Matching Items (23)
Description
This thesis shows analyses of mixing and transport patterns associated with Hurricane Katrina as it hit the United States in August of 2005. Specifically, by applying atmospheric velocity information from the Weather Research and Forecasting System, finite-time Lyapunov exponents have been computed and the Lagrangian Coherent Structures have been identified. The chaotic dynamics of material transport induced by the hurricane are results from these structures within the flow. Boundaries of the coherent structures are highlighted by the FTLE field. Individual particle transport within the hurricane is affected by the location of these boundaries. In addition to idealized fluid particles, we also studied inertial particles which have finite size and inertia. Basing on established Maxey-Riley equations of the dynamics of particles of finite size, we obtain a reduced equation governing the position process. Using methods derived from computer graphics, we identify maximizers of the FTLE field. Following and applying these ideas, we analyze the dynamics of inertial particle transport within Hurricane Katrina, through comparison of trajectories of dierent sized particles and by pinpointing the location of the Lagrangian Coherent Structures.
ContributorsWake, Christian (Author) / Tang, Wenbo (Thesis director) / Moustaoui, Mohamed (Committee member) / Kostelich, Eric (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2012-12
Description
High-dimensional systems are difficult to model and predict. The underlying mechanisms of such systems are too complex to be fully understood with limited theoretical knowledge and/or physical measurements. Nevertheless, redcued-order models have been widely used to study high-dimensional systems, because they are practical and efficient to develop and implement. Although model errors (biases) are inevitable for reduced-order models, these models can still be proven useful to develop real-world applications. Evaluation and validation for idealized models are indispensable to serve the mission of developing useful applications. Data assimilation and uncertainty quantification can provide a way to assess the performance of a reduced-order model. Real data and a dynamical model are combined together in a data assimilation framework to generate corrected model forecasts of a system. Uncertainties in model forecasts and observations are also quantified in a data assimilation cycle to provide optimal updates that are representative of the real dynamics. In this research, data assimilation is applied to assess the performance of two reduced-order models. The first model is developed for predicting prostate cancer treatment response under intermittent androgen suppression therapy. A sequential data assimilation scheme, the ensemble Kalman filter (EnKF), is used to quantify uncertainties in model predictions using clinical data of individual patients provided by Vancouver Prostate Center. The second model is developed to study what causes the changes of the state of stratospheric polar vortex. Two data assimilation schemes: EnKF and ES-MDA (ensemble smoother with multiple data assimilation), are used to validate the qualitative properties of the model using ECMWF (European Center for Medium-Range Weather Forecasts) reanalysis data. In both studies, the reduced-order model is able to reproduce the data patterns and provide insights to understand the underlying mechanism. However, significant model errors are also diagnosed for both models from the results of data assimilation schemes, which suggests specific improvements of the reduced-order models.
ContributorsWu, Zhimin (Author) / Kostelich, Eric (Thesis advisor) / Moustaoui, Mohamed (Thesis advisor) / Jones, Chris (Committee member) / Espanol, Malena (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2021
Description
This work presents a thorough analysis of reconstruction of global wave fields (governed by the inhomogeneous wave equation and the Maxwell vector wave equation) from sensor time series data of the wave field. Three major problems are considered. First, an analysis of circumstances under which wave fields can be fully reconstructed from a network of fixed-location sensors is presented. It is proven that, in many cases, wave fields can be fully reconstructed from a single sensor, but that such reconstructions can be sensitive to small perturbations in sensor placement. Generally, multiple sensors are necessary. The next problem considered is how to obtain a global approximation of an electromagnetic wave field in the presence of an amplifying noisy current density from sensor time series data. This type of noise, described in terms of a cylindrical Wiener process, creates a nonequilibrium system, derived from Maxwell’s equations, where variance increases with time. In this noisy system, longer observation times do not generally provide more accurate estimates of the field coefficients. The mean squared error of the estimates can be decomposed into a sum of the squared bias and the variance. As the observation time $\tau$ increases, the bias decreases as $\mathcal{O}(1/\tau)$ but the variance increases as $\mathcal{O}(\tau)$. The contrasting time scales imply the existence of an ``optimal'' observing time (the bias-variance tradeoff). An iterative algorithm is developed to construct global approximations of the electric field using the optimal observing times. Lastly, the effect of sensor acceleration is considered. When the sensor location is fixed, measurements of wave fields composed of plane waves are almost periodic and so can be written in terms of a standard Fourier basis. When the sensor is accelerating, the resulting time series is no longer almost periodic. This phenomenon is related to the Doppler effect, where a time transformation must be performed to obtain the frequency and amplitude information from the time series data. To obtain frequency and amplitude information from accelerating sensor time series data in a general inhomogeneous medium, a randomized algorithm is presented. The algorithm is analyzed and example wave fields are reconstructed.
ContributorsBarclay, Bryce Matthew (Author) / Mahalov, Alex (Thesis advisor) / Kostelich, Eric J (Thesis advisor) / Moustaoui, Mohamed (Committee member) / Motsch, Sebastien (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2023
Impacts of Landscape Modifications on Urban Boundary Layer Dynamics in Current and Projected Climate
Description
The planetary boundary layer (PBL) is the lowest part of the troposphere and is directly influenced by surface forcing. Anthropogenic modification from natural to urban environments characterized by increased impervious surfaces, anthropogenic heat emission, and a three-dimensional building morphology, affects land-atmosphere interactions in the urban boundary layer (UBL). Ample research has demonstrated the effect of landscape modifications on development and modulation of the near-surface urban heat island (UHI). However, despite potential implications for air quality, precipitation patterns and aviation operations, considerably less attention has been given to impacts on regional scale wind flow. This dissertation, composed of three peer reviewed manuscripts, fills a fundamental gap in urban climate research, by investigating individual and combined impacts of urbanization, heat adaptation strategies and projected climate change on UBL dynamics.
Paper 1 uses medium-resolution Weather Research and Forecast (WRF) climate simulations to assess contemporary and future impacts across the Conterminous US (CONUS). Results indicate that projected urbanization and climate change are expected to increase summer daytime UBL height in the eastern CONUS. Heat adaptation strategies are expected to reduce summer daytime UBL depth by several hundred meters, increase both daytime and nighttime static stability and induce stronger subsidence, especially in the southwestern US.
Paper 2 investigates urban modifications to contemporary wind circulation in the complex terrain of the Phoenix Metropolitan Area (PMA) using high-resolution WRF simulations. The built environment of PMA decreases wind flow in the evening and nighttime inertial sublayer and produces a UHI-induced circulation of limited vertical extent that modulates the background flow. During daytime, greater urban sensible heat flux dampens the urban roughness-induced drag effect by promoting a deeper, more mixed UBL.
Paper 3 extends the investigation to future scenarios showing that, overall, climate change is expected to reduce wind speed across the PMA. Projected increased soil moisture is expected to intensify katabatic winds and weaken anabatic winds along steeper slopes. Urban development is expected to obstruct nighttime wind flow across areas of urban expansion and increase turbulence in the westernmost UBL.
This dissertation advances the understanding of regional-scale UBL dynamics and highlights challenges and opportunities for future research.
ContributorsBrandi, Aldo (Author) / Georgescu, Matei (Thesis advisor) / Broadbent, Ashley (Committee member) / Moustaoui, Mohamed (Committee member) / Sailor, David (Committee member) / Arizona State University (Publisher)
Created2023
Description
The main objective of mathematical modeling is to connect mathematics with other scientific fields. Developing predictable models help to understand the behavior of biological systems. By testing models, one can relate mathematics and real-world experiments. To validate predictions numerically, one has to compare them with experimental data sets. Mathematical modeling can be split into two groups: microscopic and macroscopic models. Microscopic models described the motion of so-called agents (e.g. cells, ants) that interact with their surrounding neighbors. The interactions among these agents form at a large scale some special structures such as flocking and swarming. One of the key questions is to relate the particular interactions among agents with the overall emerging structures. Macroscopic models are precisely designed to describe the evolution of such large structures. They are usually given as partial differential equations describing the time evolution of a density distribution (instead of tracking each individual agent). For instance, reaction-diffusion equations are used to model glioma cells and are being used to predict tumor growth. This dissertation aims at developing such a framework to better understand the complex behavior of foraging ants and glioma cells.
ContributorsJamous, Sara Sami (Author) / Motsch, Sebastien (Thesis advisor) / Armbruster, Dieter (Committee member) / Camacho, Erika (Committee member) / Moustaoui, Mohamed (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2019
Description
I focus on algorithms that generate good sampling points for function approximation. In 1D, it is well known that polynomial interpolation using equispaced points is unstable. On the other hand, using Chebyshev nodes provides both stable and highly accurate points for polynomial interpolation. In higher dimensional complex regions, optimal sampling points are not known explicitly. This work presents robust algorithms that find good sampling points in complex regions for polynomial interpolation, least-squares, and radial basis function (RBF) methods. The quality of these nodes is measured using the Lebesgue constant. I will also consider optimal sampling for constrained optimization, used to solve PDEs, where boundary conditions must be imposed. Furthermore, I extend the scope of the problem to include finding near-optimal sampling points for high-order finite difference methods. These high-order finite difference methods can be implemented using either piecewise polynomials or RBFs.
ContributorsLiu, Tony (Author) / Platte, Rodrigo B (Thesis advisor) / Renaut, Rosemary (Committee member) / Kaspar, David (Committee member) / Moustaoui, Mohamed (Committee member) / Motsch, Sebastien (Committee member) / Arizona State University (Publisher)
Created2019
Description
This dissertation develops a second order accurate approximation to the magnetic resonance (MR) signal model used in the PARSE (Parameter Assessment by Retrieval from Single Encoding) method to recover information about the reciprocal of the spin-spin relaxation time function (R2*) and frequency offset function (w) in addition to the typical steady-state transverse magnetization (M) from single-shot magnetic resonance imaging (MRI) scans. Sparse regularization on an approximation to the edge map is used to solve the associated inverse problem. Several studies are carried out for both one- and two-dimensional test problems, including comparisons to the first order approximation method, as well as the first order approximation method with joint sparsity across multiple time windows enforced. The second order accurate model provides increased accuracy while reducing the amount of data required to reconstruct an image when compared to piecewise constant in time models. A key component of the proposed technique is the use of fast transforms for the forward evaluation. It is determined that the second order model is capable of providing accurate single-shot MRI reconstructions, but requires an adequate coverage of k-space to do so. Alternative data sampling schemes are investigated in an attempt to improve reconstruction with single-shot data, as current trajectories do not provide ideal k-space coverage for the proposed method.
ContributorsJesse, Aaron Mitchel (Author) / Platte, Rodrigo (Thesis advisor) / Gelb, Anne (Committee member) / Kostelich, Eric (Committee member) / Mittelmann, Hans (Committee member) / Moustaoui, Mohamed (Committee member) / Arizona State University (Publisher)
Created2019
Description
The effects of urbanization on ozone levels have been widely investigated over cities primarily located in temperate and/or humid regions. In this study, nested WRF-Chem simulations with a finest grid resolution of 1 km are conducted to investigate ozone concentrations O3 due to urbanization within cities in arid/semi-arid environments. First, a method based on a shape preserving Monotonic Cubic Interpolation (MCI) is developed and used to downscale anthropogenic emissions from the 4 km resolution 2005 National Emissions Inventory (NEI05) to the finest model resolution of 1 km. Using the rapidly expanding Phoenix metropolitan region as the area of focus, we demonstrate the proposed MCI method achieves ozone simulation results with appreciably improved correspondence to observations relative to the default interpolation method of the WRF-Chem system. Next, two additional sets of experiments are conducted, with the recommended MCI approach, to examine impacts of urbanization on ozone production: (1) the urban land cover is included (i.e., urbanization experiments) and, (2) the urban land cover is replaced with the region's native shrubland. Impacts due to the presence of the built environment on O3 are highly heterogeneous across the metropolitan area. Increased near surface O3 due to urbanization of 10–20 ppb is predominantly a nighttime phenomenon while simulated impacts during daytime are negligible. Urbanization narrows the daily O3 range (by virtue of increasing nighttime minima), an impact largely due to the region's urban heat island. Our results demonstrate the importance of the MCI method for accurate representation of the diurnal profile of ozone, and highlight its utility for high-resolution air quality simulations for urban areas.
ContributorsLi, Jialun (Author) / Georgescu, Matei (Author) / Hyde, Peter (Author) / Mahalov, Alex (Author) / Moustaoui, Mohamed (Author) / Julie Ann Wrigley Global Institute of Sustainability (Contributor)
Created2014-11-01
Description
The physics of waves control most of the world, in multiple forms, such as electromagnetic waves. Mathematicians and physicists have developed equations which describe the patterns in which waves evolve over time, while moving through space. Due to their partial differential form, solutions to these equations must be approximated. This study introduces a new numerical scheme to perform the approximation which is highly stable and computationally efficient. This numerical scheme is formulated with respect to Maxwell’s equations, employing spatial and temporal staggering to implement a fourth-order phase accuracy. It is then compared to the traditional Yee scheme and the Runge-Kutta 3 scheme in one-dimensional applications, revealing a similar accuracy to the Runge-Kutta 3 scheme while requiring less computations per time step. Simulations are then performed in the two-dimensional case. First, no boundary conditions are implemented, causing reflection at the edge of the spatial domain. Next, the simulation is conducted while employing absorbing boundary conditions, simulating wave propagation over an infinite spatial domain. These results are compared to the results of a large domain simulation, in which the wave propagation does not reach the boundaries. Comparing the simulations, it is concluded that the numerical scheme is stable and highly accurate when employing absorbing boundary conditions. Finally, the scheme is tested in two dimensions with wave propagation through nonlinear media, as opposed to the prior simulations which were performed as if in a vacuum. After performing spectral analysis on the resulting waves after a long-time domain simulation, the resulting angular frequencies match those expected from theory. Therefore, the scheme is concluded to be powerful in one-dimensional, two-dimensional, and nonlinear simulations, all while being computationally efficient.
ContributorsKirvan, Alex Ander (Author) / Moustaoui, Mohamed (Thesis director) / Kostelich, Eric (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
An interesting occurrence of a Rossby wave breaking event observed during the VORCORE experiment is presented and explained. Twenty-seven balloons were launched inside the Antarctic polar vortex. Almost all of these balloons evolved in the stratosphere around 500K within the vortex, except the one launched on 28 October 2005. In this case, the balloon was caught within a tongue of high potential vorticity (PV), and was ejected from the polar vortex. The evolution of this event is studied for the period between 19 and 25 November 2005. It is found that at the beginning of this period, the polar vortex experienced distortions due to the presence of Rossby waves. Then, these waves break and a tongue of high PV develops. On 25 November, the tongue became separated from the vortex and the balloon was ejected into the surf zone. Lagrangian simulations demonstrate that the air masses surrounding the balloon after its ejection were originating from the vortex edge. The wave breaking and the development of the tongue are confined within a region where a planetary Quasi-Stationary Wave 1 (QSW1) induces wind speeds with weaker values. The QSW1 causes asymmetry in the wind speed and the horizontal PV gradient along the edge of the polar vortex, resulting in a localized jet. Rossby waves with smaller scales propagating on top of this jet amplify as they enter the jet exit region and then break. The role of the QSW1 on the formation of the weak flow conditions that caused the non-linear wave breaking observed near the vortex edge is confirmed by three-dimensional numerical simulations using forcing with and without the contribution of the QSW1.
ContributorsMoustaoui, Mohamed (Author) / Teitelbaum, H. (Author) / Mahalov, Alex (Author) / College of Liberal Arts and Sciences (Contributor)
Created2013-04-16