ASU Scholarship Showcase

Major urban centers are warming due to a combination of global and local phenomena. City governments are increasingly adopting strategies to mitigate the causes and impacts of extreme heat on their populations. Among these strategies are high solar-reflectance (cool) surfaces installed on building roofs and walls. Use of cool surfaces is a cost-effective and simple strategy that replaces conventional darker surfaces with surfaces that have a high reflectance to shortwave (solar) energy.

This report reviews the recent history of cool-surface deployment efforts. This includes peer-reviewed literature, conference proceedings, and grey literature to identify challenges and barriers to wide-scale deployment of cool surfaces. We have also researched heat action plans and programs from cities and different codes and standards, as well as available incentive and rebate programs.

The review identifies challenges, barriers, and opportunities associated with large-scale deployment of cool surfaces and categorizes them broadly as being related to product development & performance or policies & mandates. It provides a foundation upon which we intend to build a roadmap for rapidly accelerating future deployments of cool surfaces. This roadmap will address identified challenges and incorporate lessons learned from historical efforts to generate a practical and actionable plan.

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.