A note on the Hecke hypothesis and the determination of imaginary quadratic fields with class-number 1

AbstractThe authors propose a hypothesis whose proof would provide, in particular, a solution of the “class-number 1” problem, recently solved by Stark and Baker

Simulating Ground-based Polarimetric Responses using AirMSPI Observations from the FIREX-AQ Campaign

Wildland fire smoke is one of the major sources of biomass-burning aerosols in the Earth's atmosphere. As the smoke plume evolves, the biomass-burning aerosols undergo aging processes that change their physical and chemical composition. Capturing rapid temporal changes is not suitable for satellites due to the time lapse between observations. Airborne remote sensing offers the ability to increase the spatial and temporal resolution of smoke plume observations compared to satellite observations. However, this increase in spatial and temporal resolution from airborne observations amplifies the need for better spatial coverage from ground-based instruments for validation. In the summer of 2019, the Airborne Multiangle Spectropolarimetric Imager (AirMSPI) was deployed during the Fire Influence on Regional to Global Environments and Air Quality (FIREX-AQ) field campaign on the NASA ER-2 high-altitude research aircraft. This aircraft performed multiple overpasses of the Williams Flats fire near the town of Spokane, Washington, USA, in August 2019, sampling smoke plumes at a georectifed spatial resolution of 10 m2. This work performs aerosol retrievals along the smoke plume observed during one flight on 7 August 2019. The retrieval methods used here follow those established by DeLeon et al. (in review) using the Generalized Retrieval of Atmosphere and Surface Properties (GRASP). Two points along the plume were selected: one at 1.35km and the other at 3.78km from the fire source. The fraction of fine mode aerosols and single scattering albedo increased at the greater distance from this wildfire source. These retrieved aerosol properties were used to simulate ground-based polarimetry in ultraviolet, visible, and infrared wavebands. For all wavebands, the maximum degree of linear polarization (DoLP) decreased farther from the source. Notably, the ultraviolet wavebands retained a higher polarimetric signal farther from the source, compared to the visible and infrared. At 865 nm the DoLP decreased from 48.5% to 14.6%. At 355 nm the DoLP decreased from 33.6% to 22.5%. These polarimetric simulations are intended to inform instrument development for ground-based detection of wildfire smoke. © 2023 SPIE.Immediate accessThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]