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**Atmospheric Measurement Techniques**
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**Research article**
22 Jun 2020

**Research article** | 22 Jun 2020

Can statistics of turbulent tracer dispersion be inferred from camera observations of SO_{2} in the ultraviolet? A modelling study

^{1}NILU – Norwegian Institute for Air Research, 2007 Kjeller, Norway^{2}Gexcon AS, 5072 Bergen, Norway^{3}PGS, 0283 Oslo, Norway^{4}Gwangju Institute of Science and Technology, 61005 Gwangju, South Korea^{5}Department of Meteorology and Geophysics, University of Vienna, 1010 Vienna, Austria

^{1}NILU – Norwegian Institute for Air Research, 2007 Kjeller, Norway^{2}Gexcon AS, 5072 Bergen, Norway^{3}PGS, 0283 Oslo, Norway^{4}Gwangju Institute of Science and Technology, 61005 Gwangju, South Korea^{5}Department of Meteorology and Geophysics, University of Vienna, 1010 Vienna, Austria

**Correspondence**: Arve Kylling (arve.kylling@nilu.no)

**Correspondence**: Arve Kylling (arve.kylling@nilu.no)

Abstract

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Atmospheric turbulence and in particular its effect on tracer dispersion may be
measured by cameras sensitive to the absorption of ultraviolet (UV)
sunlight by sulfur dioxide
(SO_{2}), a gas that can be considered a passive tracer over short
transport distances. We present a method to simulate UV camera
measurements of SO_{2} with a 3D Monte Carlo radiative transfer model
which takes input from a large eddy simulation (LES) of a SO_{2}
plume released from a point source. From the simulated images the
apparent absorbance and various plume density statistics
(centre-line position, meandering, absolute and relative dispersion, and
skewness) were calculated. These were compared
with corresponding quantities obtained directly from the LES.
Mean differences of centre-line position, absolute and
relative dispersions, and skewness between the
simulated images and the LES were generally found to be smaller than or
about the voxel
resolution of the LES. Furthermore, sensitivity studies were made to
quantify how changes in solar azimuth and zenith angles, aerosol loading
(background and in plume), and surface albedo impact the UV camera
image plume statistics. Changing the values of these parameters within realistic
limits has negligible effects on the centre-line position, meandering,
absolute and relative dispersions, and skewness
of the SO_{2} plume. Thus, we demonstrate that UV camera images of
SO_{2} plumes may be used to derive plume statistics of relevance for
the study of atmospheric turbulent dispersion.

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Kylling, A., Ardeshiri, H., Cassiani, M., Dinger, A. S., Park, S.-Y., Pisso, I., Schmidbauer, N., Stebel, K., and Stohl, A.: Can statistics of turbulent tracer dispersion be inferred from camera observations of SO_{2} in the ultraviolet? A modelling study, Atmos. Meas. Tech., 13, 3303–3318, https://doi.org/10.5194/amt-13-3303-2020, 2020.

1 Introduction

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Air motion in the lowest part of the atmosphere is bounded over land by a solid
surface of varying temperature and roughness. This part of the
atmosphere is named the planetary boundary layer
(PBL; Stull, 1988). It responds quickly to surface radiation
changes, and the air motion in the PBL is nearly always turbulent. A
substance released into this turbulent atmosphere will, at locations
downwind of its source, experience concentration fluctuations that
are important, particularly if responses are non-linear, for
example, with respect to toxicity, flammability and odour detection
(e.g. Hilderman et al., 1999; Schauberger et al., 2012; Gant and Kelsey, 2012), and
non-linear chemical reactions
(Brown and Bilger, 1996; Vilà-Guerau de Arellano et al., 2004; Cassiani et al., 2013).
The Camera Observation and Modelling of 4D Tracer
Dispersion in the Atmosphere (COMTESSA) project (https://comtessa-turbulence.net/, last access: 16 June 2020)
aims to “elevate the theory and simulation of turbulent tracer
dispersion in the atmosphere to a new level by performing completely
novel high-resolution 4D measurements”. Over short transport
distances, sulfur dioxide (SO_{2}) may be considered to be a passive
tracer. Furthermore, SO_{2} strongly absorbs radiation in part of
the UV spectrum and may thus be detected by, for example, UV-sensitive
cameras (see, for example, Kern et al., 2010b, and references therein). Within COMTESSA, six UV
cameras have been built to measure SO_{2} densities from various
viewing directions. A series of experiments with puff and continuous releases of
SO_{2} from a tower have been performed as described by
Dinger et al. (2018). It is known from measurements of volcanic
SO_{2} emissions that aerosol and viewing geometry affect the
retrieved SO_{2} amounts (Kern et al., 2013). Furthermore, variations in surface albedo
and solar zenith and azimuth angles may have an impact. The influence of
these factors on the UV camera images, the deduced SO_{2} amounts, and
density statistics needs to be quantified and, if necessary, corrected for.

Kern et al. (2013) performed radiative transfer simulations, including a
circular SO_{2} plume, to estimate the effect of plume distance,
SO_{2} amount, and aerosol on the radiance at a UV camera location.
However, to the authors' knowledge, UV camera images have not been simulated
before. We present a novel method to simulate UV camera
images of a dispersing SO_{2} plume using a 3D radiative transfer
model. The 3D description of the SO_{2} plume is provided by large
eddy simulation (LES) and is used in lieu of real
atmospheric flow. The simulated images are used to examine how various
factors (solar angles, aerosol content, and
surface albedo) affect the statistical parameters characterizing the
SO_{2} plume dispersion.
The LES providing the input to the radiative transfer
modelling, the radiative transfer model used
to simulate the camera images, and the statistical parameters
are described in
Sect. 2. The effects of solar azimuth and zenith angles, surface
albedo, background aerosol, and aerosols in the plume on plume density
statistics are presented in Sect. 3.
Furthermore, the plume density statistics from the simulated images are
compared with statistics derived directly from the LES simulations.
The paper ends with the conclusions in Sect. 4.

2 Methods

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Large eddy simulation is nowadays viewed as a popular tool in many
applied atmospheric dispersion studies, especially of the urban
environment and for critical applications such as the release of toxic
gas substances (e.g. Fossum et al., 2012; Lateb et al., 2016). LES provides
access to the 3D turbulent flow field, and it is
sometimes used as a replacement for experimental measurements at high
Reynolds numbers.
In this methodology, the large scales of the turbulent flow are
explicitly simulated while a low-pass filter is applied to the
governing equations to remove the small scales information from the
numerical solution. The effects of the small scales are then
parameterized by means of a sub-grid scale (SGS) model
(e.g. Deardorff, 1973; Moeng, 1984; Pope, 2000; Celik et al., 2009).
We used the Parallelized Large-Eddy Simulation Model (PALM; Raasch and Schröter, 2001; Maronga et al., 2015) to solve the filtered, incompressible
Navier–Stokes equations in Boussinesq-approximated form at an infinite
Reynolds number. A 3D domain of
$\mathrm{1000}\phantom{\rule{0.125em}{0ex}}\mathrm{m}\times \mathrm{375}\phantom{\rule{0.125em}{0ex}}\mathrm{m}\times \mathrm{250}\phantom{\rule{0.125em}{0ex}}\mathrm{m}$ in the along wind (*x*),
crosswind (*y*), and vertical (*z*) directions, respectively, was
simulated with a grid resolution of $nx\times ny\times nz=\mathrm{1024}\times \mathrm{384}\times \mathrm{256}$. Here $nx,ny,$ and *n**z* are the number of grid nodes
in along wind, crosswind, and vertical directions, respectively. This
implies that the size of a grid cell is 0.98^{3} m^{3}≈1 m^{3}. The release point was located at 25 and 150 m above the
ground, depending on camera view direction; see Sect. 2.2.

The neutral boundary layer was simulated as an incompressible half-channel flow at an infinite Reynolds number. The flow was driven by a constant pressure gradient. For the velocity, periodic boundary conditions were used on the lateral boundaries while on the top a strictly symmetric, stress-free condition was applied. The bottom wall was not explicitly resolved, but a constant flux layer was used as is commonly done in atmospheric simulations. Non-periodic boundary conditions were set for the passive scalar. For further information on the model set-up, see also Ardeshiri et al. (2020).

The LES calculates 3D SO_{2} concentrations as a function of time. The
SO_{2} concentrations are used as input to the 3D radiative transfer
model simulations. A total of 100 time frames were calculated with a
time resolution of 6.25 s. For the sensitivity studies one randomly
chosen time frame was used, while seven and nine randomly chosen frames
were used for the reference case calculation
(see Sect. 3). Both parts of the plume close to the
release point and further downstream were used as input for the camera
simulations. In Fig. 1 examples are provided
of the part of the plume viewed by the different cameras (see Sect. 2.2 for camera definition). Figure 1a
and b show the SO_{2} column densities
along the *y* and *z* axes, respectively, for one instant of the LES
simulation. Figure 1a shows approximately the part of
the plume seen by camera A.
Figure 1c, d, and
e show the part of the plume viewed by cameras B, C,
and D, respectively.

The UV camera images were simulated with the 3D MYSTIC Monte Carlo radiative
transfer model which was run within the libRadtran framework
(Mayer et al., 2010; Emde et al., 2010, 2016; Buras and Mayer, 2011; Mayer and Kylling, 2005).
MYSTIC includes an option to calculate the radiation impinging on a
camera with a prescribed number of pixels in a plane defined by the
location of the camera within a 3D domain and the camera viewing
direction. For this option, the MYSTIC Monte Carlo model is run in
backward mode. The MYSTIC camera simulation capabilities have earlier been used by, for example,
Kylling et al. (2013) to simulate infrared satellite images. Here it is used to
simulate radiative transfer to a UV camera at wavelengths suitable for the detection
of SO_{2}. Thus, for each camera pixel, spectra were
calculated for wavelengths ranging between 300 and 350.5 nm. The
spectral resolution was 0.1 nm in order to capture the fine structure
of the SO_{2} cross section. The spectra were
weighted with spectral response functions (about 10 nm width)
representing cameras with mounted on-band
(sensitive to SO_{2} absorption, centred at 310 nm) and off-band (barely sensitive to SO_{2}
absorption, centred at about 330 nm) filters similar to those described
by Gliß et al. (2018). Quantum efficiency of the detector and
geometrical effects related to lens/camera optics were not included in
the camera simulations.
SO_{2} plume concentrations were adopted from the LES simulations described
in Sect. 2.1, and the spectrally dependent SO_{2}
absorption cross section was taken from Hermans et al. (2009).

A finite 3D domain (bird's eye view provided in Fig. 2)
is defined for the radiative transfer simulations. The SO_{2} plume is
embedded in this domain and is viewed from the side at a distance of
about 250 m by the UV camera, which is placed 1 m above the
surface. This camera–plume distance is comparable to that used during
part of the first COMTESSA field campaign described by
Dinger et al. (2018).

Four different cameras at different locations and viewing geometries were simulated. These are summarized in Table 1.

Camera A captures the plume from its release point and about 200 m
downwind. It sees the plume released at an altitude of 25 m and thus
has a low-angle viewing elevation; see Table 1.
Cameras B, C, and D resemble a different experimental situation with the
plume release altitude of 150 m. These cameras thus have
a larger viewing elevation. Camera B is placed at the same *x*-direction
location as camera A but has a smaller horizontal field of view (FOV) to focus on the
more mature parts of the plume. Cameras C and D are placed further
downwind and view the plume about 300 and 500 m downwind from the
release point, respectively.

The LES voxel resolution is about 1 m^{3}, which at a distance of 250 m
corresponds to 0.004 rad=0.23^{∘}. To ensure
sufficient spatial sampling, the camera resolution was specified to be
about half the LES voxel resolution. To be able to see the plume at
the various camera positions the camera FOV was varied
and the number of pixels adopted to give a camera resolution of about
0.5 m at the plume.
It is noted that the UV cameras used by Dinger et al. (2018)
had 1392×1040 pixels. The reason and justification for using
fewer pixels in the simulated camera are twofold: (1) with the
simulated camera it is possible to zoom onto the plume as one always
knows where the plume is. In an experimental setting, the plume
usually covers only part of the FOV to allow for changes in wind
direction and, thus, changes in plume position. (2) The computer time
and memory requirements increase as the
number of pixels increases. It is thus advantageous to use as few
pixels as needed to cover the plume.

As the COMTESSA field campaigns are being carried out primarily in central
Norway during the summer time, solar zenith angles of
40^{∘} and 60^{∘} were considered. When not otherwise
noted (see Sect. 3.2), the
sun was assumed to be perpendicular to the camera viewing direction;
see Fig. 2.

To further save computer memory and time, a full 3D description of the plume is given only in the part of the domain containing the plume seen by the camera (red square in Fig. 2). Outside the red square, the plume is not included. Energy conservation is ensured by using periodic boundary conditions; that is, photons leaving the domain on one side enter the domain again on the opposite side. Not having periodic boundary conditions would let the photons leave the domain and thus not be accounted for. Periodic boundary conditions imply that effectively the plume within the domain keeps on repeating itself in the horizontal. Thus the plume may be seen by the camera several times if care is not taken when setting up the geometry of the computational domain, the location of the plume within the domain, and the camera. However, sometimes these “ghost” plumes are unavoidable due to the geometry and computational resources. It is noted that the “ghost” plumes get smaller and smaller in the camera view the further away they are from the domain with the camera. For camera A “ghost” plumes pose a challenge due to the low-altitude plume and camera viewing angles close to the horizon. Great care was thus taken when setting the domain size and the camera A field of view to avoid “ghost” plumes in the simulated images. Still, part of a secondary “ghost” plume is present in some of the images. These “ghost” plumes have been removed from the analysis presented below for camera A.

For representing the ambient atmosphere, the mid-latitude summer atmosphere of Anderson et al. (1986) was used. The surface albedo is small in the UV for non-snow-covered surfaces and was thus set to zero when not otherwise noted (see Sect. 3.4). Aerosols were included for specific sensitivity tests that are described in Sect. 3.3.

The radiative transfer simulations were run on a Linux cluster utilizing 10 processors in parallel, with each process needing about 10–15 GB of memory depending on whether aerosols in the plume were included or not. The MYSTIC Monte Carlo radiative transfer simulation is statistical in nature, and the simulated images thus contain statistical noise. To achieve a noise level of about the same order of magnitude as the measurements (≈1 %), a sufficient number of photons needs to be traced. For each pixel and wavelength 2000 photons were traced. This gave simulation times for one on- and one off-band image of about 120–140 h and ensured that, for the simulations without aerosol and zero surface albedo, at least 93.0 % of the pixels had radiances with a relative standard deviation <1.0 %. For simulations with background aerosols, the corresponding number is 83 %.

The apparent absorbance for the on-band camera is given by Mori and Burton (2006) and Lübcke et al. (2013) as follows:

$$\begin{array}{}\text{(1)}& {\mathit{\tau}}_{\mathrm{on}}=-\mathrm{ln}{\displaystyle \frac{{I}_{\mathrm{on},M}}{{I}_{\mathrm{on},\mathrm{0}}}}.\end{array}$$

Here, *I*_{on,M} is the on-band radiance and
*I*_{on,0} the background radiance without the SO_{2} plume.
In addition to absorption by SO_{2}, *τ*_{on} may include
absorption due to aerosol and plume condensation. Assuming that the
absorption by these other constituents varies little with wavelength
between the on- and off-band cameras, the extra absorption may be
removed by subtracting the off-band absorption as follows:

$$\begin{array}{}\text{(2)}& \begin{array}{rl}\mathit{\tau}& ={\mathit{\tau}}_{\mathrm{on}}-{\mathit{\tau}}_{\mathrm{off}}=-\mathrm{ln}{\displaystyle \frac{{I}_{\mathrm{on},M}}{{I}_{\mathrm{on},\mathrm{0}}}}+\mathrm{ln}{\displaystyle \frac{{I}_{\mathrm{off},M}}{{I}_{\mathrm{off},\mathrm{0}}}}\\ & =\mathrm{ln}\left({\displaystyle \frac{{I}_{\mathrm{off},M}}{{I}_{\mathrm{on},M}}}{\displaystyle \frac{{I}_{\mathrm{on},\mathrm{0}}}{{I}_{\mathrm{off},\mathrm{0}}}}\right),\end{array}\end{array}$$

where *I*_{off,M} and *I*_{off,0} are the off-band radiance
and the off-band background radiance, respectively. The background
images were calculated similar to the plume images but with the
SO_{2} concentration set to zero. Below, plume statistics are presented
for both *τ*_{on} and *τ*.

Ideally, plume statistics from the LES SO_{2} concentrations and image-derived SO_{2} concentrations should be compared. However, for the
images this would require simulating the geometry suitable for
tomography and tomographic reconstruction of the plume.
The slant column density (SCD) is the concentration of a gas along the
light path (typically in units of m^{−2}). It is calculated from the
LES SO_{2} concentrations by tracing individual rays corresponding
to individual camera pixels. From apparent absorbances, the SCD may be
retrieved. For SO_{2} camera measurement this is done by calibrating
the camera with SO_{2} cells and/or concurrent differential optical
absorption spectroscopy (DOAS) measurements. The calibration gives a
linear relationship between the apparent absorbance and the SCD
(see, for example, Lübcke et al., 2013). Such calibration procedures
could be simulated and used to calibrate the simulated
images. However, higher-order moments (first-order moment and upwards)
would be the same for the SCD and the apparent absorbance due to the
linear relationship between the two. Thus, below we will compare
SO_{2} SCD from the LES with apparent absorbance from the images. We
note that this comparison will not include the zeroth moment (total
mass) and that systematic biases may go undetected. While a comparison
of the total mass certainly is of interest, this would require a
systematic investigation of SO_{2} calibration using simulated images,
which is beyond the scope of this work.

For projected LES simulations and the simulated images, the vertical (in the images) plume centre-line position, meandering, absolute and relative dispersions, and the skewness were calculated (see e.g. Dosio and de Arellano, 2006). However, the absolute dispersion can only be properly defined using an ensemble or time average. As this is not possible here due to the above-mentioned computing limitations, we use the centre of the source ($\stackrel{\mathrm{\u203e}}{z}={z}_{\mathrm{0}}$) as the reference vertical position.

Each pixel in the camera images and each projection from the LES
simulations describe the integrated column amount (*ρ*_{L})
of the trace gas along the line of sight (d*L*) as follows:

$$\begin{array}{}\text{(3)}& {\mathit{\rho}}_{L}=\int \mathit{\rho}\mathrm{d}L,\end{array}$$

where *ρ* is the density of the trace gas.
The
instantaneous vertical plume centre-line position *z*_{m} is given by the following:

$$\begin{array}{}\text{(4)}& {z}_{\mathrm{m}}\left(x\right)={\displaystyle \frac{\int z{\mathit{\rho}}_{L}\mathrm{d}z}{\int {\mathit{\rho}}_{L}\mathrm{d}z}},\end{array}$$

where *x* and *z* are the horizontal and vertical positions of the
pixel, respectively.

The fluctuations of the absolute, relative, and centre-line positions are defined as follows:

$$\begin{array}{}\text{(5)}& {\displaystyle}{z}^{\prime}=z-{z}_{\mathrm{0}}\text{(6)}& {\displaystyle}{z}_{\mathrm{r}}=z-{z}_{\mathrm{m}}\text{(7)}& {\displaystyle}{z}_{\mathrm{m}}^{\prime}={z}_{\mathrm{m}}-{z}_{\mathrm{0}}.\end{array}$$

It is noted that with this definition of the absolute position,
relative and absolute dispersion are the same at the source
location, since meandering here is zero.
Also, since we set $\stackrel{\mathrm{\u203e}}{z}={z}_{\mathrm{0}}$, there will be correlations
between ${z}_{\mathrm{m}}^{\prime}$ at different *x*, which also
implies that $\stackrel{\mathrm{\u203e}}{\left({z}_{\mathrm{m}}^{\prime}\right)}$ is strictly speaking not a robust
reference for defining meandering of the plume. However, the purpose of this study
is to investigate the sensitivity of the statistical properties to
changes in various atmospheric parameters and this limitation should have
minimal impact on the results.

The absolute (*σ*_{z}), relative (*σ*_{zr}), and meandering
(*σ*_{zm}) dispersions are defined as follows:

$$\begin{array}{}\text{(8)}& {\displaystyle}{\mathit{\sigma}}_{z}^{\mathrm{2}}\left(x\right)={\displaystyle \frac{\int {\mathit{\rho}}_{L}{z}^{\prime \mathrm{2}}\mathrm{d}z}{\int {\mathit{\rho}}_{L}\mathrm{d}z}}\text{(9)}& {\displaystyle}{\mathit{\sigma}}_{z\mathrm{r}}^{\mathrm{2}}\left(x\right)={\displaystyle \frac{\int {\mathit{\rho}}_{L}{z}_{\mathrm{r}}^{\mathrm{2}}\mathrm{d}z}{\int {\mathit{\rho}}_{L}\mathrm{d}z}}\text{(10)}& {\displaystyle}{\mathit{\sigma}}_{z\mathrm{m}}^{\mathrm{2}}={\displaystyle \frac{\int {\mathit{\rho}}_{L}{z}_{\mathrm{m}}^{\prime \mathrm{2}}\mathrm{d}x}{\int {\mathit{\rho}}_{L}\mathrm{d}x}}\end{array}$$

and similarly for the skewnesses, as follows:

$$\begin{array}{}\text{(11)}& {\displaystyle}\stackrel{\mathrm{\u203e}}{{z}^{\prime \mathrm{3}}}={\displaystyle \frac{\mathrm{1}}{{\mathit{\sigma}}_{z}^{\mathrm{3}}\left(x\right)}}{\displaystyle \frac{\int {\mathit{\rho}}_{L}{z}^{\prime \mathrm{3}}\mathrm{d}z}{\int {\mathit{\rho}}_{L}\mathrm{d}z}}\text{(12)}& {\displaystyle}\stackrel{\mathrm{\u203e}}{{z}_{z\mathrm{r}}^{\prime \mathrm{3}}}={\displaystyle \frac{\mathrm{1}}{{\mathit{\sigma}}_{z\mathrm{r}}^{\mathrm{3}}\left(x\right)}}{\displaystyle \frac{\int {\mathit{\rho}}_{L}{z}_{\mathrm{r}}^{\mathrm{3}}\mathrm{d}z}{\int {\mathit{\rho}}_{L}\mathrm{d}z}}\text{(13)}& {\displaystyle}\stackrel{\mathrm{\u203e}}{{z}_{z\mathrm{m}}^{\prime \mathrm{3}}}={\displaystyle \frac{\mathrm{1}}{{\mathit{\sigma}}_{z\mathrm{r}}^{\mathrm{3}}\left(x\right)}}{\displaystyle \frac{\int {\mathit{\rho}}_{L}{z}_{\mathrm{m}}^{\prime \mathrm{3}}\mathrm{d}x}{\int {\mathit{\rho}}_{L}\mathrm{d}x}}.\end{array}$$

These various quantities were calculated both directly from the projected LES simulations and also from the camera images. The former served as a reference (“ground truth”) against which the quantities derived from the camera images were compared.

3 Results

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We first compare statistical results from the LES and simulated images reference atmospheric conditions. This comparison is made for multiple time frames and is done in order to estimate how well the camera-derived statistics may reproduce the LES statistics. Next the impact of solar angles, aerosol load, and surface albedo on plume statistics is investigated for a single time frame.

Figure 3a and
b show simulated on- and
off-band radiances, respectively, for camera A and the reference case
(no aerosol, zero surface albedo, and a solar zenith angle of
40^{∘}).

The strong absorption of SO_{2} in the on-band image is clearly
visible in Fig. 3a. There
is also a weak SO_{2} signal in the off-band image
(Fig. 3b). From the on-
and off-band images and corresponding background images not including the
SO_{2} plume, the apparent absorbance was calculated using
Eq. (2). The resulting apparent absorbance is shown in
Fig. 3c on a linear scale
and in Fig. 3d on a logarithmic
scale.
The apparent absorbance is reproduced in
Fig. 4a, while
Fig. 4b
shows the SCD calculated along the line of sight using the LES concentrations.
The plume centre line, absolute and relative dispersions, and
skewness, as defined in Eqs. (4),
(8), and (11), were calculated from the
simulated images and the LES images. These are shown
as solid lines (LES) and dotted lines (camera simulation) in
Fig. 4c and d.
Similar plots for cameras B, C, and D are presented in
Figs. 5–7.
Note that the simulated and LES images in
Figs. 4–7
differ from those in Fig. 1 due to different
viewing directions. In the latter
the plumes are viewed at a viewing angle of 0^{∘} while for
cameras A, B, C, and D the viewing angle differs from the horizontal;
see Table 1.

Overall the behaviour of the centre line, absolute and relative
dispersions, and skewness calculated from the simulated images is
similar to those from the LES densities for all cameras.
The centre line agrees well for all four cameras. For camera A,
Fig. 4, the absolute and
relative dispersions from the camera are larger than those from the
LES for the plume downwind to about 100 m (corresponding to ≈90^{∘} horizontal viewing angle) from the release point.
For camera B,
Fig. 5, all
quantities agree well, while for cameras C (Fig. 6)
and D
(Fig. 7), the
camera dispersions are larger than the LES dispersions by about
50 %–60 %, and the magnitude of the skewness from the camera is also larger.

To shed further light on the differences between the images from the radiative transfer simulation and the LES, we show the probability density function (pdf) of the column densities from the LES and simulated images in Fig. 8. These pdf's represent area sample pdf's and cover the full images.

For camera A the pdf's differ for intermediate values, where an
artificial secondary peak is created in the pdf for the simulated
image. This is most likely due to the diffusive nature of the
radiative transfer in
the young part of the plume (horizontal angle smaller than about
85^{∘}) where the LES plume is of the size a few voxels.
However, the SO_{2}
absorption signal is strong, and thus the centre line, dispersions, and
skewness agree well for the dispersed part of the plume.
For camera B the pdf's are similar, and this is reflected in the good
agreement between the statistical quantities presented in
Fig. 5. This
indicates that when the plume is large enough compared to the pixel
resolution the camera can capture the plume well.
The pdf's for camera C exhibit much the same behaviour. However, at this
further downwind location, the plume is more dispersed, and the SO_{2}
absorption signal is weaker and sometimes beyond detection (thus the lower
cut-off in the pdf of the simulated image). The weaker absorption
signal implies that the statistical noise from the Monte Carlo-based
radiative transfer simulation becomes discernible and increases the
dispersions compared to the LES (Fig. 6).
A similar situation is evident for camera D; see pdf's in
Fig. 8 and statistical quantities in
Fig. 7.

As noted above, a large number of images such as in Fig. 3 is required to estimate the parameters of interest for the description of turbulence. This is not computationally feasible with the available resources. However, it is noted that if the instantaneous statistics are correct, the ensemble statistics will also be correct. This is not necessarily true the other way around. To provide an estimate of the difference between the statistical quantities from the simulated images and the LES densities, the differences between the centre line, the absolute and relative dispersions, and the skewness were calculated for seven (camera A) and nine (cameras B, C, and D) random time steps. The mean differences and the standard deviations are summarized in Table 2.

The mean differences between the quantities from the simulated images and the
LES densities are small for cameras A and B. For the centre line and
the dispersions the differences are about or smaller than the voxel
resolution of the LES simulations.
For camera C the centre-line differences are about the LES voxel
resolution, whereas the dispersion differences increase.
Camera D differences show similar behaviour but with even larger
differences for the dispersions.
As already mentioned above, the main source for the differences is the
Monte Carlo noise in the radiative transfer simulation when the SO_{2}
signal becomes weak. This alters the
dispersions, Figs. 4–7,
and pdf's, Fig. 8. This is evident in the simulated images dispersions,
which are not as smooth as those from the LES
(Figs. 5–7).
It must also be emphasized that the densities simulated by the LES and the
apparent absorbance are not
the same physical quantities but are non-linearly connected through the
radiative transfer equation.

In Figs. 3 and
4 results were shown for
solar azimuth and zenith angles of *ϕ*_{0}=90^{∘} and *θ*_{0}=40^{∘}, respectively. The simulations were repeated for a solar zenith angle of *θ*_{0}=60^{∘} to see if this would change the plume statistics. The difference in apparent absorbance, $\mathit{\delta}\mathit{\tau}=\mathit{\tau}({\mathit{\theta}}_{\mathrm{0}}=\mathrm{60})-\mathit{\tau}({\mathit{\theta}}_{\mathrm{0}}=\mathrm{40})$, is shown in
Fig. 9.

The apparent absorbance is generally slightly smaller (on average
about 6 %) for *θ*_{0}=60^{∘} than for *θ*_{0}=40^{∘}.
Ideally the apparent absorbance is due to photons travelling along straight lines passing through the plume and into the
camera. However, photons taking other paths may also contribute to the
signal. Direct solar radiation photons contribute in the following three ways to the
camera signal through: (1) direct photons scattered behind the plume in
the direction of the camera; (2) direct photons scattered in the plume
towards the camera; and (3) direct photons scattered between the plume
and the camera in the direction of the camera. The first part is
included in the apparent absorbance and does not depend on solar
zenith angle due to the background correction. The third part is
called light dilution and does not depend on the amount of SO_{2} in
the plume. The second part depends on the amount of SO_{2} in the
plume and the solar zenith angle. The latter is because there is
relatively more direct radiation at *θ*_{0}=40^{∘} than at
*θ*_{0}=60^{∘}. Hence, more direct radiation is likely to enter
the plume for *θ*_{0}=40^{∘} and be scattered into the
camera from inside the SO_{2} plume. This explains the negative difference in
the apparent absorbance between *θ*_{0}=60^{∘} and
*θ*_{0}=40^{∘}. It is noted that in an experimental setting,
where calibrations are carried out throughout the day, solar zenith
angle variations will not necessarily give a change in SO_{2}.

Statistics were calculated as for the
*θ*_{0}=40^{∘} case and differences to this case are summarized
in Table 3, with rows labelled “*θ*_{0}=60^{∘}”.
In the table, differences are reported as the maximum difference in
units of metres.
Differences are reported both without and with the off-band
correction (Eqs. 1 and 2, respectively) to
quantify the impact of the correction.
Overall, the statistics for the *θ*_{0}=60^{∘}
results deviate little from the *θ*_{0}=40^{∘} case.
The difference in meandering, not shown in
Table 3, is negligible for this and all
sensitivity cases below and is not further discussed.

The sensitivity to the solar azimuth angle was investigated by setting
the solar azimuth angle to *ϕ*_{0}=0, 45, 135, 180, and 270^{∘},
while keeping the solar zenith angle at *θ*_{0}=40^{∘}.
The difference in absorbance is less than 0.05 % on average. The
impact on the centre line, absolute and relative dispersions, and
skewness is negligible; see rows labelled “*ϕ*_{0}=0–270^{∘}” in
Table 3. From the results no preferable solar
azimuth camera viewing direction geometry may be identified. However,
note that the azimuth angle of the background image needs to be the
same as for the image with SO_{2}.
It is noted that including
aerosols has negligible effect on the solar azimuth angle sensitivity;
see Sect. 3.3.

No aerosols were included in the simulations above. Background
aerosols may be present in both the plume and in the surrounding
atmosphere. Furthermore, aerosol may be present in the plume due to
formation of sulfate aerosol from SO_{2}. Both cases are investigated
below.

First, background aerosol with an optical depth *t*_{BG}(310)=0.5 and
a single scattering albedo (SSA) of about 0.95 at 310 nm were
included in simulations for *θ*_{0}=40^{∘} (the
aerosol_default option of uvspec was used; see Emde et al., 2016).
The difference between the simulation including
background aerosol and the aerosol-free simulation is shown in
Fig. 10a.

Including background aerosol generally gives a slightly lower apparent absorbance, which is on average about 2.5 % whether the off-band correction is excluded or included (Eqs. 1 and 2, respectively). The decrease is due to multiple scattering by the aerosol and hence less direct radiation (Kern et al., 2010a). The background aerosol had negligible effects on plume statistics (Table 3, rows labelled “BG aerosol”).

Simulations were also made with aerosol in the plume only; that is,
various amounts of aerosol
were added to the voxels containing SO_{2}. This is relevant for
non-pure SO_{2} plumes where aerosols are co-emitted, such as from
power plants, or where secondary sulfate aerosols may form in the
SO_{2} plume. The impact of both highly absorbing (SSA=0.8) and purely
scattering aerosol (SSA=1.0) was investigated. Kern et al. (2013)
concluded that if a plume contains an absorbing aerosol component the
retrieved SO_{2} columns may be underestimated. Here we estimate the
effect of aerosols in the plume on the higher-order statistics of the
plume.
Figure 10b and
c
show the difference in apparent absorbance between simulations
with and without absorbing aerosol in the plume for a relatively large
aerosol optical depth of about 0.5
(Fig. 10b)
and an unrealistic extreme case
with aerosol optical depth of about 5.0 at 310 nm
(Fig. 10c).
Results for non-absorbing aerosol are similar (not shown).

For the more realistic value, *τ*_{plume}∼0.5,
Fig. 10b,
there is little impact on the apparent absorbance. For (non-)absorbing
aerosol with SSA=0.8 (SSA=1.0), the decrease is less than 0.2 % (0.16 %)
on average with off-band correction, and the increase is less than
1.1 % (0.63 %) on average without off-band correction.
For (unrealistically) large amounts of (non-)absorbing aerosol in the
plume, *τ*_{plume}∼5.0, the apparent absorbance
decreases by less than 2 % (1.5 %) on average if off-band correction
is included; see Eq. (2). Without off-band correction,
Eq. (1), the apparent
absorbance increases by 9.5 % (5.43 %) on average. For all cases the
off-band correction reduces the influence of aerosol, as intended.
For both aerosol in plume cases and whether the off-band correction was included or not, the plume
statistics were affected to a negligible extent, as reported in rows
labelled “*τ*_{plume}” in
Table 3. However, the standard deviation of the
skewness increases largely when aerosol influence is not corrected
for or if the plume is thick and absorbing.

The sensitivity of the solar azimuth angle when including aerosols was
investigated by performing additional simulations for *ϕ*_{0}=45 and
180^{∘} for the aerosol in the plume and background aerosol cases with
*τ*_{plume}∼0.5. The solar azimuth angle sensitivity
for these cases were of the same magnitude as for the aerosol-free
simulations and thus of negligible impact.

All simulations above were made with a surface albedo *A*=0.0 to avoid
coupling between the various processes that affect the camera
images. For the wavelengths considered here the albedo for snow-free
surfaces is generally small (*A*<0.1; see for
example Wendisch et al., 2004). To test the sensitivity to snow-free
surface albedo, simulations were made for surface albedos of *A*=0.05
and *A*=0.1. In addition, a simulation was made with *A*=1.0 to
estimate the effect of fresh snow which has an albedo close to one
at UV wavelengths (Wiscombe and Warren, 1980). The background images were
calculated for each individual case. The apparent absorbance
difference for the A(0.0)–A(0.1) and A(1.0)–A(0.1) cases is shown in
Fig. 11.

The overall results are summarized in
Table 3. Decreasing the albedo from 0.1 to 0.0
gives an overall reduction in the apparent absorbance (mostly blue
colours in
Fig. 11a).
Compared to the *A*=0.1 case, the *A*=0.05 case, not shown, is about
a factor of 2 smaller in magnitude for the mean apparent
absorbance. Increasing the albedo from 0.1 to 1.0 gives an increase in
the apparent absorbance (mostly red colours in
Fig. 11b).
As mentioned above, Sect. 3.2, the apparent absorbance
is due to photons travelling along straight lines passing through the
plume and into the camera. However, photons scattered between the
plume and the camera, and multiple scattered photons within the plume,
termed the light dilution and multiple scattering effect,
respectively, may distort the apparent absorbance (Kern et al., 2012). An
additional distortion, not discussed by
Kern et al. (2012), is due to the surface albedo which gives additional
photon paths that may contribute to the camera signal. Some photons
may scatter off the surface into the plume and in the direction of the
camera. This will give increased (decreased) apparent absorbance with
increasing (decreasing) albedo for relatively large SO_{2}
concentrations; see red (blue) signal in
Fig. 11b
(a). For small SO_{2} concentrations, the light dilution effect
prevails, giving a reduction (increase) in the apparent absorbance for
increasing (decreasing) albedo; see blue (red) signal in
Fig. 11b
(a). While albedo changes may both increase and decrease the apparent
absorbance, the impact on plume statistics is minor. Thus, overall,
the surface albedo has negligible effect on the plume statistics
(Table 3).

4 Conclusions

Back to toptop
One novel
method to measure atmospheric turbulent tracer dispersion is to use UV
cameras sensitive to absorption of sunlight by SO_{2}. In this paper we
have presented a method to simulate such UV camera measurement with a
3D Monte Carlo radiative transfer model. Input to the radiative
transfer simulations are large eddy simulations (LES) of a SO_{2}
plume. From the simulated images, various plume density statistics
(centre-line position, meandering, absolute and relative dispersions, and skewness) were calculated and compared with
similar quantities directly from the LES. Mean differences between the
simulated images and the LES were generally found to be smaller or
about the size of the voxel resolution of the LES for the
centre line. For the higher-order statistics, the differences increase
as the SO_{2} absorption gets weaker for a more and more dispersed
plume.

Furthermore, sensitivity studies were made to quantify how changes in
solar azimuth and zenith angles, aerosol (background and in plume),
and surface albedo impact the UV camera image plume statistics. It
was found that changing the parameters describing these effects within
realistic limits had negligible effects on the centre-line position,
meandering, absolute and relative dispersions, and skewness of the
SO_{2} plume.

Based on the simulated UV camera images and the comparison with
the LES, it can be concluded that UV camera images of SO_{2} plumes
may be used to derive plume statistics of relevance for the study of
atmospheric turbulence.

Code availability

Back to toptop
Code availability.

The libRadtran software used for the radiative transfer simulations is available from http://www.libradtran.org (last access: 16 June 2020). The PALM model system was used for the LES, and it is available from http://palm.muk.uni-hannover.de/trac (last access: 16 June 2020).

Data availability

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Data availability.

The LES data and the radiative transfer model input and output files are available from https://doi.org/10.5281/zenodo.3898174 (Kylling et al., 2020).

Author contributions

Back to toptop
Author contributions.

AK performed the radiative transfer simulations. HA, MC, and SYP were responsible for the LES. AK prepared the manuscript with contributions from all co-authors.

Competing interests

Back to toptop
Competing interests.

The authors declare that they have no conflict of interest.

Acknowledgements

Back to toptop
Acknowledgements.

The resources for the numerical simulations and data storage were provided by UNINETT Sigma2 – the National Infrastructure for High Performance Computing and Data Storage in Norway (project nos. NN9419K and NS9419K). The reviewers' comments greatly helped improve the manuscript, and we thank them for this.

Financial support

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Financial support.

This research has been supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (COMTESSA; grant no. 670462).

Review statement

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Review statement.

This paper was edited by Ad Stoffelen and reviewed by Jakob Mann and one anonymous referee.

References

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Short summary

Atmospheric turbulence and its effect on tracer dispersion in particular may be measured by cameras sensitive to the absorption of ultraviolet (UV) sunlight by sulfur dioxide (SO_{2}). Using large eddy simulation and 3D Monte Carlo radiative transfer modelling of a SO_{2} plume, we demonstrate that UV camera images of SO_{2} plumes may be used to derive plume statistics of relevance for the study of atmospheric turbulent dispersion.

Atmospheric turbulence and its effect on tracer dispersion in particular may be measured by...

Atmospheric Measurement Techniques

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