Estimation of AOD Under Uncertainty: An Approach for Hyperspectral Airborne Data
Abstract
:1. Introduction
2. Theoretical Background
2.1. Basic Atmospheric Effect Modeling
- the total radiance as measured by the sensor, ,
- the total path radiance that consists of the light scattered in the path,
- the total ground radiance that consists of all the light reflected by the surface and traveling directly towards the sensor, ,
- the direct ground reflectance, as a fraction of resulting from direct illumination of the ground surface.
2.2. Aerosol Optical Depth
3. Datasets
3.1. The Process to Generate the Synthetic Datasets
- Spectra of materials are extracted from an existing library. The choice of materials depends on the type of surface required for an experiment. We extract the materials from the database of Jasper Ridge, spectral library [39] available in ENVI software [40] and the database of the Johns Hopkins University Spectral Library [41].
- To generate a sensor specific image, the library is resampled using the sensor response curve. For our experiments, we use response curve of the Hyperspectral Mapper (HyMap) airborne hyperspectral sensor [42].
- Depending on the number of materials, a fraction image comprising abundance of materials is required. We used, MATLAB Hyperspectral Imagery Synthesis tools, available online [43] to generate the abundance images. A convolution of a library of materials with an abundance image generates a synthetic reflectance cube.
- To transform synthetic reflectance to at-sensor radiance, the forward radiative transfer modeling is performed. Details of this modeling are given in Section 4.
- In a real dataset, sensor noise and processing noise are major sources of distortion. Sensor noise refers to the random electronic noise like dark current, processing noise occurs due to the final pre-processing steps on the reflectance datacube, e.g., spectral smoothing. We added the two types of noise to the datasets at two stages: sensor noise to the radiance cube and processing noise to the estimated reflectance cube. To observe the effect of the different noise levels we considered three levels of the correlated processing noise, with signal-to-noise ratios (SNR): 30, 40, and 50 dB, respectively. All correlated noise levels were generated from independent, normally distributed noise by low-pass filtering with a normalized cut-off frequency of for each SNR with B being the number of channels. Figure 1 shows four pixelwise estimates of reflectance at 2200 nm (band 100) when SNR of at-sensor radiance was limited to: 30, 40, 50, and 60 dB with random (white) noise. To estimate the four pixelwise reflectance, true AC parameters were employed and no correlated noise was added. When SNR of the at-sensor radiance was limited to 30 dB, 40 dB, and 50 dB the reflectance estimates were severely distorted. Further, [42] suggests that HyMap sensor is highly optimized for mineral exploration tasks which demanded high SNR. From the experiments with the noise levels and following the SNR values given in the literature, we found that sensor noise with SNR = 60 dB was a realistic choice for HyMap sensor.
3.2. Case Study: A Vegetation Surface with Usual Scattering Conditions
3.3. Case Studies: High Scattering Conditions
3.3.1. Surfaces with Spectrally Close and Spectrally Distinct Materials
3.3.2. Surfaces with Dark and Bright Materials
3.4. Real Data
4. The Forward Modeling and the Performance Discriminator
4.1. Profile of the Condition Parameters for the Usual Scattering Conditions
4.2. Pixelwise Parameter Configuration for the Usual Scattering Conditions
4.3. Profile of the Parameters for the High Scattering Conditions
4.4. Performance Discriminators
5. Estimation
5.1. Linear Model for Calibration
5.2. Searching for Reference Library Spectra
5.3. Generating the First Visibility Estimate
5.4. Iterations
5.5. Interpolation of Visibility
- Case 1: No overlapping of the neighborhood. This case accounts for the scenario when within the neighborhood of the target reference pixel , no other reference pixel fall.
- Case 2: Overlapping of the neighborhood. This case accounts for scenarios when the neighborhood of two or more reference pixels overlaps with . This occurs when two or more pixels falls within .
- Case 3: No reference pixel is available for spatial estimation. This case account for the scenario when to estimate visibility at the unsampled location, no reference pixel can be spatially linked using .
- Step 1, find the spatial variation of visibility using values estimated for Case 1 and Case 2. We distinguished three types of spatial variation in visibility: (a) vertical; (b) horizontal; and (c) diagonal. The specific variation is obtained by evaluating histograms of visibility values from line transects in vertical, horizontal, and diagonal directions. A bimodality or multimodality of the histogram from a specific line transect shows a strong variation of the visibility. For instance, if visibility is vertically varying (column wise) then the histogram obtained from the horizontal line transect shows bimodality or multimodality,
- Step 2, the histogram that shows unimodality, that is direction of non-variation of visibility, is used to generate the distribution . For instance, if visibility is vertically varying then histogram generated from the values from vertical line transect are used to generate the ,
- Step 3, for vertical and horizontal variation, a randomly sampled value from is assigned to a spatially unrelated pixel. If visibility is diagonally varying then nearest neighborhood method [57] is used to interpolate the missing value.
6. Results of Experiments with Usual Scattering and with Real Data
6.1. Specific Choices of Methods and Values
6.2. Visibility Estimation for the Simulated Dataset
6.3. Visibility Estimation for the Real Dataset
- From the real at sensor radiance cube, a set of endmembers is manually selected, whereas the corresponding pixels are called reference pixels.
- Reflectance are estimated by performing AC using various pre-selected combinations of the atmospheric condition parameters.
- From the estimated reflectance cubes spectra of the reference pixels are evaluated to check distortion in terms of shape (Section 5.3).
- The reflectance cube that corresponds to the optimal combination serves as the reference cube.
- The reference cube is transformed to obtain a pseudo at sensor radiance cube using the MODTRAN 4 forward modelling simulations with the same atmospheric conditions as used in the forward modelling of the simulated dataset.
- To the pseudo reference dataset we added 60 dB white Gaussian noise at sensor level and 30 dB correlated noise to the estimated reflectance cube, as we did for the simulated dataset.
6.4. Experiment with Spatial Variability
7. Results of Experiments with High Scattering Conditions
Specific Choices of Methods and Values
8. Discussion
9. Conclusions and Outlooks
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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True Visibility (km) | True AOD |
---|---|
1 | 4.94 |
4 | 1.42 |
7 | 0.89 |
10 | 0.68 |
15 | 0.48 |
True Visibility (km) | Set Visibility (km) | True AOD | Set AOD |
---|---|---|---|
01 | 05 | 4.94 | 1.17 |
04 | 01 | 1.42 | 4.94 |
04 | 10 | 1.42 | 0.68 |
07 | 02 | 0.89 | 2.60 |
07 | 12 | 0.89 | 0.57 |
10 | 05 | 0.68 | 1.17 |
10 | 15 | 0.68 | 0.48 |
15 | 10 | 0.48 | 0.68 |
15 | 20 | 0.48 | 0.37 |
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Bhatia, N.; Tolpekin, V.A.; Stein, A.; Reusen, I. Estimation of AOD Under Uncertainty: An Approach for Hyperspectral Airborne Data. Remote Sens. 2018, 10, 947. https://doi.org/10.3390/rs10060947
Bhatia N, Tolpekin VA, Stein A, Reusen I. Estimation of AOD Under Uncertainty: An Approach for Hyperspectral Airborne Data. Remote Sensing. 2018; 10(6):947. https://doi.org/10.3390/rs10060947
Chicago/Turabian StyleBhatia, Nitin, Valentyn A. Tolpekin, Alfred Stein, and Ils Reusen. 2018. "Estimation of AOD Under Uncertainty: An Approach for Hyperspectral Airborne Data" Remote Sensing 10, no. 6: 947. https://doi.org/10.3390/rs10060947