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Fractals and Spatial Methods for Mining Remote Sensing Imagery
The rapid increase in digital remote sensing and GIS data raises a critical problem -- how can such an enormous amount of data be handled and analyzed so that useful information can be derived quickly? Efficient handling and analysis of large spatial data sets is central to environmental research, particularly in global change studies that employ time series. Advances in large-scale environmental monitoring and modeling require not only high-quality data, but also reliable tools to analyze the various types of data. A major difficulty facing geographers and environmental scientists in environmental assessment and monitoring is that spatial analytical tools are not easily accessible. Although many spatial techniques have been described recently in the literature, they are typically presented in an analytical form and are difficult to transform to a numerical algorithm. Moreover, these spatial techniques are not necessarily designed for remote sensing and GIS applications, and research must be conducted to examine their applicability and effectiveness in different types of environmental applications. This poses a chicken-and-egg problem: on one hand we need more research to examine the usability of the newer techniques and tools, yet on the other hand, this type of research is difficult to conduct if the tools to be explored are not accessible. Another problem that is fundamental to environmental research are issues related to spatial scale. The scale issue is especially acute in the context of global change studies because of the need to integrate remote-sensing and other spatial data that are collected at different scales and resolutions. Extrapolation of results across broad spatial scales remains the most difficult problem in global environmental research. There is a need for basic characterization of the effects of scale on image data, and the techniques used to measure these effects must be developed and implemented to allow for a multiple scale assessment of the data before any useful process-oriented modeling involving scale-dependent data can be conducted. Through the support of research grants from NASA, we have developed a software module called ICAMS (Image Characterization And Modeling System) to address the need to develop innovative spatial techniques and make them available to the broader scientific communities. ICAMS provides new spatial techniques, such as fractal analysis, geostatistical functions, and multiscale analysis that are not easily available in commercial GIS/image processing software. By bundling newer spatial methods in a user-friendly software module, researchers can begin to test and experiment with the new spatial analysis methods and they can gauge scale effects using a variety of remote sensing imagery. In the following, we describe briefly the development of ICAMS and present application examples.
Automated Verification of Spatial Resolution in Remotely Sensed Imagery
Image spatial resolution characteristics can vary widely among sources. In the case of aerial-based imaging systems, the image spatial resolution characteristics can even vary between acquisitions. In these systems, aircraft altitude, speed, and sensor look angle all affect image spatial resolution. Image spatial resolution needs to be verified with estimators that include the ground sample distance (GSD), the modulation transfer function (MTF), and the relative edge response (RER), all of which are key components of image quality, along with signal-to-noise ratio (SNR) and dynamic range. Knowledge of spatial resolution parameters is important to determine if features of interest are distinguishable in imagery or associated products, and to develop image restoration algorithms. An automated Spatial Resolution Verification Tool (SRVT) was developed to rapidly determine the spatial resolution characteristics of remotely sensed aerial and satellite imagery. Most current methods for assessing spatial resolution characteristics of imagery rely on pre-deployed engineered targets and are performed only at selected times within preselected scenes. The SRVT addresses these insufficiencies by finding uniform, high-contrast edges from urban scenes and then using these edges to determine standard estimators of spatial resolution, such as the MTF and the RER. The SRVT was developed using the MATLAB programming language and environment. This automated software algorithm assesses every image in an acquired data set, using edges found within each image, and in many cases eliminating the need for dedicated edge targets. The SRVT automatically identifies high-contrast, uniform edges and calculates the MTF and RER of each image, and when possible, within sections of an image, so that the variation of spatial resolution characteristics across the image can be analyzed. The automated algorithm is capable of quickly verifying the spatial resolution quality of all images within a data set, enabling the appropriate use of those images in a number of applications.
Graph Theory Roots of Spatial Operators for Kinematics and Dynamics
Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.
Spatial Statistical Data Fusion (SSDF)
As remote sensing for scientific purposes has transitioned from an experimental technology to an operational one, the selection of instruments has become more coordinated, so that the scientific community can exploit complementary measurements. However, tech nological and scientific heterogeneity across devices means that the statistical characteristics of the data they collect are different. The challenge addressed here is how to combine heterogeneous remote sensing data sets in a way that yields optimal statistical estimates of the underlying geophysical field, and provides rigorous uncertainty measures for those estimates. Different remote sensing data sets may have different spatial resolutions, different measurement error biases and variances, and other disparate characteristics. A state-of-the-art spatial statistical model was used to relate the true, but not directly observed, geophysical field to noisy, spatial aggregates observed by remote sensing instruments. The spatial covariances of the true field and the covariances of the true field with the observations were modeled. The observations are spatial averages of the true field values, over pixels, with different measurement noise superimposed. A kriging framework is used to infer optimal (minimum mean squared error and unbiased) estimates of the true field at point locations from pixel-level, noisy observations. A key feature of the spatial statistical model is the spatial mixed effects model that underlies it. The approach models the spatial covariance function of the underlying field using linear combinations of basis functions of fixed size. Approaches based on kriging require the inversion of very large spatial covariance matrices, and this is usually done by making simplifying assumptions about spatial covariance structure that simply do not hold for geophysical variables. In contrast, this method does not require these assumptions, and is also computationally much faster. This method is fundamentally different than other approaches to data fusion for remote sensing data because it is inferential rather than merely descriptive. All approaches combine data in a way that minimizes some specified loss function. Most of these are more or less ad hoc criteria based on what looks good to the eye, or some criteria that relate only to the data at hand.
Advances in Spectral-Spatial Classification of Hyperspectral Images
Recent advances in spectral-spatial classification of hyperspectral images are presented in this paper. Several techniques are investigated for combining both spatial and spectral information. Spatial information is extracted at the object (set of pixels) level rather than at the conventional pixel level. Mathematical morphology is first used to derive the morphological profile of the image, which includes characteristics about the size, orientation, and contrast of the spatial structures present in the image. Then, the morphological neighborhood is defined and used to derive additional features for classification. Classification is performed with support vector machines (SVMs) using the available spectral information and the extracted spatial information. Spatial postprocessing is next investigated to build more homogeneous and spatially consistent thematic maps. To that end, three presegmentation techniques are applied to define regions that are used to regularize the preliminary pixel-wise thematic map. Finally, a multiple-classifier (MC) system is defined to produce relevant markers that are exploited to segment the hyperspectral image with the minimum spanning forest algorithm. Experimental results conducted on three real hyperspectral images with different spatial and spectral resolutions and corresponding to various contexts are presented. They highlight the importance of spectral–spatial strategies for the accurate classification of hyperspectral images and validate the proposed methods.
Satellites quantify the spatial extent of cyanobacterial blooms across the United States at multiple scales
Previous studies indicate that cyanobacterial harmful algal bloom (cyanoHAB) frequency, extent, and magnitude have increased globally over the past few decades. However, little quantitative capability is available to assess these metrics of cyanoHABs across broad geographic scales and at regular intervals. Here, the spatial extent was quantified from a cyanobacteria algorithm applied to two European Space Agency satellite platforms—the MEdium Resolution Imaging Spectrometer (MERIS) onboard Envisat and the Ocean and Land Colour Instrument (OLCI) onboard Sentinel-3. CyanoHAB spatial extent was defined for each geographic area as the percentage of valid satellite pixels that exhibited cyanobacteria above the detection limit of the satellite sensor. This study quantified cyanoHAB spatial extent for over 2,000 large lakes and reservoirs across the contiguous United States (CONUS) during two time periods: 2008–2011 via MERIS and 2017–2020 via OLCI when cloud-, ice-, and snowfree imagery was available. Approximately 56% of resolvable lakes were glaciated, 13% were headwater, isolated, or terminal lakes, and the rest were primarily drainage lakes. Results were summarized at national-, regional-, state-, and lake-scales, where regions were defined as nine climate regions which represent climatically consistent states. As measured by satellite, changes in national cyanoHAB extent did have a strong increase of 6.9% from 2017 to 2020 (|Kendall’s tau (τ)| = 0.56; gamma (γ) = 2.87 years), but had negligible change (|τ| = 0.03) from 2008 to 2011. Two of the nine regions had moderate (0.3 ≤ |τ| < 0.5) increases in spatial extent from 2017 to 2020, and eight of nine regions had negligible (|τ| < 0.2) change from 2008 to 2011. Twelve states had a strong or moderate increase from 2017 to 2020 (|τ| ≥ 0.3), while only one state had a moderate increase and two states had a moderate decrease from 2008 to 2011. A decrease, or no change, in cyanoHAB spatial extent did not indicate a lack of issues related to cyanoHABs. Sensitivity results of randomly omitted daily CONUS scenes confirm that even with reduced data availability during a short four-year temporal assessment, the direction and strength of the changes in spatial extent remained consistent. We present the first set of national maps of lake cyanoHAB spatial extent across CONUS and demonstrate an approach for quantifying past and future changes at multiple spatial scales. Results presented here provide water quality managers information regarding current cyanoHAB spatial extent and quantify rates of change.
Satellites Quantify the Spatial Extent of Cyanobacterial Blooms Across the United States at Multiple Scales
Previous studies indicate that cyanobacterial harmful algal bloom (cyanoHAB) frequency, extent, and magnitude have increased globally over the past few decades. However, little quantitative capability is available to assess these metrics of cyanoHABs across broad geographic scales and at regular intervals. Here, the spatial extent was quantified from a cyanobacteria algorithm applied to two European Space Agency satellite platforms—the MEdium Resolution Imaging Spectrometer (MERIS) onboard Envisat and the Ocean and Land Colour Instrument (OLCI) onboard Sentinel-3. CyanoHAB spatial extent was defined for each geographic area as the percentage of valid satellite pixels that exhibited cyanobacteria above the detection limit of the satellite sensor. This study quantified cyanoHAB spatial extent for over 2,000 large lakes and reservoirs across the contiguous United States (CONUS) during two time periods: 2008–2011 via MERIS and 2017–2020 via OLCI when cloud-, ice-, and snow-free imagery was available. Approximately 56% of resolvable lakes were glaciated, 13% were headwater, isolated, or terminal lakes, and the rest were primarily drainage lakes. Results were summarized at national-, regional-, state-, and lake-scales, where regions were defined as nine climate regions which represent climatically consistent states. As measured by satellite, changes in national cyanoHAB extent did have a strong increase of 6.9% from 2017 to 2020 (|Kendall’s tau (τ)| = 0.56; gamma (γ) = 2.87 years), but had negligible change (|τ| = 0.03) from 2008 to 2011. Two of the nine regions had moderate (0.3 ≤ |τ| < 0.5) increases in spatial extent from 2017 to 2020, and eight of nine regions had negligible (|τ| < 0.2) change from 2008 to 2011. Twelve states had a strong or moderate increase from 2017 to 2020 (|τ| ≥ 0.3), while only one state had a moderate increase and two states had a moderate decrease from 2008 to 2011. A decrease, or no change, in cyanoHAB spatial extent did not indicate a lack of issues related to cyanoHABs. Sensitivity results of randomly omitted daily CONUS scenes confirm that even with reduced data availability during a short four-year temporal assessment, the direction and strength of the changes in spatial extent remained consistent. We present the first set of national maps of lake cyanoHAB spatial extent across CONUS and demonstrate an approach for quantifying past and future changes at multiple spatial scales. Results presented here provide water quality managers information regarding current cyanoHAB spatial extent and quantify rates of change.
Sub-pixel Spatial Resolution Micro-roughness Measurements with Interlaced Stitching
In this paper we describe a method to increase the spatial resolution of surface micro-roughness measurements. As the surface specifications for precision optics become more demanding, the metrology instruments must cover a broad spatial frequency range. Generally, multiple instruments are used to cover the full range of the specifications. For example, a Fizeau interferometer would be used to test low spatial frequency surface errors, a white light interferometer would be used for mid spatial frequency errors, and an AFM would be used for high spatial frequency errors. For some precision optics, three instruments would be necessary. However, in many applications, an increase in the spatial resolution of a metrology instrument could negate the need for multiple instruments. A solution to increase the spatial resolution of micro-roughness measurements obtained using white light interferometry with "interlaced stitching" will be presented. In "interlaced stitching", multiple interferometric measurements are made as the optic under test (or the CCD array) is laterally shifted at sub-pixel increments. The measurements are then combined to construct a measurement with higher spatial resolution. Initial results obtained while implementing a similar process used to increase the spatial resolution of measurements made with a commercially available Fizeau interferometer will be presented.
Advances in Spectral-Spatial Classification of Hyperspectral Images
Recent advances in spectral-spatial classification of hyperspectral images are presented in this paper. Several techniques are investigated for combining both spatial and spectral information. Spatial information is extracted at the object (set of pixels) level rather than at the conventional pixel level. Mathematical morphology is first used to derive the morphological profile of the image, which includes characteristics about the size, orientation and contrast of the spatial structures present in the image. Then the morphological neighborhood is defined and used to derive additional features for classification. Classification is performed with support vector machines using the available spectral information and the extracted spatial information. Spatial post-processing is next investigated to build more homogeneous and spatially consistent thematic maps. To that end, three presegmentation techniques are applied to define regions that are used to regularize the preliminary pixel-wise thematic map. Finally, a multiple classifier system is defined to produce relevant markers that are exploited to segment the hyperspectral image with the minimum spanning forest algorithm. Experimental results conducted on three real hyperspectral images with different spatial and spectral resolutions and corresponding to various contexts are presented. They highlight the importance of spectral-spatial strategies for the accurate classification of hyperspectral images and validate the proposed methods.
Learning spatial response functions from large multi-sensor AIRS and MODIS datasets
We use large datasets from the Atmospheric Infrared Sounder (AIRS) and the Moderate Resolution Imaging Spectroradiometer (MODIS) to derive AIRS spatial response functions and study their potential variations over the mission. The new reconstructed spatial response functions can be used to reduce errors in the radiances in non-uniform scenes and improve products generated using both AIRS and MODIS data. AIRS spatial response functions are distinct for each of its 2378 channels and each of its 90 scan angles. We develop the mathematical model and the optimization framework for deriving spatial response functions for two AIRS channels with low water vapor absorption and various scan angles. We quantify uncertainties in the derived reconstructions and study how they differ from pre-flight spatial response functions. We show that our approach generates reconstructions that agree with the data more accurately compared to pre-flight spatial responses. We derive spatial response functions using data collected during successive dates in order to ascertain the repeatability of the reconstructed spatial response functions. We also compare the derived spatial response functions based on data collected in the beginning, the middle, and at the current state of the mission in order to study changes in reconstructions over time.
Determining True Sensor Spatial Resolution of Very High Resolution Optical Imagery
Some satellite data is delivered in images with gridded pixels. This gridded pixel size is often assumed to be the spatial resolution of the satellite sensor; however, this is not always the case. An image can be grided to any arbitrary pixel size, but the sensor resolution will remain constant. For example, an image with a pixel grid size much smaller than the sensor resolution will appear blurry along what should be sharp transitions. This discrepancy between an image’s pixel size and true sensor spatial resolution can be the source of much confusion and even misinformation among data users, which may lead them to waste time and resources on using images that do not suit their spatial resolution needs. This presentation will highlight our evaluation of the true spatial resolution of various government and commercial images in the pixel size range of 0.3 m to 60 m. Images evaluated include ESA’s Sentinel-2 (60 m, 20 m, 10 m pixels), USGS’s Landsat 8/9 (30 m & 15 m pixels), Planet’s SuperDoves (3 m pixels), BlackSky’s Globals (~1 m pixels), and the optical bands of Maxar’s WorldView-2 (2.4 m – 0.41 m pixels) and WorldView-3 (1.38 m – 0.31 m pixels). Our evaluation of true sensor spatial resolution, or ‘footprint size’ is based on the sensor’s line spread function (LSF). We calculate the width at half the height of the LSF to find the full width at half maximum (FWHM). The FWHM is how we report sensor spatial resolution. Different objects are examined for constructing the LSF depending on the sensor spatial resolution. Coarser resolution sensors in this evaluation such as Sentinel-2 and Landsat 8/9 are examined at bridges over a dark water background. The bright bridge acts as a line impulse, giving a sensor’s line spread function (LSF) in one direction. Additionally, we simulate the impacts of bridge width on the apparent LSF to obtain a true LSF without the effects of bridge width for these sensors. Finer resolution sensors will image the irregularities in bridges such as trusses, sidewalks, and in some cases painted lines, interfering with the LSF construction. Instead, these sensors are evaluated at large (60 m – 140 m) black and white checkerboards known as Cal/Val sites. At these locations, the image’s transition from black to white is extracted as an edge spread function (ESF). We calculate the derivative of this ESF to obtain the sensor’s LSF. From there, we find the FWHM as we do for the coarser resolution images. With the FWHM and pixel size, we determine how over- or under-sampled the images are. When the ratio of a sensor’s spatial resolution and the gridded image’s pixel size is less than 1, the image is considered under-sampled. In this case, each pixel’s information is unique but only a portion of that pixel’s ground area has been measured. On the other side, if the ratio is greater than 1, the image is considered over-sampled. That is, each pixel’s information is sourced from within the ground extent of the pixel and some extent outside additionally. We will show the true spatial resolution and the extent of over-/under-sampling in the imagery from ESA’s Sentinel-2 (60 m, 20 m, 10 m pixels), USGS’s Landsat 8/9 (30 m & 15 m pixels), Planet’s SuperDoves (3 m pixels), BlackSky’s Globals (~1 m pixels), and the optical bands of Maxar’s WorldView-2 (2.4 m – 0.41 m pixels) and WorldView-3 (1.38 m – 0.31 m pixels).
Visual scanning with or without spatial uncertainty and time-sharing performance
An experiment is reported that examines the pattern of task interference between visual scanning as a sequential and selective attention process and other concurrent spatial or verbal processing tasks. A distinction is proposed between visual scanning with or without spatial uncertainty regarding the possible differential effects of these two types of scanning on interference with other concurrent processes. The experiment required the subject to perform a simulated primary tracking task, which was time-shared with a secondary spatial or verbal decision task. The relevant information that was needed to perform the decision tasks were displayed with or without spatial uncertainty. The experiment employed a 2 x 2 x 2 design with types of scanning (with or without spatial uncertainty), expected scanning distance (low/high), and codes of concurrent processing (spatial/verbal) as the three experimental factors. The results provide strong evidence that visual scanning as a spatial exploratory activity produces greater task interference with concurrent spatial tasks than with concurrent verbal tasks. Furthermore, spatial uncertainty in visual scanning is identified to be the crucial factor in producing this differential effect.
On the determination of cloud cover from satellite sensors - The effect of sensor spatial resolution
The effect of sensor spatial resolution on satellite-derived estimates of cloud fractional coverage is quantified on the basis of Landsat satellite radiance data. Cloud fraction is found to depend on cloud algorithm as much as it depends on sensor spatial resolution. Even for 28.5-m spatial resolution data, large cloud fraction differences exist between algorithms. Satellite cloud retrieval algorithms depend strongly on sensor spatial resolution and/or on the optical depth of the cloud field. When present, spatial resolution effects are small (less than 0.01) for pixel diameter less than 1/4 km and are large for pixel diameter larger than 1 km. The International Satellite Cloud Climatology Project bispectral threshold gives an increase in cloud fraction of 0.11 as spatial resolution degrades from 20 m to 8 km. The spatial coherence algorithm underestimates boundary layer cloud fraction by 0.18. The use of functional box counting and an assumption of fractal scale invariance overestimates the dependence of cloud fraction for spatial scales below 1 km.
Spatial Modulation Improves Performance in CTIS
Suitably formulated spatial modulation of a scene imaged by a computed-tomography imaging spectrometer (CTIS) has been found to be useful as a means of improving the imaging performance of the CTIS. As used here, "spatial modulation" signifies the imposition of additional, artificial structure on a scene from within the CTIS optics. The basic principles of a CTIS were described in "Improvements in Computed- Tomography Imaging Spectrometry" (NPO-20561) NASA Tech Briefs, Vol. 24, No. 12 (December 2000), page 38 and "All-Reflective Computed-Tomography Imaging Spectrometers" (NPO-20836), NASA Tech Briefs, Vol. 26, No. 11 (November 2002), page 7a. To recapitulate: A CTIS offers capabilities for imaging a scene with spatial, spectral, and temporal resolution. The spectral disperser in a CTIS is a two-dimensional diffraction grating. It is positioned between two relay lenses (or on one of two relay mirrors) in a video imaging system. If the disperser were removed, the system would produce ordinary images of the scene in its field of view. In the presence of the grating, the image on the focal plane of the system contains both spectral and spatial information because the multiple diffraction orders of the grating give rise to multiple, spectrally dispersed images of the scene. By use of algorithms adapted from computed tomography, the image on the focal plane can be processed into an image cube a three-dimensional collection of data on the image intensity as a function of the two spatial dimensions (x and y) in the scene and of wavelength (lambda). Thus, both spectrally and spatially resolved information on the scene at a given instant of time can be obtained, without scanning, from a single snapshot; this is what makes the CTIS such a potentially powerful tool for spatially, spectrally, and temporally resolved imaging. A CTIS performs poorly in imaging some types of scenes in particular, scenes that contain little spatial or spectral variation. The computed spectra of such scenes tend to approximate correct values to within acceptably small errors near the edges of the field of view but to be poor approximations away from the edges. The additional structure imposed on a scene according to the present method enables the CTIS algorithms to reconstruct acceptable approximations of the spectral data throughout the scene.
When Deriving the Spatial QRS-T Angle from the 12-lead ECG, which Transform is More Frank: Regression or Inverse Dower?
Our primary objective was to ascertain which commonly used 12-to-Frank-lead transformation yields spatial QRS-T angle values closest to those obtained from simultaneously collected true Frank-lead recordings. Simultaneous 12-lead and Frank XYZ-lead recordings were analyzed for 100 post-myocardial infarction patients and 50 controls. Relative agreement, with true Frank-lead results, of 12-to-Frank-lead transformed results for the spatial QRS-T angle using Kors regression versus inverse Dower was assessed via ANOVA, Lin s concordance and Bland-Altman plots. Spatial QRS-T angles from the true Frank leads were not significantly different than those derived from the Kors regression-related transformation but were significantly smaller than those derived from the inverse Dower-related transformation (P less than 0.001). Independent of method, spatial mean QRS-T angles were also always significantly larger than spatial maximum (peaks) QRS-T angles. Spatial QRS-T angles are best approximated by regression-related transforms. Spatial mean and spatial peaks QRS-T angles should also not be used interchangeably.
The Impact of the AIRS Spatial Response on Channel-to-Channel and Multi-Instrument Data Analyses
The Atmospheric Infrared Sounder (AIRS) measures the infrared spectrum in 2378 channels between 3.7 and 15.4 microns with a very high spectral resolution of approximately 1200. AIRS footprints are approximately 1.1 by 0.6 degrees. Because AIRS is a grating spectrometer, each channel has a unique spatial response. Image rotation due to the scan mirror causes these spatial responses to rotate. In effect, each channel has 90 spatial responses, one for each scene footprint in the scan line. Although the spatial response for most channels is symmetric and nearly uniform, some channels have significantly asymmetric response. This paper reviews and describes the prelaunch measurements that characterized the spatial response functions. Next, it describes the conversion of the ground-based results into footprint-specific response functions valid in flight. Then we describe the postlaunch validation of the measurements, including centroid location, axes orientations, and a check on the full two-dimensional response functions. This latter check involves comparison of AIRS data with that of the Moderate Resolution Imaging Spectrometer (MODIS), which flies on the same platform as AIRS. An important result is that AIRS/MODIS brightness temperature comparisons are significantly improved (scatter reduced) when the AIRS spatial response is explicitly taken into account. Finally, a status report is given on attempts to fully verify the prelaunch measurements by deriving the AIRS spatial response from flight data alone.
Uncertainties in Coastal Ocean Color Products: Impacts of Spatial Sampling
With increasing demands for ocean color (OC) products with improved accuracy and well characterized, per-retrieval uncertainty budgets, it is vital to decompose overall estimated errors into their primary components. Amongst various contributing elements (e.g., instrument calibration, atmospheric correction, inversion algorithms) in the uncertainty of an OC observation, less attention has been paid to uncertainties associated with spatial sampling. In this paper, we simulate MODIS (aboard both Aqua and Terra) and VIIRS OC products using 30 m resolution OC products derived from the Operational Land Imager (OLI) aboard Landsat-8, to examine impacts of spatial sampling on both cross-sensor product intercomparisons and in-situ validations of R(sub rs) products in coastal waters. Various OLI OC products representing different productivity levels and in-water spatial features were scanned for one full orbital-repeat cycle of each ocean color satellite. While some view-angle dependent differences in simulated Aqua-MODIS and VIIRS were observed, the average uncertainties (absolute) in product intercomparisons (due to differences in spatial sampling) at regional scales are found to be 1.8%, 1.9%, 2.4%, 4.3%, 2.7%, 1.8%, and 4% for the R(sub rs)(443), R(sub rs)(482), R(sub rs)(561), R(sub rs)(655), Chla, K(sub d)(482), and b(sub bp)(655) products, respectively. It is also found that, depending on in-water spatial variability and the sensor's footprint size, the errors for an in-situ validation station in coastal areas can reach as high as +/- 18%. We conclude that a) expected biases induced by the spatial sampling in product intercomparisons are mitigated when products are averaged over at least 7 km × 7 km areas, b) VIIRS observations, with improved consistency in cross-track spatial sampling, yield more precise calibration/validation statistics than that of MODIS, and c) use of a single pixel centered on in-situ coastal stations provides an optimal sampling size for validation efforts. These findings will have implications for enhancing our understanding of uncertainties in ocean color retrievals and for planning of future ocean color missions and the associated calibration/validation exercises.