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.