1. Introduction
Because the roles of aerosols in climate change are important, they are monitored from both space and the ground by several remote sensing instruments. The space-based remote sensing instruments can make observations that have wide spatial and temporal coverage. Their products are generally validated using data collected by ground-based remote sensing instruments. Therefore, qualitative data from ground-based remote sensing instruments are important not only for studying aerosol climatology but also for validating results of space-based remote sensing instruments and numerical simulations. The ground-based remote sensing instruments for aerosol observation can be broadly divided into two groups: some radiometers, such as the CIMEL sun photometer (Holben et al. 1998) and the PREDE sky radiometer (Nakajima et al. 1996), face toward the sun with the aid of a solar tracker and scan the sky to measure sky radiance. Others, such as the Multifilter Rotating Shadowband Radiometer (MFRSR; Harrison et al. 1994) and the Rotating Shadowband Spectroradiometer (RSS; Harrison et al. 1999), measure spectral irradiances using a horizontal surface detector. Ideally, when the observations are carried out by the radiometer with the horizontal surface detector, the signal rendered by the sensor should be proportional to the cosine of the zenith angle. The deviation from this ideal response is referred to as a cosine error. Even very good sensors can reveal remarkable cosine errors at high zenith angles.
In observations conducted by the radiometer with the horizontal surface detector, the correction of the cosine error of the observed direct irradiance is possible if the calibration of the radiometer has been done at different incident angles and directions. On the other hand, the cosine error correction factor of diffuse irradiance depends on atmospheric conditions as well as solar zenith and azimuth angles. The cosine error correction factor is the factor that is required to correct the error in observed irradiance caused by the nonideal cosine response characteristic of the sensor. One has to take into account the response function of the detector and accurate atmospheric parameters while correcting the cosine error of observed diffuse irradiance. Because of this difficulty, several studies have determined the cosine error correction factor of diffuse irradiance by assuming the isotropic distribution of sky radiance (e.g., Blumthaler et al. 1996; Feister et al. 1997; Fioletov et al. 2002; Anton et al. 2008). The error induced by this assumption can be much larger at visible wavelengths than at UV wavelengths (Grobner et al. 1996).
The direct and diffuse irradiances observed by radiometers with horizontal surface detectors have been commonly used for aerosol research. For example, Petters et al. (2003), Meloni et al. (2006), Kassianov et al. (2007), and Corr et al. (2009) retrieved key aerosol optical parameters, such as aerosol optical thickness (τaer) and single scattering albedo (ω), using MFRSR-observed direct and diffuse irradiances at UV or visible wavelengths. Similarly, Kudo et al. (2010) used spectral direct irradiance observed by the grating pyrheliometer and spectral diffuse irradiance observed by the pyranometer with a shadowing cube to retrieve these parameters. Assuming that the cosine error of diffuse irradiance should not play an important role in the retrieved parameters, these studies neglected the cosine error of diffuse irradiance. The data observed in these studies might not have serious cosine errors. On the other hand, data collected by some radiometers can be associated with serious cosine errors. If such cosine errors are corrected, then the accuracy of the retrieved parameters can be upgraded.
This study presents an algorithm that can be used to retrieve τaer and ω from direct and diffuse irradiances observed by a radiometer with a horizontal surface detector by implementing detailed cosine error correction schemes. This study further investigates the effects of the cosine error and the cosine error correction technique in the retrieved aerosol optical parameters and the estimated aerosol direct effect (aerosol radiative forcing and the heating rate). This paper is organized in the following way: The instrumentation, observation site, and data are described in section 2. In section 3, an algorithm is described. Results and discussion are given in section 4. Finally, section 5 summarizes the main results and findings of this study.
2. Instrumentation, observation site, and data
a. Instrumentation
The MS-700, manufactured by EKO Instruments (Japan), is a spectroradiometer that observes spectral global irradiance at the wavelength range of 350–1050 nm at intervals of around 3.3 nm. An automated shadowband was attached to this instrument in order to observe spectral global irradiance and diffuse irradiance, simultaneously. Figure 1 shows the observation sequence of the instrument. It observes the total horizontal global irradiance with the moving band at the horizon (Irr1). The band then rotates, making the next three observations in sequence. The second (Irr2) and fourth (Irr4) observations block the strip of sky 8.6° on either side of the sun, whereas the third observation (Irr3) completely blocks the sun. Both Irr2 and Irr4 were used to correct for excess sky blocked by the band during the third observation. The correction procedure was to subtract the average of Irr2 and Irr4 from Irr1 and add this amount to Irr3 (Harrison et al. 1994), which gives the diffuse irradiance. The spectral direct irradiance was obtained by subtracting the spectral diffuse irradiance from the spectral global irradiance. The MS-700 observation data can be used in different aspects of atmospheric research. We used this instrument to study aerosols by taking data observed at the central wavelengths of 401.6, 499.2, 674.2, 871.3, and 1019.1 nm with a nominal 10-nm full width at half maximum (FWHM) bandwidth. At these wavelengths, absorption by atmospheric gases is negligible. The angular responses (cosine characteristics) of the diffuser at the incident angles of 0°, 10°, 20°, 30°, 40°, 50°, 60°, 70°, and 80° from the directions of east (90°), west (270°), south (180°), and north (0°) were measured at the company’s laboratory (International Organization for Standardization 1995). We also used data from other sources, as follows: The total columnar ozone concentration (O3) data were obtained from the Ozone Monitoring Instrument (OMI) observations. To retrieve ω more precisely by radiative transfer calculation, asymmetry parameters (g) at the wavelengths of 400, 500, 675, 870, and 1020 nm were obtained from the PREDE sky radiometer observations (Nakajima et al. 1996). We also used broadband direct irradiance (200–4000 nm) and diffuse irradiance (315–2800 nm) observed by the pyrheliometer (model CH1, Kipp and Zonen, Netherlands) and the pyranometer (model CM21, Kipp and Zonen) with a shadow ball, respectively. This study also used precipitable water vapor content (PWC) measured by the microwave radiometer (Radiometric Corporation, United States).
The observation sequence of the MS-700 spectroradiometer with a rotating shadowband. The observation sequence starts by measuring the total horizontal global irradiance with the moving band at horizon (Irr1). The band then rotates, making the next three observations in sequence. The second (Irr2) and fourth (Irr4) observations block the strip of the sky 8.6° on either side of the sun, while the third observation (Irr3) completely blocks the sun.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
The observation sequence of the MS-700 spectroradiometer with a rotating shadowband. The observation sequence starts by measuring the total horizontal global irradiance with the moving band at horizon (Irr1). The band then rotates, making the next three observations in sequence. The second (Irr2) and fourth (Irr4) observations block the strip of the sky 8.6° on either side of the sun, while the third observation (Irr3) completely blocks the sun.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
The observation sequence of the MS-700 spectroradiometer with a rotating shadowband. The observation sequence starts by measuring the total horizontal global irradiance with the moving band at horizon (Irr1). The band then rotates, making the next three observations in sequence. The second (Irr2) and fourth (Irr4) observations block the strip of the sky 8.6° on either side of the sun, while the third observation (Irr3) completely blocks the sun.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
b. Observation site
We used observation data collected at Cape Hedo (26.87°N, 128.25°E), Okinawa, Japan, as shown in Fig. 2. Cape Hedo is located at the north end of Okinawa Island. There is no industrial area near the observation site. This is the super site of the SKYNET network (http://atmos.cr.chiba-u.ac.jp) and is equipped with various instruments for aerosol, cloud, and radiation observations.
An observation site. Cape Hedo (26.867°N, 128.249°E) is located at the north end of Okinawa Island. Generally, the prevailing winds are from north to west in the spring and winter seasons, east in the summer season, and from northeast to north in the autumn season. Because the observation site is located in the vicinity of a low mountain and the sea, clouds frequently prevail over the site. The spectral surface reflectance of the observation site was approximated as a combination of 50% water, 30% soil, and 20% vegetation.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
An observation site. Cape Hedo (26.867°N, 128.249°E) is located at the north end of Okinawa Island. Generally, the prevailing winds are from north to west in the spring and winter seasons, east in the summer season, and from northeast to north in the autumn season. Because the observation site is located in the vicinity of a low mountain and the sea, clouds frequently prevail over the site. The spectral surface reflectance of the observation site was approximated as a combination of 50% water, 30% soil, and 20% vegetation.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
An observation site. Cape Hedo (26.867°N, 128.249°E) is located at the north end of Okinawa Island. Generally, the prevailing winds are from north to west in the spring and winter seasons, east in the summer season, and from northeast to north in the autumn season. Because the observation site is located in the vicinity of a low mountain and the sea, clouds frequently prevail over the site. The spectral surface reflectance of the observation site was approximated as a combination of 50% water, 30% soil, and 20% vegetation.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
c. Data
We used quality-checked data collected during March–May 2009. Spectral direct and diffuse irradiances were observed at the time resolution of 1 min by the MS-700 spectroradiometer with a rotating shadowband. The sky radiometer data were observed at the time resolution of 10 min. The spectral g values obtained from the sky radiometer were cloud screened using an algorithm of Khatri and Takamura (2009). The spectral direct and diffuse irradiances used in this study were data whose observation times matched the observation times of cloud-screened g values by a time difference less than 30 s. Because the observation site is located in the vicinity of a low mountain and the sea, clouds frequently prevail over the site. Because of the frequent cloud cover and the quality check of the observation data, only 157 samples of 17 days remained for the analysis. Broadband irradiances and PWC were observed at time resolutions of 10 s and 2 min, respectively. For the calculations of broadband irradiances in section 4, the required PWC data were obtained by averaging PWC observed 2.5 min before and after the observation times of quality-checked and cloud-screened spectral direct and diffuse irradiances. Similarly, to compare the calculated broadband irradiances with the observed values in section 4, broadband irradiances observed 2.5 min before and after the observation times of quality-checked and cloud-screened spectral direct and diffuse irradiances were averaged and used. The spectral surface reflectance of the observation site was approximated as a combination of 50% water, 30% soil, and 20% vegetation using the Santa Barbara discrete ordinate radiative transfer (DISORT) atmospheric radiative transfer (SBDART) model (Ricchiazzi et al. 1998).
3. Method
a. Retrieval of aerosol optical thickness
As shown above, we calculated Cdir(θ0, φ0) at fine grids of θ0 and φ0. For example, Fig. 3 shows the distribution of Cdir(θ0, φ0) at 499.2 nm over full domains of θ0 and φ0. In Fig. 3, the solid lines above the surface show Cdir(θ0, φ0) at coarse grids before interpolation/extrapolation.
The cosine error correction factors for direct irradiance [Cdir (θ0, φ0)] at 499.2 nm over full domains of zenith angle (θ0) and azimuth angle (φ0) after interpolation/extrapolation of laboratory-measured coarse-gridded Cdir (θ0, φ0) data, which are shown (solid lines).
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
The cosine error correction factors for direct irradiance [Cdir (θ0, φ0)] at 499.2 nm over full domains of zenith angle (θ0) and azimuth angle (φ0) after interpolation/extrapolation of laboratory-measured coarse-gridded Cdir (θ0, φ0) data, which are shown (solid lines).
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
The cosine error correction factors for direct irradiance [Cdir (θ0, φ0)] at 499.2 nm over full domains of zenith angle (θ0) and azimuth angle (φ0) after interpolation/extrapolation of laboratory-measured coarse-gridded Cdir (θ0, φ0) data, which are shown (solid lines).
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
b. Retrieval of single scattering albedo
For an ideal cosine-error-free detector, Cdif(θ0, φ0) is unity. Because 
Using known τaer, g, Ag, and O3, and more than two predefined (initially given) values of ω (in this study predefined ω values were 0.6, 0.7, 0.8, 0.9, and 1.0), calculate
- Use Eq. (6) to calculate five Dobs corresponding to five predefined ω. Such calculated Dobs values increase linearly with the increase of predefined ω because, except for ω, the other input parameters are exactly same. Therefore, the linear relationship between the calculated Dobs and predefined ω can be used with the diffuse irradiance observed by the instrument (DMS-700) to determine the actual ω (ωactual),where Dobs,upper and Dobs,lower are two consecutive Dobs values between which DMS-700 falls or becomes equal to any one of them. Similarly, ωupper and ωlower are predefined ω values corresponding to Dobs,upper and Dobs,lower, respectively. If DMS-700 is smaller than Dobs (ω = 0.6), ωactual can be obtained through extrapolation using Dobs (ω = 0.7) as Dobs,upper and Dobs (ω= 0.6) as Dobs,lower. To test the accuracy of this interpolation/extrapolation technique, we calculated Dobs for ω ranging from 0.6 to 1.0 with an interval of 0.01. These calculated Dobs values were then compared with DMS-700 to find ωactual. The latter computationally expensive technique and the previous interpolation/extrapolation technique produced nearly the same ωactual, which suggests the applicability of the interpolation/extrapolation technique.
It is further possible to calculate Cdif(θ0, φ0) (not shown in Fig. 4) using Eq. (7). For this purpose, the retrieved ωactual can be used to calculate Dideal using SBDART, and DMS-700 can be used as Dobs.
A flowchart of an algorithm to retrieve single scattering albedo (ω) at wavelength λ.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
A flowchart of an algorithm to retrieve single scattering albedo (ω) at wavelength λ.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
A flowchart of an algorithm to retrieve single scattering albedo (ω) at wavelength λ.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
To understand how error(s) in the input parameter(s) can be associated with the retrieved ω, we performed a sensitivity study. Table 1 shows the assumed values and errors of the input parameters. The relatively large errors assumed in the input parameters may resemble the upper limits of errors in the retrieved ω. Computations were performed at θ0 = 30°, φ0 = 90°, and R = 1.0 AU using the midlatitude summer atmospheric model. Taking into account the potential application of the proposed inversion technique for wavelengths other than those used in this study, we performed the sensitivity study for the spectral range of 350–1050 nm at wavelength intervals of 10 nm. Note that we used the same magnitudes of input parameters at all wavelengths, though τaer, g, and Ag can change with the wavelength. Further, PWC was assumed to be 0.0 cm. Such assumptions may not be valid in the real atmosphere, but they facilitate the understanding of how errors in the input parameters are associated with the retrieved ω at different wavelengths. Figure 5 shows an error in ω (Δω), which is defined as the difference between the ω calculated by including the error in the input parameter and the initially given ω, for each input parameter. Figure 5 suggests that the error in τaer can play a more important role at the visible and near-infrared wavelengths than at the UV wavelengths while retrieving ω. Up to the midvisible range, Δω resulting from error in τaer increased rapidly and then became nearly constant. Similarly, the error in g affects ω more in the longer wavelengths than in the shorter wavelengths. Because of the absorption of ozone in the Chappuis band, the error in O3 can cause an error in the retrieved ω at wavelengths between 450 and 760 nm, but such error is very small in magnitude. In contrast to the above-mentioned parameters, the error in Ag can affect the retrieved ω more in the UV wavelengths than in the visible and near-infrared wavelengths. For the assumed values of the input parameters and the solar position in our sensitivity study, Δω values resulting from the errors in τaer, g, Ag, and O3 were less than 0.033, 0.02, 0.005, and 0.04, respectively, in magnitudes at all wavelengths, although they varied with wavelength, as discussed above. The total error (summation of each error) ranged from 0.06 to 0.069 in magnitude for the assumed data in our sensitivity study. It is worth mentioning that the same magnitudes of errors in the input parameters can produce different Δω values if the magnitudes of the input parameters and the solar position are different. Therefore, all of these factors (errors and magnitudes of input parameters, solar position) should be taken into account while estimating the total error in the retrieved ω.
Assumed values and errors of input parameters to study errors in retrieved single scattering alebdo (ω) resulting from errors in input parameters.
Errors in single scattering albedo (ω), that is, Δω at different wavelengths (λ) resulting from errors in the input parameters of aerosol optical thickness (τaer), asymmetry parameter (g), surface albedo (Ag), and ozone concentration (O3). The assumed values and errors of input parameters are given in Table 1. For the computation, the midlatitude summer atmospheric model (McClatchey et al. 1972) was used. Computations were performed with the sun–earth distance of 1.0 AU, solar zenith angle and azimuth angle of 30° and 90°, respectively, by assuming PWC of 0.0 cm.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
Errors in single scattering albedo (ω), that is, Δω at different wavelengths (λ) resulting from errors in the input parameters of aerosol optical thickness (τaer), asymmetry parameter (g), surface albedo (Ag), and ozone concentration (O3). The assumed values and errors of input parameters are given in Table 1. For the computation, the midlatitude summer atmospheric model (McClatchey et al. 1972) was used. Computations were performed with the sun–earth distance of 1.0 AU, solar zenith angle and azimuth angle of 30° and 90°, respectively, by assuming PWC of 0.0 cm.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
Errors in single scattering albedo (ω), that is, Δω at different wavelengths (λ) resulting from errors in the input parameters of aerosol optical thickness (τaer), asymmetry parameter (g), surface albedo (Ag), and ozone concentration (O3). The assumed values and errors of input parameters are given in Table 1. For the computation, the midlatitude summer atmospheric model (McClatchey et al. 1972) was used. Computations were performed with the sun–earth distance of 1.0 AU, solar zenith angle and azimuth angle of 30° and 90°, respectively, by assuming PWC of 0.0 cm.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
4. Results and discussion
This section aims to analyze the effects of the cosine error and the cosine error correction technique on the retrieved aerosol optical parameters and the estimated aerosol direct effect. Along with the calculation described in Fig. 4 (called scenario 1), the calculations were extended in the following ways:
The cosine errors were completely neglected (scenario 2).
The cosine errors were assumed to be azimuth angle independent (scenario 3). In the calculation, the Cdir(θ, φ) terms of Eqs. (1) and (6) were replaced by the average of Cdir(θ, φ) of fixed θ, but with different φ ranging from 0° to 360° [
- An isotropic distribution of sky irradiance was assumed (scenario 4). For this assumption, Cdif can be expressed as
It is important to note that the differences in results between scenario 1 and scenario 2 (or scenario 3) are related to the angular response of the detector, whereas the differences in results between scenario 1 and scenario 4 are related to the angular response of the detector and the distribution of sky radiance. Comparisons of the results of scenario 1 with those of scenario 3 and/or scenario 4 are helpful to understand how far the assumptions of the azimuth angle–independent cosine errors and/or isotropic distribution of sky radiance are applicable to correct the observed diffuse irradiance. As suggested by Eq. (9), Cdif of scenario 4 can be calculated before retrieving ω. Therefore, it can be used to correct the observed diffuse irradiance before retrieving ω in scenario 4.
a. Effects of the cosine error and the cosine error correction technique on the retrieved aerosol optical thickness and single scattering albedo
Figure 6 shows the comparisons of τaer (scenario 1) with τaer (scenario 2) and τaer (scenario 3) at the wavelengths of 401.6, 499.2, 674.2, 871.3, and 1019.1 nm. Similarly, Fig. 7 shows the comparisons of ω (scenario 1) with ω (scenario 2), ω (scenario 3), and ω (scenario 4) at those wavelengths. To calculate ω (scenario 4) at wavelength λ, τaer (scenario 3) of wavelength λ was used. Figures 6 and 7 also show the root-mean-square error (RMSE) for each comparison. As shown in Figs. 6 and 7, τaer and ω values of scenario 2 were larger and smaller, respectively, than those of scenario 1 with relatively large RMSEs at all wavelengths. The overestimated τaer (scenario 2) values were due to the cosine errors, which underestimated ω (scenario 2) values at all wavelengths. No substantial differences appeared between τaer (scenario 3) and τaer (scenario 1) values at all wavelengths; however, relatively large differences appeared between ω (scenario 3) and ω (scenario 1) at the wavelengths of 674.2, 871.3, and 1019.1 nm. It is important to note that the cosine errors of full domains of θ and φ can affect the retrieved ω, whereas only the cosine error corresponding to the solar zenith and azimuth angles of the observation time can affect τaer. This explains the reason for the differences between ω (scenario 1) and ω (scenario 3) at certain wavelengths despite negligible differences between τaer (scenario 1) and τaer (scenario 3) at all wavelengths. For comparisons between ω (scenario 1) and ω (scenario 3) values, the higher RMSEs at the wavelengths of 674.2, 871.3, and 1019.1 nm than those at the wavelengths of 401.6 and 499.2 nm were due to dissimilar cosine errors at φ domain at different wavelengths. These results suggest that the assumption of the wavelength-independent and/or the azimuth angle–independent cosine errors may affect the quality of the retrieved ω. RMSEs for the comparisons between ω (scenario 1) and ω (scenario 4) values were larger than those for the comparisons between ω (scenario 1) and ω (scenario 3) values at all wavelengths. This may suggest that the assumption of the isotropic distribution of sky radiance may further deteriorate the quality of the retrieved ω in comparison with the previous assumption (assumption of the azimuth angle–independent cosine errors). In fact, ω values retrieved from the above-mentioned cosine error correction techniques depend strongly on Cdif values, given by Eqs. (7) or (9). Figure 8 shows Cdif as a function of θ0 for scenarios 1, 3, and 4. The Cdif (scenario 4) values were constant with θ0 because of the assumption of the isotropic distribution of sky radiance; the Cdif (scenario 1) and Cdif (scenario 3) values showed close relationships with θ0; and Cdif (scenario 1) values were more scattered even for the same θ0 because of their dependencies on the azimuth angles. The relatively more scattered Cdif (scenario 1) values at the wavelengths of 674.2, 871.3, and 1019.1 nm were due to more azimuthally inhomogeneous cosine errors at those wavelengths. Figure 8 shows that the assumption of the isotropic distribution of sky radiance can underestimate the retrieved ω at small θ0 and vice versa, and may produce ω closer to that of scenario 1 at θ0 of around 35°. Figure 8 further suggests that the cosine response of the detector caused underestimation of the actual diffuse irradiances by around 5%–11% at different wavelengths.
Comparisons of τaer (scenario 1) with (left) τaer (scenario 2) and (right) τaer (scenario 3) at the wavelengths of (a) 401.6, (b) 499.2, (c) 674.2, (d) 871.3, and (e) 1019.1 nm.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
Comparisons of τaer (scenario 1) with (left) τaer (scenario 2) and (right) τaer (scenario 3) at the wavelengths of (a) 401.6, (b) 499.2, (c) 674.2, (d) 871.3, and (e) 1019.1 nm.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
Comparisons of τaer (scenario 1) with (left) τaer (scenario 2) and (right) τaer (scenario 3) at the wavelengths of (a) 401.6, (b) 499.2, (c) 674.2, (d) 871.3, and (e) 1019.1 nm.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
Comparisons of ω (scenario 1) with (left) ω (scenario 2), (middle) ω (scenario 3), and (right) ω (scenario 4) at the wavelengths of (a) 401.6, (b) 499.2, (c) 674.2, (d) 871.3, and (e) 1019.1 nm.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
Comparisons of ω (scenario 1) with (left) ω (scenario 2), (middle) ω (scenario 3), and (right) ω (scenario 4) at the wavelengths of (a) 401.6, (b) 499.2, (c) 674.2, (d) 871.3, and (e) 1019.1 nm.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
Comparisons of ω (scenario 1) with (left) ω (scenario 2), (middle) ω (scenario 3), and (right) ω (scenario 4) at the wavelengths of (a) 401.6, (b) 499.2, (c) 674.2, (d) 871.3, and (e) 1019.1 nm.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
The cosine error correction factors of diffuse irradiances (Cdif) at the wavelengths of (a) 401.6, (b) 499.2, (c) 674.2, (d) 871.3, and (e) 1019.1 nm for (left) scenario 1, (middle) scenario 3, and (right) scenario 4.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
The cosine error correction factors of diffuse irradiances (Cdif) at the wavelengths of (a) 401.6, (b) 499.2, (c) 674.2, (d) 871.3, and (e) 1019.1 nm for (left) scenario 1, (middle) scenario 3, and (right) scenario 4.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
The cosine error correction factors of diffuse irradiances (Cdif) at the wavelengths of (a) 401.6, (b) 499.2, (c) 674.2, (d) 871.3, and (e) 1019.1 nm for (left) scenario 1, (middle) scenario 3, and (right) scenario 4.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
To show the improvement of the results resulting from the correction of the cosine errors, we calculated downwelling broadband (300–4000 nm) direct and diffuse irradiances using retrieved aerosol optical parameters and collocated observations of spectral g, PWC, O3, and approximated spectral Ag. SBDART was used for the calculation. The input aerosol data in the model were τaer, ω, and g at five wavelengths and the Ångström exponent (α). The parameter α describes the dependency of τaer on the wavelength. Here τaer, ω, and g of five wavelengths were extrapolated (interpolated) outside (inside) the spectral range of 401.6–1019.1 nm using SBDART. For the wavelengths smaller (larger) than 401.6 nm (1019.1nm), τaer was extrapolated using α and τaer of 401.6 nm (1019.1 nm), whereas ω and g were assumed to be same as those at 401.6 nm (1019.1 nm). The interpolations of τaer, ω, and g within the spectral range of 401.6–1019.1 nm were achieved by deriving the weighting factors. Readers may find a detail about interpolation/extrapolation in the “aerbwi” subroutine of the SBDART software package. The extrapolation of the aerosol optical parameters outside the spectral range of 401.6–1019.1 nm may cause small errors in the calculated broadband irradiances and aerosol direct effect because the large fractions of irradiances (direct, diffuse, and global) are confined within the spectral range of 401.6–1019.1 nm, in which the observation data were available. In addition, reasonable τaer values were provided outside the spectral range of 401.6–1019.1nm by using α, which could largely reduce the potential errors because the spectral τaer values are important in the calculations of broadband irradiances. Depending on the magnitudes of spectral τaer, ω, g, and Ag can affect the calculated diffuse irradiance. Because reasonable τaer values were provided outside the spectral range of 401.6–1019.1 nm, the error in the calculated diffuse irradiance resulting from extrapolated ω and g might not be large. Figures 9a,b show comparisons between the modeled and observed direct irradiances and diffuse irradiances, respectively. Figure 9a shows that the direct irradiances modeled using the spectral τaer (scenario 2) values were substantially lower than the observed values, whereas a good agreement between the observed and modeled direct irradiances was observed when the cosine error–corrected spectral τaer values were used in the model. This shows an improvement in the retrieved spectral τaer after correcting the cosine errors. The direct irradiances can be used as an indicator to understand the quality of the spectral τaer as long as accurate PWC data are provided in the model because the direct irradiances are mainly determined by the spectral τaer and PWC. Figure 9b shows that the observed diffuse irradiances agree well not only with the irradiances modeled using the cosine error–corrected optical parameters, but also with the irradiances modeled using the cosine error–uncorrected optical parameters. Note that a number of parameters, including τaer, ω, g, Ag, and PWC, can affect the modeled diffuse irradiance. Therefore, rather than comparing only the observed and modeled diffuse irradiances, comparisons of simultaneously observed direct and diffuse irradiances with modeled components may be more reasonable for understanding the quality of the retrieved spectral ω. In this regard, the good agreement between the observed diffuse irradiances and the values modeled using spectral τaer and ω of scenario 2 could not justify that the cosine error–uncorrected spectral ω values were closer to the true ω values because the direct irradiances modeled using the cosine error–uncorrected spectral τaer values were underestimated with relatively large disagreement, as shown in Fig. 9a. The good agreement between the observed diffuse irradiances and the values modeled using cosine error–uncorrected τaer and ω was due to the fact that the overestimated spectral τaer compensated the underestimated spectral ω while calculating diffuse irradiances. On the other hand, the good agreements of observed direct and diffuse irradiances with values modeled using cosine error–corrected τaer and ω justify that the cosine error–corrected spectral τaer and ω were closer to the true values. Though the cosine error correction technique was observed to influence the retrieved spectral ω values, noticeable differences were not found in the diffuse irradiances calculated using spectral ω values of different cosine error correction techniques. As a result, regardless of the cosine error correction technique while retrieving aerosol optical parameters, RMSEs were around 18.0 W m−2 for the comparisons of observed and modeled direct irradiances. Similarly, RMSEs were around 8.0 W m−2 for the comparisons of observed and modeled diffuse irradiances. Such results were due to the fact the cosine error correction technique could not cause noticeable differences in the retrieved spectral τaer. It has been suggested that the spectral ω can give information regarding the type of dominant light-absorbing aerosols (e.g., Bergstrom et al. 2002; Khatri et al. 2010). In this regard, the accurate estimate of spectral ω using the most reasonable cosine error correction technique (scenario 1) is important.
Comparisons between observed and modeled broadband (a) direct irradiances and (b) diffuse irradiances. Direct irradiances and diffuse irradiances were observed by the pyrheliometer (CH1) and pyranometer (CM21) with a shadow ball, respectively. The aerosol optical parameters of different scenarios were used to model the direct and diffuse irradiances.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
Comparisons between observed and modeled broadband (a) direct irradiances and (b) diffuse irradiances. Direct irradiances and diffuse irradiances were observed by the pyrheliometer (CH1) and pyranometer (CM21) with a shadow ball, respectively. The aerosol optical parameters of different scenarios were used to model the direct and diffuse irradiances.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
Comparisons between observed and modeled broadband (a) direct irradiances and (b) diffuse irradiances. Direct irradiances and diffuse irradiances were observed by the pyrheliometer (CH1) and pyranometer (CM21) with a shadow ball, respectively. The aerosol optical parameters of different scenarios were used to model the direct and diffuse irradiances.
Citation: Journal of Atmospheric and Oceanic Technology 29, 5; 10.1175/JTECH-D-11-00111.1
b. Effects of the cosine error and the cosine error correction technique on the estimated aerosol direct effect
Table 2 shows the averages and standard deviations of the 24-h-average aerosol radiative forcing at the surface and the TOA, as well as the heating rate for the aerosol optical parameters of scenarios 1, 2, 3, and 4. As discussed in section 4a, the extrapolation of aerosol optical parameters outside the spectral range of 401.6–1019.1 nm can be suggested to have small errors in the calculated direct and diffuse irradiances, which may cause small errors in the calculated broadband global irradiance and the estimated aerosol direct effect. Table 2 shows that the average values of the 24-h-average aerosol radiative forcing at the surface and the TOA as well as the heating rate for the aerosol optical parameters of scenario 2 were lower, higher, and higher, respectively, than those for the aerosol optical parameters of scenario 1 by 16.50 W m−2 (83.11%), 5.88 W m−2 (86.34%), and 0.186 K day−1 (171.50%), respectively. Such large differences suggest that the estimated aerosol direct effect can be heavily affected if the cosine errors of observed irradiances are not corrected. The 24-h-average aerosol radiative forcing at the surface and the TOA as well as the heating rate for the aerosol optical parameters of scenario 3 were lower, lower, and higher, respectively, than those for the aerosol optical parameters of scenario 1 by only 0.08 W m−2 (0.40%), 0.004 W m−2 (0.06%). and 0.0006 K day−1 (0.58%), respectively. Those data show that the assumption of azimuth angle–independent cosine errors while correcting the cosine errors of observed irradiances may have less influence on the estimated aerosol direct effect. On the other hand, the 24-h-average aerosol radiative forcing at the surface and the TOA as well as the heating rate for the aerosol optical parameters of scenario 4 were lower, higher, and higher, respectively, than those for the aerosol optical parameters of scenario 1 by 0.86 W m−2 (4.31%), 0.49 W m−2 (7.23%), and 0.01 K day−1 (10.33%), respectively. Those data show that the assumption of the isotropic distribution of sky radiance while correcting the cosine errors of observed irradiances may affect the estimated aerosol direct effect to a certain degree.
Averages and standard deviations of 24-h-average aerosol radiative forcing (ARF) at the surface and TOA as well as the heating rate for the aerosol optical parameters of scenarios 1, 2, 3, and 4.
5. Summary
This study presents an algorithm that can be used to retrieve spectral aerosol optical parameters (τaer and ω) using spectral direct and diffuse irradiances observed by a radiometer with nonideal cosine response characteristic and laboratory-measured angular response data of the detector. The interesting features of the proposed algorithm are that ω can be retrieved by considering the anisotropic distribution of sky radiance, which realistically represents the actual atmospheric scenario, and the prior information of the cosine error correction factor of diffuse irradiance is not required. The algorithm can be further used to calculate the cosine error correction factor of diffuse irradiance. After describing the algorithm, the study discusses the necessity of correcting the cosine errors of observed direct and diffuse irradiances by showing that the retrieved spectral τaer and ω can be largely overestimated and underestimated, respectively, by cosine errors, which can even mislead the estimated aerosol direct effect. The study also discusses the necessity of taking into account wavelength-, zenith angle–, and azimuth angle–dependent cosine errors by considering the anisotropic distribution of sky radiance. It is shown that the assumption of wavelength- and/or azimuth angle–independent cosine errors may affect the retrieved optical parameters and estimated aerosol direct effect to a certain degree, depending on the azimuth angle and/or wavelength dependency behaviors of the cosine errors. The study further shows that the assumption of isotropic distribution of sky radiance to correct the observed diffuse irradiance can cause errors in the retrieved ω and the estimated aerosol direct effect quantitatively by underestimating and overestimating ω at small and large zenith angles, respectively. The proposed algorithm quantified that the cosine errors of our radiometer caused underestimation of the actual diffuse irradiances from around 5%–11% at different wavelengths.
Acknowledgments
This research is supported by the Global Environmental Research Fund (B-083) of the Ministry of the Environment, Japan and “Virtual Laboratory for Diagnosing the Earth's Climate System” program of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. This research is also performed as a part of SKYNET activities by the Observational Research Project for Atmospheric Change in Troposphere (GEOSS program) of the Ministry of Education, Culture, Sports, Science and Technology, Japan. The authors are grateful to anonymous reviewers for their constructive comments.
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