Measurement method for slant visibility with slant path scattered radiance correction by lidar and the SBDART model

Yufeng Wang; Lisong Jia; Xingxing Li; Yumei Lu; Huige Di; Dengxin Hua

doi:10.1364/OE.409309

1. Introduction

Four in-built aerosol models under different weather conditions are first theoretically simulated by the SBDART model. The distribution characteristics of the direct solar irradiance and scattered radiance at each atmospheric layer are analyzed, and the contrast ratio of the object and background and the slant visibility results are discussed in detail. The results show that the distribution of atmospheric radiance differs greatly due to absorption and scattering effects for different aerosol models and thus creates different slant visibility distances at the same observation direction, which cannot be ignored in daytime measurements. Different slant visibility distances can also be obtained due to the different scattered radiances at different observation directions. Under a contrast threshold of 0.05, the slant visibility is ∼4.3 km for rural-type aerosols in the direction with a zenith angle of 61.71° and azimuth angle of 60°, and the visibility is ∼6.3 km for urban-type aerosols compared with only ∼2.2 km in the direction of an observation zenith angle of 61.71° and azimuth angle of 40°. The slant visibility under cloudy weather conditions is greatly reduced compared to that under clear weather conditions; taking urban aerosols as an example, the visibility is reduced from 6.3 km to less than 2.0 km.

Furthermore, the method combining the lidar and the SBDART model is validated by simulations under an actual atmosphere. A set of atmospheric aerosol lidar data under hazy weather are used as the simulation model to simulate the actual atmospheric scattered radiance. A list of parameters, including optical depth, single-scattering albedo, asymmetry factor and phase function of a 106-order Legendre matrix expansion, is formed as a customized input file to the SBDART model to obtain accurate slant visibility measurements. When affected by hazy weather, the slant visibility is lower than 4 km, and obvious differences in slant visibility distances are obtained at different observation directions.

The simulation results reveal that different slant visibility distances are directly determined by the differences in atmospheric scattered radiance along the slant path and verify that accurate slant visibility can be obtained by considering the correction of scattering radiation in slant directions. Additionally, the results validate the feasibility of the method combining lidar and SBDART for actual scattered radiance and accurate slant visibility measurements, which is of great scientific significance and application value in the fields of aviation, space flight and air detection.

Visibility or visual range is the distance at which a given standard object can be seen and identified with the unaided eye. Visibility can reflect atmospheric characteristics such as air pollution and air mass properties [1–4]. Generally, horizontal visibility is adopted; however, slant visibility has important scientific significance and application value in aviation, space flight, and air detection [5,6].

At present, visual observations are still the main measurement method used to assess slant visibility. Recently, several lidar visibility meters have emerged to measure slant visibility, and the retrieved averaged aerosol extinction coefficient or averaged aerosol optical thickness along the slant path by lidar are used to estimate the averaged slant visibility according to the traditional Koschmieder formula [7–9]. On the one hand, the slant visibility depends on the contrast ratio C * of the apparent brightness between the object and background along the slant path, which is affected greatly by atmospheric scattered radiation during the daytime. On the other hand, atmospheric scattered radiance mainly involves background sky radiance, which requires solving the radiative transfer equation [10–12]. This is determined by many factors such as the sun spectrum, geometric position and aerosol parameters. Therefore, further in-depth study of the measurement techniques of slant visibility is required.

Solving the radiative transfer equation directly is complex and difficult. At present, researchers in the world have developed a number of models to solve the Earth's atmospheric radiation transmission, such as Modtran, DISORT and other calculation models [13–15]. The intensity of both scattered and thermally emitted radiation can be computed at different heights and directions via these models. In China, Yang C P and Sun Y et al. carried out a series of studies on the characteristics of atmospheric radiation transmission and radiative transfer models [16,17]. Chen S P and Rao R Zh et al. also performed in-depth research in the field of atmospheric radiation measurements [18,19].

Considering the importance of atmospheric scattered radiance in daytime slant visibility measurements, a measurement method is proposed to obtain the slant visibility by the correction of slant path scattered radiance by lidar and the SBDART model, and theoretical simulations and validations are performed in this paper. In the second part, the measurement principle of slant visibility is introduced, and the SBDART model is illustrated to solve the radiative transfer equation to obtain the slant path scattered radiance. In the third part, we perform a detailed simulation of the slant path scattered radiance and the resulting slant visibility distances with different aerosol models under different weather conditions, and the direct and diffuse solar irradiance, scattered radiance per layer, and contrast ratio of the object and background are discussed. In the fourth part, the method combining the lidar and SBDART model is demonstrated under an actual atmosphere. Aerosol data from lidar are inputted to the SBDART model to obtain the actual scattered radiance and slant visibility, and a corresponding discussion is also provided. A summary and discussion are given in the last part.

2. Principle and method for slant visibility

2.1 Measurement principle for slant visibility

To identify an object from its background, it is generally required that there is enough brightness difference between the object and the background. When observing an object through a certain atmospheric distance, the visibility distance is defined as the farthest distance where one can clearly identify an object in a certain background through atmospheric observation, which can be described quantitatively by the apparent brightness contrast C* between the object and background and is given as [2,12,20,21]

(1)$${C^\ast } = \left|{\frac{{L_b^\ast{-} L_o^\ast }}{{L_b^\ast }}} \right|, $$

where L_o^* and L_b* are the apparent brightness of the object and background, respectively. The effect of the atmosphere on apparent brightness derives from two factors: (1) the weakening effect of the atmosphere and (2) the scattering effect of the atmosphere, and thus the apparent brightness of the object and background can be given as [19–21]

(2)$$\left\{ \begin{array}{l} L_o^\ast \textrm{ = }{\tau_L} \cdot {L_o} + {D_L}\\ L_b^\ast \textrm{ = }{\tau_L} \cdot {L_b} + {D_L} \end{array} \right., $$

where L_o and L_b are the intrinsic brightness of the object and the background, τ_L is the atmospheric transparency related to atmospheric optical thickness, and D_L is the brightness of a certain gas column, which generally can be expressed as [20,21]

(3)$${\tau _L} = \exp \left[ { - \int_0^L {{k_{ex}}(l)dl} } \right], $$

(4)$${D_L} = \int_0^L {A(l)\exp \left[ { - \int_0^{{l^{\prime}}} {{k_{ex}}({l^{\prime}})d{l^{\prime}}} } \right]} dl$$

where k_ex is the atmospheric extinction coefficient, the sum of the aerosol extinction coefficient and the molecule extinction coefficient, and A(l) is the brightness of the scattered light sent from a certain angle and unit length gas column to the observation direction, which is equivalent to the J element of the radiative transfer equation [20].Combined Eqs. (1)–(4), the apparent brightness contrast C* between the object and background can be obtained. To clearly identify an object, it is required that the apparent brightness contrast C * should be greater than the contrast threshold (0.02 or 0.05). This is the measurement principle for atmospheric visibility.

When observing an object in the horizontal direction, under the assumptions that the atmospheric level is uniform and that the object should be perfectly dark and the background should be perfectly bright, that is, the intrinsic contrast should be 1.0, the relationship between the meteorological visibility and the atmospheric extinction coefficient is obtained directly as follows under a contrast threshold of 0.02 [12,21]:

(5)$${R_m} = \frac{{3.912}}{{{k_{ex}}}}. $$

This is Koschmieder’s visibility formula, which is often used for horizontal visibility measurements. For lidar visibility meters, the averaged slant visibility is generally estimated according to this empirical formula [8,9]. The major problem is that the atmospheric scattering effect along the slant path is neglected, and there is no definite relationship between the slant visibility and the contrast ratio, which thus makes it impossible to obtain accurate slant visibility or may result in incorrect slant visibility results. To overcome this problem, the proposed measurement method in this paper is to achieve accurate slant visibility with the slant path scattered radiance correction technique.

When observing objects in the air or observing ground objects from high altitude, horizontal uniformity will not be satisfied, and thus, the traditional Koschmieder’s visibility formula is not applicable for slant visibility measurements. According to Eqs. (1)–(4), the slant visibility is determined by the intrinsic brightness of the object and background, the atmospheric transparency and the gas column brightness along the slant path.

Assuming that the object and background are Lambertians, their brightness can be expressed as [20]

(6)$$\left\{ \begin{array}{l} {L_o}\textrm{ = }\frac{{{I_0} \cdot {\rho_o}}}{\pi }\\ {L_b}\textrm{ = }\frac{{{I_0} \cdot {\rho_b}}}{\pi } \end{array} \right., $$

where I₀ is the total irradiance at the ground, including the direct solar irradiance and scattered irradiance, and ρ_o and ρ_b are the reflectivity of the object and background, respectively. Here, the reflection of the object is a ratio of the object radiation to the incoming solar radiation at the object, where the object radiation comes from the background atmosphere to the object along with the viewing direction. Similarly, the reflection of the background is the ratio of the background radiation to the incident solar radiation. Thus, in a certain observation cone and a certain length of gas column, Eq. (2) can be expressed as

(7)$$\left\{ \begin{array}{l} L_o^\ast \textrm{(}R,\theta ,\varphi \textrm{) = }\frac{{{I_0} \cdot {\rho_o}}}{\pi } \cdot \tau (R,\theta ,\varphi ) + D(R,\theta ,\varphi )\\ L_b^\ast \textrm{(}R,\theta ,\varphi \textrm{) = }\frac{{{I_0} \cdot {\rho_b}}}{\pi } \cdot \tau (R,\theta ,\varphi ) + D(R,\theta ,\varphi ) \end{array} \right., $$

where R is the slant range and θ and φ are the zenith angle and azimuth angle of the observation direction, respectively. Placing Eq. (7) into Eq. (1), the contrast ratio C* of the apparent brightness between the object and background along the slant path can be given as

(8)$${C^\ast }(R,\theta ,\varphi ) = \left|{\frac{{{\rho_b} - {\rho_o}}}{{{\rho_b} + \frac{\pi }{{{I_0}}} \cdot \frac{{D(R,\theta ,\varphi )}}{{\tau (R,\theta ,\varphi )}}}}} \right|. $$

Thus, the slant visibility can be determined when the contrast ratio C*(R,θ,φ) is decreased to a value of 0.05 or 0.02. In this measurement method for slant visibility, the atmospheric transparency τ can be obtained by integrating the extinction coefficient from lidar, and the total irradiance I₀ at the ground and the gas column brightness D can be provided by the SBDART model. For the reflectivity of the object and background, ρ_o and ρ_b, some theoretical values or measured values from a photometer can be adopted.

2.2 Calculation method for scattered radiance based on the SBDART model

As illustrated above, the slant visibility is affected to a great extent by the brightness of scattered radiance along a certain slant path, which requires solving the radiative transfer equation. The radiative transfer equation is numerically integrated with DISORT (discrete ordinate radiative transfer) [15]. The discrete ordinate method provides a numerically stable algorithm to solve the equations of plane-parallel radiative transfer in a vertically inhomogeneous atmosphere. SBDART is a software tool that computes plane-parallel radiative transfer in clear and cloudy conditions within the Earth's atmosphere and at the surface. In this paper, we mainly discuss the measurements of slant range visibility within a certain zenith angle, and thus, the SBDART model is adopted to obtain the scattered radiance [22–24]. This FORTRAN computer program is designed for the analysis of a wide variety of radiative transfer problems encountered in satellite remote sensing and atmospheric radiation budget studies. The program is based on a collection of well-tested and reliable physical models that have been developed by the atmospheric science community over the past few decades. A height of 100 km is the default for the top of the atmosphere, which is divided into 33 atmospheric layers from 100 km to 0 km. When inputting the initial solar irradiance, surface albedo, aerosol parameters and cloud parameters, the intensity of both scattered and thermally emitted radiation can be computed at different heights and directions.

SBDART can compute the radiative effects of several lower- and upper-atmosphere aerosol types. In the lower atmosphere, typical rural, urban, or marine conditions can be simulated using standard aerosol models. These models differ from one another in the way their extinction efficiency Q_ext, single-scattering albedo ω, and asymmetry factor g vary with wavelength and to the extent the scattering parameters depend on the surface relative humidity. When aerosol parameters are obtained by lidar, including optical thickness, single-scattering albedo and scattering phase function, an input file with a parameter list can be customized by the user, and the actual atmospheric radiance can be further obtained by the SBDART model. Thus, the proposed measurement method combines lidar and the SBDART model, and, where lidar is adopted to provide aerosol parameters and the SBDART model is used to solve the radiative transfer equation and obtain the corresponding radiance distribution; thus, the apparent brightness contrast between the object and background along the slant path can be corrected, and accurate slant visibility can be achieved. In this paper, both the built-in aerosol models and the actual atmospheric aerosol data are involved in the simulation and analysis, respectively.

It should be mentioned that the current SBDART model is generally used under the assumption of a horizontal homogenous atmosphere, and can only deal with the horizontal homogeneous stratified clouds covering the whole sky. For cumuliform clouds or clouds not covering the whole sky, the simulation will be more complicated, perhaps, a 3-D radiative transfer model is needed to fulfil the task. Also, a spherical homogenous radiative transfer model or pseudo-spherical radiative transfer model should be adopted in theory when the zenith angles are relatively large (> 75°) [25].

3. Simulation and analysis of slant visibility under clear conditions

In this section, we perform a detailed simulation of the slant path scattered radiance and conduct an in-depth analysis on the resulting slant visibility distances with different aerosol models under clear weather conditions. Four aerosol models, including rural-type, urban-type, marine-type and troposphere-type models, are involved, and the direct and diffuse solar irradiance, scattered radiance at each atmospheric layer, and contrast ratio of the object and background are discussed; the slant visibilities in different directions are further simulated and analyzed.

3.1 Simulation process with urban-type aerosols

First, the urban-type aerosol model is taken as an example to illustrate the simulation process. The main simulation parameters are as follows: the solar zenith angle and solar azimuth angle are 60° and 180°, the visibility is 23 km with a wavelength of 0.55 µm, mid-latitude summer model atmospheres are considered, and the number of viewing zenith and azimuth angles in the range of 0° - 180° is set to be 16 and 13, respectively. Figure 1(a) presents the aerosol optical depth distribution for the urban-type aerosol model. The total optical depth is the sum of the layer optical depth, and it is valued ∼0.7. The optical depth increases gradually with height, reaches ∼0.65 at 20 km, and then maintains a slow and steady trend of ∼0.7 to a height of 100 km. The optical depth is determined by aerosol concentrations from high to low ranging from the bottom to the top of the atmosphere. Using the SBDART model, the transmission characteristics of direct and diffuse solar irradiance are obtained and are shown in Fig. 1(b). The direct and diffuse solar irradiance reaching the ground is lower at ∼ 670 w·m^-2·um^-1 due to the stronger absorption effect for the urban aerosol model.

Fig. 1. Height distributions of optical depth and direct and diffuse solar irradiance for the urban-type aerosol model.

Abstract

1. Introduction

2. Principle and method for slant visibility

2.1 Measurement principle for slant visibility

2.2 Calculation method for scattered radiance based on the SBDART model

3. Simulation and analysis of slant visibility under clear conditions

3.1 Simulation process with urban-type aerosols

3.2 Simulation and analysis for four aerosol models

4. Simulation and analysis of slant visibility under cloudy conditions

5. Simulation and discussion of slant visibility under actual atmosphere

6. Conclusion

Funding

Acknowledgments

Disclosures

References

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Figures (16)

Equations (8)

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