1. Introduction
Clouds influence many aspects of atmospheric science. They play a pivotal role in modulating the energy and mass exchange processes of the earth–atmosphere system. Cloud analyses are essential not only for quantitative prescriptions of the global cloud state itself but as an ancillary product for other cloud and land surface retrievals as well. An accurate global, quantitative description of their spatial, radiative, and microphysical properties is an essential component of any comprehensive understanding of global climate and climate change processes. Global numerical weather prediction (NWP) models rely on the remote sensing of important atmospheric attributes such as temperature, water vapor, and winds in data-sparse regions. Proper retrieval of the first two properties relies on accurate prescriptions of cloud cover in satellite imager data, and the third requires the accurate detection and vertical placement of clouds. Satellite-based atmospheric aerosol prescriptions require an a priori cloud analysis to exclude their adverse influence on the retrieval of the radiatively important aerosol optical thickness and particle effective size attributes. Cloud screening is also important for earth surface monitoring applications including retrievals of albedo, vegetation health, and land cover change from space.
A central paradigm of cloud detection models in the remote sensing community is to compare satellite-observed upwelling radiance signatures to those expected for the clear atmosphere, and to infer cloud presence when these differ. For example, the Moderate Resolution Imaging Spectroradiometer (MODIS; see appendix A for a list of key acronyms used in this paper) cloud mask algorithms perform a variety of spectral tests designed to provide a level of confidence that a pixel is clear. Adjustments to satellite radiance observations for the removal of atmospheric attenuation effects reference a precomputed library of band-averaged MODTRAN transmissions that are indexed using NCEP GDAS model output (Platnick et al. 2003; Frey et al. 2008). Stowe et al. (1999) employ a radiative transfer model to generate a set of theoretically expected brightness temperatures in the three infrared Advanced Very High Resolution Radiometer (AVHRR) channels as a function of cloud radiative, optical, and microphysical properties. Observed brightness temperatures are then used as indices into these tables to retrieve the various cloud parameters. The operational GOES-R Advanced Baseline Imager (ABI) cloud mask (ACM) algorithms separate cloudy from clear pixels using model-predicted estimates of the radiative attributes of the clear state and identifying departures from it (Heidinger 2011). The ACM codes make extensive use of NWP fields coupled with the Community Radiative Transfer Model (see Ding et al. 2011), a technique that has been adopted as well at EUMETSAT for the processing of AVHRR data by Dybbroe et al. (2005a,b). In their analysis model, clear-cloud thresholds are adapted to pixel-specific atmospheric, earth surface, and view-illumination geometry conditions using cloud-free radiative transfer model simulations. Statistical techniques are also used in cloud detection models to estimate the radiative characteristics of the clear state. Lyapustin et al. (2008) present a spatial-context approach to prescribing baseline clear-sky conditions using a time series of multispectral MODIS cloud-cleared radiance observations.
The U.S. Air Force (USAF) 557th Weather Wing [formerly the Air Force Weather Agency (AFWA)] maintains and executes a satellite-based global-scale cloud analysis and forecast model whose primary purpose is to provide nowcasting and forecast products for mission planners to assess the influence of clouds on operations, principally in the 0–12-h time domain. Up until February 2016, the Cloud Depiction and Forecast System version 2 (CDFS II) employed a 10-day statistical weighting of the deviation of observed clear-atmosphere infrared brightness temperatures from a surface skin temperature model (Gustafson et al. 1994) to prescribe a priori estimates of the clear-pixel radiance for any given pixel. The starting point for these assessments is the skin (over ocean) or shelter (over land) temperature from an NWP land surface energy balance model. Dynamic adjustments to this initial guess are then made that account for the combined influence of multiple phenomena including sensor-specific bandpass widths and positions, sensor calibration errors, Earth surface emissivity variability, and attenuation by atmospheric gaseous constituents—most notably water vapor and carbon dioxide—that are present in highly variable concentrations. The operational CDFS approach is to account for all these effects collectively using a single statistically based adjustment factor.
As the CDFS global satellite constellation continues to grow (from two primary platforms in 1994 to nine platforms and 41 infrared channels as of this writing), this time series technique has proven itself inherently undesirable for three chief reasons: 1) a two-pass cloud analysis paradigm—costly to maintain and operate in real time—is required for every sensor: one overanalysis mask for cloud clearing (in order to build the clear-scene statistics) and a second for the cloud analysis itself; 2) the radiatively dominant impacts of day-to-day changes in the atmospheric state are usually not well prescribed by quasi-static and empirically set thresholds, especially on global scales; and 3) the technique breaks down when a particular region is cloudy for many days in succession. Elimination of these three limitations compels us to consider the use of a radiative transfer (RT) model in real time that provides a single means by which cloud-free brightness temperatures are made for any given pixel, sensor channel, and Earth location.
This article presents one such implementation for prescribing clear-atmosphere brightness temperatures in CDFS. This concept extends beyond those of the aforementioned community cloud analysis models in its unique ability to optimize compute processing speed while maintaining theoretical accuracy. Furthermore, this approach replaces the cloud model’s reliance on a statistical database of previous clear-sky observations that is difficult and costly to maintain with a repeatable, testable, and accurate radiative transfer modeling paradigm—three attributes that are desirable for any analysis and forecast model. We demonstrate as well that improved modeling of the atmospheric influence on infrared upwelling radiation yields more accurate cloud/no-cloud analysis results.
2. Cloud model description
The 557th Weather Wing is responsible for the production and dissemination of weather products and services in real time and on global scales. Products include comprehensive databases of meteorological observations and forecasts, maintenance of climatological databases, and space weather assessments and forecasts. The primary cloud analysis and forecast model suite is called the Cloud Depiction and Forecast System version 2. The CDFS II comprises three primary models for processing and analyzing meteorological data. 1) Cloud depiction is performed through the analysis of passive radiance observations from a global constellation of environmental satellites, conventional surface observations, and other supporting terrain, geography, and emissivity databases. The cloud depiction models provide a cloud mask and retrievals of the associated cloud attributes including phase, bases and tops, optical thickness, particle effective size, and cloud water path. 2) This multilayer cloud mask initializes two cloud forecast models. The first is a quasi-Lagrangian cloud forecast called Advect Cloud (ADVCLD; Zapotocny 2001), which is an hourly updated trajectory model that uses forecast wind fields of global numerical weather prediction models such as the Global Forecast System (GFS) and the Met Office Unified Model (MetUM) as a basis for cloud motions out to +12 h. The second is called Diagnostic Cloud Forecast (DCF; Norquist 2000), a model output statistics approach for providing diagnostic prescriptions of cloud cover out to +96 h that is updated every 6 h. Cloud predictands (e.g., cloud fraction and base and top heights) are supplied by the CDFS cloud analysis, and the weather variable predictor set contains various cloud and noncloud prognostic forecast fields from GFS and MetUM. 3) Surface skin temperature and shelter temperature analyses and forecasts are prescribed by the land surface energy balance segments of GFS and MetUM. Upper-air profiles also are used to convert retrieved cloud temperatures to pressure and/or geopotential.
a. Practical processing considerations
Similar to its AVHRR, MODIS, and GOES-R counterparts, the CDFS algorithm threshold tests are designed to detect clouds by identifying specific multispectral infrared signatures that differ from a priori quantified clear-atmosphere conditions by some user-prescribed threshold amount (see appendix B for a more detailed summary of the cloud mask model). Thus, the CDFS II algorithms require for all processed pixels an estimate of the observed radiances for cloud-free observation conditions in many infrared sensor bands. Comparable to the previously cited works—and constrained by its unique global, real-time perspective—strategies available to CDFS for characterizing the clear-atmosphere multispectral radiance signature fall into two basic classes: 1) find within a recent time series of satellite images a collocated or nearby clear-sky pixel and prescribe some time-weighted average radiance as being representative of the analysis pixel or 2) simulate with radiative transfer theory the expected clear-atmosphere radiance observations. Each strategy has performance-limiting errors that reduce the validity of downstream cloud analysis and forecast products. The most condemning dilemma of the first option is that identification of a nearby clear-atmosphere pixel requires a priori knowledge of which pixels in the satellite image are cloud filled, which itself is the end product of the analysis and not a prerequisite. Under synoptic-scale cloud conditions, the “nearby” cloud-free pixel is often hundreds of kilometers away. Temperature and water vapor profiles, as well as land surface emissivities and skin temperatures, have characteristic length scales much shorter than this. A significant risk also exists that the automated clear-pixel assessment is incorrect and that contamination of the assumed cloud-free radiance is present as a result of optically thin cirrus or partial cloud cover.
Historically, CDFS II has been implementing the option 1 statistical time series approach (Gustafson et al. 1994). The starting point for the clear-atmosphere assessments is the skin (over ocean) or shelter (over land) temperature from an NWP land surface energy balance model. Dynamic adjustments to this initial guess are then made that account for the combined influence of multiple phenomena including sensor-specific bandpass widths and positions, sensor calibration errors, Earth surface emissivity variability, and attenuation by atmospheric gaseous constituents—most notably water vapor and carbon dioxide—that are present in highly variable concentrations. The operational CDFS approach has been to account for all these effects collectively using a single adjustment factor, obtained by examining quantitatively the statistical nature of a 10-day time series record of the deviation between the first-guess NWP model surface temperature and coincident satellite-observed brightness temperatures for pixels previously classified as cloud free by a separate cloud-clearing analysis. This record is used to characterize the natural variability of the difference between the NWP and satellite-observed temperature values when no cloud is present. Daily statistics for clear regions are assembled as a by-product of a cloud-clearing analysis intentionally designed to err on the side of misclassifying a clear pixel as cloudy, as opposed to vice versa. This requires two passes through the CDFS algorithms: one for cloud detection and a second for cloud clearing. In operational cloud detection mode, the algorithm thresholds are set to provide an optimal analysis with no preference for the over- or underanalysis of clouds. In cloud-clearing mode the thresholds are set with a bias toward overanalysis that helps to ensure all cloud-contaminated pixels are properly identified and screened from influencing the clear-scene statistics.
b. Radiative transfer model requirements
The aforementioned second option requires a radiative transfer model along with a host of radiative and thermodynamic inputs to that model that include atmospheric temperature and water vapor profiles, surface emissivities and skin temperatures, and sensor bandpass response specifications. In such implementations the atmospheric state is most often prescribed by numerical weather prediction model forecast fields, which themselves are subject to error. So for option 2, even though cloud contamination is a nonissue, errors that are due to inaccuracies in the assigned atmospheric conditions will propagate into the cloud analysis. Nonetheless, improvements in NWP accuracy and spatial resolution (e.g., see Bauer et al. 2015; Simmons and Hollingsworth 2002) cause us to consider seriously the RT alternative.
Unlike the GOES-R, AVHRR, and MODIS cloud mask models, a notably unique attribute of CDFS—due to Air Force requirements for real-time cloud retrievals on global scales—is its processing of multispectral imager datasets from the full constellation of international geostationary and polar-orbiting environmental satellites including GOES, Meteosat, Himawari, DMSP, MODIS, TIROS, and MetOp. In CDFS II, the RT-simulated satellite observations must represent the monochromatic radiometric flux integrated over specific band filters of many different sensor channels. As of this writing, modeling of clear-atmosphere radiances must accurately characterize the disparate positions and bandwidths of 41 distinct sensor bandpasses in the infrared alone. Generally speaking, sufficient RT model accuracy is obtained by numerically integrating the monochromatic-radiance/instrument-response product over many, typically several thousand, wavenumber intervals within a single sensor bandpass. At this time, CDFS processes over 11 gigapixels of sensor data in real time each day and a corresponding 39 billion clear-atmosphere thermal radiances. With the advent of GOES-R ABI data and the exploitation of newly available sensor channels, CDFS will soon be processing nearly 20 gigapixels per day with a corresponding need for 119 billion cloud-free radiance calculations. It is easy to envision that a brute force pixel-level implementation of a radiative transfer model runs the risk of imposing a prohibitively heavy burden on the CDFS computing budget.
To meet this challenge, we have adopted the optimal spectral sampling (OSS) fast-forward RT model of Moncet et al. (2008) into the operational CDFS processing stream. Other fast and accurate RT models have been developed for operational processing environments [see Moncet et al. (2008) for a discussion of the various methods]. However, for our application the monochromatic nature of the OSS model provides advantages to CDFS that are not achievable with standard RT band models. Our selection of OSS is not without precedent. OSS was developed specifically to satisfy the theoretical accuracy and computational processing requirements of operational systems. OSS is currently part of the operational Joint Polar Satellite System (JPSS) for both the sounding (Divakarla et al. 2014) and cloud products retrievals (JPSS 2013) and has been chosen as the forward model for the future Meteosat Third Generation (MTG) temperature and water vapor sounding products (Rodriquez et al. 2008).
The OSS model is applicable to the entire range of conditions observed in the global atmosphere: variable gas concentrations for the dominant (e.g., water vapor) and trace (e.g., CO2, O3, NOx, SOx, CH4, and CO) absorption species over the globally expected extent of the layer temperature and pressure variability, and for the full range of cloud optical and thermodynamic conditions (Moncet et al. 2008). Because of the monochromatic basis of the OSS RT model formulation, the theoretical accuracy—relative to a high-resolution training model such as the Line-By-Line Radiative Transfer Model (LBLRTM; Clough et al. 1992, 2005)—is tunable via an automated training algorithm by simply adding nodes (for higher accuracy but with more computational expense) or removing nodes (lower accuracy but less computational expense). Thus, with OSS it is simple to trade uniquely the accuracy needs of a given application with its processing constraints on a given computer system.
In this paper we discuss our OSS implementation strategy in and subsequent benefits to the CDFS II cloud model. For this we invoke the following provisions: 1) the RT simulations are for clear-atmosphere conditions only, 2) water vapor is the only attenuating gas with variable concentrations, and 3) we limit the OSS-based RT to nonscattering simulations of only those infrared sensor bands in the CDFS II constellation. By clear atmosphere, we mean explicitly the radiance that would be observed if there was no cloud present within the field of view, within an atmosphere otherwise well represented by some upper-air thermodynamic profile of pressure, temperature, and water vapor amount. Also, we clarify provision 2 by noting that in the radiance simulations all optically active gases in a spectral band of interest indeed are included in the RT transmittance calculations, prescribing their concentrations as climatological mean (constant) values as functions of pressure and temperature. This is justified because 1) the variability of only a few absorbing gases in infrared window channels, including water vapor, is represented well in the NWP forecast model data, and 2) for the majority of the CDFS infrared channels of interest, water vapor is the dominant absorber. The exceptions are the carbon dioxide channels, which are currently modeled using accepted global mean concentrations, considering that for forecast models the prediction of CO2 local variability remains challenging. We note nonetheless that the OSS implementation is flexible enough to model any number of variably concentrated gases, and an assessment of this need will be a part of future studies.
As of this writing, the full suite of infrared sensor channels whose data are processed in real time by CDFS II comprises 41 distinct bandpasses. This number will increase to 50 with the expected arrival of GOES-R ABI data in the fall of 2016. Water vapor is the primary absorber in all of these channels except for the carbon dioxide channels. Each band falls into one of five major spectral classes: midwavelength infrared (MWIR, 3.6–4.1 μm), water vapor (WV, 6.2–7.9 μm), longwave infrared (LWIR, 8.4–8.7 μm), thermal infrared (TIR, 10–13 μm), and carbon dioxide (CO2, 13.15–13.45 μm). In the following sections, specific band designations always begin with one of these five prefixes and are usually followed by a lowercase suffix (e.g., MWIRa, TIRc) that indicates a subchannel portion of the major spectral class. Table 1 summarizes the CDFS II satellites and their corresponding sensor channels.
Compilation of infrared sensor channels and associated band positions for all satellites in the CDFS II constellation. A channel’s central wavelength (μm) is listed in the table only if it is a component of a particular satellite sensor. See appendix A for a list of acronyms referenced in this paper.
3. Infrared radiative transfer
In the majority of infrared channels used in CDFS II very nearly 100% of the upwelling radiance is an emitted energy flux. The source of these emissions is the earth’s surface and intervening atmosphere, including clouds if present. However, there are a few infrared channels, eight in CDFS II as of this writing, that in the daytime are sensitive as well to incident solar radiance that has been reflected spaceward by clouds and/or the earth’s surface. These bands occupy the MWIR region between approximately 3.5 and 4.1 μm.
A theoretically expected upwelling radiance can be computed using Eqs. (3.1)–(3.3) once the land surface emissivity ϵSFC, the surface skin temperature TSFC, and the atmospheric temperature and transmittance profiles T(τ) and τ are prescribed. Infrared emissivities are obtained from the EOS MODIS climatologies (Wan and Li 1997) for overland pixels, and the emissivity model of Nalli et al. (2008) is used over oceans as a function of satellite view zenith and ocean-surface wind speed. If a particular channel wavelength does not coincide precisely with one of those in the database, the emissivity from the wavelength’s nearest neighbor is selected. All other input variables are obtained from a land surface energy balance model and/or NWP model datasets that are valid at the satellite observation time.
Band-integrated radiances
4. Optimal spectral sampling
Given the processing load burden and the impracticality of using a line-by-line strategy for the clear-sky radiance computations, we are motivated to find a method for computing Eq. (3.5) with the goal of maximizing theoretical accuracy and minimizing N, and in such a way as to be tailored for CDFS user-prescribed accuracy and compute-speed requirements. Optimal spectral sampling (Moncet et al. 2008) is an RT modeling technique that provides a solution to this problem. Before discussion of OSS’s application to our particular need, we first summarize the physical basis for the model.
Consider first the mathematical nature of the wavenumber dependence of ITOA(νn) inside a typical satellite sensor bandpass. Figure 1 contains an example of the structure of the monochromatic ITOA(νn), converted into brightness temperature and plotted here, in one of the Meteosat SEVIRI water vapor channels. Ignore for the moment the vertical dashed lines. This plot was generated using N = 2309 wavenumber intervals that are inside the half-power positions of the SEVIRI 6.3-μm water vapor bandpass, each with spectral width Δν = 0.1 cm−1. The recurring and quasi-cyclic nature of these calculations leads one to wonder whether their mathematical character is at least somewhat repetitive and predictable. In other words, given a brightness temperature at one wavenumber interval is it possible to predict with accuracy the brightness temperatures in many other intervals? If so, this mathematical behavior is repeatable and may be more efficiently quantifiable using some subset of intervals along with an appropriate numerical weighting of some sort.
Sample plot of monochromatic brightness temperatures for a midlatitude, moderately moist atmosphere in the Meteosat Second Generation SEVIRI 6.39-μm water vapor band. Between its bandpass limits of 5.42 and 7.69 μm, this channel contains N = 5437 [see Eq. (3.5)] wavenumber intervals, each of width 0.1 cm−1, and for each of which an average radiance and associated brightness temperature was computed and plotted. The vertical colored lines denote the five node selections {νk}k=1,2, … ,5 [see Eq. (4.1)] for this particular sensor/channel combination. See text for further details.
Citation: Weather and Forecasting 31, 3; 10.1175/WAF-D-15-0077.1
Under these conditions it makes sense to consider, from a purely mathematical perspective, that it may not be necessary to perform the monochromatic calculations hundreds and often several thousands of times whenever a band-averaged radiance estimate 
OSS is well suited for the compute-intensive CDFS application since it not only identifies an optimal subset of K wavenumber intervals {νk}k=1,2, … ,K for some K ≪ N, but also prescribes the corresponding weights for each monochromatic interval or node radiance ITOA(νk). We replaced the least squares fitting approach adopted by Moncet et al. (2008) with a simple stepwise multivariate regression procedure, using this superset of monochromatic radiances {ITOA(νn)}n=1,2,3, … ,N [recall Eq. (3.5)] as explanatory predictors of the band-weighted radiance 
For regression training we used the European Centre for Medium-Range Weather Forecasts (ECMWF) set of 52 profiles that encompass the variations in temperature and water vapor amount expected among global atmospheres (see Matricardi 2009; Chevallier 2002). Starting with the ECMWF profiles, we further expanded the training set to seven satellite-view zenith angles θSAT between 0° and 60°, chosen as being evenly spaced in secant-θSAT space (specifically, 0.0°, 31.0°, 41.4°, 48.2°, 53.1,° 56.9°, and 60°). This range was chosen to coincide with the range of view-zenith angles in the satellite data that are processed by CDFS II. The upper bound of the zenith angle range may be extended out to 70° in the near future as part of a CDFS effort to investigate the impacts of expanding geostationary coverage poleward. For now however, with seven zenith angles for each of 52 profiles, the total number of member profiles in our training dataset is 364.
The profiles are then mapped to the standard 101-level upper-air grid described in Strow et al. (2003). Each profile then serves as input into an RT model that invokes Eq. (3.5) and generates the set of 364 outcome (predictand) radiances 
a. The forward RT model
The number of nodes K and the node locations νk, each selected by the stepwise regression, are driven entirely by the user-prescribed matching accuracy εtol between the radiances obtained using the fast radiative transfer model [Eq. (4.1)] and the more computationally burdensome but highly accurate RT model given by Eq. (3.5). The stepwise wavenumber-interval selection process is terminated as soon as the regression-estimated radiances [Eq. (4.1)] match the true radiances [Eq. (3.5)], for all theoretically expected atmospheric conditions, to within some user-prescribed RMS accuracy, expressed here in terms of kelvins for the emitted thermal radiances 
Once computed, the OSS regression coefficients {ak} and node positions {νk} are fixed for each satellite and sensor combination unless on-orbit sensor degradation is quantified via a response function, when future satellites are launched with a different sensor configuration and/or response functions, or future investigation and experience reveals a need for the fast RT model to have a greater regression-matching accuracy εtol or increased compute speeds. As of this writing the radiances estimated using the fast OSS RT model for CDFS II have been trained to RMS < 0.2 K from truth in the infrared, and an RMS < 0.001 reflectance in the solar MWIR bands.
An example of an OSS training outcome is provided in Fig. 1, which contains a plot of the monochromatic brightness temperatures for the half-power wavelengths of the SEVIRI WVa water vapor channel, along with the associated node selections. Each node is denoted by a vertical, colored dashed line. In this particular instance five nodes were selected out of a possible N = 5437 wavenumber intervals, providing an increase in computational speed of 1087:1.
Table 2 contains the training results for each of the sensor channels that are current members of the CDFS II constellation. For the TIR channels in CDFS II only a single node (for window channels) or at most a handful of nodes (for water vapor or CO2 absorption bands) is required to reproduce the truth radiances with an RMS TOA brightness temperature accuracy of 0.2 K or better for ITH, or an RMS TOA reflectance accuracy of 0.001 or better for ISUN. Computational speed improvements of two or three orders of magnitude are realized by this numerical technique relative to that prescribed by the full-blown RT model in Eq. (3.5). Additionally, only one node is needed to achieve a model/truth reflectance RMS < 0.001 for all eight of the CDFS MWIR channels that have a surface-reflected solar contribution in the daytime.
List of the N:K ratios, the number of 0.1 cm−1 spectral intervals N, and OSS nodes K for all sensor bands in the CDFS II constellation. Training tolerances are 0.2 K for the thermal channels and 0.001 reflectance for the MWIR solar channels.
Regression errors between truth and OSS for the 364-member radiance training set routinely exhibit a normal distribution with zero bias, as shown in Fig. 2. This means that the OSS training technique does not favor one particular instance of atmospheric conditions over any other. The zero-centered Gaussian distribution speaks also to the uniformly representative nature of the 52-member ECMWF atmospheric profile training set with respect to globally varying atmospheric conditions.
Distribution of OSS training errors for the 364-member atmospheric training set and for the GOES 11-μm TIRa channel.
Citation: Weather and Forecasting 31, 3; 10.1175/WAF-D-15-0077.1
b. Numerical considerations
We note here that the transmittance profiles τ and τ* are computed on the NWP grid for satellites directly overhead (i.e., for zenith angle θSAT = 0). Application of these zenith-path profiles τ(θSAT = 0) to a slant-path satellite pixel (where 0 ≤ θSAT ≤ θMAX) is quickly achievable in OSS by invoking the relation τ(θSAT) = τ(0)1/cosθ. This easy adjustment is possible only because of the monochromatic node nature of the OSS model. In contrast, many other band models explicitly include the satellite-view angle as a transmittance predictor (e.g., Strow et al. 2003), which requires extra pixel-level transmittance profile computations that would limit any substantive savings in radiance compute times.
The surface emission contribution to the upwelling node radiance is computed and added to the atmospheric terms on the finescale satellite-pixel grid. The leading earth surface term in the above equation has two important components—ϵSFC and TSFC—that are routinely available at a fine spatial resolution. Unlike the atmospheric terms, which contain integrals (loops) over the number of atmospheric layers in the NWP profile, the surface contribution has only one term, the Planck function 
Following this implementation paradigm in CDFS II, we routinely achieve processing speeds of a few nanoseconds per pixel for the window channels (e.g., in the MWIR, LWIR, and TIR), and just a bit longer for the broader and more spectrally complex water vapor and carbon dioxide absorption bands (WV and CO2).
c. Atmospheric transmittance profiles
5. Spectral class training
For each sensor band listed in Table 2 the monochromatic training radiances are for wavenumbers ν ∈ [νLO, νHI] that fall inside the nonzero portion of that band’s specific sensor response function. This regression approach is termed channel training since the predictor-radiance wavenumbers fall within the local confines of the channel bandpass. This leads to node selection points that are generally band unique.
We have argued that gains in computational speed without forfeiture of RT model accuracy have substantive value in CDFS II cloud model applications. Although the time savings offered by channel training are significant, there are even more savings that can be realized through further exploitation of the OSS training paradigm.
The fundamental premise of the channel-training technique is that a strong and computationally efficient mathematical association exists between the monochromatic training radiances and the band-integrated radiances. This in part is due to the quasi-repetitive nature of the monochromatic radiances themselves (e.g., see Fig. 1), which in turn is due to the discrete nature of the absorption frequencies and line shapes in the atmospheric environment. It stands to reason that such an association, which does not argue for a direct physical causation of why certain nodes are selected for certain channels, might also exist between the band-integrated radiances 
With this supposition in mind we perform yet another automated stepwise regression (recall section 4), but this time the monochromatic training radiances span the entirety of wavenumbers that are represented at least once in the collection of channel response functions within a particular spectral class. We train simultaneously all 8 channels of the CDFS MWIR class, all 10 channels of the WV, all 4 channels of the LWIR, all 17 of the TIR, and all 4 of the CO2a spectral classes. The result for each sensor spectral class is a single set of KCLASS nodes that are valid for all satellite sensor channels within that class. We refer to this type of training as spectral class training, since the training sets contain monochromatic radiances for nonlocal wavenumbers that often lie outside a particular sensor’s response function but nonetheless fall within a region of the spectrum common to other nearby satellite sensors. Spectral-class node selection training results with εtol = 0.001 (for MWIR solar reflectances) and εtol = 0.2 K (for all thermal emission channels) are summarized in Table 3. Note that OSS requires only 30 nodes to accurately model the upwelling clear-atmosphere radiances in all 40 infrared sensor channel instances in the CDFS II constellation. Overall, this represents a reduction from 20 644 monochromatic wavenumber intervals down to 30 nodes, only 0.15% of the total. Table 4 contains the spectral-class training accuracy results for all the CDFS II infrared sensors.
Number N of 0.1-cm−1 spectral intervals Δν and the corresponding number of unique OSS channel and global-training nodes KCH and KCLASS, respectively, for each of the five CDFS II spectral classes. The table entry format is N: KCH: KCLASS.
A list of the OSS spectral-class training accuracies for the CDFS infrared channels. RMS accuracies (with units of kelvins for the emitted thermal channels, and bidirectional reflectance for the reflected solar channels) were obtained using a global εtol = 0.2 K for the thermal radiance training and εtol = 0.001 reflectance for the reflected solar radiance training.
6. Modeling performance and results
Figure 3 contains an example of the structure of monochromatic transmittance τ(νn), for a vertical atmospheric path, across the MWIR spectral class. Also plotted are the individual sensor response functions. Figure 3 helps to illustrate an important benefit of OSS to CDFS. The cloud detection algorithms are of the generic class of threshold detection tests that compare observed radiance conditions to those expected for a clear atmosphere. Substantive differences between the two indicate cloudy conditions. Here “substantive” is quantifiable as a user-prescribed threshold that must account for the influence of the cloudy (signal) and clear-atmosphere (noise, from the point of view of cloud detection) portions of the pixel upwelling radiances.
(top) Sample plot of monochromatic transmittances for a midlatitude, moderately moist atmosphere in the MWIR class of wavelengths. Collectively, all CDFS MWIR bandpasses fall within 3.32 and 4.55 μm, which contains an overall N = 8041 [see Eq. (3.5)] wavenumber intervals, each of width 0.1 cm−1, and for each of which a total-path atmospheric transmittance was computed and plotted. The vertical red colored lines denote the six spectral-class node selections {νk}k=1,2, … ,6 [see Eq. (4.1)] for this particular combination of channels. (bottom) Plot of the CDFS MWIR channel response functions. The numbers plotted next to the sensor names denote how many nodes from the six-node MWIR spectral-training superset are required for OSS modeling of that particular sensor with an RMS < 0.2 K. See text for further details.
Citation: Weather and Forecasting 31, 3; 10.1175/WAF-D-15-0077.1
During the past 40 years, global cloud retrievals at the 557th Weather Wing have relied heavily on the empirical setting of these thresholds by human analysts. Thresholds are manually tuned so that, in the eyes of the image analyst, the cloud masks appear reasonable with respect to the cloud patterns discernible in the imagery by the human eye. With the ever-increasing number of satellites in the global constellation it was quickly realized that these thresholds needed to be set independently for each individual satellite, without a clear understanding of why. Retrospectively, in large part this was due to the wavelength-varying influence of the atmosphere in any given spectral class, as evidenced in Fig. 3 for the CDFS MWIR channels by the superposition of the disparate response functions (bottom) with respect to atmospheric transmittance (top). Although there are many MWIR channels, each has a unique wavelength-differential water vapor influence, and some of the wider geostationary channels are influenced additionally by carbon dioxide attenuation.
It is not hard to imagine the burden imposed on analysts who are charged with balancing the threshold settings for seasonal land cover changes and the day-to-day variations in atmospheric conditions that mask the influence of cloud properties on the upwelling radiances. The adoption of OSS into a CDFS clear-atmosphere RT paradigm means that analysts can prescribe threshold settings that focus more directly on multispectral cloud signatures, leaving the highly variable atmospheric radiative influence to the real-time RT model.
Image map of the differences between LBLRTM and OSS clear-atmosphere upwelling brightness temperature estimates for the GOES 11-μm TIRa channel and for a global atmospheric snapshot valid at 1800 UTC, Wednesday, 29 Sep 2010.
Citation: Weather and Forecasting 31, 3; 10.1175/WAF-D-15-0077.1
Figure 5 summarizes the results of comparisons between sensor-observed and OSS-estimated clear-atmosphere brightness temperatures for the SEVIRI 10.78-μm TIRa channel. The statistics are for a set of 509 542 cloud-free pixels (285 556 over-ocean pixels and 223 986 overland pixels) from a Meteosat image scene over East Africa and the western Indian Ocean. The dashed curves denote corresponding differences for the CDFS II prior to OSS implementation. Ocean and land biases of the dashed distributions are approximately 1.5 and 6 K, respectively. The solid curves represent the OSS clear-pixel differences for the same image scene. Note that these biases are lower, 0.66 K for ocean and 0.91 K for land, and their distributions are tighter, exhibiting substantive improvements in CDFS’s operational ability to prescribe theoretically the atmospheric influence on clear-atmosphere upwelling brightness temperatures. From an automated cloud-detection perspective, it is much more advantageous to manage smaller biases and spreads with empirically tuned thresholds when the modeled-minus-observed differences are highly predictable. These observed differences are subject to three sources of error: 1) the theoretical accuracy of the reference model against which OSS is trained, 2) the OSS training accuracy, and 3) the goodness of the NWP inputs into the RT model and the accuracy of the land and ocean surface emissivities. For the CDFS application we train against LBLRTM, a well-validated, state-of-the-art line-by-line RT model (see, e.g., Alvarado et al. 2013; Shephard et al. 2009). Significant control over the second error source above is in the hands of the user who can prescribe any desired OSS/reference model training-error tolerance, deferring the issue of RT model accuracy to the custodians of the reference model (in this case, LBLRTM). However, control over the third error source is clearly more elusive since CDFS has little choice but to use global NWP datasets. Nonetheless, it is evident from these frequency distributions that the advantages provided to CDFS by an OSS RT capability outweigh any inaccuracies in the input NWP atmospheric temperature and water vapor profiles. Improvements brought about by OSS are indeed notable.
Frequency distributions of the differences between observed and OSS-estimated clear-atmosphere upwelling brightness temperatures for a Meteosat image scene. Solid curves represent the OSS–SEVIRI differences, and the dashed curves are for the CDFS assessments of clear-atmosphere brightness temperatures prior to the OSS implementation. It is likely that at least part of the right-side tails of the distributions represent cloud-contaminated pixel observations. See text for further details.
Citation: Weather and Forecasting 31, 3; 10.1175/WAF-D-15-0077.1
a. Advances in cloud mask quality
In this section, we present two examples that compare the CDFS OSS cloud mask against the 10-day clear-statistics mask. For each mask option, OSS and statistical, both of the full suites of CDFS cloud detection algorithms that were run are identical, only the clear-scene radiance techniques differ. Special focus is placed here on low boundary layer clouds at night since they have a weak thermal contrast with the underlying background. Of all the nighttime cloud multispectral tests in CDFS, the success of the low cloud algorithms most heavily relies on accurate prescriptions of clear-scene brightness temperatures. Thus any improvements in the nighttime low cloud mask provide evidence of the improvements that OSS brings to CDFS.
The center image in Fig. 6 contains an example of a single-channel OLS thermal infrared grayscale image over the ocean. Black denotes cloud-free pixels, and the contrasting grayscales depict a stratiform cloud deck in the nighttime marine boundary layer. The sole OLS nighttime cloud detection test is a simple threshold technique that uses the 11-μm infrared channel and therefore relies heavily on an accurate estimate of the cloud-free brightness temperature. The top image in Fig. 6 shows in red overlay the CDFS cloud mask obtained using the 10-day statistical clear-scene technique (recall section 2a), and the bottom image is the mask obtained using the OSS RT technique. Two main points are illustrated by this example. First, from a visual inspection it is seen that the OSS-based cloud mask is more complete and correctly so. The statistical clear-scene technique (top) misses a large portion of the stratus and stratocumulus in the upper center of the image. In contrast many more of these clouds are detected accurately by the OSS technique (bottom).
(middle) Sample OLS TIRa image of nighttime marine stratocumulus, along with the CDFS cloud masks obtained using the 10-day (top) statistical and (bottom) OSS clear-atmosphere brightness temperature estimates. In the top and bottom panels, red pixels are cloud filled and gray/black pixels are clear. See text for further details.
Citation: Weather and Forecasting 31, 3; 10.1175/WAF-D-15-0077.1
Second, note that the boxlike structure of the cloud mask in the top image in Fig. 6 (10-day statistics) is not evident in the bottom (OSS based) cloud mask. Section 3a highlights the ability of the OSS RT technique to capture small-scale and smoothly varying horizontal gradients in atmospheric temperature and water vapor profiles, to the extent that they are well represented in the NWP fields. The radiative influence of these smoothly varying effects is well modeled by OSS, which in turn results in clear-atmosphere brightness temperature estimates that are truly made at the pixel resolution. In contrast the statistical 10-day clear-scene analysis has a 24-km spatial resolution. Deviations of the cloud-cleared brightness temperatures from the NWP surface temperature field are maintained and therefore applied in real time by CDFS at this coarser resolution. When prescriptions of these deviations are error prone, the influence on the spatial context of the overall cloud mask is evidenced, as seen here, as a boxlike pattern whose appearance is artificial.
An example of another nighttime cloud deck is contained in Fig. 7, this time observed by MODIS just west of Baja. The center image is a color composite in which low water droplet clouds appear reddish and high thin cirrus are blue and bright gray. Dark brown and black denote cloud-free ocean pixels, and the contrasting colors clearly depict a stratiform cloud deck in the nighttime marine boundary layer. The top image in Fig. 7 shows via a red overlay the CDFS cloud mask obtained using the 10-day statistical clear-scene technique, and the bottom image is the mask obtained using the OSS RT technique. From a visual inspection it is seen again that the OSS-based cloud mask is more accurate than its statistical counterpart. The 10-day clear-scene technique (Fig. 7, top) misses almost all of the stratus and stratocumulus present in the western two-thirds of the image. In contrast most of these clouds are detected correctly by the OSS technique (bottom).
(middle) Sample MODIS 3.7/11/12-μm RGB color composite image of nighttime marine stratocumulus, along with the CDFS cloud masks obtained using the 10-day (top) statistical and (bottom) OSS clear-atmosphere brightness temperature estimates. Central Baja California is found on the right side of the image. In the top and bottom panels, red pixels are cloud filled and black pixels are clear. See text for further details.
Citation: Weather and Forecasting 31, 3; 10.1175/WAF-D-15-0077.1
b. Improved cloud-top retrievals
One more example of the positive impact that OSS has on CDFS cloud retrievals is in obtaining cloud-top height by converting the retrieved cloud-top temperature to altitude using a valid NWP temperature and geopotential profile. In general, with longwave emissivities routinely close to one, water droplet cloud tops are well estimated since their observed brightness temperatures are very close to the physical temperature of the cloud tops. The only adjustment that needs to be made to the upwelling TIR brightness temperature is that which prescribes the influence of atmospheric water vapor attenuation above the cloud top. Semitransparent cirrus clouds on the other hand are a bit more challenging. Upwelling infrared radiance observations in a cirrus field of view contain contributions from both the cloud and the underlying surface, and the extent to which this is true depends on an ice cloud emissivity that spans the full range 0 < ϵ ≤ 1. To retrieve a cirrus physical temperature, it is therefore necessary to identify and isolate the cirrus signal from the overall cloud-plus-ground radiance observation. This, in turn, requires an estimate of the pixel clear-atmosphere radiance.
Up until recently CDFS had no easy method for estimating clear-atmosphere upwelling radiances for cloudy cirrus pixels. Techniques were devised wherein the clear radiance would be chosen as that observed in a nearby cloud-free pixel—cloud free, that is, according to the cloud mask (e.g., see d’Entremont et al. 2009). This approach brought with it three critical shortcomings. 1) If the cloud mask contained any errors (e.g., false clears), then these would impact adversely the clear-atmosphere prescriptions and subsequent cirrus retrievals. 2) Oftentimes “nearby” would be hundreds of kilometers from the cirrus pixel. 3) An image ingest sector frequently would be completely cloudy so as to obviate this technique altogether. The only recourse was to assume that the observed cirrus TIRa brightness temperature, although higher than the physical temperature of the thin cirrus itself, was the true physical temperature of the cloud. With higher-than-actual cloud-top temperature prescriptions came routine underestimates of retrieved cloud-top heights, with the highest errors for the most optically thin clouds.
Using GOES data over the southwest United States and adjacent Pacific during a 63-day case study in March and April 2011, 2307 cirrus-top retrievals, with and without OSS, were matched with corresponding space-based CALIOP lidar observations for truth. The left panel in Fig. 8 illustrates CDFS cloud-top retrievals using the nearest-neighbor clear-pixel radiance technique, and the right-hand panel shows results when using OSS. The left-hand scatterplot depicts overall reasonable agreement of cirrus cloud-top height with the lidar observations, although the retrievals exhibit lower biases for the highest cirrus and higher biases for the lowest cirrus. Retrieval errors have a 1.45-km RMSE, and the correlation between the retrieved and true cloud tops is good.
Scatterplots of CDFS-retrieved cloud-top heights for optically thin cirrus with (left) the blackbody assumption and (right) the more physically correct RT theory with OSS prescriptions of the clear-atmosphere contributions to upwelling radiance.
Citation: Weather and Forecasting 31, 3; 10.1175/WAF-D-15-0077.1
In contrast the right-hand panel in Fig. 8 illustrates how the CDFS cirrus-top retrievals improve when OSS is used to prescribe and remove the clear-atmosphere contributions from the cirrus-pixel upwelling radiances. It is seen that isolating the cirrus radiances in this manner yields more accurate retrievals of the cirrus tops. CDFS analysis errors are lower with a 1.23-km RMSE, and no strong bias is evident throughout the entire 6–15-km cloud-top range. Additionally, the correlation between the retrieved and true cloud tops is comparatively very strong at r = 0.852.
7. Summary remarks
Optimal spectral sampling is a computationally fast and theoretically accurate RT model that has been incorporated into the USAF CDFS II in support of global-scale, real-time cloud detection and analysis. OSS balances computation speed with theoretical accuracy in a way that uniquely suits CDFS’s real-time processing requirements. The unique monochromatic nature of OSS supports both individual and multiple-channel/instrument training options. For the CDFS application we have presented a multichannel approach featuring spectral-class training that provides a single set of node wavenumber positions for a large collection of instruments in a given spectral region but from different satellite platforms. Only the mathematical node weights are instrument/channel dependent. For our current application the training error tolerances between OSS and the reference LBLRTM have RMS accuracies of 0.2 K or less in the thermal infrared bands, and 0.001 bidirectional reflectance or less for the solar contributions to daytime MWIR radiances. With these tolerances we have achieved a reduction in compute processing time of over three orders of magnitude for both channel and spectral-class training, while an error analysis using an independent ½° global NWP field shows that the OSS-generated TOA radiances match the LBLRTM radiances to well within training tolerances for over 99% of the NWP domain grid points.
Before the introduction of OSS into CDFS, clear-atmosphere brightness temperature estimates were made using a 10-day running distribution of radiances for cloud-free pixels. This statistical database had large overhead costs associated with it. First, the “cloud free” determination was made only after a second independent run of the CDFS threshold-based multispectral cloud mask algorithms. This postprocessing step employed cloud test thresholds that were deliberately tuned to favor assessments of false clouds, ensuring to the extent possible on operational global scales that the remaining clear-pixel mask was indeed representative only of cloud-free conditions. Running the global nephanalysis twice, once for the operational products and again for the clear-atmosphere statistics, incurs substantive computational costs that include the maintenance of a large statistical database, and requires having to keep track of two sets of cloud test thresholds. Even with liberal thresholds (by “liberal” we mean that if an incorrect pixel-level cloud/no-cloud decision is made, it is more likely that a clear pixel has been classified as cloudy), there remains still the possibility of cloud contamination in the 10-day statistical running average. Furthermore, these statistics have to be compiled and tabulated on global scales as functions of satellite, sensor channel, geography type, viewing geometry, and time of day in order to provide a useful clear-atmosphere radiance depiction to the CDFS cloud detection algorithms.
OSS replaces all these dependencies with a deterministically based method for estimating clear-atmosphere radiance conditions in real time. There is now no need for a second cloud-clearing model run, and no need for maintenance of a large and complex statistical clear-radiance dataset. We have argued in this paper also for the quantitative value-added enhancements to CDFS that have been brought about by the implementation of OSS. Among these improvements is that the new cloud detection thresholds are focused more exclusively on multispectral cloud signatures as opposed to having to empirically allot for both the cloud signatures and errors in the clear-scene statistical database. Finally, the OSS clear-atmosphere radiance approach eliminates concerns of cloud contamination in the clear-scene statistics.
Acknowledgments
The work reported here was supported in part by 557th Weather Wing’s Systems Engineering, Management, and Sustainment II (SEMS II) Contract FA4600-08-D-0002, with additional support from internal AER funding.
APPENDIX A
Key Acronyms Used in This Paper
Table A1 contains expansions of acronyms found in the text.
Key acronyms and terms used in this paper.
APPENDIX B
A Brief Synopsis of the 557th Weather Wing Cloud Depiction and Forecast System
CDFS cloud processing is divided into two main steps: 1) cloud detection and 2) deterministic (radiance based) cloud property retrievals. The cloud detection portion of the processing generates a cloud mask that provides a cloud/no-cloud determination and a cloud-phase specification (ice particles or water droplets) on a pixel-by-pixel basis [i.e., at sensor resolution; see d’Entremont and Gustafson (2003)]. The cloud mask retrievals specifically exploit the differential wavelength dependence of cloud microphysical and thermodynamic properties on upwelling TOA radiances, as prescribed by deterministic radiative transfer models.
The cloud detection algorithm is actually a suite of tests that use spectral signatures present in satellite sensor datasets to discriminate clouds from clear-atmosphere pixels. Various techniques are employed including simple temperature thresholds, interchannel comparisons, and comparisons between the channel data and spectral information characterizing the clear-scene surface. Some tests require sensor data from channels that are not present on all satellites. Thus, the processing path of the algorithm varies dynamically with each satellite system. Each spectral discriminant test requires logic to determine first whether the required sensor channel data are available. For those satellites that do not have the necessary channels to run a particular test, that test is simply not applied and the algorithm proceeds on to the next test.
The selection of tests applied to each pixel in the analysis scene is a function of the level of solar illumination and the available sensor channels. Some tests are applicable only during solar-illuminated conditions, some require nonsolar conditions, and some tests are completely independent of solar illumination.
After the cloud detection tests are complete, a final cloud/no-cloud and cloud-phase (ice particles versus water droplets) determination is made for each pixel, depending on the collective result of the individual cloud tests. Implicit is the assumption that no one spectral signature is expected to classify all clouds within a scene. Rather, each test is designed to exploit a different cloud spectral signature and the final cloud analysis is obtained by optimally combining results from the set of individual tests. Our real-time cloud mask algorithms are mature and generate consistent, repeatable results for all view-and-illumination geometries and cloud types, not only for the U.S. geostationary satellites but for the constellation of international environmental satellites as well.
In the second stage of cloud analysis processing a second algorithm deterministically discerns from the calibrated radiance observations (for all pixels identified as cloudy by the cloud mask codes) retrievals of cloud-top height, temperature, and pressure; cloud-base height; 11-μm infrared bulk emissivity and 550-nm visible extinction optical thickness for the vertical path between cloud base and cloud top; a phase-dependent liquid or ice water path (defined as the vertical column integration of cloud water); and the cloud particle size distribution effective diameter (d’Entremont and Gustafson 2006a,b).
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