Exploiting MODTRAN Radiation Transport for Atmospheric Correction: The FLAASH Algorithm A. Berk a, S. M. Adler-Golden a, A. J. Ratkowski b, G. W. Felde b, G. P. Anderson b, M. L. Hoke b, T. Cooley b, J. H. Chetwynd b, J. A. Gardner b,c, M. W. Matthew a, L. S. Bernstein a, P. K. Acharya a, D. Miller d, P. Lewis e a
b
Spectral Sciences, Inc., Burlington, MA 01803 (
[email protected]) Air Force Research Laboratory, Space Vehicles Directorate, Hanscom AFB 01731 c University of Arizona, Tucson, AZ 85721 d SITAC, Fairfax, VA 22033 e NIMA, Reston VA 20191
Abstract -Terrain categorization and target detection algorithms applied to Hyperspectral Imagery (HSI) typically operate on the measured reflectance (of sun and sky illumination) by an object or scene. Since the reflectance is a non-dimensional ratio, the reflectance by an object is nominally not affected by variations in lighting conditions. Atmospheric Correction referred to as Atmospheric 'Compensation', 'Characterization', etc.) Algorithms (ACAs) are used in applications of remotely sensed HSI data to correct for the effects of atmospheric propagation on measurements acquired by air and space-borne systems. The Fast Lineof-sight Atmospheric Analysis of Spectral Hypercubes (FLAASH) algorithm is an ACA created for HSI applications in the visible through shortwave infrared (Vis-SWIR) spectral regime. FLAASH derives its 'physics-based' mathematics from MODTRAN4. Keywords: Hyperspectral Imagery, Radiative Transfer, Remote Sensing, MODTRAN, FLAASH, Atmospheric Correction
FLAASH draws on existing spectral analysis methods and codes that have been developed for both research and general use (e.g., [1, 2, 3, 4, 5]). It is designed as a generalpurpose code and has been developed in parallel with upgrades to MODTRAN [6], the radiative transfer (RT) algorithm that provides the physical understanding behind the mathematical assumptions in FLAASH, in order to take advantage of the latest improvements in accuracy and speed. FLAASH is currently interfaced with MODTRAN4 [7, 8, 9] and provides the following capabilities: •
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1 Background on FLAASH development The atmospheric correction algorithm/code FLAASH (Fast Line-of-sight Atmospheric Analysis of Spectral Hypercubes) is a software package developed by the Air Force Research Laboratory, Space Vehicles Directorate (AFRL/VS), Hanscom AFB and Spectral Sciences, Inc. (SSI) to support the analyses of visible-to-shortwave infrared (Vis - SWIR) hyperspectral and multispectral imaging sensors. The main objectives are to: provide accurate, physics-based derivation of atmospheric properties such as surface pressure (surrogate for relative altitude), water vapor column, aerosol and cloud overburdens, to incorporate those same quantities into a correction matrix, and, finally, to invert 'radiance-at-detector' measurements into 'reflectance-atsurface' values. Atmospheric correction serves a critical role in the processing of remotely sensed image data, particularly with respect to identification of pixel content. Efficient and accurate realization of images in units of reflectance, rather than radiance, is essential for building consistency into the development, maintenance, distribution, and analysis of any library of such images, acquired under a variety of measurement conditions.
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Default support for AVIRIS and HYDICE, with full options for User Specification for similar hyperspectral near-IR/visible/UV imaging sensors; Graphical user interface for performing MODTRAN4 spectral calculations, including data simulations (based on IDL), with a commercial version available through ENVI [10]; Data-derived column water vapor, relative surface altitude (from column oxygen) and cloud-mask image files and displays, plus an aerosol estimate, each derived from MODTRAN4-based calculations, built into accessible Look-Up Tables (LUTs); Atmospherically corrected images (i.e., surface spectral reflectances) for non-thermal wavelengths (mid-IR through UV), including an image-sharpening 'adjacency ' correction, with an internal ‘polishing’ algorithm.
FLAASH options for interfacing to MODTRAN5 and for processing of multi-spectral imaging (MSI) data such as Landsat and MTI are under development. MODTRAN5 will provide many new options including finer spectral resolution and treatment of auxiliary atmospheric gases. The atmospheric correction algorithm/code’s primary capabilities center on retrieval of spectrally resolved atmospheric and surface properties for the individual pixels within an entire data cube, measured in a defined viewing geometry, by fully employing MODTRAN4’s radiative transfer capabilities; see Figure 1.
first and second terms are not identical. The ρe(numerator) represents a weighted average reflectance over the surface region (typically around 1 km in width when viewed from a high-altitude sensor) that contributes to atmospherically scattered photons leaving the ground and arriving at the sensor. The ρe(denominator) represents an average reflectance over an even larger region, representative of photons that left the surface once, but have then been re-scattered, via S, back to the surface and then into the sensor. However, because S is small and the differences in the size of the two averaging regions are not critical, the two averaged reflectances may be equated with little error.
Figure 1. Top (left to right) – Radiance image and associated FLAASH-processed reflectance image, without and with the adjacency correction. Bottom – Associated endmember extractions for each image.
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Description of FLAASH
As noted above, FLAASH processes radiance images with spectral coverage from the mid-IR through UV wavelengths where thermal emission can be neglected. For this situation the spectral radiance L* at a sensor pixel may be parameterized as [11, 12, 13, 14]
L* =
Bρ e Aρ + + L*a 1 − ρe S 1 − ρe S
(1)
where ρ is the pixel surface reflectance, ρe is an average surface reflectance for the surrounding region, S is the spherical albedo of the atmosphere (capturing the backscattered surface-reflected photons), L*a is the radiance backscattered by the atmosphere without reaching the surface, and A and B are surface independent coefficients that vary with atmospheric and geometric conditions. All of the variables are implicitly wavelength dependent. The first term in (1) corresponds to the radiance reaching the surface (from both sky-shine and direct solar illumination) that is backscattered directly into the sensor, while the second term corresponds to the radiance from the surface that is rescattered by the atmosphere into the sensor. Equation (1) applies rigorously to monochromatic light. However, because S is small (of order 10-2 to 10-1 for clear sky) and surface reflectance terms are generally slowly varying spectrally, the radiance-reflectance relationship is sufficiently linear that (1) accurately describes the spectrally-degraded radiance, derived from the convolution of the monochromatic radiance. The spatially averaged reflectance, ρe, is used to account for "adjacency effects", i.e., radiance contributions that, because of atmospheric scattering, originate from parts of the surface not in the direct line of sight between sensor and targeted pixel. Strictly speaking, the ρe in the numerator of the second term and in the denominators of both the
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FLAASH begins by accessing user-supplied parameters, specifying: a) the hyperspectral data type, b) the sensor that was used to obtain the data, and c) any 'known' information MODTRAN needs for generating atmospheric information (‘metadata’ related to the conditions of the acquisition, such as sensor altitude, solar and viewing geometry). A response “channel function”, describing the spectral resolution and response characteristics for the sensor, is either generated or otherwise predefined. The preliminary column water vapor is retrieved on a pixel-by-pixel basis. The FLAASH algorithm uses MODTRAN calculations that loop over a series of staged water profiles in order to create a water vapor Look-Up Table (LUT), which is generated by applying a scale factor to the nominal water profile of the model atmosphere. To insure that there is sufficient column water variability to encompass the actual conditions of the measurement, even if the model atmosphere is not well chosen, a MODTRAN restriction (that imposes a physical limit of 100% relative humidity at each atmospheric level) is ignored. While this assumption violates the saturation characterization of the atmosphere, it typically does not adversely impact the Vis-SWIR spectroscopy. Furthermore, the 100% RH limit is somewhat arbitrary unless independent temperature profile data is accessed. [NOTE: the presumption of supersaturation in the thermal spectral range may have significant impact upon the calculated radiances.] The basis of the retrieval algorithm is the strong dependence/correlation of water vapor column amount to the ratio of ‘reference’ (the shoulders of the absorption band) and ‘absorption’ (center of the same absorption band) radiances. The retrieved water vapor also depends somewhat on the absolute values of these radiances, which vary most directly with the surface reflectance. This dependence arises because the amount of water absorption in the atmospherically-scattered and surface-reflected radiance components is slightly different; the absorption is generally smaller for the atmospherically scattered photons, which avoid the high concentration of water vapor close to the ground. A three-dimensional LUT is then built around these dependencies. The LUT-captured water vapor column amount (in increments ranging from low to very high values) for both the “absorption” and the “reference” bandpasses must span
the full range of expected values. For simplicity, the adjacency effect is ignored in this preliminary water retrieval, so that ρe and ρ are taken as equal in (1). The MODTRANgenerated A+B, S, and L*a coefficients are then used to simulate a set of absorption and reference radiances L* for a finely-spaced series of reflectances (0, 0.01, 0.02 ... 0.99, 1.00). The result is a set of triples, consisting of {column water vapor, reference radiance, absorption radiance} that span both the entire expected range of water column and surface reflectances. These values are initially evenly spaced in the dependent variable to be retrieved (water vapor) but not in the independent variables (measured radiance). The triples are transformed into an evenly gridded, 2dimensional LUT, for which the reference radiance and ratio are the independent variables and the water vapor is the dependent variable. This 2-dimensional LUT is then searched to retrieve the water vapor. In occasional instances, the reference radiance or ratio value may lie outside the LUT. In such cases the pixel is flagged to denote LUT failure, and the water vapor for that pixel is then replaced by the average of the valid retrievals for the scene. FLAASH also generates a cloud "mask" that identifies cloud-containing pixels in a scene. At the present time, the main uses of the cloud mask are (1) to indicate regions where the atmospheric correction is corrupted/contaminated by opaque or translucent clouds, and (2) to flag pixels that need to be removed from the calculation of L*e (the ‘adjacency’ smoothing radiance). Because clouds do not contribute to the near-surface pixel cross-talk, cloud-filled pixels are replaced by the scene average radiance. Following [15, 16], the FLAASH cloud mask algorithm is based on combining tests for brightness, color balance, and low column water in the visible and SWIR regions. A second component to the cloud mask uses the brightness of the 1.38 µm water vapor band to identify cirrus or other high-altitude clouds, including transparent or otherwise tenuous occurrences, following the approach of [17]. Under clear sky conditions, the center of this band is very dark, as the photons must traverse the entire water vapor column to the surface; the two-way path is generally opaque. However, when cirrus clouds are present, the photon path is at least partially truncated at the altitude of the cloud, diminishing the absorption and allowing the reflectance/scattering of the solar irradiance by the cloud particles to be observed. This mask for cirrus clouds, then, is predicated upon detecting an enhanced brightness. Specifically FLAASH uses the radiance values measured in one or two channels nearest 1.375 µm. While any truly opaque cloud (including cirrus) triggers the replacement of the associated cloud-filled pixels with a ‘scene average’ value when calculating the adjacency field, the cirrus cloud mask is only a flag, and the pixel radiance continues to be used within the adjacency correction; see below.
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To implement adjacency correction in both the reflectance calculation and the aerosol retrieval, it is necessary to convolve the data cube over a point-spread function that describes the atmospheric scattering of ground-reflected photons into the sensor pixel. This convolution must be performed after the application of the cloud mask. FLAASH currently assumes that the point-spread function is a modified radial exponential, independent of both wavelength and visibility to first order. [In reality, both wavelength and visibility impact the radial extent of adjacency contamination, since the spectral cross-talk among neighboring pixels is attributed to atmospheric scattering.] The width (radius) of the point-spread function is determined from a MODTRAN-based single-scattering calculation that accounts for the sensor altitude, a presumed or derived aerosol scale height and a nominal aerosol phase function. The spatial convolution is then performed. The result is a new data cube of spatially convolved spectral radiance, denoted L*e. The visibility or aerosol overburden (optical column, not vertical structure) is currently addressed through a general reflectance ratio-based algorithm, retrieving only the scene-average aerosol amount. The algorithm is based on the empirical observation by [18] that for natural dark terrain (primarily vegetation) the reflectances at certain wavelengths, such as 0.66 µm and 2.1 µm, are in nearly a fixed ratio (for these wavelengths, the ratio is between 0.4 and 0.5). There are obviously other approaches to aerosol overburden determination, some involving the Angstrom slope methodology [19], which is also now incorporated into MODTRAN4 as an additional option for inclusion of aerosol optical properties. After the atmospheric retrievals are performed, (1) is solved for the pixel surface reflectances in all of the sensor channels. The solution is based on a method in which the spatially averaged radiance image L*e (as derived above) is used to estimate the averaged reflectance ρe. This is done using an approximate equation derived from (1):
L*e =
( A + B )ρe + L* 1 − ρe S
a
(2)
As in (1), the variables are all wavelength- (or equivalently, channel-) dependent. Starting from the known L*e for each pixel and the coefficients A, B, S and L*e (which are extracted from the MODTRAN radiance simulations), Equation (2) is solved for ρe. The result is inserted into (1), which is then solved for the reflectance, ρ. As a final step, ‘polishing’, a term coined by [20] to describe a mathematical renormalization method for removing artifacts from reflectance spectra using only the data itself, can be applied to the new ‘reflectance’ cube. When properly implemented, polishing dramatically reduces spurious, systematic spectral structure due to wavelength regis-
tration errors and molecular absorption residuals while leaving true spectral features of the surface intact. It is important to note that polishing can also hide any incorrect application of an atmospheric correction algorithm, due to wavelength shifts, and otherwise inaccurate implementation. To the extent that residual sharp features in reflectance can be correlated with atmospheric transmittance or solar irradiance features, then the process can be iterated.
3
MODTRAN
MODTRAN4 [6, 9], as employed in FLAASH calculations, requires only a subset of the full suite of MODTRAN capabilities. All versions of MODTRAN4 include the important H2O band corrections of [21]. For the purpose of creating required LUTs, compatible to the sensor specifications and metadata, MODTRAN need only employ some downward viewing angle (typically nadir or moderately offnadir) with designation of the solar zenith angle and sensor altitude. For some purposes, the flight line intersection with the sun line can create an azimuthal dependence not yet fully captured by FLAASH. A new MODTRAN4 capability employs a faster multiple scattering approach, based on tuned spectral selection for full DISORT [22] calculations, while producing a complete spectral suite for the faster MODTRAN-default multiple scattering option [23]. A ratio of the two calculations is derived for each pair of overlapping values, with that scaling interpolated between all the intervening ISAAC-only values. This process is most accurate in atmospheric windows where the multiple scattering effects are most significant. Additionally, MODTRAN4 features pressure dependent profile option (MODEL=8), user-specified cloud spectral phase functions, O2 collision bands, the CKD2.4 H2O continuum [24], a 5 cm-1 band model, improved phase function representation for DISORT, and HITRAN2k + 2001 Updates [25]. In summary, the MODTRAN4 radiative transfer code, with its correlated-k Beer’s Law algorithm [26, 27] can efficiently and accurately calculate the scattering and absorption signatures of realistic molecular, aerosol and cloudy environments in the lower and middle atmosphere. The current approach for molecular absorption accommodates line overlap and partial correlations between both molecular species and the solar irradiance, while maintaining internal band model spectral resolution at either 1 cm-1, 5 cm-1 or 15 cm-1 binning. Preliminary verification, validation and assessment (VV & A) of MODTRAN4, Version 2 have shown it capable of improved syntheses, analyses and detection of total (direct plus scattered) solar and thermal energy components for cloud and aerosol decks, plumes and other realistic, non-clear sky conditions. Validation is typically provided through two avenues. The first involves direct comparisons with line-by-line calculations, as exemplified by FASE (FASCODE for the En-
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vironment, [28]). DoD and DOE jointly developed the FASE line-by-line (LBL) algorithm from FASCODE [29] with its optimized line-shape decomposition algorithm [30]. FASE can be considered the molecular standard for layer effective optical depths, single scattering albedos, and transmittances. Direct comparisons with FASE enable the MODTRAN4 algorithm to be refined for more flexible spectral resolution plus efficient and accurate determination of those layer quantities necessary for multiple scattering applications; e.g. DISORT [22] and a simpler 2-stream model [23]. The second validation step centers on comparisons against a variety of measurements, including those made with airborne sensors such as AVIRIS [31], in the visible through short-wave infrared (SWIR), and HIS (High-resolution Interferometric Spectrometer, e.g. [32]), in the mid-wave and long-wave infrared (MWIR and LWIR), both under both clear and clouded skies. Even broad-band measurements, related to cavities and integrating spheres, have served as MODTRAN4 validation tests; a large DOE/NOAA campaign [33], designed to intercompare a suite of pyrgeometers, has employed MODTRAN4 to provide both a common wavelength transfer among instruments and a tool for translation of sonde data into radiance calculations.
4
Conclusion
FLAASH is now in commercial release (RSI/ENVI) [10]; it has a foundation based on the atmospheric physics and spectroscopy contained in MODTRAN4, Version 2, released in 2002. Both FLAASH and MODTRAN4v2 have been used in a number of experimental assessments, which, in turn, serve to revalidate the codes and establish their functionality. Future efforts will continue to focus on accuracy evaluations, improvements, particularly with respect to aerosol, cloud and surface characterization.
5
Acknowledgment
The work at Spectral Sciences, Inc. was supported by US Air Force Contract F19628-91-C-0145 and F19628-98C-0048. The release of MODTRAN4 has been greatly facilitated by the collaboration between AFRL and John Schroeder, of ONTAR Corp.
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