Long-term monitoring of geodynamic surface deformation using SAR interferometry

Thesis (Ph.D.) University of Alaska Fairbanks, 2014Synthetic Aperture Radar Interferometry (InSAR) is a powerful tool to measure surface deformation and is well suited for surveying active volcanoes using historical and existing satellites. However, the value and applicability of InSAR for geodynamic monitoring problems is limited by the influence of temporal decorrelation and electromagnetic path delay variations in the atmosphere, both of which reduce the sensitivity and accuracy of the technique. The aim of this PhD thesis research is: how to optimize the quantity and quality of deformation signals extracted from InSAR stacks that contain only a low number of images in order to facilitate volcano monitoring and the study of their geophysical signatures. In particular, the focus is on methods of mitigating atmospheric artifacts in interferograms by combining time-series InSAR techniques and external atmospheric delay maps derived by Numerical Weather Prediction (NWP) models. In the first chapter of the thesis, the potential of the NWP Weather Research & Forecasting (WRF) model for InSAR data correction has been studied extensively. Forecasted atmospheric delays derived from operational High Resolution Rapid Refresh for the Alaska region (HRRRAK) products have been compared to radiosonding measurements in the first chapter. The result suggests that the HRRR-AK operational products are a good data source for correcting atmospheric delays in spaceborne geodetic radar observations, if the geophysical signal to be observed is larger than 20 mm. In the second chapter, an advanced method for integrating NWP products into the time series InSAR workflow is developed. The efficiency of the algorithm is tested via simulated data experiments, which demonstrate the method outperforms other more conventional methods. In Chapter 3, a geophysical case study is performed by applying the developed algorithm to the active volcanoes of Unimak Island Alaska (Westdahl, Fisher and Shishaldin) for long term volcano deformation monitoring. The volcano source location at Westdahl is determined to be approx. 7 km below sea level and approx. 3.5 km north of the Westdahl peak. This study demonstrates that Fisher caldera has had continuous subsidence over more than 10 years and there is no evident deformation signal around Shishaldin peak.Chapter 1. Performance of the High Resolution Atmospheric Model HRRR-AK for Correcting Geodetic Observations from Spaceborne Radars -- Chapter 2. Robust atmospheric filtering of InSAR data based on numerical weather prediction models -- Chapter 3. Subtle motion long term monitoring of Unimak Island from 2003 to 2010 by advanced time series SAR interferometry -- Chapter 4. Conclusion and future work

Parameter estimation by implicit sampling

Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use implicit sampling in parameter estimation problems, where the goal is to find parameters of a numerical model, e.g.~a partial differential equation (PDE), such that the output of the numerical model is compatible with (noisy) data. We use the Bayesian approach to parameter estimation, in which a posterior probability density describes the probability of the parameter conditioned on data and compute an empirical estimate of this posterior with implicit sampling. Our approach generates independent samples, so that some of the practical difficulties one encounters with Markov Chain Monte Carlo methods, e.g.~burn-in time or correlations among dependent samples, are avoided. We describe a new implementation of implicit sampling for parameter estimation problems that makes use of multiple grids (coarse to fine) and BFGS optimization coupled to adjoint equations for the required gradient calculations. The implementation is "dimension independent", in the sense that a well-defined finite dimensional subspace is sampled as the mesh used for discretization of the PDE is refined. We illustrate the algorithm with an example where we estimate a diffusion coefficient in an elliptic equation from sparse and noisy pressure measurements. In the example, dimension\slash mesh-independence is achieved via Karhunen-Lo\`{e}ve expansions

Nonparametric Uncertainty Quantification for Stochastic Gradient Flows

This paper presents a nonparametric statistical modeling method for quantifying uncertainty in stochastic gradient systems with isotropic diffusion. The central idea is to apply the diffusion maps algorithm to a training data set to produce a stochastic matrix whose generator is a discrete approximation to the backward Kolmogorov operator of the underlying dynamics. The eigenvectors of this stochastic matrix, which we will refer to as the diffusion coordinates, are discrete approximations to the eigenfunctions of the Kolmogorov operator and form an orthonormal basis for functions defined on the data set. Using this basis, we consider the projection of three uncertainty quantification (UQ) problems (prediction, filtering, and response) into the diffusion coordinates. In these coordinates, the nonlinear prediction and response problems reduce to solving systems of infinite-dimensional linear ordinary differential equations. Similarly, the continuous-time nonlinear filtering problem reduces to solving a system of infinite-dimensional linear stochastic differential equations. Solving the UQ problems then reduces to solving the corresponding truncated linear systems in finitely many diffusion coordinates. By solving these systems we give a model-free algorithm for UQ on gradient flow systems with isotropic diffusion. We numerically verify these algorithms on a 1-dimensional linear gradient flow system where the analytic solutions of the UQ problems are known. We also apply the algorithm to a chaotically forced nonlinear gradient flow system which is known to be well approximated as a stochastically forced gradient flow.Comment: Find the associated videos at: http://personal.psu.edu/thb11

CMB Lensing Power Spectrum Biases from Galaxies and Clusters using High-angular Resolution Temperature Maps

The lensing power spectrum from cosmic microwave background (CMB) temperature maps will be measured with unprecedented precision with upcoming experiments, including upgrades to ACT and SPT. Achieving significant improvements in cosmological parameter constraints, such as percent level errors on sigma_8 and an uncertainty on the total neutrino mass of approximately 50 meV, requires percent level measurements of the CMB lensing power. This necessitates tight control of systematic biases. We study several types of biases to the temperature-based lensing reconstruction signal from foreground sources such as radio and infrared galaxies and the thermal Sunyaev-Zel'dovich effect from galaxy clusters. These foregrounds bias the CMB lensing signal due to their non-Gaussian nature. Using simulations as well as some analytical models we find that these sources can substantially impact the measured signal if left untreated. However, these biases can be brought to the percent level if one masks galaxies with fluxes at 150 GHz above 1 mJy and galaxy clusters with masses above M_vir = 10^14 M_sun. To achieve such percent level bias, we find that only modes up to a maximum multipole of l_max ~ 2500 should be included in the lensing reconstruction. We also discuss ways to minimize additional bias induced by such aggressive foreground masking by, for example, exploring a two-step masking and in-painting algorithm.Comment: 14 pages, 14 figures, to be submitted to Ap

Quantifying methane and nitrous oxide emissions from the UK and Ireland using a national-scale monitoring network

The UK is one of several countries around the world that has enacted legislation to reduce its greenhouse gas emissions. In this study, we present top-down emissions of methane (CH4) and nitrous oxide (N2O) for the UK and Ireland over the period August 2012 to August 2014. These emissions were inferred using measurements from a network of four sites around the two countries. We used a hierarchical Bayesian inverse framework to infer fluxes as well as a set of covariance parameters that describe uncertainties in the system. We inferred average UK total emissions of 2.09 (1.65–2.67) Tg yr−1 CH4 and 0.101 (0.068–0.150) Tg yr−1 N2O and found our derived UK estimates to be generally lower than the a priori emissions, which consisted primarily of anthropogenic sources and with a smaller contribution from natural sources. We used sectoral distributions from the UK National Atmospheric Emissions Inventory (NAEI) to determine whether these discrepancies can be attributed to specific source sectors. Because of the distinct distributions of the two dominant CH4 emissions sectors in the UK, agriculture and waste, we found that the inventory may be overestimated in agricultural CH4 emissions. We found that annual mean N2O emissions were consistent with both the prior and the anthropogenic inventory but we derived a significant seasonal cycle in emissions. This seasonality is likely due to seasonality in fertilizer application and in environmental drivers such as temperature and rainfall, which are not reflected in the annual resolution inventory. Through the hierarchical Bayesian inverse framework, we quantified uncertainty covariance parameters and emphasized their importance for high-resolution emissions estimation. We inferred average model errors of approximately 20 and 0.4 ppb and correlation timescales of 1.0 (0.72–1.43) and 2.6 (1.9–20 3.9) days for CH4 and N2O, respectively. These errors are a combination of transport model errors as well as errors due to unresolved emissions processes in the inventory. We found the largest CH4 errors at the Tacolneston station in eastern England, which may be due to sporadic emissions from landfills and offshore gas in the North Sea

Measurements of Secondary Cosmic Microwave Background Anisotropies with the South Pole Telescope

We report cosmic microwave background (CMB) power spectrum measurements from the first 100 sq. deg. field observed by the South Pole Telescope (SPT) at 150 and 220 GHz. On angular scales where the primary CMB anisotropy is dominant, ell ~< 3000, the SPT power spectrum is consistent with the standard LambdaCDM cosmology. On smaller scales, we see strong evidence for a point source contribution, consistent with a population of dusty, star-forming galaxies. After we mask bright point sources, anisotropy power on angular scales of 3000 50 at both frequencies. We combine the 150 and 220 GHz data to remove the majority of the point source power, and use the point source subtracted spectrum to detect Sunyaev-Zel'dovich (SZ) power at 2.6 sigma. At ell=3000, the SZ power in the subtracted bandpowers is 4.2 +/- 1.5 uK^2, which is significantly lower than the power predicted by a fiducial model using WMAP5 cosmological parameters. This discrepancy may suggest that contemporary galaxy cluster models overestimate the thermal pressure of intracluster gas. Alternatively, this result can be interpreted as evidence for lower values of sigma8. When combined with an estimate of the kinetic SZ contribution, the measured SZ amplitude shifts sigma8 from the primary CMB anisotropy derived constraint of 0.794 +/- 0.028 down to 0.773 +/- 0.025. The uncertainty in the constraint on sigma8 from this analysis is dominated by uncertainties in the theoretical modeling required to predict the amplitude of the SZ power spectrum for a given set of cosmological parameters.Comment: 28 pages, 11 figures, submitted to Ap