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Abstract
The profile of aerosol extinction coefficient can help understand the air pollution transportation and development of the atmospheric boundary layer. The charge-coupled device (CCD)-laser aerosol detection system (CLADS) was widely used to measure the profile of aerosol extinction coefficient, which has excellent resolution near the ground. Traditionally, a constant aerosol scattering phase function and single scattering albedo (SSA) is assumed when retrieving the profile of aerosol extinction coefficient using the measured signals from CLADS. Sensitivity studies in this research show that aerosol scattering phase function leads to an uncertainty up to 462% of the retrieved profile of aerosol extinction coefficient, while SSA leads to an uncertainty up to 25%. A new method is proposed to derive the profile of aerosol extinction coefficient by using two CCD cameras. The aerosol scattering phase function can be determined by minimizing the difference between profiles of aerosol extinction coefficient from the two CCD cameras without any assumption. The profile of aerosol extinction coefficient can be retrieved with high accuracy by using our optimized aerosol scattering phase function. This method is validated by simulation studies where the relative difference between the pre-parameterized aerosol extinction profile and retrieved aerosol extinction profile is below 6%. This dual CCD detection system is employed in a field measurement and proved to be reliable. Our proposed method can obtain more accurate profile of aerosol extinction coefficient for further works about air pollution and atmospheric boundary layer development.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Aerosol plays an important role in the climate change through its direct and indirect effects [1]. Profile information of aerosol is critical for understanding the contribution of aerosol to air pollution transportation [2–4], boundary layer processes [5,6], and climate change [7]. The vertical profile of aerosol extinction coefficient (${\alpha _{aero}}(z )$) is one of the most important aerosol optical properties. However, limitations exist when determining the ${\alpha _{aero}}(z )$ due to its high spatial and temporal variation. Light detection and ranging (lidar) technique is most frequently used to monitor the ${\alpha _{aero}}(z )$ continuously. The lidar system includes elastic backscatter lidar [8,9], Raman lidar [10,11], and high-spectral-resolution lidar [12,13] etc. There is one common shortcoming for these typical lidar instruments. They cannot measure the ${\alpha _{aero}}(z )$ near the ground due to the well-known overlap zone of lidar system [14]. However, most of aerosols are concentrated within the boundary layer at low altitude.
Recently, a new kind of instrument named charge coupled device laser aerosol detection system (CLADS) was developed and widely used to measure the vertical profile of aerosol optical properties [5,15,16]. This system consists of a continuous laser emitter and a charge coupled device (CCD) camera. The CCD camera was used as a detector to capture the side scattering light from the laser beam. With this technique, the aerosol at near-ground altitude can be profiled with excellent resolution.
When retrieving ${\alpha _{aero}}(z )$ from CLADS signals, the aerosol phase function ($P{f_{aero}}({\theta } )$) is necessary. However, the $P{f_{aero}}({\theta } )$ is hard to obtain and there is no commercial instrument that can be used to measure the ambient $P{f_{aero}}({\theta } )$. Traditionally, a constant $P{f_{aero}}({\theta } )$ is assumed and used in retrieving the ${\alpha _{aero}}(z )$. The $P{f_{aero}}({\theta } )$ of different aerosol varies significantly [17], so great uncertainties of the retrieved ${\alpha _{aero}}(z )$ may arise due to this assumption. Even if the ambient $P{f_{aero}}({\theta } )$ can be measured, the vertical variation of $P{f_{aero}}({\theta } )$ can also cause large uncertainties in retrieving ${\alpha _{aero}}(z )$. However, the uncertainties of the retrieved ${\alpha _{aero}}(z )$ associated with assumed $P{f_{aero}}({\theta } )$ is not well known yet.
In this research, sensitivity studies were carried out to investigate the uncertainties of the retrieved ${\alpha _{aero}}(z )$ using a predefined constant $P{f_{aero}}({\theta } )$. Results show that great uncertainties as large as 462% exist for the retrieved ${\alpha _{aero}}(z )$.
A novel method using dual CCD detection system (DCDS) was developed to retrieve the ${\alpha _{aero}}(z )$. Two CCD cameras are placed at different distances from a laser emitter. Because of different distances, the scattering angles of signals received by the 2 CCD cameras at the same altitude are different. Then, the $P{f_{aero}}({\theta } )$ can be determined by an optimization algorithm. Using the constrained $P{f_{aero}}({\theta } )$, the ${\alpha _{aero}}(z )$ can be retrieved with high accuracy. This method was validated by simulation studies and field measurements.
2. Instrumentation
The geometric design of the DCDS is shown in Fig. 1(a). The DCDS includes two parts: emitting part and receiving part. The emitting part is a solid continuous laser emitter with 532nm wavelength. A quarter-wave plate is mounted in front of the emitter to change the laser polarization state from linear to circular. The receiving part includes two laptops, two CCD cameras with 10 mm F2.8 fisheye lenses, and optical filters mounted between the cameras and lenses. The optical filter can decrease the background noise from the sky radiation. Each CCD camera is controlled by one laptop respectively. The two CCD cameras are placed in different distance to the laser emitter. With 2 CCD cameras, 2 independent CLADS are formed with the same laser emitter.
3. Methodology
3.1 Traditional retrieval method of CLADS
Each CCD pixel has a field of view angle d$\theta $ which can be calculated with the focus length of fisheye lens based on the equisolid projection principle. In Fig. 1(b), dz is the vertical resolution of CLADS at altitude z. According to the geometric structure, the scattering light signals in different altitudes z with different scattering angles $\theta $ are captured by different pixels. The altitude of each pixel with signal captured in the image can be derived with D and d$\theta $. The equation of return signal for the CLADS can be expressed as
where E(z) is the scattered signal, K is the calibration factor depending on the optical efficiency of CLADS, EL is the emitted laser energy, SP is the received area of each pixel, β(θ, z) is the total scattering function of air and aerosol, and TZ and TR are the transmittances of laser light from across a distance z and R, respectively.As the geometry shown in Fig. 1(b), the altitude z, distance R, and the scattering angle $\theta $ related as
A simplified formula can be derived from Eq. (1) and Eq. (2) as With the assumption that there are no aerosol particles around the altitude of signal at minimum under the no-cloud and no-sandstorm condition, the scattering function of aerosol can be solved from Eq. (3). Then, with a presupposed $P{f_{aero}}({\theta } )$ and a presupposed single scattering albedo (SSA), the ${\alpha _{aero}}(z )$ can be obtained as Where ${\beta _{aero}}(\theta )$ is the scattering function of aerosol, and ${\omega }$ is SSA. Details of the aerosol extinction profile retrieval algorithm can be found at Bian, et al. [5].3.2 Uncertainties of the traditional method of retrieving ${\alpha _{aero}}(z )$
From the discussion above, the $P{f_{aero}}({\theta } )$ and SSA are necessary, but cannot be obtained when retrieving the ${\alpha _{aero}}(z )$ from CLADS signals. The presupposed $P{f_{aero}}({\theta } )$ and SSA may lead to great uncertainties of the retrieved ${\alpha _{aero}}(z )$. A sensitivity study was conducted to investigate the uncertainties associated with assuming a $P{f_{aero}}({\theta } )$ and SSA. The signal profile used in the experiment is obtained from CLADS measurement at Peking University, Beijing, China, at 17:25 local time (LT) on December 14, 2017. Traditionally, the $P{f_{aero}}({\theta } )$ and SSA are chosen the same typical values of the corresponding type of aerosols from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) aerosol products [17]. The SSA varies significantly between 0.8 and 1.0 [17]. In the same retrieval process, the upper and lower bounds of SSA were used. As shown in Fig. 2(a), the ${\alpha _{aero}}(z )$ retrieved with the lower bound of SSA are at most 25% larger than that with the upper bound of SSA. As for the $P{f_{aero}}({\theta } )$, 8 typical different $P{f_{aero}}({\theta } )$ s of different aerosol types of works of Aerosol Robotic Network (AERONET) and CALIPSO [17–19] were used. For a given measured CLADS signal profile, the ${\alpha _{aero}}(z )$ s are retrieved using $P{f_{aero}}({\theta } )$ s mentioned above. As shown in Fig. 2(b), different $P{f_{aero}}({\theta } )$ s can cause a very large difference in the retrieved ${\alpha _{aero}}(z )$ s. Of all the results, the maximum relative difference is 462%. Considering the data used in the experiment were obtained in Beijing located in North China Plain, $P{f_{aero}}({\theta } )$ s of CALIPSO background and marine aerosol types can be excluded. Even though, the maximum relative difference of the rest types is still 116%. In conclusion, the aerosol phase function is a more important source of uncertainty for the ${\alpha _{aero}}(z )$ retrieval algorithm than SSA.
The $P{f_{aero}}({\theta } )$ measured on the ground at the same time as ${\alpha _{aero}}(z )$ measurement is a better choice to reduce the error. However, according to the geometric structure of CLADS, the $P{f_{aero}}({\theta } )$ values of each angle needed for ${\alpha _{aero}}(z )$ retrieval are actually different at different altitudes. From the works about obtaining profiles of aerosol optical properties, it can be seen that the $P{f_{aero}}({\theta } )$ varies greatly with altitude [20,21]. There will be a great error in replacing the profile of $P{f_{aero}}({\theta } )$ with the $P{f_{aero}}({\theta } )$ measured on the ground. The best option for ${\alpha _{aero}}(z )$ retrieval is to measure the vertical profile of $P{f_{aero}}({\theta } )$. However, obtaining the profile of $P{f_{aero}}({\theta } )$ is a far more complicated task than obtaining ${\alpha _{aero}}(z )$, which makes the best option impossible. Thus, a practicable way to solve this problem needs to be proposed. New method of retrieving the ${\alpha _{aero}}(z )$ with DCDS
Fig. 2. (a) Retrieved ${\alpha _{aero}}(z )$s with minimum and maximum of SSA; (b) Retrieved ${\alpha _{aero}}(z )$s with 9 different aerosol phase functions.
The DCDS measurement based on the retrieval algorithm was developed for reducing the uncertainty of $P{f_{aero}}({\theta } )$ in retrieving ${\alpha _{aero}}(z )$. The method used in DCDS measurement is called $P{f_{aero}}({\theta } )$ optimization algorithm. Our proposed method can obtain a more accurate estimation of $P{f_{aero}}({\theta } )$ for a specific retrieval process. Then a more accurate ${\alpha _{aero}}(z )$ can be retrieved.
The theory of the optimization algorithm is described as follows. Ideally, if the presupposed $P{f_{aero}}({\theta } )$s used in CCD1 and CCD2 measurements are accurate, ${\alpha _{aero}}(z )$s retrieved from the 2 measurements should be equal. Considering that if there is a deviation between the $P{f_{aero}}({\theta } )$s used in the retrieval algorithm and the true values, the retrieved ${\alpha _{aero}}(z )$ of CCD1 measurement (Ext1) and that of CCD2 measurement (Ext2) will deviate from the true ${\alpha _{aero}}(z )$. Therefore, there will be a difference between the Ext1 and Ext2 (Diff of Ext) due to the inaccurate $P{f_{aero}}({\theta } )$s. The Diff of Ext is a function of $P{f_{aero}}({\theta } )$s. When the $P{f_{aero}}({\theta } )$s approach the true ones, the Diff of Ext will tend to 0. In reverse, if the Diff of Ext approaches 0, the $P{f_{aero}}({\theta } )$s may tend to the true values. If 2 $P{f_{aero}}({\theta } )$s that make the Diff of Ext minimum are found, then the 2 $P{f_{aero}}({\theta } )$s will be regarded as more accurate estimations of true ones. This is an optimization problem.
Gradient descent (GD) is used in the $P{f_{aero}}({\theta } )$ optimization algorithm to do the optimization. GD is an iterative optimization algorithm for finding the minimum of a target function. The target function is called optimization target. To find a local minimum of optimization target, steps are taken proportional to the negative of the gradient (or of the approximate gradient) of the function at the current point. After enough steps are taken, the point where the optimization target at a local minimum can be approached. In this study, an optimized GD algorithm named Adam is adopted in which the step length can self-adjust in each iteration [22]. This GD algorithm can revise the $P{f_{aero}}({\theta } )$s to reduce the Diff of Ext repeatedly, and finally find the optimal $P{f_{aero}}({\theta } )$s for retrieving ${\alpha _{aero}}(z )$.
The flow chart of the phase function optimization algorithm is shown in Fig. 3. The process of the optimization algorithm is described as follows.
The phase functions used in CCD1 measurement (Pf1) and in CCD2 measurement (Pf2) can be regarded as a vector x=(Pf1, Pf2), and ${\alpha _{aero}}(z )$ is a function of phase function. Thus the Diff of Ext can be considered as a function of x. The Diff of Ext is defined as
First, the initial value of x is given by measuring $P{f_{aero}}({\theta } )$ on the ground, which is noted as x = x0=(Pf10, Pf20). Then the x will be revised iteratively. In each time, the x is iterated from xn to xn+1. The subscript n denotes the number of iterative times. The xn+1 is calculated as
To prevent Pf1 and Pf2 from being too discontinuous in the process of optimization, the deviation of Pf1 and Pf2 out of variable range (Dev of Pf) is introduced as a regularization term to restrict the variable range of Pf1 and Pf2. In Fig. 3, the optimization target includes two parts, Diff of Ext (F(x)) and Dev of Pf (L(x)). The only modification needs to be done in the above GD process is to substitute F(x) by F(x)+wL(x) (w is a weight factor to make F(x) and L(x) at the same order of magnitude) in Eq. (6). The Dev of Pf is defined as
4. Validation and discussion
4.1 Simulation based validation
4.1.1 Data used in simulation
The data of ${\alpha _{aero}}(z )$ used as true value in simulation are the results of CLADS measurement at Peking University, Beijing, China, at 17:25 local time (LT) on December 14, 2017. The sounding data used to get the air scattering information are downloaded from the website of University of Wyoming weather data (http://www.weather.uwyo.edu/upperair/sounding.html).
4.1.2 Simulation process
A simulation experiment has been designed and conducted to confirm the effectiveness of $P{f_{aero}}({\theta } )$ profile optimization algorithm. The true values of the ${\alpha _{aero}}(z )$, the $P{f_{aero}}({\theta } )$ profiles (pftrue1 and pftrue2), the aerosol single scattering albedo (ω=0.9), and the scattering function profile of air molecules of the atmosphere are assumed to be known in the simulation. Then the signal captured by a CCD camera can be calculated by the equation in the aerosol extinction profile retrieval algorithm. In the simulation, the D1 is 60 meters, and the D2 is 30 meters. Thus, signals captured by CCD1 and CCD2 can be simulated respectively. The signal of CCD1 is denoted as signal1, and that of CCD2 is denoted as signal2.
Initial phase functions for two measurements (pfaero1 and pfaero2) are needed to start the optimization algorithm. In this simulation, initial pfaero1 and pfaero2 are both derived from the CALIPSO aerosol products of the polluted continental aerosol type. The pftrue1 and pftrue2 are modified versions of pfaero1 and pfaero2.
In the two CCD measurements, for the same $\theta $, the values of phase functions are different because the aerosols are detected at different altitudes. Thus pftrue1 and pftrue2 are assumed to be different in this simulation. However, when near the ground, pftrue1 and pftrue2 should be close because when $\theta $ tends to $\frac{\pi }{2}$, the two measurements are approaching the same altitude as shown in Eq. (2a). On the basis of pfaero1 and pfaero2, some modifications are done to reflect this difference in pftrue1 and pftrue2. The pftrue1 and pftrue2 are calculated as
Where $\varepsilon (\theta )$ is defined in Eq. (9) and $\rho $ here is 0.5 in this simulation. Figure 4 shows the true ${\alpha _{aero}}(z )$, simulated signals, and true phase functions (pftrue1 and pftrue2) in simulation. The pftrue and the initial pfaero are designed to be close when $\theta $ tends to $\frac{\pi }{2}$ as can be seen from Eq. (12).Fig. 4. Signal simulation demonstration: (a) the ${\alpha _{aero}}(z )$ used as true value in simulation; (b) simulated signals captured by CCD1 and CCD2 calculated through phase functions in (c) and ${\alpha _{aero}}(z )$ in (a) based on the equation in the aerosol extinction profile retrieval algorithm; (c) true aerosol phase functions for simulating signals captured by CCD1 and CCD2 respectively. The CCD1 and CCD2 are shown in Fig. 1.
To evaluate the result of simulation, 2 relative error variables are defined. The first one is Ep, which represents the deviation of pfaero to their true values pftrue:
4.1.3 Results of simulation study
The results of the simulation experiment are shown in Fig. 5. After the phase function optimization process, both extaero1 and extaero2 are very close to exttrue while there is almost no difference between extaero1 and extaero2. The pfaero1 and pfaero2 are closer to their true values pftrue1 and pftrue2 after the optimization process than in the initial state, respectively. Although the pfaero1 and pfaero2 are not exactly equal to pftrue1 and pftrue2, it seems that the optimized pfaero1 and pfaero2 are accurate enough to retrieve a better estimate of exttrue. The Diff of Ext in the initial state is $1.92 \times {10^8}$, while after optimizing process it decreases to $5.95 \times {10^4}$. The Diff of Ext has dropped by 99.97%. In the initial state, Ep(pfaero1, pftrue1) is 23.42%, and Ep(pfaero2, pftrue2) is 40.04%. After optimizing, Ep(pfaero1, pftrue1) is 5.73%, and Ep(pfaero2, pftrue2) is 14.72%. The pfaeros are more accurate after optimizing as the above relative error values show. In the initial state, Ek(extaero1, exttrue1) is 25.89%, and Ek(extaero2, exttrue2) is 31.16%. After optimizing, Ek(extaero1, exttrue1) is 4.34%, and Ek(extaero2, exttrue2) is 5.87%. Though the target of optimizing is to reduce Diff of Ext, the Eks of both extaeros are also reduced greatly after optimizing.
Fig. 5. Results of the simulation experiment: figure (a), (b), and (c) are of the initial state, and figure (d), (e), and (f) are of the state after phase function optimization process. In figure (a) and (d), extaero1 (green solid line) is the ${\alpha _{aero}}(z )$ retrieved from the CCD1 measurement, extaero2 (red solid line) is the ${\alpha _{aero}}(z )$ retrieved from the CCD2 measurement, and exttrue (black solid line) is the true value of ${\alpha _{aero}}(z )$; in figure (b) and (e), pfaero1 (green solid line) is the phase function used in ${\alpha _{aero}}(z )$ retrieval algorithm for CCD1 measurement, pftrue1 (black solid line) is the true phase function we want to achieve, and the green dotted lines on both sides of pfaero1 are the upper and lower bounds of the variable range of pfaero1 in optimization algorithm; in figure (c) and (f), pfaero2 (red solid line) is the phase function used in ${\alpha _{aero}}(z )$ retrieval algorithm for CCD2 measurement, pftrue2 (black solid line) is the true phase function we want to achieve, and the red dotted lines on both sides of pfaero1 are the upper and lower bounds of the variable range of pfaero2 in optimization algorithm. By comparing (a) and (d), it is obviously that after optimization process, the difference between extaero1 and extaero2 is nearly disappear and both extaero1 and extaero2 are very close to exttrue. By comparing (b) and (e), (c) and (f), pfaero1 and pfaero2 are closer to their true values pftrue1 and pftrue2 after the optimization process than in the initial state.
The simulation experiment confirms that the phase function optimization algorithm is effective. It can obtain accurate $P{f_{aero}}({\theta } )\textrm{s}$ by reducing the difference between ${\alpha _{aero}}(z )$s from 2 CCD measurements. Then a more accurate ${\alpha _{aero}}(z )$ can be retrieved with the accurate $P{f_{aero}}({\theta } )\textrm{s}$.
4.2 Field application
4.2.1 Data used in field measurement
When in field measurement, the initial phase function is derived by measurement of aerosol phase function on the ground. In this study, the aerosol phase function on the ground is derived from the particle number size distribution (PNSD) data and the Mie-scattering model. The PNSD at dry state ranging from 3nm to 10µm was observed jointly by an Aerodynamic Particle Sizer (APS, TSI Inc., USA, Model 3321) and a Scanning Mobility Particle Sizers (SMPS, TSI Inc., USA) with a temporal resolution of 10 min, and the relative humidity (RH) of sampling air is controlled at lower than 30%. The observing site is at the roof of the College of physics, Peking University, Beijing, China. The RH at these measurement time were lower than 40% so the PNSD of dry aerosols can be used to obtain the ambient aerosol phase function on the ground. Measurements were made at three different times in 2018: 21:30 on March 27, 20:15 on April 1, and 20:15 on April 2.
4.2.2 Results of field measurement
The results of measurement on March 27 (see Fig. 6) show when there is a big gap between initial retrieved ${\alpha _{aero}}(z )$ from 2 CCD measurements, the optimizing is effective to reduce it. The Diff of Ext in initial state is $2.82 \times {10^7}$, and that after optimization is $6.43 \times {10^6}$. The decrease of Diff of Ext is 77.2%. In results of measurement on April 1 (see Fig. 7), the Diff of Ext in initial state is $1.98 \times {10^7}$, and that after optimization is $4.46 \times {10^6}$. The decrease of Diff of Ext is 77.5%. Results of measurement on April 2 (see Fig. 8) show the optimizing can hardly reduce the gap between the results, when the initial retrieved ${\alpha _{aero}}(z )$ from 2 CCD measurements are already close. The Diff of Ext in initial state is $7.39 \times {10^6}$, and that after optimization is $6.90 \times {10^6}$. The decrease of Diff of Ext is 6.6%.
Fig. 6. Results of measurement at 21:30 on March 27, 2018: figure (a), (b), and (c) are of the initial state, and figure (d), (e), and (f) are of the state after phase function optimization process. In figure (a) and (d), extaero1 (green solid line) is the ${\alpha _{aero}}(z )$ retrieved from the CCD1 measurement, extaero2 (red solid line) is the ${\alpha _{aero}}(z )$ retrieved from the CCD2 measurement. In (b), (c), (e), and (f), the black solid line is the initial phase function used in aerosol extinction coefficient profile retrieval algorithm, which is derived from particle number size distribution and Mie scattering model; the green solid line pfaero1 is the phase function used in the CCD1 measurement and the red solid line pfaero2 is the phase function used in the CCD2 measurement; the green and red dotted lines are the upper and lower bounds of phase function range of pfaero.
4.2.3 Discussion
The results of field measurements show that the derived ${\alpha _{aero}}(z )$s may be more accurate than the initial ones because of smaller gap between ${\alpha _{aero}}(z )$s from 2 CCD measurements. When the optimizing can hardly reduce the gap between the initial results from 2 CCD measurements because the 2 results are already close to each other, the $P{f_{aero}}({\theta } )$s measured on the ground are close to the true ones. This may be because the shape of the PNSD is nearly constant in the vertical direction as the aerosol is well mixed in the boundary layer. When there is a big gap between the initial 2 CCD measurements, the optimizing process can reduce it greatly by making the $P{f_{aero}}({\theta } )$s deviate from the initial states. This might be caused by that the shape of the PNSD is variable in the vertical direction. The joint measurement with a remote sensing instrument which can measure the aerosol extinction coefficient profile such as Raman lidar or high spectral resolution lidar (HSRL) would be useful to evaluate the performance of this methodology.
4.3 Uncertainty analysis
There are two main sources that determine the uncertainties of the results of $P{f_{aero}}({\theta } )$ optimization algorithm: 1) uncertainties caused by algorithm and 2) uncertainties caused by measurement. Besides, the initialized $P{f_{aero}}({\theta } )$ is also a source of uncertainties.
4.3.1 Uncertainties caused by algorithm
The $P{f_{aero}}({\theta } )$ optimization algorithm is based on ${\alpha _{aero}}(z )$ retrieval algorithm and an assumption that the difference between two retrieved ${\alpha _{aero}}(z )$s is all on account of the error of $P{f_{aero}}({\theta } )$s used in retrieval process. In fact, there are other factors that may also contribute to the difference between two retrieved ${\alpha _{aero}}(z )$s, such as errors of SSA and errors caused by assumptions in ${\alpha _{aero}}(z )$ retrieval algorithm.
The main assumptions of the ${\alpha _{aero}}(z )$ retrieval algorithm include: horizontal homogeneity of aerosol distribution and no aerosol around the altitude of signal at minimum. In this study, the distances between CCD camera and laser emitter are less than 60 m. The assumption that the horizontal aerosol distribution in the atmosphere are homogeneous can hold in such a small space range. As for the other assumption that there is no aerosol around the altitude of signal at minimum, it is also reasonable because aerosols concentrated in the boundary layer with a height usually less than 2 km and all the altitudes of signals at minimum are above 3 km. The CLADS has been applied to retrieve the nocturnal boundary layer structure [5] and the nocturnal aerosol optical depth [24], and the results of CLADS in these works proved to be reliable. These works proved the rationality of the 2 assumptions in the ${\alpha _{aero}}(z )$ retrieval algorithm.
As analyzed above, error of SSA is one of the most important sources of uncertainty to the $P{f_{aero}}({\theta } )$ optimization algorithm. To test the influence of error of SSA on the $P{f_{aero}}({\theta } )$ optimization algorithm, 2 simulations where the values of SSA are 0.8 and 1.0 were done respectively. Other data used in simulations are the same as that in 4.1.1. In the simulations, the true value of SSA is 0.9. As shown in Fig. 9, when SSA is smaller than the true value (SSA = 0.8), the retrieved ${\alpha _{aero}}(z )$ is overestimated. When SSA is larger than the true value (SSA = 1.0), the retrieved ${\alpha _{aero}}(z )$ is underestimated. However, no matter SSA is too large or too small, there is no systematic deviation of the optimized $P{f_{aero}}({\theta } )$. The relative errors of ${\alpha _{aero}}(z )$s (Ek) and $P{f_{aero}}({\theta } )$s (Ep) defined in Eq. (13) and Eq. (14) were calculated. As shown in Table 1, when the error of SSA increased from 0 to 11.11%, the error of retrieved ${\alpha _{aero}}(z )$ increased from 4.34% to 10.73% (SSA = 0.8) or 9.04% (SSA = 1.0) for CCD1, and increased from 5.87% to 10.65% (SSA = 0.8) or 10.28% (SSA = 1.0) for CCD2. On the other hand, the error of the optimized $P{f_{aero}}({\theta } )$ changed from 5.73% to 5.24% (SSA = 0.8) or 5.96% (SSA = 1.0) for CCD1, and reduced from 14.72% to 6.82% (SSA = 0.8) or 7.46% (SSA = 1.0) for CCD2.
Fig. 9. Results of simulation with different SSA: figure (a) and figure (c) are results of CCD1 measurement, and figure (b) and figure (d) are results of CCD2 measurement. Figure (a) and figure (b) show retrieved ${\alpha _{aero}}(z )$s under different SSA values and the real ${\alpha _{aero}}(z )$ in simulation. As shown in these figures, the red dotted line is on the right side of the green solid line and the blue solid line is on the left side of the green solid line, which means systematic deviation appears in the retrieved ${\alpha _{aero}}(z )$ with the increase of SSA error. Figure (c) and figure (d) show derived $P{f_{aero}}({\theta } )$s under different SSA values and the real $P{f_{aero}}({\theta } )$s in simulation. As shown in these figures, red, blue and green lines are entangled with each other, which means deviation in the derived $P{f_{aero}}({\theta } )$ does not increase significantly with the increase of SSA error.
Table 1. Relative errors of aerosol extinction coefficient profile and phase function profile retrieved with different values of SSA in simulation experiments.
The simulations confirm that the error of SSA has little effect on the optimized $P{f_{aero}}({\theta } )$, though it has a systematic impact on the results of ${\alpha _{aero}}(z )$ retrieval. Since the error of SSA has little effect on the optimized $P{f_{aero}}({\theta } )$, it will not significantly affect the uncertainty of ${\alpha _{aero}}(z )$ caused by $P{f_{aero}}({\theta } )$. The simulations prove the effectiveness of the $P{f_{aero}}({\theta } )$ optimization algorithm.
4.3.2 Uncertainties caused by measurement
The source of uncertainties caused by measurement include the distance between CCD camera and the laser emitter and the uncertainty of instruments. The distance will affect the resolution of photos captured by CCD camera, and thus affect the signal-to-noise ratio (SNR). The smaller the distance is, the higher the SNR of low-altitude signal is, and the lower the SNR of high-altitude signal is. Bian [25] estimated the effect of different distances ranged from 120m to 155m on the retrieval results, which shows the uncertainty introduced by the distance is not significant.
Considering works done through CLADS before, it is convincing that uncertainties caused by measurement of CLADS are within reasonable range [5,24,26].
4.4 Robust test of the retrieval method with empirical $P{f_{aero}}({\theta } )$
As analyzed in the simulation and field application experiments above, the new method to retrieve ${\alpha _{aero}}(z )$ with CLADS performs well when the $P{f_{aero}}({\theta } )$ measured on the ground is available as initial $P{f_{aero}}({\theta } )$. However, when $P{f_{aero}}({\theta } )$ measurements on the ground is unavailable sometimes, empirical $P{f_{aero}}({\theta } )$ must be used as the initial $P{f_{aero}}({\theta } )$. To test the performance of the new method in this case, the $P{f_{aero}}({\theta } )$ of CALIPSO polluted continental aerosol type is used as initial $P{f_{aero}}({\theta } )$ with the data introduced in 4.2.1.
When the empirical phase function is used in the new method, the condition that the values of $Pf(\theta )$ are reliable near the ground but unreliable at high altitude no longer holds. Thus, the constraint of phase function described in Eqs. (8)–(9) need to be modified as
Where $\rho $ is as same as that in Eq. (9). This modification eliminates the reservation of values of $Pf(\theta )$ near the ground in the optimization process.The results are shown in Figs. 10–12. For the case of measurement at 21:30 on March 27, 2018, the Diff of Ext in initial state is $5.06 \times {10^7}$, and that after optimization is $3.18 \times {10^6}$. The decrease of Diff of Ext is 93.7%. For the case of measurement at 20:15 on April 1, 2018, the Diff of Ext in initial state is $1.60 \times {10^7}$, and that after optimization is $3.57 \times {10^6}$. The decrease of Diff of Ext is 77.7%. For the case of measurement at 20:15 on April 2, 2018, the Diff of Ext in initial state is $1.46 \times {10^7}$, and that after optimization is $2.22 \times {10^6}$. The decrease of Diff of Ext is 84.7%.
Although there are errors led by the empirical $Pf(\theta )$, these results prove that the new method is workable with the empirical $Pf(\theta )$ in the absence of $Pf(\theta )$ measured on the ground.
Fig. 10. Results of measurement at 21:30 on March 27, 2018 with empirical initial phase function: same as Fig. 6
Fig. 11. Results of measurement at 20:15 on April 1, 2018 with empirical initial phase function: same as Fig. 6.
Fig. 12. Results of measurement at 20:15 on April 2, 2018 with empirical initial phase function: same as Fig. 6.
5. Conclusions
Vertical profiles of aerosol extinction coefficient are critical for understanding the contribution of aerosol to air pollution transportation, boundary layer processes, and climate change. Recently, CLADS has been widely used to measure ${\alpha _{aero}}(z )$ with excellent resolution at near-ground altitudes. However, the aerosol phase function is always assumed when retrieving the ${\alpha _{aero}}(z )$ from CLADS signals. Our sensitivity studies show that assuming a $P{f_{aero}}({\theta } )$ in retrieval process can lead to an uncertainty up to 462%.
A new method of using DCDS measurements was proposed in the study. With this method, the uncertainties of retrieved ${\alpha _{aero}}(z )$ from assuming a $P{f_{aero}}({\theta } )$ can be reduced significantly. This method uses two CCD cameras placed at different distances from a laser emitter to capture the side scattering signals of the same laser beam. By reducing the difference between the two retrieved ${\alpha _{aero}}(z )$s from two CCD, more accurate $P{f_{aero}}({\theta } )$s can be constrained by our optimization algorithm. This method is validated by our designed simulations studies.
There are two main types of uncertainties determine the uncertainty of the new method: uncertainties caused by algorithm and uncertainties caused by measurement. However, these uncertainties have little influence on the accuracy of the retrieved ${\alpha _{aero}}(z )$.
This system has been applied in a field measurement at the roof of the College of physics, Peking University, Beijing, China between March and April 2018. The field measurement has proved that our proposed method is applicable in the field study. Besides, these cases are tests with empirical $Pf(\theta )$, and the new method still performs well in reducing the Diff of Ext.
The new method is practical and effective. Compared with the traditional CLADS method, the new method only needs an additional CCD camera and an optimization algorithm. The complex process of obtaining the vertical profile of $P{f_{aero}}({\theta } )$ is avoided, while the large uncertainty of ${\alpha _{aero}}(z )$ introduced by assumed $P{f_{aero}}({\theta } )$ can be reduced significantly.
Funding
National Natural Science Foundation of China (41590872); Natural Science Foundation of Beijing Municipality (8184076, 8194080).
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