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    Schematic of the radiance paths illuminating the bridge and water surface.

  • View in gallery

    Calibration scheme based on bridge lights.

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    VIIRS DNB low-light imagery of east China at 1733 UTC 9 Oct 2012.

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    2D and 3D views of the VIIRS DNB night-light for Hangzhou Bay Bridge and Donghai Bridge. (a) 2D view of night-light for Hangzhou Bay Bridge, (b) 2D view of night-light for Donghai bRidge, (c) 3D view of night-light for Hangzhou Bay Bridge, and (d) 3D view of night-light for Donghai Bridge.

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    DNB radiance over Hangzhou Bay Bridge for 2-yr time series with 16-day sampling interval. (a) Pixel radiance values along Hangzhou Bay Bridge for different cases. (b) Averaged radiance data of 2 yr over the chosen parts of Hangzhou Bay Bridge with 16-day sampling interval. (c) Corresponding lunar illumination.

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    DNB radiance over the Donghai Bridge for the 2-yr time series with 16-day sampling interval. (a) Pixel radiance values along Donghai Bridge for different cases. (b) Averaged radiance data of 2 yr over the chosen parts of Donghai Bridge with 16-day sampling interval. (c) Corresponding lunar illumination.

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    Comparison between the predicted and observed DNB HGS radiance values for each case: (a) Hangzhou Bay Bridge and (b) Donghai Bridge.

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    Scatterplot of the predicted and observed radiance: (a) Hangzhou Bay Bridge and (b) Donghai Bridge.

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Calibration Method of Low-Light Sensor Based on Bridge Lights

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  • 1 College of Meteorology and Oceanography, People’s Liberation Army University of Science and Technology, Nanjing, China
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Abstract

Many quantitative uses of the nighttime imagery provided by low-light sensors, such as the day–night band (DNB) on board the Suomi–National Polar-Orbiting Partnership (SNPP), have emerged recently. Owing to the low nighttime radiance, low-light calibration at night must be investigated in detail. Traditional vicarious calibration methods are based on some targets with nearly invariant surface properties under lunar illumination. However, the relatively stable light emissions may also be used to realize the radiometric calibration under low light. This paper presents a low-light calibration method based on bridge lights, and Visible Infrared Imaging Radiometer Suite (VIIRS) DNB data are used to assess the proposed method. A comparison of DNB high-gain-stage (HGS) radiances over a 2-yr period from August 2012 to July 2014 demonstrates that the predictions are consistent with the observations, and the agreement between the predictions and the observations is on the order of −2.9% with an uncertainty of 9.3% (1σ) for the Hangzhou Bay Bridge and −3.9% with an uncertainty of 7.2% (1σ) for the Donghai Bridge. Such a calibration method based on stable light emissions has a wide application prospect for the calibration of low-light sensors at night.

Corresponding author address: Prof. Dr. Wei Yan, College of Meteorology and Oceanography, PLA University of Science and Technology, 60 Shuanglong Street, Nanjing 211101, China. E-mail: 18913979082@163.com

Abstract

Many quantitative uses of the nighttime imagery provided by low-light sensors, such as the day–night band (DNB) on board the Suomi–National Polar-Orbiting Partnership (SNPP), have emerged recently. Owing to the low nighttime radiance, low-light calibration at night must be investigated in detail. Traditional vicarious calibration methods are based on some targets with nearly invariant surface properties under lunar illumination. However, the relatively stable light emissions may also be used to realize the radiometric calibration under low light. This paper presents a low-light calibration method based on bridge lights, and Visible Infrared Imaging Radiometer Suite (VIIRS) DNB data are used to assess the proposed method. A comparison of DNB high-gain-stage (HGS) radiances over a 2-yr period from August 2012 to July 2014 demonstrates that the predictions are consistent with the observations, and the agreement between the predictions and the observations is on the order of −2.9% with an uncertainty of 9.3% (1σ) for the Hangzhou Bay Bridge and −3.9% with an uncertainty of 7.2% (1σ) for the Donghai Bridge. Such a calibration method based on stable light emissions has a wide application prospect for the calibration of low-light sensors at night.

Corresponding author address: Prof. Dr. Wei Yan, College of Meteorology and Oceanography, PLA University of Science and Technology, 60 Shuanglong Street, Nanjing 211101, China. E-mail: 18913979082@163.com

1. Introduction

The Suomi–National Polar-Orbiting Partnership (SNPP) satellite launched on 28 October 2011 is a prototype operational satellite of the Joint Polar Satellite System (JPSS) that ushered in a new generation of low-Earth-orbiting satellites (Miller et al. 2012; Hillger et al. 2013). The day–night band (DNB) of the Visible Infrared Imaging Radiometer Suite (VIIRS) mounted on the SNPP significantly enhances the nighttime imaging capability because it overcomes some of the limitations of its predecessor, the operational line scanner (OLS) on the Defense Meteorological Satellite Program (DMSP), such as geometric distortion, a lack of accurate calibration, and low spatial resolution (Miller et al. 2005; Lee et al. 2010; Lewis et al. 2010; Kuciauskas et al. 2013). Compared to the OLS, which has a nominal spatial resolution of ~2.8 km and no onboard calibration for visible channels, the DNB has a finer spatial resolution of 742 m that is constant across the entire scan, and it is calibrated using an onboard solar diffuser (SD), which was not previously possible (Liang et al. 2014). This panchromatic (0.5–0.9 μm) solar reflective band is mainly used to provide weather- and climate-related data and other Earth features from bright daylight to low-light conditions under a quarter moon. To cover this extremely wide dynamic range from 3 × 10−9 to 0.02 W cm−2 sr−1, the DNB employs three gain stages: a low gain stage (LGS) for daytime, medium gain stage (MGS) for twilight, and high gain stage (HGS) for nighttime. For the on-orbit calibration, the low gain is determined using an SD (Mills et al. 2010). The HGS/MGS and MGS/LGS gain ratios are determined at the transition regions of the adjacent gain stages, where the lower gain stage is sensitive but the higher gain stage is not saturated (Jacobson et al. 2010). Then, the midgain and high gain can be obtained based on the low gain and the gain ratios.

The DNB HGS cannot be calibrated directly using the SD due to pixel saturation and must therefore rely on the transfer of LGS calibration. Thus, the radiometric accuracy requirements should be evaluated using other calibration methods. The radiance of other visible-spectrum light, such as integrated starlight, zodiacal light, and airglow, which are collectively referred to as diffuse illumination, multisource (DIM) emissions, is much lower than that of moonlight (Miller et al. 2012), and hence, moonlight is the main light source at night.

Similar to other reflectance solar bands calibrated at daytime using sunlight, the vicarious calibration methods based on some targets with nearly invariant surface properties under lunar illumination can be used to evaluate the radiometric accuracy. Liao et al. (2013) selected Railroad Valley Playa, Nevada, as the calibration target to calibrate the HGS of DNB. The results show that the observed radiance values are higher than the predicted radiance values simulated by MODTRAN, version 5 (MODTRAN5), and the radiometric calibration uncertainty is about 15%. However, the stray light contamination and the variable moisture content, which may underestimate this uncertainty, are not considered. Further, Shao et al. (2013) performed vicarious calibration based on some ice sheet regions, such as Dome C in Antarctic and Greenland in the Northern Hemisphere. They claimed that the reflectance values derived from DNB observations are consistent with the reflectance values derived from Hyperion observations. However, the comparison results are affected by some limitations, such as atmospheric absorption of moonlight and uncertainty in the lunar irradiance model. Ma et al. (2015) proposed the use of deep convective clouds (DCCs) as calibration targets under lunar illumination to evaluate the calibration accuracy of DNB HGS, and the lunar irradiance model combined with the SCIATRAN was used to simulate the top-of-the-atmosphere reflectance values of the DCCs. A comparison between the simulations and the measurements for a 1-yr period shows that the DNB HGS data are calibrated on orbit within a −4.9% ± 8.8% uncertainty range near full moon. However, the erroneously identified calibration targets, lightning contamination, and inherent limitations of the lunar irradiance model are the remaining uncertainties in both the simulated and observed reflectance values.

All the radiometric calibration methods of DNB HGS mentioned above are based on reflected moonlight. However, the low-light sensor not only provides atmospheric and surface reflectance views using reflected lunar illumination but also captures light emissions (cities, fishing fleet lights, aurora, lightning, and other terrestrial sources) (Miller et al. 2013). Thus, it is important to investigate whether relatively stable light emissions can be used to realize the radiometric calibration of low-light sensors. Cao and Bai (2014) provided a quantitative analysis of light emissions (fishing fleets, bridges, and cities) and found that the bridge lights, which are relatively stable, can be used to evaluate the DNB HGS calibration, since bridges are typically made of concrete with a moderate level of reflectance and the water below it has low reflectance. However, the predicted in-band radiance values at the satellite sensor, which are estimated using only the fundamental radiometry method, are compared with the observed radiance values. Many factors, such as the lunar illumination contribution and the diffuse radiance of light sources, are not considered. Furthermore, an applicable method and scheme for the low-light calibration were not given.

In this paper, we present a more detailed investigation of low-light calibration based on bridge lights, and propose a new method and scheme for low-light calibration based on bridge lights. Section 2 provides an overview of the theory and the scheme of the low-light calibration based on bridge lights. Section 3 introduces the datasets of the study. Section 4 compares the predicted radiances with the observed radiances of DNB HGS to validate the feasibility of using bridge lights to calibrate DNB HGS. The limitations of this method are also discussed in this section. Finally, section 5 summarizes the conclusions of our study.

2. Methodology

a. Method for low-light calibration based on bridge lights

This calibration method is based on the physical statements and mathematical formulations of the radiative transfer of the moonlight and bridge lights. Figure 1 shows a schematic of the radiance paths illuminating the bridge and water surface. The red, green, and blue paths represent the direct transmission of moonlight, the diffuse transmission of the moonlight, and the upwelling surface radiance reflected by the atmosphere back to the water surface, respectively. Furthermore, the cyan and white paths represent the radiance illuminated by the bridge lights.

Fig. 1.
Fig. 1.

Schematic of the radiance paths illuminating the bridge and water surface.

Citation: Journal of Atmospheric and Oceanic Technology 33, 6; 10.1175/JTECH-D-15-0225.1

When the pixel is filled with water and is not contaminated by other lights, such as city and bridge lights, the balance between the downward and upward flux densities can be described as follows:
e1
where is the water surface reflectance (assuming a Lambertian surface), is the upward water surface radiance, is the cosine of the lunar zenith angle, is the top-of-the-atmosphere (TOA) irradiance of the moon, is the total optical depth, is the diffuse transmittance for moonlight, and is the aerosol reflectance. In this equation, the right-hand side represents the downward flux density, which is composed of the three components shown in Fig. 1: the direct transmission of the moonlight, the diffuse transmission of the moonlight, and the upwelling surface radiance reflected by the atmosphere back to the water surface. Then, can be solved using Eq. (1) as follows:
e2
When viewed from the satellite, the at-aperture radiance can be computed as follows:
e3
where is the cosine of the satellite zenith angle and is the diffuse transmittance at the upward path to the satellite. The first and second terms on the right-hand side of Eq. (3) represent the direct and diffuse transmissions of the upward water surface radiance. The third term, , represents the observed radiance that is reflected and scattered by the atmosphere without ground interaction. The fourth term, , represents the contribution of DIM at night. However, some inherent uncertainty remains in this assumption owing to the response function of the low-light sensor, which may not be at full maximum in band. The impact of the response function should be considered in the proposed calibration method in a future study.
Similarly, when part of the bridge over the water is contained in a pixel, the balance between the downward and the upward flux density can be described as
e4
where is the effective surface albedo, represents the surface upward radiance over bridge regions, and represents the upwelling radiance from the reflected bridge lights. As the Lambertian source size is much smaller than the pixel size, the upwelling radiance of the reflected bridge lights can be described as
e5
where is the area (m2), is the angle between the area surface normal and the line of observation, and is the in-band radiance exitance from the target, which can be estimated using the following equation according to Cao and Bai (2014):
e6
where is the electrical power of the lightbulb on the bridge, is the solid angle of the lightbulb and is nominally , is the electrical power efficacy, and is the number of lamps per pixel. Thus, a part of the bridge should be straight so that the number of lamps per pixel can be calculated more conveniently. The terms and represent the Lambertian reflectance of bridge deck and water, respectively. Further, and represent the effective solid angle intercepted by the area of the illuminated bridge and water surface, respectively.
Thus, the upward radiance can be solved by Eq. (4) as follows:
e7
When viewed from the satellite, can be computed as follows:
e8
Comparing Eqs. (3) and (8), the at-aperture radiance difference can be characterized as
e9
According to Remer and Kaufman (1998) and Johnson et al. (2013), for an aerosol optical depth of 1. Thus, the terms and can be considered to be very small and can be eliminated from Eq. (9) because the aerosol optical depth is generally much lower than 1. Then, Eq. (9) can be rewritten as
e10

The first and second parts on the right-hand side of Eq. (10) represent the contribution of bridge lights and moonlight, respectively. The moonlight radiance term depends on the term . As the bridge deck area in the pixel is much smaller than the pixel area, the moonlight radiance contribution is relatively small owing to the small term. Equation (10) is actually used in this paper for the comparison of the predicted and observed radiance.

Traditionally, the digital counts of pixels with water and with part of the bridge for the low-light sensor can be obtained. The at-aperture radiance difference can be calculated using Eq. (10). Thus, based on linear regression, the calibration gain can be determined by comparing the digital count differences of the low-light sensor with the calculated radiance differences,
e11

It should be noted that the proposed calibration method is based on the bridge night-light at the pixel level. Thus, the observed radiances should be associated with the spatial response of the low-light sensor. This study assumes that the spatial response functions of the low-light sensor, both along track and cross track, are an approximately rectangular function. Therefore, there will be some inherent uncertainty in this assumption for the low-light sensor with no rectangular spatial response function.

b. The calibration scheme of low-light sensor based on bridge lights

In light of the radiance calibration model deduced hereinbefore, the calibration scheme of the low-light sensor based on bridge lights is given in Fig. 2. First, the bridge targets should be selected to ensure that part of the bridge is straight and that the radiance of the bridge lights are above the minimum radiance specification (Lmin) of the low-light sensor with no cloud contamination. Second, we obtain the corresponding observation geometry, such as lunar zenith angle (LZA) and lunar phase angle (LPA), to calculate the TOA lunar irradiance using the lunar irradiance model (Miller and Turner 2009). Additionally, the characteristics of bridge lamps, such as the electrical power of the lightbulb, electrical power efficacy, and effective solid angle intercepted, are investigated. Third, the surface reflectance values, atmospheric profiles, aerosols, and other input parameters are obtained and input into the radiative transfer model to calculate the at-aperture radiance difference using Eq. (10). Then, the pixels over the bridge and water backgrounds are selected and averaged to calculate the digital count difference. Finally, the at-aperture radiance differences are compared with the corresponding digital count differences to obtain the gain and offset of the low-light sensor.

Fig. 2.
Fig. 2.

Calibration scheme based on bridge lights.

Citation: Journal of Atmospheric and Oceanic Technology 33, 6; 10.1175/JTECH-D-15-0225.1

3. Datasets

In this study, the VIIRS DNB data are used to assess the proposed low-light calibration method based on bridge lights. Three VIIRS data products—namely, the VIIRS DNB sensor data record (SDR; SVDNB), the VIIRS DNB SDR geolocation content summary (GDNBO), and the VIIRS cloud cover/layers environment data record (VCCLO)—are utilized for the calibration. The SVDNB product provides the calibrated TOA radiance for each pixel and the quality flag information. The GDNBO product provides the corresponding latitude, longitude, lunar zenith angle, lunar azimuth angle, lunar phase angle, satellite zenith angle, and satellite azimuth angle. The VCCLO product, which provides the pixel-level cloud layer identification, pixel-level cloud type identification, and pixel-level cloud cover/layers (CCL) quality flags, is used to eliminate the chosen bridge targets contaminated by clouds. Traditionally, the at-aperture radiance differences of the DNB HGS can be predicted and the calibration coefficients can be obtained by comparing the digital count differences of the DNB HGS with the predicted at-aperture radiance differences. However, the radiances of the DNB HGS based on the transfer of calibration from the LGS are contained in the VIIRS DNB SDR, while the digital counts are not. Thus, the radiance differences are predicted and compared with the DNB HGS observations to validate the proposed calibration method.

Bridge lights are a good night-light point source because of their relative stability. However, not all bridges are suitable for calibration. For selecting bridge targets, the following three criteria must be met. First, the integrated radiance of the pixel over the bridge should be above Lmin (3 nW cm−2 sr−1). Second, a part of the bridge should be straight to ensure that the number of lamps within the pixel can be counted more accurately. As the lamps on the bridges are equally spaced, the number of lightbulbs in a pixel can be easily calculated. Third, the radiance of the pixel over the bridge should not be contaminated by other lights, such as city lights.

Figure 3 shows VIIRS DNB low-light imagery of east China at 1733 UTC 9 October 2012. The imagery was produced using the SNPP VIIRS DNB SDR. The radiance data were scaled logarithmically between [−11.5, −9.0] log (W cm−2 sr−1) and plotted using a linear grayscale color palette. Figures 3a and 3b represent the Hangzhou Bay Bridge and Donghai Bridge at nearly nadir view, respectively. The bridge lights of both bridges are clearly visible in the imagery. To further investigate the characteristics of both bridges, the night-light radiances of the Hangzhou Bay Bridge and Donghai Bridge over an area of 24 px2 are shown in Figs. 4a and 4b, respectively. In these figures, the vertical axis represents the pixels at the along-track direction, whereas the horizontal axis represents the pixels at the cross-track direction. Further, a 3D view of the VIIRS DNB night-light for the Hangzhou Bay Bridge and Donghai Bridge are shown in Figs. 4c and 4d, respectively, using CloudCompare, which is an open-source software package originally designed for 3D point cloud processing and is especially suitable for comparisons between datasets (Cao and Bai 2014). The radiance of both bridge lights within a pixel is found to be larger than Lmin (3 nW cm−2 sr−1), and parts of both bridges are straight with no city light contamination. Thus, both bridges satisfy the above-mentioned criteria. Further, the radiances of bridge lights within a pixel in different parts of the bridges are different owing to a different number of lamps within a pixel, and the radiance of the bridge lights within a pixel for the bridges is different because of the difference in the characteristics of bridge lamps. The radiances of the (12,15) pixel in Fig. 4a and the (17,11) pixel in Fig. 4b are much larger than those of the other pixels. The buildings for scenery may account for the reason. Thus, different targets may be identified by the difference in radiances. The low-light sensor may be calibrated if the night-light of the bridges is stable.

Fig. 3.
Fig. 3.

VIIRS DNB low-light imagery of east China at 1733 UTC 9 Oct 2012.

Citation: Journal of Atmospheric and Oceanic Technology 33, 6; 10.1175/JTECH-D-15-0225.1

Fig. 4.
Fig. 4.

2D and 3D views of the VIIRS DNB night-light for Hangzhou Bay Bridge and Donghai Bridge. (a) 2D view of night-light for Hangzhou Bay Bridge, (b) 2D view of night-light for Donghai bRidge, (c) 3D view of night-light for Hangzhou Bay Bridge, and (d) 3D view of night-light for Donghai Bridge.

Citation: Journal of Atmospheric and Oceanic Technology 33, 6; 10.1175/JTECH-D-15-0225.1

In this study, the Hangzhou Bay Bridge and Donghai Bridge are selected for the calibration of VIIRS DNB. Based on Google map images and Fig. 4, we found that the deck of the Hangzhou Bay Bridge is straight from the (19,22) pixel to the (23,23) pixel in Fig. 4a and the deck of the Donghai Bridge is straight from the (5,4) pixel to the (15,12) pixel in Fig. 4b. Thus, the parts of the bridges away from the city are suitable for calibration. When the bridge is obtained by VIIRS DNB at different view geometries, the number of lamps within a pixel is not the same due to the change in the angle between the cross track and the bridge. To obtain data with near-identical view geometry, we chose the VIIRS DNB data over the bridge every 16 days following the orbital repeat cycle for 2 years from August 2012 to August 2014. The spatial response is slightly different in each zone because 32 aggregation zones were utilized for the DNB in order to realize a constant spatial resolution of 742 m across the entire scan. In aggregation zone 1, the along-track and cross-track spatial responses are both rectangular. Therefore, the data considered are only those at near-nadir observation in aggregation zone 1 so as to eliminate the uncertainty caused by the nonrectangular spatial response.

4. DNB HGS calibration assessment based on bridge lights

a. DNB data analysis over bridges

As mentioned in section 2a, the radiance values from both bridge night-light sources and the water background are needed. Thus, pixels containing light emissions from the chosen part of the Hangzhou Bay Bridge and the Donghai Bridge must be identified from the background pixels. As shown in Figs. 4a and 4b, an area of 3 px2 located five pixels away from the bridges is chosen for the background pixels, and water background radiances are calculated by the average of all radiances within this region. From Fig. 3, the angle between the cross track and the chosen part of the Hangzhou Bay Bridge is 71.6°, while the angle between the cross track and the chosen part of the Donghai Bridge is 56.3°. Therefore, one or two pixels may contain part of bridges in the cross-track direction. The pixel with the maximum radiance in the cross-track direction is identified as a bridge pixel. Further, if the radiance of the pixel with the second-largest radiance in the cross-track direction is larger than 1.5 times the background radiance, then this pixel is also identified as a bridge pixel. Thus, the second-largest radiance is added to the maximum radiance to obtain the bridge radiance in the along-track direction. Then, the at-aperture radiance difference between the radiance of bridge pixels and the radiance of the background in the along-track direction was calculated. If two pixels in the cross-track direction are identified as the bridge pixels, then the at-aperture radiance difference is obtained by subtracting 2 times the radiance of the background from the radiance of the bridge pixel in the along-track direction. Finally, the at-aperture radiance difference on the left-hand side of Eq. (10) is calculated from the average of radiance differences in the along-track direction.

The VIIRS DNB data from August 2012 to August 2014 are utilized for the analysis. By eliminating the scenes in which pixels over bridges are contaminated by clouds, 16 cases of DNB data over the Hangzhou Bay Bridge and 15 cases over the Donghai Bridge with near-identical view geometry are identified using the aforementioned criteria. The results of the DNB radiance data over the Hangzhou Bay Bridge and the Donghai Bridge are presented in Figs. 5 and 6, respectively. Figures 5a and 6a show the pixel radiance values along the bridges for different cases. The chosen parts of the bridges for calibration are relatively stable, and the pixel radiance values along the both bridges are higher than Lmin. Additionally, there is a correspondence between the different cases of radiance along the bridge. Figures 5b and 6b show the 2-yr averaged radiance data over the chosen parts of the Hangzhou Bay Bridge and the Donghai Bridge, respectively, with a 16-day sampling interval. The black line is for the averaged radiance data over the chosen parts of bridge. The green line is for the averaged radiance data over the nearby background. In addition, the red line is for the averaged radiance data over the chosen parts of bridge that subtract the averaged radiance data over the nearby background. The corresponding LZAs and LPAs are shown in Figs. 5c and 6c. Several features can be seen in the time series. First, the averaged radiance data over the background can reflect the TOA lunar radiance to some extent, which means that some spikes in the time series may be associated with lunar illumination. The averaged radiance data over the background are higher than 2 nW cm−2 sr−1 on 26 November 2012, 29 January 2013, 9 August 2013, and 16 January 2014. The LZAs and LPAs are lower than 50°, which means the TOA lunar radiance in these cases are larger than the radiance in other cases. Second, there is generally a positive correspondence between the averaged radiance data over the bridge and that over the background. The averaged radiance data over the background can be associated with lunar illumination. Third, the radiance values for different cases show a relatively large variation. As shown in Eq. (10), the bridge lights reflected by the bridge deck, the bridge lights reflected by the water surface, and the moon illumination contribute to the at-aperture radiance over a bridge pixel. The radiance of the bridge lights reflected by the bridge deck is relatively stable, and the contribution of moon illumination can be eliminated by subtracting the averaged radiance data over the background to obtain the averaged radiance data over the bridge. As the water reflectance relay on the suspended sediment concentration and the suspended sediment concentration are variable over time for the Hangzhou Bay, the radiance of the bridge lights reflected by the water surface can mainly account for the variation in the radiance values. In addition, the atmospheric effects and the traffic lights, which are transient, may also be associated with the variable radiance values. Finally, the averaged radiance values over the Hangzhou Bay Bridge minus the averaged radiance values over the corresponding background for nearly all cases are in the range of 0.6–1.0 × 10−8 W cm−2 sr−1, and the radiance values over the Donghai Bridge minus the averaged radiance values over the corresponding background for nearly all cases are in the range of 1.5–2.0 × 10−8 W cm−2 sr−1.

Fig. 5.
Fig. 5.

DNB radiance over Hangzhou Bay Bridge for 2-yr time series with 16-day sampling interval. (a) Pixel radiance values along Hangzhou Bay Bridge for different cases. (b) Averaged radiance data of 2 yr over the chosen parts of Hangzhou Bay Bridge with 16-day sampling interval. (c) Corresponding lunar illumination.

Citation: Journal of Atmospheric and Oceanic Technology 33, 6; 10.1175/JTECH-D-15-0225.1

Fig. 6.
Fig. 6.

DNB radiance over the Donghai Bridge for the 2-yr time series with 16-day sampling interval. (a) Pixel radiance values along Donghai Bridge for different cases. (b) Averaged radiance data of 2 yr over the chosen parts of Donghai Bridge with 16-day sampling interval. (c) Corresponding lunar illumination.

Citation: Journal of Atmospheric and Oceanic Technology 33, 6; 10.1175/JTECH-D-15-0225.1

b. DNB radiance estimation over bridges

To validate the observed radiance for the bridge from VIIRS DNB discussed earlier, the bridge lights on the Hangzhou Bay Bridge and the Donghai Bridge were investigated first. As for the Hangzhou Bay Bridge, the angle between the chosen part of the bridge and the cross track is 71.6° from the DNB image, and the bridge length contained in each pixel is 782 m. According to the Chinese department of transportation, the light poles are 42 m apart. Therefore, there are 37.2 lamps contained in each pixel, which includes both sides of the bridge. As for the Donghai Bridge, the angle between the chosen part of the bridge and the cross track is 56.3° from the DNB image, and the bridge length contained in each pixel is 892 m. Therefore, there are 71.36 lamps contained in each pixel since the light poles are 25 m apart. According to previous studies (Elvidge et al. 2010; Cao and Bai 2014), high-pressure sodium (HPS) lamps used on both bridges have an electrical-to-radiant power conversion efficacy of 30%, and 95% of the radiant power from the HPS is captured by the DNB since the HPS spectra is mainly within the DNB spectral response range. Further, the HPS lamp electrical power is 250 W for both bridges. We assume that the lamp radiates into a space. The effective solid angle intercepted by the area of the illuminated bridge surface and water surface can be calculated based on the geometry of the lamp setup. The bridge surface reflectance is retrieved from Landsat 7 surface reflectance high-level data products. To avoid variable water reflectance values, the water reflectance is obtained from Landsat 7 surface reflectance high-level data products around the same time for each case.

To predict the DNB radiance over bridges, SCIATRAN, which is a comprehensive software package for modeling radiative transfer processes (Rozanov et al. 2005; Rozanov et al. 2013), was used to simulate the direct and diffuse transmittance of the upward radiance. In the radiative transfer model, many input parameters are needed. The input atmospheric profiles are provided from the National Centers for Environmental Prediction reanalysis data at 0000 UTC of the corresponding day. The aerosol is modeled by LOWTRAN 7 data, and the aerosol optical thickness (AOT) are taken from Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) level 2 products and MODIS 8-day global aerosol products. Owing to the low frequency of the overpasses, the AOT are obtained from the CALIPSO level 2 products around the same time for each case. If the retrieved AOT are invalid, then the MODIS 8-day global aerosol products are used to obtain the AOT for each case. We assume that, for a given atmospheric layer, the upward direct and diffuse transmittances equal the downward direct and diffuse transmittances, per the reciprocity principle (Johnson et al. 2013). Based on this assumption and using the radiative transfer model, we estimate the direct and diffuse transmissions on the right-hand side of Eq. (10).

A comparison between the predicted and observed DNB HGS radiance values is presented in Fig. 7. The predictions are consistent with the observations. The observed radiance of Hangzhou Bay Bridge is 8.07 × 10−9 ± 1.47 × 10−9 W cm−2 sr−1 and the predicted radiance of Hangzhou Bay Bridge is 7.78 × 10−8 ± 1.28 × 10−9 W cm−2 sr−1, whereas the observed radiance of the Donghai Bridge is 1.74 × 10−8 ± 1.86 × 10−9 W cm−2 sr−1 and the predicted radiance of the Donghai Bridge is 1.67 × 10−8 ± 1.84 × 10−9 W cm−2 sr−1. Thus, the predicted radiance values are slightly different with the observed radiance values. Some uncertainties may account for these differences. First, the lamps are assumed to be radiating into a space due to a lack of specific details on the viewable angles, and this can cause some uncertainties in the radiance estimation. Second, some uncertainties are caused by the actual solid angle of the illuminated area and the reflectance of the surface obtained from other satellites. Third, the atmospheric profiles and aerosols are not measured in situ. Fourth, some uncertainties exist in the radiative transfer model. Finally, the predicted radiance values were underestimated due to some clouds around the bridges and the traffic lights, which are transient.

Fig. 7.
Fig. 7.

Comparison between the predicted and observed DNB HGS radiance values for each case: (a) Hangzhou Bay Bridge and (b) Donghai Bridge.

Citation: Journal of Atmospheric and Oceanic Technology 33, 6; 10.1175/JTECH-D-15-0225.1

To further investigate the calibration, the scatterplots of the predicted and observed radiance for both bridges are shown in Fig. 8. Nearly all points are located in this uncertainty range from −15% to 15%, which means that the predictions are consistent with the observations. It is also noted that one point is beyond the 15% uncertainty range in Fig. 8a. We visually inspected every night image and found that the cities around the bridges were under a cloudy sky on 18 March 2013, and thus scatter radiance of the clouds contributed to the observed radiance. The figure also shows that the agreement between the DNB measurements and the simulations is on the order of −2.9% with an uncertainty of 9.3% (1σ) for the Hangzhou Bay Bridge and −3.9% with an uncertainty of 7.2% (1σ) for the Donghai Bridge. The results are in agreement with those of previous studies (Liao et al. 2013; Ma et al. 2015).

Fig. 8.
Fig. 8.

Scatterplot of the predicted and observed radiance: (a) Hangzhou Bay Bridge and (b) Donghai Bridge.

Citation: Journal of Atmospheric and Oceanic Technology 33, 6; 10.1175/JTECH-D-15-0225.1

Overall, although some uncertainties exist owing to the cloud scatter radiance, traffic lights, and some approximations in the predicted radiance calculation, the predictions are generally consistent with the observations. Based on the proposed calibration method, the agreement between the DNB measurements and the simulations is on the order of −2.9% with an uncertainty of 9.3% (1σ) for the Hangzhou Bay Bridge and −3.9% with an uncertainty of 7.2% (1σ) for the Donghai Bridge. Because of the large variability and uncertainties in the input parameters, many of which are not actually known well for the time of observations, the proposed method based on bridge lights presented here provides more of a consistency check between the predicted values and the DNB calibration but does not provide an absolute calibration of the DNB HGS. However, this represents a new technique for low-light sensor calibration.

5. Conclusions

This paper reports on a low-light calibration method based on bridge lights, which is based on the physical statements and mathematical formulations of the radiative transfer of the moonlight and bridge lights. The VIIRS DNB data are used to assess the proposed calibration method. Based on the criteria of the minimum radiance specification and no city light contamination, the Hangzhou Bay Bridge and the Donghai Bridge are selected as the calibration targets for the calibration of the VIIRS DNB. A comparison of DNB HGS radiances for a 2-yr period from August 2012 to July 2014 demonstrates that the predictions are consistent with the observations. The agreement between the predictions and the observations is on the order of −2.9% with an uncertainty of 9.3% (1σ) for the Hangzhou Bay Bridge and −3.9% with an uncertainty of 7.2% (1σ) for the Donghai Bridge, based on the proposed calibration method.

There are some uncertainties in the predicted and observed radiances of the DNB HGS that are due to the cloud scatter radiance, traffic lights, some approximations in the predicted radiance calculation, and inherent limitations of the radiative transfer model. The calibration accuracy can be improved by using a more accurate radiative transfer model, a more effective way to reduce the cloud scatter, and better in situ information about the lights. In addition, if a better light source, such as an integrating sphere that radiates upward directly, can be designed, then some uncertainties caused by surface reflectance and in situ information of light may be eliminated and the predicted radiance may be precisely calculated. Investigations on designing such a light source are underway. If we have a more stable and accurate calibration model based on bridge lights or self-designed lights, then we could realize absolute calibration based on lights at night in the future. Therefore, a calibration method based on stable light emissions will be a new research area in the calibration of low-light sensors at night.

Acknowledgments

The authors thank Dr. V. V. Rozanov for his assistance with the radiative transfer simulation, and the SCIATRAN working group for making SCIATRAN publicly available. We acknowledge the SNPP VIIRS science team for providing high-quality products. The SNPP VIIRS data products were downloaded from online (http://www.class.ncdc.noaa.gov/saa/products/welcome). The Landsat 7 surface reflectance high-level data products were downloaded from online (https://espa.cr.usgs.gov/login/?next=/). This work was supported by the National Natural Science Foundation of China (Grants 41375029, 41505016, 41575028). Finally, the authors thank the anonymous reviewers for their constructive suggestions.

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