A Validation of the Multivariate and Minimum Residual Method for Cloud Retrieval Using Radiance from Multiple Satellites

Cloud parameters, such as cloud top pressure and effective cloud fraction, are useful for cloud initialization in numerical weather prediction (NWP) (e.g., Wu and Smith, 1992; Bayler et al., 2000; Hu et al., 2006). Since clouds vary considerably in their horizontal and vertical extent due to the circulation pattern of the atmosphere and the distribution of oceans and continents, it is crucial to develop a fast and efficient algorithm to estimate real-time cloud information in NWP studies (Aulignè et al., 2011) to achieve fresh cloud analysis products.

Modern polar orbiting and geostationary satellites orbiting Earth provide continuous flows of data with a high spectral resolution and a full geographical coverage. Measurement of cloud properties from satellites can supplement surface observations and in-situ studies by detecting cloud properties globally with larger temporal and spatial scales (Rossow et al., 1993). The International Satellite Cloud Climatology Project (ISCCP) (Rossow and Schiffer, 1991) has developed cloud detection schemes using visible and infrared window radiances. The ISCCP comprises polar and geostationary satellite data, providing a fundamental, reference dataset of global cloud properties for many years. However, the ISCCP data are usually not real-time and not related to physical changes in the atmosphere (Evan et al., 2007). (Chahine, 1975) proposed a method based on the principle of minimization of the root-mean-square difference between observed and calculated radiances to determine cloud top height and cloud amount. Similarly, the CO₂ slicing technique directly employs radiance observations with or without other prior information (Smith et al., 1974; Menzel et al., 1983; Smith and Frey, 1990) to obtain cloud parameters by comparing cloudy and clear radiances in the CO₂ emission band. The Minimum Local Emissivity Variance (MLEV) method (Huang et al., 2004) calculates local variances of spectral cloud emissivity for a number of first-guess cloud pressure levels and finds the optimal solution for the single-layer cloud emissivity spectrum. Encouraged by the merits of variational methods for retrieving cloud parameters (Eyre and Menzel, 1989; Li et al., 2004), a new cloud retrieval and detection method, the Multivariate Minimum Residual (MMR) algorithm, has been introduced and preliminarily validated (Aulignè, 2014a; 2014b).

The MMR approach differs from other cloud retrieval schemes in several aspects: (2) It can retrieve both cloud masks (with cloudy/clear binary information) and multi-layer clouds for each field-of-view, instead of solely providing cloud mask information, as is the case for the approach at the US National Oceanic and Atmospheric Administration's (NOAA) Satellite and Information Service (NESDIS) (Goldberg et al., 2003), or single-layer clouds as in other studies (e.g., Pavelin et al., 2008; McNally, 2009); (3) It is feasible to obtain cloud profiles using the MMR scheme on any grid network with a host model, usually with which the background field is obtained and on which grid the MMR scheme is conducted using a radiative transfer model; (4) The MMR algorithm is efficient and simple to run, which is particularly suitable for real-time NWP application. The observed radiance and background field are two major inputs for the MMR scheme, without the need for other prior information [e.g. the channels' peak heights (McNally and Watts, 2003)], or the simultaneous availability of sources from independent imagers [Moderate Resolution Imaging Spectroradiometer (MODIS), Advanced Very High Resolution Radiometer (AVHRR), Advanced Infrared Sounder (AIRS)-Visible/Near Infrared (VisNIR)]; (5) The MMR scheme can make synergistic use of any satellite radiance observations with infrared channels available, which makes retrieving clouds in real-time possible for both regional and global domains.

(Aulignè, 2014b) conducted a pilot validation of the MMR scheme based on AIRS, and found it to be comparable to the cloud detection method of (McNally and Watts, 2003) in terms of the identification of cloud-free channels, instead of discarding the whole pixel when the cloud is detected. The cloud liquid water and ice mixing ratios retrieved from MMR cloud fractions using AIRS observations improved the first-guess hydrometer fields for the data assimilation (Aulignè, 2014b) with the semi-empirical method of (Hu et al., 2006). In (Aulignè, 2014b), the use of an MMR cloudy radiance operator to assimilate cloudy radiances was applied to AIRS observations for preliminary testing purposes.

As independent output cloud information from the MMR scheme is directly related to the input radiance according to the channel numbers, it is especially interesting to examine the MMR cloud retrieval algorithm in the use of more satellite sensors, even with smaller channel numbers. In this study, the MMR algorithm of Aulignè (2014a, 2014b) is assessed and validated using radiances from various satellites in terms of retrieving 3D cloud fractions on each model level of the host model for each pixel. The MMR algorithm, as a cloudy radiance operator for multiple sources of radiance observations, is also further validated.

This paper is arranged as follows. A brief description of the MMR algorithm is provided in the following section. Section 3 describes the radiance observations, the background model with its data assimilation system, and the radiative transfer models (RTMs) used in this study. Experiments designed to account for the variety of cloudy characteristics are also illustrated in section 3. Section 4 examines the robustness of the MMR algorithm by comparing the cloud retrievals with other cloud products and among instruments. A validation of the MMR algorithm as a cloudy radiance operator, and sensitivity tests with different RTMs, are provided in section 5. Conclusions and future work are outlined in section 6.

Figure 1.  (a) Schematic representation of cloud retrievals on model levels for one pixel, where c=c₁,c₂,…,c_n is the array of vertical cloud fractions for n model levels and c₀ is the fraction of clear sky. The gap distance (units: km) between two neighboring pixels as a function of scan positions with different fields of view for (b) AIRS and (c) IASI, in which the scan indices 45 and 30 are nadir points for AIRS and IASI respectively.

The MMR scheme (Aulignè, 2007; 2014a; 2014b) is an approach towards retrieving cloud fractions and cloud top pressures. The modeled R_{Ν_ c} is calculated as \begin{equation} \label{eq1} R_{\nu_{ c}}(c_0,c_1,c_2,\ldots,c_{n})=c_0 R_{\nu_{ r}}+\sum_{k=1}^n{c_kR_{\nu_{k}}} ,(1) \end{equation} with $$ \left\{ \begin{array}{l} 0\le c_k \le 1, \forall k\in [0,k] \\[1mm] \displaystyle c_0 +\sum\limits_{k=1}^n {c_k =1}, \end{array} \right. $$ where R_{Ν_k} is the radiance calculated assuming the existence of an overcast black cloud at the model level k of the host model, with which the MMR algorithm is conducted, and R_{Ν_ r} is the radiance calculated under clear sky conditions by the RTM from the model first guess at wavenumber Ν. Here, the vector c=c₁,c₂,…,c_n is the array of vertical cloud fractions for n model levels, and c₀ is the fraction of clear sky. Figure 1a shows the schematic for one pixel. A cloud with a given fraction on one model level is considered to block the radiation from its lower levels. The radiation originating from the lower levels contributes to the observation from satellites only with the residual fractions on the current level. Hence, there are no overlap cloud issues in the MMR framework. The MMR scheme retrieves the cloud fraction c_k for each model vertical level k by minimizing a cost function, \begin{equation} \label{eq2} J(c_0,{c})=\dfrac{1}{2}\sum_\nu{[R_{\nu_{ c}}-R_{\nu_{ o}}]}^2 , (2)\end{equation} where R_{Ν_ o} is the observed radiance at wavenumber Ν. The algorithm, N2QN1 (double-precision constrained version of the minimization routine, M1QN3), developed by (Gilbert and Lemarèchal, 1989) at the National Institute for Research in Computer Science and Control (INRIA), France, is used in constrained minimization by forcing the cloud fractions c=c₁,c₂,…,c_n and c₀ between 0 and 1. The output c=c₁,c₂,…,c_n relies heavily on the independent input radiance information from different channels. Thus, the MMR scheme is especially suitable for hyperspectral infrared sounders. As Eq. (3) minimizes the residual between observed and modeled radiances, the Planck function makes it difficult to compare radiance at different frequencies. In this study, we normalize the residuals by the clear radiance calculated by the RTM as \begin{equation} \label{eq3} J(c_0,{c})=\dfrac{1}{2}\sum_v\left[\dfrac{R_{\nu_{ c}}-R_{\nu_{ o}}}{R_{\nu_{ r}}}\right]^2 . (3)\end{equation} The training of the cloud retrieval scheme consists of finding c=c₁,c₂,…,c_n that allows the best fit between the cloudy radiances and the observations. Apart from the cloud fractions retrieved directly by the algorithm, the cloud top pressures can also be derived. The cloud top level k_ top is an indirect diagnostic of the MMR scheme, which is also used in this study for validation. k_ top is searched and determined as the last vertical level from surface to top, at which the retrieved cloud fraction is larger than 1%, i.e., \begin{equation} \label{eq4} c_{k_{ top}}>0.01. (4)\end{equation} The model output for pressure on the level k_ top is then used to determine the cloud top pressure.

Satellite radiances used in this study include those from MODIS, AIRS, the Infrared Atmospheric Sounding Interferometer (IASI), the Geostationary Operational Environmental Satellites (GOES) Sounder, and the GOES Imager. These measurements include radiances from visible, near-infrared, and infrared spectral regions with high-spectral resolutions and are available at spatial scales of a few hundred meters to a few tens of kilometers. Table 1 shows the instruments' native resolutions, swath widths, and channels used. The twice-daily temporal resolution from polar orbiters and continuous flow of observations from geostationary satellites make these instruments well suited for the comprehensive study of some significant weather events. It is interesting to conduct intercomparisons among cloud retrievals from these instruments.

MODIS, onboard the National Aeronautics and Space Administration (NASA) Earth Observing System (EOS) Terra or Aqua satellites, provides multi-spectral broadband measurements and cloud products (details available at http://modis.gsfc.nasa.gov/). It scans radiances in 36 spectral bands (ranging in wavelength from 0.4 μm to 14.4 μm) from an orbital altitude of 705 km with a rather high spatial resolution (∼1 km).

IASI is a high-spectral-resolution infrared sounder onboard the Meteorological Operation (MetOp) series of European meteorological polar-orbiting satellites (Blumstein et al., 2004). It measures the radiances emitted from Earth in 8461 channels, covering the spectral interval 645-2760 cm^-1 (wavelength from 3.62 μm to 15.5 μm) at a spectral resolution of 0.5 cm^-1 (apodized). There are 30 viewing positions on the measurement track, spaced by approximately 3.3 degrees, symmetrical to the nadir. In this study, we use a subset of 616 channels, which were pre-selected by the National Centers for Environmental Prediction (NCEP) from all 8461 channels in MetOp-A IASI radiances.

AIRS, onboard Aqua (Aumann et al., 2003), has similar spectral and spatial coverage and resolution to IASI. However, it is a grating spectrometer rather than an interferometer with 90 ground footprints along its cross track. It measures Earth's outgoing radiation at 0.4 to 1.0 μm and 3.7 to 15.4 μm. For the purpose of this study, we constructed a subset of 281 channels (pre-selected by NCEP) out of all 2378 channels.

Although at a lower spectral resolution, geostationary instruments provide near continuous observations over the observation domain. GOES is part of NOAA's Geostationary Operational Environmental Satellite system (Menzel and Purdom, 1994). The GOES Sounder has 18 thermal infrared bands, plus a low-resolution visible band (19-channel), ranging in wavelength from 3.74 μm to 14.71 μm. Its field of view is 8 km and is sampled every 10 km. In this study, we use GOES-13 Sounder (east) and GOES-15 Sounder (west) to obtain cloud fractions over the continental United States domain.

The GOES-13 Imager used in this study is a five-channel (one visible, four infrared) imaging radiometer designed to sense radiant and solar reflected energy. The central wavelengths for channels 1-5 are 0.62, 3.9, 6.5, 10.6, and 13.3 μm, respectively.

Figure 2.  (a) The cloud mask from the GOES 13/15 retrieval valid at 1900 UTC 3 June 2012, in which the blue color represents the cloudy area and the white color represents the clear area. The integrated cloud mask (units: %) over one column obtained from individual sensors using the MMR scheme for (b) AIRS, (c) GOES-Sounder, (d) IASI, (e) MODIS, and (f) GOES-Imager valid at 1900 UTC 3 June 2012.

Figure 3.  The N _f, N _m, and N _h locations for individual sensors for (a) AIRS, (b) GOES-Sounder, (c) IASI, (d) MODIS, and (e) GOES-Imager valid at 1900 UTC 3 June 2012.

The Weather Research and Forecasting (WRF) model (Skamarock et al., 2008) was used in this study as the host model. The cloud retrieval, observation preprocessing, and quality control procedures were essentially incorporated into the framework of WRF data assimilation (WRFDA) system (Barker et al., 2012), when modeling the cloud fractions. The Community Radiative Transfer Model (CRTM) (Han et al., 2006; Liu and Weng, 2006) and the RTM for NOAA's TIROS (Television Infrared Observation Satellite) Operational Vertical Sounder (RTTOV) (Eyre, 1991; Saunders et al., 1999) were used as the radiance forward operator for computing the clear-sky radiance and the radiance given overcast clouds at each model level.

A regional domain over continental United States was used with various cloud types. The domain for experiments had a 15 km grid spacing on a 415× 325 horizontal grid in longitude and latitude respectively and 40 vertical levels with the model top at 50 hPa. The MMR scheme searched the cloud top using approximately 130 hPa as the highest extent in this study. Channels in the longwave CO₂ band were used in the MMR algorithm, as the CRTM can provide a satisfactory simulation of the temperature-sensitive channels with the background from the WRF model (Xu et al., 2013).

This paper presents cloud retrieval experiments for 24 independent hours from 0000 UTC to 2300 UTC 3 June 2012 from various satellite sensors. Figures 1b and c show the gap distance between two neighboring pixels as a function of scan positions with different fields of view for AIRS and IASI. The indices 45 and 30 stand for the nadir points for AIRS and IASI respectively. For each satellite pixel, the cloud fractions were extrapolated to the four vicinal model grid points. Gaps between two pixels along the measurement line for AIRS and IASI are relatively large, especially for pixels with large scan angles (Fig. 1). For example, for pixels on the edge (with large fields of view), the gap is more than 35 km. Thus, we conducted extrapolations (gap filling) for the cloud fractions representative for one pixel with an adaptive radius corresponding to the scan angles. The adaptive radius for each pixel was consistent with the actual distance between its two neighboring pixels along the scan track (from nadir to swath edge). It was found that cloud retrievals using the extrapolation scheme with scan angle-dependent radius were better than those without extrapolations or with extrapolations using a fixed radius for pixels off-nadir, with errors well below formal uncertainty. The MMR algorithm retrieved cloud fractions on each pixel for each sensor independently and sequentially. For example, the MMR scheme processed radiances from EOS-aqua after retrieving clouds with radiances from EOS-terra (AM). For the overlapping region, the cloud fractions from EOS-aqua (PM) would overwrite those from EOS-terra. A similar extrapolation was conducted for AIRS, but only for the first four pixels close to the edges of the scan line. Sensitivity experiments, similar to the above experiments but using RTTOV, were conducted to evaluate the robustness of the MMR scheme in terms of using different RTMs.

Figure 4.  (a) Equitable threat scores and (b) BIAS scores for the grid points, in which both GOES retrievals and MMR cloud retrievals are available based on the results from 0000 UTC 3 June 2012 to 2300 UTC 3 June 2012.

In this section, to compare the cloud mask retrieved from different sensors for all the tested hours, a large and uniform coverage of cloud mask was required. In this study, we chose the GOES imager as a reference to validate the MMR method for the continental United States domain. In addition, the MMR-retrieved cloud products were compared to existing cloud products from independent platforms, such as CloudSat (Stephens et al., 2002) and EOS-Aqua (MODIS) (Platnick et al., 2003) to verify the retrievals from the MMR scheme. Although these references are not the "truth", they serve as guidelines to see how much agreement there is among retrievals from different radiance observations. Validations and comparisons were conducted on the model grid for future NWP applications. We present the equitable threat scores (ETS) and bias scores for both the retrieved cloud mask and cloud top pressures, which are defined as follows (Schaefer, 1990): $$ { ETS}=\dfrac{N_{ h}-N_{ r}}{N_{ h}+N_{ m}+N_{ f}-N_{ r}} , $$ with $$ N_{ r}=\dfrac{(N_{ h}+N_{ m})(N_{ h}+N_{ f})}{N_{ t}} , $$ and $$ { BIAS}=\dfrac{N_{ h}+N_{ f}}{N_{ h}+N_{ m}} , $$ where N _t is the number of samples for verification, N _h is the number of samples of both the reference and MMR retrievals meeting or exceeding the threshold, N _m is the number of samples of the reference only meeting or exceeding the threshold, N _f is the number of samples of the MMR retrieval only meeting or exceeding the threshold. ETS scores range from -1/3 to 1, where 0 indicates no skill and 1 is a perfect score. Bias scores indicate whether the retrieval system has a tendency to underestimate (BIAS<1) or overestimate (BIAS>1) events.

Figure 5.  Scatter plots of MMR cloud retrieved versus MODIS Level 6 cloud top pressures (units: hPa) from (a) AIRS, (b) MODIS at 0800 UTC, (c) AIRS, (d) MODIS at 0900 UTC, (e) AIRS, and (f) MODIS at 1100 UTC. Regression lines (blue lines) with their regression equations are also denoted.

We define the MMR-retrieved cloud mask as the integrated cloud fractions on each model level over the whole column (by summing c₁+c₂+…+c_n) for each pixel. Figure 2 shows the cloud masks obtained from five sensors (AIRS, MODIS, IASI, GOES-Sounder, and GOES-Imager) at 1900 UTC with the MMR scheme, and the cloud mask products from GOES 13 and GOES 15. Generally, the cloud masks from all the sensors matched well with the cloud mask from the GOES retrieval. We found good spatial agreement within a single instrument, although the cloud fraction on each pixel was estimated independently. The total cloud fractions from AIRS were slightly larger than those from MODIS (e.g., the areas in the vicinity of the black circle in Figs. 2b and e), indicating that there was relatively larger contrast between the clear-sky radiances and observed radiances from AIRS than that from MODIS. The combination of the cloud mask from EOS-aqua and EOS-terra (Fig. 2e) showed close agreement with the reference in Fig. 2a. We did not see any obvious gap or discontinuity where radiances from the two sensors overlapped. The cloud mask from IASI radiances agreed well with the imagery, albeit with some discontinuities due to the relatively low spatial resolution at the edge (e.g., the areas in the vicinity of the black circle in Fig. 2d). The cloud mask with the GOES-Imager matched the reference very well, providing a near full coverage (Fig. 2f). With higher spatial resolutions, fewer gaps of the cloud fraction fields of the GOES-Imager and MODIS were filled compared to those from IASI radiances. The cloud fractions from the GOES-Sounder were also comparable to those from other sensors.

Figure 3 shows the N _h, N _f and N _m locations for the five sensors at 1900 UTC with GOES retrieval products as reference. We masked the reference field as cloudy when there was a record of a cloud mask in the GOES retrieval products, and we masked the MMR retrieved output as cloudy when the total cloud fractions of one column was larger than zero. Both the reference fields and MMR-retrieved fields were interpolated to the same 0.1^°× 0.1^° grid with a binary mask (0 for clear and 1 for cloudy), before we conducted the comparison for verification. Note that the MMR cloud mask retrieval hit the GOES retrieval products for most of the cases for these sensors. MMR slightly underestimated the cloud mask from IASI and MODIS, while the MMR scheme produced better cloud mask retrievals from the GOES-Imager, GOES-Sounder, and AIRS. There is a large area off the coast of California with missing clouds in Figs. 3c and d. We found that these were low-level clouds (∼950 hPa), which frequently occur in this area (not shown), indicating that very low clouds are poorly detected by the MMR scheme.

Figure 4 shows the ETS and bias scores based on the results from 0000 UTC to 2300 UTC. The MMR scheme yielded the highest scores with the GOES-Imager data, but overestimated the cloud mask with the largest bias scores. The MMR scheme also produced high ETS scores with the GOES-Sounder data, with overall least bias. The MMR scheme provided better consistency between the cloud mask with the reference data with AIRS than with MODIS and IASI. Consistent with Fig. 3, the MMR scheme underestimated the cloud mask with MODIS and IASI.

The scatter plots of the MMR-retrieved cloud top pressures from AIRS and MODIS radiances against the MODIS MYD06 cloud top pressures (http://modis-atmos.gsfc.nasa.gov/MOD06_L2/) are illustrated in Fig. 5. Three sub-periods of the MYD06 cloud retrieval products were chosen to approximate the validation time (0800 UTC in Figs. 5a and b; 0900 UTC in Figs. 5c and d; and 1100 UTC in Figs. 5e and f). Results from other examples during daytime hours were similar (not shown). The MMR scheme seems robust in retrieving the cloud top pressures from AIRS and MODIS, with correlation greater than 0.7 for most cases. Using AIRS data, the statistics showed much better agreement with the MYD06 cloud retrieval products, with high correlations of greater than 0.8. An overestimation of cloud height from MODIS was observed, especially for 0800 UTC and 0900 UTC. In Figs. 5b and d, there are two groups of horizontally aligned points. This is because the MMR scheme searches the cloud top using approximately 130 hPa as the highest extent. The cloud top pressures for those extremely high clouds were all marked as approximately 130 hPa. These results on cloud top pressures are not surprising, because the accuracy in retrieving cloud top pressures and cloud profiles decreases with fewer channels from observations. For MODIS data, the less information in the observations of retrieving the cloud profile, the more the under-determined the problem becomes.

Figure 6 presents the ETS scores of the cloud top pressure from 0000 UTC to 2300 UTC for the thresholds of 300, 500, 700, 850, and 950 hPa. The reference cloud top pressure fields from GOES retrievals and the MMR cloud top pressure outputs were both interpolated to the same model grid. When the model-retrieved and reference cloud top pressures were both lower than the given threshold, we defined a hit event. When only the model-retrieved cloud top pressures were lower than the given threshold, we defined a false alarm event. A miss event happened when the model-retrieved cloud top pressure was higher than the threshold, while the reference cloud pressure was lower than the threshold. Overall, mid-level clouds (700 and 850 hPa) were better detected than higher clouds (300 and 500 hPa), indicating that for high clouds (existing as ice-clouds), the hypothesis of an effective emissivity (i.e., the cloud emissivity multiplied by the cloud fraction) is inaccurate. Low clouds (e.g., 950 hPa) were poorly detected by most sensors, which is consistent with the theoretical demonstration of (Aulignè, 2014a) in which the low clouds are less represented in the set of leading eigenvectors of the cloud fraction analysis error. The MMR scheme obtained the highest scores for most of the thresholds from AIRS and IASI. It showed better agreement using AIRS in detecting the cloud height than using MODIS with the GOES reference retrieval. It was also noticeable that the ETS scores for the GOES-Imager were better than or comparable with those from MODIS. Even with fewer channels from observations, the MMR solution was an "overly smoothed" estimation of the true vertical profile, starting from a uniform clear prior guess.

Figure 6.  Equitable threat scores for the thresholds of 950, 850, 700, 500, and 300 hPa on the grid points, in which both GOES retrievals and MMR cloud retrievals are available from 0000 UTC 3 June 2012 to 2300 UTC 3 June 2012.

The cloud fractions from AIRS and MODIS were compared to CloudSat data. CloudSat is an experimental satellite that uses radar to observe clouds and precipitation from space. CloudSat provided the first global survey of cloud profiles and cloud physical properties and measures the vertical structure of clouds and precipitation from space primarily through 94 GHz radar reflectivity measurements. An orbit of CloudSat consists of approximately 39 400 profiles.

Figure 7 shows the standard radar reflectivity profiles from the "2B-GEOPROF" products (Mace, 2004) and cloud fraction cross sections along the CloudSat orbit tracks for 0800 UTC, 0900 UTC, and 1100 UTC. The cloud distributions and thickness from AIRS and MODIS were in good agreement with the radar reflectivity for the cross sections. The cloud fractions from AIRS were slightly larger than those from MODIS at 0900 UTC, which can also be seen in Fig. 2. Cloud fractions from AIRS were much closer to the reference than those from MODIS in terms of obtaining the cloud height, because the MMR scheme overestimated the cloud top height from MODIS for most cases (Figs. 7c, f, and i). This is consistent with the results of (Li et al., 2005), when using MODIS and AIRS in a one-dimensional variational retrieval method. With rather high spatial resolution, the cloud mask from the MMR scheme from MODIS showed better agreement with the reference. The MMR scheme failed to identify some clear scenes between two clouds for some cases from AIRS (e.g., the clear scenes in the black circles in Figs. 7d-f). The correlation coefficients between the CloudSat products and the MMR cloud retrievals and the ETSs are also given in Table 2. Model retrievals were interpolated to the reference fields. We marked the fields with 0 for clear and 1 for cloudy before conducting the statistical comparison. Since a very small drift of clouds patterns or height in the MMR outputs away from what CloudSat observed could cause large bias in the statistics, the correlations between the cloud patterns from CloudSat and those from the MMR outputs were not low, relatively. Nevertheless, the MMR scheme has shown some meaningful skill in detecting cloud profiles. Generally, the accuracy of the MMR scheme in detecting mid-level clouds (e. g., 3 and 5.5 km) was found to be higher than detecting higher or lower clouds (9 and 2.5 km respectively). The cloud profiles from the MMR scheme with AIRS radiances agreed better with the CloudSat cloud profiles in most cases.

Figure 7.  The radar reflectivity (units: dBZ) cross sections from CloudSat (left panels), the MMR retrieved cloud fractions (units: %) cross sections obtained from AIRS (center panels), and MODIS (right panels) along the Aqua path nadir: (a-c) valid at 0800 UTC 3 June 2012; (d-f) valid at 0900 UTC 3 June 2012; and (g-i) valid at 1100 UTC 3 June 2012.

Figure 8.  Observed and CRTM-calculated brightness temperature (units: K) for channel 267 (wavelength: around 13.774 μm) over land (a) without the MMR scheme and (b) with the MMR scheme for AIRS; and (c) without the MMR scheme and (d) with the MMR scheme for MODIS, valid at 0900 UTC 3 June 2012.

Evidence shows that cloud indicates the occurrence of dynamically important weather. Thus, areas known to be important in the development of forecast errors in NWP are often cloudy (McNally and Watts, 2003). The adoption of cloudy radiance can allow for a much better use of available data and avoid discarding potentially helpful information. Equation (2) can be used as a cloudy radiance operator with the cloud fractions to be derived. The resulting cloudy radiances R_{Ν_ c} are simulated by linearly combing the clear-sky calculated radiance R_{Ν _ r} and the array of radiance R_{Ν _k} calculated assuming the existence of an overcast black cloud at the model level k by the RTM. As a linear operator, the MMR scheme is relatively inexpensive and less dependent on background hydrometeors.

Figure 8 shows the observed and CRTM-calculated brightness temperature (T _b) for channel 267 (wavelength: around 13.774 μm) over land without (R_{Ν _ r}) and with (R_{Ν _ c}) the MMR scheme for AIRS and MODIS. Clouds are usually colder than the surface (land or water) with a radiative impact, which is usually negative. There were significant warm biases in the CRTM-calculated Tbs without the MMR scheme versus observations (Figs. 8a and c). By simulating the cloud fractions, the MMR scheme corrected the warm bias (simulated T _b minus observed T _b) accordingly, with reduced mean, standard deviation, and root-mean-square error. Indeed, warmer observations (compared to background brightness temperature) existed for pixels over land (with T _b values larger than 270 K in Figs. 8a and c, marked by the black circle), likely corresponding to clear radiances with improper skin temperature or surface emissivity. In those situations, MMR did not change the simulated T _b for these pixels (Figs. 8b and d), indicating that there was no misinterpretation for an error in skin temperature or surface emissivity. Results from other channels produced similar patterns (not shown).

Figure 9a presents the observed minus background radiance departure for IASI for all observations (filled symbols), and clear observations (open symbols) at 0300 UTC 3 June 2012. It can be seen that, for channels sensitive to levels from the lower stratosphere down to the middle troposphere (approximately channel 16 to 300), these departures were very similar. These departures calculated for all observations were slightly larger than those for clear observations, especially for temperature channels sensitive to lower levels (channel 300 to 420). In overcast conditions, sources of large variance, such as surface skin temperature and low-level humidity, were essentially obscured. Departures using the MMR cloudy observation operator have been found to be comparable to the departures under overcast conditions (e.g., McNally, 2009, Fig. 3). Figure 9b presents histograms of observed minus background radiance departure for IASI based on the data in Fig. 9a for all observations and clear observations. We can see that, for both populations with all and clear observations, the departures are quite symmetrical. The MMR scheme collected twice the amount of observations for all observations than for clear observations. Consistent with Fig. 9a, the MMR scheme collected more data with cold departures for the "all observations" population than for the "clear observations" population. Hence, the MMR scheme seems to possess the capability to reproduce the cloud radiance effect for IASI radiance as a fast and linear observation operator.

As the MMR algorithm works by comparing the RTM-calculated radiance with observations, it is interesting to examine the robustness of the MMR algorithm with respect to different RTMs (e.g., CRTM and RTTOV). We conducted sensitivity experiments using RTTOV and CRTM for AIRS and MODIS. Figure 10 shows observation minus simulated radiance departures with and without the MMR scheme based on 25 553 and 102 321 pixels for AIRS and MODIS, respectively, to examine the capability of the scheme in fitting the observations. For AIRS, there were consistently larger differences between the clear-sky and measured radiance (without the MMR scheme) from RTTOV, compared to the differences from CRTM, especially in longwave channels (channel 15-950) (Figs. 10a and b). For MODIS, RTTOV showed a slightly smaller value of departure compared to CRTM for the channels in use (channel 32-36) without the MMR scheme. As expected, we obtained slightly larger magnitudes of cloud fractions for AIRS and smaller magnitudes of cloud fractions for MODIS from RTTOV (not shown). Comparable means and standard deviations of the departures with the MMR scheme were observed using both CRTM and RTTOV.

Figure 9.  (a) Observed minus background radiance departure (units: K) for all observations (filled symbols) and clear observations (open symbols), and (b) histograms of observed minus background radiance departure for IASI for all observations (blue bars) and clear observations (red bars), at 0300 UTC 3 June 2012.

Using both CRTM and RTTOV, the MMR scheme successfully removed large differences between the calculated and observed radiances by the calculation of the cloud fractions variationally, with a bias close to zero for most of the channels and a reduced standard deviation (from ∼10 K to ∼2 K). For AIRS, although the MMR algorithm was applied to individual longwave channels (from approximately channel 15 to channel 950), large reductions of bias for other channels were also noticeable. Large differences were seen for O₃-sensitive channels around 9.6 μm (channel number ∼1000) and shortwave channels (channel number >2000). This is because no O₃ profiles were used in the RTMs in the above calculations, and shortwave channels are usually contaminated by solar spectra during daytime hours.

Similarly, reductions for both the mean and standard deviation of innovations with the MMR scheme for MODIS were also obvious, especially for the channels used in the MMR procedure (channel 32-36) (Figs. 10c and d). As discussed above, the contrast between the clear-sky and observed radiance determines the magnitude of the retrieved cloud fractions. As expected, departures from AIRS were larger, with absolute values close to 9 K for most of the channels in use (channel 15-950), than those from MODIS, with absolute values less than 9 K from channel 32 to 36. This is consistent with the results presented in section 4, in which the MMR scheme yielded slightly larger values of cloud fraction using AIRS than MODIS.

Figure 10.  (a) Mean and (b) standard deviation of observation minus simulated brightness temperature departures (units: K) with and without the MMR scheme for AIRS with 25553 pixels; (c) mean and (d) standard deviation of observation minus simulated radiance departures with and without the MMR scheme for MODIS with 102 321 pixels, using both CRTM and RTTOV at 0900 UTC 3 June 2012.

The MMR cloud retrieval algorithm aims to retrieve both cloud masks and multi-layer clouds for each field-of-view on any grid network with a host model with the aid of an RTM. It is fast and easy to run, since only two inputs are required (observed radiances and the background field). Through synergistic use of multiple satellite radiances with infrared channels available, it is possible to retrieve real-time cloud products for both regional and global domains, which are of high potential value for NWP and other applications.

In this study, radiances from multiple satellites onboard both geostationary and polar-orbiting satellites were used to validate the MMR scheme developed within the WRFDA system. To assess the reliability of this algorithm, intercomparisons of cloud retrievals using the MMR scheme from different sensors were carried out. The MMR cloud retrievals were also compared to other independent cloud products from CloudSat, MODIS, and GOES.

The MMR scheme proved to be robust in retrieving the quantitative cloud mask. Good spatial agreement within a single instrument was found, although the cloud fraction on each pixel was estimated independently. The retrieved cloud properties showed good agreement using radiances from multiple satellites, especially for the vertically integrated cloud mask, for all the sensors used in this study. The algorithm produced realistic cloud top pressures when compared to other cloud products, with an accuracy varying with the sensors' spectral resolutions. The accuracy of the MMR scheme in detecting mid-level clouds was found to be higher than for higher and lower clouds. The accuracy in retrieving cloud top pressures and cloud profiles increased with more channels from observations. Even with fewer channels from observations, the MMR solution was an "overly smoothed" estimation of the true vertical profile, starting from a uniform clear prior guess. Hence, the MMR could be used as a useful tool when diagnosing cloud locations. The cloud locations from the MMR scheme could be converted to improve the model first guess in cloud microphysical parameters, e. g., using the (semi-) empirical method of (Hu et al., 2006).

The retrieval algorithm also showed some meaningful skills in simulating the cloudy radiance as a linear observation operator, discriminating between NWP error and cloud, and reproducing the cloud radiance effect for radiance observations. This linear observation operator is attractive for its high computational efficiency and advantage in simulating multi-layer clouds over other, single-layer only, studies (e.g., Pavelin et al., 2008; McNally, 2009). The retrieval scheme was also found to be robust based on different RTMS (CRTM and RTTOV). The potential for using the MMR operator to assimilate cloudy radiances to improve temperature and moisture fields in cloudy regions (e.g., Pavelin et al., 2008; McNally, 2009), but with multi-layer clouds, will be of great interest to most NWP centers.

Apart from the validation of the MMR scheme for multiple radiances in this study, synergistic use of radiances from multiple sensors is also an important aspect, which will be further investigated in the future. For example, the MMR scheme could be improved by enhancing the horizontal interpolation approaches for AIRS and IASI based on the prior cloud mask from other sensors and/or by adding the cloud fraction background constraint in the MMR minimization procedure. Nowcasting of the 3D cloud fractions via the WRF model in a rapid-update cycling mode is also planned, to improve the short-term forecasting of clouds. The influence of cloudy affected radiances on analyses performed using the MMR cloudy radiance operator is another interesting aspect for future work. Finally, the use of cloud liquid water and ice mixing ratios retrieved from the MMR cloud fractions using multiple radiance resources to pre-process the first guess will be discussed and detailed in a follow-up paper.