ANOVA, p<0.001), and
therefore differences in α′ resulted from diverging kch values
estimated at 3.5±0.7 (n=74), 3.1±0.4 (n=131) and 2.5±0.6 (n=142) cm h-1 in Villasjön, Inre Harrsjön, and
Mellersta Harrsjön, respectively (mean ±95 % CI). Synthesis
studies show that scaling parameter values can vary between 0.1 and 0.7 over
the range of moderate to high dissipation rates computed for the Stordalen
Mire lakes (Eq. 5: ε=10-7–10-5 m2 s-3)
(Esters et al., 2017;
Wang et al., 2015, and references therein). In such cases ε has
been measured directly with acoustic Doppler or particle image velocimetry
and compared with independent estimates of k using chambers
(Gålfalk
et al., 2013; Tokoro et al., 2008; Vachon et al., 2010; Wang et al., 2015),
eddy covariance observations
(Heiskanen et al.,
2014), or the gradient flux technique (Zappa et al.,
2007) and a sparingly soluble tracer, such as CO2 or SF6. Measured
and modelled lake CO2 fluxes agree reasonably well if Eqs. (4) and (5)
are used with a multi-study mean α′ of 0.5
(Bartosiewicz
et al., 2015; Czikowsky et al., 2018; Erkkilä et al., 2018; Mammarella
et al., 2015), but the agreement is less clear for CH4 fluxes
(Bartosiewicz et al., 2015). The observed
variability in α′ could be explained by chemical or biological
factors that limit surface exchange or by the variable contributions of
wind sheltering, atmospheric stability, and within-lake stratification and
mixing. Here, the low α′ value may imply an underestimation of k
derived from chamber observations or an overestimation of dissipation rates
used in the modelling of gas transfer velocities.
An underestimation of chamber-derived gas transfer velocities may have
resulted from an overestimation of Caq in Eq. (1). This can occur if
significant methane oxidation takes place at the air–water interface. This
additional removal process would invalidate the implicit assumption in Eqs. (1)
and (2) that the dissolved CH4 concentration measured in the bulk fluid
is representative of the concentration in the diffusive sublayer. Omitting
oxidation would bias Δ[CH4] high and kch low. Laboratory
gas exchange experiments have demonstrated methanotrophy in the ∼1µm thick surface microbiome (bacterioneuston) of seawater
(Upstill-Goddard et al., 2003). While we are not aware of similar
experiments in freshwater, CH4 oxidation is ubiquitous in northern
lakes and can be substantial even in the epilimnion (Martinez-Cruz et al.,
2015, Thottathil et al., 2018). The Stordalen Mire lakes remained oxygenated
throughout the ice-free season and CH4 stable isotopes indicate that
between 24 % (Villasjön) and 60 % (Inre and Mellersta Harrsjön)
of CH4 in the water column was continually oxidized
(Jansen et al., 2019). This may explain not only the
low scaling parameter value compared to those found with other tracers, but
also why α′ was higher in Villasjön (0.31, n=67) than in the
deeper lakes (0.17–0.25, n=267) (Fig. S1). However, more
work is needed to establish how methanotrophy is partitioned between the
air–water interface, where it would affect estimation of k, and the deeper
water column and sediment. An increase in surface concentrations which
typically occurs at night would not have been manifest
(Crill et al., 1988; Czikowsky et al., 2018) because
there was, apart from the period just after thaw of the ice cover in 2017, no significant
CH4 accumulation below the mixing layer throughout the ice-free
seasons. Indeed, CH4 concentrations within the 0.1–1 m surface layer
of the deeper lakes (Table 2) were not significantly different from those at
greater depth (Inre Harrsjön: 12.2±2.7 mg m-3, n=292;
Mellersta Harrsjön: 17.7±4.9 mg m-3, n=405; means
±95 % CI).
An overestimation of gas transfer velocities computed with the surface
renewal model may result if actual dissipation rates are lower than we
compute. This occurs under high wind shear when more of the introduced
turbulent kinetic energy is used for mixing the water column and deepening
the mixing layer and less is dissipated
(Ivey and Imberger, 1991; Jonas et
al., 2003). When this occurs, the coefficient on u∗w3 in Eq. (5)
may have a lower value (Tedford et al., 2014),
which translates to a reduced estimate of ε and increased
α′ values. A similar decrease in ε can be assumed
during heating, when strong stratification (N>25 cph) dampens
turbulence dissipation
(MacIntyre et
al., 2010, 2018); however, such stratification was intermittent in our study
(Fig. 5f–h).
Reduced gas transfer velocities and between-lake differences in kch
could also be due to differences in atmospheric forcing. First, the wind
speed may have been lower over the lakes than on the Mire due to the slight
elevation (< 1 m) of the surrounding peatland hummocks
(Markfort et al., 2010). The wind-sheltering effect of
tall shrubs (Betula nana L; Malmer et al., 2005) on the
shores of the deeper lakes (Fig. 1) was readily noticed during sample
collection, particularly in Mellersta Harrsjön. Second, atmospheric
stability was different over the three lakes. The atmosphere was stable
(z/LMO,a>0) over Mellersta Harrsjön, Inre Harrsjön,
and Villasjön during 29 %, 21 %, and 22 % of the ice-free periods
(2009–2017), respectively, with drag coefficients ∼16 % lower than
their neutral value during these times. The effect was more pronounced when
winds were light during daytime heating, with somewhat higher frequency
during autumn. Colder incoming stream water flowing into Mellersta
Harrsjön may have contributed to lower surface water temperatures in
this lake (Table 3), with the discrepancy more noticeable as lake level rose
(Fig. 5e–h). More frequent periods with a stable atmosphere above Mellersta
Harrsjön reduced sensible and latent heat fluxes and are a likely cause
of the increased stratification of the surface layer: water at 0.1 m was
sometimes 0.5 to 2 ∘C warmer than at 0.3 m in
Mellersta Harrsjön (5 % of the time during ice-free seasons) when
temperatures were isothermal in the upper 0.5 m in Villasjön and Inre
Harrsjön. Greater near-surface stratification coupled with lower winds
than measured on the Mire would have led to the lower values of k and
α′ obtained in this lake. While this analysis points to the
challenges in modelling fluxes when meteorological instrumentation is not
situated on the lakes, it also suggests that a solution is to use lower
values of α′ when modelling k for sheltered water bodies.
In summary, the model scaling parameter α′ computed in this study
is lower than the theoretical value of 0.37 and 0.5 recently obtained
in eddy covariance studies in which CO2 fluxes were measured and
modelled. The discrepancy may be explained by surface CH4
concentrations decreasing due to microbial oxidation over the same timescale
as our chamber measurements. Alternate explanations take into account the
magnitude of wind shear and degree of sheltering. Differences in α′
between lakes indicate the care required in modelling emissions from
sheltered lakes; the overall cooler surface water temperatures in the lake
with greater stream inflows point to a new control on emissions. That is,
when stream inflows lead to surface water temperatures cooler than air
temperature in sheltered lakes, a stable atmosphere results, which leads to a
reduced momentum flux, lower emissions, and a longer time over which methane
oxidation can occur. The cooling effect may be especially pronounced in
northern landscapes underlain by permafrost, where the temperature of
meltwater streams and subsurface flow in the active layer remain low
throughout the year. Thus, these comparisons of modelled and measured fluxes
point to new areas of research.
Summary and conclusions
In this study we combined a unique, multi-year dataset with a modelling
approach to better understand environmental controls on turbulence-driven
diffusion-limited CH4 emissions from small, shallow lakes. Floating
chambers estimated the seasonal mean flux at 6.9 mg m-2 d-1 and
illustrated how the flux depended on temperature and wind speed. Wind shear
controlled the gas transfer velocity while thermal convection and release
from storage were minor drivers of the flux. CH4 fluxes and surface
concentrations fitted an Arrhenius-type temperature function (Ea′=0.88–0.97 eV), suggesting that emissions were strongly coupled to rates of
methanogenesis in the sediment. However, temperature was only an accurate
proxy of the flux on averaging timescales longer than a month. On shorter
timescales, wind-induced variability in the gas transfer velocity, mixing-layer depth, and storage decoupled production from emission rates. Transient
changes in the lake mixing regime allowed for periodic CH4 accumulation
and resulted in an inverse relationship between wind speed and surface
concentrations. In this way, the air–water concentration difference acted as
a negative feedback to emissions and prevented complete degassing of the
lakes, except at high wind speeds (U10≥6.5 m s-1).
Freshwater flux studies are increasingly focused on understanding mechanisms
and developing proxies for use in upscaling efforts and process-based
models. Simple temperature- or wind-based proxies can yield accurate flux
estimates, but model parameters, such as Ea′ and α′, must be
calibrated to local conditions to reflect relevant biotic and abiotic
processes at appropriate timescales. Our study highlights the importance of
non-linear feedbacks, such as shallow lake degassing at high wind speeds, as
well as microbial removal processes and the need to consider the timescale
over which fluxes occur relative to the timescale over which CH4 can be
oxidized. More work is needed to quantify the importance of microbial
removal processes at the air–water interface of freshwater ecosystems.
Advanced gas transfer models can only improve the accuracy of flux estimates
if they are paired with observations that capture the meteorological
conditions over the lake and the spatio-temporal variability of dissolved gas
concentrations. Therefore, field measurements remain necessary to inform,
calibrate, and validate models. Our results indicate that the timescale of
driver variability can inform the frequency of field measurements necessary
to yield representative datasets for novel proxy development.
Data availability
Data are available at https://www.bolin.su.se/data/ or upon request from the corresponding author. Surface renewal
model code is available by contacting Sally MacIntyre.
The supplement related to this article is available online at: https://doi.org/10.5194/bg-17-1911-2020-supplement.
Author contributions
JJ, MW, and PMC designed the study. Fieldwork and laboratory measurements were
conducted by JJ, JS, and MW. SM developed the surface renewal model code,
with contributions from AC. JJ performed the analyses and prepared the
manuscript with contributions from BFT, PMC, and SM.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
We thank the McGill University
researchers (David Olefeldt, Silvie Harder, and Nigel Roulet) for the data
they provided from the carbon flux tower.
We are grateful to David Bastviken for validating our implementation of the
chamber headspace equilibration model. We thank the staff at the Abisko
Scientific Research Station (ANS) for logistic and technical support. Noah Jansen created the schematic of the floating chamber pair. We thank Carmody McCalley, Christoffer Hemmingsson, Emily Pickering-Pedersen, Erik Wik, Hanna Axén, Hedvig Öste, Jacqueline Amante, Jenny Gåling, Jóhannes West, Kaitlyn Steele, Kim Jäderstrand, Lina Hansson, Lise Johnsson,
Livija Ginters, Mathilda Nyzell, Niklas Rakos, Oscar Bergkvist, Robert Holden, Tyler Logan, and Ulf Swendsén for their help in the field.
Financial support
This research has been supported by the National Science Foundation, Division of Arctic Sciences (grant nos. 1204267 and 1737411 to Sally MacIntyre), Vetenskapsrådet (grant nos. 2015-06020 (ICOS), 2007-4547, and 2013-5562 to Patrick Crill), and the Natural Sciences and Engineering Research Council of Canada (grant no. NSERC RGPIN-2017-04059).
Review statement
This paper was edited by Gwenaël Abril and reviewed by two anonymous referees.
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