PRELIMINARY SENSITIVITY STUDY OF AEROSOL LAYER HEIGHT FROM SYNTHETIC MULTIANGLE POLARIMETRIC REMOTE SENSING MEASUREMENTS

Many previous studies have shown that multiangle, multispectral polarimetric remote sensing can provide valuable information on aerosol microphysical and optical properties, in which the aerosol layer height (ALH) is an important parameter but with less studies, especially in the near-ultraviolet (near-UV) and visible (VIS) wavelength bands. Based on the optimal estimation (OE) theory and information content analysis method, we focus on the sensitivity study of ALH with the synthetic data in the near-UV and VIS wavelength in the range of 410-865 nm, and further to assess the capability of multiangle intensity and polarization measurements for the retrieval of ALH. Unified Linearized Vector Radiative Transfer Model (UNL-VRTM) has been used as the forward model to simulate the intensity and polarized radiance at the top of atmosphere (TOA), as well as the Jacobians of TOA results with respective to corresponding parameters. The degree of freedom for signal (DFS) and a posteriori error are introduced to quantity the information content of ALH from the intensity and polarization measurements, respectively. By assuming the surface type, aerosol model, aerosol loads, prior errors and observation geometries, the sensitivity of ALH has been preliminarily investigated. The sensitivity study results show that the near-UV and polarization measurements are the important source of information content for the aerosol height retrieval in satellite remote sensing.


INTRODUCTION
Aerosol vertical distribution plays an important role in the study of radiative forcing, air quality, aerosol scattering in trace gas and ocean colour retrievals (Haywood and Boucher, 2000;Wang and Christopher, 2013;Butz et al., 2011;Gordon, 1997). For the active remote sensing, the aerosol vertical distribution can be effectively measured, such as the ground-based, airborne and space-borne measurements (Winker et al., 2010). While for the passive satellite remote sensing, the oxygen (O2) A and B bands are usually used to study the aerosol vertical distribution based on synthetic data and real measurements (Sanghavi et al., 2012;Ding et al., 2014;Saders et al., 2015;Xu et al., 2017bXu et al., , 2019. Many previous studies have shown that multiangle, multispectral polarimetric remote sensing can provide valuable information on aerosol microphysical and optical properties (Waquet et al., 2009;Hasekamp et al., 2011;Dubovik et al., 2011;Wu et al., 2015;Hou et al., 2018), in which the aerosol layer height (ALH) is one of important parameters but with less studies, especially in the near-ultraviolet (near-UV) and visible (VIS) wavelength bands (Wu et al., 2016).
The vertical distribution of aerosol is complex, which is not homogeneous due to the various structure depend on the height. The uncertainties from the treatment of the columnar atmosphere as homogeneous and independent as the height inevitably lead to the variations in aerosol optical features in model calculations (Bi et al., 2016). ALH is common used in the model calculation, while in the observational measurement, it is always instead of * Corresponding author: lizq@radi.ac.cn planetary boundary layer height (PBLH). The planetary boundary layer is the lowest layer of the atmosphere, which contains the vast majority of aerosols of the low troposphere. ALH is an important factor of atmospheric diffusion ability, which determines the vertical disperse range of pollutants emitted from the ground .
As the flagship of the environment and atmosphere observation satellite in the Chinese High-resolution Earth Observation System (CHEOS) program (Gu and Tong, 2015), Gaofen-5 (GF-5) has been launched in May 2018, and the Directional Polarization Camera (DPC) is one of payloads (Li et al., 2018;Zheng et al., 2019). By inheritance the technology of Polarization and Directionality of the Earth's Reflectances (POLDER) (Deuzé et al., 2001), The DPC employed a charge coupled device (CCD) detection unit and realized spatial resolution of 3.3 km under a swath width of 1850 km, which has integrated 3 polarized channels (490, 670, 865nm) together with 5 non-polarized bands (443, 565, 763, 765, 910 nm). Besides, the Multi-Viewing-Channel-Polarization Imager (3MI) developed by EUMETSAT for the time-frame 2020-2040, will measure the radiance at the top of atmosphere (TOA) in 12 spectral channels, in which 9 channels will be polarized, including 410, 443, 490, 555, 670, 865, 1370410, 443, 490, 555, 670, 865, , 1650410, 443, 490, 555, 670, 865, , 2130410, 443, 490, 555, 670, 865, nm (Marbach et al., 2013. In this paper, we focus on the preliminary sensitivity study of ALH with the synthetic data in the near-UV and VIS wavelength, and further to assess the capability of multiangle intensity and polarization measurements for the retrieval of ALH. For sensitivity study, the degree of freedom for signal (DFS) and a posteriori error of ALH have been employed. By assuming the surface type, aerosol model, aerosol loads, prior errors and multiviewing observation geometries, the sensitivity of ALH could be systematically analysed and discussed. In section 2, we briefly describe the real aerosol vertical distribution based on the ground lidar measurements. Subsequently, we present the sensitivity study methodology in section 3, and then conduct the analysis of information content based on these synthetic measurements in section 4. Finally, we give the conclusions in section 5.

AEROSOL VERTICAL DISTRIBUTION
The common measurements of ALH are taken by radiosonde, Sodar, microwave radiometer and Lidar, of which lidar is the effective way to retrieve the continue variation of the ALH (Collaud et al., 2014;. The Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) has the capability to estimate the large-scale region ALH from space since 2006 (Winker et al., 2010). Meanwhile, similar measurements of the airborne Cloud Physics Lidar (CPL) has been utilized in many aircraft campaigns to profile the optical properties aerosol and cloud (McGill et al., 2002;Wu et al., 2016). Additionally, the ground-based lidar can provides more accurate measurements with high signal-to-noise ratio and time continuity (Wiegner et al., 2014;Tucker et al., 2009;Yang et al., 2013). From the profile of aerosol extinction coefficients, we can clearly obtain the vertical distribution of aerosol. Based on the Fernald method, the aerosol extinction coefficient can be calculated (Fernald, 1984). Figure 1 shows the mean extinction coefficients of aerosol from a ground lidar called CE370 by CIMEL in France, which is located in the Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences in Beijing Wang et al., 2019). We can see that the aerosol mainly exists in the height below 1 km, where the extinction coefficients grows with a large gradient. At the height of 300 m, it seemly the concentration gets the peak value. However, it should be noted that due to the insufficient overlap, the uncertainty of measurement below 200m is large.
For lidar measurement, wavelet covariance transform is the most comment used method to identify ALH (Gamage and Hagelberg, 1993;Yang et al., 2013;Wang et al., 2019). The upper boundary of the AHL can be determined by the maximum variation gradient of the backscattering signal attenuated by aerosol (Seibert et al., 2000). From Figure 2, it is demonstrated that ALH starts to increase gradually from 08:00 a.m. and reaches its maximum at nearly 14: 00 p.m. From the midnight, ALH goes down rapidly and holds steady until the sunrise. Actually, the ALH shows a diurnal cycle from rising to decreasing along with the variation of the sunlight radiation.

DFS and Posterior Error
Following the optimal estimation (OE) theory (Rodgers, 2000;Dubovik et al., 2011), we have the forward model as where is a state vector to be retrieved, the vector contains these parameters that are not contained in but quantitatively influence the TOA measurements, is an observation vector, F means a forward model, and means an experimental error term integrated by the observation noise and forward model uncertainty.
For the sensitivity study, the averaging kernel matrix can be represented as where the superscript "−1" is the inverse operation of matrix, a means the error covariance matrix of the a priori estimate a , the Jacobians matrix corresponds to the partial derivatives of ( ) with respect to x. Besides, ϵ is the covariance matrix of the error from both the measurements and the forward model with in which y is the measurement error covariance matrix, b is the error covariance matrix for a vector of forward model, and b is the Jacobians matrix of measurements with respect to the vector (Frankenberg et al., 2012;Hou et al., 2018a, b).
The DFS of each individual retrieved parameter is equal to , , and in the range of 0 and 1. , = 1 means that the observation is able to fully characterize the truth of x , and , = 0 means that the observation do not contain any information on x at all. In other words, the closer the value of , to 1, the better the retrieval of parameter x . Meanwhile, a posteriori error covariance matrix ̂ can be written as which means the statistical uncertainties in retrieved ̂ caused by measurement noise and the propagation of errors, and the posterior errors (absolute errors) are equal to the square root of diagonal elements (Hou et al., 2018a;Li et al., 2018).

Forward Simulations and Parameter Settings
To simulate the TOA measurements and corresponding Jacobian results in the near-UV and VIS wavelength from 410 nm to 865 nm of 3MI, Unified Linearized Vector Radiative Transfer Model (UNL-VRTM) is used as the forward model (Wang et al., 2014). UNL-VRTM integrates the VLIDORT code (Spurr et al., 2006), a linearized Mie code, a linearized T-Matrix code, a Rayleigh scattering module, line-by-line gas absorption calculation with HITRAN database, and some easy-used surface modules including the bidirectional reflectance distribution function (BRDF) and bidirectional polarized reflectance distribution function (BPDF). Based on UNL-VRTM, many studies have been carried to analyse the information content and develop the inversion algorithm for retrievals from the various measurements (Chen et al., 2017;Ding et al., 2016;Hou et al., 2016Hou et al., , 2017Hou et al., , 2018aXu et al., , 2017aXu et al., , b, 2018Xu et al., , 2019Li et al., 2018;Zheng et al., 2019aZheng et al., , 2019b. The kernel-driven BRDF model used in UNL-VRTM for surface reflectance can be written as ( 0 , , , ) = iso ( ) + 1 ( ) geom ( 0 , , ) + 2 ( ) vol ( 0 , , ), where 0 and v respectively represent the cosine of solar zenith angles and viewing zenith angle; iso , geom and vol respectively corresponds to the isotropic, geometric-optical (Lisparse kernel) and volumetric (Ross-thick kernel) surface scattering, iso ( ); 1 ( ) and 2 ( ) are the coefficients of the BRDF kernels at the wavelength . For the surface polarized reflectance, the used BPDF is where 1,2 ( , ) represent the polarized component of the Fresnel reflection matrix, is the reflective index of the vegetative matter, means the half the phase angle, NDVI is the normalized difference vegetation index, and is the only free linear parameter (Maignan et al., 2009). In this paper, he parameters of the BRDF and BPDF of vegetated surface are chosen from the work of Litvinov et al. (2011), which will not be discussed here anymore (Hou et al., 2019). In order to obtain the synthetic data of multiangle for sensitivity study, 2 typical multi-viewing observation geometries are considered with the combinations of different solar zenith angles ( 0 ), viewing zenith angles ( v ) and relative azimuth angles ( ) to represent the observations in different location. Figure 3 illustrates the polar-plot observational geometries, in which the radius corresponds to the v change from 0° to 60° with the step of 20°, and the polar angle means change from 0° to 360°, as well as the position of Sun also defined with = 0° (Zheng et al., 2019a). Here, the geometry = 0° means the observer and Sun are in the same direction and also in the same side of main plane, while = 180° represents the opposite direction and side of main plane, so as the definition in other polar-plot figures. For the sensitivity study of ALH, Table 1 lists the number of used bands combination with the multi-viewing intensity and polarization measurements, in which No.1 means only the 410 nm wavelength is used, and then add the next VIS wavelength in sequence until all of the 6 wavelength bands are used from 410 to 865 nm. Figure 4 illustrates the angular distribution of BRDF results in 410 nm and the angular distribution of wavelengthindependent BPDF results for the vegetated surface. The angular distribution of BRDF results for other bands are not shown here.
For the aerosol vertical profile parameter settings in UNL-VRTM, the exponentially decreasing profile with scale height given is used (Wang et al., 2014;Xu and Wang, 2017), which can be written in the form as where 0 is the columnar aerosol optical depth (AOD), and we set the scale height is equal to 2 km in this study. Besides, we  set the other aerosol parameters of particle size distribution and complex refractive index with fine-dominated aerosols and AOD = 0.8 at 550nm by following the work of Hou et al. (2017Hou et al. ( , 2018. For the information content analysis of ALH in the near-UV and VIS wavelength bands, the state vector only contains one parameter, that is with the vector where 0 f and 0 c represents the fine-mode and coarse-mode columnar volume concentration respectively, ( ) is the surface BRDF at the wavelength . The measurement vector can be defined as in which, , and are the TOA measured Stokes elements, the superscript 1 − are used to note each viewing in multiple observation. Correspondingly, the Jacobian vector and matrix .
For the error covariance matrix here we set = 75% with 1.5 km, and with prior error of 20% for 0 f and 0 c , and 10% for ( ). For the measurement error covariance matrix, we have By considering the integrated effects of instrumental noise with radiometric calibration and polarimetric accuracy uncertainties, we assume that the errors of measurements are 5% for both the intensity and the polarization for the sensitivity study (Li et al., 2018). To obtain the synthetic data for the sensitivity study of ALH, 2 multi-viewing observation cases are considered, and the TOA synthetic data are calculated using UNL-VRTM with the vegetated surface and fine-dominated model, in which the aerosols are mixed by the fine-and coarse-mode particles with the fine-mode fraction of columnar volume concentration FMF = 0.8 (Hou et al., 2017(Hou et al., , 2018. Figure 5 shows the angular distribution of TOA normalized radiance and polarized radiance in 410 nm. Here, the normalized radiance is equal to the first Stokes element , while the normalized polarized radiance is calculated by √ 2 + 2 . Figure 6 shows the angular distribution of Jacobians of TOA Stokes elements ( , and ) with respect to the aerosol parameters 0 f and the in 410 nm, respectively. Due to limited space, the angular results in other wavelengths are not shown here.

Sensitivity Study Results
For the DFS and posterior errors of each used bands combination listed in Table 1, we consider the multi-viewing measurements of only intensity and combined with polarization together respectively, and then calculate the mean results of 2 multiviewing observation cases as the final results.  Figure 7 shows the DPS of ALH along the number of used bands presented in the format of histogram. For the measurements of intensity, the DFS of ALH increases from 0.59 to 0.62 with the increasing number of used bands from 1 to 6 in the range of 410-865nm in sequence. While combining the measurements of polarization with intensity together, the information content of ALH has a significant improvement, and the DFS of ALH increase from 0.94 to 0.98. Figure 8 illustrates the posterior errors of ALH along the number of used bands with 75% priori errors of AHL (absolute priori errors 1.5 km). When only the intensity measurements are used, the absolute posterior error decreases form 0.64 km to 0.61 km in the range of 410-865 nm in in sequence. After the polarization measurements are added, the absolute posterior error can decrease from 0.38 km to 0.21 km. That is to say, the polarization can provide more useful information and constraints for the retrieval of ALH from multi-viewing measurements. Figure 7. The DPS of ALH along the number of used bands for "only intensity" and "intensity + polarization" multi-viewing measurements. Figure 8. The posterior errors of ALH along the number of used bands for "only intensity" and "intensity + polarization" multiviewing measurements with 75% priori errors of ALH.

CONCLUSIONS
In the paper, based on the OE theory and information content analysis method, the sensitivity study of aerosol layer height is carried out with the synthetic data in the range of 410-865 nm, and the capability of multiangle intensity and polarization measurements for the retrieval of ALH has been preliminarily assessed. UNL-VRTM is used as the forward model to calculate the normalized radiance and polarized radiance at the top of atmosphere (TOA), as well as the Jacobians of TOA results with respective to corresponding parameters. The degree of freedom for signal (DFS) and a posteriori error are introduced to quantity the information content of ALH from the intensity and polarization measurements, respectively. By assuming the vegetated surface type, fine-dominated aerosol model, aerosol loads, prior errors and 2 typical multiple observation geometry cases, the preliminarily sensitivity study results show that the near-UV and polarization measurements are the important source of information content for the aerosol height retrieval in satellite remote sensing.