Inter-comparison between the Aerosol Optical Properties Retrieved by Different Inversion Methods from SKYNET Sky Radiometer Observations over Qionghai and Yucheng in China

This study analyzed the aerosol optical properties derived by SKYRAD.pack versions 5.0 and 4.2 using the radiometer measurements over Qionghai and Yucheng in China, two new sites of the sky radiometer network (SKYNET). The volume size distribution retrieved by V5.0 presented bimodal patterns with a 0.1–0.2 μm fine particle mode and a 5–6 μm coarse particle mode both over Qionghai and 20 Yucheng. The differences of the volume size distributions between the two versions were very large for the coarse mode with a radius of over 5 μm. The mean values of single scattering albedo (SSA) at 500 nm retrieved from V5.0 were approximately 0.02 lower, but 0.03 higher than those from V4.2 in Qionghai and Yucheng, respectively. The average imaginary part of the complex refractive index (mi) retrieved from V5.0 at all wavelengths was systemically higher than those by V4.2 over Qionghai. Moreover, the 25 differences between the real parts of the complex refractive index (mr) obtained using the two versions were within 4.25% both at Yucheng and Qionghai. The seasonal variability of the aerosol properties over Qionghai and Yucheng were investigated based on SKYRAD.pack V5.0. The seasonal average SSA during the winter was larger than those in other seasons in Yucheng, while the lowest SSA values occurred in winter over Qionghai. Meanwhile, the mr showed a minimum in winter over both sites. The 30 results can provide validation data in China for SKYNET to continue improving the data-processing and inversion method. The results provide valuable references for continued improvement of the retrieval algorithms of SKYNET and other aerosol observational networks. Atmos. Meas. Tech. Discuss., https://doi.org/10.5194/amt-2019-39 Manuscript under review for journal Atmos. Meas. Tech. Discussion started: 6 March 2019 c © Author(s) 2019. CC BY 4.0 License.

Using a sun/sky radiometer to measure both direct solar beam and angular sky radiance is the most common method for a reliable and continuous estimate of detailed aerosol properties over mega-cities around the world. Many aerosol ground-based observation networks were established to understand the 10 aerosol optical properties, validate the inversion products of satellite remote sensing, and indirectly evaluate their effect on climate (Uchiyama et al., 2005;Takamura and Nakajima, 2004;Nakajima et al., 2007). SKYNET, the focus of this study, is a ground-based research network of using sky radiometers (PREDE Co., Ltd., Tokyo, Japan) with observation sites principally located in Asia and Europe (Che et al., 2014). 15 The direct solar and angular sky radiance data measured by the sky radiometers are processed to obtain the aerosol optical properties, such as aerosol optical depth (AOD), single scattering albedo (SSA), complex refractive index, and volume size distribution function (SDF) using SKYRAD.pack, which is the official retrieval algorithm of the SKYNET network (Nakajima et al., 1996) having several different versions. SKYNET currently uses the SKYRAD.pack algorithm version 4.2 (Takamura and Nakajima, 20 2004). The aerosol retrievals derived from SKYRAD.pack version 4.2 algorithm have been used to investigate the regional and seasonal characteristics of aerosols for climate and environmental studies and validate satellite remote sensing results (e.g., Kim et al., 2004;Che et al., 2008;Campanelli et al., 2010;Estellés et al., 2012a;Wang et al., 2014;Che et al., 2018). Recently, a new SKYRAD.pack version 5.0 was proposed to improve SSA retrievals (Hashimoto et al., 2012), there are few applications of 25 SKYRAD V5.0 in China, and it was just preliminarily used to retrieve aerosol optical properties over Beijing in China (Che et al., 2014).
This study presents the aerosol optical properties over Qionghai and Yucheng by using SKYRAD.pack V5.0 and V4.2 from SKYNET sky radiometer measurements during February 2013 to February 2015. Atmos. Meas. Tech. Discuss., https://doi.org/10.5194/amt-2019-39 Manuscript under review for journal Atmos. Meas. Tech. Discussion started: 6 March 2019 c Author(s) 2019. CC BY 4.0 License. This work is designed to achieve the following objectives: (1) investigate the difference of the aerosol optical properties derived by SKYRAD.pack V5.0 and V4.2 over the two SKYNET sites; and (2) analyze the seasonal variability of aerosol optical properties over Qionghai and Yucheng based on SKYRAD.pack V5.0. The results presented in this study provide valuable references for continued improvement of the retrieval algorithms of SKYNET and other aerosol observational networks. 5 2 Site description, instrumentation, and inversion method

Site Geo-information and Instrumentation
The sky radiometer (Model POM-02, PREDE Co. Ltd.) was deployed at Qionghai and Yucheng from February 2013 and January 2013, respectively. The PREDE-POM02 model was equipped with an InGaAs detector to measure the direct solar irradiance and the sky diffuse radiance at 11 wavelengths, 10 namely, 315,340,380,400,500,675,870,940,1020,1627, and 2200 nm. The data from five channels at 400, 500, 675, 870, and 1020 nm were used here to retrieve the aerosol optical properties over Qionghai and Yucheng. The full angle field of view is 1.0°, while the minimum scattering angle of measurement is approximately 3°. The sky radiance is measured at 24 predefined scattering angles and at regular time intervals. The sky radiometer operates only during daytime and collects data regardless of the sky 15 conditions. Its dynamic range is 107. The typical measurement interval is 10 min. The precision of the in-situ method was estimated to be within 1-2.5% depending on the wavelength (Campanelli et al., 2004

Inversion method
The aerosol optical properties (i.e., AOD, SSA, complex refractive index, and volume SDF) were 25 derived in this study by using SKYRAD.pack V4.2 and V5.0. Within the SKYRAD.pack code, the inversion schemes were used to derive the single scattering term β(Θ) from the measurements of the normalized sky flux R(Θ) and retrieve the aerosol SDF v(r) (as a function of particle radius, r) from data β(Θ) and AOD τ. The inversion of β(Θ) was performed through a non-linear iterative method. Each step Atmos. Meas. Tech. Discuss., https://doi.org/10.5194/amt-2019-39 Manuscript under review for journal Atmos. Meas. Tech. Discussion started: 6 March 2019 c Author(s) 2019. CC BY 4.0 License. of the loop contained the procedure for retrieving v(r) using a constrained linear or a non-linear iterative method.
The retrieved v(r) in each iteration step was used as an input parameter for the radiative transfer model (Nakajima and Tanaka, 1988) to simulate R(Θ), which was compared with the measured R(Θ) to evaluate the root mean square difference ε(R). The maximum number of iterations and the tolerance 5 parameter for the convergence of R were set as 20 and 0.1%, respectively.
The retrieval of v(r) from β(Θ) and τ data in SKYRAD.pack V4.2 was conducted using a constrained linear method. The inversion method consisted of a linear matrix formulation, in which the solution stability was controlled by the requirement that it agrees both with the input data and the imposed weighted constraints (Nakajima et al., 1983). 10 f=Kx+ε. (1) where f is the vector of the β(Θ) and τ data, and x is a state vector containing the values of size distribution vi = v(r i ) with r i equidistant on a logarithmic scale (i.e., ln (r i + 1 ) − ln (r i ) = const. The components of vector ε were the error of each datum, K = K (m(λ)), a matrix of the kernel coefficients calculated for the fixed values of the complex refractive index (m(λ)). 15 V4.2 used the iterative relaxation method of Nakajima et al. (1983Nakajima et al. ( , 1996 to remove the multiple scattering contribution and derived an optimal solution using a statistical regularization method (Turchin and Nozik, 1969) by minimizing the following cost function as proposed by Phillips (1962) andTwomey (1963): where B is a smoothing matrix used to generate a priori information that forces the solution x to be a smooth function of ln(r); and γ is a Lagrange multiplier coefficient to minimize the first term of the right-hand side of Eq.
(2). The solution of Eq. (1) provided a smooth retrieval of the size distribution v(r) corresponding to the minimum of e2 defined by Eq. (2). In such an approach, both the solution v(r) and e2 depended on the assumed value of the complex refractive index m(λ). The complex refractive index 25 m(λ) in each iteration was also evaluated together with v(r), but the retrieved m(λ) can only be chosen from the predefined set of values.
The m(λ) values in SKYRAD.pack V5.0 were directly included in the state vector x. Eq. (1) becomes non-linear, and V5.0 solved it using the non-linear maximum likelihood method defined by Rodgers (2000). This method was based on the Bayesian theory. 30 where p is the probability density function defined as the Gaussian distribution; and x and f denote the state and measurement vectors, respectively. Accordingly, x was chosen in the maximum likelihood method, such that the posterior probability p(x|f) becomes the maximum under the condition that a priori information is already given. We obtained the following equation in the tangential space to be solved by 35 a Newtonian method by organizing this non-linear equation, such that p(x|f) = max: (4) where x k is the solution at the k th iteration step; f k =f(x k ) is an observation modeled using x k ; x a is the a priori value of x; S e is the measurement error covariance matrix; S a denotes the covariance matrix defined by a priori and state values, S a =(x-x a )(x-x a ) T ; and U is the Jacobi matrix, ∂f/∂x . The retrieval algorithm used in V5.0 allowed a rigorous retrieval of both the aerosol size distribution and the spectral complex refractive index.
The non-linear inversion has a strong dependence on the estimation of the first-guess solution.

Results and discussion
The results retrieved by SKYRAD.pack V4.2 were used to compare with the results retrieved by SKYRAD.pack V5.0. The inter-comparisons of the volume size distribution, single scatter albedo, and refractive index between V5.0 and V4.2 were based on 2517 measurements for 349 days over Qionghai and 6502 measurements for 307 days over Yucheng. Considering a relatively low retrieval accuracy of 15 SSA when AOD < 0.2 (Hashimoto et al., 2012), only the measurements with AOD > 0.2 were selected to be effective values in this study.

Inter-comparison of the volume size distribution results between SKYRAD V4.2 and V5.0
Aerosol size properties are one of the most important sources of information for both the observation and modeling of radiative forcing (Dusek et al., 2006). The volumes at each bin were monthly averaged 20 during the experiment period, for V4.2 and V5.0 over Qionghai and Yucheng (Figs. 1a, b). As V5.0 uses an a priori SDF of a bimodal log-normal function (Hashimoto et al., 2012), the volume SDF derived by V5.0 generally showed the classic bi-mode patterns at both Qionghai and Yucheng. The SDF from V5.0 showed two peaks at radii of 0.17 μm and 5.29 μm at the two sites. The SDF retrieved by V4.2, was generally similar to V5.0 at radius < 5 μm. However, V4.2 showed a predominant peak at 25 the coarse mode with a radius over 10 μm. The large differences at radius over 5 μm are probably because of the strong constraint on the SDF for the coarse mode particles applied in V5.0 (Hashimoto et al., 2012). Figures 1a and b showed that there were larger differences in volume SDF of the coarse mode between V4.2 and V5.0 at Qionghai than those at Yucheng.

Inter-comparison of the single scatter albedo results between SKYRAD V4.2 and V5.0
As a key variable in assessing the climatic effects of aerosols, the SSA is defined as the ratio of the 5 scattering coefficient and the extinction coefficient. It characterized the absorption properties of aerosols and an important quantity in evaluating aerosol radiative forcing. The SSA value is mostly dependent on the shape, size distribution, and concentration of the aerosol particles.

Inter-comparison of the refractive index results between SKYRAD V4.2 and V5.0
The real part of the refractive index (m r ) represents scattering. A higher m r indicates a higher scattering. 5 The imaginary part of the refractive index (m i ) represents absorption of the aerosols and is an important quantity in evaluating the aerosol radiative forcing.
Contrary to the single scattering albedo, the averaged m i retrieved from V5.0 at all wavelengths were systemically higher than those by V4.2 over Qionghai (Table 1). The mean values of m i retrieved from V4.2 were approximately 0.007, 0.005, 0.002, 0.005, and 0.005 lower than those from V5.0 for the five 10 channels of 400, 500, 675, 870, and 1020 nm, respectively, over Qionghai. The averaged m i retrieved by V5.0 was 0.003, 0.005, and 0.008 higher at 400, 870, and 1020 nm wavelengths, respectively, but 0.005 and 0.003 lower at 500 and 675 nm, respectively, than those retrieved by V4.2 in Yucheng.
The frequency distributions of m i values at 500nm retrieved by V5.0 and V4.2 are given in Fig. 3a and b for all the instantaneous data. In Qionghai site, the frequency histogram of m i by V4.

Seasonal variability of the aerosol optical properties over Qionghai and Yucheng based on SKYRAD.pack V5.0 5
The analysis of the 500 nm channel was chosen because it was widely quoted in sun photometric and remote sensing applications and generally representative of visible band wavelengths (Estellés et al., 2012b). Four seasons were considered in this paper (i.e., spring (March-May), summer (June-August), autumn (September-November), and winter (December-February)) to investigate the seasonal variations of the aerosol optical properties over Qionghai and Yucheng based on SKYRAD.pack V5.0. 10

AOD
The AOD was representative of the aerosol loading in the atmospheric column and important for the identification of the aerosol source regions and the aerosol evolution.
The AOD showed a distinct seasonal variation over both Qionghai and Yucheng. Figure 5a showed that the seasonal averaged AOD over Qionghai had higher values in spring, winter and autumn while 15 lower in summer. The background wind in Qionghai is the northeasterly wind from November through April, and the wind would import pollutants from South China into Hainan. In Yucheng, the AOD averages were commonly higher in summer and spring than in winter and autumn, the maximum average of 0.98 occurring in summer maybe was caused by hygroscopic effects. The high AOD in spring was likely related to the long-range transportation of dust from northern/northwestern China.   The SSA values showed a relatively uniform seasonal distribution in Qionghai. The SSA averages were approximately 0.90, 0.89, 0.89, and 0.88 in spring, summer, autumn, and winter, respectively. The mean SSA at 500 nm in Yucheng was significantly larger than that in Qionghai. The highest and lowest 10 monthly average SSAs in Yucheng were found in February (0.97) and November (0.89) respectively.
The seasonal mean SSA during the winter was larger than those in other seasons. Unlike the highest SSA value found in winter, the lowest SSA over Qionghai appeared in winter, it was mainly caused by the increase of the absorbing aerosol.  Fig. 6a, the fraction of the fine aerosol particles was much smaller in summer than for the other seasons. Meanwhile, the fraction of the coarse mode aerosol particles was larger than that in spring and winter probably because of the monsoonal influence, increase of the sea salt particles of a relatively large size, and decrease of the anthropogenic aerosol.

Volume Size Distribution 15
As shown in Fig. 6b, the coarse-mode particle in Yucheng has a much larger spread compared to the 5 volume distribution of the fine-mode particle. In spring, the volume of the coarse aerosol particles relative to the whole was much larger than for the other seasons in Yucheng probably because of the presence of the dust particles transported from the northwest of China (Zhao et al., 2018b).