Article
回転式遮蔽バンド付き分光放射計による放射量計測の不確かさ
キーワード:
rotating shadow-band radiometer,
error estimation of aerosol optical depth,
radiation measurement
2021 年 99 巻 6 号 p. 1547-1561
詳細
2021 年 99 巻 6 号 p. 1547-1561
A rotating shadow-band spectroradiometer system is a powerful tool for surveying light in an environment. It can provide the following spectral components of the solar irradiance without using any traditional solar tracking tool: direct normal irradiance (spDNI), diffuse horizontal irradiance (spDHI), and global horizontal irradiance (spGHI). Both irradiances, spDNI and spDHI, are derived from the combination of spGHI observations at different shadow-band positions. The shadow-band system induces basic errors caused by the imperfect corrections of the diffuse irradiance shadowed by band. To restrict the basic errors to < 2 %, the band slant-angle should be < 72° for a usual operating condition of the MS-700 spectroradiometer manufactured by EKO Instruments Co., Ltd., with the MB-20 shadow-band system for MS-700. The errors in the spDNI and spDHI estimation are evaluated quantitatively by using realistic models that consider instrumental and atmospheric conditions. Estimates of spDNI can result in optical depth errors. The relative error in this estimation is described by using a correction coefficient Cfwd defined by the ratio of the true diffuse irradiance simulated by the shadowed irradiance to the approximate value observed. The value of Cfwd depends on the magnitude of the aerosol optical depth as well as the aerosol type. This error analysis should help in improving the accuracy of this system of measurements.
Particles suspended in the atmosphere have two major effects on the modification of the weather and climate through changes in the received solar radiation and cloud formation, known as direct and indirect effects. In recent decades, both effects have been investigated, with a focus on climate change issues (e.g., Kim et al. 2005; Nakajima et al. 2007; Bi et al. 2014). The direct effect of aerosols on the climate is relatively straightforward to assess. It can be evaluated if the aerosol optical characteristics are known [i.e., aerosol optical depth (AOD), single scattering albedo (SSA), and asymmetry factor (ASY)]. Although the radiative transfer mechanism in the atmosphere on how to use such information is known, the distribution of the optical characteristics at the global scale poses a challenge because the aerosols come from different sources and have different chemical compositions.
As described in Pachauri et al. (2014), the uncertainties of the aerosol effects are larger than those of the global greenhouse gases. The biggest part of these uncertainties is due to the lack of knowledge on cloud formation and related mechanisms. Global information on aerosol properties is another issue because these properties are fundamental for both effects. Satellite programs are the most effective for obtaining large-scale information. Moderate-Resolution Imaging Spectroradiometer (MODIS) sensors onboard Terra and Aqua (https://terra.nasa.gov/about; https://aqua.nasa.gov; https://modis-images.gsfc.nasa.gov/MOD04_L2/doi.html), developed by National Aeronautics and Space Administration (NASA), have gathered substantial information on aerosols and clouds. Recently, geostationary satellites, such as Himawari-8/9, launched and operated by Japan Aerospace Exploration Agency (JAXA) and Japan Meteorological Agency (JMA), started to collect aerosol and cloud information using improved sensors and algorithms. The P-Tree System operated by JAXA can supply quasi-real-time information of aerosol and cloud as well as other products, such as short wave radiation and chlorophyll-a (https://www.eorc.jaxa.jp/ptree). These products cover large geographical regions with homogeneous quality and can provide information on diurnal variability. Such information can extend what is known from missions such as the A-train configuration (Stephens et al. 2018).
The scientific reliability/accuracy of satellite products must be assessed through evaluation against ground observations. The Sky radiometer network (SKYNET) has been established for validating the JAXA Global Imager (GLI) products (Takamura et al. 2009), as well as those from the NASA Aerosol Robotic Network (AERONET) (Holben et al. 1998). The main instrument of the network for both products is a radiometer that can measure sky brightness at several wavelengths relevant for obtaining information on the radiative characteristics of aerosols. Because directional sky radiances are strongly dependent on particulate matter suspended in the atmosphere (Nakajima et al. 1983), aerosol parameters have been derived under clear sky conditions and provided to the community and researchers (http://atmos3.cr.chiba-u.jp/skynet/data.html).
Spectral irradiance is useful for many fields not only of the atmospheric environment but also engineering targets. A Multifilter Rotating Shadow-band Radiometer (MFRSR) is one of the typical instruments utilized. It is frequently used to get simultaneous measurements of spectral direct and diffuse radiation (Harrison et al. 1994) as described in Augustine et al. (2000). Another spectral radiometer, MS-700, with a diffraction grating has been used to estimate aerosol parameters (Khatri et al. 2012). In all these instruments, the shadow-band system plays a basic role to separate two components of irradiance, direct normal irradiance and diffuse horizontal irradiance, derived from the global irradiance measurements. This separation of observed irradiances can allow the simultaneous estimation of the optical characteristics of aerosols and clouds as well as characteristics of precipitable water (Alexandrov et al. 2009) and/or the amount of ozone in the atmosphere.
Observations from radiometers can be affected by errors such as calibration accuracy, temperature dependence and other sources under various observational conditions even if there is no human error in operation. When using the shadow-band system, another source of error is the analysis procedure. The issue addressed in this analysis is how to compensate correctly for the scattered radiation shadowed by a band. The accuracy of the aerosol/cloud products retrieved from these kinds of instrument data will be sensitive to such correction schemes.
This paper discusses errors originating from the shadow-band measurement system when only the nominal geometrical correction method is used. In this simulation analysis, typical aerosol models are used for qualitative and quantitative estimation of irradiance. The effects of the estimation error of the optical depth as well as the direct and diffuse solar irradiance are also discussed.
At several sites of the SKYNET observation network, we have installed spectroradiometers (MS-700 manufactured by EKO Instruments Co., Ltd.) with a shadow-band system (MB-22), shown in Fig. 1. MS-700 measures global solar radiation spectrally using an inline Charge-Coupled Device sensor with a grating connected to a diffuser and a glass fiber tube for the solar input. MB-22 can be used to separate direct normal irradiance (spDNI) from the global horizontal irradiance (spGHI) and estimate diffuse horizontal irradiance (spDHI). The rotating axis of the band is set in parallel with the north–south direction. It is inclined at 15° from the horizontal level (diffuser level) to the south side for northern latitudes to avoid the effect of the radiation reflected from the driving unit itself. The view angle of the shadow-band from the diffuser is 8.6° in width. Tables 1a and 1b provide the detailed specifications. The basic concept is similar to the MFRSR (Harrison et al. 1994). These are unique and powerful tools for simultaneous observation of spGHI and spDNI with a single sensor unit and are relatively low cost and easy to operate.
Observation system for spectral irradiance with shadow-band. Tables 1a and 1b list the detailed specifications of MS-700 and MB-22. The driving unit is installed with an inclined angle (rotating axis) of 15° to avoid the effect of light reflected by itself.
However, when estimating the spDNI derived from the observed spGHI, the biggest issue is the accuracy of the spDNI caused by an uncertain estimate of the scattered light around the sun of the shadow region. This depends on the aerosol size distribution and its optical depth, and consequently, it is not easy to compensate for the effect of collecting more reliable spDNIs. Moreover, the error of the estimate of the spDNI is affected by instrumental conditions, such as the rotating system and band width. We analyze the errors in the estimation of spDNI and spDHI due to the aerosol type and density using an MS-700 shadow- band system.
During normal operation, the band can move in four steps for radiation compensation. First, it stays at a level lower than the horizontal surface of the diffuser/sensor to get the spGHI (Iobs1). Then, it moves to the second position that is at 10° behind from the center of the sun (Iobs2). After obtaining these data, it moves again to receive only the diffuse radiation (Iobs3) without direct solar radiation. At this moment, the center of the band is partly normal to the solar direction. Finally, the shadow-band is set at 10° ahead of the sun (Iobs4). By using this sequence, a set of four data can be obtained for one scan. The second and fourth data are used to partially compensate for the excess diffuse radiation blocked by the band during the third (direct blocked) measurement.
The observed data, Iobs1–Iobs4, are described as follows,
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In the above equations, we omit a suffix of wavelength dependency for simplicity. From these equations, spDNI and spDHI are as follows:
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To focus on the band effects, hereafter, correction coefficients, γ1 and γ2 are assumed to be 1.0. Note that practical diffuser/sensors have imperfect cosine law (γ1 ≠ 1) even if only a little. When the variable ΔF3 can be estimated accurately under certain conditions, Eqs. (5) and (6) can provide correct spDNIs and spDHIs, as well as spGHI. In the usual measurements, however, this cannot be made clear. Thus, the unknown variable ΔF3 is approximated using the following equations:
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The correction coefficient Cfwd in Eq. (7) is a correction factor due to a stronger forward scattering ΔF3 than ΔF2 or ΔF4. This depends on the directional pattern of the diffuse solar radiation. Hence, the variation of Cfwd should be evaluated by changing the size distribution and the optical depth of aerosols. In practice, there are other reasons: One is the difference of the solid view angles for each band position due to the band-driving geometry; the other is the difference of the cosine effect. Thus, each diffuse irradiance ΔFi is inherently different. As expected, these effects increase with the decreasing solar altitude.
Using Eqs. 5, 6, and 7, we obtain:
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In common data analysis practice, the correction coefficient, Cfwd, is assumed to be 1 because of the lack of information on the correction. Consequently, the relative errors (REs) in spDNI and spDHI are:
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Based on the above, we estimate the band-shadowing effects and discuss errors on the spDNI and spDHI through simulation of this shadow-band system using well-known aerosol types. Simultaneously, the error (Δτ) in the optical depth can be estimated, as follows:
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The simulation is performed only at a wavelength of 500 nm because it is sufficient for obtaining trends of the estimation error of spDNI and spDHI due to the shadow-band system.
Two-step simulations are performed. In the first step, the performance of the shadow-band system is examined precisely by using an isotropic sky brightness, and the reduction of the diffuse irradiance by band blockage is calculated for each of the three steps around the sun position. In the second step the total observation errors are estimated by introducing realistic atmospheric models with several aerosol types. The key is to obtain the accurate diffuse irradiance shadowed by each band position.
To achieve a realistic performance, instrumental and operative parameters for the MB-22 are those used in routine operations. In the simulation, it is assumed that the band movement can be perfectly followed by the accurate solar position without any mechanical error. As described in Section 2, the band rotates and stops regularly following the observation sequence.
Irradiances incident to the diffuser/sensor are simulated under four aerosol conditions in the atmosphere as the most sensitive parameters. The basic atmospheric model selected is “Mid Latitude Summer” developed by McClatchey et al. (1972) with a surface pressure of 1013.25 hPa. Precipitable water content and ozone amount are somewhat different from the original ones; however, these have no effect in these simulations, and ozone has a weak absorption. Other minor gases are default in the atmospheric model. Four typical aerosol models are adopted. These are described in Shettle and Fenn (1979). These aerosol models have a function of modification of the size distribution by hygroscopic growth of aerosol particles (Hänel 1976). This function affects the Ångström exponent (AE) through changes in the aerosol size distribution, as well as the simulated irradiances. To estimate quantitatively the effects of the analysis method for the shadow-band technique, the AOD ranges from 0.001 to 2.0 at 500 nm (Table 2). Radiative transfer calculations are performed using the SBDART model, which is based on a scheme of a discrete ordinate method (Ricchiazzi et al. 1998). The radiance output of scattered solar radiation is for 1° resolution at zenith and azimuth direction for the sky dome. By using the quadratic interpolation of the original database, the integration over the region shadowed by each band is performed for every 0.1° step.
A band slant angle is defined by an angle formed by two planes, namely, the band plane and the vertical plane including the north-south direction. It is a unique instrumental parameter in comparison with the solar zenith and azimuth angle. Table 2 provides the location and date for the calculation. These are not essential for the results. Sky patterns of brightness are calculated for every 15 min step from 5:00 to 19:00.
First, we simulate accurately the movement of the shadow-band. Figure 2 shows examples of two times, 5:00 JST (left) and 12:00 JST (right) on June 22, 2016. These examples in the polar coordinate show that the azimuthal angle is measured clockwise, that is, the north at the top, and 90° at the east, and the zenith angle is in the radial direction. Outer black circles in both panels mean the horizon with a zenith angle of 90°. Three closed lines colored blue, black, and red show band edges corresponding to band positions 2, 3 and 4, respectively. Small red dots in band position 3 demonstrate the solar position at respective times. Parts of each band are located below the horizon of the diffuser/sensor. Consequently, the effective field-of-view angles (FOVs) for each band position are quite different when the sun is close to the horizon. From these figures, it is clear that the difference between ΔF2 and ΔF4 is geometrically increasing with the lower band/solar position. Figure 3a indicates the time series of the FOV of the sensor toward each band and their false irradiances corresponding to each band movement. In the figure, the input radiance is assumed to be isotropic. Thus, geometrical errors can be estimated quantitatively for the system. The upper three curves (right scale) show trends of each FOV for each band movement, and the lower ones (left scale) are false irradiances in arbitrary units. The patterns of FOV variation are relatively flat about the local noon as expected, and the irradiance patterns are changing with time because the cosine effect to the received irradiance is clearly reflected. In both cases, these patterns are symmetric about the local noon.
Examples of shadow-band movement. The bands are projected on the polar coordinate. Blue, black, and red curves show edge patterns of band positions 2, 3, and 4, respectively, and, for different times: 5:00 JST and 12:00 JST of June 22, 2016. Small red dots in both circles mean the solar position. The outer circle shows the horizon (zenith angle is 90°) of the sky. The band positions outside the circles are below the horizon.
(a) Time series for each band, of the fieldof- view angle (FOV) represented by the upper three solid curves, and the virtual radiation (ΔF) incident into a region shadowed by the band, represented by the lower three curves. The incident radiation is assumed to be unity, so these curves mean variations combined with the cosine characteristic and field-of-view angle. (b) Time series of virtual radiation and the difference between the expected irradiance ΔF3 (for isotropic radiation) and the mean irradiance approximated by both side ones (ΔF2 and ΔF4). (c) Relative difference between the expected irradiance and the mean irradiance approximated by ΔF2 and ΔF4, as functions of the solar zenith and band slant angles. For less than 72° band slant angle, the fundamental error due to the cosine characteristic including the band geometry is approximately < 2 %. The relative airmass corresponding to the solar zenith angle is plotted as a reference.
The correction error for the shadow region of band position 3 is dependent on the value of Cfwd in Eq. (7). Before estimating the impacts by using realistic aerosol types, Fig. 3b shows the diurnal variation of ΔF3 and ΔFmean (equal to 
) for isotropic inputs. In the figure, the RE between them, 
, is also plotted with time. Less than 2 % RE is shown around the relatively stable period with time, and then, in the outer region, it rapidly increases. Figure 3c plots show the variation of RE as functions of the solar zenith and band slant angle. This fundamental error due to the cosine and geometric pattern (FOV difference) of each band position should be considered when processing observations. From the simulation with isotropic radiation input, a valid restriction condition in data analysis should be assumed to obtain reliable spDNI and spDHI. Accordingly, we adopt the slant angle of the band (“Band_slant angle” in Fig. 3c) as a common index for a valid evaluation.
The restriction for the fundamental error in the simulation is set to be 2 %. It means that the value of Cfwd corresponds to 1.02. Figure 3c shows that it would translate to ∼ 72° in band slant angle. The solar zenith angle is ∼ 69° in this case, and the corresponding relative airmass is ∼ 2.8 as a limiting edge, as shown in Fig. 3c. We discuss, within these criteria, the error estimation, which ranges from 6:15 JST to 17:00 JST for the day (June 22).
When using this rotating shadow-band system, such fundamental errors are certain to happen. In addition, errors caused by actual observations and their analysis must be considered as well as the insufficient correction of forward scattering.
4.2 Simulation using typical aerosol typesIn our simulations, as Table 2 shows, four typical aerosol types are introduced. These have been modeled by Shettle and Fenn (1979) and already built in the SBDART code. These types do not necessarily cover all types of various aerosols in the real atmosphere, e.g., desert aerosol (Wandinger et al. 2016). However, they are sufficient for illustrating the typical effects of different aerosols. Table 3 shows the aerosol parameters, such as SSA, ASY at 500 nm, and AE, used in the simulation.
Two examples for different times, 8:00 JST and 11:45 JST, are shown as sky brightness patterns in Figs. 4a and 4b, respectively. These are shown only for the Oceanic aerosol type, for simplicity. The upper panels, (i)–(iv), in both figures indicate radiance patterns (W m−2 sr−1 µm−1) with different AODs, 0 (Rayleigh), 0.01, 0.1, and 1.0, and the lower ones, (v)–(viii), are for irradiance patterns (W m−2 µm−1) for unit solid angle. Solar positions are expressed as a small red dot in each panel. As a reference, band positions at the time are also displayed. Note that the color code is different between the upper and lower panels.
(a) Examples of simulated sky brightness without direct solar radiation. Each brightness pattern corresponds to different AODs: 0 (Rayleigh atmosphere), 0.01, 0.1, and 1.0, respectively, from left to right in two panels' series (upper and lower). The upper panels' series shows the radiance pattern (W m−2 sr−1 µm−1) and the lower panels' series is the irradiance pattern (W m−2 µm−1) for a unit solid angle. The solar position is θ0 = 49.0°, φ0 = 88.5° at 8:00 JST, which is plotted as a small red dot in each panel. Note that the color codes of the radiance and irradiance patterns are different. As a reference, band positions are shown in each pattern. (b) Examples of simulated sky brightness. Same as (a) except for the time of 11:45 JST (θ0 = 12.2°, φ0 = 183.7°).
It is clear that the Rayleigh atmosphere has no strong forward scattering as expected and it increases rapidly around the sun with increasing AOD. These patterns are different for different aerosol types not shown here, but basic trends are similar to each other. Irradiance patterns of the lower panels are more concentric compared with radiance patterns because of the cosine effect. Such a concentric pattern is gradually distinctive with increasing solar altitude, as shown in Fig. 4b. It is easily understandable that the difference in each shadow region must be dependent on the band slant angle and AOD.
Diffuse irradiances shadowed by each band are calculated as ΔF2 to ΔF4. An example is shown in Fig. 5a. It has an Oceanic aerosol type with AOD of 0.2. The lower light blue line in Fig. 5a indicates the relative difference (right scale) in the correction method. This curve is stable for smaller zenith angles and rapidly changing with time near the sunrise and sunset. Figure 5b shows the change of Cfwd as functions of band slant angle and solar zenith angle for a period of the limited fundamental error of < 2 %. The maximum value of Cfwd reaches ∼ 1.36 for AOD of 0.2. The three-dimensional pattern of the Cfwd variation is shown as a function of AOD and time for the Oceanic aerosol type in Fig. 6a. The diurnal variation is not the same for different AODs. The most remarkable feature in the pattern is the peak values for usual AOD ranges. It is due to the related variation between incident direct and diffuse solar radiation with AOD changes. When the AOD gradually increases, the diffuse radiation also increases till ∼ 1 and then it decreases because of the rapid decrease of the direct solar radiation. Figure 6b shows examples of this variation of shadowed irradiances as a function of AOD × SSA × Airmass. The correction coefficients Cfwd are also plotted by dash-dotted lines in the figure to understand the relation between them. The peak positions of Cfwd are shifted from the irradiance ones. The saddle pattern in Fig. 6a is almost the same as the other three types except for their magnitudes. Figure 6c depicts the variation of Cfwd for different aerosol types with a variation of AOD × SSA, where these patterns are almost the same including each peak point except for the magnitude. These are the daily mean values with the standard deviation for the limited time domain. Aerosol impacts are clearly seen in the variation of Cfwd from these figures. The peak point of Cfwd for AOD (or AOD × SSA) is not the same as that for the diffuse radiation, but the trend is similar to the pattern of the shadowed diffuse radiation. Expectedly, the Oceanic type shows the largest value of Cfwd among the four aerosol types because of its larger particles. Based on this, Fig. 6d plots show the relation between AE and Cfwd, with AODs ranging from 0.01 to 1.0. The smaller AE can give a bigger error in general. However, note that the maximum value of Cfwd for each aerosol type is not the biggest AOD in the figure because of its AOD dependency, as shown in Fig. 6c.
(a) Simulated diffuse irradiance shaded by each band position, 2–4. The atmosphere is the Oceanic aerosol type with an AOD of 0.2. ΔF3 corresponds to the position of shading the direct solar radiation. ΔF2 and ΔF4 show shaded irradiances for band position 2 (−10°) and position 4 (+10°). ΔFmean is the arithmetic mean of ΔF2 and ΔF4, and the relative difference is defined by (ΔFmean − ΔF3)/ΔF2. (b) Correction coefficient Cfwd defined by ΔF3/ΔFmean as a function of the solar zenith and band slant angles. Curves are plotted with a fundamental error of < 2 %.
(a) Variation of the correction coefficient Cfwd as a function of AOD and time. This 3-D pattern is for the Oceanic aerosol type. Other types show similar patterns except for their magnitudes. (b) Examples of diffuse irradiance shadowed by a band and the corresponding Cfwd, as a function of AOD × SSA × Airmass. Solid and broken lines colored in blue (11:45) and orange (6:30) are true and approximated values, respectively. The ratios, Cfwd on the right scale are shown by dash-dotted lines. (c) Variation of mean correction coefficient Cfwd as a function of AOD × SSA. Each value is averaged for the same AOD during a certain period, with a fundamental error of < 2 %. Each error bar is the standard deviation of the daily mean. (d) Relation between Cfwd and Ångström exponent for four aerosol types. Error bars in each line are the same as in (c).
Errors in spDNI and optical depth estimation (ErrspDNI in Eq. 10 and Δτ in Eq. 12) can be derived using the simulated data. Figure 7 is an example of a diurnal variation for the Oceanic aerosol with AOD of 0.2. Large cat ears can be seen in the ErrspDNI around the time of sunrise and sunset due to the unbalanced FOV of each band. These are rejected automatically when analyzing data, based on the explanation provided before. Thus, the ErrspDNI ranges from 1.2 % to 4.1 % within the effective domain of the band slant angle (or time) in this example. Moreover, the Δτ induced from the spDNI error is approximately −0.011 to −0.014 for AOD of 0.2. These errors might not be serious but are not negligible. The relatively small effects to spDNI and τ, despite the large correction coefficient Cfwd, are because part of the corrected irradiance in the diffuse radiation is much smaller than the spDNI value itself.
Figure 8a depicts the same error, ErrspDNI, as a function of AOD × SSA for four aerosol types. The magnitude of ErrspDNI is different for each aerosol type as expected, even if each aerosol type has the same AOD. It can increase with an increase in AOD; however, it can decrease depending on the parameter of AOD × SSA × Airmass. Examples with AOD of 1.0 are shown in Fig. 8b. It is clear that the lines of ErrspDNI show peaks dependent on the AOD × SSA × Airmass. As a reference, the estimated spDNIs are plotted as well as the true spDNI, in the figure. These lines of spDNIs almost overlap because of their small differences. Although the magnitude of spDNI is consistently decreasing as well as the absolute error of spDNI with the increase in AOD, the RE of spDNI ErrspDNI is increasing for small values of AOD × SSA × Airmass and then decreasing over a certain value depending on AOD. Thus, the ErrspDNI changes with a similar pattern to Cfwd in Fig. 6c. A part of such variations is included in the rightmost points at AOD = 1.5 of Fig. 8a. Namely, the ErrspDNI varies from approximately 5–11 % at AOD = 1 of four aerosol types and 2–5 % at AOD = 0.5. It is also plotted as a function of Cfwd, as shown in Fig. 8c. Seven AODs are used in the figure, the same as for Fig. 8a. The error bars for each line are also the same as before. The upper ends of each line in Fig. 8c show values for AOD = 1.5, and the lower left side is for AOD = 0.01.
(a) Estimation error in spDNI as a function of AOD × SSA for four aerosol types. Seven AODs are used for each aerosol type, such as 0.01, 0.05, 0.1, 0.2, 0.5, 1.0, and 1.5. The error bars are due to the daily variation for the effective time domain. (b) Examples of spDNI and ErrspDNI as a function of AOD × SSA × Airmass for four aerosol types with AOD of 1.0. The estimated spDNIs (spDNI_est) for each aerosol type overlap on the same lines due to small differences. The patterns of ErrspDNI show peaks depending on the aerosol type. (c) Relative error in spDNI as a function of Cfwd. Seven AODs are used as in (a) for each aerosol type. The upper ends of each line are for AOD = 1.5. The error bars are the same as in (a).
Based on these features, the estimation error (Δτ) in optical depth can be retrieved simultaneously, as shown in Figs. 9a and 9b. The relative error Δτ/τ is dependent on the magnitude of AOD as well as the aerosol type. These reflect the trend of ErrspDNI, as expected. As seen in Fig. 9a, the relative errors Δτ/τ of the daily average, range from approximately 3–4 % or less for Tropospheric, Rural and Urban types, and < 6 % for Oceanic type at AOD = 1.0. The right ends of each line are for AOD of 1.5. Larger airmasses have larger errors than the averages. Figure 9b shows the relation between Δτ/τ and Cfwd. In the figure, the lowest (negatively biggest) ends of each line are for AOD = 1.5 and the uppermost points are for AOD = 0.01. This corresponds to Fig. 8c. It is clear that depending on their aerosol type, the AOD change strongly affects the estimation error. This suggests that the Δτ/τ is also dependent on the AE. Figure 10 shows their relation. The dependency on AE is plotted with six AOD parameters, 0.01–1.0, for each aerosol type. The smaller AE can give a larger error, as a rough standard. For example, the optical depth estimation under the rural or urban atmosphere with usual AOD might be expected to show approximately 3–4 % RE at most. Oceanic aerosol type is a little far from the other three types because of rich coarse mode particles by hygroscopic growth. Based on this figure, radiation measurements in the atmosphere containing rich particles of coarse mode like oceanic or desert dust particles should be carefully analyzed. The information of AE is a good indicator for the rough error estimation, which can be deduced by spectral observation.
(a) Relative error in optical depth as a function of AOD × SSA. The four lines with error bars indicate different aerosol types for seven AODs, namely, 0.01, 0.05, 0.1, 0.2, 0.5, 1.0, and 1.5. The rightmost ends of each line are for AOD = 1.5. (b) Estimation error in optical depth as a function of Cfwd. The four lines with error bars indicate different aerosol types for seven AODs, namely, 0.01, 0.05, 0.1, 0.2, 0.5, 1.0, and 1.5. The lowest ends of each line are for AOD = 1.5, and the smallest (upper) points are for AOD = 0.01.
Relation between Δτ/τ and Ångström exponent.
SSA is one of the most important parameters on the aerosol impact in climate research. Diffuse radiation measurements can provide the possibility to determine the SSA (Khatri et al. 2012). Consequently, the spDHI can be estimated by using Eq. (9). In this case, the RE ErrspDHI is obtained by using Eq. (11). Figures 11a and 11b show the ErrspDHI estimate as functions of AOD × SSA and Cfwd, respectively. The maximum error points (lowest of each line in the figure) for each aerosol type are visible. For example, the Oceanic aerosol type shows a ErrspDHI of ∼ 4 % for the worst case. In general, these points are mainly dependent on the aerosol size distribution through a correction coefficient Cfwd. Figure 11b shows the relation between ErrspDHI and Cfwd. It shows a unique feature of the linear relation between them. Based on this, a rough estimate of the RE could be performed. The ErrspDHI can be estimated by the AE as shown in Fig. 12 for AOD parameters ranging from 0.01 to 1.0. The error is strongly dependent on AOD as well as on the AE index. Although the smaller AOD can give a smaller RE in spDHI, the largest error shows AOD of 0.5 (light blue line in Fig. 12), as also seen in Fig. 11a. This is due to the dependence of the relation between AOD and corresponding diffuse radiation.
(a) Relative error in spDHI estimation as a function of AOD × SSA. Each aerosol type shows the minimum points during a range of 0.1 to 1.0 AOD × SSA. (b) Same as (a) except for as a function of Cfwd. The minimum point of the error for the Oceanic aerosol type corresponds to the maximum Cfwd.
Relative error in spDHI estimation as a function of the Ångström exponent (AE) with different AODs, ranging from 0.01 to 1.0. Four aerosol types are shown corresponding to their AEs.
The errors discussed above are summarized in Table 4 for two typical AODs of 0.5 and 1.0. Each value in the table is a daily mean with the standard deviation for the effective time domain. These AODs are considered to be under normal atmospheric conditions. Such errors might occur when using a common correction technique, Cfwd = 1. Thus, if an appropriate value of Cfwd is introduced in the actual analysis, these errors might shrink. These results can help to improve the analysis method for obtaining more accurate aerosol parameters.
A spectral radiometer with a shadow-band system is a unique and powerful tool for various fields, such as solar radiation, atmospheric and biological environment, and air quality. The objective of a rotating shadow-band is to separate spDNI and spDHI from directly observed spGHIs. When performing the separation, a suitable correction scheme is required for the diffuse irradiance shadowed by the band. The accuracy of the estimated irradiances is dependent on this correction scheme. Based on the most popular correction technique for this system, errors in spDNI and spDHI estimation are discussed in detail using realistic instrumental parameters with four typical aerosol types.
The key issue is the accuracy of the correction of diffuse irradiances shadowed by the band. Even if the instrumental system has no error, such as cosine characteristics of the sensor/diffuser and calibration including observation errors, the usual correction method can give errors because of the underestimation of the forward scattering and asymmetric positions of the shadow-band for correction. First, fundamental errors based on the correction method itself are estimated by using uniform isotropic radiance as input. When the slant angle of the shadow-band is < 72° with realistic parameters of the system, the RE in the diffuse irradiance of shadow region between the true value and its approximation is < 2 %. This error is inevitable when using this system. It can be caused by the difference of the shadow-band positions for correction, which equals the difference of the cosine effect of the diffuser/sensor. Over the 72°, the error rapidly increases so that the estimated spDNI and spDHI might not be usable. Note that the value of the limited angle of the shadow-band is dependent on the parameters used in the shadow-band system.
The REs in the estimated spDNI and spDHI, using realistic atmospheres with four typical aerosol types, namely, Rural, Urban, Oceanic and Tropospheric, as compiled by Shettle and Fenn (1979), and considered within the basic error of 2 %. The AOD at 500 nm in the simulation yields 11 cases from 0.001 to 2.0, which can cover usual atmospheric conditions. As seen from the simulation, the correction coefficient Cfwd for the forward scattering region of the shadowband is strongly dependent on AOD (or AOD × SSA). It increases and then reaches a peak and afterward it decreases when the AOD (or AOD × SSA) is increasing. These phenomena originate from the relation between spDNI and spDHI with the AOD change. The coefficient Cfwd for the Oceanic aerosol type shows larger values than the other aerosol types because it is enriched with coarse particles. This trend is confirmed by the correlation with the AE.
The relative error in the spDNI estimation shows a variation from 2 % to 5 % at AOD of 0.5 and from 5 % to 11 % at AOD of 1 for the four aerosol types. Based on these results, the relative error in the optical depth estimation varies within 2–5 % at AOD of 0.5 for four aerosol types, almost the same as the spDNI estimation. In contrast, the spDHI estimation has a unique maximum error of ∼ 4 % for the AOD range of 0.1–1.0 for the Oceanic aerosol type. The AOD increase over the range is at the origin of the decrease in the spDHI error, and the error variation against Cfwd shows roughly a linear relationship with the weak aerosol type dependency.
These features can help to improve the accuracy of the spDNI and spDHI estimation.
This study is partly supported by a Grant-in-Aid for Scientific Research (C) 17K05650 from Japan Society for the Promotion of Science, Japan Aerospace Exploration Agency (PI no. ER2GCF211, contract no. 19RT000370), and “Virtual Laboratory for Diagnosing the Earth's Climate System” program of MEXT, Japan.
The authors are grateful to Prof. R. Pinker of the University of Maryland for helpful discussions and comments on the manuscript. We would like to thank Prof. H. Irie of the Center for Environmental Remote Sensing, Chiba University for maintaining the SKYNET observation and data management, and Dr. Dim Jules Rostand for his careful reading and comments on the manuscript.
