Retrieval of radiative and microphysical properties of clouds from multispectral infrared measurements
© The Author(s). 2016
Received: 29 May 2016
Accepted: 26 September 2016
Published: 21 October 2016
Satellite remote sensing of the macroscopic, microphysical, and optical properties of clouds are useful for studying spatial and temporal variations of clouds at various scales and constraining cloud physical processes in climate and weather prediction models. Instead of using separate independent algorithms for different cloud properties, a unified, optimal estimation-based cloud retrieval algorithm is developed and applied to moderate resolution imaging spectroradiometer (MODIS) observations using ten thermal infrared bands. The model considers sensor configurations, background surface and atmospheric profile, and microphysical and optical models of ice and liquid cloud particles and radiative transfer in a plane-parallel, multilayered atmosphere. Measurement and model errors are thoroughly quantified from direct comparisons of clear-sky observations over the ocean with model calculations. Performance tests by retrieval simulations show that ice cloud properties are retrieved with high accuracy when cloud optical thickness (COT) is between 0.1 and 10. Cloud-top pressure is inferred with uncertainty lower than 10 % when COT is larger than 0.3. Applying the method to a tropical cloud system and comparing the results with the MODIS Collection 6 cloud product shows good agreement for ice cloud optical thickness when COT is less than about 5. Cloud-top height agrees well with estimates obtained by the CO2 slicing method used in the MODIS product. The present algorithm can detect optically thin parts at the edges of high clouds well in comparison with the MODIS product, in which these parts are recognized as low clouds by the infrared window method. The cloud thermodynamic phase in the present algorithm is constrained by cloud-top temperature, which tends not to produce results with an ice cloud that is too warm and liquid cloud that is too cold.
KeywordsCloud optical thickness Cloud-top height Effective particle radius Ice cloud Optimal estimation method Satellite remote sensing
Clouds play a vital role in regulating the Earth’s radiation budget, through shortwave cooling and longwave warming effects (Ramanathan et al. 1989). The cloud radiative effects depend on the type of cloud, and thus, the radiation budget is controlled by the occurrence of various types of clouds (Hartmann et al. 1992), which complicates our understanding of cloud roles in the climate system. In particular, the radiative effects of ice clouds are not well understood, partly because the optical properties of ice clouds are not well quantified (Baran 2009), which is a major source of uncertainty in ice cloud representations in global climate models. There are discrepancies in satellite observation climatology of ice clouds, and improvement of ice cloud processes is still a challenge (e.g., Waliser et al. 2009). Climatology and spatial and temporal variations of clouds on various scales are also important to understand cloud response and feedback in climate systems. Satellite remote sensing can provide constraints for global cloud properties that are useful for developing cloud parameterizations. Macroscopic, microphysical, and optical properties are generally used in satellite remote sensing of clouds. There are specialized methods for each property, including cloud fraction, cloud-top properties (temperature/pressure/height), cloud thermodynamic phase, cloud optical thickness (COT), and cloud-particle effective radius (CER).
There are two passive remote sensing methods that are commonly used for cloud optical and microphysical properties: infrared (IR) window (split-window) (Inoue 1985; Parol et al. 1991; Giraud et al. 1997) and visible/shortwave IR (VIS/SWIR) bispectral (Nakajima and King 1990) approaches. IR window cloud retrieval is suitable for optically thin high clouds with COT of 0.1–5 (e.g., Garnier et al. 2012), whereas the VIS/SWIR method is suitable for optically thick clouds with COT greater than 1 (Nakajima and King 1990; Platnick et al. 2003). We have developed an IR method to retrieve COT and CER by using the 8.5, 11, and 12 μm bands of the moderate resolution imaging spectroradiometer (MODIS) onboard the Aqua satellite (Iwabuchi et al. 2014). In this method, inversion was based on the optimal estimation method (Rodgers 2000), which simultaneously fits the physics model to measurements and diagnoses rigorous uncertainties and retrieval quality. The optimal estimation method has been used widely for cloud remote sensing (Cooper et al. 2003; Heidinger and Pavolonis 2009; Watts et al. 2011; Walther and Heidinger 2012; Poulsen et al. 2012; Sourdeval et al. 2013; 2015; Wang et al. 2016). In a previous work (Iwabuchi et al. 2014), cloud retrieval was applied only to the ice phase cloud, and the a priori cloud-top temperature (CTT) was independently estimated by the CO2 slicing technique (Menzel et al. 2008) in the MODIS operational product. Thus, the retrieval was strongly constrained by cloud-top prior information and affected by the CTT accuracy in the MODIS product. Because the CTT retrieval itself can depend on COT and microphysical properties, the overall retrieval performance can be obtained if the cloud-top height (CTH), COT, and effective radius are retrieved simultaneously from the window and absorption bands.
In addition, the cloud thermodynamic phase is important because liquid and ice clouds play different roles in regulating the Earth’s radiation budget and hydrological cycle. Although cloud retrieval using passive sensors usually assumes single-layer ice or liquid clouds, it leads to substantial errors in estimated cloud optical and microphysical properties if there is a multilayer cloud system or if the assumed cloud phase is wrong (Davis et al. 2009). Recent studies using active remote sensing from CloudSat and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellites have obtained a globally averaged multilayered cloud occurrence of 25–28 % (Li et al. 2015). A cloud analysis algorithm should include methods for detection and property retrieval of multilayered cloud systems and determination of the cloud phase.
In this paper, an optimal estimation-based cloud retrieval algorithm is presented, where COT, CER, cloud-top pressure (CTP), and surface temperatures are simultaneously retrieved from measurements in ten thermal IR (TIR) bands of MODIS including the window and CO2 and water vapor absorption bands. Combined use of TIR bands enables the cloud thermodynamic phase to be distinguished and allows the method to be used for multilayer clouds, as previous pioneering studies suggest. The cloud retrieval algorithm is developed as part of the Integrated Cloud Analysis System (ICAS), which we develop in this study. This paper is organized as follows. The “Methods” section describes the source data used for cloud analysis, the cloud retrieval algorithm, the forward model, and the measurement and model errors, which are thoroughly quantified by model-to-model and model-to-observation comparisons. In the “Results and Discussion” section, retrieval errors are evaluated based on retrieval simulations in idealized cases, to understand the advantages and limitations of the algorithm. The algorithm is applied to a MODIS granule, and the retrieved cloud properties are compared with the MODIS Collection 6 (C6) operational product. The conclusion is given in the “Conclusions” section.
Characteristics of MODIS bands used in this study
Center wavelength (μm)
Band range (μm)
H 2 O
H 2 O, CH4
H2O, N2O, CH4
H2O, CO2, O 3
H2O, CO2, O3
H2O, CO2, O3
H2O, CO2, O3
H2O, CO2, O3
where B is the Planck function, \( \lambda \) is the wavelength, and \( \phi \) is the response function of each MODIS band. The band mean Planck function is precalculated for different temperatures, and the Akima interpolation (Akima 1970) is used to calculate the function or its inverse function, the BT, from the look-up table.
Summary of MODIS operational product data used in the retrieval algorithm
1.25 °, 42 levels
Sea surface temperature
8 day mean
Land surface temperature
8 day mean
Land surface emissivity
Trace gas concentration
Sea surface temperature data are from the MODIS 8 day mean level 3 product that is based on the TIR split window method (Brown et al. 1999). The root-mean-square error (RMSE) of SST by the split window method is evaluated as 0.35 K. Sea surface emissivity is determined by using the Fresnel equations for a flat sea surface based on the complex refractive index and the satellite zenith angle. The effects of a rough surface, including the effects of multiple reflection and wind direction, are sufficiently small for our purposes when the satellite zenith angle is 60 ° or less (Masuda 2012). The complex refractive index of seawater is synthesized from that of pure water based on Downing and Williams (1975) with a correction for the salinity effect based on Friedman (1969).
The land surface temperature is from the MODIS land 8 day mean level 3 product (MYD11C2), which is based on the day–night algorithm (Wan and Li 1997). For each day and night satellite overpass, the 8 day mean values are available in the product. In the present study, the land surface temperature is temporarily interpolated by considering the diurnal variation. The RMSE of the land surface temperature is less than 1 K (Wan et al. 2004; Wang et al. 2008). The land surface emissivity is from the baseline-fit emissivity database (BFED) monthly mean product (Seemann et al. 2008). Spectral interpolation is used to infer land surface emissivity in the MODIS bands, assuming that the emissivity is linear to the wavelength as recommended by the BFED documentation. The RMSE of land surface emissivity in the BFED is 0.01 or less in the IR window region and about 0.015–0.025 in the other TIR bands.
A physics-based forward model is developed and used in the cloud retrieval algorithm. The forward model takes auxiliary data for the atmospheric profile and background surface properties mentioned above, and it computes the BTs and their partial derivatives with respect to several atmospheric and surface variables. The radiative transfer is calculated by using the correlated k-distribution (CKD) method with six quadrature points for each band. The optimization method of Sekiguchi and Nakajima (2008) is used to determine the CKD coefficients from line-by-line radiative transfer calculations with the HITRAN2012 database (Rothman et al. 2013) and the continuum absorption model (Mlawer et al. 2012). Modeled gas species include water vapor, carbon dioxide, ozone, nitrous oxide, carbon monoxide, and methane.
The bulk optical properties of clouds are precalculated and tabulated for ice and liquid clouds with different particle size distributions and ice crystal habit distributions considering the spectral response function of MODIS spectral bands. In the forward model calculation, the optical properties are interpolated with respect to the CER from the look-up table by using the Akima interpolation. The optical properties of water droplets are computed by the Lorenz-Mie theory. The optical properties of ice particles are obtained from a database published by Yang et al. (2013), who used a combination of the discrete dipole approximation and the improved geometrical optics method for randomly oriented ice crystals of various shapes. Several models of particle habit distribution are incorporated into the model, including solid column, plate, column aggregate, the general habit mixture (Baum et al. 2011; Cole et al. 2013), and the two-habit model (Liu et al. 2014), with different degrees of surface roughness. In the present study, the column aggregate model with very rough surfaces is used because it is assumed in obtaining the MODIS C6 cloud product. TIR measurements are not strongly sensitive to the ice habit assumptions (Cooper et al. 2006).
Total radiance at the top of atmosphere is computed by the sum of components emergent from all atmospheric layers and the background surface. Band mean radiance calculated by integration over the CKD terms is converted to the BT.
The error of this approximate radiative transfer model is evaluated by comparing the model with an accurate model based on the discrete ordinate method for a variety of atmosphere and cloud states. Correction formulae based on a cubic polynomial for BT bias are developed for each band. After the bias correction, the RMSE reaches a maximum of 0.3 K in band 29, where the scattering effect is strong compared with other TIR bands. The two-stream approximation enables fast calculations, whereas the errors from the radiative transfer approximation are sufficiently small. For cloud retrieval, uncertainties in atmospheric profile and background surface properties are a major source of errors in the forward model.
where S a is an error covariance matrix of the a priori x a, and S e is a measurement–model error covariance matrix. The Levenberg-Marquardt method is used to obtain a minimized J, at which the solution converges. The final value of J is the retrieval cost, which represents the degree of fit between the model and measurement. The criterion that J is sufficiently small with an optimal solution is set as J < 2m, where the m is a number of the observation vector elements. A feature of the optimal estimation is that the uncertainty of the solution can be diagnosed quantitatively with an error covariance matrix. In addition, diagnostics of the estimation quality, such as the degree of freedom for signal (DOFS) and the information content, are obtained.
The cloud inversion is tried first with a single-layer cloud. If an optimal solution is obtained, the single-layer assumption is accepted. Otherwise, an inversion with a double-layer assumption is tried. A double-layer cloud solution is accepted if J is smaller than that of the single-layer assumption and the COT of the upper cloud is less than 8. This is because TIR measurements lose sensitivity to the lower cloud under the double-layer cloud assumption if the upper COT is more than about 8. The state vector includes cloud properties such as cloud water path (CWP), CER, CTP, and background surface temperature in single-layer cloud cases. With nonlinearity in mind, logarithms of CTP, CWP, and CER are elements of the state vector. The top-pressure of the lower cloud is inferred in double-layer clouds, instead of background surface temperature, as a similar double-layer cloud retrieval is proposed by Watts et al. (2011).
which has a value between 1 and 2: Q is 1–1.5 for liquid and 1.5–2 for ice. If the cloud phase costs for liquid and ice phase assumptions have similar values, then Q is nearly 1.5, which means that cloud phase determination is ambiguous.
Assumptions and prior information
B liq = 20 m, B ice = 20 m,
A liq = 400 m, A ice = 2000 m,
W liq = 0.06 kg m–2, W ice = 0.02 kg m–2.
The cloud base pressure is determined from H and atmospheric temperature and pressure profiles.
A priori information and prescribed ranges of the elements of the solution vector
COT, liquid clouds
COT, ice clouds
T sfc (K), ocean
T’ sfc – 2.1
T’ sfc + 2.1
T sfc (K), land
T’ sfc – 9
T’ sfc + 9
Liquid cloud properties
ln[r e (μm)]
Ice cloud properties
ln[r e (μm)]
For liquid clouds, P flz < P top < 0.96P sfc, T a = 5 °C
For ice clouds, 0.9P trp < P top < P mlt, T a = –55 °C
where P a is a priori CTP, and P min and P max are the lower and upper limits of CTP, respectively, determined as previously mentioned.
Measurement and model errors
Observations and models may have bias and noise-like error components arising from various error sources. Model errors include (1) error due to radiative transfer approximations, (2) errors from the representation of atmosphere with a finite number of atmospheric layers, (3) errors in the sea or land surface emissivity, (4) uncertainty in atmospheric temperature and gas concentration profiles, (5) error from assuming the cloud base pressure, (6) uncertainty of the ice habit model and particle size distribution, and (7) error from the vertical and horizontal heterogeneity of the clouds. Each error component may depend on the state of the atmosphere and the background surface, which make it complicated to quantify the error covariance matrix appropriately.
Simple assumptions can be made about several error components. The RMSE of sea surface temperature is assumed as 0.7 K in the inversion by considering daily and diurnal variations in sea surface temperature and possible differences between clear-sky and cloudy cases. According to the observations of Newman et al. (2005), the RMSE of sea surface emissivity due to the uncertainty of seawater optical constants is estimated to be approximately 0.001 at satellite zenith angles of less than 60 °. Over land, the surface temperature and emissivity in cloudy cases are likely to differ significantly from those in clear-sky cases, although the magnitude is uncertain. The RMSE of land surface temperature is assumed as 3 K in this study, although precise quantification is required in the future. BFED land surface emissivity product (Seemann et al. 2008) is created by using the MODIS land surface emissivity product. The error covariance matrix of the land surface emissivity is constructed considering the MODIS product error and the BFED modeling error documented in the literature.
The right-hand side contains the errors from radiative transfer approximation, S e,RTM, atmospheric profile uncertainty, S e,atm, and measurement noise, S e,noise. S e,RTM is small, as previously described.
Because not all error sources are included in Eq. (13), initial tests show that the model does not fit the measurements well if Eq. (13) is used directly in the cloud property inversion. The uncertainty due to the horizontal and vertical heterogeneity in clouds and the uncertainty in the optical properties of ice particles from the ice habit model are not included in Eq. (13). These uncertainties are difficult to quantify; however, based on by trial and error, we artificially set the diagonal elements of the error covariance matrix obtained from Eq. (13) as 20 % larger.
Results and discussion
Retrieval error evaluation by simulations
The errors and performance of cloud retrieval are tested by retrieval simulations. Measurement signals with errors are simulated by the forward model calculations for perturbed atmospheric and surface states with random noise that obey the error covariance matrices assumed above. Retrieval errors are evaluated by comparing the retrieved cloud properties from the noise-superimposed measurement signals with the initial values. This methodology is identical to that used by Iwabuchi et al. (2014). For each state, a series of 1000 retrieval simulations are performed to evaluate the mean bias error and the RMSE. The satellite viewing zenith angle ranges from 0 ° to 60 °, and a tropical atmosphere is assumed with a sea surface temperature of 300 K.
Application to tropical cloud systems
Figure 8 shows that the radar–lidar product detects many pixels with a high cloud top. The upper clouds cover wide areas, and parts of the left and right sides of the figures are covered with thick clouds. Middle-level clouds are present in the middle of the figures. The MERRA atmospheric profile shows that the CTT of the middle cloud is about –20 °C. The upper part of the high clouds probably consists of small ice particles and it can be detected only by lidar (green). The CTH obtained from ICAS tends to be lower than that of the radar–lidar product and close to the cloud top detected by cloud radar (blue and yellow). The top height of ICAS varies from 5 to 17 km, whereas the radar–lidar product has a more uniform top height with an altitude of around 15 km. Similar to the ICAS cloud top, the cloud top detected by radar is more variable than the cloud top detected by lidar. This is an expected limitation of ICAS because previous studies have shown that IR measurements are not sensitive to very optically thin clouds, which can be sensed only by lidar and not by radar (Watts et al. 2011). ICAS detects more pixels with a cloud top above 15 km compared with radar–lidar products. Some pixels correspond to CTHs that are higher than the lidar measurements (around region C). This is probably an erroneous retrieval because the ICAS results are influenced primarily by the uncertainty of the atmospheric profile, and possibly by the ice habit assumption and vertical inhomogeneity within the cloud, yielding an ICAS cloud top near the tropopause that is too high compared with the lidar measurement. Red crosses in Fig. 8c denote the cloud top of the lower cloud of the double-layer cloud retrieval in ICAS. Several parts of the second layer top in ICAS match the cloud top of the third cloud layer in the radar–lidar profile, although there are parts that deviate greatly. The cloud tops of the upper cloud layer in double-layer cases are well estimated, similar to single-layer cloud cases. ICAS misses most multilayer clouds at longitudes of 146.35 °–146.45 ° (region A), where the upper first and second cloud layers are detected only by lidar. ICAS wrongly identified these pixels as single-layer cloud and retrieved CTHs between the first and second cloud layers. A similar problem occurs at longitudes of 146.1 °–146.2 ° (region B). In these cases, the uppermost cloud is too optically thin, and ICAS cannot identify the upper cloud in a multilayer cloud system, probably because the retrieval with the single-layer cloud assumption has an optimal solution with clouds at the wrong height. These results suggest that the algorithm requires re-examination and improvement.
An optimal estimation-based cloud retrieval algorithm has been developed to estimate the optical and physical properties of clouds simultaneously from measurements of several TIR bands. A major source of modeling errors is uncertainties in atmospheric profiles, which are usually difficult to quantify. In this study, they are assessed by direct comparison of the clear-sky observations over the ocean with the model calculations. This type of model-measurement comparison is important for developing cloud retrieval algorithms. A feature of the present algorithm is that the COT and the CTH is retrieved well for optically thin clouds by simultaneously fitting the model to the measurement in multiple TIR bands. Although the cloud top inferred from TIR measurement fluctuates with the cloud top from the cloud radar profile, the topmost parts of clouds seen only in the lidar profile are not detected well by TIR measurements. Compared with MODIS C6 operational products, COT of less than 5 agrees well, although CER deviates greatly. CTH estimates agree well for optically thick clouds when the MODIS product is based on the CO2 slicing method, whereas there is significant disagreement in CTHs between the present study and C6 products for optically thin clouds at the cloud edges. In the present algorithm, the determination of the cloud thermodynamic phase is strongly constrained by a priori knowledge about cloud phase dependence on the CTTs. It guarantees that ice clouds that are too warm and water clouds that are too cold are not retrieved; however, more statistical verification of the temperature dependence should be performed by increasing the number of cases.
The present algorithm will be used in studies with observations from the Himawari-8 satellite, a Japanese next-generation geostationary meteorological satellite, which has been operated by the Japan Meteorological Agency since 7 July 2015 and carries a visible-to-IR imager with greatly improved radiometric, spectral, spatial, and temporal resolution (Bessho et al. 2016). The development strategy used in this study will be used to create an algorithm for Himawari-8. The algorithm will have several modifications to accommodate the different spectral bands and will have improvements to the multilayer cloud retrieval and cloud phase discrimination. CALIPSO lidar measurements are suitable for retrieving optically thin cloud and reliable cloud phase discrimination (Hu et al. 2009). Using depolarization lidar comparison on a global scale, would help determine the performance of the TIR-based algorithm. In the future, further comparison of collocated data from different cloud products will be performed to characterize respective strengths and limitations of different methods.
Baseline-fit emissivity database
Brightness temperature difference
Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation
Cloud-particle effective radius
Cloud optical thickness
Degree of freedom for signal
Integrated Cloud Analysis System
Mean bias error
Moderate resolution imaging spectroradiometer
The authors are grateful to Prof. Hajime Okamoto of Kyushu University, Japan, for providing the cloud mask data made from CloudSat/CALIPSO data and Dr. Shuichiro Katagiri of Kyushu University, Japan, for the valuable comments during this study.
The MODIS data were obtained from the NASA websites.
This work was promoted and supported by Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Number 25287117.
Availability of data and materials
Data will not be shared because the main results of this paper are development of cloud retrieval technique and described fully in this paper.
HI proposed the topic, conceived and designed the study, and conducted major parts of the study. M. Saito collaborated with the corresponding author in the development of the inversion module and carried out the evaluations of forward model and retrieval errors. YT collaborated with the corresponding author in the development and evaluation of the forward model and carried out the analysis using the MODIS data. NSP carried out the comparison analysis using CloudSat/CALIPSO product data. M. Sekiguchi developed the CKD model. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
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