On-orbit radiometric calibration of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) visible and near-infrared (VNIR) band involves vicarious calibration using reflectance-based method, onboard lamp calibration, and cross-calibration with Moderate Resolution Imaging Spectroradiometer (MODIS) onboard Terra. The ASTER calibration was evaluated with reference to MODIS using an improved cross-calibration algorithm in the previous study (Obata et al., Sensors, 2017). In the present study, the evaluation is expanded by using other sensors that are highly calibrated, including the Landsat 7 Enhanced Thematic Mapper Plus (ETM+) and Landsat 8 Operational Land Imager (OLI). The objective of the present study is to evaluate radiometric calibration of ASTER VNIR band using MODIS, ETM+, and OLI counterparts over Railroad Valley Playa for the period from 2000 to 2018. Results indicate that ASTER bands 1 and 2 are in average 4.2-4.5% and 1.8-3.3% greater than MODIS/ETM+ and that ASTER band 3N agrees well with MODIS/ETM+. The behavior of ASTER surface reflectances along time shows similar trend to that of OLI. The number of sample data for ASTER and OLI comparison should be, however, increased for accurate analysis of statistics. Nevertheless, insights obtained by cross-comparisons provide beneficial information for evaluating ASTER radiometric calibration. The consistency among radiometric calibrations of multiple sensors is of significance importance in the context of data continuity and sensor fusion studies.
Information on the relationships between pairs of wavelength bands is useful when analyzing multispectral sensor data. The soil isoline is one such relationship that is obtained under a constant soil spectrum. However, numerical determination of the soil isoline in the red and NIR reflectance subspace is problematic because of singularities encountered during polynomial fitting. In our previous work, this difficulty was effectively overcome by rotating the original red-NIR subspace by an angle identical to a soil line slope. In the context of hyperspectral data analysis, the applicability of this approach should be investigated thoroughly for band combinations other than red-NIR. The objective of the present study was to expand the applicable range of band combinations to 400–2500 nm by conducting a set of numerical simulations of radiative transfer. Soil isolines were determined numerically by varying soil reflectance and biophysical parameters. The results demonstrated that, as shown previously for the red-NIR band combination, singularities can be avoided for most band combinations through use of the rotation approach. However, for some combinations, especially those involving the shortwave infrared range, the rotation approach gave rise to a further numerical singularity. The present findings thus indicate that special caution should be exercised in the numerical determination of soil isoline equations when one of the chosen bands is in the shortwave infrared region.
The remotely sensed reflectance spectra of vegetated surfaces contain information relating to the leaf area index (LAI) and the chlorophyll-a and -b concentrations (Cab) in a leaf. Difficulties associated with the retrieval of these two biophysical parameters from a single reflectance spectrum arise mainly from the choice of a suitable set of observation wavelengths and the development of a retrieval algorithm. Efforts have been applied toward the development of new algorithms, such as the numerical inversion of radiative transfer models, in addition to the development of simple approaches based on the spectral vegetation indices. This study explored a different approach: An equation describing band-to-band relationships (vegetation isoline equation) was used to retrieve the LAI and Cab simultaneously from a reflectance spectrum. The algorithm used three bands, including the red edge region, and an optimization cost function was constructed from two vegetation isoline equations in the red-NIR and red edge-NIR reflectance subspaces. A series of numerical experiments was conducted using the PROSPECT model to explore the numerical challenges associated with the use of the vegetation isoline equation during the parameter retrieval of the LAI and Cab. Overall, our results indicated the existence of a global minimum (and no local minima) over a wide swath of the LAI-Cab parameter subspace in most simulation cases. These results suggested that the use of the vegetation isoline equation in the simultaneous retrieval of the LAI and the Cab provides a viable alternative to the spectral vegetation index algorithms and the direct inversion of the canopy radiative transfer models.
This study introduces derivations of the soil isoline equation for the case of partial canopy coverage. The derivation relied on extending the previously derived soil isoline equations, which assumed full canopy coverage. This extension was achieved by employing a two-band linear mixture model, in which the fraction of vegetation cover (FVC) was considered explicitly as a biophysical parameter. A parametric form of the soil isoline equation, which accounted for the influence of the FVC, was thereby derived. The differences between the soil isolines of the fully covered and partially covered cases were explored analytically. This study derived the approximated isoline equations for nine cases defined by the choice of the truncation order in the parametric form. A set of numerical experiments was conducted using coupled leaf and canopy radiative transfer models. The numerical results revealed that the accuracy of the soil isoline increased with the truncation order, and they confirmed the validity of the derived expressions.
A previously proposed vegetation isoline equation suffers from errors if the soil background of a canopy layer is bright. These errors arise from the truncation of the second- and higher-order terms that represent photon interactions between the canopy and the soil. An isoline equation that includes a second-order interaction term is introduced. The equation was initially derived by explicitly including a second-order interaction term in both the red and near-infrared (NIR) reflectance spectra (symmetric approximation). We also examined an alternative model in which the interaction term was included only in the NIR band (asymmetric approximation). In this model, the derived isolines tend to shift upward (overcorrection effects). Numerical experiments revealed that the errors in the isoline obtained by the asymmetric approximation were reduced in magnitude to nearly one-fifth of the errors in the previously proposed method. Its accuracy was higher than that of the symmetric approximation, despite the fact that the asymmetric approximation included fewer terms than the symmetric approximation. The improved model accuracy resulted from the overcorrection effects, which compensated for the truncation error. With the simplicity and improved accuracy, the current isoline equations provide a good alternative to the previous approach.
This study describes the derivation of an expression for the relationship between red and near-infrared reflectances, called soil isolines, as an orthogonal concept for the vegetation isoline. An analytical representation of soil isoline would be useful for estimating soil optical properties. Soil isolines often contain a singular point on a dark soil background. Singularities are difficult to model using simple polynomial forms. This difficulty was circumvented in this work by rotating the original axis and employing a vegetation index-like parasite parameter. This approach produced a soil isoline model that could yield any desired level of accuracy based on the use of an index-like parameter. A technique is further introduced for approximating the removal of the parasite parameter from the relationship by truncating the higher-order terms during the derivation steps. Numerical experiments by PROSAIL were conducted to investigate the influence of the truncation errors on the accuracy of the approximated soil isoline equation. The numerical results showed that truncating terms of order greater than two in both bands, yielded negligible truncation errors. These results suggest that the derived and approximated soil isoline equations may be useful in other applications, such as the analysis and retrieval of soil optical properties.
This study investigated the mechanisms underlying the scaling effects that apply to a fraction of vegetation cover (FVC) estimates derived using two-band spectral vegetation index (VI) isoline-based linear mixture models (VI isoline-based LMM). The VIs included the normalized difference vegetation index, a soil-adjusted vegetation index, and a two-band enhanced vegetation index (EVI2). This study focused in part on the monotonicity of an area-averaged FVC estimate as a function of spatial resolution. The proof of monotonicity yielded measures of the intrinsic area-averaged FVC uncertainties due to scaling effects. The derived results demonstrate that a factor ξ, which was defined as a function of “true” and “estimated” endmember spectra of the vegetated and nonvegetated surfaces, was responsible for conveying monotonicity or nonmonotonicity. The monotonic FVC values displayed a uniform increasing or decreasing trend that was independent of the choice of the two-band VI. Conditions under which scaling effects were eliminated from the FVC were identified. Numerical simulations verifying the monotonicity and the practical utility of the scaling theory were evaluated using numerical experiments applied to Landsat7-Enhanced Thematic Mapper Plus (ETM+) data. The findings contribute to developing scale-invariant FVC estimation algorithms for multisensor and data continuity.
We developed a unique methodology that spectrally translates the enhanced vegetation index (EVI) across sensors for data continuity based on vegetation isoline equations and derived a moderate resolution imaging spectroradiometer (MODIS)-compatible EVI for the visible/infrared imager/radiometer suite (VIIRS) sensor. The derived equation had four coefficients that were a function of soil, canopy, and atmosphere, e.g., soil line slope, leaf area index (LAI), and aerosol optical thickness (AOT). The PROSAIL canopy reflectance and 6S atmospheric models were employed to numerically characterize the MODIS-compatible VIIRS EVI. MODIS-compatible VIIRS EVI values only differed from those of MODIS EVI by, at most, 0.002 EVI units, whereas VIIRS and MODIS EVI values differed by 0.018 EVI units. The derived coefficients were sensitive mainly to LAI and AOT for the full- and a partial-covered canopy, respectively. The MODIS-compatible EVI resulted in a reasonable level of accuracy when the coefficients were fixed at values found via optimization for model-simulated and actual sensor data (83 and 41% reduction in the root mean square error, respectively), demonstrating the potential practical utility of the derived equation. The developed methodology can be used to obtain a spectrally compatible EVI for any pair of sensors in the data continuity context.
Differences in spectral response function among sensors have known to be a source of bias error in derived data products such as spectral vegetation indices (VIs). Numerous studies have been conducted to identify such bias errors by comparing VI data acquired simultaneously by two different sensors. Those attempts clearly indicted two facts: 1) When one tries to model a relationship of two VIs from different sensors by a polynomial function, the coefficients of polynomial depends heavily on region to be studied: 2) Although increase of the degree of polynomial improves the translation accuracies, this improvement is very limited. Those facts imply that a better functional form than a simple polynomial may exist to model the VI relationships, and also that the coefficients of such a relationship can be written as a function of variables other than vegetation biophysical parameters. This study tries to address those issues by deriving an inter-sensor VI relationship analytically. The derivation has been performed based on a relationship of two reflectances at different wavelengths (bands), called soil isoline equation. The derived VI relationship becomes a form of rational function with the coefficients that depend purely on the soil reflectance spectra. The derived relationship has been demonstrated numerically by a radiative transfer model of canopy, PROSAIL. It is concluded that a rational function is a good candidate to model inter-sensor VI relationship. This study also shows the mechanism of how the coefficients of such a relationship could vary with the soil reflectance underneath the canopy.
Retrieval of biophysical parameters from remotely sensed reflectance spectra often involves algebraic manipulations,
e.g. spectral vegetation index, to enhance pure signals from a target of one‘s interest. An underlying
assumption of those processes is an existence of high correlation between an obtained value from the manipulations
and amount of the target object. These correlations can be seen in scatter plots of reflectance spectra as
isolines that represent a relationship between two reflectances of different wavelengths (bands) under constant
values of physical parameters. Therefore, modeling the isolines would contribute to better understanding of
retrieval algorithms and eventually to improve their accuracies. The objective of this study is to derive one such
relationship observed under a constant spectrum of soil surfaces, known as soil isolines, in red-NIR reflectance
space. This work introduces a parametric representation of the soil isolines (soil isoline equation) with the parameter
obtained by rotating the red-NIR reflectance space by approximately a quarter of pi radian counter
clockwise. The accuracy in the soil isoline equation depends on the order of polynomials used for the representations:
It was investigated numerically by conducting experiments with radiative transfer models for vegetation
canopy. The results showed that when the first-order approximation were employed for both bands, the accuracy
of the parametric representations/approximations of the soil isolines is approximately 0.02 in terms of mean
absolute difference from the simulated spectra (with no approximation). The accuracies improved dramatically
when one retains the polynomial terms up to the second-order or higher for both bands.
KEYWORDS: Vegetation, Reflectivity, Error analysis, Sensors, Detection and tracking algorithms, Climate change, Climatology, Near infrared, Information science, Information technology
Fraction of vegetation cover (FVC) has been used for environmental studies of both regional and global scale,
and data products of similar kinds have been generated from several agencies. Although there are differences
in sensors/datasets used and algorithms employed among those products, many of those use spectral mixture
analysis either directly or indirectly, and/or assume an essence of spectral mixture in their models. In the
FVC estimations, noises in reflectance spectra of both target and endmember are propagated into the estimated
FVC. Those propagation mechanisms such as patterns and degree of influences need to be clarified analytically,
where this study tries to contribute. The objective of this study is to investigate characteristics of the noise
propagation into the estimated FVC based on one of the linear mixture models known as VI-isoline based LMM.
In order to facilitate analytical discussions, the number of endmember spectra is limited into two. In addition,
a band-correlated noise is assumed in both reflectance spectrum of a target pixel and endmember spectra of
vegetation and non-vegetation surfaces. The propagated error in FVC from those spectra is analytically derived.
The derived expressions indicated that the characteristic behavior of the propagated errors exists such that there
are certain conditions among the band correlated noises which result in the cancellations of propagated errors
on FVC value (it looks as if the spectra are noise-free). Findings of this study would reveal unknown behavior
of the propagated noise, and would contribute better understanding of FVC retrieval algorithms of this kind.
Area-averaged vegetation index (VI) depends on spatial resolution and the computational approach used to calculate the VI from the data. Certain data treatments can introduce scaling effects and a systematic bias into datasets gathered from different sensors. This study investigated the mechanisms underlying the scaling effects of a two-band spectral VI defined in terms of the ratio of two linear sums of the red and near-infrared reflectances (a general form of the two-band VI). The general form of the VI model was linearly transformed to yield a common functional VI form that elucidated the nature of the monotonic behavior. An analytic investigation was conducted in which a two-band linear mixture model was assumed. The trends (increasing or decreasing) in the area-averaged VIs could be explained in terms of a single scalar index, ην, which may be expressed in terms of the spectra of the vegetation and nonvegetation endmembers as well as the coefficients unique to each VI. The maximum error bounds on the scaling effects were derived as a function of the endmember spectra and the choice of VI. The validity of the expressions was explored by conducting a set of numerical experiments that focused on the monotonic behavior and trends in several VIs.
Differences in spatial resolution among sensors have been a source of error among satellite data products, known as a scaling effect. This study investigates the mechanism of the scaling effect on fraction of vegetation cover retrieved by a linear mixture model which employs NDVI as one of the constraints. The scaling effect is induced by the differences in texture, and the differences between the true endmember spectra and the endmember spectra assumed during retrievals. A mechanism of the scaling effect was analyzed by focusing on the monotonic behavior of spatially averaged FVC as a function of spatial resolution. The number of endmember is limited into two to proceed the investigation analytically. Although the spatially-averaged NDVI varies monotonically along with spatial resolution, the corresponding FVC values does not always vary monotonically. The conditions under which the averaged FVC varies monotonically for a certain sequence of spatial resolutions, were derived analytically. The increasing and decreasing trend of monotonic behavior can be predicted from the true and assumed endmember spectra of vegetation and non-vegetation classes regardless the distributions of the vegetation class within a fixed area. The results imply that the scaling effect on FVC is more complicated than that on NDVI, since, unlike NDVI, FVC becomes non-monotonic under a certain condition determined by the true and assumed endmember spectra.
Retrieval of biophysical parameters from satellite data (including hyperspectral data) often involves algebraic manipulation of band reflectance (e.g. spectral vegetation index) that is either empirically or theoretically justified to enhance signals from target of interest. Use of these algebraic manipulation for parameter retrieval bases on a fundamental assumption such that relationship among reflectances varies along with the amount of target object. Therefore, investigation of such relationships among reflectance of different wavelength would serve for better understanding of retrieval
algorithm. The objective of this paper is to derive relationships among reflectances, known as vegetation isoline equation, for a system of layers that consists of atmosphere, vegetation, and soil layers. Vegetation isoline equation is a relationship between two reflectance of different wavelength, which has been a basis of several vegetation indices, and also used directly for retrieval of biophysical parameter such as fraction of green cover. The derivation was performed to increase its accuracy in approximation by including higher-order interaction terms of photons between the canopy and soil layers. To validate the derived expression regarding its accuracy, a series of numerical experiments were conducted using a set of radiative transfer model to simulate reflectance spectra at the top of atmosphere. It is concluded that approximation error of the newly derived expression becomes approximately one order smaller than the error of the previously derived isoline equation which includes only up to the first-order interaction term under various atmospheric conditions.
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