In this study, giant aerosols are observed by cloud radar in a systematic way and for a long time period. In this section, first, the radar equations are presented. Afterwards, we use scattering simulations to determine the sizes of the atmospheric particles that can be detected by the cloud radar according to its sensitivity. Finally, we present the novel methodology that has been developed to detect giant aerosol particles by using the MIRA36 cloud radar.
2.2.1. Radar Equations
The radar reflectivity Z depends on the number and size of the atmospheric particles. However, the most commonly used parameter is the radar equivalent reflectivity factor . In the following, the radar equation and the definition of the radar equivalent reflectivity factor are presented.
The radar equation for a point target is
where
is the received power,
is the transmitted power,
is the antenna gain,
is the normalized antenna pattern,
is the radar wavelength,
L is the power loss introduced by the components between the antenna and the low noise amplifier (LNA),
R is the distance to the target, and
is the radar backscattering cross-section of the target.
The radar equation for the mean power for volume filling distributed targets is
where
V is the radar resolution volume. The radar reflectivity
is used instead of the backscattering cross-section:
Then, assuming that the radar reflectivity is uniform within the radar resolution volume and substituting
, we obtain
Introducing the equivalent radar resolution volume at the distance
R,
, the radar equation for a distributed target is
The equivalence between the radar reflectivity
and the radar equivalent reflectivity factor
is
where
is the dielectric constant of the observed target. For the MIRA36 cloud radar, the dielectric constant used is the one relative to water, which is
, with an estimated maximum error of
and an influence on
of
dB [
27]. As the dielectric constant affects the
results and its value for dust at
GHz is unknown, the uncertainty introduced by this could be high.
Assuming that the Rayleigh approximation is valid and all the targets are spherical,
:
where
N corresponds to the number of particles and
D to their diameter. It is usually expressed in dBZ, decibel relative to Z, with Z being measured in mm
6 m
−3.
Finally, using
the radar equation can be written as
For simplicity, in this study the radar equivalent reflectivity factor will be denominated as reflectivity Z.
Regarding the radar polarization measurements, the LDR gives an indication of the asphericity of the targets, is usually expressed in dB, and is calculated as the ratio between the power received in the cross-polarized channel and in the co-polarized channel:
2.2.2. Scattering Simulations and Sensitivity Limits
The cloud radar operating wavelength determines the atmospheric constituents it can detect. Since most airborne aerosols are smaller than cloud droplets or rain drops, it is important to quantify the radar capability to detect aerosols with different particle effective radii.
The interaction of electromagnetic radiation with a particle cannot be solved analytically; therefore, accurate calculations for real particles are difficult. Moreover, these interactions are conditioned by many different parameters, such as the wavelength of the radiation, size, shape, composition, and roughness of the particle and its complex refractive index. Nevertheless, good results can be obtained by approximating the particles using simplified shapes such as homogeneous spheres and spheroids. The Mie theory describes the scattering using the spherical approximation, which is valid for many categories of real particles, such as urban and sea-salt particles. Many of the particles, though, cannot be accounted for as spheres, and for those, the Mie theory does not give satisfactory results. This is the case for mineral dust and volcanic ash. Several approaches have been proposed to model the optical properties of such particles. The most widely used approach is to approximate the aerosol population by a mixture of randomly oriented spheroids [
28,
29]. While the true shape of the atmospheric aerosols is probably not spheroidal, the light scattered by an ensemble of particles with random orientations and shapes makes the individual scattering characteristics of each particle less pronounced.
In the specific case of non-spherical particles with rotational symmetry scattering field calculation, the T-matrix approach is especially suited [
30]. The T-matrix method is based on the expansion of the incident and scattered fields in vector spherical wave functions, which are used to compute the electromagnetic scattering by single, homogeneous non-spherical particles [
31]. The T-matrix approach has been shown to be an efficient method for scattering calculations involving rotationally symmetric non-spherical particles, such as spheroids, cylinders, two-sphere clusters, and Chebyshev particles [
32].
At every scattering process, either the degree or the nature of the electromagnetic wave polarization can change. A convenient way to describe the polarization state of light is through the Stokes vector. The Stokes vector can be defined through a set of ideal measurements [
33] and is defined as
where the Stokes parameters,
, are a complete description of the state of light [
34]:
represents the total intensity beam,
the horizontally or vertically polarized light,
the
° or
° polarized light, and
the circularly polarized light.
The change in the state of light caused by the scattering processes can be defined as
where
and
are the incident and scattered light state in the format of Stokes vectors, and
F is the Müller matrix:
The elements of this matrix depend on the direction of radiation propagation and the wavelength, and completely describe the properties of a scattering element.
In this study, we use the T-matrix method for randomly oriented, rotationally symmetric scatterers [
35] to compute the Müller matrix of aerosols at the cloud radar wavelength.
From the Müller matrix, which is the output of Mishchenko’s scattering code, the equivalent reflectivity (
) and linear depolarization ratio (LDR) can be calculated [
36]:
where
corresponds to the Müller matrix elements (Equation (
12)) and
N to the number concentration.
The range of considered T-matrix input parameters is reported in
Table 1. The number concentration range was set based on Lasher-Trapp and Stachnik [
37], who studied the variability of giant and ultragiant aerosols over the eastern Great Lakes region during a campaign with aircraft data. As we were unable to find the complex refractive index for dust at the cloud radar wavelength (
mm), we searched for the refractive indices of dust reported in the literature at other wavelengths. In Zhang et al. [
38], they presented a recollection of refractive indexes for dust with different mineralogical compositions between 0.2 and 50
m, which shows that the refractive index changes significantly between different wavelengths. At 800 nm, the refractive index real part ranges between 1.4 and 2.9, whilst the imaginary part falls between
and 0.015. At 50
m, the ranges are 1.8–5.9 and 0.02–1.5 for the real and imaginary parts, respectively. In the study of Weinzierl et al. [
39], they presented the refractive index of volcanic aerosols and dust between 350 and 800 nm. At 800 nm, the same wavelength that we selected from [
38], the refractive index for dust was
, and for volcanic it was
. Given the high variability of the complex refractive index that we see at different wavelengths, and that the values for dust and volcanic particles are relatively similar at the same wavelength (800 nm), we decided to use the complex refractive index found by Adams et al. [
40] for volcanic particles at the radar operating frequency (
GHz):
.
Figure 1 reports the estimated theoretical reflectivity at
mm for spherical particles depending on their size and number concentration, assuming a gamma particle distribution. The reflectivity is increasing together with the particle effective radius, which is the surface-area-weighted mean radius, and the number concentration; with the highest increase associated with the particle size. The signal is the result of the complex size distribution, which can be represented using different aerosol modes. As previously mentioned, according to the manufacturer, the radar sensitivity threshold is
dB at 1 km at a time resolution of 10 s and averaging 200 spectra; reflectivity values above this value are highlighted using white horizontal lines. These values are in line with giant aerosol observations in the atmosphere, such as Exton et al. [
41], who found total particle concentrations of a few-per-centimeter cubed in the range 1–23.5
m, and of about 0.1–0.5 cm
−3 in the range 5–150
m, and with the measurements performed during the First Aerosol Characterization Experiment (ACE-1), which measured particles with dry radii on the order of 6 to 12
m in concentrations between
and
cm
−3 [
5].
Therefore, given the radar sensitivity, the T-matrix scattering calculations, and the aerosols’ size and number concentration in the atmosphere, we can affirm that the cloud radar is sensitive to giant and ultragiant aerosols.
2.2.3. Detection Methodology
The microwave radiation emitted by the radar probes the atmospheric vertical structure and receives echoes caused by different kinds of scatterers (hereinafter: targets). The target discrimination is essential for interpreting the cloud radar observations, and in many cases, this operation can be accomplished by using the different Doppler velocities and LDR. In the cloud radar MIRA36 algorithms, following the noise (the so-called clutter) removal, the targets are classified into clouds, rain, and plankton, with the latter being the radar term used to describe non-hydrometeor targets (i.e., insects). Ka and W-band cloud radars (35 and 94 GHz, respectively) detect almost exclusively insect targets on warm cloudless days [
42,
43]. Indeed, radar has been applied to the study of insects for more than 40 years. Since wind-borne insect migration occurs on a colossal scale, far exceeding (at least in numerical terms) the migratory flux of birds [
44], and giant and ultragiant volcanic aerosols can be detected by Ka-band radars [
22,
23,
45,
46], it can be assumed that the non-hydrometeor (plankton) echoes consist of insect and aerosol returns only. Therefore, a strategy was developed based on insect characteristics and behavior to detect and subtract them from the radar signals, keeping the aerosol returns only.
The first of the insect characteristics that have to be taken into account is their vertical evolution throughout the day. The depth of the insect layer follows the diurnal variation of the atmospheric boundary layer (ABL) with a minimum during the night-time, sharply increasing in the morning, and reaching a maximum in the afternoon. According to this daily evolution, represented in
Figure 2, crepuscular, diurnal, and nocturnal insects can be identified with almost no overlap between them. Crepuscular species take off during the morning twilight period, with small numbers and a generally short-lived flight, although they occasionally continue for some time, and day-time layers are reported [
44]. Day-flying migrants take off from mid-morning onward, as atmospheric convection develops, and generally descend in the late afternoon; occasionally, small numbers of day-flying species continue their migration into the night [
44]. Nocturnal species typically have a mass take off at dusk and fly throughout the night following the stratification of the nocturnal BL [
47,
48,
49,
50,
51]. Therefore, they tend to concentrate into layers of shallow depth but broad horizontal extent [
52,
53,
54,
55].
In
Figure 3, the daily evolution of the Doppler vertical velocity measured by the cloud radar for two continuous days in July 2013 is presented. During these two days, there were clear sky conditions except for some cirrus clouds around 4 km a.s.l. on 29 July 2013 after 18 UTC. The insects’ daily evolution can be observed for both days. On 28 July 2013, a layer of nocturnal insects is detected between 00:00 and 03:30 UTC, approximately. Then, at dawn, the diurnal insects start to take off, progressing throughout the day, reaching higher altitudes (up to 2.5 km a.s.l.) along with the evolution of the convective atmospheric boundary layer (ABL). After sunset, two layers of nocturnal insects can be observed, which continue onto the next day. On 29 July, the two nocturnal insect layers from the previous day merge into the diurnal insects group layer, which was detected starting from dawn. A similar evolution for the daily insect group is observed, even though on the second day the measured vertical Doppler velocities and the height reached by the insects are lower. Around 15 UTC, during the day-time, a group of insects is lifted. After sunset, nocturnal insects take off as well, but in this case, their flight ends well before midnight.
Typically, the insect size range is of the order of millimeters, whereas the aerosol size range after atmospheric transport can reach up to a few hundred microns. Considering that the radar reflectivity is proportional to the sixth power of the diameter of the scatterers, aerosols are only detectable in range gates free of insects. Therefore, only the lofted layers relative to the areas where the insects fly are searched for and further processed.
Figure 4 illustrates the approach developed with this purpose. First, according to the cloud radar original classification [
56], the plankton (non-hydrometeor) layers are looked for. Due to the speckled nature of the cloud radar images, it was established that the lofted layers should have 600 pixels at least (10 samples in height × 60 samples in time), which corresponds to a 300 m thick layer that lasts for 10 min. Second, the misclassification of the outer cloud and rain pixels into the plankton category that is frequently performed by the original cloud radar classification algorithm needs to be overcome. With this purpose, the cloud and rain areas are expanded 2 min in time and 120 m in range to create a cloud mask. This mask includes the clouds and rain regions, including their outer originally misclassified pixels. Third, the cloud base height detected by the ceilometer is also included into the mask in order to avoid inserting misclassified clouds into the process. Finally, after applying the cloud mask, the remaining layers are classified into lofted or not lofted, depending on their minimum height. In
Figure 5, an example of the plankton layers identification is presented.
After the identification of the plankton lofted layers via the process that we just described, a series of tests based on the insect behavior in the atmosphere are carried out to distinguish between the aerosol and insect layers. The different criteria are based on entomology studies and consider atmospheric variables such as the temperature and the wind. The key features of insects layers are explained next.
Two aspects of the insects’ relationship with temperature were considered: (a) the ceiling (maximum height) of the insect layer can be approximated by the 10 °C isotherm in most cases, even though there is a tendency of insects to tolerate lower temperatures after prolonged periods with temperatures lower than average [
57]; and (b) the insect layers during the night-time are frequently located near the inversion top height [
48].
Regarding the insects’ behavior with respect to the wind, it was found that (a) they do not fly at a wind speed on the Beaufort wind force scale higher than 5 close to the ground [
58], which corresponds to a mean wind speed of 10 m s
−1; and that (b) the aerosol layers tend to follow the 3D wind vector, while insects usually have more random behavior.
Finally, concerning the relationship of the insects with the convection, the ABL, and the height, it is known that (a) insects tend to be concentrated in plumes of rising air [
59]; (b) there are usually many more insects within the convective ABL than above it [
60]; and (c) migrating insects typically fly at high altitudes, sometimes as high as 2 or 3 km above the ground [
54].
Figure 6 illustrates the developed methodology based on the entomology criteria outlined above. In order to perform the following screening steps, ancillary information is required. Temperature and wind profiles from radiosondes are used, if available, within a temporal difference of 2 h (we assume that within this time interval the measured profiles are still representative of the actual conditions). In any other case, profiles provided by the MWR and the ECMWF model are used for temperature and wind, respectively.
In the first step, the layers that have more than 60% upward Doppler velocities are classified as insects. If not, then it is a possible aerosol layer and moves through the second screening step. In the second step, which is only applied during the night, the layer location relative to the temperature inversion height is used as the screening metric. If more than 10% of the layer is located within 500 m higher or lower than the temperature inversion height, it is classified as an insect layer. If not, it moves ahead in the classification procedure. In the third screening step, four tests are applied:
Is the temperature of more than 90% of the points below 0 °C? This test is based on Luke et al. [
57] (the ceiling of the insect layer can be approximated by the 10 °C isotherm, even though they can tolerate lower temperatures after prolonged periods with temperatures lower than average). We set the temperature threshold to 0 °C to account for the insects’ behavior during periods colder than average.
Are more than 90% of the layer pixels located above 3 km? This test is based on Gatehouse [
54] (migrating insects typically fly at high altitudes, sometimes as high as 2 or 3 km above the ground), from which we used the maximum height.
Is the corresponding horizontal wind speed of at least 90% of the layer pixels over 10 m s
−1? This test is based on Møller [
58] (insects do not fly at a wind speed on the Beaufort wind force scale higher than 5 close to the ground, which corresponds to a mean wind speed of 10 m s
−1).
Is the difference in angle between the layer and the isotachs time–height cross-section orientation lower than
°? This test is based on Møller [
58] (the aerosol layers tend to follow the 3D wind vector, while insects usually have a more random behavior); therefore, we are comparing the layer orientation to the isotachs, which are the lines connecting points of equal wind speed.
The layer that meets at least one of these conditions is classified as aerosol. If not, it falls into the insect category. In the definition of these four tests, we decided to be conservative in order to avoid misclassifying insects as aerosol layers. Also, in the first three tests, we defined that the criteria should be met by ≥90% of the points in order to account for the speckled nature of the cloud radar images. In the fourth test, this was not possible because the time–height cross-section orientation of the layers is used.
As radar measurements alone cannot provide unique information on whether giant aerosols are embedded in the insect layers due to their highly differing sizes, it is necessary to check independent measurements to further scrutinize the results obtained from the cloud radar. For this reason, the insect layers are submitted to an additional screening criterion. The size distribution retrievals from the AERONET sun photometer during the insect layer are averaged. Then, if the effective radius of the coarse mode is smaller than m, it is considered to be an insect layer, whilst otherwise we assume that is a layer of insects with embedded giant aerosols. This means that in both cases the layers contain insects, but when the effective radius of the coarse mode retrieved by the sun photometer is ≥2.5 m, giant aerosols are also present. The AERONET aerosol size distribution is only used in the case of lofted layers during the day-time, when the sun photometer is operating. As this criterion was defined for our relatively pollution-free station and AERONET measurements are columnar, our classification could be affected by pollution in the lower part in the atmosphere. During the night-time, the atmospheric conditions are generally more stable and, in addition, the cases occurring in this period are checked for the temperature inversion.
During the definition of our methodology, the thresholds used in the different steps to classify a layer as aerosols were defined in a conservative way to ensure that insect layers are not classified as aerosols (i.e., setting the temperature threshold at the layer height at 0 °C or using the maximum height of 3 km). The downside of this is that some giant aerosol layers might be classified as insect layers.