Journal topic
Atmos. Meas. Tech., 12, 6037–6047, 2019
https://doi.org/10.5194/amt-12-6037-2019
Atmos. Meas. Tech., 12, 6037–6047, 2019
https://doi.org/10.5194/amt-12-6037-2019

Research article 21 Nov 2019

Research article | 21 Nov 2019

# Retrieval of cloud properties from spectral zenith radiances observed by sky radiometers

Retrieval of cloud properties from spectral zenith radiances observed by sky radiometers
Pradeep Khatri1, Hironobu Iwabuchi1, Tadahiro Hayasaka1, Hitoshi Irie2, Tamio Takamura2, Akihiro Yamazaki3, Alessandro Damiani2, Husi Letu4, and Qin Kai5 Pradeep Khatri et al.
• 1Center for Atmospheric and Oceanic Studies, Graduate School of Science, Tohoku University, Sendai, Japan
• 2Center for Environmental Remote Sensing, Chiba University, Chiba, Japan
• 3Climate Research Department, Meteorological Research Institute, Tsukuba, Japan
• 4Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing, China
• 5School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou, China

Abstract

1 Introduction

Clouds play an important role in driving the climate system and hydrological cycle (Rosenfeld et al., 2014). The accurate representation of clouds in the global climate model remains one of the largest uncertainties (Forster et al., 2007). Clouds are observed from space with various sensors onboard satellites, and the observations are vital in understanding more about cloud characteristics and their roles in the climate system and hydrological cycle. The quality assurance of cloud properties from satellite observations is an important task in cloud remote sensing, although it is challenging, primarily due to the lack of standard data representing different atmospheric conditions. Compared with the routine observation of aerosols through surface networks, such as AERONET (Aerosol Robotic Network; https://aeronet.gsfc.nasa.gov/, last access: 15 November 2019) and SKYNET (http://atmos3.cr.chiba-u.jp/skynet/, last access: 15 November 2019), the observation of clouds from the surface is performed at a limited number of stations, and most of the observation data are not easily accessible. As the recent instruments belonging to AERONET and SKYNET can be used for cloud remote sensing along with aerosol remote sensing, it is important to develop innovative techniques to retrieve cloud properties by using data observed by those instruments. This can help the satellite remote-sensing community to validate cloud products and help the whole cloud research community to study clouds in more detail by using high-resolution surface data.

Here, we develop a retrieval algorithm based on an optimal estimation method, namely, a maximum a posteriori method (Rodgers, 2000). We use three carefully selected wavelengths to retrieve COD and CER simultaneously. An on-site calibration method is proposed to address the filter degradation problem while analyzing long-term observation data. Although the algorithm is developed using sky radiometer data, it is equally applicable for sun photometer data. The paper begins with a brief description of the sky radiometer in Sect. 2. The methodology, retrieval error, and quality assessment of retrieved products are discussed in Sects. 3–5, respectively. Finally, the conclusion is presented in Sect. 6.

Figure 1Schematic of the study method.

3 Methodology

A schematic of the study method is shown in Fig. 1. We use sky radiances (E) observed at three longer wavelengths (0.87, 1.02, and 1.627 µm), excluding 2.2 µm, which is not used for two main reasons. First, our statistical analysis suggests that the number of unphysical data (observation data recorded as 0) for 2.2 µm is high; thus, 2.2 µm is excluded to increase the retrieval number. Second, the longest wavelength used by AERONET is 1.64 µm; so the proposed algorithm could be easily used for sun-photometer-observed data as well. Wavelengths shorter than 0.87 µm are not used to avoid the effect of aerosols as far as possible. Observed E can be converted to the transmittance (T) by

$\begin{array}{}\text{(1)}& T\left(\mathit{\lambda }\right)\phantom{\rule{0.125em}{0ex}}=\phantom{\rule{0.125em}{0ex}}\frac{\mathit{\pi }E\left(\mathit{\lambda }\right)}{{\mathit{\mu }}_{\mathrm{0}\mathrm{\Delta }\mathrm{\Omega }\left(\mathit{\lambda }\right){F}_{\mathrm{0}}\left(\mathit{\lambda }\right)}},\end{array}$

where μ0 is the cosine of the solar zenith angle, ΔΩ is the calibration constant for sky radiance, which is also called the solid view angle by the SKYNET community, F0 is the calibration constant for direct intensity, and λ is the wavelength. ΔΩ for 0.87, 1.02, and 1.627 µm can be determined from the solar disk scan during very-clear-sky days (Nakajima et al., 1996). Although the current IL method can be used to determine temporal F0 for the first two wavelengths (0.87 and 1.02 µm), it is less suitable for water-absorbing wavelengths, such as 1.627 µm. For 1.627 µm, F0 derived from the NL method can be used, but the NL is less practical to implement routinely in short time intervals (e.g., each month) to derive temporal F0. We prefer to use temporal F0 for all wavelengths to include filter degradation with time (e.g., Khatri et al., 2014). To derive temporal F0 at 1.627 µm, we use an alternative IL method, as proposed by Khatri et al. (2014). In brief, aerosol data (refractive index and volume size distribution) and the direct intensity observed at 1.627 µm (F1.627) are used. The aerosol optical thickness (τaer) depends primarily on the aerosol size distribution, and the refractive index makes a small contribution to τaer (King et al., 1978; Khatri and Ishizaka, 2007). Thus, the refractive index at 1.02 µm, which is the highest wavelength for routine aerosol retrieval, is assumed to be the same as for 1.627 µm while calculating τaer at 1.627 µm from the volume size distribution using a Mie calculation. The optical air mass (m) and sun–earth distance (R) are calculated from the latitude and longitude of the observation site and time. Similarly, the Rayleigh scattering optical depth at 1.627 µm (τRay,1.627), though small in magnitude, is calculated from the atmospheric pressure of the observation site. Finally, the Beer–Lambert law, $\mathrm{ln}\left({F}_{\mathrm{1.627}}{R}^{\mathrm{2}}\right)=\mathrm{ln}{F}_{\mathrm{0},\mathrm{1.627}}-\left({\mathit{\tau }}_{\mathrm{aer}}+{\mathit{\tau }}_{\mathrm{Rayleigh}}\right)m$ is used to determine ln F0,1.627, which is the natural logarithm of the calibration constant of the direct intensity at 1.627 µm. This is calculated using data for all clear-sky periods of each month to correlate ln (F1.627R2) with (τaer+τRayleigh)m. The outlier that decreases the correlation most is detected and removed in each iteration until the condition of the correlation coefficient (r≥0.997) is satisfied. To understand the quality of the ln F0,1.627 values calculated with this method, we compare them with data from an independent standard method. In the standard method, a calibration constant is derived by performing collocated observations with field and master instruments. Figure 2 compares ln F0,1.627 for three different sky radiometers at the observation sites of Hedo-misaki (26.87 N, 128.25 E), Fukue-jima (32.75 N, 128.68 E), and Sendai (38.26 N,140.84 E). There is good agreement between our method and the standard method for all three sky radiometers. The relative difference (as a percentage), defined as the difference between our method and the standard method normalized by the value of the standard method and then multiplied by 100, is also shown and is less than 0.05 % for all sky radiometers. This confirms the validity of our proposed method, which is inexpensive and easy. Thus, the proposed method can be used to determine the temporal variation of ln F0,1.627, which is useful for analyzing long-term observation data by mitigating the filter degradation problem. By using the volume size distribution and refractive indices of the wavelengths, the proposed method can be used for 0.87 and 1.02 µm as well. There is a negligible difference in the values obtained by the IL method and this method for the first two wavelengths. This study uses the values obtained from the proposed method for all wavelengths to avoid the difficulty of reading ln F0 from different files.

Figure 2Comparison of the direct intensity calibration constant (ln F0) values at the water-absorbing wavelength of 1.627 µm for the standard method (calibration using the master instrument) and our on-site method for sky radiometers at Hedo-misaki (26.87 N, 128.25 E), Fukue-jima (32.75 N, 128.68 E), and Sendai (38.26 N, 140.84 E). The difference is also shown, which is the difference (as a percentage) between the proposed method and the standard method normalized by the value of the standard method and multiplied by 100.

Along with the T values of three wavelengths obtained from Eq. (1), we use precipitable water content (PWC) and spectral surface albedo data, which are obtained from radiosonde observations (http://weather.uwyo.edu/upperair/sounding.html, last access: 15 November 2019) and MODIS observations (product MCD43A4), respectively. Finally, COD and CER are retrieved simultaneously by minimizing the cost function (J).

$\begin{array}{}\text{(2)}& \begin{array}{rl}J& ={\left(\mathbit{x}-{\mathbit{x}}_{\mathrm{a}}\right)}^{T}{\mathbf{S}}_{\mathrm{a}}^{-\mathrm{1}}\left(\mathbit{x}-{\mathbit{x}}_{\mathrm{a}}\right)+{\left[\mathbf{y}-\mathbf{F}\left(\mathbit{x},\mathbf{b}\right)\right]}^{T}\\ & {\mathbf{S}}_{y}^{-\mathrm{1}}\left(\mathbf{y}-\mathbf{F}\left(\mathbit{x},\mathbf{b}\right)\right],\end{array}\end{array}$

where x is a state vector, xa is an a priori vector, Sa and Sy are error covariance matrices for the a priori and measurement, respectively, y is the measurement vector, F is the forward model, and b is the model parameter vector (ancillary data). The terms x, y, and b are defined as

$\begin{array}{rl}\mathbit{x}& =\left(\begin{array}{l}\mathrm{ln}\mathit{\tau }\\ \mathrm{ln}{r}_{e}\end{array}\right),\phantom{\rule{1em}{0ex}}\mathbf{y}=\left(\begin{array}{l}\mathrm{ln}{T}_{\mathrm{1.627}}\\ \mathrm{ln}{T}_{\mathrm{1.02}}\\ \mathrm{ln}{T}_{\mathrm{0.87}}\end{array}\right),\\ & \mathrm{and}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\mathbit{b}=\left(\begin{array}{l}W\\ \begin{array}{l}{A}_{\mathrm{1.627}}\\ {A}_{\mathrm{1.02}}\\ {A}_{\mathrm{0.87}}\end{array}\end{array}\right),\end{array}$

where τ and re are COD and CER, respectively, and W and Aλ are the PWC and surface albedo at wavelength λ, respectively. Both Sa and Sy are assumed to be diagonal matrices. xa and the diagonal elements of Sa are determined from 1-year data for water cloud properties observed over Japanese SKYNET sites by the Advanced Himawari Imager (AHI) sensor onboard Himawari-8, a Japanese geostationary satellite. The diagonal terms for Sy are determined based on a simulation of perturbations in T(λ) generated from 300 random Gaussian noises of error sources, as discussed in Sect. 4. SBDART (Santa Barbara DISORT Atmospheric Radiative Transfer model; Ricchiazzi et al., 1998) is used for forward modeling, and the Levenberg–Marquardt method is used to minimize the cost function. The total number of iterations is set as 50. If the solution does not converge within 50 iterations, the analysis is discarded. As highlighted in Sects. 1 and 4, transmittance signals may not always be characterized by unique COD or CER values. Consequently, the initial values of COD and CER used for iteration can be important when searching the plausible set of COD and CER values. To address this important issue, we first approximate the initial COD and CER values to start the iteration. The approximation is done by searching a set of COD and CER values by comparing observed T1.627T1.02 and T1.02 with the LUT of corresponding values modeled for COD values of 1–64 and CER values of 2–32 µm in steps of 1 µm. T1.627T1.02 generally decreases with the increase of COD; whereas when COD increases, T1.02 increases first until reaching the peak value, and then it starts to decrease. Thus, T1.627T1.02 and T1.02 can be used simultaneously to determine the range of COD and CER values in which the true values are likely to fall. A set of COD and CER values that generate the smallest root mean square difference between the observed and modeled values is used for the initial values in the iteration.

Figure 3Mean bias error (MBE) values for the retrieved (a) cloud optical depth (COD) and (b) cloud particle effective radius (CER) and (c) the total number of successful retrievals for the assumed error in transmittance; (d)(f) same as (a)(c) but for the assumed error in surface albedo; (g)(i) same as (a)(c) but for the assumed error in precipitable water content; (j)(l) same as (a)(c) but for all error sources. The 100 % unsuccessful retrieval is shown in black.

4 Retrieval error

To understand the performance of the proposed algorithm for different types of input data (transmittance and ancillary data), retrieval errors are calculated by assuming errors on them. The retrieval errors are calculated for COD and CER values in the ranges of 1–64 and 2–32 µm, respectively, in steps of 1 µm. The simulations are performed for solar zenith and azimuth angles of 30 and 0, respectively, by assuming that the cloud phase is a water cloud. We assume 1 % error in ln F0(λ), which is significantly larger than the maximum error in ln F0(λ) shown in Fig. 2 and discussed in Sect. 3. This large error in ln F0(λ) is assumed to incorporate errors in T(λ) generated from other possible sources, such as radiance measurement and ΔΩ(λ) estimation. Similarly, we assume a surface albedo of 0.15 for all three wavelengths and a PWC of 1.5 cm by assuming errors of ±0.025 and ±1.0 cm, respectively. F0(λ) in an actual data analysis is the instrument signal equivalent to the measurement performed at the top of the atmosphere (TOA); however, the incident irradiance at TOA (W m−2 nm−1) calculated from the radiative transfer model is used as F0(λ) for error evaluation simulations discussed in this section. For each set of known COD and CER values, 100 random Gaussian noises for each error source are added in the retrieval to simulate 300 sets of COD and CER values. The successful retrievals (J≤3) are used to calculate the mean bias error (MBE) as

$\begin{array}{}\text{(3)}& \mathrm{MBE}=\frac{{\sum }_{i=\mathrm{1}}^{n}\left(\frac{{S}_{i}}{{T}_{r}}\phantom{\rule{0.125em}{0ex}}-\phantom{\rule{0.125em}{0ex}}\mathrm{1}\right)}{n},\end{array}$

Si and Tr are the ith simulated and true values, respectively, and n is the total sample number. Only the MBE is discussed here because the error map evaluated in other forms, such as the root mean square error (RMSE), contains the same qualitative information. Figure 3 shows the MBE for COD (first column), MBE for CER (second column), and total number of successful retrievals (third column) for each type of error separately and in combination. Figure 3a–c, d–f, g–i, and j–l correspond to the errors in the transmittance, surface albedo, PWC, and all sources, respectively. The 100 % unsuccessful retrieval is shown in black. The retrieval is more uncertain mainly when COD is less than ∼15. Regardless of the error source, the retrieval error is high, especially for small (CER < ∼7µm) and large (CER > ∼13µm) cloud droplets. In general, the error domains of CER are expanded by overlapping the error domains of COD. This suggests that the error in input data affects CER retrieval more than COD retrieval. Among the three error sources, the error in transmittance can dominate the effect of the remaining two error sources. The successful retrieval number corresponding to each error source suggests that in the domains of ∼8 < COD < ∼16 with CER > ∼13 and CER < ∼7µm, the algorithm has difficulty fitting the measured transmittances with modeled values. These domains have high retrieval errors (first and second columns). The high errors in COD and CER are extended further for COD < ∼8 despite the sufficient number of successful retrievals. The contour lines for T(λ) in Fig. 4a, b, and c for wavelengths of 0.87, 1.02, and 1.627 µm, respectively, can help to understand these domains. The T(λ) values in Fig. 4a–c correspond to no error in the input data.

Figure 4Contour plots of transmittances at the wavelengths of (a) 0.87, (b) 1.02, and (c) 1.627 µm for the solar zenith and azimuth angles of 30 and 0, respectively. The transmittance values are given within the contour lines. Different colors are used for 1.627 µm to make it easy to distinguish. COD is the cloud optical depth; CER is the cloud particle effective radius.

First talking about unsuccessful retrievals noted for the ∼8 < COD < ∼16 and CER > ∼13µm domain, the T(λ) values hardly change as CER increases above ∼13µm (Fig. 4a–c). As a result, the CER retrieval above ∼13µm is uncertain, and the retrieved CER is generally underestimated. T(λ) contour lines falling within ∼8 < COD < ∼16 appear again for COD < ∼2. Therefore, to search for the best set of COD and CER values by trying to fit the inputted T(λ) values with the modeled values, the algorithm can mistakenly search for a plausible solution in this small COD domain. If this happens, the retrieval may not be confined within J≤3. The algorithm is likely to compensate for such underestimated CERs by overestimating CODs (Fig. 3a and b and j and k).

Similarly, for failed retrievals for CER < ∼7µm, a non-uniform change in T(1.627µm) associated with the change in CER (Fig. 4c) can be an important factor. The non-uniform response of CER to the change of T(1.627µm) can mislead the algorithm, while searching for the best set of COD and CER may force the algorithm to shift wrongly to the COD < ∼2 domain to search for a plausible solution. Both CER and COD may be overestimated for CER > ∼7µm. Despite a sufficient number of successful retrievals, there are high errors in the retrieved values for COD < ∼8. Similar to the error domains discussed above, the retrieval errors are mainly confined to large and small values of CER. The peak values of T(λ) generally fall within $\sim \mathrm{3}\le$ COD $\le \sim \mathrm{6}$. Both the forward scattering and absorption can increase with the increase of COD along with the increase in multiple scattering; the increase in T(λ) before the peak value is due to the dominance of forward scattering over absorption, and the opposite is true for the decrease in T(λ) after the peak value. In other words, the competition between forward scattering and absorption is at its maximum to increase or decrease T(λ) within this COD range. CER is as important as COD in the increase or decrease of T(λ), and the algorithm must consider changes in COD and CER while searching for a plausible set of COD and CER. Thus, there is a high probability for the ambiguous solution of COD and CER within this COD range. Therefore, even a small degree of error in input data can change both COD and CER considerably from their true values. Though weak, this phenomenon can be still active in the vicinity of this COD range to bring error in retrieved values, even for COD < ∼3. The weak CER response towards T(λ) for large CERs plays an important role in introducing errors in retrieved values for large CERs. A very complicated distribution of T(1.627µm) for CER < ∼7µm, as discussed above, can be an important factor for errors noted for relatively small CERs. Further, the appearance of same T(λ) values for larger CODs, as discussed above, can be the next important factor for errors noted within COD < ∼2.

Overall, the retrieval error in COD is smaller than that in CER, suggesting that the transmittance-based cloud remote sensing is better for COD retrieval than for CER retrieval. Except for those error domains, the magnitudes of the retrieval errors are small. For example, for COD > 15 and all types of errors, the 5th, 50th, and 95th percentile values of the MBE for retrieved COD values are −2.0 %, −0.6 %, and 0.82 %, respectively, and for retrieved CER values they are −4.1 %, −0.51 %, and 7.2 %, respectively. For reference, the maximum (minimum) retrieval errors for COD ≥20 and CER =10µm for a spectral method proposed by McBride et al. (2011) are ∼7 % (∼2 %) and ∼52 % (∼14 %) for COD and CER, respectively. In Sect. 5, we examine the quality of the retrieved cloud properties based on a comparison with standard data obtained from independent sources.

Figure 5Comparison of modeled and observed broadband (a) radiances and (b) irradiances for modeled values using sky radiometer cloud proprieties for the observation site at Chiba (35.62 N, 140.10 E) for 2016. Comparison results for broadband radiances (c) and (d) the irradiance for modeled cloud properties corresponding to the Advanced Himawari Imager.

5 Comparison with data from independent sources

## 5.2 Satellite cloud products

As part of validating the water cloud products of MODIS and the AHI using surface radiation data, Khatri et al. (2018) compared water cloud properties retrieved from sky radiometers at the SKYNET observation sites of Chiba, Hedo-misaki, and Fukue-jima with those of MODIS and AHI observations for October 2016 to December 2017. They used surface irradiance data, and the validation results using sky radiometer and surface irradiance data were qualitatively similar. A good (poor) agreement was shown for COD (CER) between sky radiometer and satellite products in Khatri et al. (2018). They compared sky radiometer results with results of collocated satellite pixels by selecting samples with a time difference of less than 1.25 min, which is half the temporal resolution of the AHI observations over Japan. The distance between the pixel center and the observation site was less than 1 km, and they performed parallax correction for satellite products.

Figure 6Scatterplot of broadband radiances and irradiances observed with a narrow-angle radiometer and a wide-angle pyranometer at Chiba (35.62 N, 140.10 E) during January–March 2016. The solid line represents y=2πx.

Figure 7Comparison of sky radiometer cloud optical depths (CODs) with the (a) MODIS and (b) Advanced Himawari Imager CODs for observation sites at Chiba (35.62 N, 140.10 E), Hedo-misaki (26.87 N, 128.25 E), and Fukue-jima (32.75 N, 128.68 E) from October 2015 to December 2016.

Figure 8Same as Fig. 7 but for a comparison of cloud particle effective radii (CERs).

Although the qualitative information reported by Khatri et al. (2018) and the comparisons in Figs. 7 and 8 of this study are similar, there are differences in Figs. 7 and 8 compared to the comparison plots shown in Khatri et al. (2018). The application of data screening criteria in this study generally screened out data with large differences between the sky radiometer and satellite sensors. These large differences in the previous comparison probably arose from the different FOVs of the satellite sensor and sky radiometer while observing inhomogeneous clouds. Thus, the comparison results presented in this study by addressing the cloud inhomogeneity problem more logically should give more accurate and refined information than those presented in Khatri et al. (2018).

6 Conclusions

Code and data availability
Code and data availability.

Data and retrieval code are available from the corresponding author upon request.

Author contributions
Author contributions.

PK, HI, and TH developed the study framework and code. HI, TT, AY, and AD generated data. HL and QK helped in advancing the study's framework and writing the paper. All co-authors read the paper and provided suggestions and comments.

Competing interests
Competing interests.

The authors declare that they have no conflict of interest.

Special issue statement
Special issue statement.

Acknowledgements
Acknowledgements.

This research is supported by the 2nd Research Announcement on the Earth Observations of the Japan Aerospace Exploration Agency (JAXA) (PI no. ER2GCF211, contract no. 19RT000370), a Grant-in-Aid for Scientific Research (C) (no. 17K05650) from the Japan Society for the Promotion of Science (JSPS), the “virtual laboratory for diagnosing the earth's climate system” program of MEXT, Japan, and the CREST/JST research fund (grant no. JPMJCR15K4).

Financial support
Financial support.

This research has been supported by the Japan Aerospace Exploration Agency (PI no. ER2GCF211, contract no. 19RT000370), the Japan Society for the Promotion of Science (JSPS) (grant no. 17K05650), and the CREST/JST (grant no. JPMJCR15K4).

Review statement
Review statement.

This paper was edited by Teruyuki Nakajima and reviewed by two anonymous referees.

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