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  • View in gallery

    Remote sensing toolkit algorithm flowchart.

  • View in gallery

    Slant-path geometry for path profile extraction. The black circles represent varying vertical altitudes. The red line represents the sensor path from a space-based sensor to the ground, and the blue shell represents a spherical shell cloud that the sensor path intersects. The red dashed line depicts a sensor path for a target that is specified by a location with an altitude AGL, in which case the path continued until ground intersection. The red points depict atmospheric layer intersections with the sensor path, while purple points represent layer midpoints used for layer atmospheric characterizations, and the black points represent the dynamically added layers for clouds that ensure all cloud properties are included in radiative transfer calculations.

  • View in gallery

    The 15 000 random sample locations for diffuse transmission analysis. Blue points represent clouded conditions (9890), while red points represent a CFLOS between the surface and the observer (5110).

  • View in gallery

    Spectral diffuse transmission for nadir geometry at 15 000 random sample dates, times, and locations as seen in Fig. 2. Blue lines represent cloud-free conditions, while gray lines represent various clouded conditions.

  • View in gallery

    Diffuse band transmission distribution and probability for nadir geometry. The histogram in yellow depicts 9890 cloud-free simulations, the histogram in red represents 5110 clouded simulations, the blue histogram represents the intersection of clouded and cloud-free cases, and the purple histogram represents all cases.

  • View in gallery

    Worldwide climatology for diffuse transmission at nadir geometry based on random 15 000 samples. Gray lines depict the spectral diffuse transmission in the 300–1300-nm band for all samples. Solid lines represent the 10th–90th percentiles and the spectral mean, while dashed lines represent the band transmission for a 5800-K blackbody source.

  • View in gallery

    Evaluation of the number of samples required for analysis for worldwide climatology. The effect of increasing the number of samples is demonstrated via the solid lines, which represent the respective percentiles of band transmission, and the dashed lines, which represent the minimum, maximum, and mean values.

  • View in gallery

    Representative spectral response and source functions. The blue curve depicts a nominal sensor response function in the 300–1300-nm band, while the red curve depicts the spectral source function of a 5800-K blackbody.

  • View in gallery

    Diffuse band transmission distribution and probability, including sensor response function effects. The histogram in yellow depicts 9890 cloud-free simulations, the histogram in red represents 5110 clouded simulations, the blue histogram represents the intersection of clouded and cloud-free cases, and the purple histogram represents all cases.

  • View in gallery

    Worldwide climatology for diffuse transmission based on 15 000 random samples, including sensor response function effects. Gray lines depict the spectral diffuse transmission in the 300–1300-nm band for all samples. Solid lines represent the 10th–90th percentiles and the spectral mean, while dashed lines represent the band transmission for a 5800-K blackbody source.

  • View in gallery

    Spectral angle variance in 15 000 worldwide climatology samples. (top) The distribution of spectral angle difference between the spectral mean and the 15 000 samples. (bottom) The two spectral diffuse transmission signatures with the greatest spectral angle difference.

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A Remote Sensing and Atmospheric Correction Method for Assessing Multispectral Radiative Transfer through Realistic Atmospheres and Clouds

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  • 1 Department of Engineering Physics, Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio
  • | 2 Department of Engineering Physics, Air Force Institute of Technology, Wright-Patterson Air Force Base, and Applied Research Solutions, Beavercreek, Ohio
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Abstract

The ability to quickly and accurately model actual atmospheric conditions is essential to remote sensing analyses. Clouds present a particularly complex challenge, as they cover up to 70% of Earth’s surface, and their highly variable and diverse nature necessitates physics-based modeling. The Laser Environmental Effects Definition and Reference (LEEDR) is a verified and validated atmospheric propagation and radiative transfer code that creates physically realizable vertical and horizontal profiles of meteorological data. Coupled with numerical weather prediction (NWP) model output, LEEDR enables analysis, nowcasts, and forecasts for radiative effects expected for real-world scenarios. A recent development is the inclusion of the U.S. Air Force’s World-Wide Merged Cloud Analysis (WWMCA) cloud data in a new tool set that enables radiance calculations through clouds from UV to radio frequency (RF) wavelengths. This effort details the creation of near-real-time profiles of atmospheric and cloud conditions and the resulting radiative transfer analysis for virtually any wavelength(s) of interest. Calendar year 2015 data are analyzed to establish climatological limits for diffuse transmission in the 300–1300-nm band, and the impacts of various geometry, cloud microphysical, and atmospheric conditions are examined. The results show that 80% of diffuse band transmissions are estimated to fall between 0.248 and 0.889 under the assumptions of cloud homogeneity and maximum overlap and are sufficient for establishing diffuse transmission percentiles. The demonstrated capability provides an efficient way to extend optical wavelength cloud parameters across the spectrum for physics-based multiple-scattering effects modeling through cloudy and clear atmospheres, providing an improvement to atmospheric correction for remote sensing and cloud effects on system performance metrics.

Denotes content that is immediately available upon publication as open access.

For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dr. Steven T. Fiorino, steven.fiorino@afit.edu

Abstract

The ability to quickly and accurately model actual atmospheric conditions is essential to remote sensing analyses. Clouds present a particularly complex challenge, as they cover up to 70% of Earth’s surface, and their highly variable and diverse nature necessitates physics-based modeling. The Laser Environmental Effects Definition and Reference (LEEDR) is a verified and validated atmospheric propagation and radiative transfer code that creates physically realizable vertical and horizontal profiles of meteorological data. Coupled with numerical weather prediction (NWP) model output, LEEDR enables analysis, nowcasts, and forecasts for radiative effects expected for real-world scenarios. A recent development is the inclusion of the U.S. Air Force’s World-Wide Merged Cloud Analysis (WWMCA) cloud data in a new tool set that enables radiance calculations through clouds from UV to radio frequency (RF) wavelengths. This effort details the creation of near-real-time profiles of atmospheric and cloud conditions and the resulting radiative transfer analysis for virtually any wavelength(s) of interest. Calendar year 2015 data are analyzed to establish climatological limits for diffuse transmission in the 300–1300-nm band, and the impacts of various geometry, cloud microphysical, and atmospheric conditions are examined. The results show that 80% of diffuse band transmissions are estimated to fall between 0.248 and 0.889 under the assumptions of cloud homogeneity and maximum overlap and are sufficient for establishing diffuse transmission percentiles. The demonstrated capability provides an efficient way to extend optical wavelength cloud parameters across the spectrum for physics-based multiple-scattering effects modeling through cloudy and clear atmospheres, providing an improvement to atmospheric correction for remote sensing and cloud effects on system performance metrics.

Denotes content that is immediately available upon publication as open access.

For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dr. Steven T. Fiorino, steven.fiorino@afit.edu

1. Introduction

Atmospheric and weather variability play a significant role in military and civilian aerial operations. Clouds present a particularly complex challenge, as they cover up to 70% of Earth’s surface, and their multiple-scattering effects play a significant role in the radiative transfer process. While traditional applications have primarily focused on characterizing cloud cover and type, the fielding of directed energy weapons (DEW) that are susceptible to atmospheric effects across the electromagnetic spectrum have highlighted the need for accurate and realistic atmospheric characterization and predictive performance modeling, but the need for realistic, accurate, and correlated vertical profiles of atmospheric conditions extends far beyond DEW. Remotely sensed multi-, hyper-, and ultraspectral sensor data are particularly susceptible to atmospheric effects, with scattering in optically thick media such as clouds presenting one of the greatest challenges. Accounting for these effects requires detailed knowledge of atmospheric variability, which in turn requires an expanded environmental database beyond the typical deterministic or “standard” atmospheres utilized by many modern radiative transfer models.

To this end, the Air Force Institute of Technology (AFIT) has produced an atmospheric characterization and radiative transfer code, the Laser Environmental Effects Definition and Reference (LEEDR; Fiorino et al. 2014). LEEDR is a verified and validated atmospheric propagation and radiative transfer code that creates physically realizable vertical and horizontal profiles of meteorological data (Hall et al. 2016). Coupled with numerical weather prediction (NWP) model output, LEEDR enables analysis, nowcasts, and forecasts for radiative effects expected for real-world scenarios. In addition, LEEDR provides standardized models for representative cloud microphysical parameters. However, remote sensing applications are often significantly impacted by the dynamic nature of atmospheric clouds and poorly described by standardized models, thus requiring a near-real-time characterization of actual weather conditions for operational use in atmospheric correction and analysis operations.

The capability to accurately assess the narrowband or broadband spectral effects of clouds is of particular importance to the intelligence community, yet any existing models and simulations are limited in distribution and highly specialized for particular sensors of interest with limited applicability to the research community. Previous studies have shown the feasibility of using Air Force weather data for characterizing single and multiple scattering through clouds at optical wavelengths (Roadcap et al. 2015). This research seeks to describe the development of an integrated internal LEEDR capability leveraging these external datasets relevant to cloud microphysical properties in a near-real-time environment. LEEDR’s modularity and ability to ingest NWP data are exploited to develop a new capability for extending optical wavelength observations of cloud parameters across the spectrum for physics-based modeling of multiple-scattering radiative transfer effects through clouds at wavelengths ranging from the ultraviolet (UV) to radio frequencies (RF).

A brief description of the existing LEEDR model is presented in section 2, including a complete description of the external data sources and updated model assumptions, structure, and implementation. Section 3 highlights model results analyzed in the context of worldwide diffuse transmission probabilities for calendar year 2015. A brief summary of the findings and future research directions are given in section 4.

2. Remote sensing toolkit development

To facilitate near-real-time analysis of multiple-scattering effects across the spectrum, a new remote sensing methodology or toolkit based on LEEDR was developed. This new feature set adds to the LEEDR’s existing capabilities and is depicted in Fig. 1. The algorithm incorporates external data sources, accounts for remote-sensor-path profile generation through varying atmospheres and clouds, applies LEEDR’s unique atmospheric characterization algorithms, and scales the outputs for use in LEEDR’s internal radiative transfer algorithm or export to other models. The components of the toolkit are further described, starting with existing LEEDR capabilities, in the sections that follow.

Fig. 1.
Fig. 1.

Remote sensing toolkit algorithm flowchart.

Citation: Journal of Atmospheric and Oceanic Technology 36, 2; 10.1175/JTECH-D-18-0078.1

a. LEEDR background

LEEDR enables the creation of vertical profiles of temperature, pressure, water vapor content, optical turbulence, and atmospheric particulates and hydrometeors as they relate to line-by-line layer extinction coefficient magnitude at any wavelength from the UV to RF (200 nm–8.6 m). In addition to being an atmospheric characterization tool, LEEDR also provides radiative transfer modeling capability. LEEDR’s novel capabilities are focused on the application of a temporally and spatially varying atmospheric boundary layer through the use of its correlated probabilistic databases in the production of its vertical data profiles. This enables a statistical likelihood to be attached to the realistic atmospheric profiles that differ significantly from using “standard” atmospheric profiles [e.g., the U.S. Standard Atmosphere, 1976 (COESA 1976)] in engineering analyses or simulations (Fiorino et al. 2008). Fiorino et al. (2014) and Shirey (2016) demonstrated that the inclusion of real-time correlated weather forecasts in profile generation has been shown to significantly increase the predictive performance of LEEDR when coupled with surface observations. LEEDR’s utilization of climatological data as well as its atmospheric databases and probabilistic correlation method have been extensively described in earlier publications (Fiorino et al. 2008, 2014; Burley et al. 2017).

Employing adiabatic lapse rates within the boundary layer as done in LEEDR allows the relative humidity to vary dramatically, often increasing from a surface value below 50% to approximately 100% near the top. Realistic depictions of boundary layer dynamics significantly impact modeled aerosol size distributions and thus attenuation caused by scattering, as water soluble aerosols grow in size with increased humidity. This effect is not captured when modeling with standard atmospheric data, as the temperature and moisture (dewpoint) do not lapse realistically in standard atmospheres (Fiorino et al. 2008).

Molecular absorption calculations are made by combining line strength data from the high-resolution transmission (HITRAN) 2008 database with temperature, dewpoint, and pressure vertical profiles for the top 13 atmospheric constituents. LEEDR treats both Rayleigh scatter for atmospheric molecules and aerosol scattering via Mie scattering theory, and uses dimensionless Mie extinction, scattering, and absorption efficiencies via the Wiscombe Mie scattering module (Wiscombe 1980) to calculate volume extinction, scattering, and absorption coefficients for each unique set of aerosol and weather conditions (Burley et al. 2017). The same module also provides phase function values for use in multiple-scattering calculations.

Aerosol size distributions are modeled as a lognormal size distribution of the form
dN(r)d(logr)=N(2π)1/2log(σ)exp[(logrlogrM)22(logσ)2],
where N is the total particle number density per unit volume and is normalized to 1. The rM value is the modal (or median) radius, and σ is the standard deviation for the aerosol species. The wavelength-specific normalized extinction, scattering, and absorption cross sections, σe,s,a(λ), respectively, are obtained by integrating over the range of radii (the cross sections can easily be converted to volume extinction coefficients with the total number concentration). LEEDR includes several standard types of aerosols for consideration in addition to the Global Aerosol Data Set (GADS) utilized in this study. Defined on a 5° grid worldwide, Köpke et al. (1997) specify that GADS provides a geospecific realistic aerosol profile with multiple types and distributions. LEEDR hydrometeors currently include raindrops, drizzle drops, cloud droplets, ice spheres (ice fog), and ice crystals (cirrus clouds), which are all distributed with type-specific distributions and assumed to be spheres, with the exception of cirrus ice crystals, which are considered hexagonal columns. Further details on the humidity-altered aerosol and hydrometeor size distributions can be found in previously published work (Fiorino et al. 2014; Burley et al. 2017).

b. External data sources

While LEEDR contains internal databases of microphysical aerosol and hydrometeor properties as well as a novel method for creating correlated, physically realizable profiles of meteorological and environmental effects from climatology, it can also incorporate external data sources for NWP data. The NWP descriptions of meteorological conditions and near-real-time observations of clouds can significantly improve LEEDR’s predicative and analytical capability for remote sensing.

The Global Forecast System (GFS) model is a global, hydrostatic weather forecast model produced by the National Centers for Environmental Prediction (NCEP). The current GFS Global Spectral Model is operated at its standard 0.5° horizontal resolution grid, but an additional operational dataset at 0.25° grid resolution is available dating to late 2014. Both models are run four times per day, each with 3-h forecast time steps out to 240 h, followed by a lower-temporal-resolution extension period at 12-h time steps out to 384 h. The model runs on 64 vertical, unequally spaced sigma levels. This means the pressure levels in the model are normalized by dividing level pressure by the surface pressure, σ = p/ps, compressing the levels so that none of the model pressure levels exist below Earth’s surface. The 64 model levels extend up to a minimum pressure level of 0.03 hPa, but the output product includes only 26 levels with a top pressure level of 10 hPa. For this reason, the top of the GFS coverage volume in the available datasets is typically around 30–32 km, based on location. The gridded model output is publicly available for download through the NOAA National Operational Model Archive and Distribution System (NOMADS) server in a standardized General Regularly-Distributed Information in Binary Form (GRIB; NOAA 2016, 2018). The subset of available parameters utilized in this study include pressure, temperature, relative humidity, and surface altitude, yet many more, including precipitation, winds, and particle concentrations/mixing ratios, are included.

While LEEDR contains climatological databases for aerosol concentrations and optical properties that are scaled with appropriate (NWP) meteorological values, the hydrometeor databases represent model cloud conditions chosen to fit a wide spectrum of measurements and are designed to be representative of a generalized cloud type (Hess et al. 1998). With the continuing advances in remote sensing, particularly space based, a need for near-real-time cloud analysis has steadily emerged. The Air Force’s 557th Weather Wing provides global operational weather support to the U.S. Air Force and U.S. Army to include reliable cloud analysis. However, primary cloud analysis has historically focused on total cloud cover and cloud type in support of the aviation community and not necessarily on the physical properties of the clouds. The World-Wide Merged Cloud Analysis (WWMCA) product is the integrated worldwide cloud output from the 557th’s current Cloud Depiction and Forecast System (CDFS), according to AFWA (2013).

WWMCA utilizes analysis of data from multiple environmental satellites, conventional surface observations, and other supporting databases. Each data product is analyzed using separate cloud detection algorithms specifically designed to exploit the specific information content from system-specific sensors. Products from individual sensors and datasets are merged and gridded on a 16th mesh polar stereographic grid to provide a snapshot of the atmospheric cloud state and then transferred to a 0.25° latitude–longitude grid for distribution. In the utilized data, merged cloud parameters are provided at up to four unique layers. Cloud parameters of interest include the cloud-top height (CTH), cloud-base height (CBH), total cloud cover, cloud type, cloud water path (CWP; g m−2), ice water percentage, cloud effective particle size or diameter (CED; 8–120 µm), and cloud optical depth (COD; 0–50 per layer, 200 maximum total) at 550 nm. COD is derived from passive sensors and thus representative at the top of the cloud, but it is not necessarily below the cloud top. Archived WWMCA data products are available to U.S. Department of Defense (DoD) agencies and their contractors through the 14th Weather Squadron.

c. Profile generation

1) Path definition

The first step in assessing radiative transfer along a remote sensing path is to define the atmospheric and cloud properties along that path. Typical radiative transfer programs assume a vertical profile and assume horizontal homogeneity. This is the case when using a standard or climatological profile in LEEDR. In this toolkit, the user specifies latitude, longitude, and height [m above ground level (AGL)] for the beginning and the end of the path, and spherical Earth geometry is assumed. In addition, the user specifies the number of points to assess meteorological conditions along the desired slant path. The upper point can extend beyond the top of the atmosphere, such as for a satellite in orbit. This is depicted in Fig. 2.

Fig. 2.
Fig. 2.

Slant-path geometry for path profile extraction. The black circles represent varying vertical altitudes. The red line represents the sensor path from a space-based sensor to the ground, and the blue shell represents a spherical shell cloud that the sensor path intersects. The red dashed line depicts a sensor path for a target that is specified by a location with an altitude AGL, in which case the path continued until ground intersection. The red points depict atmospheric layer intersections with the sensor path, while purple points represent layer midpoints used for layer atmospheric characterizations, and the black points represent the dynamically added layers for clouds that ensure all cloud properties are included in radiative transfer calculations.

Citation: Journal of Atmospheric and Oceanic Technology 36, 2; 10.1175/JTECH-D-18-0078.1

If the user-defined path does not intersect the surface of Earth (at the bottom) or the top of the atmosphere (defined as 100 km), then the path is extended and the intersection coordinates are determined via a ray tracing technique. In this manner, the complete profile is calculated for the Earth intersection point and the intersection with the top of the atmosphere, and the user is free to use only a subsection of the path if desired. A complete slant-path length is determined using plane triangle geometry and the law of cosines. From the endpoints, forward reckoning is used to determine the location of path points at a specified range. The default number of data points along the path is set at 200, but it can be modified by the user. Additionally, the algorithm automatically determines whether the path spacing results in path points that exceed half of the resolution of the grids defining GFS and WWMCA parameters (0.5° and 0.25°). If so, the path spacing is automatically scaled downward by adjusting the number of path points until this condition is satisfied, thus ensuring that the horizontal variation in the data is accounted for to the maximum extent possible based on data resolution.

2) Data extraction

Based on the endpoint locations for the path of interest, GFS and WWMCA data are sorted and extracted. A bounding box with a minimum of at least one grid point larger than the maximum extent of the path points is extracted, gridded, and used as a basis dataset for trilinear interpolation. Accordingly, meteorological conditions (temperature, dewpoint, relative humidity) are all interpolated with consideration for both horizontal and vertical variations. It is important to note that these interpolated slant-path profiles are not guaranteed to be compliant with the physics used to obtain the original meteorological profile data, yet any variations are expected to be minor.

The advantage to extracting a limited dataset as a basis for interpolation is the computational expense saved in generating an interpolant because the GFS data are stored in pressure levels and must be converted to altitudes at each gridpoint location considered. In cases where a predefined region of interest (latitude–longitude bounded area) is interrogated multiple times, it is more efficient to build a single interpolant and reuse it for various geometry configurations.

Cloud data extraction is programmed for use with the WWMCA dataset provided in GRIB. However, with trivial modifications for input data format, this algorithm can be used for any cloud property dataset that provides the same type of data as WWMCA (cloud top and bottom, COD, CWP, CER, etc.). In this model, clouds are assumed to be spherical shells with a defined top and bottom centered on the respective grid point. It must be noted that these shells are currently assumed to cover the entire grid cell and thus have the same horizontal resolution of the data. The cloud properties are assumed to remain constant within the cloud, regardless of altitude. Since up to four different cloud layers can be defined for any latitude–longitude combination, it is essential to determine whether the path traverses through a particular layer. Furthermore, it is possible that the path point lies within a cloud but the entire path segment does not. For accurate radiative transfer calculations, the full extent of the path through the cloud must be determined and modeled accurately. Consequently, simply determining whether a path point lies within a spherical shell cloud is not enough. Rather, the intersection of the path with the cloud boundaries must be determined, and the calculated path points must be modified to include these new points that describe the cloud boundaries. This cloud geometry determination is visualized in Fig. 2.

The extent of a spherical shell cloud intersected along a path is determined from the latitude–longitude–altitude combination of the cloud top and bottom and the angular geometry of the path. The cloud height characteristics are described at each data grid point. Because of the spherical Earth assumption, the heights remain constant until the boundary of the next grid point. Therefore, the finite horizontal dimension of clouds is based on the horizontal resolution of the input data, which was 0.25° for this study. For each cloud present at any altitude along the line of sight, a slant-path distance from the bottom of the ground intersection point to the cloud altitude is determined using plane triangle geometry. Forward reckoning is then used to determine the latitude and longitude of the cloud top and bottom. Because the slant path to the bottom of the cloud is not guaranteed to intersect the cloud (higher or lower cloud may be present but not intersected), a test must be performed to determine whether the intersection occurs in the vicinity of the data point. Five possible conditions exist as follows:

  1. Slant path intersects cloud top and cloud bottom.
  2. Slant path intersects cloud bottom and cloud side.
  3. Slant path intersects cloud top and cloud side.
  4. Slant path intersects cloud sides.
  5. Slant path does not intersect cloud.

For conditions 1 and 5, the calculation of the portion of the slant path that traverses the cloud is trivial. For conditions 2–4, in which one of the four cloud sides is possibly intersected, this determination is far from simple. The approach taken here is first to determine which of the cloud sides is intersected by gridding the slant path between the cloud top and the cloud bottom and to determine via the distance from the cloud latitude–longitude boundaries which of the four sides is intersected. Then the distance coordinates of the actual intersection point are iteratively determined by increasing the grid spacing of the path between the cloud top and bottom until the error between the latitude or longitude corresponding to the side of interest falls below a threshold.

Once the slant-path coordinates for the cloud bottom and top intersection have been determined, they are added to the slant profile. The result is a path profile that has consistent spacing between path points except where it passes through a cloud. In this case the cloud boundary points are included. By including the cloud boundaries, the profile can be used to determine radiative transfer effects without altering the effects of clouds caused by poor geometry resolution. Finally, the slant-path points are bisected, and the meteorological properties at the midpoint are calculated. This enables a value for each layer, which is required by some radiative transfer codes. Standard output is corrected for surface elevation so that final values are given in altitude AGL. The algorithm returns a slant-path profile to include cloud microphysical properties and meteorological conditions.

d. Cloud effects modeling

Cloud liquid water content and cloud effective radius (CER; CED/2) have repeatedly been shown to be the most critical parameters in describing the optical properties of clouds. The CER is defined as the ratio of the third moment to the second moment of the cloud particle distribution,
re=0dNdrr3dr0dNdrr2dr,
where dN/dr is the cloud droplet distribution. Historically, several different distributions have been used to describe cloud particles, yet the two most consistently reported are the lognormal distribution and the modified gamma distribution given by
dNdr=Narαexp[αγ(rrmod)γ]=Narαexp(Brγ),
where N is the total number density and rmod is the mode or characteristic radius. The parameters α and γ describe the shape of the distribution, and N × a is a normalization constant. Maintaining the total number density N as a portion of the normalization constant allows the liquid water content to be altered without changing the size distribution (Hess et al. 1998). Extensive studies have shown that the CER is far more significant than the actual shape or width of the size distribution in describing the optical properties of liquid water clouds as calculated by Mie theory. Hu and Stamnes (1993) demonstrated that for most wavelengths, the differences between optical properties of clouds with equivalent CER but different distributions (lognormal and modified gamma) with entirely different widths were generally bounded by a maximum of 8%. Satellite retrievals of the CER and optical depth are acquired through the use of various algorithms, but they generally depend on measuring the reflection function in nonabsorbing and absorbing spectral channels [usually the visible and from microwave infrared (MWIR) to longwave infrared (LWIR)] and comparing the results to forward-modeled calculations spanning the set of possible cloud properties as demonstrated by Nakajima and King (1990). Since the forward modeling of the reflectance function requires knowledge of the entire vertical profile to include surface parameters for emissivity, the algorithm depends on several different outside data sources to correctly model radiance. The CTH is acquired by relating the cloud brightness temperature to NWP atmospheric temperature data.
The WWMCA cloud optical properties for liquid water clouds are computed using an eight-stream adding–doubling radiative transfer model that is driven using prescribed values of liquid water path (LWP) and CED. Treatment for ice clouds requires more consideration, as ice particles take on numerous shapes and sizes based on atmospheric conditions and geographic location. WWMCA retrievals are currently based on parameterized conditions for retrievals in specific geographic regions. Traditional satellite-based retrievals of cirrus water path can have large uncertainties that depend on the type of cirrus size distribution and ice-particle shapes that are assumed and are less consistent than liquid water cloud retrievals. From the derived water path and CED, optical depth can be obtained via
τ=34ρ0Qextdndrr2dr0dndrr3dr×CWP,
where Qext is the far-field extinction efficiency and ρ is the density of water or ice. In the visible, Qext ≈ 2, so Eq. (4) can be approximated as described in AFWA (2013),
τ=3×CWPρDeff.

Roadcap et al. (2015) examined WWMCA for single and multiple scattering through clouds at optical wavelengths. In their analysis, effective cloud optical depth was analyzed in relation to diffuse versus direct transmission for a select number of locations. While WWMCA was found to capture large-scale spatial variation of COD and effective cloud optical depth was found to be accurate compared to Mie calculations for polydisperse modified gamma cloud distributions, the lack of single-scatter parameters for closure of the multiple-scatter radiative transfer problem was specifically highlighted as a current deficiency. While the current state of cloud property collection does not allow for these parameters to be directly obtained, and current processing methods cannot calculate this information in a timely manner for operational distribution, this toolkit provides a means to automatically integrate WWMCA and NWP data for multiple-scattering calculations over any wavelength of interest.

It is important to note that the cloud optical properties for a given WWMCA grid point may not be self-consistent, in the sense that they may not satisfy Eq. (5). This is because slight variations occur when considering the complete Mie theory needed to obtain Qext in Eq. (4), but more so because each WWMCA grid point represents a relatively large geographical area (0.25° × 0.25°) over which a representative value is reported. The determination of cloud optical properties independently via averaging or statistical methods does not necessarily guarantee that the reported value remains consistent. For this reason, consistency is forced by assuming accuracy of CED and CWP and the use of Eq. (4) to determine optical depth.

The same consistency issue over a geographic area can arise for WWMCA-reported cloud-top heights and cloud bottoms. Within each grid box, a statistical method is applied to determine the extent of pixel-level CTH and CTB values; and in the merging process of multiple datasets, a representative value is assigned to each grid location based on the available data from AFWA (2013). CTH is known to be most accurate, as passive sensors cannot “see” through optically thick clouds. For the purposes of this model, cloud tops and bottoms are set at the WWMCA-reported levels, implicitly making the assumption that the relatively small variance in true cloud position will not make a significant impact on radiative transfer calculations.

Fitting a cloud size distribution from satellite data can be accomplished by fitting the CER to a modified gamma distribution as described in Eq. (3). Two assumptions must be made in order to fit this distribution. The first is that the distribution can be described based on the CER and a cloud effective variance (CEV), resulting in a form of the modified gamma distribution such that
dNdr=Nar(13νeff)/νeffexp(rreffνeff),
where γ=1, νeff is the effective variance of the distribution, and N × a is the normalization coefficient. The second assumption that must be made is the value of νeff. The radiative transfer models used to derive CER, COT, and CWP inherently assume a value for νeff. The Atmospheric Radiation Measurement (ARM) program assumes an effective variance value of 0.10 (Minnis et al. 1998), the International Satellite Cloud Climatology Project uses 0.15 (Rossow and Schiffer 1999), and the Moderate Resolution Imaging Spectroradiometer (MODIS) team uses 0.13 (Nakajima and King 1990; Arduini et al. 2005). The model described here allows the user to match the effective variance to the dataset used. Ongoing research suggests that the effective variance optimal value may best be modeled as variable (Arduini et al. 2005). This toolkit assumes the accuracy of the satellite-derived optical properties and models them accordingly.
Relating the satellite-derived CER and CEV to the modified gamma distribution of Eq. (6) used in LEEDR’s characterization of weather effects is accomplished via the transformations
γ=1,
α=13νeffνeff,
rmod=ανeffreff,and
B=αrmod.
The volume extinction coefficient βext is calculated via
βext=0dndr(Qextπr2)dr,
assuming a normalization coefficient N × a = 1, where Qext is calculated via Mie theory for the specified distribution. Using the cloud thickness obtained from the WWMCA-reported CTH and CBH, N × a is scaled so that the optical depth of the reported cloud matches the calculated optical depth, as described by
N×a=τβext×(CTHCTB).

By scaling the optical depth of a custom number distribution derived from satellite retrievals of CER and COD, this toolkit models the actual cloud extinction, including both absorption and scattering, for a spherical shell cloud for all wavelengths of interest. Radiative transfer theory can then be applied utilizing the resulting phase functions and extinction coefficients.

e. Profile scaling

Radiative transfer programs are usually level or layer based; thus, the computational expense and numerical stability (dependent on implementation) are a function of the number of layers required to realistically define the atmosphere. It is often desired to reduce the number of layers to the minimum required for accurate representation of atmospheric effects. This toolkit seeks to minimize the amount of atmospheric data required by assessing the optical thickness of the individual layers and combining optically thin layers. The use of a weighted average for the aerosol-, molecular-, and weather-induced scattering phase functions ensures that the scattering effects are described predominantly by those regions in which they are most present. The end result is a combined optical-depth-scaled atmospheric profile that includes absorption and scattering coefficients in addition to the component scattering phase functions for molecular, aerosol, and weather effects.

The phase functions output from LEEDR are calculated for the molecular, aerosol, and weather/hydrometeor scattering processes. To determine a single overall phase function for radiative transfer, each of these must be combined. This is accomplished by combining normalized phase functions via a weight proportional scattering optical depth. Furthermore, many applications require a phase function expanded in terms of Legendre polynomials. Explicit techniques for integrating the Legendre coefficients for phase function expansion are not well discussed in the literature and vary widely in accuracy. Schuster demonstrated that using Gaussian quadrature for integration and using the number of quadrature points equal to the number of desired Legendre expansion terms provides the greatest accuracy for highly peaked, anisotropic phase functions, such as those for aerosols and clouds (Schuster 2004). For this reason, Gaussian quadrature–derived Legendre coefficients are provided as an output.

3. Diffuse transmission climatology

The remote sensing toolkit developed to supplement LEEDR’s capabilities provides a new capability for analyzing and assessing cloud impacts on remote sensing operations. Of particular interest is the diffuse transmission through various clouds and the climatological limits they impose on operations.

The external GFS and WWMCA data sources used in this analysis are worldwide in extent with 0.5° and 0.25° resolution, respectively. For the purposes of this research, a subset of data was chosen for analysis to facilitate multiple attempts at modeling under various input conditions. A total of 15 000 random data points were selected from the worldwide grid without preference, as depicted in Fig. 3, via a random number generator. The sample points spanned the entire year of 2015 for the times 0000, 0600, 1200, and 1800 UTC. Blue points represent locations where the nadir-viewing line of sight passed through a cloud at some level of the atmosphere. Red points represent locations that had a cloud-free line of sight (CFLOS). Of the 15 000 points, 9890 were clouded and 5110 were cloud free.

Fig. 3.
Fig. 3.

The 15 000 random sample locations for diffuse transmission analysis. Blue points represent clouded conditions (9890), while red points represent a CFLOS between the surface and the observer (5110).

Citation: Journal of Atmospheric and Oceanic Technology 36, 2; 10.1175/JTECH-D-18-0078.1

For each point, the remote sensing toolkit was employed to determine the diffuse transmission for a nadir geometry configuration. The model was run with a U.S. Standard Atmosphere, 1976 (COESA 1976), for altitudes above 30 000 m, and a GFS-defined atmosphere with WWMCA-derived clouds for altitudes below 30 000 m. The diffuse transmission of light was determined by modeling a diffuse Lambertian point source propagated through the derived atmospheric profile utilizing a 16-stream DISORT multiple-scattering routine, as described by Stamnes et al. (2000). For this study, surface reflection/albedo interactions were not considered. Diffuse transmission results at nadir geometry can be seen in Fig. 4, where the blue lines represent cloud-free samples and the gray lines represent clouded conditions. The spread of modeled outputs spans the spectrum for clouded conditions, while the cloud-free cases are generally high transmission and tightly concentrated.

Fig. 4.
Fig. 4.

Spectral diffuse transmission for nadir geometry at 15 000 random sample dates, times, and locations as seen in Fig. 2. Blue lines represent cloud-free conditions, while gray lines represent various clouded conditions.

Citation: Journal of Atmospheric and Oceanic Technology 36, 2; 10.1175/JTECH-D-18-0078.1

To establish diffuse transmission climatologies for remote sensing applications, the results from 15 000 simulations were analyzed for band transmission over the spectral band of 300–1300 nm. Figure 5 depicts the probability distribution of diffuse band transmission for cloud, cloud free, and all cases combined. It is interesting to note that two nearly separate distributions appear between clouded and cloud-free conditions. A slight overlap is observed near 0.8 diffuse transmission. For clouded conditions, the distribution has three distinct modes, indicating that diffuse transmission can be broadly classified not only by the presence of clouds, but by the relative transmission. These three modes may be partially attributable to cloud type, with distinction between cumulus, stratus, and cirrus. Cirrus clouds are more heavily weighted toward higher transmissions. Cumulus cloud transmission values are generally weighted toward lower transmissions relative to the total distribution for all cloud types. However, distributions categorized by each individual cloud type still show a distinct trimodal distribution, suggesting that this classification does not fully account for the trimodal distribution. The maximum diffuse transmission observed is attributed to a cloud-free case, while the minimum transmission observed is attributed to a clouded case. Additionally, despite the three observable modes, there is appreciable probability of diffuse transmission across the entire range, which indicates that the wide range of cloud-microphysical properties induces significant variability. Such variability suggests simulation of those specific conditions is necessary to ascertain diffuse transmission with certainty.

Fig. 5.
Fig. 5.

Diffuse band transmission distribution and probability for nadir geometry. The histogram in yellow depicts 9890 cloud-free simulations, the histogram in red represents 5110 clouded simulations, the blue histogram represents the intersection of clouded and cloud-free cases, and the purple histogram represents all cases.

Citation: Journal of Atmospheric and Oceanic Technology 36, 2; 10.1175/JTECH-D-18-0078.1

Establishing percentiles of interest for diffuse transmission is accomplished via the cumulative discrete probability function. A specific percentile of performance refers to the diffuse transmission level at which the cumulative probability function is equal to the percentile of interest. Figure 6 visually depicts 10th–90th spectral and band transmission percentiles, as well as the spectral and band mean values. These percentiles can be used as performance limits for sensor employment. For example, the area between the 10th and 90th percentiles bounds 80% of the data, and one can reasonably expect that a random sample will fall between the limits imposed by these percentiles (0.248–0.844 for band transmission) with an 80% confidence level.

Fig. 6.
Fig. 6.

Worldwide climatology for diffuse transmission at nadir geometry based on random 15 000 samples. Gray lines depict the spectral diffuse transmission in the 300–1300-nm band for all samples. Solid lines represent the 10th–90th percentiles and the spectral mean, while dashed lines represent the band transmission for a 5800-K blackbody source.

Citation: Journal of Atmospheric and Oceanic Technology 36, 2; 10.1175/JTECH-D-18-0078.1

Confidence in the calculated percentiles is dependent on utilizing a representative sampling of data for calculations. This analysis considers the 2015 calendar year, sampled temporally on the hour at 0000, 0600, 1200, and 1800 UTC to coincide with GFS NWP model outputs. Subject to these limitations, it must be determined whether 15 000 samples accurately represent the dataset as a whole. While sample locations and times are randomly chosen, it is unlikely that only a few samples will accurately capture the performance distribution depicted in Fig. 6. Figure 7 shows the incremental change in percentile and mean band transmission as the number of samples increases from 1 to 15 000. With a single sample, all percentiles have the same value and then diverge as sampling increases. Large differences in values are evident through the first ~1000 samples. As sampling increases to 15 000, the behavior becomes asymptotic, indicating that the amount of sampling is large enough to encompass the variability in the underlying dataset. Also shown in Fig. 7 are the minimum and maximum values among the samples. Notably, the maximum samples and percentile reach a convergent asymptote far more quickly than the minimum and lower percentiles, indicating that the minimum values are far less frequently sampled than the higher values, consistent with Fig. 5. Increasing the number of samples will only lend further confidence to the established climatology and may be necessary if percentiles between 0 and 10 are of primary interest.

Fig. 7.
Fig. 7.

Evaluation of the number of samples required for analysis for worldwide climatology. The effect of increasing the number of samples is demonstrated via the solid lines, which represent the respective percentiles of band transmission, and the dashed lines, which represent the minimum, maximum, and mean values.

Citation: Journal of Atmospheric and Oceanic Technology 36, 2; 10.1175/JTECH-D-18-0078.1

The results in Fig. 6 are unfiltered in the sense that they represent the raw transmission between source and sensor. The effects of a specific sensor response have not been applied or considered in conjunction with the spectral features of the source function. The same analysis can be directly applied to samples where diffuse transmission is combined with a sensor response function, such as that depicted in blue in Fig. 8. For the purposes of this analysis, a 5800-K representative blackbody emission as illustrated by the red curve in Fig. 8 was assumed as the source function.

Fig. 8.
Fig. 8.

Representative spectral response and source functions. The blue curve depicts a nominal sensor response function in the 300–1300-nm band, while the red curve depicts the spectral source function of a 5800-K blackbody.

Citation: Journal of Atmospheric and Oceanic Technology 36, 2; 10.1175/JTECH-D-18-0078.1

As seen in Fig. 9, the addition of this particular response function shifts the entire distribution to lower diffuse transmission with the maximum value well below 60%. The shape of clouded, cloud-free, and all cloud cases remains relatively unchanged with a slight overlap between the cloud and cloud-free conditions. It is important to note that this represents the total diffuse transmission between the source and the sensor with respect to the 5800-K blackbody and reduction in value compared to diffuse transmission without sensor impacts.

Fig. 9.
Fig. 9.

Diffuse band transmission distribution and probability, including sensor response function effects. The histogram in yellow depicts 9890 cloud-free simulations, the histogram in red represents 5110 clouded simulations, the blue histogram represents the intersection of clouded and cloud-free cases, and the purple histogram represents all cases.

Citation: Journal of Atmospheric and Oceanic Technology 36, 2; 10.1175/JTECH-D-18-0078.1

Figure 10 is analogous to Fig. 8 but also applies the sensor response function. The effects are clearly seen in the spectral signatures of the diffuse transmission, as they closely mimic the shape of the sensor response function. There is far greater variability in the spectral transmission across the band than in Fig. 8 for each sample and subsequent percentile. Additionally, the respective band transmissions are significantly lower. Note that the peak spectral response and the band transmission tend to have a greater separation than in the nonresponse function case, indicating a greater variability in spectral versus band transmission differences. The convergence of sampling data is consistent with the case that does not apply a sensor response (not shown).

Fig. 10.
Fig. 10.

Worldwide climatology for diffuse transmission based on 15 000 random samples, including sensor response function effects. Gray lines depict the spectral diffuse transmission in the 300–1300-nm band for all samples. Solid lines represent the 10th–90th percentiles and the spectral mean, while dashed lines represent the band transmission for a 5800-K blackbody source.

Citation: Journal of Atmospheric and Oceanic Technology 36, 2; 10.1175/JTECH-D-18-0078.1

Spectral angles are used by the remote sensing community to evaluate hyperspectral imagery for the purpose of comparing spectral similarity between two spectra. Spectral angles are used in this study to assess the variation in spectral diffuse transmission signatures in the developed worldwide climatology. A spectral angle is defined as the n-dimensional angle between two spectra that are treated as vectors in space where, in this case, n is the number of wavelengths in the spectral band under consideration. A value of 90° represents two signatures that are opposite of each other in terms of direction, while a value of 0° indicates two identical signatures in terms of direction. The spectral angle does not consider the magnitude of the signatures; therefore, two signatures of the same shape or angle but different magnitude would be assessed as zero. Figure 11 shows the distribution of spectral angle differences between the spectral mean diffuse transmission and the 15 000 different samples. Overall, the spectral angle differences are relatively small considering that the possible values range from 0° to 90°. However, the lack of nonzero values suggests that each cloud condition is unique and produces a unique spectral signature. While the band transmission values may be comparable, the particular inputs and physical processes have been uniquely captured in the model. Thus, starting with a physics-based model reveals a trend in output performance that can be described with climatological bounds at a given confidence level. For reference, the bottom portion of Fig. 11 shows the two spectral transmission signatures that are most different as measured by the spectral angle.

Fig. 11.
Fig. 11.

Spectral angle variance in 15 000 worldwide climatology samples. (top) The distribution of spectral angle difference between the spectral mean and the 15 000 samples. (bottom) The two spectral diffuse transmission signatures with the greatest spectral angle difference.

Citation: Journal of Atmospheric and Oceanic Technology 36, 2; 10.1175/JTECH-D-18-0078.1

4. Conclusions

Real-time inclusion of cloud data in atmospheric radiative transfer modeling is critically important when assessing many remote sensing applications and scenarios. Historically, modeling and simulation have relied on standard atmospheres to gauge and bracket sensor performance to limiting conditions. While this is useful in design studies and performance comparisons, it does little to identify realistic and actual atmospheric conditions that pose a threat to successful operational employment. LEEDR is a verified and validated atmospheric characterization and radiative transfer code that creates physically realizable vertical and horizontal profiles of meteorological data; and coupled with NWP model output, LEEDR enables analysis, nowcasts, and forecasts for radiative effects expected for real-world scenarios. Remotely sensed multi-, hyper-, and ultraspectral sensor data are particularly susceptible to atmospheric effects, with scattering in optically thick media such as clouds presenting one of the greatest challenges. In this study, LEEDR has been coupled with the U.S. Air Force’s WWMCA cloud data in a new toolset that enables radiance and direct/diffuse transmission calculations through clouds from UV to RF wavelengths.

This research leveraged NWP, to include the WWMCA data, and focused on diffuse transmission in the 300–1300-nm band and the development of worldwide cloud climatology for sensor performance. In this band, percentiles for diffuse transmission were established for the 10th–90th percentiles under various engagement assumptions with limiting performance between 0.248 and 0.889. The inclusion of an arbitrary sensor response function significantly alters the results and demonstrates the need for sensor-specific modeling in the spectral regions of interest. Furthermore, the spectral signatures are shown to possess variability across the band. Dependent on application, the broad standard cloud type classification system may not be sufficient in characterizing sensor performance in terms of diffuse transmission.

It must be noted that while this research develops a system capable of examining the complex interactions of clouds and atmospheric conditions and their effects on remote sensing systems, the methods described are based on various assumptions that have potentially large implications. The fact that worldwide climatology can be established with confidence using a relatively small number of samples is promising for future modeling efforts, but these specific bounds and percentiles should be used with caution.

Limited by the availability of worldwide cloud data and the wide variability of cloud types provided in the datasets, the subgrid cloud variation was not addressed in this study. Rather, a simple but likely unrealistic homogeneous cloud was assumed across the entire cloud layer. By running multiple calculations utilizing the independent pixel (column) approximation and spatially averaging based on an assumed or known distribution such as the gamma distribution, it is expected that diffuse transmission would increase. Homogeneous clouds almost certainly overestimate absorptance and likely skew the results. Additionally, cloud overlapping is assumed to be a maximum overlap scheme, as opposed to using a random overlap scheme. This also adds to increased absorptance and reduced transmission through layered clouds. Surface reflectivity is not considered. In essence, the calculations performed here assume a worst-case scenario when concerned with overall transmission from surface to space. Follow-on research to this study could incorporate subgrid-scale cloud variations and reduce the plane-parallel biases with the methods outlined in Cahalan and Joseph (1989), Barker et al. (1996), and Oreopoulos and Barker (1999).

While the application of this software greatly extends current capabilities, it comes with a computational cost. Effectively analyzing site and worldwide cloud climatologies for various conditions, geometries, and locations requires significant computational power in the form of cluster and high-performance computing environments. Each calculation performed here varied in computational time but took approximately a minute when averaged across all samples. While this research examined 15 000 cases for 2015 and suggested that climatological limits were effectively established for most percentiles considered, given sufficient resources, a multiyear climatology could be established. Expanding the data to include multiple years has the potential to change the number of samples required to confidently establish performance limits because of additional variations in the underlying data. Future efforts to identify and quantify the influence of particular cloud and atmosphere microphysical parameters on total system performance metrics via robust statistical methods would further enable faster physics-informed parameterizations for reduced computational expense. Additionally, further research into atmospheric correction, the process of removing atmospheric absorption and scattering effects to obtain surface reflectance characterizations, for observed diffuse transmittance and radiances would also be significant for materials and plume detection and identification purposes.

This improved model, which provides an efficient way to integrate LEEDR with WWMCA and NWP data, extends optical wavelength observations of cloud parameters across the spectrum for physics-based modeling of multiple-scattering effects through cloudy and clear atmospheres. While this research was focused on the 300–1300-nm band, the ability to describe a realistic atmosphere for any location worldwide and any wavelength in the spectrum opens the door to new analysis possibilities. Inclusion of microphysical properties for clouds provides unique physics-based results for each model run and insight into actual sensor performance expectations. Derived from a single optical wavelength, the ability to probe any spectral band or line is invaluable. While operational systems, particularly in the intelligence community, are focused on system-specific configuration, a detailed and versatile research model enables a broad range of atmospheric-data-driven analyses previously unavailable for remote sensing applications.

Acknowledgments

The authors thank the U.S. Air Force for sponsoring and supporting the dissertation research of the lead author. Additionally, the authors are appreciative of the comments and suggestions of two thoughtful reviewers, who significantly improved the paper. The views expressed in this paper are those of the authors and do not necessarily reflect the official policy or position of the U.S. Air Force, the Department of Defense, or the U.S. government.

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