Using fractal downscaling of satellite precipitation products for hydrometeorological applications

The objective of spatial downscaling strategies is to increase the information content of coarse datasets at smaller scales. In the case of quantitative precipitation estimation (QPE) for hydrological applications, the goal is to close the scale gap between the spatial resolution of coarse datasets (e.g., gridded satellite precipitation products at resolution L × L) and the high resolution (l × l; L»l) necessary to capture the spatial features that determine spatial variability of water flows and water stores in the landscape. In essence, the downscaling process consists of weaving subgrid-scale heterogeneity over a desired range of wavelengths in the original field. The defining question is, which properties, statistical and otherwise, of the target field (the known observable at the desired spatial resolution) should be matched, with the caveat that downscaling methods be as a general as possible and therefore ideally without case-specific constraints and/or calibration requirements? Here, the attention is focused on two simple fractal downscaling methods using iterated functions systems (IFS) and fractal Brownian surfaces (FBS) that meet this requirement. The two methods were applied to disaggregate spatially 27 summertime convective storms in the central United States during 2007 at three consecutive times (1800, 2100, and 0000 UTC, thus 81 fields overall) from the Tropical Rainfall Measuring Mission (TRMM) version 6 (V6) 3B42 precipitation product (~25-km grid spacing) to the same resolution as the NCEP stage IV products (~4-km grid spacing). Results from bilinear interpolation are used as the control. A fundamental distinction between IFS and FBS is that the latter implies a distribution of downscaled fields and thus an ensemble solution, whereas the former provides a single solution. The downscaling effectiveness is assessed using fractal measures (the spectral exponent β, fractal dimension D, Hurst coefficient H, and roughness amplitude R) and traditional operational scores statistics scores [false alarm rate (FR), probability of detection (PD), threat score (TS), and Heidke skill score (HSS)], as well as bias and the root-mean-square error (RMSE). The results show that both IFS and FBS fractal interpolation perform well with regard to operational skill scores, and they meet the additional requirement of generating structurally consistent fields. Furthermore, confidence intervals can be directly generated from the FBS ensemble. The results were used to diagnose errors relevant for hydrometeorological applications, in particular a spatial displacement with characteristic length of at least 50 km (2500 km2) in the location of peak rainfall intensities for the cases studied. © 2010 American Meteorological Society.

Analytic expressions for the constitutive parameters of magnetoelectric metamaterials

Electromagnetic metamaterials are artificially structured media typically composed of arrays of resonant electromagnetic circuits, the dimension and spacing of which are considerably smaller than the free-space wavelengths of operation. The constitutive parameters for metamaterials, which can be obtained using full-wave simulations in conjunction with numerical retrieval algorithms, exhibit artifacts related to the finite size of the metamaterial cell relative to the wavelength. Liu showed that the complicated, frequency-dependent forms of the constitutive parameters can be described by a set of relatively simple analytical expressions. These expressions provide useful insight and can serve as the basis for more intelligent interpolation or optimization schemes. Here, we show that the same analytical expressions can be obtained using a transfer-matrix formalism applied to a one-dimensional periodic array of thin, resonant, dielectric, or magnetic sheets. The transfer-matrix formalism breaks down, however, when both electric and magnetic responses are present in the same unit cell, as it neglects the magnetoelectric coupling between unit cells. We show that an alternative analytical approach based on the same physical model must be applied for such structures. Furthermore, in addition to the intercell coupling, electric and magnetic resonators within a unit cell may also exhibit magnetoelectric coupling. For such cells, we find an analytical expression for the effective index, which displays markedly characteristic dispersion features that depend on the strength of the coupling coefficient. We illustrate the applicability of the derived expressions by comparing to full-wave simulations on magnetoelectric unit cells. We conclude that the design of metamaterials with tailored simultaneous electric and magnetic response-such as negative index materials-will generally be complicated by potentially unwanted magnetoelectric coupling. © 2010 The American Physical Society.

Seismic Response Analysis of a Full-Scale Base-Isolated Structure via Measurements and Modeling

The full-scale base-isolated structure studied in this dissertation is the only base-isolated building in South Island of New Zealand. It sustained hundreds of earthquake ground motions from September 2010 and well into 2012. Several large earthquake responses were recorded in December 2011 by NEES@UCLA and by GeoNet recording station nearby Christchurch Women's Hospital. The primary focus of this dissertation is to advance the state-of-the art of the methods to evaluate performance of seismic-isolated structures and the effects of soil-structure interaction by developing new data processing methodologies to overcome current limitations and by implementing advanced numerical modeling in OpenSees for direct analysis of soil-structure interaction.

This dissertation presents a novel method for recovering force-displacement relations within the isolators of building structures with unknown nonlinearities from sparse seismic-response measurements of floor accelerations. The method requires only direct matrix calculations (factorizations and multiplications); no iterative trial-and-error methods are required. The method requires a mass matrix, or at least an estimate of the floor masses. A stiffness matrix may be used, but is not necessary. Essentially, the method operates on a matrix of incomplete measurements of floor accelerations. In the special case of complete floor measurements of systems with linear dynamics, real modes, and equal floor masses, the principal components of this matrix are the modal responses. In the more general case of partial measurements and nonlinear dynamics, the method extracts a number of linearly-dependent components from Hankel matrices of measured horizontal response accelerations, assembles these components row-wise and extracts principal components from the singular value decomposition of this large matrix of linearly-dependent components. These principal components are then interpolated between floors in a way that minimizes the curvature energy of the interpolation. This interpolation step can make use of a reduced-order stiffness matrix, a backward difference matrix or a central difference matrix. The measured and interpolated floor acceleration components at all floors are then assembled and multiplied by a mass matrix. The recovered in-service force-displacement relations are then incorporated into the OpenSees soil structure interaction model.

Numerical simulations of soil-structure interaction involving non-uniform soil behavior are conducted following the development of the complete soil-structure interaction model of Christchurch Women's Hospital in OpenSees. In these 2D OpenSees models, the superstructure is modeled as two-dimensional frames in short span and long span respectively. The lead rubber bearings are modeled as elastomeric bearing (Bouc Wen) elements. The soil underlying the concrete raft foundation is modeled with linear elastic plane strain quadrilateral element. The non-uniformity of the soil profile is incorporated by extraction and interpolation of shear wave velocity profile from the Canterbury Geotechnical Database. The validity of the complete two-dimensional soil-structure interaction OpenSees model for the hospital is checked by comparing the results of peak floor responses and force-displacement relations within the isolation system achieved from OpenSees simulations to the recorded measurements. General explanations and implications, supported by displacement drifts, floor acceleration and displacement responses, force-displacement relations are described to address the effects of soil-structure interaction.

Robust Uncertainty Quantification and Scalable Computation for Computer Models with Massive Output

Uncertainty quantification (UQ) is both an old and new concept. The current novelty lies in the interactions and synthesis of mathematical models, computer experiments, statistics, field/real experiments, and probability theory, with a particular emphasize on the large-scale simulations by computer models. The challenges not only come from the complication of scientific questions, but also from the size of the information. It is the focus in this thesis to provide statistical models that are scalable to massive data produced in computer experiments and real experiments, through fast and robust statistical inference.

Chapter 2 provides a practical approach for simultaneously emulating/approximating massive number of functions, with the application on hazard quantification of Soufri\`{e}re Hills volcano in Montserrate island. Chapter 3 discusses another problem with massive data, in which the number of observations of a function is large. An exact algorithm that is linear in time is developed for the problem of interpolation of Methylation levels. Chapter 4 and Chapter 5 are both about the robust inference of the models. Chapter 4 provides a new criteria robustness parameter estimation criteria and several ways of inference have been shown to satisfy such criteria. Chapter 5 develops a new prior that satisfies some more criteria and is thus proposed to use in practice.