AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus PublicationsGöttingen, Germany10.5194/amt-11-6169-2018Observation of turbulent dispersion of artificially released SO2 puffs with UV camerasTurbulent dispersion of artificially released SO2 puffsDingerAnna Solvejgasd@nilu.nohttps://orcid.org/0000-0002-7563-031XStebelKerstinhttps://orcid.org/0000-0002-6935-7564CassianiMassimoArdeshiriHamidrezaBernardoCiriloKyllingArvehttps://orcid.org/0000-0003-1584-5033ParkSoon-YoungPissoIgnaciohttps://orcid.org/0000-0002-0056-7897SchmidbauerNorbertWassengJanStohlAndreashttps://orcid.org/0000-0002-2524-5755NILU – Norwegian Institute for Air Research, 2007 Kjeller, NorwayInstitute of Environmental Physics, University of Heidelberg, 69120 Heidelberg, GermanyAires Pty. Ltd., Mount Eliza, Vic 3930, AustraliaCenter for Earth and Environmental Modeling Studies, Gwangju Institute of Science and Technology, Gwangju, Republic of KoreaAnna Solvejg Dinger (asd@nilu.no)14November201811116169618830June201810July201821September20181November2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://amt.copernicus.org/articles/11/6169/2018/amt-11-6169-2018.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/11/6169/2018/amt-11-6169-2018.pdf
In atmospheric tracer experiments, a substance is released into the turbulent
atmospheric flow to study the dispersion parameters of the atmosphere. That
can be done by observing the substance's concentration distribution downwind
of the source. Past experiments have suffered from the fact that observations
were only made at a few discrete locations and/or at low time resolution. The
Comtessa project (Camera Observation and Modelling of 4-D Tracer
Dispersion in the Atmosphere) is the first attempt at using ultraviolet (UV)
camera observations to sample the three-dimensional (3-D) concentration
distribution in the atmospheric boundary layer at high spatial and temporal
resolution. For this, during a three-week campaign in Norway in July 2017,
sulfur dioxide (SO2), a nearly passive tracer, was artificially released
in continuous plumes and nearly instantaneous puffs from a 9 m high tower.
Column-integrated SO2 concentrations were observed with six UV SO2
cameras with sampling rates of several hertz and a spatial resolution of a
few centimetres. The atmospheric flow was characterised by eddy covariance
measurements of heat and momentum fluxes at the release mast and two
additional towers. By measuring simultaneously with six UV cameras positioned
in a half circle around the release point, we could collect a data set of
spatially and temporally resolved tracer column densities from six different
directions, allowing a tomographic reconstruction of the 3-D concentration
field. However, due to unfavourable cloudy conditions on all measurement days
and their restrictive effect on the SO2 camera technique, the presented
data set is limited to case studies. In this paper, we present a feasibility
study demonstrating that the turbulent dispersion parameters can be retrieved
from images of artificially released puffs, although the presented data set
does not allow for an in-depth analysis of the obtained parameters. The 3-D
trajectories of the centre of mass of the puffs were reconstructed enabling
both a direct determination of the centre of mass meandering and a scaling of
the image pixel dimension to the position of the puff. The latter made it
possible to retrieve the temporal evolution of the puff spread projected to
the image plane. The puff spread is a direct measure of the relative
dispersion process. Combining meandering and relative dispersion, the
absolute dispersion could be retrieved. The turbulent dispersion in the
vertical is then used to estimate the effective source size, source timescale and the Lagrangian integral time. In principle, the Richardson–Obukhov
constant of relative dispersion in the inertial subrange could be also
obtained, but the observation time was not sufficiently long in comparison to
the source timescale to allow an observation of this dispersion range. While
the feasibility of the methodology to measure turbulent dispersion could be
demonstrated, a larger data set with a larger number of cloud-free puff
releases and longer observation times of each puff will be recorded in future
studies to give a solid estimate for the turbulent dispersion under a variety
of stability conditions.
Introduction
A substance (a “passive scalar”)
injected into a turbulent atmospheric flow exhibits complex dynamical
behaviour. Its distribution is stochastic, and the probability density
function (PDF) of the scalar concentration field exhibits the signature of
large fluctuations, which can depart substantially from Gaussian behaviour
e.g.. This behaviour can be difficult to capture with
models. The direct numerical simulation of turbulence DNS,
e.g. is not feasible at Reynolds numbers typical for the
atmospheric boundary layer (ABL). Although some Eulerian turbulence
properties seem to converge also at relatively low Reynolds number
e.g., the Lagrangian dispersion
statistics in general, and the relative dispersion in particular, require a
high Reynolds number to converge and this poses challenges to both DNS and
laboratory observations e.g..
Other models used for tracer dispersion (e.g. Large Eddy Simulation or
Lagrangian particle models) require parameterizations and/or validation based
on atmospheric observations e.g..
Atmospheric tracer experiments are needed for constraining dispersion
parameters. The first plume characterization experiments in the early 20th
century were based on photographs of smoke clouds
. More recent experiments released gaseous
tracers such as sulfur dioxide (SO2), sulfur hexafluoride or
perfluorocarbons at one point and sampled concentrations in a network of
ground stations (and sometimes by aircraft) downwind. The experiments carried
out from the late 1950s to the early 1970s were the basis for many tools used
in dispersion modelling . As described in
, the Prairie Grass experiment , where near
source (<1 km) dispersion of SO2 was measured under many stability
conditions was perhaps the one most useful for dispersion model validation.
However, none of these experiments could capture the three-dimensional (3-D)
evolution of the dispersing plume in detail.
While the mean concentration is often highly accessible to atmospheric
measurements, fewer atmospheric observations are available for the higher PDF
moments (variance, skewness, kurtosis). Yet, the higher moments are crucial
if the relationship between the concentration fluctuations and their
consequences is non-linear . For instance, toxicity,
flammability and odour detection depend on exceedances of concentration
thresholds e.g., and
non-linear chemical reactions are influenced by tracer fluctuations if the
reaction and turbulence timescales are similar .
Atmospheric measurements of the concentration fluctuations in a dispersing
plume have been performed by different groups and with different techniques
. The most comprehensive
observations were made with lidars measuring the backscattered signal from
smoke particles . Other
studies have used lidars to measure SO2 concentrations
. A particular advantage of lidars is that they can
measure concentrations throughout the ABL and not only near the Earth's
surface, where most in situ measurements have been made. Nevertheless, even
lidars provide only 1-D measurements and, when scanning, cannot provide high
time resolution in 2-D or 3-D. Thus, the 3-D concentration distribution has
never been measured at high time resolution.
The 3-D concentration field is needed to evaluate the meandering and relative
dispersion process in the three physical directions. An important point to
recognize is that the production and dissipation of concentration fluctuation
for a dispersion scalar are intimately linked to the process of relative
dispersion of puffs and the related process of centre of mass meandering
. Therefore, parameterized expressions of
relative dispersion are used in defining simplified models of concentration
fluctuations e.g..
One possibility to indirectly measure 3-D tracer concentrations at high time
and space resolution (thus able to capturing concentration fluctuations) are
ultraviolet (UV) cameras. These cameras can measure sulfur dioxide (SO2)
column concentrations with a sampling frequency of several hertz
. Non-uniform cloud cover in the image background
can cause inhomogeneous illumination of the sky, which complicates the SO2
column concentration retrieval of SO2 camera images. While efforts have
been made to correct cloud effects , it is generally
recommended to measure during clear-sky conditions
. To date, SO2 cameras have been used mostly
to monitor SO2 emissions from volcanoes , power plants
and ships . While each
individual camera measures only 2-D distributions of SO2 column
concentrations, a combination of several such cameras should allow a
tomographic reconstruction of the 3-D SO2 distribution.
However, to our knowledge such a tomographic setup has never been used
successfully. The Comtessa project (Camera Observation and Modelling
of 4-D Tracer Dispersion in the Atmosphere) is the first attempt at using
camera observations to study tracer dispersion in the ABL. For this, we
artificially release SO2 into the atmosphere and observe its dispersion
with UV cameras.
In this paper, we present results from the first Comtessa field
campaign, which was conducted to test our new instrumentation. Not all
equipment was fully operational yet, but we were nevertheless able to collect
a valuable data set using six UV cameras and meteorological instrumentation.
Here, we first describe the release experiments (Sect. )
and how a tomographic setup of UV cameras can be used to quantify the
dispersion of artificially released SO2 puffs in the ABL (Sects. and ). However, note that a fully
resolved tomographic reconstruction is not necessary for this retrieval and
is not presented in this paper. As an example, the 3-D trajectories and
spreads of six puffs within a short time interval of 60 s are reconstructed
(Sect. ). Then, the time evolution of puff meandering,
relative and absolute dispersion are retrieved enabling estimations of
turbulent timescales (Sect. ). The data set does not
contain a sufficiently large number of puffs for a reliable statistical
analysis; however, the feasibility of the method is demonstrated.
Artificial release experiment
The first Comtessa campaign was performed at a military training
ground (11.5∘ E, 61.4∘ N) about 28 km northeast of the small
city of Rena, Norway, from 3 to 21 July 2017. The experimental site is
located in a remote forested mountain area at an altitude of 850 m above sea
level. It is a fenced-in flat gravel field with dimensions of about
900 m × 400 m, which is normally used for ammunition testing by
the Norwegian military. Three 9 m high masts equipped with eddy
covariance measurement systems were set up to measure the turbulent fluxes of
heat and momentum. From the top of one of the masts, pure SO2 gas was
released, piped from SO2 bottles at the ground using a commercial blower.
The blower speed was set such that the release was nearly isokinetic. That
was achieved by adjusting the flow in the pipe to the wind speed monitored
online with a sonic anemometer at source elevation. The pipe had a diameter
of 12.5 cm at the release point. Figure shows a picture of
the top of the release mast.
Top of the release tower.
The weather conditions were generally not favourable for our experiment, with
several cyclones passing over Fennoscandia during the campaign period. Daily
average temperatures at a meteorological station located in the immediate
vicinity (Rena øvingsfelt) ranged between 6.8 and 11.7 ∘C, except
for the last 2 days when they rose above 13 ∘C. On 13 of the 19 campaign days, precipitation was recorded, and winds were often strong (up to
9 m s-1). Conditions were suitable for instrument testing on several
days, but clear-sky conditions were rare. The best conditions were
encountered on 20 July when a ridge of high pressure built over southern
Fennoscandia. While even on that day there was no period when the sky was
entirely free of clouds, there were periods with relatively little cloud
cover, enabling clear-sky camera observations for some viewing directions and
yielding clouded scenes for the other cameras. In this paper, we will
therefore present results only for this day.
On 20 July, SO2 was released during several experiments, including both
several continuous plumes (between 07:19 and 09:53 UTC) and nearly-instantaneous
puffs (between 10:24 and 10:47 UTC). In this paper, however, only analyses of the
puff experiments will be presented. Six identical UV SO2 cameras observed
the SO2 releases, resulting in column-integrated SO2 concentration
images from six directions. The six SO2 cameras observed an overlapping
volume of roughly 40 m × 40 m × 20 m, centred circa 18 m
downwind of the release point. The cameras were arranged on the ground in a
half circle with a radius of 160 m around this volume. The release point is
visible in the field of view of every camera. Additionally, a meteorological
tower, located a few hundred metres northwest of the release tower, is
visible in the field of view of some cameras. A map of the setup is shown in
Fig. and detailed quantitative information can be found in
Appendix .
Map of the experimental setup. The cameras' FOVs are indicated in green. The sun position (yellow) and
the cloud cover (gray) as observed at 10:30 UTC are sketched on the map. Coordinates are given relative to the release location.
The SO2 cameras were custom-built for the Comtessa project
(Fig. ). At the core of each SO2 camera are two UV
cameras from PCO (pco.ultraviolet), which record images at two different
wavelengths. The wavelengths are selected by mounting two Asahi Spectra
band-pass filters (10 nm bandwidth) at 310 and 330 nm, respectively, in
front of the cameras. The filters are mounted between the CCD sensor and a
25 mm quartz lens from Universe Kogaku. This setup attenuates radial
sensitivity changes due to different light paths through the filter for
off-axis rays compared to mounting the filters in front of the lens
. The cameras' CCD sensors have Ni=1392 pixel columns and
Nj=1040 pixel rows, resulting in a image resolution of a few centimetres
at object distances of a few hundred metres. The camera properties are
summarised in Table . During the experiment, the
exposure times were chosen manually such that the 14-bit-sensor was roughly
80 % saturated. On 20 July, the exposure times for the 310 nm camera were
between 160 and 200 ms at apertures of f/2.8. Further, each camera
contains an AvaSpec-ULS2048x64 spectrometer from Avantes for robust
SO2-calibration. The spectrometer is coupled via a 3×200µm cross
section converter fibre from loptek to a telescope, pointing in the same
direction as the UV cameras. The telescope consists of a quartz lens from
Thorlabs with 100 mm focal length and a Hoya U-330 filter which prevents
stray light to enter the detector. This setup results in a telescope field of
view of 0.572∘ which corresponds to a disk with a 52-pixel diameter
within the UV camera image. In the future, a built-in GPS will be used to
obtain accurate space and time information. However, during the experiment in
summer of 2017, the GPS data were not yet recorded and, therefore, the
individual SO2 cameras were synchronised in time by tracking of distinct
SO2 features after the experiment (see Appendix for
details).
Summary of SO2 camera properties.
Propertypixel numberNi×Nj1392×1040pixel sizesi×sj4.65 µm × 4.65 µmfocal lengthf25.06 mm (λ=266 nm)field of view14.7∘×11.1∘filter wavelengthλ310 and 330 nm
SO2 camera and PC (camera 5). In the background, the release and measurement towers are visible.
Meteorological measurements were collected on the release tower at three
vertical positions (2, 5.4 and 8.7 m) using a state-of-the-art
measuring system from Campbell Scientific. It included sonic anemometers at
all three levels (model CSAT3A and CSAT3B, respectively) measuring three wind
components and sonic temperature with 50 Hz sampling frequency.
Additionally, an EC150 gas analyser was coupled to the lowest level. It
simultaneously measured water vapour and carbon dioxide densities at 50 Hz,
as well as the atmospheric pressure and temperature at lower frequency.
During the puff release experiment on 20 July, the mean wind velocity at the
source was 5.22 m s-1 and the fluctuations of the vertical velocity
component were σw2=0.283 m2 s-2. The derived value of the
Obukhov length L=-6.22 indicates an unstable atmosphere with convective
conditions. Further measured and derived parameters are summarised in Table and the applied post-processing of the wind data is
detailed in Appendix .
Turbulent dispersionDescription of turbulent dispersion
The absolute dispersion σi2 describes the spread of a scalar
relative to a fixed origin along the coordinate axis i. Mathematically,
σi2 is the variance of the 1-D mean concentration distribution along
the considered axis. demonstrated that the absolute
dispersion is directly linked to the Lagrangian autocorrelation function of
the motion of one particle. According to Taylor's theory and assuming
homogeneity and an exponential autocorrelation function see
e.g. the evolution of the absolute dispersion with time t in
the vertical coordinate z is modelled as
σz2(t)=2⋅w′2‾⋅TL2tTL-1-exp-tTL,
with the vertical velocity w(t) and the vertical Lagrangian timescale
TL. Assuming homogeneity, the variance of the vertical velocity
σw2=w′2‾ can be obtained from the velocity monitored by
a sonic anemometer placed at the source location. Given the very short range
of our current measurements this is an acceptable approximation. The
Lagrangian timescale TL cannot be measured directly by a fixed point
measurement, instead the Eulerian timescale TE can be obtained from such
measurements. assumed that the Lagrangian and Eulerian time
scales have a fixed ratio β=TL/TE. The proportionality constant
β can be found using the relationship proposed by ,
βi≈0.7,
where i=σwu‾ is the turbulence intensity in the
along wind direction with mean velocity u‾.
Measured turbulence parameters from 10:27 to 10:32 UTC.
ParameterSymbolValuedirect measurementsmean wind velocityu‾5.22 m s-1fluctuations, along-windσu2=u′2‾2.29 m2 s-2fluctuations, across-windσv2=v′2‾0.861 m2 s-2fluctuations, verticalσw2=w′2‾0.283 m2 s-2turbulence intensityi0.102Obukhov lengthL-6.22 mflux Richardson numberRf-0.988friction velocityu*0.249 m s-1fit to energy spectrum Ew(k)energy dissipationϵ0.015 m2 s-3Eulerian integral time, verticalTE,w3.07 sLagrangian integral time, verticalTL,w21.1 sRatio of integral timesβ6.87
The absolute dispersion of an ensemble of puffs (or clusters of particles)
can be assumed to be partitioned between two statistically independent
components: the meandering of the puffs as a whole with respect to the source
location, and the spread of the puffs around their centre of mass, called
relative dispersion. This is sketched in Fig. . In
mathematical terms, the variance of the mean concentration distribution
σi2 is decomposed as a sum of the variance of the centre of mass
distribution σm,i2 and the variance of the concentration of the
puff relative to its centre of mass σr,i2,
σi2(t)=σm,i2(t)+σr,i2(t).
Experimentally, the variances are obtained by averaging over multiple
realisations of single puffs.
Sketch of a puff release. The centre of mass trajectory of a single puff (red)
meanders around the mean trajectory of a puff ensemble, while the puff additionally spreads around
its centre of mass. Consequently, the absolute dispersion can be separated into the meandering of
the centre of mass trajectories and the variance of the puffs' concentration relative to their
centre of mass. Both are obtained using data from a large number of realizations of single puff releases.
A cluster of particles released at the same time from a finite source will
follow slightly different paths and form a distribution around its centre of
mass. The relative dispersion is therefore influenced by the source size
r0, i.e. the initial separation of the particles. For an initial particle
separation (puff size) in the inertial subrange of turbulence, i.e. larger
than the Kolmogorov length scale and smaller than the length scale of (local)
energy containing eddies, the particle separation will be first influenced by
the source size and then become independent of the initial separation
e.g.Eqs. A1–A6. Based on inertial range
scaling arguments e.g. , the characteristic timescale
of the source is given by ts=(r02/ϵ)1/3, where ϵ is
the mean dissipation of turbulent kinetic energy. The following Eqs. (4)–(6)
are valid for puff sizes in the inertial subrange of turbulence, which was
observed in our experiment (see Appendix for
details).
showed that for t≪ts the spread of a puff, or
cluster of particles, is dominated by the initial velocity differences
between the particles (“ballistic regime”)
〈r2〉=113Ckϵ2/3r02/3⋅t2+r02 for t≪ts,
where Ck is the Kolmogorov's constant for the longitudinal structure
function in the inertial subrange. Here, r is the 3-D separation
between two particles of the cluster and 〈r2〉 is
the ensemble mean square separation between all particles of the cluster.
In homogeneous isotropic turbulence, 〈r2〉 is
related to the 1-D relative dispersion as σr,i2=〈r2〉/6see, e.g. . Equation
() reduced to the vertical component reads then
σr,z2(t)=σr,z02+6-2/3⋅113Ckϵ2/3σr,z02/3t2,
with the 1-D initial vertical separation σr,z02=r02/6.
For larger times t≫ts, the rate of change of particle separation
becomes independent of the initial separation, and the spread of the puff is
proportional to the Richardson–Obukhov constant Cr according to the
Richardson–Obukhov scaling e.g..
〈r2〉=Cr⋅ϵ⋅t3+r02 for t≫ts
The value of the Richardson–Obukhov constant is uncertain, as it is difficult
to estimate from experiments and numerical simulations see for a
detailed discussion. However, Cr and the directly related
relative dispersion are important for models as the relative dispersion
defines the effective rate of mixing of a puff and therefore the decay rate
of concentration fluctuations e.g..
Turbulent dispersion from image data
Videos of column-integrated concentrations (CIC) of an instantaneous release
of a passive tracer can be used to measure different aspects of turbulent
dispersion, especially when simultaneous images from different directions are
available. The CIC images contain direct information about the puffs'
position and spread projected to the image plane (see Fig.
for a sketch and Fig. for an example image). The image
plane is spanned by two discrete coordinate axes i=[1,..,Ni] and
j=[1,..,Nj], describing the image columns and rows.
We define a rectangular extension of the projected puff, the so-called
region of interest (ROI), to distinguish different puffs that may be present
in the image, and to reduce the impact of noise. Then, the total signal
Stot of the puff (or, in statistical terms, the zeroth moment of the
column-integrated concentration PDF) is given by
Stot=∑i,j in ROIS(i,j),
where S(i,j) is the CIC at pixel (i,j).
The centre of mass (CM) of the puff in the image plane (first moment of the
column-integrated concentration PDF) is given by
icmjcm,=1Stot∑i,j in ROIS(i,j)ij.
The spread of mass around its centre as given by the variance (2nd moment of
the column-integrated concentration PDF) is described by the weighted
covariance matrix C. The diagonal elements of C are the
spreads of the SO2 puff in the image plane along the image columns and
rows, respectively. Accordingly, the horizontal spread along pixel columns is
given by
C1,1=1Stot∑i,j in ROI(i-icm)2⋅S(i,j)=1Stot∑i,j in ROIi2⋅S(i,j)-icm2,
The spread along pixel rows C2,2 is calculated equivalently.
Sketch of the field of view of two cameras from above. The three-dimensional SO2
puff (yellow) in the world coordinate system (x,y,z) is projected to the two-dimensional image plane (i,j).
The centre of mass in the image plane corresponds to a solid angle in the world coordinate system (red).
The apparent size of a pixel scales with the distance to the object plane (grey area).
However, retrieving quantitative dispersion parameters such as the total mass
from the camera images requires that the pixel dimensions in the virtual
object plane, containing the puff, are known. A pixel is, strictly speaking,
a solid angle defined by the focal length of the camera lens f. Thus, for
knowing the apparent width of the pixel at the position of the puff, the
distance d of the SO2 puff to the camera needs to be known. Then, the
apparent width of a pixel sp(d) is given by
sp(d)=si⋅d-ff,
where si is the physical width of the pixel on the CCD sensor. The height
of the pixel in the virtual object plane is calculated analogously and it is
equal in case of a sensor with square pixels. In the following, square pixel
are assumed for simplicity.
Example of a SO2 CIC image from a SO2 camera (camera 4). The image contains two SO2
puffs marked by the detected ROI (white rectangle). Artefacts produced by a cloud are visible in the upper right corner.
When the puff's 3-D extension is small in comparison to the distance from the
puff's CM to the camera, differences in distance over the puff's extension
can be neglected and a constant scaling can be assumed for the whole ROI.
Scaling the CIC images with the pixels' apparent area sp2, relates the
image to a global reference system. It follows for the total mass M of a
puff
M=sp2(d)⋅Stot,
and the horizontal puff spread in square metres
C1,1[m2]=sp2(d)⋅C1,1[pixel2].
The spread describes the mass distribution relative to the centre of mass and
projected to the image plane. It is hence connected to the relative
dispersion. Depending on the relative orientation of the mean wind direction
and the camera's optical axis, it can equal the vertical, along- or
across-wind direction in some cases. In other cases, assumptions of the plume
shape have to be made (e.g. Gaussian plume) or a 3-D reconstruction of the
distribution is necessary. When detecting the puff's CM with more than one
camera, the CM position in a global coordinate system can be reconstructed.
For analysing the statistical nature of the turbulent dispersion, an ensemble
of puff releases is required. Then, the meandering is calculated from the
variance of the 3-D CM positions and the relative dispersion is connected to
the measured puff spread.
Retrieval of CM trajectories and spread of artificially released puffs using a tomographic setup of SO2 cameras
In this study, SO2 CIC images recorded simultaneously
with six UV SO2 cameras are the basis for the retrieval of puff spreads.
An example of such an image can be seen in Fig. and the
imaging technique will be described in the following
Sect. . The puffs are detected automatically within the
image using common image processing techniques
(Sect. ). This allows for calculating the CM and
spread of the puff projected to the image plane. Making use of the
tomographic setup of six cameras (see Figs. and ) and the previously measured, projected CMs, the 3-D
trajectories are reconstructed (Sect. ). The 3-D
trajectories then allow for scaling the measured puff spreads to square
metres.
SO2 camera imaging technique
The SO2 camera method is based on
the principle of absorption spectroscopy of backscattered sunlight. Gaseous
SO2 molecules exhibit a distinct, wavelength-dependent absorption cross
section in the ultraviolet σ(λ), where λ is the
wavelength. The relationship between the light intensity before and after
passing through a SO2 cloud – I0(λ) and I(λ) – is
described by the Beer–Lambert law
I(λ,L)=I0(λ)⋅exp-∫0Lσ(λ)⋅c(l)dl,=I0(λ)⋅exp-σ(λ)⋅S.
where c(l) is the SO2 concentration at position l along the light path
l∈[0,L] through the SO2 cloud and S=∫0Lc(l)dl is the SO2
slant column density (SCD) along this light path. Generally, radiative
transfer effects (e.g. multiple-scattering inside the SO2 cloud and light
dilution ) have to be taken into account when
translating the slant column density to the column-integrated concentration.
However for this study, the effects are negligibly small due to the absence
of aerosol and the small extension and short distance of the SO2 puffs to
the cameras. Therefore, the slant column densities correspond nearly exactly
to the column-integrated concentrations and are used as such throughout the
publication.
The SO2 cameras record intensity images of the SO2 cloud I(λ).
Images of the clear sky intensity I0(λ) can be measured in the same
direction when the SO2 cloud is not present (i.e. before or after a
release experiment). The SO2 slant column density S is proportional to
the optical density τ(λ), which is retrieved from the two images
by
τ(λ)=-lnI(λ)I0(λ)=σ(λ)⋅S.
Using a narrow bandpass filter in the ultraviolet (typically 310 nm), a
narrow spectral band of strong SO2 absorption is selected. While
high-precision laboratory measurements of the SO2 absorption cross section
σ(λ) are available e.g., calibration
from τ(λ) to S is nevertheless necessary due to uncertainties of
the exact filter function. The measured optical density images τ are
approximated to SO2 SCDs by linear regression using absolute measurements
of the SCDs
S=aτ+b,=-alnI(λ)I0(λ)+b,
where a and b are calibration constants. Such measurements are available
from images of gas cells containing a known amount of SO2 and/or from
spectra of a built-in spectrometer . Making use of the
differential optical absorption spectroscopy (DOAS) technique, a time series
of precise point measurements of the SO2 SCD corresponding to a small
pixel area within the camera images can be retrieved and correlated to the
image time series.
Moving meteorological clouds behind the SO2 cloud can change the
illumination of backscattered sunlight between the two images I0(λ)
and I(λ). This leads to artefacts in the retrieved SCD images which
can be of the same magnitude as the SO2 signal. While SO2 camera
measurements under cloudy conditions should therefore be avoided if possible,
we could obtain only such measurements due to the weather conditions during
the experiments.
In this publication, the background images I0 were taken from the same
direction between two puff releases and the images were calibrated using the
built-in spectrometer. Note that, contrary to typical applications
e.g., measurements at only one wavelength
(λ=310 nm) can be used for the analysis due to the absence of
broadband absorption from additional aerosol in the SO2 cloud. More
details on the retrieval steps used in this publication can be found in the
Appendix .
Detection of individual puffs in image plane
The position and spread of individual SO2
puffs are tracked from the release point automatically. For that, rectangular
ROIs containing the full puff need to be detected. Such a detection can be
difficult for several reasons. (1) The images partly contain up to two puffs
and artefacts from clouds, which can imitate SO2 absorption. (2) Small
fractions of the puffs can separate completely from the puffs. (3) The images
are noisy, making correct identification of pixels with low SO2 values at
the edges of the puffs difficult.
In consequence, the ROI has to be large enough to contain the full puff but small enough to exclude additional puffs and clouds.
To overcome these challenges, we choose an approach combining iterative
tracking from the release point and applying signal thresholds to two
noise-reduced versions of the original image. In this way, the ROI could be
detected robustly and the total signal, CM and spread of the puff could be
retrieved from the original image. Details of the detection algorithm can be
found in Appendix . Further, this approach allows the
tracking of several puffs in the same image frame as long as they are separable.
Single clouds can be ignored if they are not at the same position as the
puffs and even the position of a puff in front of an overcast sky can be
constrained spatially, even if not fully detected.
3-D trajectories and pixel scaling
The previously retrieved CMs projected to
the image planes of the cameras can be used to retrieve the 3-D trajectories
of the CM in the global coordinate system. These allow for calculating the
distances between a puff and the individual cameras at any given time.
Subsequently, the scaling factor (Eq. ) for the other moments
of the PDF (Eqs. and ) can be determined.
The individual images of the six cameras are recorded at irregular time
intervals due to differences in exposure and read-out times. Combining the
irregular image times, the derived 3-D trajectories in the global coordinate
system were retrieved on an arbitrary-chosen discrete, regular time grid.
Here, 250 ms was chosen so that at least one image of every camera lies
within each interval. The time series of the CM image coordinates of the six
cameras are synchronised and interpolated to this common time grid.
For every time step and each camera, the line-of-sight line from the position
of the camera through the detected CM in the image plane at (icm,jcm) is determined by calculating the azimuth and elevation angle. The
azimuth angle of the CM is the sum of the camera's azimuth angle α of
the optical axis and the relative azimuth angle of the CM to the optical axis
αcm=α+arctan(icm-ic)⋅sif,
where icm is the pixel column of the CM, ic=Ni2 is the
pixel column containing the optical axis (approximated by the central pixel),
si is the physical pixel width on the CCD sensor and f is the focal
length. The elevation angle is calculated analogously based on the camera's
elevation angle and the pixel row jcm of the CM.
At every time step, the position of the CM in the global reference system is
then calculated based on the line-of-sight lines of all available cameras
using a least squares optimisation: the CM is the point in the global
reference system which minimises the square distance to all lines. The CM can
be calculated for every time step for which data from at least two cameras
were available. However, in this analysis data from at least three cameras
were used in order to reduce discontinuities caused by uncertainties in the
cameras' position and pose. The reconstructed 3-D trajectories can then be
used to determine the distances between the cameras and the puffs at any
given, individual image time.
Results
On July 20 between 10:24 and 10:47 UTC, a total of 140 puffs were released
almost instantaneously, each puff containing between 0.8 and 1.2 g of SO2.
The differences in mass originate from the manual opening and closing of the
release valve.
Due to the changing cloud cover, the analysis of the SO2 camera images
requires that background images are selected manually every 30 to 40 s of
data. Additionally, puffs overlapping with clouds or each other limit the
analysis further. Hence, for this feasibility study, results for a continuous
1-minute interval (10:29:50 to 10:30:50 UTC), containing six subsequent puffs
are presented.
Centre of mass coordinates of six subsequent puffs projected to the image planes of the
six SO2 cameras. For cameras 4 and 5, a meteorological tower is visible in the image background.
This tower is located a few hundred metres northwest of the release tower.
The six puffs can be tracked with all cameras in the image plane
(Fig. ) and the 3-D CM trajectories can be
reconstructed successfully over up to 58 m
(Figs. –). Typical
distance to extension ratios are around 100, justifying the assumption of
constant scaling throughout the ROI. The puffs move in two dominant
directions (approx. 0 ∘ and 30 ∘) in good agreement with
the overall measured wind direction. Figure displays
the evolution of the moments of the spatial distribution (total mass,
horizontal and vertical spread) of the six puffs. These are discussed in more
detail in the following.
CM trajectories of the six observed puffs and the ensemble average.
Horizontal projection of the CM trajectories of the six puffs observed with six SO2 cameras.
The left panel shows an overview of the camera positions relative to the reconstructed trajectories.
The right panels shows a blow-up of the rectangular area marked in the left panel. The colour code
represents the travel time since release. The mean trajectory and its standard deviation are displayed with black pluses.
Vertical projections of the CM trajectories to the altitude–north plane. The colour code
represents the travel time since release. The mean trajectory and its standard deviation are displayed
with black pluses. Note that the x axis scales 6× larger than the y axis.
Total SO2 mass
The total SO2 mass of the puffs is conserved, since loss mechanisms
(e.g.
dry deposition and oxidation of SO2) can be neglected on such short time
scales as the ones observed. A change of the measured absolute mass and
differences between the signals of different cameras are indications of
measurement biases and limitations. These include besides others the cameras'
detection limits, incomplete detection of the puff by the derived ROI,
additional signals (both negative and positive) from cloud artefacts,
uncertainties in the trajectory retrieval and thus the scaling parameter, and
radiative transfer effects.
The upper panel in Fig. shows the total mass of the
puffs as observed by four of the six cameras. Cameras 5 and 6 were excluded
due to overly pronounced additional signals from the cloudy sky. The
background images including the cloud cover for each camera were optimised
for the time of the second displayed puff (indicated by shaded area). For
this puff, the retrieved total SO2 masses from the four cameras show good
agreement: the mass first increases to circa 1.2 g SO2 while the puff is
released and then stays constant for all cameras until the puff is no longer
tracked. For the other puffs – and thus increasing time difference to the
background images – the relative differences between the cameras increases
(up to 50 %).
The total mass is strongly affected by clouds, which add both negative and
positive signals to the total mass. For camera 3, single clouds are visible
along the full pathway of the puff, resulting in a generally overestimated
signal. For cameras 2 and 4, single clouds appear only from the middle of the
image. Thus in this case an underestimation of the total mass starts only a
few seconds after the release. Cameras 5 and 6 (not shown), however, fail to
reproduce the released total mass even for the second puff. Camera 1 observes
the puffs free of additional signal from clouds and hence catches the correct
mass. However, due to it's frontal alignment to the puff's propagation
direction, subsequent puffs might overlap. This was the case for the three
puffs between 10:30:20 and 10:30:50 UTC. For these puffs no separate mass or
spread information can be extracted.
As the mass cannot be retrieved accurately for all data points, it can be
assumed that the puff spread would be affected in a similar way by the
additional signal due to clouds or overlapping puffs. Therefore, such data
points should be discarded from the analysis of the turbulent dispersion.
Only measurements for which the total mass lies within a physically
reasonable range (here, 1.0 to 1.3 gs-1) are included for further
discussion.
Total mass, horizontal spread and vertical spread (lower panel) of six subsequent puffs.
Only data from cameras 1–4 are shown due to significant cloud signals in camera 5 and 6. The
background images, and thus cloud cover, were reconstructed from the shaded time period. The
shaded data points are discarded because their corresponding mass lies outside the expected range (1.0–1.3 g).
Puff spread
Figure shows the puff spread (Eqs. and ) in the image plane for four cameras. It is pointed
out that these puff spreads are projected to the camera's object plane at the
position of the puff. Hence only the puff spread perpendicular to the
camera's optical axis is measured (see Fig. ).
In the horizontal, the cameras' relative orientation lead to different projections and thus not directly
comparable puff spreads. Camera 1 views the puffs almost frontal and thus the retrieved puff spreads are
across-wind in first approximation. Cameras 2 and 3 view the puffs nearly perpendicular to their propagation
direction, hence they measure approximately the along-wind spread and their results agree reasonably well.
The limited comparability of the cameras and the short data set of only six
puffs does not allow for a further analysis in terms of horizontal
dispersion.
The elevation angles of the cameras are comparably small (2.3–3.9∘). The vertical projection to the image plane is negligibly small
for these elevation angles (cos(3.9∘)=0.998). Hence the measured
vertical puff spreads correspond to the real vertical spread of the puff and
thus are comparable between the cameras. The measured values of the four
cameras agree with each other. In the following discussion only the vertical
puff spread is considered for simplicity.
Turbulent dispersion in the vertical
For the analysis of the turbulent dispersion it would be necessary to observe
a large number of instantaneous releases under stationary atmospheric
conditions. For this study, only six subsequent puffs were selected due to
the limitations of the measurements under cloudy conditions. The total
analysed time span is 60 s. Hence, the following discussion of the
results should be considered as a demonstration of method rather than a
robust estimate for parameterization of turbulent dispersion.
Meandering
The vertical meandering σm,z2 was calculated as the variance of
the ensemble average of the CM trajectories. The shortest trajectory of the
six puffs extended over 8 s after release. The ensemble average was
calculated for every time step up to this time in order to give a constant
weight to all detected trajectories (i.e. at every point in time, the same
number of trajectories is averaged). Figure
shows the meandering for the six puffs and, additionally, it shows the
meandering when additional puff trajectories from the full duration of the
experiment are included.
Meandering in the vertical. The black curve shows the ensemble average over the six puffs.
The meandering is sensitive to the chosen ensemble. The coloured dashed and dotted curves show the
meandering calculated for different numbers of puffs, selected by varying the time interval (line style)
and the minimum trajectory lengths (colour).
This enabled an assessment of the uncertainty of the meandering estimate. The
number of included trajectories was varied by simultaneously reducing the
minimum trajectory length and increasing the time interval. Including a
different number of puffs can lead to both a higher and lower
σm,z2. The meandering is generally larger when more trajectories
are included, particularly in the first few seconds all values lie above the
meandering for the six puffs only. The meandering calculated from the full
time period at medium trajectory lengths (7 s) was up to two times higher.
The increase might originate from atmospheric variability or from the poor
statistics. Additionally, a decreasing trend with increasing minimum
trajectory length can be observed. This might be explained by the
experimental setup. Some trajectories could get discarded during the data
processing due to, e.g. clouds in the background or the puff moving out of the
field of view. This leads to an effective data reduction to only certain
directions and therefore an underestimation of the vertical meandering. In
conclusion, the meandering shows a high dependence on the included
trajectories, which can be only resolved if a higher number of puffs is
available.
Relative dispersion
The relative dispersion is the spread of the SO2 distribution around its
centre of mass. It can therefore be estimated for each individual puff.
The spread of the six puffs, averaged over cameras 1–4, and their ensemble
average are plotted on a double logarithmic scale in
Fig. . The observed relative dispersion does not
show a clear transition from the t2 to the t3 regime. In facts, the
slope suggests that only the initial t2 regime is observed. That means
that the largest observed puff length scales are still affected by the
initial separation and, consequently, the puff dispersion according to the
Richardson–Obukhov scaling (t3 regime) could not be observed in this
experiment. A wider field of view of the cameras would result in longer
observation times, which enable an estimate of the Richardson–Obukhov
constant by fitting Eq. () to the
extended data using the measured value for the energy dissipation.
Relative dispersion in the vertical on a log–log scale. The coloured curves show the
dispersion of individual puffs and the black points show the ensemble average over these individual
puffs. The source size was estimated by a linear fit to the ensemble average (dashed black line).
The resulting source size was used to calculate the predicted curve by Eq. ()
(solid line) and estimate the source time (dotted black line).
Absolute dispersion in the vertical (solid black line). Relative dispersion and meandering
are shown with dotted and dashed black lines, respectively. Two parameterizations of Taylor's theorem
are plotted: modelled from the sonic anemometer data (blue) and fitted to the measured absolute
dispersion (red). For dispersion times much smaller than the Lagrangian timescale, the absolute
dispersion can be approximated by a t2-dependency (green).
The well-defined t2 expansion regime (the linear part with a slope of 2 in
Fig. ) allows for estimating the effective
vertical source size. Following Eq. (), the
resulting vertical source size is fitted to σr,z0=8.3 cm and
compares to the radius of the release outlet (6.25 cm). The increased number
can be explained by the jet created at the source by the blower. Assuming an
isotropic source, the source timescale was estimated to ts=(6⋅σr,z02/ϵ)1/3=2.6 s from the vertical source size and
energy dissipation rate ϵ. The resulting time lies in the middle of
the observed time period, making it possible to theoretically observe the
onset of the transition to the inertial subrange.
Absolute dispersion
The absolute dispersion describes the spreading of particles relative to a
fixed origin. It is calculated as the sum of meandering and relative
dispersion (Eq. ). In
Fig. the 1-D absolute dispersion in the vertical
dimension is displayed. The figure contains two parameterizations
(w′2‾, TL) of Taylor's theorem (Eq. ). In
both cases, w′2‾ is taken from the sonic anemometer data close
to the source. The estimate of the Lagrangian timescale differs: TL is
either modelled from the measured Eulerian timescale TE,z=3.07 s from
the same anemometer data using the empirical constant β=6.87
(Eq. ) or fitted to the absolute dispersion retrieved from the
image data. The modelled Lagrangian time is TL,zmodel=21.1 s and the
fitted one is TL,zfit=5.9 s. The fitted Lagrangian timescale
relates to the measured Eulerian timescale with βfit=TL,zTE,z=1.9 and lies within the previously reported range
of 1 to 10 see, e.g..
Here we report the absolute dispersion during the first 8 s after the
release. Hence, all measurements were recorded at times below both the
modelled and the measured Lagrangian timescales. For times much smaller
than the true Lagrangian timescale, the absolute dispersion can be
approximated by a quadratic relation, σz2≈σw2‾t2, independent of the Lagrangian timescale, hence
making an estimation of the latter nearly impossible for short observation
times. Therefore, even if a retrieval of the Lagrangian timescale from the
current image data is possible, it is not reliable since the puff observation
time does not exceed the Lagrangian timescale.
Further, the absolute dispersion was observed close to the source when it is
dominated by the meandering (σm2≈10σr2). The
absolute dispersion has therefore an uncertainty similar to that of the
meandering (see Sect. above).
Conclusions and future work
During the first Comtessa experiment, the passive tracer SO2 was
released in the ABL to study its dispersion based on images from six UV
SO2 cameras. As a proof-of-concept, the absolute dispersion, as well as
the relative dispersion and meandering of an ensemble of six puffs could be
retrieved by performing a reconstruction of the 3-D trajectories of the centre
of mass positions of instantaneous puff releases. The measured absolute
dispersion understates both the modelled and fitted parametrizations of
Taylor's theorem due to underestimation of the puff meandering.
We showed that a tomographic setup of six cameras is in principle suited to
measure the main statistical characteristics of the puff dispersion in the
ABL. However, the data set was limited by several points: (1) Artefacts from
clouds in the image are falsely interpreted as SO2 making an automatic
SO2 retrieval difficult. For the data amounts necessary for a meaningful
statistical analysis of puff releases, the data set should contain cloud free
data to enable automatic retrieval. (2) Some propagation directions might get
systematically discarded during the data processing. This would lead to an
underestimation of the puff meandering. (3) The release of the SO2 puffs is
only nearly instantaneous, leading to elongated puffs. This puts an
uncertainty on the relative dispersion estimate, in particular for the
along-wind coordinate.
It is desirable to determine a value for the Richardson–Obukhov constant and
the higher moments of the concentration distribution in order to constrain
atmospheric turbulence models. A robust estimate for the Richardson–Obukhov
constant of relative dispersion and Lagrangian integral timescales could be
obtained from a larger data set of longer tracked single puffs. Such a data
set is planned to be produced during follow-up Comtessa field
campaigns. The same concept as for the first campaign should be used but on a
larger scale i.e. releasing larger amounts of SO2. Higher amounts of SO2 will
increase the images' signal-to-noise ratio and facilitate observations
at larger distances to the tower. Consequently, this increases the cameras'
field-of-view enabling puff observations over longer distances and times.
Further, several conclusions regarding the camera placement could be drawn
from the first campaign: (1) Cameras should not observe the puffs frontal as
it is impossible to separate overlapping puffs in the analysis. Alternatively
the time between two releases has to be sufficiently long to allow a clear
puff separation. (2) If possible, release experiments should only be performed
on cloud-free days or at least the cameras have to be positioned such that
the clouds do not appear on the projected trajectories of the puffs. (3) Further, it should be possible to observe all propagation directions of the
puffs to avoid biases in the meandering towards a certain direction. The used
half-circle offers a good solution.
In the case of a cloud free data set, the presented method can be applied
fully automatically. Hence, providing a larger and cloud free data set opens
the door for statistical analysis of puff dispersion. Further under cloud
free conditions, the underlying imagery can be used to conduct a complete
tomographic reconstruction of SO2 concentration, which will be invaluable
for constraining models of atmospheric boundary-layer dispersion.
The raw measurement data and the python code used for data analysis is available
from the authors upon request. The code is based on the pyplis toolbox .
Details on the artificial release experimentReconstruction of the setup
Precise knowledge of the experimental setup is
necessary for the reconstruction of 3-D trajectories. During the field
campaign, the distances of the cameras to the release tower and the angle
towards north were measured using a theodolite. Comparing the pixel
coordinate of the top of the release tower in the camera image with the
tower's position, the three angles defining the camera pose (azimuth,
elevation and tilt) were extracted. The results are shown in
Table .
Camera temporal synchronisation
As no GPS time information was yet available during
the experiment, the image time series of the six SO2 cameras had to be
synchronised manually after the experiment. To this end, the release time of
18 subsequent puff releases between 10:29 and 10:31 UTC were detected for every
camera. Due to the distinct movement of the puffs within the turbulent flow,
the puffs could be clearly correlated in the images of all cameras. The
relative temporal offset Δti between camera i to camera 1 was
then calculated from the time difference of the first frame, on which a puff
was visible.
Δti=ti,start-t1,start
The temporal offset was averaged over 18 observed puffs between 10:29 and
10:31 UTC and is given relative to camera 1 in Table . The
accuracy of the temporal offset is limited by the discrete sampling frequency
which in turns is constrained by the exposure and readout time.
Relative differences in recorded (system) time stamps and exposure times (at 10:30 UTC).
CameraΔti [s]Δtexp [s]1–0.1620.15±0.100.1636.23±0.080.1746.28±0.080.1651.04±0.080.2060.61±0.100.17Data processing of the eddy covariance measurements
Meteorological measurements taken
between 10:27 and 10:32 UTC have been used to obtain the parameters reported
in Table .
Before the actual post processing, the collected data was treated by the
LICOR EddyPro software system for despiking e.g. and for applying the triple rotation correction
that nullify the average vertical and across-wind
components, and the v′w′‾ Reynolds stress component. This means
that the coordinate system is aligned with the measured mean wind direction;
see also for a description of the corrections applied in
EddyPro.
The values for the mean wind u‾ and the three turbulent fluxes
σu2, σv2, σw2 are reported at 8.7 m close to the
source location. The energy spectrum Ei(k) of the ith velocity
component, where k is the wavenumber, is the Fourier transform of the
autocorrelation function of that velocity component and was calculated
according to, e.g. p.312 and using Taylor's hypothesis.
The friction velocity u* was estimated by using the Reynolds stress
component at two metres as u*2=|u′w′‾|. The Obukhov length L is
defined as
L=-u*3θv‾κgw′θv′‾,
where θv is the virtual potential temperature, κ≈0.4 is
the von Kármán constant, g is the gravitational acceleration and
w′θv′‾ is the vertical turbulent flux of virtual potential
temperature. We used the sonic temperature as an approximation of virtual
temperature as discussed in, e.g. . As a consistency check,
the flux Richardson number was calculated at z=5.4 m using
Rf=w′θv′‾gθvu′w′‾δu‾δz.
In convective conditions, the flux Richardson number has a similar value to
z/L (here, -0.868) e.g. and our measurements
(Rf=-0.988) are in good agreement.
The mean dissipation of turbulent kinetic energy ϵ was obtained by
fitting a Kolmogorov spectrum E(k)=Ckϵ2/3k-5/3 to the
inertial range of the measured spectrum for the along-wind component of
velocity using the method discussed in detail by . The value
of the Kolmogorov constant Ck=0.49 was taken according to measurements and
theory of homogeneous isotropic turbulence e.g.. We observe a well-developed inertial subrange starting at a length
scale of about 9 m and the differences between estimates of ϵ based
on the three different velocity components are limited to about 30%. The
Eulerian integral timescale of the vertical velocity component TE,w was
obtained by fitting an exponential decay to the autocorrelation function for
the measured 5 min time series. The Lagrangian integral scale TL,w
was estimated from the Eulerian one by using the empirical fixed ratio β=TL,wTE,w proposed by and
, see Eq. () of the main paper.
Details on image processing methodsComtessa SO2 slant column density retrieval
The raw intensity images have to go through several
retrieval steps to get the final product, the SO2 slant column densities.
For a detailed, general description; see, e.g. or
. In the following all images are corrected for the dark
signal, which was recorded daily after the release experiments.
Sky masks are defined for every camera based on local intensity thresholds.
The sky masks separate the images in two regions according to whether the
intensity contains a reflected component or only backscattered sunlight.
Sunlight can be reflected from the ground, topography in the background, and
structures such as the release tower and antennas. This reflected region is
completely ignored in the further analysis.
The optical density images of the SO2 puffs are calculated according to
Eq. () from a SO2-containing and SO2-free background image.
The SO2-free background image is selected from the time series of puff
releases. Typically, this image is cloud-free and can be scaled to the base
intensity of an individual SO2-containing image recorded at a later time
e.g.. However, due to the partly strong cloud cover, a
background image containing the exact cloud structures but no SO2 is
necessary for the analysis. Such an image cannot be scaled to the changing
base intensity with time and is thus constrained to a short analysis period
of few tens of seconds for quantitative analysis. Therefore, a “patchwork”
image from the same time series during the puff release between 10:30:00 and
10:30:10 UTC was selected for every camera. If a puff was present in this image,
the respective image area was cut and replaced by the same area of an image
several seconds later without the puff present in this area.The calibration
from optical densities to SCDs is performed using the built-in DOAS
spectrometer.
Algorithm description: tracking of individual puffs in image plane
Figure depicts the
tracking algorithm schematically. The algorithm is based on three copies of
the original image (see Fig. ): (1) the original
high-resolution image, (2) an image which was blurred with a 2-D Gaussian
function (mean: 1, sigma: 5) and (3) a low-resolution image which was
sub-sampled to (87×65 pixel) using image pyramids. The images are
increasingly noise-reduced and have consequently lower detection limits for
SO2. The average standard deviations for the three image types are (1) 2.4e16 molec cm-2, (2) 1.75e16 molec cm-2, and
(3) 5.0e15 molec cm-2.
Flow diagram of the tracking algorithm. The puffs are detected iteratively based on the
previous detection and two noise-reduced versions of the original image. The conditions for a
valid ROI can be found in the text.
Puff detection based on noise-reduced images, here for camera 1 at 10:30:12. The ROI
is detected in a blurred image based on the position of the CM in the previous image (a).
A low resolution image is used to detect connected areas above a threshold (b). The combination
of both detections gives the resulting ROI, which is used to calculate the CM, total signal
and spread in the original image (c).
Sensitivity of the reconstructed trajectories to the removal of data from a single
camera. The trajectory colour indicates which camera was removed from the calculation, the
black trajectory is based on data from all cameras. The time indicates the release time of
the puff. In the altitude–north plots, the horizontal line represents the release altitude.
The puffs are tracked iteratively from the release point. Therefore, the image
coordinates of the release point and the start image of the individual puffs
have to be provided manually. The tracking will start from this image. After
every successful detection of the ROI, the next image will be loaded.
First the ROI is detected within the blurred image around the last-known
position of the puff. That is the release point for the first image, and the
CM of the previous image for all other images. A 50×50 ROI is set
around this point. Then the ROI is increased incrementally by single image
rows and columns. New pixel rows or columns are added to the ROI if they
contain at least 5 % pixel above a threshold of 3.5e16 molec cm-2. The
threshold is chosen as the double of the standard deviation to suppress noise
and cloud artefacts effectively. The ROI contains the central part of the
puffs but not necessarily separated fractions and weak tails.
Weak tails and separated fractions can be detected within the low-resolution
image which suppresses noise 4 times more compared to the blurred image. The
image is separated into connected regions containing a significant signal. A
pixel is considered to contain a signal if 25 % of the pixels in a 5×5
neighbourhood are above a threshold. This methods detects the SO2 puffs
and clouds alike, thus a separate selection is necessary to identify the
puffs. The detected ROIs are rescaled to the original resolution and compared
to the previously detected ROI from the blurred image. If the previously
found ROI immerses completely in a new ROI, it will be replaced by the larger
ROI. In this way, the full area of puffs including tails close to the
detection limit and separated SO2 patches are included.
When the final ROI of a puff is determined, the total signal, CM and spread
of the puff are calculated within this ROI based on the original image.
For the next image, the CM of the previous image is used as a starting point
for the ROI which is determined equivalently. The procedure is repeated until
an invalid ROI is detected. This is the case when the puff touches the image
borders or moves in front of non-sky areas such as the ground or vegetation
and topography on the horizon. In these cases, the ROI would no longer
contain the complete puff. Further, the tracking stops when it is likely that
cloud artefacts are tracked instead of the puff. This can be indicated by
jumps in the CM or a sudden increase or decrease of the ROI.
Sensitivity of trajectory retrieval to single camera
The 3-D CM trajectories are calculated by triangulation based on the
individual 2-D CM trajectories of the six cameras. While using a least-square
method including all six cameras reduces effects from uncertain camera
position and pose and clouds, data from only two cameras would be in
principle sufficient for reconstructing the 3-D trajectory. To determine the
sensitivity to possibly inaccurate data obtained from certain cameras, we
repeated the trajectory retrievals excluding systematically information from
one camera (Fig. ).
The retrieved 3-D trajectories show no particular sensitivity to a single
camera view, suggesting that none of the cameras adds crucial or false
information to the reconstruction.
Excluding the data from the cameras containing the most pronounced cloud
cover (3,5,6) does not shift the retrieved trajectories outside the
1σ-range of the trajectory including all cameras. Hence, we argue
that information from such cameras can be used for the trajectory
reconstruction even if they fail to fully detect and separate the puff from
cloud artefacts.
Videos of puff releases
The online supplement contains videos of the six puff releases recorded with
the six cameras. The videos are available at the online repository Zenodo:
10.5281/zenodo.1299638 (Dinger, 2018).
The detected ROI and CM are indicated on every image frame. The images were
noise-reduced (Gaussian filter with σ=5) to increase the visibility of
the puffs for the human eye. Note that the influence of cloud cover becomes
more evident as the time difference between background image and image frame
increases. Further, the times of the background images can be seen in the
video: the image background noise cancels to zero for this time according to
Eq. (). In some videos, additional absorption from small insects
flying through the cameras' field of view are visible in the form of straight
lines.
ASD, AS and MC wrote the manuscript.
KS, MC, AK, AS and IP contributed with discussion to the manuscript.
ASD analysed the camera data and developed the methodology.
MC, HA, and SYP analysed the eddy-covariance measurements towards turbulence.
AS, MC and KS designed the Comtessa experiment.
IP modelled the optimal setup of the UV cameras.
ASD, KS, MC, HA, SYP, NS, JW and AS contributed to the field experiment.
The SO2 cameras have been designed by CB, KS and developed by KS, ASD and CB.
The authors declare that they have no conflict of interest.
Acknowledgements
The Comtessa project has received funding from the European Research Council
(ERC) under the European Union's Horizon 2020 research and innovation programme under grant agreement no. 670462.
Edited by: Huilin Chen
Reviewed by: Jean-François Smekens and one anonymous referee
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