Determining the fluctuation of PM_2.5 mass concentration and its applicability to Monin-Obukhov similarity

In this manuscript, a method based on the nonlinear relationship between mass concentration of fine-particle and visibility is introduced to obtain the high-frequency mass concentration and vertical mass flux of PM_2.5 during a haze pollution process. The high-frequency sampling was obtained using a visibility meter upgraded by our research group. To make the results more reliable, we restricted the service conditions of this method, that is, RH < 80% and the limited visibility value (15 km herein). The method was applied to a period of pollution from 27 December 2018 to 7 January 2019 at the Pingyuan site, located in the North China Plain. A 1-Hz fluctuation of the mass concentration of PM_2.5 was obtained, as was the vertical turbulent flux of the mass concentration of PM_2.5. The mean flux of the mass concentration of PM_2.5 for the entire 13 days was 0.022 μg m^-2 s^-1. The turbulent fluxes in five short-term pollution cases lasting for several hours or several days were -0.015 μg m^-2 s^-1, -0.03 μg m^-2 s^-1, 0.053 μg m^-2 s^-1, 0.023 μg m^-2 s^-1 and 0.075 μg m^-2 s^-1. Then, the relationship between the absolute value of the vertical flux of PM_2.5 mass concentration w^'c^'¯ and many turbulent variables showed that the vertical flux decreases exponentially with the increase of variables such as turbulent kinetic energy, standard deviation σ_u, σ_w, horizontal mean wind U, momentum flux τ and heat flux H. However, the absolute value of the vertical flux w^'c^'¯ was not affected by the value of the mass concentration of PM_2.5. The turbulent characteristics of PM_2.5 were also analysed. Under unstable conditions, the normalized standard deviation of PM_2.5σ_c/C_∗=20.07-zL^-1/3, where c is mass concentration of PM_2.5, C_∗ is scale of PM_2.5. The normalized spectra (nS_PM(n)/σ_c²) followed the Kolmogorov form, n^-2/3, where n is frequency, and the co-spectra of deviation of vertical wind speed and mass concentration of PM_2.5 (nC_wPM(n)/σ_wσ_c) was n^-4/3. Finally, the universal function of the mass concentration of PM_2.5 was calculated. The fitted curves for unstable and stable conditions were φ_czL=4.01-9.8zL^-1/2 and φ_czL=4.01+1.2zL. Although the observed values of the universal function of the mass concentration of PM_2.5 were widely scattered with respect to z/L, the trend is obvious. The measurements show that PM_2.5 has similar properties to regular scalars such as potential temperature or water vapor. Particularly, the measurement shows a good trend to satisfy the traditional Monin-Obukhov similarity theory (MOST). However, further experiments should be implemented for verification and to provide a more accurate coefficient.