Matching Items (3)
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- All Subjects: Radial basis functions
- Genre: Doctoral Dissertation
- Creators: Platte, Rodrigo
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
Divergence-free vector field interpolants properties are explored on uniform and scattered nodes, and also their application to fluid flow problems. These interpolants may be applied to physical problems that require the approximant to have zero divergence, such as the velocity field in the incompressible Navier-Stokes equations and the magnetic and electric fields in the Maxwell's equations. In addition, the methods studied here are meshfree, and are suitable for problems defined on complex domains, where mesh generation is computationally expensive or inaccurate, or for problems where the data is only available at scattered locations.
The contributions of this work include a detailed comparison between standard and divergence-free radial basis approximations, a study of the Lebesgue constants for divergence-free approximations and their dependence on node placement, and an investigation of the flat limit of divergence-free interpolants. Finally, numerical solvers for the incompressible Navier-Stokes equations in primitive variables are implemented using discretizations based on traditional and divergence-free kernels. The numerical results are compared to reference solutions obtained with a spectral
method.
The contributions of this work include a detailed comparison between standard and divergence-free radial basis approximations, a study of the Lebesgue constants for divergence-free approximations and their dependence on node placement, and an investigation of the flat limit of divergence-free interpolants. Finally, numerical solvers for the incompressible Navier-Stokes equations in primitive variables are implemented using discretizations based on traditional and divergence-free kernels. The numerical results are compared to reference solutions obtained with a spectral
method.
ContributorsAraujo Mitrano, Arthur (Author) / Platte, Rodrigo (Thesis advisor) / Wright, Grady (Committee member) / Welfert, Bruno (Committee member) / Gelb, Anne (Committee member) / Renaut, Rosemary (Committee member) / Arizona State University (Publisher)
Created2016
Description
Solving partial differential equations on surfaces has many applications including modeling chemical diffusion, pattern formation, geophysics and texture mapping. This dissertation presents two techniques for solving time dependent partial differential equations on various surfaces using the partition of unity method. A novel spectral cubed sphere method that utilizes the windowed Fourier technique is presented and used for both approximating functions on spherical domains and solving partial differential equations. The spectral cubed sphere method is applied to solve the transport equation as well as the diffusion equation on the unit sphere. The second approach is a partition of unity method with local radial basis function approximations. This technique is also used to explore the effect of the node distribution as it is well known that node choice plays an important role in the accuracy and stability of an approximation. A greedy algorithm is implemented to generate good interpolation nodes using the column pivoting QR factorization. The partition of unity radial basis function method is applied to solve the diffusion equation on the sphere as well as a system of reaction-diffusion equations on multiple surfaces including the surface of a red blood cell, a torus, and the Stanford bunny. Accuracy and stability of both methods are investigated.
ContributorsIslas, Genesis Juneiva (Author) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Espanol, Malena (Committee member) / Kao, Ming-Hung (Committee member) / Renaut, Rosemary (Committee member) / Arizona State University (Publisher)
Created2021