On the Semi-Automatic Retrieval of Biophysical Parameters Based on Spectral Index Optimization
Abstract
:1. Introduction
- Band selection: Typically, most SIs are mathematical formulations consisting of two or three sensor spectral bands (B). How then, do we evaluate with a high enough scrutiny, whether the most sensitive spectral bands—with respect to biophysical parameter retrieval—have been selected? This question is especially relevant in view of the high number of bands associated with imaging spectrometry [32];
- SI formulation: Typically, the normalized difference (ND) formulation is applied, i.e., (B2 − B1)/(B2 + B1). But again, how do we assess, whether the applied ND formulation is the most accurate one with respect to biophysical parameter retrieval? Even given high spectral resolution multi- or hyperspectral reflectance data, there is no reason to assume that a two-band SI formulation leads to the most accurate empirical relationship [33];
- Fitting function: A regression model is typically reduced to a linear fitting exercise, directly or indirectly by prior transformation to linearity. Also here, the question is, whether the regression function selected is the most accurate one? Typically, saturation effects are common for dense canopies [14,15].
2. ARTMO Software Package
- The choice to specify or select spectral band settings specifically for various existing air- and space-borne sensors or user defined settings, typically for recently developed or future sensor systems;
- The option to simulate large datasets of top-of-canopy (TOC) reflectance spectra for sensors sensitive in the optical range (400 to 2500 nm). Look-up tables (LUT) can be generated, which are stored in a relational SQL database management system;
- Finally, various retrieval scenarios can be selected and run using EO reflectance datasets.
- ARTMO v3 is designed modularly. Its modular architecture offers the possibility for easy addition (or removal) of components, such as RTM models and post-processing modules;
- The MySQL database is organized in such a way that it supports the modular architecture of ARTMO v3. This avoids redundancy and increases the processing speed. For instance, all spectral datasets are stored as binary objects;
- New retrieval toolboxes are incorporated. They are based on parametric and non-parametric regression as well as physically-based inversion using a LUT. This has led to the development of a: (1) “Spectral Indices assessment toolbox”; (2) “Machine Learning Regression Algorithm toolbox” [41]; and (3) “LUT-based inversion toolbox” [12].
2.1. ARTMO Spectral Indices (SI) Toolbox
2.2. Add Spectral Index
2.3. SI Settings
2.4. Calibration/Validation Assessment
2.5. Retrieval
3. Assessment and Mapping Applications
3.1. Used Data
3.2. Experimental Setup
4. Results & Discussion
4.1. Optimized SI’s
- With regard to SI formulations, no strong evidence has been found that the widely used ND formulation outperforms the less popular SR formulation. Though, it is also recognized that the main argument for using ND types of indices is not the improved correlation performance in comparison to SRs, but rather the (at least to some extent) improved comparability of different observation times/dates and the possible reduction of effects of varying illumination intensity (shades, etc.), due to the inherent normalization of the value range [47]. The ND outperformed the SR for both LAI and LCC only when a second order polynomial is applied as a fitting function. However, when a conventional linear regression is applied, ND performs similar (LCC) or superior (LAI) to SR;
- While the polynomial fit outperforms to some extent the linear regression fitting scenario, the linear fit model is nonetheless accurate as well. For instance, the best linear regression fit outperforms the more sophisticated exponential and power curve fitting approaches significantly for both, LAI and LCC;
- For the majority of the most accurate regression functions, about the same spectral band locations were assessed as being optimal for biophysical parameter retrieval. For LAI, two-band formulations are optimal at 570, 555, 539 and 707 nm with the second band at 2453 or 2421 nm. For LCC two-band locations at 692 nm and 632 nm with the second band at 1661–1698 nm or 1200–1340 nm performed best.
4.2. Correlation Matrices
- SR and ND formulations lead to the same spectral regions exhibiting strong correlations between the LAI/LCC biophysical parameters and the two-band SIs. For instance, similar patterns for B2 in the visible spectral region can be observed. However, the ND power and logarithmic functions fail as good fitting functions for several band combinations. Specifically, they provide lower regression accuracies for B1 (740–1000 nm) and B2 (1400–2200 nm);
- Similar patterns with strong and low correlation values are found across the different curve fitting functions assessed. This suggests that the major impact on retrieval accuracy in EO does not originate from the chosen curve fitting but rather from the spectral dimension. Though, local differences do occur. These local differences are particularly pronounced along exponential, power and logarithmic fittings, characterized by quite low correlation values. Hence, the following sections are limited to the discussion of linear and polynomial curve fits;
- For LAI, Figure 8 shows that the most important spectral region for retrieval is the 539–707 nm region for the B1band, whereas B2 is located in the longwave SWIR. Notice the hourglass shape in the SWIR region. A second spectral region of maximal r2 for B1 is the 1300–1500 nm region as well as the region at 1400–1800 nm. These regions are spectrally quite broad, meaning that the spectral indices do not require very narrow and hence precisely positioned spectral bands, at least for the samples that were used in this study for the generation of the empirical relationships;
- For LCC, Figure 8 shows that the most important spectral region for retrieval is the visible region, particularly the red region until the red edge. B2 is spectrally located in the shortwave SWIR. Another sensitive zone, having the same B1 (around 692 nm) as in the first case, has its second band B2 in the NIR range as well as in the longwave SWIR. Note that these spectral areas are covered by broad spectral bands.
4.3. LAI & LCC Mapping
- For LAI, both, the ND polynomial and ND linear regression models, lead to the same calibration result (RMSE = 0.61; r2 = 0.83) and accordingly to very similar LAI maps. This example provides confidence that a linear regression is able to deliver adequate LAI maps, when appropriate spectral bands are selected; i.e., green spectral region (B1: 539–570 nm) in combination with the longwave SWIR (B2: 1970–2453 nm). Rapid saturation of the LAI in function of the SI is thereby avoided. The map shows areas with a high LAI quite clearly (irrigated circular fields). Areas with a low LAI—senescent crops to bare soil surfaces—elicit a zero value LAI (white color code);
- Conversely, when using SR for LAI mapping, prominent spatial differences appeared for the linear versus polynomial and logarithmic regression models. Particularly, a linear regression exhibits problematic behavior, since LAI variations for senescent regions significantly deviate from the other LAI mapping results. Due to variable soil contribution, a simple linear fit will never be able to capture the variability for near zero LAI values compatible with high LAI values. A logarithmic fitting function seems to lead to more consistent LAI maps. Nevertheless, although the ND type yields considerably poorer calibration results, both maps yield similar LAI patterns. The spatial similarity of the three best performing fitting functions (SR, logarithmic, ND linear and ND polynomial) provide confidence in the realism of the maps produced;
- With regard to LCC mapping, the spatial similarity between the SR and ND polynomial fits and the degree of detail is remarkable. However, interpretation becomes difficult for areas earlier identified as having low LAI values in the LAI map and showing high LCC values in the LCC map. One interpretation may be that the nature of a polynomial of second degree fit leads to retrievals of high LCC values at near-zero SI values. Another problem might be related to the difficulty of upscaling. For the areas where the canopy is very sparse, i.e., the LAI is low, it becomes harder to perceive the chlorophyll pigments in the leaves with a moderate spatial resolution of 1–4 m, even if the chlorophyll concentration in the small leaves is relatively high;
- Logarithmic ND fits, along with linear SR and ND fits, elicit the most realistic LCC patterns; with spatial patterns conform to those of the best LAI maps.
4.4. Towards a New Generation of Spectral Indices
- Development and evaluation of generic SIs by using RTMs including viewing and solar geometry. ARTMO includes turbid (e.g., SAIL) as well as explicit 3D RTMs (e.g., FLIGHT). Evidently, the validity of the most optimal models will be assessed using in situ validation data;
- New types of index formulations will be developed and tested across the full optical spectrum. Only SR and ND indices have been assessed here. Yet, alternative mathematical formulations are to be tested as well, e.g., the formulations used for soil adjusted vegetation index (SAVI), enhanced vegetation index (EVI), weighted difference vegetation index (WDVI) or more complex ones;
- Although in this paper only two-band formulations have been assessed, the SI toolbox offers the option for a systematic analysis of a full optical spectrum of band combinations with SI formulations of up to ten different bands in the range of 400 to 2500 nm. Since there is no reason to believe that two-band indices lead to the most successful SI models, this multiple band approach may lead to the development of more accurate and sensitive spectral indices.
5. Conclusions
Acknowledgments
Conflicts of Interest
- Author ContributionsJuan Pablo Rivera developed the toolbox presented here, developed this paper’s study concept, performed the experiments and contributed to writing the manuscript. The co-authors of this manuscript significantly contributed to all phases of the investigation: Jochem Verrelst supervised the research project and contributed to research design as well as manuscript writing. Jesus Delegido contributed to the experimental work, and Frank Veroustraete and José Moreno contributed to manuscript editing.
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Index type | Fitting function | B1 (nm) | B2 (nm) | SI model | abs. RMSE | NRMSE (%) | r2 |
---|---|---|---|---|---|---|---|
LAI: | |||||||
ND | polynomial | 570 | 2453 | LAI = −1.366ND2 + 6.154ND + 1.976 | 0.61 | 12.51 | 0.83 |
SR | logarithmic | 555 | 2453 | LAI = 2.291 log(SR) + 1.924 | 0.61 | 12.10 | 0.83 |
ND | linear | 555 | 2453 | LAI = 5.023ND + 1.922 | 0.61 | 12.80 | 0.83 |
SR | polynomial | 539 | 2421 | LAI = −0.621SR2 + 3.754SR −0.760 | 0.63 | 15.58 | 0.82 |
SR | linear | 539 | 2421 | LAI = 1.751SR + 0.504 | 0.70 | 16.32 | 0.77 |
SR | exponential | 2118 | 2171 | LAI = 0.000238e8.783SR | 0.72 | 11.85 | 0.77 |
ND | exponential | 707 | 2453 | LAI = 0.712e2.721ND | 0.75 | 13.13 | 0.77 |
ND | power | 707 | 2453 | LAI = 4.670ND0.548 | 0.77 | 19.06 | 0.77 |
SR | power | 539 | 2421 | LAI = 1.951SR1.112 | 0.82 | 14.64 | 0.76 |
ND | logarithmic | 462 | 524 | LAI = 3.888 log(ND) + 6.947 | 0.85 | 18.23 | 0.74 |
LCC: | |||||||
ND | polynomial | 692 | 1686 | LCC = −227.499ND2 + 281.410ND − 36.924 | 4.21 | 7.75 | 0.93 |
SR | polynomial | 692 | 1661 | LCC = −8.114ND2 + 60.997ND − 61.553 | 4.30 | 7.64 | 0.92 |
ND | logarithmic | 692 | 1340 | LCC = 43.578 log(ND) + 63.272 | 4.70 | 10.18 | 0.91 |
SR | linear | 692 | 1340 | LCC = 7.455SR + 4.707 | 4.70 | 20.24 | 0.91 |
ND | linear | 692 | 1340 | LCC = 90.290ND − 14.808 | 4.21 | 10.75 | 0.90 |
SR | logarithmic | 692 | 1200 | LCC = 26.447 log(ND) − 2.990 | 5.53 | 11.54 | 0.87 |
SR | exponential | 692 | 1215 | LCC = 91.164e−4.235SR | 6.00 | 11.25 | 0.87 |
ND | power | 632 | 1698 | LCC = 127.581ND2.119 | 28.06 | 365.5 | 0.87 |
ND | exponential | 632 | 1257 | LCC = 2.110e3.827ND | 6.64 | 12.80 | 0.84 |
SR | power | 707 | 723 | LCC = 7.281SR2.938 | 8.28 | 13.19 | 0.76 |
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Rivera, J.P.; Verrelst, J.; Delegido, J.; Veroustraete, F.; Moreno, J. On the Semi-Automatic Retrieval of Biophysical Parameters Based on Spectral Index Optimization. Remote Sens. 2014, 6, 4927-4951. https://doi.org/10.3390/rs6064927
Rivera JP, Verrelst J, Delegido J, Veroustraete F, Moreno J. On the Semi-Automatic Retrieval of Biophysical Parameters Based on Spectral Index Optimization. Remote Sensing. 2014; 6(6):4927-4951. https://doi.org/10.3390/rs6064927
Chicago/Turabian StyleRivera, Juan Pablo, Jochem Verrelst, Jesús Delegido, Frank Veroustraete, and José Moreno. 2014. "On the Semi-Automatic Retrieval of Biophysical Parameters Based on Spectral Index Optimization" Remote Sensing 6, no. 6: 4927-4951. https://doi.org/10.3390/rs6064927