Simple PDF models for convectively driven vertical diffusion |
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| Institution: | 2. Department of Atmospheric Sciences, Nanjing University, Nanjing, P.R.C.;3. Meteorology and Assessment Division, Atmospheric Sciences Research Laboratory, Research Triangle Park, NC 27711, U.S.A.;1. Samsung Advanced Institute of Technology, Samsung Electronics Co., Ltd., 130 Samsung-ro, Yeongtong-gu, Suwon-si, Gyeonggi-do 443-803, Republic of Korea;2. School of Urban, Architecture and Civil Engineering, Pusan National University, 2, Busandaehak-ro 63beon-gil, Geumjeong-gu, Busan 46241, Republic of Korea;1. Key Laboratory of Clean Energy Conversion Technologies, The University of Nottingham Ningbo China, Ningbo 315100, PR China;2. Institute of Clean Coal Technologies, East China University of Science and Technology, Shanghai 200237, PR China;3. Department of Chemical and Environmental Engineering, The University of Nottingham Ningbo China, Ningbo 315100, PR China;4. Department of Chemical and Environmental Engineering, The University of Nottingham, University Park, Nottingham NG7 2RD, UK;1. School of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an 710049, China;2. Key Laboratory of Carbonaceous Wastes Processing and Process Intensification of Zhejiang Province, University of Nottingham Ningbo China, Ningbo 315100, China;3. College of Safety and Environmental Engineering, Shandong University of Science and Technology, Qingdao 266000, China;4. Materials Interfaces Center, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, Guangdong, China;5. Municipal Key Laboratory of Clean Energy Conversion Technologies, The University of Nottingham Ningbo China, Ningbo 315100, China;1. Key Lab of Aerosol Chemistry and Physics, SKLLQG, Institute of Earth Environment, Chinese Academy of Sciences, Xi’an, Shaanxi, 710061, China;2. University of the Chinese Academy of Sciences, Beijing, 100049, China;3. School of Human Settlements and Civil Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, China;4. State Key Laboratory of Atmospheric Boundary Layer Physics and Atmospheric Chemistry, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100029, China;5. CAS Center for Excellence in Quaternary Science and Global Change, Xi’an, Shaanxi, 710061, China;1. School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai, 200093, China;2. School of Energy and Power Engineering, Dalian University of Technology, 116023, Dalian, China;3. Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing, 100190, China |
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| Abstract: | The mode of vertical velocity in convective boundary layers (CBLs) is usually negative and the probability distribution function (PDF) of w, Pw, is rarely symmetric except near the top and bottom of CBLs. Consequently, vertical diffusion from elevated sources is usually asymmetric and exhibits a descending mode of concentration, causing higher peak surface concentrations than predicted by Gaussian models. The main concentration (χ) effects, we argue, can be modeled using the simplest of PDF diffusion models, with tracers responding to Pw at the source height with straight line trajectories and simple reflection at the surface and zi, the mixing depth. The critical element is the choice of Pw. Two Pw models are offered, a bi-Gaussian (BG) and a Gaussian-ramp (GR) formulation. Both have some observational support, and the resulting PDF models are mathematically tractable. Analytical solutions for key variables are given; these show some surprising contrasts between the BG and GR models, but both can approximate laboratory and numerical modeling results for ∝χdy patterns. A diverse selection of atmospheric turbulence measurements is presented; for measures that reflect asymmetry in Pw, the data show wide ranges and do not lend support to any particular form of Pw. Recent lidar measurements of oil fog plumes are presented that show a large variability in ∝χdy patterns, even with substantial averaging periods. The only concurrent turbulence measurement that strongly correlates with the observed vertical diffusion of oil fog is the mode of wind elevation angle. A simple adaptation of the BG model is recommended that fits the average peak ∝χdy and distance of occurrence as observed so far. |
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