Kenta Obata

Derivation of Relationships between Spectral Vegetation Indices from Multiple Sensors Based on Vegetation Isolines

An analytical form of relationship between spectral vegetation indices (VI) is derived in the context of cross calibration and translation of vegetation index products from different sensors. The derivation has been carried out based on vegetation isoline equations that relate two reflectance values observed at different wavelength ranges often represented by spectral band passes. The derivation was first introduced and explained conceptually by assuming a general functional form for VI model equation. This process is universal by which two VIs of different sensors and/or different model equations can be related conceptually. The general process was then applied to the actual case of normalized difference vegetation index (NDVI) from two sensors in a framework of inter-sensor continuity. The derivation results indicate that the NDVI from one sensor can be approximated by a rational function of NDVI from the other sensor as a parameter. Similar result was obtained for the case of soil adjusted VI, enhanced VI, and two-band variance of enhanced VI.

Scaling Effect of Area-Averaged NDVI: Monotonicity along the Spatial Resolution

Changes in the spatial distributions of vegetation across the globe are routinely monitored by satellite remote sensing, in which the reflectance spectra over land surface areas are measured with spatial and temporal resolutions that depend on the satellite instrumentation. The use of multiple synchronized satellite sensors permits long-term monitoring with high spatial and temporal resolutions. However, differences in the spatial resolution of images collected by different sensors can introduce systematic biases, called scaling effects, into the biophysical retrievals. This study investigates the mechanism by which the scaling effects distort normalized difference vegetation index (NDVI). This study focused on the monotonicity of the area-averaged NDVI as a function of the spatial resolution. A monotonic relationship was proved analytically by using the resolution transform model proposed in this study in combination with a two-endmember linear mixture model. The monotonicity allowed the inherent uncertainties introduced by the scaling effects (error bounds) to be explicitly determined by averaging the retrievals at the extrema of theresolutions. Error bounds could not be estimated, on the other hand, for non-monotonic relationships. Numerical simulations were conducted to demonstrate the monotonicity of the averaged NDVI along spatial resolution. This study provides a theoretical basis for the scaling effects and develops techniques for rectifying the scaling effects in biophysical retrievals to facilitate cross-sensor calibration for the long-term monitoring of vegetation dynamics.

Inter-Algorithm Relationships for the Estimation of the Fraction of Vegetation Cover Based on a Two Endmember Linear Mixture Model with the VI Constraint

Measurements of the fraction of vegetation cover (FVC), retrieved from remotely sensed reflectance spectra, serves as a useful measure of land cover changes on the regional and global scales. A linear mixture model (LMM) is frequently employed to analytically estimate the FVC using the spectral vegetation index (VI) as a constraint. Variations in the application of this algorithm arise due to differences in the choice of endmember spectra and VI model assumptions. As a result, the retrieved FVCs from a single spectrum depend on those choices. Therefore, the mechanism underlying this dependency must be understood fully to improve the interpretation of the results. The objective of this study is to clarify the relationships among algorithms based on the LMM. The relationships were derived analytically by limiting both the number of endmembers and the spectral wavelength band to two each. Numerical experiments were conducted to demonstrate and validate the derived relationships. It was found that the relationships between two algorithms of this kind could be characterized by a single parameter that was determined by the endmember spectra and the coefficients of a VI model equation used in the algorithms.

Derivation of a MODIS-compatible enhanced vegetation index from visible infrared imaging radiometer suite spectral reflectances using vegetation isoline equations

Abstract 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.

Spectral Cross-Calibration of VIIRS Enhanced Vegetation Index with MODIS: A Case Study Using Year-Long Global Data

In this study, the Visible Infrared Imaging Radiometer Suite (VIIRS) Enhanced Vegetation Index (EVI) was spectrally cross-calibrated with the Moderate Resolution Imaging Spectroradiometer (MODIS) EVI using a year-long, global VIIRS-MODIS dataset at the climate modeling grid (CMG) resolution of 0.05°-by-0.05°. Our cross-calibration approach was to utilize a MODIS-compatible VIIRS EVI equation derived in a previous study [Obata et al., J. Appl. Remote Sens., vol.7, 2013] and optimize the coefficients contained in this EVI equation for global conditions. The calibrated/optimized MODIS-compatible VIIRS EVI was evaluated using another global VIIRS-MODIS CMG dataset of which acquisition dates did not overlap with those used in the calibration. The calibrated VIIRS EVI showed much higher compatibility with the MODIS EVI than the original VIIRS EVI, where the mean error (MODIS minus VIIRS) and the root mean square error decreased from −0.021 to −0.003 EVI units and from 0.029 to 0.020 EVI units, respectively. Error reductions on the calibrated VIIRS EVI were observed across nearly all view zenith and relative azimuth angle ranges, EVI dynamic range, and land cover types. The performance of the MODIS-compatible VIIRS EVI calibration appeared limited for high EVI values (i.e., EVI > 0.5) due likely to the maturity of the VIIRS dataset used in calibration/optimization. The cross-calibration methodology introduced in this study is expected to be useful for other spectral indices such as the normalized difference vegetation index and two-band EVI.

Derivation and approximation of soil isoline equations in the red-near-infrared reflectance subspace

Abstract 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.

Investigation of inter-sensor NDVI relationships based on analytical representation of soil isolines

This study introduces an analytical approach to derive a relationship between values of Normalized Difference Vegetation Index (NDVI) obtained from datasets of two sensors with different band passes in the context of inter-sensor cross-calibration of such vegetation index (VI) products. Derivation of the relationship has been performed based on a concept of soil isolines. Starting from the soil isoline equations, an inter-sensor NDVI relationship was derived and represented by a system of equation with a single common parameter. In the derived form of NDVI relationship, all the coefficients were written by the soil reflectances (independent of canopy layer.) The functional form of the relationship becomes rational function of the first-order polynomials, when the soil isoline equations are approximated by the form of first-order polynomials. Those results indicate a functional form suitable to model a relationship of NDVI from two sensors.

Analysis of the Scaling Effects in the Area-Averaged Fraction of Vegetation Cover Retrieved Using an NDVI-Isoline-Based Linear Mixture Model

The spectral unmixing of a linear mixture model (LMM) with Normalized Difference Vegetation Index (NDVI) constraints was performed to estimate the fraction of vegetation cover (FVC) over the earth’s surface in an effort to facilitate long-term surface vegetation monitoring using a set of environmental satellites. Although the integrated use of multiple sensors improves the spatial and temporal quality of the data sets, area-averaged FVC values obtained using an LMM-based algorithm suffer from systematic biases caused by differences in the spatial resolutions of the sensors, known as scaling effects. The objective of this study is to investigate the scaling effects in area-averaged FVC values using analytical approaches by focusing on the monotonic behavior of the scaling effects as a function of the spatial resolution. The analysis was conducted based on a resolution transformation model introduced recently by the authors in the accompanying paper (Obata et al., 2012). The maximum value of the scaling effects present in FVC values was derived analytically and validated numerically. A series of derivations identified the error bounds (inherent uncertainties) of the averaged FVC values caused by the scaling effect. The results indicate a fundamental difference between the NDVI and the retrieved FVC from NDVI, which should be noted for accuracy improvement of long-term observation datasets.

Soil isoline equation in red-NIR reflectance space for cross calibration of NDVI between sensors

An underlying assumption in retrievals of biophysical and geological parameters from remotely sensed satellite data is an existence of inter-band relationship. Such relationships are often visualized as isolines in cross plots of reflectance spectra. One type of isolines observed under constant soil properties is the soil isoline, which would provide useful information in retrievals of soil parameters. The purpose of this study is to derive such a relationship observed in a red-NIR reflectance subspace under a fixed condition of soil surface (constant reflectance spectrum of the soil surface). The derived expression is then used to relate two NDVI values observed by different pairs of wavelengths in the context of inter-sensor cross calibrations of NDVI. The derived expressions are demonstrated numerically with radiative transfer models of leaf and canopy. The results indicate validity of the derived expression and their potential to be used for determining an appropriate functional form in modeling a relationship between two NDVIs from different sensors.

Monotonicity of Area Averaged NDVI as a Function of Spatial Resolution based on a Variable Endmember Linear Mixture Model

Choice of area averaging strategy to produce data of normalized difference vegetation index (NDVI) is one of the sources of uncertainty, which is eventually propagated into the simulation results of global climate changes. The purpose of this paper is to investigate this scaling effects of NDVI, especially, on its monotonicity as a function of spatial resolution defined as a number of sampling points within a target area. A simple two-endmember linear mixture model (LMM) is used to analyze the differences among the results of area averaged NDVI with different resolutions. It is proofed analytically that the area averaged NDVI changes monotonically as the spatial resolution becomes higher (more number of sampling points within a fixed area) under the two-endmember LMM, only if a certain condition is satisfied. On the other hand, when the condition is not satisfied, the monotonic behavior of the averaged NDVI value is no longer guaranteed even within an assumption of two-endmember LMM.