Uncertainty Propagation of Atmospheric Correction Parameters

The main objective of this thesis was to quantify the propagation of
uncertainty in a layered processing system as applied in Processing and
Archiving Facilities (PAF). A framework is presented that is suited for the
purpose. Practical uncertainty estimates are then obtained in estimating a
re
ectance product using three parameters: Column Water Vapour (CWV),
Aerosol Optical Depth (AOD), and the adjacency range. We demonstrate
the propagation of uncertainty from the re
ectance product to application
products, by focusing on unmixing i.e. retrieving materials and their
proportional abundances present in each pixel. The thesis is divided into six
chapters.
After the rst introductory chapter, the second chapter introduces uncertainty
and the framework.
The third chapter presents a generic method to quantify the sensitivity of
re
ectance to CWV concentration, AOD, and adjacency range parameters
via the atmospheric correction modelling (AC). The approximate dispersion
in re
ectance estimates was related to the contribution of each parameter by
performing a Sensitivity Analysis (SA) using a Fourier Amplitude Sensitivity
Test (FAST). We studied the eects of surface albedo on Sensitivity Indices
(SI) for three target surfaces in the spectral range 0.42{0.96 µm: a dark target
(water), a bright target (bare soil), and a target with a low albedo in the
visible and a high albedo in the near infrared range (vegetation). For AOD,
high ( 0.9) SI values were observed at the non-water absorption wavelengths.
For CWV concentration, high SI values were observed at wavelengths with
strong absorption features and if the surface albedo was high. For the dark
target, the eect of AOD was prominent throughout the spectral range. We
found that the sensitivity of re
ectance to CWV concentration and AOD is a
function of the wavelength, strength of the absorption features, and surface
albedo. Such information provided a greater insight into how to deal with
absorption, scattering, and adjacency range type parameters.
The fourth chapter presents a generic method for a qualitative and
quantitative analysis of uncertainty propagation from values of the CWV
concentration and AOD to the fractional abundances derived from unmixing.
Both Fully Constrained Least Squares (FCLS) and FCLS with Total
Variation (FCLS-TV) were applied to estimate abundance maps. We used
ve simulated datasets contaminated by various noise levels. Three datasets
cover two spectral scenarios with dierent endmembers. On those a univariate and a bivariate analysis were carried out on CWV concentration
and AOD. The other two datasets were used to analyse the eect of surface
albedo. The analysis identied trends in performance degradation caused by
the gradual shift in parameter values from their true value. The maximum
achievable performance depends upon spectral characteristics of the datasets,
noise level, and surface albedo. As expected, under noisy conditions
FCLS-TV performs better than FCLS. This experiment helped in addressing
various concerns pertaining to quantifying the propagation of uncertainty
like identifying the best ways to report the propagation of uncertainty.
Propagation of uncertainty was expressed both by measuring various
quantities at pixel level and at scene level. In addition, we addressed the
question on how to incorporate the eect of noise and surface albedo. We
found that unmixing provided a greater insight into how to incorporate a
wider range of applications to the propagation framework.
The fth chapter presents a generic method to estimate and calibrate
concentration of CWV under uncertainty. The method iteratively estimates
the concentration of CWV from the pre-estimates of target surface
re
ectances. The method was free from assumptions, in contrast to at-sensor
radiance based CWV concentration estimation methods. We considered two
cases: (a) CWV concentration was incorrectly estimated in a processing
chain; (b) CWV concentration was not estimated in a processing chain. To
solve (a) we used the incorrect estimations as initial values to the proposed
method during calibration, whereas for (b), CWV concentration was
estimated without initial information. Next, we combined the two scenarios,
resulting in a generic method to calibrate and estimate CWV concentration.
We utilised the Hyperspectral Mapper (HyMap) and Airborne Prism
EXperiment (APEX) instruments for the synthetic and real data
experiments, respectively. Noise levels were added to the synthetic data to
simulate real imaging conditions. For performance assessment, we compared
the proposed method with two state-of-the-art methods. The developed
method performed better than the two methods used for comparison. The
developed method minimised the absolute error close to zero, within only
8{10 iterations. It thus suits existing PAFs where the number of iterations is
an important consideration. Finally, the method is simple to implement and
can be extended to address other atmospheric trace gases.
The sixth chapter presents a generic method to estimate AOD under
uncertainty. AOD was estimated using the pre-estimates of surface
re
ectance. Assumptions concerning retrieval uncertainty and instrumental
errors were less in
uential than for methods based upon the at-sensor
radiance. Using simulated data from HyMap instruments and real data from
Apex instruments, this resulted in an iterative pixelwise estimation of AOD
from estimates of re
ectance. Noise levels were added to the simulated data
to simulate real imaging conditions. Results show that the proposed method
requires 6{8 iterations. It thus suits existing PAFs where the number of
iterations is an important consideration. Further, the method is free from
assumptions for the at-sensor radiance based estimation methods. Finally,
the method is simple to implement, it reduces the processing time in PAFs,
and it can be extended to address other AC parameters.