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- All Subjects: Ionosphere
- All Subjects: Time Delay
- Creators: Kostelich, Eric J.
Description
Earth-system models describe the interacting components of the climate system and
technological systems that affect society, such as communication infrastructures. Data
assimilation addresses the challenge of state specification by incorporating system
observations into the model estimates. In this research, a particular data
assimilation technique called the Local Ensemble Transform Kalman Filter (LETKF) is
applied to the ionosphere, which is a domain of practical interest due to its effects
on infrastructures that depend on satellite communication and remote sensing. This
dissertation consists of three main studies that propose strategies to improve space-
weather specification during ionospheric extreme events, but are generally applicable
to Earth-system models:
Topic I applies the LETKF to estimate ion density with an idealized model of
the ionosphere, given noisy synthetic observations of varying sparsity. Results show
that the LETKF yields accurate estimates of the ion density field and unobserved
components of neutral winds even when the observation density is spatially sparse
(2% of grid points) and there is large levels (40%) of Gaussian observation noise.
Topic II proposes a targeted observing strategy for data assimilation, which uses
the influence matrix diagnostic to target errors in chosen state variables. This
strategy is applied in observing system experiments, in which synthetic electron density
observations are assimilated with the LETKF into the Thermosphere-Ionosphere-
Electrodynamics Global Circulation Model (TIEGCM) during a geomagnetic storm.
Results show that assimilating targeted electron density observations yields on
average about 60%–80% reduction in electron density error within a 600 km radius of
the observed location, compared to 15% reduction obtained with randomly placed
vertical profiles.
Topic III proposes a methodology to account for systematic model bias arising
ifrom errors in parametrized solar and magnetospheric inputs. This strategy is ap-
plied with the TIEGCM during a geomagnetic storm, and is used to estimate the
spatiotemporal variations of bias in electron density predictions during the
transitionary phases of the geomagnetic storm. Results show that this strategy reduces
error in 1-hour predictions of electron density by about 35% and 30% in polar regions
during the main and relaxation phases of the geomagnetic storm, respectively.
technological systems that affect society, such as communication infrastructures. Data
assimilation addresses the challenge of state specification by incorporating system
observations into the model estimates. In this research, a particular data
assimilation technique called the Local Ensemble Transform Kalman Filter (LETKF) is
applied to the ionosphere, which is a domain of practical interest due to its effects
on infrastructures that depend on satellite communication and remote sensing. This
dissertation consists of three main studies that propose strategies to improve space-
weather specification during ionospheric extreme events, but are generally applicable
to Earth-system models:
Topic I applies the LETKF to estimate ion density with an idealized model of
the ionosphere, given noisy synthetic observations of varying sparsity. Results show
that the LETKF yields accurate estimates of the ion density field and unobserved
components of neutral winds even when the observation density is spatially sparse
(2% of grid points) and there is large levels (40%) of Gaussian observation noise.
Topic II proposes a targeted observing strategy for data assimilation, which uses
the influence matrix diagnostic to target errors in chosen state variables. This
strategy is applied in observing system experiments, in which synthetic electron density
observations are assimilated with the LETKF into the Thermosphere-Ionosphere-
Electrodynamics Global Circulation Model (TIEGCM) during a geomagnetic storm.
Results show that assimilating targeted electron density observations yields on
average about 60%–80% reduction in electron density error within a 600 km radius of
the observed location, compared to 15% reduction obtained with randomly placed
vertical profiles.
Topic III proposes a methodology to account for systematic model bias arising
ifrom errors in parametrized solar and magnetospheric inputs. This strategy is ap-
plied with the TIEGCM during a geomagnetic storm, and is used to estimate the
spatiotemporal variations of bias in electron density predictions during the
transitionary phases of the geomagnetic storm. Results show that this strategy reduces
error in 1-hour predictions of electron density by about 35% and 30% in polar regions
during the main and relaxation phases of the geomagnetic storm, respectively.
ContributorsDurazo, Juan, Ph.D (Author) / Kostelich, Eric J. (Thesis advisor) / Mahalov, Alex (Thesis advisor) / Tang, Wenbo (Committee member) / Moustaoui, Mohamed (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2018
Description
Cancer is a worldwide burden in every aspect: physically, emotionally, and financially. A need for innovation in cancer research has led to a vast interdisciplinary effort to search for the next breakthrough. Mathematical modeling allows for a unique look into the underlying cellular dynamics and allows for testing treatment strategies without the need for clinical trials. This dissertation explores several iterations of a dendritic cell (DC) therapy model and correspondingly investigates what each iteration teaches about response to treatment.
In Chapter 2, motivated by the work of de Pillis et al. (2013), a mathematical model employing six ordinary differential (ODEs) and delay differential equations (DDEs) is formulated to understand the effectiveness of DC vaccines, accounting for cell trafficking with a blood and tumor compartment. A preliminary analysis is performed, with numerical simulations used to show the existence of oscillatory behavior. The model is then reduced to a system of four ODEs. Both models are validated using experimental data from melanoma-induced mice. Conditions under which the model admits rich dynamics observed in a clinical setting, such as periodic solutions and bistability, are established. Mathematical analysis proves the existence of a backward bifurcation and establishes thresholds for R0 that ensure tumor elimination or existence. A sensitivity analysis determines which parameters most significantly impact the reproduction number R0. Identifiability analysis reveals parameters of interest for estimation. Results are framed in terms of treatment implications, including effective combination and monotherapy strategies.
In Chapter 3, a study of whether the observed complexity can be represented with a simplified model is conducted. The DC model of Chapter 2 is reduced to a non-dimensional system of two DDEs. Mathematical and numerical analysis explore the impact of immune response time on the stability and eradication of the tumor, including an analytical proof of conditions necessary for the existence of a Hopf bifurcation. In a limiting case, conditions for global stability of the tumor-free equilibrium are outlined.
Lastly, Chapter 4 discusses future directions to explore. There still remain open questions to investigate and much work to be done, particularly involving uncertainty analysis. An outline of these steps is provided for future undertakings.
In Chapter 2, motivated by the work of de Pillis et al. (2013), a mathematical model employing six ordinary differential (ODEs) and delay differential equations (DDEs) is formulated to understand the effectiveness of DC vaccines, accounting for cell trafficking with a blood and tumor compartment. A preliminary analysis is performed, with numerical simulations used to show the existence of oscillatory behavior. The model is then reduced to a system of four ODEs. Both models are validated using experimental data from melanoma-induced mice. Conditions under which the model admits rich dynamics observed in a clinical setting, such as periodic solutions and bistability, are established. Mathematical analysis proves the existence of a backward bifurcation and establishes thresholds for R0 that ensure tumor elimination or existence. A sensitivity analysis determines which parameters most significantly impact the reproduction number R0. Identifiability analysis reveals parameters of interest for estimation. Results are framed in terms of treatment implications, including effective combination and monotherapy strategies.
In Chapter 3, a study of whether the observed complexity can be represented with a simplified model is conducted. The DC model of Chapter 2 is reduced to a non-dimensional system of two DDEs. Mathematical and numerical analysis explore the impact of immune response time on the stability and eradication of the tumor, including an analytical proof of conditions necessary for the existence of a Hopf bifurcation. In a limiting case, conditions for global stability of the tumor-free equilibrium are outlined.
Lastly, Chapter 4 discusses future directions to explore. There still remain open questions to investigate and much work to be done, particularly involving uncertainty analysis. An outline of these steps is provided for future undertakings.
ContributorsDickman, Lauren (Author) / Kuang, Yang (Thesis advisor) / Baer, Steven M. (Committee member) / Gardner, Carl (Committee member) / Gumel, Abba B. (Committee member) / Kostelich, Eric J. (Committee member) / Arizona State University (Publisher)
Created2020