1. Introduction

The climate system is experiencing unprecedented changing under the influence of human activity. Scientists worldwide are making continuous efforts to quantify and model the climate change. However, the complicated physical and chemical interactions between clouds and aerosols, as well as instantaneous changes in atmosphere greatly contribute to the difficulty of modeling radiation budget [1]. With advantage of better temporal and spatial resolution, lidar has become one of the fundamental techniques of atmosphere profiling research. With ground-based lidars could only monitor information on limited scales, space-borne lidars can observe the planet in global scale and complement the detection of existing ground-based lidars. Therefore, space-borne lidars have great potential to provide accurate global estimates of the aerosol direct radiative effect (DRE). The Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO), on which the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) loaded, has shown its great power in offering a worldwide and continuous observations of clouds and aerosols [2], and providing an unprecedented opportunity to investigate the vertical structure of global atmosphere. However, studies showed that CALIOP has a relatively large error comparing to other measurements [3] as a result of a backscatter lidar system, incapable of measuring the lidar ratio. On the contrary, the high-spectral-resolution lidar (HSRL) employs an ultra-narrow spectral discrimination filters to separate the Mie-Rayleigh scattering signal, and get direct retrieval of particulate optical properties with high accuracy. The most popular spectral discrimination filters used in HSRLs are interferometric filters and atomic/molecular vapor filters. The Earth Clouds, Aerosols and Radiation Explorer (EarthCARE) will load a Fabry–Pérot interferometer (F-P) based HSRL, named the HSRL ATmospheric LIDar (ATLID) [4]. The airborne 3β + 2α HSRL project developed by NASA equips with an unsaturated iodine vapor filter [5]. Due to the unrivaled suppression on Mie signals and the loose field of view (FOV) tolerance, iodine vapor filter is massively deployed in HSRLs at 532 nm. On the other hand, interferometric filters are more flexible for working wavelength, but require high accuracy assembly and adjustment. China is developing its own space-borne atmospheric lidar, the Aerosol & Carbon Detection Lidar (ACDL), which also employs an HSRL based on iodine absorption cell for aerosol detection and an Integrated Path Differential Absorption (IPDA) Lidar for CO2 detection [6]. As long as this space-borne lidar is under development, comprehensive evaluations are essential to optimize the chosen parameters.

In our previous study, we have discussed the design of spectral discrimination filters of ground-based HSRL [7,8]. We also noticed that, only few analyses focused on space-borne HSRLs. In this study, we would like to evaluate the performance of the space-borne HSRL for aerosol and cloud optical properties (ACHSRL), which is part of the ACDL and responsible for atmospheric particulate detection. The ACHSRL employs an iodine absorption filter as the spectral discrimination filter. We first give a brief introduction of the general principle of the ACHSRL in Section 2. Following is the error analysis model of the ACHSRL for optimization. Monte-Carlo simulation was performed to verify the error model, and the result showed they did match well between each other. In Section.3, we will discuss the critical parameter, iodine cell temperature. In Section 4, a comparative test of the ACHSRL and the CALIOP in the respect of detection accuracy will be presented and this test shows that ACHSRL has smaller uncertainty on particulate optical properties measurement. Finally, concluding remarks will be given in Section 5.

2. Theory and method

2.1 HSRL principle

The basic scheme of the ACHSRL at 532 nm is illustrated in Fig. 1. Backscattered light collected by the telescope is split into three channels, e.g., a parallel channel, a perpendicular channel, and a molecular channel, which are denoted with subscripts ∥, ⊥, M (Molecular), respectively, in this paper. Taking advantage of the different spectral width of Mie scattering and Rayleigh scattering, HSRL could discriminate these two signals with an ultra-narrow spectral filter [9]. Rayleigh scattering consists of a Cabannes-Brillouin central line and pure rotational Raman lines (PRR). Since the PRR is usually filtered out by interference filter, only the central Cabannes-Brillouin scattering line are considered in this paper [10]. The ACHSRL employs an iodine vapor absorption filter in the molecular backscatter channel to block the Mie scattering, as shown in Fig. 1(b). Usually, the lidar equation consists two unknown parameters, thus the equation is ill posed and in Fernald algorithm, lidar ratio has to be assumed [11]. The ACHSRL employs an iodine vapor absorption filter in the molecular backscatter channel to block the Mie scattering, as shown in Fig. 1(b). This channel adds one more equation so that the ill posed retrieval problem could be avoided [9,12].

 

Fig. 1 Basic principle of Chinese ACHSRL (a) Functional block diagram of ACHSRL at 532 nm, (b) Illustration for an iodine cell based HSRL return spectra [13].

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The detected lidar signals can be written as

$P$ = measured power

_$C$ = channel constant, which summarize the performance of the lidar system

$\beta$ = volume backscatter co^{efficient at altitude} $z$

$\alpha$ = volume extinction co^{efficient at altitude} $z$

_$T$ = one-way transmittance from the lidar to the scattering volume at altitude $z$

_{$f_m$} = high-spectral-resolution filter transmission of Cabannes-Brillouin scattering

_{$f_p$} = high-spectral-resolution filter transmission of Mie scattering

$O\left(z\right)$ = overlapping factor

_{$\left(z-z_0\right)$} = range from the satellite to the sampled volume, $z$ is satellite altitude.

The subscripts m and p stand for Cabannes-Brillouin scattering and particulate scattering, respectively. Owing to the long distance between the satellite and target atmosphere, the overlapping factor $O\left(z\right)$, which results from the combination of all geometric effects, is set to 1. The key parameter, $f_m$, relates to the temperature and pressure of the atmospheric, the transmittance of the iodine vapor absorption line, and the laser wavelength as

Through algebraic calculation from Eqs. (1)-(3) [13], the aerosol optical properties, e.g., backscatter coefficient, optical depth and extinction coefficient, could be derived as

Usually, ${\delta }_m$ could be set to a constant, and is mostly affected by the full width of half magnitude (FWHM) of the interference filter [15]. $B^i\left(z\right)=\left[P^i\left(z\right){\left(z-z_0\right)}^2\right]/\left[C^{i}O\left(z\right)\right]$ is the normalized, range and geometric overlap-corrected lidar return signals [13], and $\chi \left(z\right)\text{=}{B}^{\parallel }\left(z\right)\text{/}{B}^M\left(z\right)$ is the intensity ratio of the parallel channel signal to the iodine channel signal. Besides, ${\alpha }_{O_3}\left(z\right)$ represents the ozone volume extinction coefficients at 532 nm.

2.2 Error analysis

Following our former evaluation in [7], by Cheng et al, the particulate backscatter coefficient relative error (PBCRE) and extinction coefficient absolute error (PECAE) could be derived as

The error model contains the contribution of random noise and systemic noise, where ${\eta }_{{\beta }_p}^i$ represents PBCRE, ${\sigma }_{\tau }^i$ represents particulate optical depth error (PODE), and superscripts $\chi$, $\delta$, $f_m$, and $f_p$, indicate the sources of the error. ${\eta }_{{\beta }_p}^{\chi },{\eta }_{{\beta }_p}^{\chi }$ and ${\sigma }_{\tau }^{\chi },{\sigma }_{\tau }^{B^M}$ mainly comes from the observation noise, while ${\eta }_{{\beta }_p}^{f_m},{\eta }_{{\beta }_p}^{f_a}$ and ${\sigma }_{\tau }^{f_m},{\sigma }_{\tau }^{f_p}$ depend on the calibration precision and the stability of iodine cell temperature and laser frequency [7]. Detailed symbol interpretations are listed in Appendix A. Concerning aerosol extinction coefficient, it is hard to conduct error analysis as there exists derivatives in Eq. (9), but the derivatives process in Eq. (9) is replaced by differential process in actual detection. Thus, Eq. (9) could be rewritten as

As this paper focuses on the error sources related to HSRL hardware design, we ignored the uncertainties from atmospheric auxiliary parameters, such as temperature and pressure [7]. Subsequently, a Monte-Carlo simulation is performed to verify the error model.

2.3 Configuration

To quantify the uncertainty, the specification of the ACHSRL is presented in Table 1 [16]. The satellite will be launched into a 705-km circular sun-synchronous polar orbit, which processes through one complete revolution each year, so the satellite always maintains the same relationship with the sun. The 40 Hz laser repetition rate takes the fundamental horizontal resolution to 167 m, and the 50 MHz digitization rate determines the fundamental vertical resolution of the lidar profile to be 3 m. The laser wavelength is set to the center wavelength of iodine 1110 absorption line [8,16]. The pulse energy and the telescope diameter are the fundamental parameters that determine the signal-to-noise ratio (SNR). Theoretically, higher pulse energy and larger telescope diameter lead to higher SNR, but this will also increase the power consumption and satellite volume. So it is appropriate to take a balance of the performance and body volume of ACHSRL [17].

Table 1. Specification of ACHSRL at 532 nm for Numerical Simulation

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The receiver system takes the balance of SNR of different channels into consideration. More backscattering light is split into the molecular channel, instead of the parallel channel. Therefore, the optical efficiency of the parallel channel is 0.16, while that of molecular channel is 0.375. The optical efficiency takes all the optical relay system efficiencies into account, such as the splitting prism and background light filter. In Section 3.1, the SNR issue of molecular channel will be further discussed. The iodine pool is a 10 cm length saturated cell. The cell temperature is set to 39°C and the finger temperature is set to 37°C. This is an optimization result, which will be further explained in Section 3.1.

When these parameters in Table 1 are inserted as inputs of Eqs. (1)-(4), the backscattering signals in the three channels are generated. Using Eqs. (12)-(15), the theoretical error ranges of aerosol or cloud optical properties are simulated. In the analysis below, a Monte-Carlo simulation is conducted to examine the error model, i.e., Eqs. (12)-(15). After the Monte-Carlo verification, the error model is adopted to the optimization of the high-spectral-resolution filter and the assessment of the detection accuracy of ACHSRL.

2.4 Monte-Carlo simulation verification

An atmosphere scene is built with reference to the models used to testify the performance of CALIPSO [18]. Three layers are set at different heights to imitate clouds and aerosols. Key properties of these layers, namely, optical depth, lidar ratio and depolarization ratio are listed in Table 2. As for multiple scattering effect [19], it is largely dependent on the FOV of the telescope [20], which is not the focus of this paper. Referring to the CALIPSO data [21], multiple scattering factor of cirrus is 0.75, while that for aerosol varies from 0.6 to 0.95. According to our calculation, the uncertainty caused by the variation of multiple scattering factor is about one-tenth of that induced by the effect of signal noise. Therefore, the multiple scattering factor is not given in Table 2. In the simulation below, $\eta \left(z\right)$, multiple scattering factor, is set to 1.

Table 2. Scene Descriptions for the Profile Input into the Simulation

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In this Monte-Carlo simulation, echo signals in all three channels are corrupted by the noises, for instance, shot noise, solar background noise, dark current noise, and thermal noise etc. The SNR are estimated as follows [17],

Figure 2 shows the Monte-Carlo simulation results. Figure 2(a) is the particulate backscatter coefficient retrieval result, while Fig. 2(b) and 2(c) are the total optical depth and particulate extinction coefficient, respectively. The Monte-Carlo results are denoted by blue scatters, while the red dash lines are calculated by the error model in Section 2.2. In Fig. 2(a), the PBCRE are calculated only at these altitudes where particulate matters exist. Because, theoretically, PBCRE becomes infinite when the particulate backscatter coefficient is zero. As shown in Fig. 2, most of the blue scatters are within the red lines, suggesting that the Monte-Carlo simulation matches well with the error propagation theory model, which are inferred from Eqs. (12)-(15).The simulated backscatter signals is averaged 30 times in horizontal direction and 20 times in vertical direction. Therefore, the horizontal resolution is 5 km and the vertical resolution is 60 m. Besides, as the molecular channel wipes out most Mie scattering, its SNR is lower than the other two channels. So, to enhance the SNR of molecular channel, the vertical resolution is further decreased to 480 m, i.e., the backscatter echo averages 160 times in vertical resolution. The three layers, two cirrus layers and an aerosol layer, are easy to identify from the inversion of particulate backscatter coefficients. However, only the strong cirrus layer at 10 km is obvious in the retrieval result of particulate extinction coefficients. This phenomenon suggests that it may be better to detect aerosol/cloud layer from the retrieval results of backscatter coefficients for ACHSRL.

 

Fig. 2 Comparison between Monte-Carlo results and error model for (a) Particulate backscatter coefficient, (b) Particulate optical depth, (c) Particulate extinction coefficient

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So far, the error model is proposed and verified by Monte-Carlo simulation. In the following section, the theoretical error model is applied to optimize the iodine cell and access the ACHSRL performance.

3. Discussion

In Section 3, the error model proposed in Section 2 is used to study methods for improving the high-spectral-resolution filter performance. As a key module of ACHSRL, the iodine filter must be carefully designed. In addition, the error model is utilized to assess the performance of ACHSRL with the measured particulate optical properties data from CALIPSO observations worldwide.

3.1 Iodine filter

As we have pointed out, f_m and spectral discrimination ratio (SDR, the ratio of f_m to f_p) are the key parameters of spectral discrimination filter [7]. The trade-off between them is made in this subsection. Forkey proved that iodine finger temperature determines the transmission function of iodine vapor filter, while the iodine cell temperature has little effect on this transmission curve and therefore has little effect on SDR and f_m [22]. Thus, iodine cell temperature is always set to be two degrees higher than iodine finger temperature in the following study for convenience.

Figure 3 reveals the relationship of iodine filter characteristics and PBCRE at 10.6 km of the simulated scene in Section 2.4. Figure 3(a) shows that, compared with SDR, f_m is more critical to the retrieval accuracy. When the SDR is larger than about 400, the increase in SDR could not contribute much of the improvement of the retrieval uncertainty. On the other hand, a larger f_m greatly increase the detection accuracy. For example, when the SDR is 400, if f_m changes from 0.25 to 0.35, PBCRE decreases from 18.22% to 15.50%. On the contrary, when f_m is 0.25 and SDR changes from 400 to 4000, the PBCRE reduces from 18.22% to 17.90%.

 

Fig. 3 The function of retrieval error and high-spectral-resolution filter settings, (a) the PBCRE at 10.6 km changes with the f_m and SDR, (b) the trend of SDR and PBCRE at 10.6 km with iodine cell temperature. As iodine cell temperature rises, SDR increases exponentially, but the PBCRE does not decrease or increase monotonically.

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However, SDR and f_m show opposite trends with the change of iodine vapor cell temperature. It is impossible to obtain a large SDR and f_m simultaneously. When the temperature of iodine cell rises, SDR increases but f_m decreases. Figure 3(b) shows that a larger error will be yielded when the cell temperature is too low [23]. For every distinct spectral discrimination filter, an optimization point could be found at the smallest PBCRE, like in Fig. 3(b). For the ACHSRL discussed in this paper, 39°C is the best choice for iodine cell temperature and the iodine finger temperature should be set to 37°C.

In the simulation, we found that the main source of detection uncertainty incomes from the low SNR. The uncertainties caused by the variation of f_m and f_p, e.g., ${\eta }_{{\beta }_p}^{f_m}$ and ${\eta }_{{\beta }_p}^{f_{\text{a}}}$, are very small, thus are neglected hereinafter. Besides, f_p, the transmission of Mie scattering through the iodine absorption cell is also very small, e.g., 10⁻⁴ - 10⁻⁶. It is usually set to be zero in practice [5].

3.2 Actual atmosphere optical properties

In Section 2.4, an atmosphere model is employed to verify the error model. Here, the CALIPSO measurement data is used to quantify the uncertainty of the developing ACHSRL. Figure 4 is the monthly global aerosol distribution on land. Figure 4(a) shows the monthly averaged global aerosol optical depth (AOD), which is obtained by aggregating the particulate extinction coefficients over all vertical bins. Figure 4(b) is the monthly averaged particulate extinction coefficient at 1.0 km above ground surface level. The particulate extinction coefficients data comes from CALIPSO level 3 data in June 2015. In this paper, continental aerosol is the prime focus, thus, the aerosols above the sea are ignored.

 

Fig. 4 Aerosol loading distribution map, (a) monthly averaged aerosol optical depth, (b) the PBL (1 km above land surface) aerosol extinction coefficient (km⁻¹).

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Using the data shown in Fig. 4 and the error model in Section 2.2, the PBCRE and PECAE of the planet boundary layer were estimated and shown in Fig. 5. As shown in Fig. 5(a), most of the PBL PBCRE in high aerosol loading area are below 30%, such as Sahara Desert, Indian Peninsula and North China Plain, etc. On the other hand, the distribution of PECAE is more even and most of the extinction uncertainties are between 0.1 km⁻¹ and 0.2 km⁻¹, as shown in Fig. 5(b). This is because the retrieval of particulate extinction coefficient largely relies on the detection of molecular backscattering signal, and the distribution of the atmosphere molecules usually does not vary too much.

 

Fig. 5 Theoretical measurement error of ACHSRL, (a) the PBL PBCRE (%), (b) the PBL PECAE (km⁻¹)

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In the next section, the CALIOP Level 2 particulate optical properties data in June 2015, in a selected area, is adopted to the error estimating process. Furthermore, the detection accuracy of CALIOP and ACHSRL are compared.

4. Comparison with CALIPSO

Up to now, only CALIOP successfully provides a global profile of clouds and aerosols for years. CALIOP is the primary instrument onboard CALIPSO. The released product data of CALIOP is defined by different levels, level 1B data is the processed instrument data at full resolution, while level 2 data includes atmospheric properties derived using measurements from multiple CALIPSO instruments. The level 3 data product is the averaged atmospheric variables mapped onto uniform space-time grids. As the ACHSRL will fly in the same sun-synchronous orbit height as CALIOP, it is reasonable to compare the measurement uncertainty of the two satellites to check the necessity of next generation space-borne lidar. South Japan area, 32°N-37°N, 130°E −141°E, is picked out for a statistical analysis. South Japan is on the transport path of China aerosols to North America [24]. If the particulate matters can be more measured with better accuracy by ACHSRL, it will be beneficial to the aerosol transport study. In this section, the aerosol/cloud backscatter and extinction coefficient in CALIOP 5 km aerosol/cloud profile level 2 data product are utilized to generate the simulated signal of ACHSRL, and the corresponding uncertainties of these coefficients in the same CALIOP data products are used to compare with the uncertainties estimation of ACSHRL. The chosen area is shown in Fig. 6.

 

Fig. 6 The aerosol optical depth measurement in South Japan, June 2015. Red rectangle is the chosen area, and the color bar indicates monthly averaged aerosol optical depth calculated using CALIPSO level 3 all sky aerosol extinction profile. The Z-dimension is the surface altitude.

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We chose the CALIPSO level 2 profile data in June 2015 for the comparison because clouds and aerosols are more active during the summer. In June 2015, 18 CALIPSO tracks crossed the selected area. These tracks and attenuated backscatter profiles are shown in Fig. 7. Figure 7(a) displays the day profiles, and Fig. 7(b) shows the night. The difference between Fig. 7(a) and 7(b) is obvious. First of all, the orbital directions are different. Besides, although the aerosol and cloud layer are visible both day and night, the SNR of the CALIOP is much better at nighttime than at daytime [25].

 

Fig. 7 Attenuated backscatter profiles of CALIPSO in South Japan in June 2015, dates are indicated separately, (a) day orbits, (b) night orbits. Some orbit tracks overlap each other and are indicated by satellite icons.

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Following the error model of Eqs. (12)-(15), the PBCRE and PECAE of ACHSRL are calculated and their distributions are counted. These distributions are compared with the uncertainty distributions of the CALIOP’s product, Level 2 profile data. The error assessment procedure is repeated for all the data over the selected spatial grid, in June 2015, and the statistics of PBCRE and PBCAE are shown in Fig. 8. More than 73.63% of the PBCRE of ACHSRL is below 40%, while that of CALIPSO is 30.72%. Regarding PECAE, more than 76.01% for ACHSRL are below 0.2 km⁻¹, compared with 56.97% for CALIPSO. Even with simple and conventional retrieval procedure of HSRL, the designing ACHSRL outperforms CALIOP on detection accuracy.

 

Fig. 8 The statistical distribution of (a) PBCRE and (b) PECAE for CALIOP (blue bars) and ACHSRL (orange bars).

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The statistics in Fig. 8 leads to evident conclusion that ACHSRL has intrinsic advantage on atmospheric detection. But, the advantage on PECAE, i.e., the retrieval accuracy of extinction coefficient, is not so obvious, mostly due to the low energy level of molecular channel and the elementary retrieval algorithm. Considering the complex algorithm CALIOP employed, the detection accuracy of ACHSRL can be improved greatly with better algorithm developed [26]. In [26], Willem et al utilized the spatial and temporal information in continuous signal profiles, whereas current lidar algorithms only use the information content of single profiles.

The same comparison process is conducted in high aerosol loading regions. Similar conclusions could be draw, the advantage on retrieving backscatter coefficient using ACHSRL is prominent, while the advantage on PECAE is not outstanding as on PBCRE.

5. Summary

In this paper, a designed space-borne HSRL, the ACHSRL, is proposed and its detection uncertainty of particulate optical properties is analyzed. We first present an error model for particulate backscatter coefficient and extinction coefficient retrieval by ACHSRL. Monte-Carlo simulation further validates the error model. Following that, we use the error model to optimize the temperature setting of iodine cell. The analysis in Section 3 shows that the iodine vapor filter should maintain high transmission of the molecular backscatter signal while keeping reasonable suppression to Mie backscattering. For the ACHSRL discussed here, 39°C for iodine cell and 37°C for iodine finger are suitable temperatures to reduce the detection error.

The following detection accuracy assessment, based on the level 3 monthly averaged CALIOP data and the error model constructed in Section 2.2, demonstrates that the PBCRE of ACHSRL in high aerosol loading areas are quite low, mostly below 30%, and the PECAE is between 0.1 km⁻¹ and 0.2 km⁻¹. Finally, through the comparison test between ACHSRL and CALIOP, the HSRL exhibits promising ability on atmospheric detection. One-month CALIOP particulate optical property profiles in south Japan were collected and analyzed. The result shows 73.63% of the PBCRE of ACHSRL are below 40%, while that of CALIPSO is 30.72%. As for PECAE, 76.01% of ACHSRL are below 0.2 km⁻¹, compared with 56.97% for CALIOP. The estimation of the ACHSRL performance reveals space-borne HSRL is a valuable instrument and powerful mean to study the global aerosol and cloud distribution and their transportation.