Introduction
Methane is the third most important greenhouse gas after water vapor and
carbon dioxide, and its concentration in the atmosphere has increased from a
pre-industrial value of 0.7 parts per million by volume (ppmv) to its current
value of approximately 1.85 ppmv. Methane sources are varied, with major
contributors being anthropogenic (including fossil and agricultural) as well
as natural. Often multiple sources occur in the same vicinity, for example
emissions from gas wells collocated with agricultural fields or with pasture for
grazing livestock.
In the past few years there have been increased efforts to understand how
methane emissions, as well as carbon dioxide, might change from the Arctic
region in response to warmer temperatures and references
therein. For
example, temperatures in the Alaskan North Slope have increased
0.6 ∘C per decade for the last 30 years. Likewise, in that
same time period the minimum extent of Arctic sea ice at the end of the
summer has decreased from 8 to 5 million km2. Until this past
century late-summer sea ice extent was
10 million ± 1 million km2 over the past 1500 years
. Global methane concentrations have also varied during
this time period, with atmospheric increases slowing down in the 1990s,
leveling off in the early part of the 21st century and have been increasing again
since 2007 with concentrations reaching 1.8 ppmv in 2010 based on several
surface-based observation networks . It has been
postulated that the increase could be from Arctic wetlands
.
A brief look at the carbon stock in the Arctic reveals why it has garnered so
much attention. The Arctic permafrost region contains between 1330 and
1580 Pg of carbon in the tundra surface layer (0–3 m depth), yedoma
deposits, and rivers. An additional quantity is contained in deeper deposits
and sub-sea permafrost . Arctic carbon stock represents
about a third of the total global surface carbon pool and increases to 50 %
when accounting for the deeper soils . As the climate
continues to warm, this carbon is vulnerable to thaw and decomposition by
microbes, potentially leading to large increases in methane and carbon
dioxide emissions. Methane from anaerobic reduction of organic carbon stocks
in permafrost is particularly important, having a warming potential more than
twenty times that of carbon dioxide on a 100-year timescale and greater yet
over shorter time periods . The correlation between a
warming Arctic and the release of methane and carbon dioxide from northern
wetlands and ocean clathrates is strongly evident in the paleoclimate record
. This relationship is also seen (1) in current
observations of methane release from thermokarst lakes formed from melting
Arctic permafrost each spring and summer
, (2) in
ebullition from deep sea sediments ,
and (3) from airborne campaigns .
The North Slope of Alaska is covered by several different land classes though
dominated by permafrost. Access to the interior normally requires aircraft,
except along the Dalton Highway (Rt. 11) from Fairbanks to Prudhoe Bay. The
lack of infrastructure, especially roads, makes continuous ground-based
measurements difficult except near major settlements. This sparsity of
data increases the uncertainty in regional bottom-up estimates of carbon
flux. At the same time top-down estimates based on inversion modeling from
measured concentration profiles rely on knowledge of flux sources on the
ground to determine which sources are dominating the emissions in areas like
the North Slope, with its multitude of broad-scale emitters and point sources.
A scale gap exists between process-level studies on the ground and
large-scale regional estimates from remotely sensed data or inversion-model
results. Airborne measurements, especially from low-flying aircraft, have the
potential to bridge this gap. Flux measurements from low-flying aircraft
coordinated with surface measurements promote extension of the detailed
surface-flux measurements to the larger regional scale by mapping the
heterogeneity in the fluxes over these larger areas.
Eddy covariance is a direct way to determine in situ the exchange (flux) of
mass, momentum, and energy between the atmosphere and the surface. Turbulent
winds and concentrations are measured at a high sample rate, and their covariance
yields the flux. With stationary instruments the wind and concentration
measurements can be routinely obtained, and eddy covariance from fixed sites
is widely represented in the literature as a way of obtaining the flux of a
quantity between the surface and atmosphere. Obtaining eddy covariance
measurements from a moving aircraft presents some unique challenges including
accurately measuring turbulent wind velocity relative to the ground and
measuring concentrations at a sufficiently high data rate. Furthermore, if the
flux from the aircraft is to be a good proxy for a measurement taken at the
surface, it needs to be sampled close to the ground. The appropriate distance
varies depending on boundary layer height, turbulence, and the footprint size
of interest. Several groups have successfully measured carbon dioxide and
heat flux from low-flying aircraft in the Arctic , Europe
, Asia
, and continental USA .
Here we present methane fluxes taken during the summer of 2013 in the North
Slope of Alaska and use the data to explore several questions. For example,
how representative are towers' footprints of other instances of the remotely
determined land-cover class in which they were placed? In principle a
stationary site can measure all manner of properties and state variables in
the soil, the vegetation, and the air, within and above the canopy. Much can
be learned about the bacteria, soil chemistry, canopy storage, and other
quantities relevant to the exchange of mass, momentum, and energy with the
surface. But all of this is known only at a particular site. How
representative is that site of other locations that to remote sensors appear
similar? Are there land-cover classes that are particularly indicative of
emissions of a given trace gas? Can the land class so identified
be used as a quantitative predictor of a particular type of soil chemistry?
This is relevant in assessing the regional methane emissions from remote
sensing. Methane in particular has a fairly complex chemistry in the soil
involving state quantities such as the (sub-canopy) soil temperature and the
height of the water table. These are measurable only in situ, so that having
a proxy indicator such as vegetation cover would be valuable. Interval
quantities
sensible remotely, such as normalized difference vegetation index (NDVI), air
temperature, and other vegetative indexes that correlate with carbon dioxide
do not correlate with methane . Vegetation
classifications determined remotely, however, have been shown in other
regions to be useful for estimating regional methane emissions
e.g., in upscaling from ground measurements.
Aircraft, though more limited in what they can measure than fixed sites, are
very mobile providing the opportunity to sample many instances of the same
remotely sensed class over the landscape. From this multi-instance sample one
can assess how representative the single fixed site is. One can also assess
the strength of the variability within the given land surface class for later
investigation from the surface. In remote parts of the earth, in particular,
if surfaces of recognizably similar character (class) can be shown to have
comparable emissions properties, considerable effort can be saved over a
surface-based survey. Alternatively, large variation within a class that is
not currently well predicted by some remotely measurable interval quantity
will be seen as requiring additional effort for in situ measurements to find
an effective monitoring program for methane emissions from that surface class.
Methods
Picture of the FOCAL system flying near the NOAA/ATDD flux tower in
North Slope, AK.
Six
flight tracks flown by FOCAL during August 2013 are shown in white. Flights
are given in the figure as DD.HH:MM, where DD is the date in August and HH:MM
is the time (UTC -10) of the middle of the flight rounded to the nearest
half-hour. Flight tracks are shown only for the portions flown within 25 m
of the ground. The underlying chart gives the NSSI-assigned land-cover class
produced from LandSat 30 m Thematic Mapper data. The yellow triangle
locates the NOAA/ATDD flux tower.
To measure methane emissions over large areas of the North Slope, the Flux
Observations of Carbon from an Airborne Laboratory (FOCAL) system was flown
during August 2013 out of Deadhorse Airport, Prudhoe Bay, AK. FOCAL, pictured
in Fig. flying near the NOAA Atmospheric Turbulence
and Diffusion Division (NOAA/ATDD) flux tower, consisted of three main parts:
the aircraft, a Diamond DA-42 from Aurora Flight Sciences; a turbulence
probe, the Best Airborne Turbulence (BAT) Probe from NOAA/ATDD; and a fast
methane and water instrument from the Anderson Group at Harvard University.
Data presented in the results section were obtained during six flights
between 13 and 28 August (Fig. and
Table , Sayres and Dobosy, 2013).
During three of these flights the aircraft made repeated passes near the
NOAA/ATDD tower that was set up for comparisons. The other three flights were
flown as grid patterns over large regional areas
(∼ 50 km × 50 km) to better sample the heterogeneity of
different land types over a large region. These flights consisted
both of profiles from the bottom of
the boundary layer (∼ 5–10 m) up to ∼ 1500 m altitude and
also long transects (∼ 50 km) at
low altitudes (< 25 m) that are used to access surface flux using eddy
covariance.
Flights used in the analysis along with location, time of day, mean
air temperature, and surface land classes.
Flight date1
Location
Start time
End time
Temperature2
Dominant land classes3
DD.HH:MM
UTC -10
UTC -10
(∘C )
13.09:30
Tower
08:19
10:22
16
Sedge, Mesic sedge, Lakes, Sag River, FWM
25.18:00
Tower
17:43
19:49
5
Sedge, Mesic sedge, Lakes, Sag River, FWM
27.11:30
Western grid
09:40
13:00
6
Sedge, FWM, Lakes, Tussock tundra
27.19:00
Tower
16:46
20:02
10
Sedge, Mesic sedge, Lakes, Sag River, FWM
28.10:00
Western grid
08:39
11:39
11
Tussock tundra, Lakes, FWM, and Sedge
28.15:00
Eastern grid
13:59
15:44
16
Sedge, Mesic sedge, Lakes, Kuparuk River, FWM
1 All flights are during August 2013. DD is the local date of
the flight and HH:MM is the middle time of the flight rounded to the nearest
half-hour. 2 Temperature calculated as mean temperature recorded by
instrument during flight time and below 100 m.
3 Land classes are given in order of largest percent coverage first.
FOCAL instrumentation
Fluxes of trace gases are covariances between turbulent winds and
fluctuations in gas concentrations. The airborne methane flux calculations
rely on having fast measurements of both turbulent wind velocity and dry-air
mixing ratio, with the two quantities being coordinated in time and space to
within an error much smaller than the measurement interval.
To measure turbulent wind, temperature, and pressure NOAA/ATDD developed the
Best Aircraft Turbulence (BAT) probe in the 1990s as a pioneering low-cost solution for mobile
atmospheric turbulence measurements . The BAT probe consists of a hemisphere, 15.5 cm
in diameter, with nine pressure ports located at selected positions on the
probe head. The vertical and horizontal pairs of ports measure the
differential pressure between them to calculate the angle of attack and side
slip, respectively. Static pressure is taken from the average of the
pressures measured at the four diagonal pressure ports corrected for non-zero
attack and sideslip angles. Dynamic pressure is measured from the difference
between the pressure measured at the center hole and the static pressure,
again adjusted for non-zero values of the angles of attack and sideslip. These
pressure measurements are combined with a known model for flow over a
hemisphere to determine 3-D wind direction and speed relative
to the probe. The velocity of the probe relative to the ground is measured by
three interconnected instrument systems: a GPS/INS system located near the
center of gravity (CG) of the aircraft, accelerometers located in the probe,
and two additional GPS antennas, one on the BAT probe and the other atop the
main cabin . The BAT probe
digitizes samples at 1600 s-1, applies a low-pass filter to
suppress aliasing, and subsamples at 50 s-1. The wind
measurements are synchronized with the 50 s-1 signal from the
GPS/INS system.
Before the FOCAL
system was assembled, the BAT probe was
characterized in a wind tunnel . A similar BAT probe was
also tested in flight on a different aircraft hereafter
V2013. After the FOCAL system was assembled, similar
calibration maneuvers were flown in preparation for and during the Alaska
campaign. As part of a calibration flight on the evening of 27 August in
Alaska, we performed the yaw maneuver described by V2013 and obtained a
residual contamination less than 10 %, as described there. A pitch maneuver
described by V2013 was performed resulting in contamination of 10 % for the
high-frequency pitching (1.6 s period), which was the best executed of the
pitch test's three parts and is the severest test.
The methane instrument draws air from an inlet located 8 cm aft of the BAT
probe turbulence measurements. Flow of air through the axis is
controlled by a dry scroll pump located in the back of the aircraft. Air from
the inlet passes through 1.25 cm diameter tubes into the nose and forward
luggage bay sections of the aircraft. The pressure of the air is controlled
by a proportional solenoid valve and a pressure control board that uses
pressure measured at the detection axis to feed back on the valve orifice
position. The actual detection axis is located in the port-side forward
luggage bay. The methane instrument uses integrated cavity output
spectroscopy (ICOS) to measure CH4, H2O, and N2O
. The ICOS instrument uses a high-finesse optical cavity
composed of two high-reflectivity mirrors (R=0.9996) to trap laser light
for a period on the order of 2 µs producing effective path lengths
of 103 times the mirror separation. For the fast methane sensor used
in this deployment, a small ICOS cell (25 cm in length; mirrors 5 cm in
diameter) was built that combines the sensitivity and stability of ICOS with
a small sample volume to attain high flush rates (17 s-1),
permitting a sample rate of 10 s-1. Using the wavelength region
around 1292 cm-1 (7.74 µm), measurements of methane
achieved a precision of 7 ppbv (1σ, 1s). Due to the
high variability of water in the troposphere, water vapor measurements are
required with any trace gas measurements in order to quantify dilution
effects caused by changes in water vapor content as well as changes to
spectroscopic line broadening .
Well-defined absorption features of water vapor and its isotopologues as well
as nitrous oxide are obtained in the same sweep of the laser, therefore the
same instrument provides simultaneous measurements of nitrous oxide and water
vapor along with methane. This technique provides an extremely high
signal-to-noise ratio as well as robust measurement in flight and has been
the basis for several ICOS flight instruments built by this group
. Periodic calibration in
flight using calibrated gas cylinders tracks the drift over the course of the
flight and from flight to flight.
To match the vertical wind's sample rate, gas series are interpolated to
50 s-1 using cubic splines. On some of the flights a buffer
overflow problem (since corrected) caused sample loss leaving an irregular
time series of samples between 3 and 4 s-1. The irregularity was
readily handled by the interpolation to produce a signal, implicitly low-pass
filtered with a stop band above about 1.5 Hz, down from the full 5 Hz
(10 s-1). Plots of spectra and cospectra of the data streams of
the vertical wind and of the trace gases' dry-air mixing ratios were prepared
and are presented by . To assess the potential loss of flux
due to the lost samples, the full 10 s-1 gas data stream available
from flight 25.18:00 was subsampled in two modes. One subsample was evenly
spaced at 3 s-1; the other more randomly spaced between 3 and
4 s-1, representing flight 13.09:30. These were interpolated by
cubic spline, which does not appreciably add higher-frequency components to
the gas data streams above the (effective) Nyquist frequency of the original
signal (5 Hz for 25.18:00 and about 1.5 Hz for 13.09:30). The test
indicated a loss of about 10 % of the flux for either subsample. This was
considered acceptable for the present study.
High-frequency spectral corrections were not used in computing the fluxes
presented here. The resulting loss is less than 10 %, as confirmed in the
implicit filtering test above. A second test, differing only in the filter
used provides further confirmation. A four-pole Butterworth low-pass filter
is applied forward and backward to cancel the phase shift. Four cases were
simulated using data from flights 25.18:00 and 13.09:30.
Filter the gas series to a 2 Hz cutoff (half-power). This first reduction has almost no effect on 13.09:30 since it is already filtered as discussed above.
Filter the gas series to 2 Hz; also filter the vertical wind to 2 Hz. This had a small additional effect. The flux published in this paper used the full-frequency wind data.
Same as 1, but filter gases to 1 Hz.
Same as 2, but filter both gases and vertical wind to 1 Hz.
All filters were implemented on the merged wind and gas data series at
50 s-1. The simulation provides an upper bound on the loss of flux
above the 5 Hz cutoff frequency of the full gas data streams. Cutting the
effective Nyquist frequency down to 2 Hz and then further to 1 Hz cuts more
and more deeply into spectral ranges having increasingly significant
contribution to the flux. This is reflected in the results: 10 % loss at
2 Hz Nyquist frequency and 28 % loss at 1 Hz. The results indicate that
the fraction of flux lost from frequencies higher than 5 Hz is less than
10 %. Future work will, however, include exploration of these estimation
techniques.
Finally, to evaluate the dependence of the measured methane flux on the
height above the ground, a regression of the 3 km running flux (see
Sect. ) from flight 13.09:30 was run against flight altitudes
ranging from 5 to 45 m. A quadratic regression was required, yielding a
significant positive slope but significant negative curvature. The regression
line reached a maximum at an intermediate point before the maximum height
above ground. More importantly, the regression explained only 10 % of the
variance.
There were two other small instruments that augmented FOCAL's capabilities: a
radar altimeter, for height above ground which is essential for accurate
footprint calculations, and a visible-light camera, which provided a visual
record of the terrain directly under the aircraft to check the accuracy of
the remotely sensed products used for primary landscape classification. The
Aurora Flight Sciences' version of the DA-42, named the Centaur, is a
twin-engine aircraft which has several characteristics that make it an ideal
platform for the work discussed here. The Centaur's twin-engine configuration
leaves the entire center fuselage available for instrumentation and sampling.
The aircraft is electrically and structurally well adapted for carrying a
sophisticated scientific payload, having ample spare power from its two
alternators and ideally located hard points for the probe and the
spectroscopic equipment.
Turbulence measurements
Eddy covariance is a direct way to determine the exchange of mass (e.g.,
trace gases), momentum, and energy between the atmosphere and the surface. In
principle for a gas, the covariance between the turbulent fluctuating gas
concentration and the turbulent vertical wind component determines the flux.
Since the flux thus obtained is assumed to represent the exchange at the
surface, the airplane is flown as low as is safely possible, typically below
30 m . Flux measurements from fixed surface sites,
important complements to the airborne measurements, provide extended temporal
coverage at selected locations as well as validation of the airborne flux
measurements.
The mass flux of a minor gas constituent in air, such as methane, is
calculated following , . Let
ρa be the partial density of air apart from water vapor
and w be the vertical wind velocity. Then ρaw is the
dry-air mass flux, which is expanded into base state and turbulent departure
with the base state represented by an overbar and the departure by a prime:
ρaw=ρaw‾+(ρaw)′.
Since dry air is not exchanged with the surface, ρaw‾=0. The flux of a gas is then the covariance of the turbulent dry-air
mixing ratio c′ with the turbulent dry-air mass flux (ρaw)′:
F=(ρaw)′c′‾.
Unlike from a stationary tower, measuring the turbulent vertical wind
component from an airplane requires finding the small (vector) sum of the
airspeed and the ground speed, two large, nearly canceling vectors. Since
both vectors fluctuate rapidly and independently, many independent
measurements must be made with precise synchrony at high accuracy and sample
rate. Since turbulent fluctuations can be less than 0.1 ms-1,
the two large velocities must each be accurate within 0.1 ms-1.
Four samples define the minimum effectively resolvable turbulent eddy size,
about 5 m at 50 samples per second and 60 ms-1.
Methane flux measurements
Running flux method
The running flux method (RFM) is commonly used in the space/time domain for
eddy covariance analysis of airborne fluxes e.g.,. The
RFM calculates the mean flux over a contiguous integration length (e.g.,
3 km). As opposed to a stationary tower, which averages in time, the
aircraft is moving over the landscape, so that fluxes are more appropriately
averages over distance. Here we use the same notation as
F=∑k=1N(ρdw)k′ck′Vk∑k=1NVk,
where ρa, w′, and c′ are defined as in
Eq. () and V is the airspeed of the aircraft. The sum is over
N consecutive samples, and the denominator is the spatial averaging length.
For the analysis presented here we use a 3 km window that is moved by 1 km
increments so that, unlike the normal practice with tower data, there is
overlap between adjacent calculated fluxes to provide somewhat finer spatial
localization. The RFM quantitatively describes the relationship between
measured flux and underlying surface features of scales comparable to the
averaging length or larger. This method works well as shown by
, who found a 4 km moving average on the US Great Plains
to be an appropriate compromise between uncertainty in flux estimation and
resolution of landscape-scale heterogeneity. In the Arctic in 2013, the much
smaller mixed layer depth gave rise to smaller turbulence scales. Ogive
analysis of the frequency distribution showed 3 km to suffice as the
integration distance . However, heterogeneity in the
resulting flux estimates was large. Repeated flight segments gave variable
results likely due to changes in winds and sampling footprints and to the
integration lengths being longer
than the scale of the underlying surface features. Nevertheless, there was
good agreement between methane fluxes calculated by the RFM using 3 km
integration centered near the tower location and fluxes computed directly
from the tower measurements (see Sect. ). Using the
RFM over the small-scale heterogeneity of the North Slope's surface features,
however, limits the ability to isolate the flux contributions from individual
surface classes.
The flux fragment method (FFM) divides the covariance measurements
into small fragments whose footprints can be attributed to different
landscape features or classes. In the figure the landscape has been divided
into lakes and two types of land, for example wet sedge and fresh water
marsh. Footprints are calculated for each fragment and footprints that lie
mostly (> 85 %) on a single land type are assigned to that land type.
All footprints for a given land type can then be summed and divided by the
cumulative path length in air.
Flux fragment method
The flux fragment method (FFM) was conceived to assess the homogeneity in
properties of a remotely determined land class over multiple instances
occurring in patches on the landscape. Often such patches are too small for a
traditional RFM . The FFM, while based on the same
statistical foundation as eddy covariance, uses a conditional sampling scheme
whereby the flux, of methane for example, is compiled from many τ s
“fragments” fi of methane fluxes along a transect, each given by
fi=δt∑k=1nτ[(ρdw)k′ck′Vk]i,Li=δt∑k=1nτ[Vk]i.
Here n is the number of samples per second, δt is the sample
interval, and everything else is defined as in Eq. ()
except that instead of summing over a large distance, such as 3 km, the sum
is only over a few samples. Note, however, that the departure quantities used
to form the fragments are relative to the same base state as in
Eq. (), a base state of 3 km scale or more, determined by
ogive analysis to be an upper limit for the turbulence
present at the time of measurement. The fragments therefore contain
information on all scales from the Nyquist wavelength of the sample rate up
to the 3 km scale of the spectral gap determined from the ogive analysis.
However, the air packets quantified by the fragments are also short enough to
have likely interacted with a single surface class. So long as any
significant secondary circulations are accounted for in the base state, the
turbulent atmosphere on all its scales can be postulated to repeat over the
landscape in a fairly random fashion. A contiguous sample (i.e, without gaps)
should not therefore be required. The sample only needs to be sufficiently large
to include multiple instances of boundary layer structures at each scale. An
aircraft moving at airspeed 60 ms-1 covers 216 km in an hour
encountering 72 instances of 3 km turbulence structure. A sufficiently
prevalent land surface class, whether found in large or small patches is
very likely to provide a sufficient sample. Samples which are too short can
be discovered in confidence intervals developed by bootstrap resampling as
was done by . A more sophisticated bootstrap procedure
developed in conjunction with analysis of these 2013 data by
follows .
In the data presented here the fragments are 1 s sums
(τ=1 s) of approximately 60 m length. The fragments, labeled
fi, do not constitute a Reynolds average individually. That is, an
individual fragment, though containing all turbulent scales, is only a short
grab sample. Fragments provide a meaningful flux estimate only in aggregate.
They can be grouped, for example, by land-surface class, determined from footprint
estimation (Fig. ). Fluxes are calculated only for those
land-surface-class groups whose total length is greater than 3 km. The sum over
each group divided by the cumulative length of all fragments in the group
provides the mean flux from the associated land-surface class as given by
FS=∑i∈Sfi∑i∈SLi.
Methane fluxes measured from the flux tower compared with fluxes
measured by the FOCAL system. Tower methane fluxes (top plot) are 30 min
means plotted versus day of year. The flights (13.09:30, 25.18:00, and 27.19:00
on DOY 225, 237, and 239, respectively) each included repeated passes near the
tower. The orange circle gives the mean over these passes of the
RFM-determined 3 km flux centered nearest the tower. Fluxes by FFM
were aggregated by surface class over the whole flight. The length of the
line along the time axis represents the period over which the data were
taken, typically 1.5 h. Lower panels show details for each flight
day, labeled by day of year (DOY), with vertical bars showing the 95 %
confidence interval based on bootstrap analysis. Bars are offset along the
x axis for clarity.
Flux footprints near the tower (yellow triangle) for the three tower
flights (13.09:30, 25.18:00, and 27.19:00). They are laid over the
NSSI-classified land-cover map (see Fig. ). The top
panel facilitates identifying the surface classes under each footprint. The
flight track, always passing downwind of the tower, is shown as black points,
each giving the starting position of a flux fragment. The darker and redder
ribbon color represents greater probability of contribution to the total flux
as described in the text. Red arrows indicate the mean direction of the wind.
The part of the flight track used in the near-tower RFM calculation is
located between the magenta brackets.
The FFM is most appropriate in a region that is heterogeneous on small scales
(100 m to 3 km), but relatively homogeneous on large scales such that many
instances of the surface class, or other classification used to group the
fragments, are sampled during the flight (see for the
full description of the method). Initial assessments of the data presented
here indicate that the FFM is well suited for application to the North Slope,
where Arctic tundra is interspersed with thermokarst lakes, bogs, fens and
bare ground. First, land-cover data are classified using a current land-cover
image at 100 m resolution or better (e.g., LandSat). We use this to establish
transects flown at altitudes typically 10 to 30 m above ground; as low as
safely possible. These are flown repeatedly and coordinated with
eddy covariance towers for validation and temporal continuity. The base state
is then defined, representing in principle the deterministic (non-turbulent)
mesoscale component of the flow. Flux fragments are calculated using 1 s
sums of squares and cross products of departures from the base state.
Finally, a footprint model is applied to estimate the level of influence of
each surface class on each fragment. See Sect. for
examples of how FFM is used to interpret these data.
For the questions to be addressed in this paper the footprint model provides
a measure of a fragment's membership in the fuzzy set
associated with each surface class, treated as a categorical variable.
Fragments having a sufficient level of membership for a particular surface
class are assigned to that class. Setting the membership criterion above 0.5 restricts all fragments to a maximum of one class. A meaningful subset of the available fragments, further grouped into non-intersecting subsets according to their primary surface of origin, can thus be obtained.
We use the parameterization scheme developed by from a set
of runs of a backward Lagrangian model for a range of
heights, stability measures, and other turbulence quantities that are measured
from the aircraft. The required turbulence quantities are computed from
averages taken over the length of each flight leg, where the flight leg is
defined as the straight segment, between turns, over which the collected data
are used. The more recent 2-D version , which
was considered too computationally intensive to be included in the present
study, was not considered necessary because of the footprint's current
restricted use as a membership criterion to assign a selected subset of
fragments to the surface categories. The degree of overlap was assessed,
however, for future reference. Using the measurements from the convective
daytime case 13.09:30, the 2-D model yielded a footprint with a
full width of about 250 m (±1σy) at the location of maximum
crosswind-integrated probability, 93 m upwind of the sensors. Since the
probabilities are weighted towards the middle of the footprint and the land
classes tend to be homogeneous on the order of at least 300 m, using the
1D version of the model is acceptable given our focus on
categorical classification and our strict membership criterion (85 %). With
interval quantities the weighted distribution of sources over the full
2-D footprints will be required.
The flux estimate for each land surface class is the sum of the fragments in
the associated group divided by their accumulated length. The number of
fragments necessary to provide a robust result can be determined by bootstrap
resampling . For the data presented here 3 km or ∼ 50
fragments suffice.
The questions to be answered by the FFM, using a fuzzy-logic approach
to assign surface classes to fragments and then to
conditionally sample them based on those classes, are the following:
What is the mean flux over all measured instances of each surface class?
What surface classes dominate the methane emissions, and by how much?
How much does the flux over each class vary? Is there a spatial pattern to the variation? The variability
will come both from the prevailing atmospheric environment and the heterogeneity of the emissions within the same class.
How well does a particular instance represent all similar instances over the landscape?
Land surface classification
The land surface on the North Slope can be divided into different classes
based on dominant plant species, topography, soil content, and soil moisture.
The North Slope Science Initiative (NSSI) has identified 24 classes using
Landsat Thematic Mapper (TM) 30 m resolution land-cover maps in conjunction
with field surveys . These classifications are plausible
proxies for properties that have been shown to be primary drivers of methane
production and emission, including water table height, soil temperature, and
emission pathways such as sedge roots. The areas sampled by FOCAL
(Fig. ) were covered by patches of wet sedge, mesic
sedge – dwarf shrub, fresh water marsh, tussock tundra, and open water. Open
water is visible from the air, and includes lakes of various sizes and origin
along with rivers. Coastal waters, however, are excluded for this analysis.
By definition in the tussock tundra land class, shrubs more than 20 cm tall
occupy less than 25 % of the surface, and tussocks occupy more than 35 %.
The sites are cold, poorly drained and underlain by moderately moist (mesic)
to wet mineral soils with silty to sandy texture and a shallow surface
organic layer surrounding the tussocks. Wet sedge sites are defined as those
with sedge species accounting for more than 25 % of the cover and Sphagnum
for less than 25 %. Soils range from acidic to non-acidic, are saturated
during the summer, and typically have an organic layer over silt or sand.
Mesic sedge–dwarf shrub has shrubs less than 25 cm tall covering more
than 25 % of the area, and sedge cover is also more than 25 %. Soil
surface is generally mesic, but sometimes wet and is calcareous to acidic.
The fresh water marshes (FWM) are semi-permanently flooded, but some have
seasonal flooding, and the water depth typically exceeds 10 cm. Soils are
muck or mineral, and the water can be nutrient-rich.
We use land classes defined by a remote measurement, as opposed to soil
properties such as moisture, organic carbon content, temperature, etc.
because the remotely based definition is more appropriate to comparing to
larger regional-scale models and satellites. Thus the land class here is
usually a proxy for general classifications of areas with different soil
moisture and other properties which are likely the primary drivers of
differences in methane emissions. Certain plants such as sedge, however, have
been shown to act as conduits directly facilitating methane release from the
soil to the atmosphere through the plants' vascular system
.
In order to distinguish the contribution to the total methane flux from
individual land classes and to assess the variability across ecotopes, the data
are filtered to only include flux fragments having a membership score of at
least 85 %, determined by integrating the length of the footprint's
centerline weighted by the crosswind-integrated probability density that the
flux came from a single surface class. Increasing this threshold increases
the link between the calculated flux and a single land class, but reduces the
number of footprints available for the analysis, thus widening the confidence
interval. Varying the threshold between 80 and 95 % produces only a small
effect on the quantification of flux from each land class. We find that
85 % is a good compromise between singling out individual land classes
while still retaining a sufficient data set. For the flight speed of the
Centaur at low altitude and wind conditions during the flights, the length of
the footprint contributing more than 90 % of the flux for each 60 m
fragment varied between 100 and 800 m. The above filter eliminates about a
third to half of the flux fragments from each flight. Of those, we limit the
land classes to those where the total number of flux fragments is more than
50 fragments or an equivalent distance of 3 km. The flux fragments are
summed and then divided by the total integration length for each land class (Fig. ).
Plot of methane flux derived using RFM versus distance from flux
tower for two flight legs on 25 August. Positive (negative) distance is east
(west) of the tower position. The east to west transect (blue) was flown
30 min after the west to east transect (orange). Black circles are the
methane flux measured by the tower at the time nearest to when the aircraft
passed the tower.
Mean methane fluxes by land surface class derived using the FFM for
each of six flights as given in the legend. Dates of flights are given as day
of month in August followed by the time of the middle of the flight. Bars
give the instrument uncertainty (red) and the 95 % confidence interval as
calculated using bootstrapping (blue).
Tower measurements
Starting a few weeks before the flight campaign and throughout the month of
August, a small portable flux tower was installed at 70.08545∘ N, 148.57016∘ W, just south of Prudhoe Bay off
the Dalton Highway. During that time the tower recorded CO2 flux, CH4
flux, latent heat flux, sensible heat flux, air temperature, and incoming
radiation. Soil temperature probes were used to record soil temperature at 2,
5, 10, and 20 cm depth at three different locations around the tower. The
tower was situated in an area dominated by sedge grass, and the surrounding
area's water table was frequently near the surface such that the surroundings
were puddled and muddy, especially in late August 2013. On the NSSI map the
area is labeled as wet sedge. Low light and limited convective mixing are
common on the North Slope of Alaska, and data collected in very weak winds do
not provide reliable eddy covariance flux measurements. Consequently, data
were removed from the final set when the standard deviation of the vertical
wind speed was less than 0.1 ms-1.
Results and discussion
Comparison between aircraft and tower fluxes
On 13, 25, and 27 August the FOCAL aircraft flew repeated passes over a
constant northeast/southwest track near the tower affording direct comparison
between eddy covariance methane fluxes measured from the tower and from the
moving aircraft in both RFM and FFM modes (Fig. ). The
flight track was displaced north or south depending on the forecast wind
direction so that the aircraft footprint could pass over the tower footprint.
For the northerly winds on 13 and 25 August, the flight track was displaced
south of the tower. For the easterly winds of 27 August the track passed
north of the tower.
Two factors, diurnal and seasonal, influenced the fluxes at the tower site
(Fig. ). The flight 13.09:30 on 13 August (DOY 225) was
in the daytime earlier in August, when the turbulence was stronger and the
soil temperatures at 10 cm depth were 10–14 ∘C. The
30 min mean methane fluxes at the tower ranged from 1 to 2.5 µgm-2s-1. The flights 25.18:00 and 27.19:00 on 25 and 27 August
(DOY 237 and 239) were in the evening and later in August with weaker
turbulence and lower soil temperatures of 3–6 ∘C at 10 cm
depth. Most 30 min mean methane fluxes ranged from 0.5 to 1.3 µgm-2s-1. The observed variation with soil temperature is
consistent with previous studies e.g.,. Aircraft
methane fluxes were compared with the tower in two modes: as local RFM, the
mean over all transects of a flight of the 3 km flux blocks downwind of and
centered nearest to the tower, and as FFM, the mean of the fragments from wet
sedge gathered from the whole 50 km transect and the whole flight.
Agreement between the aircraft and tower by local RFM (orange circle), near
the tower but not differentiated by surface class, is within the confidence
intervals of the data from 13.09:30 and 25.18:00. For 27.19:00 the aircraft
measured significantly lower methane flux by local RFM than the tower. By FFM
from wet sedge (red line), the same surface class as the tower but not local
to it, the methane flux from 13.09:30 agrees very well with the magnitude of
the flux measured on 13 August at the tower. However, for 25.18:00 the FFM
flux from wet sedge is significantly lower than the 25 August tower
measurement. It is likewise for 27.19:00, though the FFM flux over wet sedge
is closer to the corresponding tower flux on 27 August than is the flux
calculated by the local RFM.
The results from the three near-tower flights represent three different
situations. On 27 August (flight 27.19:00), the footprint of the airborne
measurement (Fig. , bottom panel) differed from that of
the tower. On that flight the footprint analysis indicates the highest
probability of influence on the RFM flux (red to maroon contours in Fig. 5)
to be over open water, not wet sedge, for at least half the range (the 3 km
length centered nearest to the tower in the downwind direction). Lakes have
been shown to be sporadic hotspots of methane ebullition, but at least at
the time of flight these lakes showed very low methane emissions. On
27 August, the sedge, which makes up more than twice as much of the transect
as the lakes, is visible to the FFM, but not to the local RFM near the tower.
Also, the turbulence on August 27.19:00 was weak, with σw∼0.15 ms-1. This is a case where some signal may have been lost
due to insufficient sample rate for the altitude, or perhaps because the
measurement was made above the shallow layer of “constant” flux. This is a
tradeoff that plagues evening and morning flights. Notable about flight
27.19:00 is its demonstration of the need for, and difficulty of obtaining,
matching footprints when comparing flux measurements from different
instruments.
On 25 August, the local RFM produced a good match with the tower, in contrast
to the (distributed) FFM. Plotting the entire set of RFM fluxes from 25.18:00
yielded a surprise (Fig. ), where the tower appears to be
in a local hotspot. This may also be the case on August 27.19:00, where the
flux from the wet sedge around the tower is stronger than the FFM flux from
the wet sedge measured by the aircraft. Plots of methane flux against the
height of airborne measurement and the strength of turbulence (σw)
suggested no simple dependence on these. This flight dramatically shows the
hazards inherent in relying on point measurements, which are potentially in
non-representative locations, to estimate the area-wide flux. Also note in the
middle lower panel of Fig. that the flux of
1 µgm-2s-1 at the tower, though isolated in space, was
not isolated in time.
On 13 August everything matched. For flight 13.09:30 the wind was light and
the mixing strong (σw∼0.45 ms-1). The warm soil
produced a strong methane flux, and the methane flux measured at the tower
matched the local RFM flux near the tower as well as the FFM flux from the
distributed patches of wet sedge. Importantly, both the summer daytime
(13.09:30) and autumn evening (25.18:00) flights showed that when there is
reasonable overlap between the tower and aircraft footprints, the flux
measurements from the aircraft agree with those from the tower adding another
level of validation to the aircraft data.
Regional methane fluxes
During August 2013 FOCAL measured methane fluxes from a variety of ecotopes
across the North Slope. There are six flights used in this analysis; four in
the daytime and two in the evening (18:00–19:00 UTC -10) which were
covered individually in the last section. Keeping that discussion in mind,
these data are comparable as a set. Based on the tower data, which exhibit
strong and regular diurnal cycles of carbon dioxide and latent heat (not
shown), methane has a generally weak diurnal cycle. The sharp feature in the
tower trace on 13 August (DOY 225) very likely has a diurnal component, but
its shape suggests more than just solar input. This discussion, therefore,
will focus on the seasonal change and the methane emission characteristics of
the various surface classes (Figs. and
).
The land cover varies over the North Slope, so different flights sampled
different classes of land cover (see Table and
Fig. ). Wet sedge was the most prevalent and thus was
sampled on each flight, except for flight 28.10:00 on the morning of
28 August. Other land surface classes such as bare ground, dwarf shrub, and
low-tall willow were also observed but in insufficient quantity to calculate
a statistically significant flux. Prevalent near the tower site, which was
sampled on 13, 25, 27 August, were wet sedge, mesic sedge–dwarf shrub,
some lakes, the Sagavanirktok (Sag) River, and fresh water marsh. Soil
temperatures in mid-August varied by 1.5 ∘C with a mean soil
temperature of 8 ∘C at 5 cm depth. By the end of August soil
temperatures had dropped to a mean of 3 ∘C. Wet sedge showed
the strongest correlation with soil temperature, with fluxes falling from
2.1 µgm-2s-1 on 13 August to less than 0.5 µgm-2s-1 by the end of August. This relationship held true for
emissions from the Sag River with emissions falling from 1 µgm-2s-1 to near 0. Wet sedge, followed by the Sag River, had the
largest observed flux of any of the land classes sampled during the first
half of August. The other land classes have smaller, more variable fluxes on
most flights so that surface class alone does not distinguish them. Most
likely the true variability, contributing to the large confidence intervals,
is caused by heterogeneity within the surface class in sub-surface soil
temperature and water table height. However, within that we can still derive
a mean flux based on a large regional sample. Once the soil cools, wet sedge
shows reduced, though still positive, flux of methane consistent with the
other surface classes measured such as mesic sedge and lakes. The Sag River
shows close to zero methane flux. Lakes showed no trend. It should be noted,
however, that the number of lakes sampled on 13 August was small and the flux
variable as indicated by the large 95 % confidence interval. While data
from the other land classes sampled on 13 August were sparse, emissions from
fresh water marsh and tussock tundra during the second half of August were
similar to those from lakes and the two sedge classes.
Airborne measurements made during August 2013 are consistent with findings
from other studies. reported sites dominated by sedge
and wet soils having methane emissions ranging from 0.46 to 1.6 µgm-2s-1 with a median value of 0.87 µgm-2s-1
across multiple permafrost sites. Other studies at single locations fall into
this same range. For example, measured methane fluxes
from a wet sedge site in Happy Valley, AK during August of 1995 ranging from
0.38 to 1.5 µgm-2s-1 and measured
wet sedge near Barrow with emissions of 0.39 ± 0.03 µgm-2s-1 with short periods of higher emissions up to
1.1 µgm-2s-1. Emissions from mesic sedge sites near the
Sag River, though south of the areas measured by FOCAL, showed fluxes of 0.35
to 0.58 µgm-2s-1 in the first half of August falling to
0.12 to 0.23 µgm-2s-1 in the second half of August
.
Emissions from lakes tend to be more variable than the land classes. Measured
emissions from individual lakes ranged from 0.25 to 6.3 µgm-2s-1 across various thermokarst and other lakes in the North
Slope . These fluxes are reported
as means over a year, so emission rates during short periods of time may be
lower or higher for an individual lake. While FOCAL did not sample the same
lakes as in the aforementioned studies, during the flights near the tower,
multiple passes over the same lakes allowed for measuring emissions from individual lakes. On 13 August, five lakes were sampled with sufficient frequency
to produce a statistically significant flux. The flux for individual lakes
ranged from 0 to 2.6 µgm-2s-1 with a mean for all lakes
sampled of 0.18 µgm-2s-1. On 27 August four lakes were
measured with emissions ranging from 0.09 to 0.18 µgm-2s-1. The mean methane flux from lakes over the period of the
flights shows little flux, except for the lakes sampled on the morning flight
of 28 August. These are in a different area 250 km west of the tower. Those
lakes show an aggregate mean of 0.36 µgm-2s-1, the only
flux measured from lakes that was statistically significantly positive
(Fig. ). These data are consistent with the rates
measured by the above studies.
Conclusions
The FOCAL campaign during the summer of 2013 showed how methane fluxes could
be successfully measured over large regions using airborne eddy covariance
measurements from a small, low-flying aircraft. The data were analyzed in the
space/time domain with both a running flux method using traditional eddy
covariance and the flux fragment method (FFM), a variant using a conditional
sampling scheme. Other techniques such as wavelet analysis that rely on the
frequency domain to look at the same questions would be worth exploring in
the future. A comparison of the theory behind FFM with the theory behind the
wavelet method is included in .
Comparison of the airborne measurements to those of a tower showed that the
data were quantitatively comparable when there was good overlap between the
tower footprint and aircraft footprint. However, along the flight track local
conditions dominated the flux especially in the transition season from summer
to fall in late August. Comparing wet sedge at the tower site with wet sedge
west of the tower showed a factor of 2 difference in methane emissions
during the latter half of August which underscores the importance of regional
measurements as fluxes can be heavily dependent on spatial heterogeneity
even over relatively short distances. During the middle of the summer fluxes
from wet sedge were more homogeneous across the area flown.
Measurements of methane fluxes over the North Slope of Alaska in August showed
a strong correlation with soil temperature consistent with previous studies.
Wet sedge showed the highest persistent methane emissions with mean fluxes
about 2 µgm-2s-1 in the first half of August falling to
0.2 µgm-2s-1 in the latter half of August. Emissions
from the Sag River showed a similar trend, while other land surface classes
were not sampled enough during the first half of August to provide a
statistically significant sample. Individual lakes sampled near the tower
showed a large range of emissions varying from near 0 to 2.6 µgm-2s-1 consistent with the range of lake emissions reported in
the literature.
Aircraft measurements of surface flux can play an important role in bridging
the gap between ground-based measurements and regional measurements based on
inversion modeling or budget-box models. While airborne campaigns
are generally more costly than ground-based measurements, these costs can be
minimized by using small aircraft. For areas that are logistically
challenging to access, such as the North Slope, airborne eddy covariance
presents the easiest and least expensive way to directly measure surface
fluxes regionally with large coverage.