ASU Scholarship Showcase

Tikhonov regularization for projected solutions of large-scale ill-posed problems is considered. The Golub{Kahan iterative bidiagonalization is used to project the problem onto a subspace and regularization then applied to nd a subspace approximation to the full problem. Determination of the regularization, parameter for the projected problem by unbiased predictive risk estimation, generalized cross validation, and discrepancy principle techniques is investigated. It is shown that the regularized parameter obtained by the unbiased predictive risk estimator can provide a good estimate which can be used for a full problem that is moderately to severely ill-posed. A similar analysis provides the weight parameter for the weighted generalized cross validation such that the approach is also useful in these cases, and also explains why the generalized cross validation without weighting is not always useful. All results are independent of whether systems are over- or underdetermined. Numerical simulations for standard one-dimensional test problems and two- dimensional data, for both image restoration and tomographic image reconstruction, support the analysis and validate the techniques. The size of the projected problem is found using an extension of a noise revealing function for the projected problem [I. Hn etynkov a, M. Ple singer, and Z. Strako s, BIT Numer. Math., 49 (2009), pp. 669{696]. Furthermore, an iteratively reweighted regularization approach for edge preserving regularization is extended for projected systems, providing stabilization of the solutions of the projected systems and reducing dependence on the determination of the size of the projected subspace.

Summer daytime cooling efficiency of various land cover is investigated for the urban core of Phoenix, Arizona, using the Local-Scale Urban Meteorological Parameterization Scheme (LUMPS). We examined the urban energy balance for 2 summer days in 2005 to analyze the daytime cooling-water use tradeoff and the timing of sensible heat reversal at night. The plausibility of the LUMPS model results was tested using remotely sensed surface temperatures from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) imagery and reference evapotranspiration values from a meteorological station. Cooling efficiency was derived from sensible and latent heat flux differences. The time when the sensible heat flux turns negative (sensible heat flux transition) was calculated from LUMPS simulated hourly fluxes. Results indicate that the time when the sensible heat flux changes direction at night is strongly influenced by the heat storage capacity of different land cover types and by the amount of vegetation. Higher heat storage delayed the transition up to 3 h in the study area, while vegetation expedited the sensible heat reversal by 2 h. Cooling efficiency index results suggest that overall, the Phoenix urban core is slightly more efficient at cooling than the desert, but efficiencies do not increase much with wet fractions higher than 20%. Industrial sites with high impervious surface cover and low wet fraction have negative cooling efficiencies. Findings indicate that drier neighborhoods with heterogeneous land uses are the most efficient landscapes in balancing cooling and water use in Phoenix. However, further factors such as energy use and human vulnerability to extreme heat have to be considered in the cooling-water use tradeoff, especially under the uncertainties of future climate change.