1.School of Physical Science and Technology, Southwest Jiaotong University, Chengdu 611756, China 2.Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China Received Date:2019-03-01 Accepted Date:2019-05-14 Available Online:2019-08-01 Abstract:We investigate the extinction coefficients of the surface atmospheric aerosol over the Large High Altitude Air Shower Observatory (LHAASO), located at the Haizi Mountain, Daocheng County, China. To this end, we utilize the Longtin model, Mie scattering theory, and experimental data obtained by the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO). Our theoretical calculations show that the total extinction coefficients of the atmospheric aerosol at the wavelength of 200–500 nm are inversely proportional to the laser wavelength, and influenced by the wind speed. From July 2015 to October 2016, the extinction coefficient of the surface atmospheric aerosols at 532 nm wavelength reached 0.04 km?1 with no wind, while it increased to 0.1 km?1 with gusts. In this period, the extinction coefficients of the surface atmospheric aerosol at 532 nm wavelength, obtained by the CALIPSO, change from 0.01 to 0.07 km?1, which is less than the values obtained the theoretical calculation and larger than the average of Tibetan Plateau in 2006?2016. These calculations and experimental evidence provide important arguments to the model of atmospheric aerosol to be applied in the calibration of LHAASO. Our results suggest that the extinction coefficients over LHAASO require further study, including research on the size distribution, shape, concentration of aerosols particles, wind dependence, relative humidity dependence, etc.
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2.1.Longtin model
The Longtin model was developed by David R. Longtin et al., and it is actually a wind-dependent desert aerosol model, firstly applied in the Air Force Geophysics Laboratory. In this model, mineral dust particles are separated into three major components depending on their composition, using different log-normal size distributions and sets of indices of refraction for each component. The components include carbonaceous particles, water soluble particles, and sand. The sand component consists of two kinds of particles, pure quartz and quartz contaminated with a small amount of hematite (iron oxide, Fe2O3). Local wind conditions provide the mechanism to inject and transport aerosols, while wind also provides a mechanism for the generation of additional aerosols by a sandblasting process. The change of size distribution and mass concentrations of the aerosols that are injected into the air is a result of wind erosion. In this model, the volume (mass) of the water soluble and carbonaceous particles remain the same as that for background condition, in which the volume fractions for carbonaceous particles, water soluble particles, and sand were calculated to be 0.299, 0.001, 0.70, respectively, using information on particle concentration and the volume of the single particle. The extra mass loading due to the wind arises from sand. The mass loading equation is the basis for the wind speed dependence, which is expressed as follows.
$ c = 52.77 e^{0.30 u}, $
(1)
where c is the mass concentration in $ ug $ m?3 of air, u is the wind speed in m·s?1 at a height of 10 m. Thus, the different size distribution and concentration for each component of the aerosol will be evaluated in the Mie scattering calculations based on the equation and local wind condition. More detailed parameters on each component are provided in Table 1 [9].
aerosol component
wind speed/ (m·s?1)
size distribution parameter
radius range in Mie calculation/μm
particle concentration/ (particles·cm?3)
mean radius/μm
variance
carbonaceous
0–30
0.0118
0.301
0.0005-100
368.509
water soluble
0–30
0.0285
0.35
0.0005-100
3673.889
0
6.24
0.277
0.05-100
0.002
5
7
0.304
0.05-200
0.007
10
7.76
0.331
0.05-300
0.015
sand
15
8.52
0.358
0.05-600
0.034
20
9.28
0.384
0.05-750
0.072
30
10.8
0.438
0.05-1000
0.339
40
12.32
0.492
0.05-1000
1.963
Table1.Aerosol size distribution, integral range of the size, and concentration of aerosols' dependence on wind speed.
The Mie scattering calculation for the extinction coefficient, scattering coefficient, and absorption coefficient is performed separately for each component and then weighted according to their volume fraction of the total aerosol. The total coefficient is the sum of different components, as follows:
where i refers to the particle type. 22.2.Parameter estimation -->
2.2.Parameter estimation
Mie scattering occurs when the size of the aerosol particles is close to the wavelength of the incident light. To improve the calculation efficiency with the Mie scattering theory, D$ _n $ is defined as follows [19]:
where m is the complex refractive index of spherical particles relative to the ambient medium, $ x = k\alpha $ is the size parameter, $ \alpha $ the radius of the sphere and k = 2$ \pi/\lambda $, is the wave number and $ \lambda $ the wavelength in the ambient medium. $ \psi _n (x) $ is an equation related to semi-odd Bessel functions of the first kind, and $ \xi _n (x) $ is an equation related to semi-odd Hankel functions of the first kind. Generally, the extinction efficiency factor $ Q_{\rm ext} $, scattering efficiency factor $ Q_{\rm sca} $, and absorption efficiency factor $ Q_{\rm abs} $, are referred to as the attenuation efficiency factor all together. $ Q_{\rm ext} $ denotes the ratio of extinction cross-sectional area to the maximum geometric area, and $ Q_{\rm abs} $, ratio of absorbtion cross-sectional area, $ Q_{\rm sca} $ has the similar definition.
When the imaginary part of the m and Im(m) are lower than $ 13.78({\rm Re}(m))^2-10.8{\rm Re}(m)+3.9 $ [20], the upward iteration method is more efficient than the downward iteration method, and the calculation error is guaranteed to be less than $ 10^{-10} $. The recurrence formula can be used to obtain $ D_n(mx) $
where $ \lim\limits_{n \to \infty}{D_n} = 0 $, $ D_n $ is calculated from $ n = n_{\max} $ to $ n = 1 $. $ n_{\rm start} $ equals to $ {\rm INT}(\max\{n_{\max},|mx|\}+16) $ and $ D_n|_{n = n_{\rm start}} = 0 $. The extinction effect of atmospheric aerosol is the superposition of all effects from the aerosol particles in the air. The extinction coefficient $ k_{\rm ext} $, scattering coefficient $ k_{\rm sca} $, and absorption coefficient $ k_{\rm abs} $ describe the total optical attenuation. For atmospheric systems with uneven size distribution of the particles, the formula for the extinction coefficient is
where $ [r_{\min},r_{\max}] $ is the range of particle size, and $ N(r) $ is the distribution of particle concentration, which usually refers to the sum of several logarithmic normal distributions.
where $ N_i $ is particle number density, $ R_i $ is mean particle radius, and $ \lg \sigma _i $ is logarithmic standard variance. 22.3.Theoretical results -->
2.3.Theoretical results
The detector on the CALIPSO emits the laser at a wavelength of 532 nm. Under this condition, the complex refractive indices $ m $ (assume the imaginary part is greater than 0) are as follows: $ 1.75+0.45i $ (carbonaceous particle), $ 1.53+10^{-7}i $ (water soluble particle), 1.548+ $ 10^{-8}i $ (sand containing pure quartz only), 1.607+3.98× $ 10^{-3}i $ (sand containing 5% hematite), and 1.666+8.09× $ 10^{-3}i $ (sand containing 10% hematite). During the calculations, we assume that sand particles comprise 50% sand of pure quartz only and 50% sand containing 10% hematite. The results on the attenuation efficiency factors of the four types of particles are shown in Fig. 1 to Fig. 4, and each extinction efficiency factor exhibits drastic vibration when particle size is small. As the radius of particle is greater than 20 μm, $ Q_{\rm ext} $ is around two, while the absorption efficiency factors of water soluble particle and sand of pure quartz are close to zero. However, this is different for carbonaceous particles and sand containing 10% hematite. $ Q_{\rm abs} $ is, as the size of particle increases, stable around the value of one. Thus, a conclusion can be drawn that the real and imaginary parts of the complex refractive index are related to the scattering and absorption of light, respectively. When the imaginary part of $ m $ is relatively larger, the absorption efficiency factor is bigger. Figure1. (color online) Carbonaceous particle attenuation efficiency dependence on radius.
Figure2. (color online) Water soluble particle attenuation efficiency dependence on radius.
Figure3. (color online) Sand containing pure quartz only particle attenuation efficiency dependence on radius.
Using Equations (10)–(12) and related parameters, the extinction coefficients, dependent on wind speed and the wavelength of the income light, are presented in Fig. 5. As the wavelength increases, the extinction coefficient of particles decreases. When the wind speed rises, the size and concentration of sand in aerosol particles increase, so the extinction coefficient becomes bigger, too. The higher the wind speed is, the faster the extinction coefficient rises. Figure5. (color online) Extinction coefficient of particles at different wavelengths and wind speeds.
During the period from July 16, 2015 to April 24, 2016, at the site of LHAASO station, a total of 6816 hours included wind occurrence, and this period can be used to calculate the local aerosol extinction coefficient. As the satellite observation data discussed below is collected mainly at around 7 p.m., the time interval of 7 p.m. to 8 p.m. is selected for theoretical calculation. In Fig. 6, the blue curve shows that the extinction coefficient varies with time, whereas the red curve represents the temporal variation extinction coefficient in the case of gust wind speed. The average wind speed is taken as the mean wind speed within one hour, and the gust wind speed is taken as the maximum value of the wind speed within one hour. Under average wind speed conditions, the extinction coefficient changes from 0.0415 km?1 to 0.051 km?1, whereas in the gust wind speed, which is generally high, the extinction coefficient is also high, ranging from 0.0414 km?1 to 0.1041 km?1. Figure6. (color online) Theoretical value of night extinction coefficient at the site of LHAASO from July 16, 2015 to April 24, 2016.