Thermokarst features are widespread in ice-rich regions of the
circumpolar Arctic. The rate of thermokarst lake formation and
drainage is anticipated to accelerate as the climate warms. However,
it is uncertain how these dynamic features impact the terrestrial
Arctic carbon cycle. Methane (CH4) and carbon dioxide
(CO2) fluxes were measured during peak growing season using
eddy covariance and chambers at Illisarvik, a 0.16 km2
thermokarst lake basin that was experimentally drained in 1978 on
Richards Island, Northwest Territories, Canada. Vegetation in the
basin differs markedly from the surrounding dwarf-shrub tundra and
included patches of tall shrubs, grasses, and sedges with some bare
ground and a small pond in the centre. During the peak growing season,
temperature and wind conditions were highly variable, and soil water
content decreased steadily. Basin-scaled net ecosystem CO2
exchange (NEE) measured by eddy covariance was
-1.5 [CI95%±0.2] gC-CO2m-2d-1; NEE followed
a marked diurnal pattern with no day-to-day trend during the study
period. Variations in half-hourly NEE were primarily controlled by
photosynthetic photon flux density and influenced by vapour pressure
deficit, volumetric water content, and the presence of shrubs within
the flux tower footprint, which varied with wind direction. Net
methane exchange (NME) was low (8.7 [CI95%±0.4] mgCH4m-2d-1) and had little impact on the
growing season carbon balance of the basin. NME displayed high spatial
variability, and sedge areas in the basin were the strongest source of
CH4 while upland areas outside the basin were a net
sink. Soil moisture and temperature were the main environmental
factors influencing NME. Presently, Illisarvik is a carbon sink during
the peak growing season. However, these results suggest that rates of
growing season CO2 and CH4 exchange rates may
change as the basin's vegetation community continues to evolve.
Introduction
The northern permafrost region stores approximately 50 % of global
organic soil carbon in 16 % of the terrestrial land area (Tarnocai
et al., 2009). Thermokarst landscapes account for approximately
20 % of the land area in this region and hold about half of its
organic soil carbon (Olefeldt et al., 2013). Lake
thermokarst landscapes are widespread in poorly drained, sedimentary
permafrost lowlands with excess ground ice volume and constitute about
a third of all thermokarst area (French, 2017; Olefeldt et al., 2013).
Thermokarst lakes are a prominent landscape feature of the western
Canadian Arctic (Mackay, 1999; Marsh et al. 2009; Lantz and Turner,
2015). These lakes drain, sometimes catastrophically, forming drained
thermokarst lake basins (DTLBs) via bank overflow, ice wedge erosion,
coastal erosion, and stream migration (Billings and Peterson, 1980;
Mackay, 1999). Lake formation and drainage are a natural part of the
thaw lake cycle, but it is anticipated that climate change will
accelerate or disturb this cycle, potentially altering the regional
carbon balance (Jones et al., 2018).
Net ecosystem exchange (NEE), ecosystem respiration (ER), and gross
primary productivity (GPP), where NEE=ER-GPP,
are lower in the Arctic than warmer regions but have significant
seasonal cycles and variability between vegetation types (Virkkala
et al., 2018). Future trajectories in NEE will in large part be
governed by ER (Biasi et al., 2008; Cahoon et al., 2012). Dominant
vegetation types in the western Canadian Arctic are erect-shrub tundra
and wetlands (Walker et al., 2005). Growing season NEE is typically
negative across these units throughout the Arctic, indicating a net
CO2 sink as GPP exceeds ER in part due to cold and/or
anoxic soil conditions (Virkkala et al., 2018; Lafleur et al.,
2012). Annual NEE can be positive or negative with large variation in
GPP linked to annual weather variability (Virkkala et al., 2018,
McGuire et al., 2009). Arctic net methane exchange (NME) is positive
because wetland areas are strong methane (CH4) sources while
upland areas with better drainage can be net sinks (Whalen and
Reeburgh, 1990; McGuire et al., 2009; Sturtevant and Oechel, 2013).
Thermokarst lakes are well-recognized sources of CH4 (Walter
et al., 2007), which is 28 times as potent as carbon dioxide
(CO2) on a 100-year timescale (IPCC, 2014). Thermokarst
lake formation and expansion is expected to exert a positive feedback
on climate change and accelerate Arctic warming in the near term, but
modelling suggests that drainage may limit expansion and result in
decreased lake area by the end of the century (van Huissteden et al.,
2011). Post drainage, DTLBs undergo rapid ecological succession. In
colder tundra environments, wet meadows or polygonal landscapes
dominated by sedges, grasses, and rushes will form (Lara et al.,
2015). In slightly warmer boreal and transitional regions, DTLBs
often become dominated by willows and other shrubs (Lantz and Turner,
2015).
Carbon exchange in DTLBs of various ages has been examined in a few
studies, almost exclusively focused on the Barrow Peninsula in
northern Alaska. DTLB NEE during the growing season is negative with the
greatest CO2 uptake in younger basins and decreasing net
uptake as basins age in this region (Zona et al., 2010; Zulueta
et al., 2011; Sturtevant and Oechel, 2013; Lara et al., 2015). DTLB
source–sink strength of CH4 was found to be highly variable
depending on vegetation and ground conditions (Lara et al., 2015).
NME is highest in wet meadows and remnant ponds but considerably
reduced in areas with better drainage (Zona et al., 2009,
2012; Lara et al., 2015). There may be regional variations in the
carbon balance of DTLBs. For example, a shrub-dominated ancient DTLB
known as Katyk in the Indigirka lowlands of Siberia shows considerably
higher growing season carbon uptake than young Alaskan DTLBs with
comparable NME (van der Molen et al., 2007;
Parmentier et al., 2011). Similarly, DTLBs in the western Canadian
Arctic may have different carbon fluxes than Alaskan DTLBs due to
differences in climate and vegetation composition.
In this study, fluxes of CO2 and CH4 were measured
at Illisarvik, an experimentally drained thermokarst lake basin on
Richards Island in the western Canadian Arctic, Northwest Territories,
Canada. Fluxes of CO2 and CH4 were measured during
the peak growing season using a combination of closed chamber and eddy
covariance (EC) measurements. NEE was calculated from fluxes,
and storage change and was separated into ER and GPP. Here we report
on (1) the spatial and temporal variability of the NEE and NME during
the growing season, (2) the vegetation and environmental factors
influencing NEE and NME, (3) how the growing season carbon balance at
Illisarvik compares to other DTLBs, and (4) potential future carbon
balance trajectories as Illisarvik's vegetation communities continue
to evolve.
MethodsStudy site and data collection
The study took place at Illisarvik, a DTLB on Richards Island
(69∘28′47.5′′ N, 134∘35′18.7′′ W), which was drained
experimentally in 1978 (Mackay, 1997). Illisarvik has since served as
the focus of studies on permafrost growth, active layer development,
and vegetation succession (Ovenden, 1986; Mackay and Burn, 2002;
O'Neil and Burn, 2012; Wilson et al.,
2019). At the nearby Tuktoyaktuk climate station mean annual air
temperature (Ta) is -10.1 ∘C, July is
the warmest month with a mean of 11 ∘C, and January is
the coldest at -27 ∘C. Mean annual precipitation is
160.7 mmyr-1, the majority falling as rain in the summer
and autumn. Snow cover typically lasts from mid-September or early
October to late May (Environment Canada, 2016). Tuktoyaktuk is 60 km east of Illisarvik and in similar
proximity to the coast so the climatology is expected to be similar at
Illisarvik.
Dominant species or landscape feature within the vegetation/cover
classes. Unit codes correspond to the map in Fig. 1a.
Unit codeVegetation classDominant species/landscape feature1aShrubSalix alaxnesis (tall willow)1bShrubSalix glauca (low willow)1cShrubAlnus viridis subsp. crispa (alder)2aSedge marshCarex aquatilis (sedge)2bSedge marshArctophila fulva (pendant grass)3Grass meadowPoaceae spp. (grasses), Eriophorum angustifolium (cotton grass)4aSparse coverSparse vegetation4bSparse coverBare ground5PondsHippuris vulgaris (mare's tail), open water6aOutside of basinDwarf-shrub tundra: Salix spp. and Betula nana (birch)6bOutside of basinFen6cOutside of basinOcean
In the 39 years since drainage, Illisarvik has undergone rapid
vegetation succession. After drainage, there were two remnant
ponds. In the first 5 years after drainage, vegetation colonized
the basin margins and wetter areas (Ovenden, 1986). By 1999, low
vegetation had proliferated across most of the basin and taller
willows had become established along the basin margins (Mackay and
Burn; 2002). By 2010, some of the willows had grown to be 3 m
in height (O'Neil and Burn; 2012). Current vegetation at Illisarvik is
diverse relative to the dwarf-shrub tundra of the surrounding uplands
(Table 1); the basin hosts a mix of woody shrubs (Salix
spp., Betula spp., and Alnus spp.), wetland
vegetation (Carex aquatilis, Arctophila fulva, etc.), and
various grasses (Pocacea spp.) (Wilson et al., 2019). The
basin is partly ringed by a terrace of peat that formed after a
partial drainage event ∼5000 years BP and supports vegetation
similar to the uplands (Michel et al., 1989). An ancient DTLB is
located 100 m to the south of the Illisarvik basin, and the
Arctic Ocean is to the west of the basin, separated by a ridge of
upland tundra about 50 m wide at its narrowest
(Fig. 1).
(a) Map of the distribution of vegetation classes at Illisarvik,
with the footprint climatology (FClim) over the study period, the
locations of the chambers, and the eddy covariance (EC) system. The
alphanumeric labels correspond to the unit codes in Table 1. (b) Legend for
the map in (a). (c) Oblique drone image of Illisarvik, taken at the 16:40 23 July 2016 view from E of DTLB towards W. The basin and EC system are
shown on the image using the same symbology as (a).
A vegetation survey of species composition and abundance was done on a
50 m grid in and around the basin during the 2016 study period
(Wilson et al., 2019). A vegetation map was created with 10 units
based on plant functional type and vegetation structure, with
sub-units denoting sub-canopy vegetation. The unit boundaries between
grid points were estimated visually by traversing the grid
lines. Additional survey data on vegetation units and canopy height
were collected manually with a GPS in the proximity of the EC station
because greater resolution was needed for footprint modelling. Aerial
imagery was collected on 23 July over two flights using a Phantom 2
drone (DJI, Shenzhen, China). The GPS points and drone imagery were
used to cross-reference and modify the map of Wilson
et al. (2019). The 10 units were then aggregated into six broader
surface cover classes (listed from largest to smallest areal fraction
within the footprint climatology (FClim); see Sect. 2.3 for
definition): shrub, grass, sedge, upland, sparse, and water
(Fig. 1 and Table 1).
Weather and soil measurements
Weather data were logged on a CR1000 data logger (Campbell Scientific
Inc, Logan, UT, USA; CSI) at 5 min intervals. Net all-wave
radiation (Rn) and photosynthetic photon flux density
(PPFD) were measured with a NR Lite net radiometer (Kipp and
Zonen, Delft, Netherlands) and a SQ-110 quantum sensor (Apogee
Instruments, Logan, UT, USA), respectively, 3.2 m above the
grass surface on the main EC system tripod (Fig. 1). A shielded HMP35
(CSI) recorded Ta and relative humidity (RH)
2 m above the surface. A tipping bucket rain gauge (R.M Young
Company, Traverse City, MI, USA) was placed 3 m to the west of
the main tripod. Soil temperature and moisture were measured within
soil pits in two different vegetation types near the tripod: grass
(30 m to the east) and shrub (40 m to the
north). Measurements were made of ground heat flux (G) with
custom-made heat flux plates, soil temperatures (Ts)
with custom type-T thermocouples at depths of 0.08 m, and
0–20 cm integrated volumetric water content (VWC) with CS616
water content reflectometers (CSI). The soil measurements were
recorded at 30 min intervals on CR10x data loggers (CSI). The
climate and soil stations operated uninterrupted from 10 July (day
192) and 11 July (day 193), respectively, until 7 August 2016 (day
220). On 11 July and 6 August thaw depth was measured at each of the
10 chamber sites (see below). Thaw depth was measured by inserting a
graduated steel probe into the ground to the point of refusal. Each site
was probed five times: the median value has been used as the thaw
depth at each location. On 12 and 15 July, a large herd of reindeer
(∼500 animals) visited Illisarvik. They mostly avoided the tripod
but did graze near it for about an hour on 12 July, which may have
affected greenhouse gas fluxes.
EC fluxes
An EC system was placed in the southwestern portion of the basin
(69∘28′47.82′′, -134∘35′18.6′′) and measured
fluxes of CO2 (FCO2) and CH4
(FCH4) for the full study period between 10 July and
7 August 2016. The EC system consisted of an open-path infrared
CO2/H2O gas analyzer (IRGA) (model LI-7500, LI-COR Inc.,
Lincoln, NE, USA; LI-COR), an open-path CH4 analyzer (model
LI-7700, LI-COR), and a CSAT3 sonic anemometer (CSI) mounted on a
tripod at a measurement height (zm) of 3 m
(Fig. 2). The EC data and air pressure (Pa) were logged
at 10 Hz on the LI-7550 analyzer interface unit (LI-COR). The
CSAT3 was oriented to the northeast (40∘) because climatology
for Tuktoyaktuk indicated northerly and easterly winds are typical for
July and August (Environment Canada, 2016).
(a) Half-hourly air and soil temperatures, displayed along with
photosynthetic photon flux density (PPFD). (b) Hourly soil volumetric water
content and daily total precipitation. (c) Half-hourly FCO2 (green) and
NEENN (grey) and (d) half-hourly FCH4 (red) and NMENN (grey).
Half-hourly fluxes were calculated with EddyPro v.6.2.0 (LI-COR). The
software performed statistical assessments (Vickers and Mart, 1997),
performed low- and high-frequency spectral corrections (Moncrieff et al., 1997
and 2004), performed a double rotation (Wilczak et al., 2001), applied the WPL
correction to account for density fluctuations (Webb et al., 1980),
and computed quality control (qc) flags (Mauder and Foken, 2004). Post-processing treatments included storage correction (calculating the
net flux as the sum of the observed scalar flux and the rate of change
in scalar concentration at zm), filtering fluxes by
friction velocities (u∗) below 0.1 ms-1,
removing qc flags = 2 (Mauder and Foken, 2004), and the mean
absolute deviation spike removal algorithm (Papale et al., 2006).
Additionally, observations with mean winds of 220±30∘ were removed to avoid uncertainties associated
with the wake of the sonic anemometer, and observations were removed
during precipitation events and when the open-path analyzers indicated
there were any other obstructions within the path (Aubinet et al.,
2012). The data were gap-filled using neural networks (NNs) which have
been applied to FCO2 and FCH4 in other
studies (Moffat et al., 2010; Dengel et al., 2013). Details of the NN
methodology are described in Appendix A.
The flux footprint represents the influence of upwind areas on a
measured scalar flux, and the footprint climatology is the average of
individual footprints over a time period. Evaluation of the flux
footprints and climatology helps evaluate the reliability of the
dataset and estimate the source area of each individual half-hourly EC
flux measurement. A scalar flux Fc sampled at (0,0,zm), where zm is the height of
the EC instrumentation, can be represented as the integral of the flux
footprint function f(x,y) and the distribution of sources–sinks
(Qc) over a domain D (Kljun et al., 2015):
Fc0,0,zm=∫DQc(x,y)f(x,y).
The flux contribution of upwind source areas increases sharply upwind
from the measurement location to a peak and then decreases gradually with
increasing distance (Schmid, 2002). The empirically derived flux
footprint function of Kljun et al. (2015) was used to estimate the
source area of each half-hourly flux measurement.
The model requires boundary layer heights which were not measured
on site. Half-hourly boundary layer heights were interpolated from
3 h estimates obtained from the Global Data Assimilation System
of the US National Oceanic and Atmospheric Administration. The model
also requires the aerodynamic roughness length (z0), which is
influenced by the canopy height and spacing. Canopy height
(Ch) varied considerably within the basin (from >1m in the north to ∼0m in the bare-ground
areas). Canopy height variability was lower in the vicinity of the EC
tripod but ranged from 0.35 to 0.55 m with a few taller shrubs
approaching 1 m. Median z0 was calculated for 30∘
wind sectors following Paul-Limoges et al. (2013). This calculation
was performed for near-neutral conditions: -0.05≤zmL≤0.05, where L is the Obukhov length. The z0 for each wind
sector was found to be insensitive to zero-plane displacement height,
d, as zm≫d, so the mean value of d around the
tripod was used, where d=2/3Ch. Zero-plane
displacement did not change significantly over the course of the study
so z0 remained fixed over the study period for each wind sector.
For each half-hourly flux observation, f(x,y)i was solved at
1 m2 resolution over a 1 km2 domain centred on
the EC tripod. Then, f(x,y)i values were intersected with the surface
classes to determine the relative contribution of each surface type to
each flux observation (referred to as FShrub,
FSedge, etc.). The footprint function is technically
infinite so a fraction of each f(x,y)i was not contained within
the model domain. The out-of-domain source fraction ranged from
1.8 % to 4.9 % with a mean of 3.2 % and was assumed to
have minimal impact on the analysis. The flux footprint climatology
(FClim) was calculated by averaging the half-hourly flux
footprints over the study period and is shown in Fig. 1. Table 2 shows
the flux contribution of each vegetation class.
The surface cover class fractions of the basin, along with the mean
source area fractions of the footprint climatology (FClim) and the range
of source area fractions for individual half-hourly observations shown in
brackets.
In addition to EC measurements, fluxes of CO2 and
CH4 were sampled using a static non-steady-state chamber
flux technique on 11 dates between 12 July and 5 August 2016 (Laforce,
2018). Nineteen chamber collars were located at 10
sites, eight sites within and two outside the basin (Fig. 1). Each
surface cover class was represented by at least one chamber site,
except for open water. At each vegetated site a pair of collars were
installed 20 cm apart, except at the “sparse” site where
only one collar was installed. The above-ground biomass was removed
from one of the collars at each vegetated site. There were three
replicates (six collars) for the shrub class; two for the sedge;
grass, and upland tundra; and no replicates for the Sparse class. PVC
collars 30 cm long and 24.3 cm in diameter were
inserted to a depth of approximately 15 cm. The chambers were
34 cm tall and made out of polycarbonate covered in black
opaque tape to maintain dark conditions inside the chamber (for more
details, see Martin et al., 2018). The chambers contained a small
vent (10 cm coiled 1/8 in. diameter copper pipe) to ensure a
constant pressure during measurements. The opaque chamber fluxes of
CO2 provided an independent estimation of ER. This helped
characterize ER given the challenges with standard NEE partitioning
techniques at high-latitude sites during the Arctic summer as noted in
Sect. 2.5.1.
Chamber flux measurements were made between 09:00 and 17:00 starting at
a different collar set each day to randomize the sampling order to
avoid a bias due to diurnal patterns. During gas flux measurements,
the chambers were sealed to the top of the collars within a groove
filled with water, and five 24 mL air samples were collected
into evacuated 12 mL vials sealed with doubled septa. Each
vial contained a small amount of magnesium perchlorate to dry the air
sample. Samples were collected at 0, 5, 10, 15, and 20 min
after the chambers were set on the collars. Air within the chamber was
mixed with a 60 mL syringe attached to a three-way stopcock
before each air sample was taken. Samples were stored until analysis
1 month later at Carleton University. The integrity of the vials
through shipping, storage, and analysis was confirmed using a subset
filled with helium before the field season began.
Concentrations of CO2, CH4, and N2O were
determined using a CP 3800 gas chromatograph (Varian Inc., Palo Alto,
CA, USA) as described by Wilson and Humphreys (2010). Three replicates of five CO2/CH4 standards
varying from 383.1 to 15 212.6 ppmCO2 and from
1.08 to 22.11 ppmCH4 were included in every set of
measurements to create a linear relationship between gas concentration
and chromatogram area. The chamber fluxes of CO2 and
CH4 (FC) were calculated as follows:
FC=VPARTdcdt,
where (dc/dt) is the linear rate of change in the
mixing ratio of the gas, A is the chamber area
(0.0464 m3), V is the chamber volume (between 0.0182 and
0.0242 m3 adjusted for collar depth at each collar
location), R is the ideal gas constant, P is pressure in pascals, and
T is the air temperature in kelvin. P and T values corresponding
to the time of each measurement were obtained from the EC
station. Visual inspection of the linear trend of gas concentrations
(dc/dt) was used to identify and remove spurious point measurements
associated with analysis errors, leaking chambers (isolated decreases
in concentration), and contamination or ebullition events (isolated
increases in concentration) (0.3 %, 0.7 %, and 2.0 % of
CO2 samples and 2.1 %, 0.5 %, and 1.1 % of
CH4 samples, respectively). In all flux measurements, at
least three or more gas samples remained so that dc/dt and its
coefficient of determination (R2) were determined using least-squares
linear regression. We did not use R2 as an additional quality control
criterion as many of our CH4 fluxes were near zero and
tended to have low R2 values due to only small variations in the point
sample concentrations (see also Clark et al., 2020). A total of 40 % and
32 % of the 227 CH4 flux measurements and 97 % and
92 % of the 227 CO2 flux measurements had R2 over 0.80
and 0.90, respectively. No flux measurements were removed from the
analysis. Positive fluxes indicate emissions of gases to the
atmosphere, and negative fluxes indicate uptake by the surface.
Upscaling
Chamber fluxes of ER were upscaled from the plot scale (individual
chamber) to the footprint scale using the footprint-weighted average
method and to the basin scale using the area-weighted average method
(Budishchev et al., 2014). The chamber ER and air temperature from the
EC tripod (Ta) were used to determine R10, the base
respiration at 10 ∘C, and Q10, the
temperature sensitivity coefficient, using Eq. (3) for five of the six
surface classes (Fig. 1) (Laforce, 2018) (Table 3).
ER=R10Q10(Ta-10)10
Half-hourly footprint-scale estimates (ERFS) were
calculated by multiplying ER derived from Eq. (3) for each surface
class by the footprint source area fraction and summing over
classes. Basin-scale estimates (ERBS) were estimated the
same way but using the mean source area fractions of the basin
(Table 2). As there were no open water class ER estimates, ER from
open water was assumed to be zero.
The ER temperature sensitivity (Q10) and base respiration
(R10) estimated by Laforce (2018) and estimated from nighttime EC
footprint observations.
In contrast to ER, there are no standard empirical functions to
estimate temporal variations in NME. Instead, we used ordinary least-squares regression (OLS) to estimate NME. The most important
environmental controls over FCH4 were VWC and
Ts (discussed below). Continuous observations of these
factors at the flux chambers were not available; instead chamber NME values
were grouped by vegetation class and fit to VWC and
Ts measured in the soil pits near the EC station. Half-hourly footprint-scale (NMEFS) and basin-scale
(NMEBS) estimates were then made using the OLS
parameters for each surface class using the same procedures for
ERFS and ERBS.
Factor selection and gap filling
We used an exploratory approach to identify the smallest set of
factors that best predicted half-hourly EC-derived NEE and NME without
overfitting the dataset using a series of neural networks (NNs). We
started with 10 factors: four meteorological variables (PPFD,
Ta, vapour pressure deficit (VPD) computed using
the Ta and relative humidity (RH) data, and three-dimensional wind speed (U)
measured using the CSAT3 sonic anemometer), two soil variables
(VWC and Ts averaged between the two soil pits
near the EC tripod), and four source area fractions (shrub, FShrub; grass, FShrub; sedge
FSedge; and upland, FUpland). The four
source area variables correspond to surface classes sampled by the
chambers. We excluded water (FWater) and sparse
(FSparse) fractions because its average contribution to
the EC observations was only 0.2 % and 2.2 %, respectively,
and there were no chamber measurements for the water class while
chamber measurements indicated ER was low and NME was not
significantly different from zero for the sparse class. A number of
these prediction factors were highly correlated, but it was necessary
to include them so the model could account for source area
heterogeneity.
The NNs were trained iteratively on bootstrapped datasets. First NNs
were trained on each factor individually, and the one with the lowest
mean squared error (MSE) was selected. Next, NNs were trained on that factor in combination
with one of the remaining nine. The best performing additional factor
was again selected, and this process was repeated until MSE failed to
improve. The most parsimonious model was identified using the 1
standard error (SE) rule. Dybowski and Roberts (2001) give
the standard error of a bootstrap estimate of a given error metric
(e.g. θ=MSE) to be
SEboot(θ)=1B-1∑b=1B(θb-θboot)2,
where θboot is the mean of the bootstrapped
samples. The smallest set of factors where θboot was
within one SEboot of the minimum θboot
for both NEE and NME was selected for further analysis. The outputs
from the selected models are referred to as NEENN and
NMENN. NN modelling was done using the Keras
Python library (Chollet et al., 2015); see Appendix A for a more
detailed explanation of the NN analysis.
Multiple imputation (MI) was then used to gap-fill the NEE and
NME with the NEENN and NMENN, respectively
(Vitale et al., 2018). Of the 1296 half-hourly flux observations
28.9 % of FCO2 and 31.3 % of FCH4 were
missing or filtered out. There were a few gaps in the source area
fractions needed to gap-fill the flux time series because the
footprint function is not valid when u∗<0.1ms-1. When source area fractions were missing, they
were gap-filled by using the mean source area fraction observed for
winds within ±5∘ of the observed wind direction. The
meteorological and soil data were continuous and did not need to be
gap-filled.
Flux partitioning
NEE is negative when there is net uptake of CO2 by the
ecosystem and positive when there is net emission. ER and GPP are
always positive, ER represents the sum of heterotrophic and
autotrophic respiration, and GPP represents photosynthetic uptake of
CO2. Night-time NEE observations (e.g. PPFD≤10µmolm-2s-1) are typically used to quantify
ER because GPP is ∼0 (Aubinet et al., 2012). We fit the limited
night-time EC observations available (n=95) to Eq. (3) for
comparison with the ER measured using the chambers. We used the fitted
values to model daytime ER and approximate NEE by fitting the daytime
data to a light response curve (Aubinet et al., 2012).
NEE=12cαPPFD+β-(αPPFD+β)2-4αβcPPFD+ER
Here α is the initial slope of the light response curve,
β is GPP at saturation, and c is a curvature parameter. These
estimates are referred to as ERQ10 and NEEQ10.
Some NN analyses of NEE have trained separate models for night-time
and daytime conditions for partitioning purposes (Papale and
Valentini, 2003). However, these methods are not practical during the
Arctic summer as the sun did not set at Illisarvik until 28 July, over
halfway through the study period. There were not enough night-time
samples to train a separate NN. Instead, we estimated ER by
calculating NEENN at
PPFD = 0 µmolm-2s-1 for all observations,
henceforth referred to as ERNN. This is a projection
outside of the observed parameter space resulting in greater
uncertainty and a wider confidence interval around ERNN
than NEENN. Calculation of confidence intervals for NN
outputs is discussed in Appendix A.
Factor analysis
The trained NNs were used to investigate how individual factors
influenced NEE and NME. The partial first derivative of the model
response to one controlling factor was calculated while keeping all
other inputs fixed. For example, the partial first derivative,
∂NEE∂PPFD, is an
approximation of the NEE light response curve under a specific set of
conditions. Similarly, NMENN can be used to approximate
NME response to controls like VWC or Ts. For both
fluxes, the selected models contained at least one source area
fraction variable, indicating the vegetation type(s) which had
significant influence over NEE and NME. Additionally, we mapped
NEENN and NMENN to 100 % coverage for
individual surface classes to see how fluxes at Illisarvik may change
as vegetation succession continues. For example, to project to
100 % sedge coverage, we set the other surface classes to 0 %
and left the other environmental factors unchanged. This allows for an
estimation of how carbon fluxes may change if vegetation succession
leads Illisarvik to look more like the DTLBs studied in Alaska.
Results
During the 29 d study, half-hourly Ta and
Ts ranged between 0.4 and 26.2 ∘C and
4.4 and 11.0 ∘C, respectively (Fig. 2a). Day length
and maximum solar altitude decreased from 24 to 19.25 h and
41.6 to 35.4∘, but daily PPFD was more
influenced by variations in cloud cover. Precipitation (19 mm)
fell on 14 of the 28 d with trace snowfall on three of those
days, but VWC of the soils decreased throughout the period
(Fig. 2b). At the onset of the study period, VWC was high and
soils were saturated with ponding in the sedge areas. By the end of
the study most of this surface water had dried up. On 11 July average
thaw depth (cm) was 37, 45, 51, 64, and 81 at upland, sedge, grass, shrub,
and sparse classes, respectively. By 6 August, average thaw depth had
increased to 45, 62, and 66 cm at upland, sedge, and grass
surface classes and over 100 cm at both the shrub and sparse
classes.
A strong low-pressure system stalled off the coast between day of year
(DOY) 199 and 204. This caused westerly winds to occur much more
frequently than is typical for July and August. The 50 %, 80 %,
and 90 % flux FClim contours are shown in
Fig. 1a. Mean source area fractions indicate the EC observations were
skewed towards the grass surface class and under-sampled for the shrub
class, but the range of surface classes sampled was diverse enough to
allow for testing of the impact of source area fraction on the fluxes
(Table 2).
EC observations
Half-hourly observations of FCO2 and
FCH4 along with the NEENN and
NMENN used to gap-fill the time series are shown in
Fig. 2c and d. Gap-filled daily NEE ranged from -3.7 to
-0.2 gC-CO2m-2d-1 with a mean of
-1.5 [CI95%±0.2] gC-CO2m-2d-1. Day-to-day variability was considerable but
there was no notable trend in NEE over the peak growing season. The
half-hourly NEE during the study period reached a minimum of
-10.4 µmolCO2m-2h-1 just before
solar noon and peaked at 4.7 µmolCO2m-2h-1 around midnight (Fig. 2c). NEENN was
used to gap-fill the flux data because it was in good agreement with
FCO2 observation (r2=0.91). Daily
ERNN was estimated to be 2.2 [CI95%±0.9] gC-CO2m-2d-1 with corresponding GPP
of 3.7 gC-CO2m-2d-1. ERNN was in poor agreement (R2=0.35, n=95) with night-time FCO2
observations. For comparison, Eq. (3) provided a better fit (R2=0.47) with night-time EC data, and ERQ10 was estimated to be
3.0 gC-CO2m-2d-1. However,
NEEQ10 did not fit FCO2 as well (r2=0.80)
as NEENN.
Gap-filled daily NME was modest and decreased over the study
period. It ranged from 2.0 to 25.1 mgC-CH4m-2d-1 with a mean of 8.7 [CI95%±0.4] mgC-CH4m-2d-1 (Fig. 2d).
NMENN was used to gap-fill the flux data because it
provided a reasonable fit (r2=0.62) to FCH4
observations. NME did not constitute a significant component of the
carbon balance and thus the flux footprint area was a carbon sink
during the peak growing season with negative global warming potential (GWP) after accounting for
the greater GWP of CH4 (IPCC, 2104).
Chamber observations
ER was highest in the sedge, upland, and grass classes where fluxes
were very similar at 5.5 [CI95%±1.2], 5.4
[CI95%±1.2], and 4.9 [CI95%±0.7] gC-CO2m-2d-1. Shrub ER was
significantly less (3.5 [CI95%±0.6] gC-CO2m-2d-1) than the
other vegetated classes, and sparse ER was the lowest among the classes
(2.0 [CI95%±0.3] gC-CO2m-2d-1)
(Fig. 3a). The Q10 and R10 values also differed between
vegetation classes: ER in the sedge class was the most sensitive to changes
in air temperature, and modelled values provided the best fit (R2=0.82) to observations. Upland and grass had the highest base
respiration and fit observations moderately well (Table 3).
Box plot of (a) ER, (b) NME, and (c) NME fluxes measured using closed
chambers, grouped by vegetation class. The orange lines represent the
median, blue stars represent means, the boxes indicate the interquartile
range (Q1–Q3), the whiskers indicate Q1-(1.5×IQR) and
Q3+(1.5×IQR), and
the circles represent outliers extending beyond the whiskers. Note the scale
for (c) sedge is different.
NME was more variable between vegetation classes than ER (Fig. 3b and
c). Sedge was a very strong CH4 source at 114.7
[CI95%±15.3] mgC-CH4m-2d-1. Shrub and
grass were very weak sources, 0.7 [CI95%±0.3] and
0.4 [CI95%±0.3] mgC-CH4m-2d-1,
respectively. Sparse was neutral. Upland was a net CH4 sink
-1.1 [CI95%±0.4] mgC-CH4m-2d-1. Sedge and shrub NME values were positively
correlated with Ts (r=0.61, p<0.01; r=0.35, p=0.04) and VWC (r=0.58, p<0.01; r=0.5, <0.01). They also had a positive correlation with
Ta, while upland NME was negatively correlated with
Ta. Grass and sparse did not have any significant
correlations.
Footprint-scaled chamber fluxes were 59 % and 47 % higher than
ERNN or gap-filled NME, respectively. Mean
ERFS was
3.5 gC-CO2m-2d-1
[CI95%±0.1], it fit ERQ10 very well (R2=0.95) as would be expected and ERNN moderately well
(R2=0.46). Mean NMEFS was 12.8 [CI95%±1.3] mgC-CH4m-2d-1; it did
not fit NMENN well (R2=0.30). At the basin scale,
ERBS (3.4 [CI95%±0.1] gC-CO2m-2d-1) was slightly
lower than ERFS because of the exclusion of upland
areas. NMEBS was higher (15.2 [CI95%±0.1] gC-CO2m-2d-1) because of
the greater sedge fraction in the basin than the footprint
(Table 2).
NEE response to environmental factors and vegetation type
NEENN (r2=0.91) was estimated using four factors:
PPFD, VPD, VWC, and
FShrub. PPFD is the primary control over NEE: a NN
trained on PPFD alone provided a reasonable fit (r2=0.83). The three additional factors, VPD, VWC, and
FShrub, helped NEENN fit a wider variety of
conditions. Examining the partial first derivative of
NEENN under different conditions provides interpretation
of the modelled light response curves (Fig. 4). The minimum values
represent the peak light use efficiency and are analogous to α
in Eq. (5) (Fig. 4b). With increasing PPFD, light use becomes
less efficient and approaches zeros as the light response nears light
saturation (Fig. 4b).
(a) Modelled NEE response to PPFD under different VPD conditions
and (b) the partial first derivatives of NEE with respect to PPFD. (c)
Modelled ER (dashed line) and NEE (solid line) response to VWC at different
Shrub% values and (d) the partial first derivatives of ER (dashed lined) and
NEE (solid line) with respect to VWC. NEE in (c) was calculated at PPFD = 600 µmolm2s-1. The shaded areas in (a) and (c) are
95 % confidence intervals and grey circles are the EC observations.
VPD was a secondary control over NEE. Increasing VPD
increased peak light use efficiency and net CO2 uptake until
a threshold, above which it had a strong limiting effect (Fig. 4a and
b). For example, under dry atmospheric conditions
(e.g. VPD = 1.5 kPa), peak light use is less efficient
(-12 nmolCO2µmol-1 photon) than under more
humid conditions (-18 nmolCO2µmol-1
photon). The value of this VPD threshold was dependent upon soil
moisture: from 1 kPa when VWC was highest to
0.25 Pa
when VWC was low. Mapping NEENN and
ERNN at FShrub=100 %, FShrub=0 %, and FShrub=36 % (FClim)
shows that VWC and FShrub were the primary controls
over ER and thus influenced NEE (Fig. 4c and d). We can see from the
partial first derivates of NEENN that increasing
VWC increases ER from shrub areas. In the absence of shrubs,
increasing VWC inhibits ER, although it is important to note
that variations in VWC were subtle, ranging from 51.7 % to
59.0 %. The partial first derivative of NEENN shows
that VWC slightly limits NEE from non-shrub areas and
significantly reduces it in shrub areas.
NME response to environmental factors and vegetation type
NMENN (r2=0.62) was estimated using five factors:
FSedge, FShrub, VWC, TS,
and U. NME was more variable and less dependent on any one factor
than NEE, which is why the NMENN needed an extra factor and
had a lower r2 score. The source area had a significant effect on
NME, and it was encouraging that the model contained
FSedge and FShrub since sedge and shrub were the strongest
CH4 source and largest footprint component,
respectively. These two factors can combine to map NME under three
general situations: we can extrapolate to FSedge=100 % and FShrub=0 % or FSedge=0 % and FShrub=100 %, or we can represent actual
FClim, where FSedge=11 % and
FShrub=37 % (Table 2). Some upland tundra was
included in theFClim estimate, which reduced NME.
(a) Modelled NME response to VWC at different source area fractions
and (b) the partial first derivatives of NME with respect to VWC. (c) Modelled
NME response to Ts at different source area fractions and (d) the
partial first derivatives of NME with respect to Ts. The shaded areas
in (a) and (c) are 95 % confidence intervals and grey circles are the EC
observations.
VWC was the primary climatic driver identified by
NMENN. Wetter soils had a consistent positive effect on
NME, which was strongest when FSedgewas high (Fig. 5a and
b). Between the driest and wettest conditions, estimated NME increased: by
an order of magnitude at FSedge=100 %, 4-fold at
FShrub=100 %, and from neutral to a source at
FClim (Fig. 5a). Higher Ts generally had a
negative effect on NME (Fig. 5c and d). The negative correlation
between Ts and VWC (r=0.54, <0.01) may have
contributed to this result. NMENN performance improved
less with the addition of U, indicating the NMENN was
near saturation and its effects are less relevant. Higher U had a weak
limiting effect on NME when VWC was high and increased NME when
VWC was low (not shown).
DiscussionCarbon balance and controlling factors
Compared to other DTLBs, Illisarvik has drier soils and greater shrub
and grass cover (Table 4). Peak growing season CO2 uptake at
Illisarvik was greater than at most wet-sedge-dominated DTLBs
(Table 4; Zona et al., 2010, Sturtevant and Oechel, 2013; Lara et al.,
2015). These differences may be due to differences in the periods of
observation and year-to-year variability but may also be due to the
presence of more productive shrubs and slightly warmer climate at
Illisarvik. Mean 1980–2010 Ta at Utqiaġvik (formerly
Barrow, AK) is -11.2 ∘C (US National Climate Data
Centre, 2020). Tuktoyaktuk, the closest
station to Illisarvik, is 1.1∘ warmer. Shrub cover is expected
to have a number of impacts on the microclimate and carbon cycle of
Arctic tundra (e.g. Myers-Smith et al., 2011). Typically, greater
deciduous shrub cover is expected to increase GPP as a result of
greater leaf area and photosynthetic potential compared to
graminoid-dominated tundra (Sweet et al., 2015; Street et al.,
2018). GPP was greater at Illisarvik compared to the young wet-sedge-dominated DTLBs in Alaska (Zona et al., 2010). It was more similar to
Katyk, which has significant dwarf-shrub cover, predominately
Betula nana and Salix pulchra (van der Molen et al.,
2007).
Growing season (gs) daily range in eddy-covariance-derived NEE and
NME from drained thermokarst lake basins (DTLBs) and other select
wetland and coastal tundra sites across the Arctic.
SiteSite characteristicsNEE g C-CO2m-2d-1NME mg C-CH4m-2d-1StudiesIllisarvikYoung DTLBs,low and tallshrub/grass/wet sedge-1.58.7(this study)Various DTLB, Barrow Peninsula, AlaskaYoung DTLB,wet-sedge tundra-1.1b, -0.9d, -0.8c18.4a, 26.1d, 44.0cZona et al. (2009)a and (2010)b, Sturtevant and Oechel (2013)c, Lara et al. (2015)dMedium DTLB,wet-sedge tundra-0.7b, -0.6d, -0.4c27.0d, 41.3cOld DTLB,wet-sedge tundra-1.0b, -0.4d, 0.1c24.2d, 38.7cAncient DTLB,wet-sedge tundra0.4d21.7dKatyky, Indigirka lowlands, SiberiaAncient DTLB,dwarf-shrub andwet-sedge tundra-1.3e36.0fVan der Molen et al. (2007)e, Budishchev et al. (2014)f
The periods of study
measurements for the study observations are as follows.a Mid-June–end of July.b 12 June–28 August 2007, Fig. 4.c 11 June–25 August 2011.d Upscaled
chamber estimates, exact dates not specified.e Mean 15 June–31 August 2003–2006.f 5 July–4 August 2009.
Differences in ER among tundra environments can be related to
substrate availability, soil moisture and temperature, and thaw depth,
among other factors (Sturtevant and Oechel, 2013). The “snow-shrub
hypothesis” (Sturm et al., 2001) describes the potential for greater
snow trapping in shrub communities which insulates soils in winter,
leads to increased decomposition and nutrient availability, and
promotes further shrub growth. At Illisarvik, snow blowing in off the
Arctic Ocean results in large snow drifts within the basin where snow
depth correlates with vegetation height (Wilson et al., 2019). Wilson
et al. (2019) concluded that the soils within the Illisarvik basin
were warmer than those of the surrounding dwarf-shrub tundra in part
through these snow–shrub interactions. Although our chamber
observations suggested shrub ER is lower than ER from other vegetation
classes, this may have been an artifact as the taller shrubs (>40cm) could not fit inside the chambers. In another study,
chamber ER increased with greater shrub cover in upland tundra (Ge
et al., 2017). ER at Illisarvik was greater than the ER observed at
both the young wet-sedge DTLB in Barrow (Zona et al., 2010) and at the
shrub–wet-sedge DTLB at Katyk where thaw depth was much shallower (45
to >100cm at Illisarvik vs. 25 to 40 cm at Katyk;
van der Molen et al., 2007). The importance of FShrub in
describing temporal variations in half-hourly NEE within the flux
footprint at Illisarvik is further evidence of the importance of shrub
cover on tundra carbon cycle processes in this environment.
PPFD and VPD were the most important factors for
predicting half-hourly NEE. This was to be expected as they are
typically the primary controls over GPP (Aubinet et al., 2012). The
limiting effects of VPD are consistent with another study using NN to
analyze NEE at a deciduous forest site (Moffat et al.,
2010) and have been found at other tundra sites
(Euskirchen et al., 2012; López-Blanco et al., 2017). VWC
was also important at Illisarvik. Zona et al. (2010) found VWC
could explain 70 % of the variability in daily peak season ER in a
young DTLB. Similarly, Kittler et al. (2016) found drier soils
increased ER and decreased NEE after a wet tundra drainage experiment
in Siberia, consistent with our results at Illisarvik when
FShrub was low.
As expected, NME at Illisarvik was about half that observed at the
Alaskan DTLB sites where soils were wetter with greater sedge cover
(Table 4, Zona et al., 2009; Lara et al., 2015). NME at Katyk was even
higher than the Barrow DTLBs and had a significant impact on the
greenhouse gas (GHG) balance for this site (van der Molen et al.,
2007; Parmentier et al., 2011). In our NN modelling of NME at
Illisarvik, FSedge was the most important factor for
predicting half-hourly FCH4. Sedges are aquatic plant
species with aerenchymatous tissues that act as conduits for
CH4 from below the water table to the atmosphere and limit
CH4 oxidation by methanotrophs in aerobic surface soils (Lai
et al., 2009). The inclusion of FShrub
further refined the model, allowing it to better fit the site-specific
distribution of vegetation types. Budishchev et al. (2014) found shrub
and sedge fraction had a significant influence on FCH4
at Katyk. Vegetation type is the dominant control over NME across
multiple tundra landscapes and our results further support that
(Davidson et al., 2016).
VWC was the second most important factor, which was expected as
CH4 production occurs in anaerobic environments and has been
linked to variability in CH4 emission in many other studies
(e.g. Zona et al., 2009; Nadeau et al., 2013; Olefeldt et al.,
2013). Soil temperature (Ts) was the third most
important factor. Higher Ts values increase the oxidation
potential of methanotrophs (Liu et al., 2016; King and Adamsen, 1992),
so this result was expected for the drier portions of the basin and
upland tundra. However, this was not expected for the sedge areas
because most studies find NME in sedges is positively correlated to
Ts (Olefeldt et al., 2013). The negative correlation
between Ts and VWC may partly explain this.
Upscaling
ERFS and NMEFS were about 59 % and
47 % greater than the gap-filled EC estimates. Discrepancies
between EC and chamber observations are common and have been
attributed to differences in measurement techniques, the small sample
size of chamber observations, and sampling bias since all chamber
measurements were taken during the day with fair weather (Katayanagi
et al., 2005; Chaichana et al., 2018). Meijide et al. (2011) found
that chamber NEE could be up to twice as large as EC observations, and
Riederer et al. (2014) also found chamber NME estimates were about
30 % higher than EC estimates. Others have been more successful,
yielding upscaled chamber NME fluxes within 10 % of EC
observations (Zhang et al., 2012; Budishchev et al., 2014; Davidson
et al., 2017). A potential reason for the disagreement with
ERFS may be the lack of direct observations by the EC
system under low-light conditions. Another potential source of error
for the upscaling is inaccuracies in the vegetation map.
Future trajectories
Presently, peak growing season carbon uptake at Illisarvik is greater
than similarly aged landscape features on the Barrow Peninsula, Alaska,
and more similar to levels observed at Katyk, Siberia. NME is well
below levels observed at any other DTLB studied, making this site a
stronger GHG sink than other DTLBs. However, the basin at Illisarvik
will continue to evolve, and the trajectory it takes could
significantly alter its carbon balance. Historically, DTLBs on
Richards Island and the Tuktoyaktuk Peninsula evolve into sedge
wetlands, as do DTLBs on the Barrow Peninsula (Ovendend, 1986; Lara
et al., 2015). Active maintenance of the outlet channel at Illisarvik
has artificially lowered soil moisture and flooding and potentially
limited this transition thus far (C. Burn, personal communication,
2016).
If Illisarvik follows the same trajectory as older DTLBs in the area
and becomes dominated by sedge wetlands, NME will increase
significantly. Figure 5a shows that with extrapolations to full sedge
cover (FSedge=100 %), NME would be similar to values
on the Barrow Peninsula (Zona et al., 2009). If the basin instead
transitions into a shrub-dominated DTLB similar to those of Old Crow
Flats, Yukon (Lantz and Turner, 2015),
NMENN would remain similar to current levels, meaning the
basin would remain a weak source of CH4. These are
projections well beyond FClim fractions observed, so
confidence in the specific values predicted is low.
The effects of changing shrub and sedge cover on Illisarvik's growing
season NEE are less straightforward than on NME, partly because shrub
cover had less overall influence on
NEENN. Figure 4c shows that the model suggests ER decreases
and NEE increases with increasing shrub coverage when soils are
slightly drier but has the opposite effect under wetter
conditions. To our knowledge, only a few winter season (e.g. Zona
et al., 2016) and no year-round studies of DTLB NEE and NME have been
published to help evaluate the factors influencing carbon losses
through the non-growing-season months. Further observation year-round
is needed to better understand the implications of continued
vegetation change for the carbon balance of DTLBs such as Illisarvik.
Conclusions
This study investigated NEE, GPP, ER, and NME in the Illisarvik
experimental DTLB using EC and chamber data. To our knowledge this is
the first such study conducted in a DTLB outside of the Barrow
Peninsula or Siberia. Illisarvik is a carbon sink during the growing
season with NME only having a small effect on the net carbon
balance. Our flux observations were generally in agreement with other
studies but show how shrub-dominated DTLBs such as Illisarvik and
Katyk in Siberia differ from sedge-dominated DTLBs on the Barrow
Peninsula. Illisarvik's growing season net carbon uptake was greater
than young and ancient DTLBs on the Barrow Peninsula and more similar
to the shrub-dominated ancient DTLB in Siberia. NME at Illisarvik was
lower than all published DTLB studies, likely due to better drainage
and more diverse vegetation. A longer, more comprehensive study would
be needed to resolve the annual carbon budget for Illisarvik.
Chamber measurements of ER and NME from different land cover classes
within and outside the Illisarvik basin added context to the EC
observations. Vegetation class (and associated difference in terrain
and soil properties) had only a small but significant impact on NEE
and ER but was one of the dominant controls over NME. Sedge areas were
a strong source of CH4, other vegetation types in the basin
were weak sources, and upland areas were a net sink. These results
suggest that NME in particular will change as the Illisarvik DTLB
vegetation communities continue to evolve.
Neural network analysis and uncertainty calculations
Typically, NEE is gap-filled using flux-partitioning algorithms that
model ER and GPP separately using TS and PPFD,
respectively (e.g. Lee et al., 2017; Aubinet et al., 2012). However, this method requires night-time observations
and thus does not perform well for Arctic summertime measurements due
to the limited number of samples available during low-light
conditions. There are no widely agreed upon functional relationships
for gap-filling NME since CH4 production and consumption
vary considerably between both different land cover types and
environmental conditions. Some methods that have been used include
general linear models (GLMs) (Zona et al., 2009), mean diurnal
variation (Nadeau et al., 2013), and classification and
regression trees (CARTs) (Nadeau et al., 2013; Sachs et al., 2008). We
attempted to use a GLM and CART but they were not flexible enough to
account for source area variability.
Neural networks (NNs) are flexible machine-learning methods that are
ideally suited to perform non-linear, multivariate regression. They
make no a priori assumptions about the functional relationships
between the factors and responses (Melesse and Hanley, 2005; Desai
et al., 2008). NNs are universal approximators; given enough hidden
nodes a NN is capable of mapping any continuous function to an
arbitrary degree of accuracy (Hornik, 1991). If all relevant climate
and ecosystem information is available to a network, the remaining
variability can be attributed to noise in the measurement (Moffat
et al., 2010).
NNs have been shown to be among the best performing methods for
gap-filling NEE data for temperate forest and wetland sites (Papale
and Valentini, 2003; Moffat et al., 2007; Knox et al.,
2016). They have also been used to gap-fill NME time series in
sub-Arctic wetlands, tundra sites, and wet-sedge tundra (Dengel
et al., 2013). NNs have been used to identify and model factors
influencing NEE and to partition NEE into ER and GPP (Moffat et al.,
2010). NNs have even been used to upscale fluxes from the ecosystem
level to the continental scale (Dou and Yang, 2018; Papale
et al., 2003).
A NN approximates a true regression function F(X):
F(X)=t(X)-ε(X),
where t(X) is the target function and ε(X) the noise
(Khosravi et al., 2011). X=[x0,x1,…,xM], where x0=1 is a bias term and [x1,…,xM]
represents the independent variables. M denotes the number of independent
variables. The network approximates F(X) as f(X,w) by mapping the
relationship between X and the target. Here we used feed-forward
dense NNs with a single hidden layer:
fX,w=∑h=1Hβhg∑m=0Mγhmxm.g(⋅) is a non-linear transfer function; here we
used the rectified linear activation unit (ReLu) (Anders and Korn,
1999). H denotes the number of hidden nodes in the network and must
be assigned before training. Too many hidden nodes and the NN will
overfit the training data, too few and it will underfit. Early
stopping will prevent NNs from overfitting training sets (Weigend and Lebaron,
1994; Tetko et al., 1995). Therefore, it is
more important to ensure a NN has enough hidden nodes to adequately
map the target function (Smith, 1993). We set H to a function of M, the number of targets (1), the number of training samples (N), and a scaling parameter (a) which was set to 2:
H=Na×(M+1).
This rule of thumb ensures a NN has sufficient flexibility to
approximate the target response. The weights w=[β1…βN,γ10…γNM] are randomly
initialized and after each model iteration are updated by
back-propagating the error through the network. N denotes the number
of observations or targets. The error metric most commonly used is the
mean squared error, MSE:
MSE=∑i=1Nf(Xi)-ti2.
The weights are adjusted in the direction that will decrease the error,
and training continues until a stopping criterion is reached. We chose
to set aside 20 % of the training data as a test set to be used
for early stopping, and we terminated training when the MSE of the test
set failed to improve for 10 consecutive iterations.
The averaged mean squared error (θ) of the bootstrapped
neural network model validation datasets, with error bars showing 1
standard error (SE). The x axis shows models of increasing size from left to
right (one to nine factors), and the label indicates the factor added to the model
at each step. The blue line indicates the 1 SE rule threshold, and the red
bar indicates the model selected by the 1 SE rule.
FCH4 estimated by a RF using the same factors as the NN
model. The colours correspond to the scenarios in Fig. 5a. VWC was estimated
over the range from 0.45 to 0.65.
Bootstrapping is used to account for model variability and estimate
confidence and prediction intervals by training NNs on B different
realizations of the dataset, where B is the number of bootstrapped
samples, we used B=30 (Heskes, 1997; Khosravi et al.,
2011). An individual NN generates point outputs approximating a target
function with no information on the confidence in those estimates
(Khosravi et al., 2011). However, there are usually multiple
f(X,w) values that approximate F(X) because of the random
weight initializations (Weigend and LeBaron, 1994). As such, there are
two sources of error we are concerned with, the accuracy of our
estimation of F(X) and the accuracy of our estimates with respect
to the target. A confidence interval describes the first (e.g. F(X)-f(X,w)) while a prediction interval describes the
latter (e.g. t(X)-f(X,w)) (Heskes,
1997). By definition, a prediction interval contains the confidence
interval because
t(X)-f(X,w)=[F(X)-f(X,w)]+ε(X).
For b=1…B, a random sample with replacement of size p is
drawn from the original dataset. Setting p equal to the size of the
original dataset yields a set of B training sets each containing
approximately 67 % of the original dataset. The 33 % leftover
from each bootstrap sampled can be used for model validation (Heskes,
1997). The average of our ensemble of networks can then serve as our
approximation of F(X):
F(X)=1B∑b=1Bfb(X,w).
The variance of the model outputs is
σ2(X)=1B-1∑b=1Bfb(X,W)-F(X)2.
A confidence interval (CI) for F(X) can be calculated as F(X)±t(1-∝,df)σ(X), where
t is the Student t score, 1-α is the desired
confidence level, and df is the degrees of freedom which are set to
the number of bootstrapped samples B. NN performance can be seen to
improve with the inclusion of more factors, until the model saturates
and becomes over-parameterized (Fig. A1).
Random forests (RFs) are said to be among the best performing gap-filling methods for NME (Kim et al., 2020), and it has been claimed
that aggregating many regression trees in a RF prevents overfitting
(Breiman, 2001). We did not find this to be the case. Following the
methods outlined in Kim et al. (2020): a RF with 400 trees and no
restrictions on tree size fit FCH4 nearly perfectly
(R2=0.98). Without considerable limitations on tree size, the
RF will just learn the dataset rather than the relationships
present. It is our view that this tree is extremely overfit, as
highlighted by the example in Fig. A2. Further, RFs do not allow for
straightforward visualization functional relationships in a
dataset. Plotting FCH4 against VWC, which is the
dominant environmental control identified, does not reveal a meaningful
relationship like Fig. 5a and c. You can look at an individual
decision tree within the RF, but those are difficult to interpret
beyond the first few splits, and each tree will be different. Lastly,
RFs are incapable of projecting beyond the parameter space observed,
which limited their applicability for this study (Fig. A2). This
presents an issue because many gaps in EC data arise from data
filtering (e.g. clear calm nights, precipitation events) and are by
definition outside the parameter space observed.
Code and data availability
Our data and code are available on GitHub:
https://github.com/June-Spaceboots/Illisarvik_CFluxes (Skeeter, 2019).
Author contributions
JS, AC, and GH designed the EC study. AL and EH designed the chamber study.
JS collected, processed, and analyzed the EC data. AL and EH collected the
chamber data with help from JS. AL and EH processed the chamber data. JS
designed and conducted the NN analysis. JS prepared the manuscript with
input from all co-authors.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
Funding was provided by the Canada Foundation of Innovation and the Natural Sciences and Engineering Research Council (NSERC) of Canada. Additional logistical support was provided by the Polar Continental Shelf Program, Natural Resources Canada.
Financial support
This research has been supported by the Canada Foundation for Innovation – IF 2015 (grant no. 33600), NSERC Discovery Grants Program (grant no. RGPIN-2017-03958), NSERC Discovery Grants – Northern Research Supplement (grant no. RGPNS-503529), and NSERC Discovery Grants Program – Accelerator Supplement (grant no. RGPAS-507854).
Review statement
This paper was edited by Lutz Merbold and reviewed by Norbert Pirk and one anonymous referee.
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