Anisotropy, derived from the Reynolds stress tensor, is closely related to turbulent energy and transport, and can be quantified using two parameters: x_B and y_B. Scale-dependent properties of anisotropy from diverse observational experiments are investigated with the help of the Hilbert-Huang transform method. The mean y_B-x_B trajectories in the barycentric map are visualized as curve clusters under different stratification conditions. Specifically, x_B increases from 0.4 to 0.9 with the increasing scale of motions, while y_B initially rises from 0.5 to 0.7 before decreasing to 0. Trajectories deviating from this pattern in individual cases help distinguish non-turbulent motions and reconstruct turbulence data. This analysis reveals approximately 30% to 80% overestimation of turbulent fluxes. Therefore, anisotropy demonstrates potential for quantifying turbulent transport in the atmospheric boundary layer.

To investigate the effectiveness of anisotropy in reflecting characteristics of atmospheric turbulence, the data are selected from multiple observational sites across different underlying surfaces and in different seasons.

The 255-m meteorological tower in Tianjin is located in the PBL Meteorological Observation Station, Tianjin Meteorological Administration, which is representative of the typical urban landscape with profound anthropogenic influences. The turbulent data from sonic anemometers (CSAT-3, Campbell Scientific, Inc., Logan, UT, USA) are acquired from the meteorological tower at 80m orienting towards East, which can provide the three-dimensional wind speed and the sonic temperature data. The fast-response observation of gases are conducted with the Open Path CO₂/H₂O Analyzer (LI-7500, LI-COR, Inc., Lincoln, NE, USA) installed at 80m, providing density time series of CO₂ and water vapor. The sampling frequencies of the instruments above are all 10 Hz. There are also observation of mean wind speed (Cup and vane anemometer, Changchun Meteorological Instrument Ltd., Changchun, China) and mean temperature and humidity (HMP45C, Campbell Scientific, Inc., Logan, UT, USA) at a total of 15 levels. The gradient data are calculated as the averaged finite difference of the mean variables from 5 levels from 40m to 120m. The observational data were collected from July 1 to August 31, 2017. For more information about the Tianjin Station, refer to Ye et al. (2015) and Wei et al. (2018).

The Naiman station is located in Horqin Sandy Land in the Naiman County of Inner Mongolia. The underlying surface is nearly flat and homogeneous, consisting mainly of sandy land with low and open shrubs, which is typical of a semiarid continental monsoon climate, and there is few human activity. The sonic anemometers and Open Path CO₂/H₂O Analyzer are the same as Tianjin Station at 8m orienting towards West, with the same sampling frequencies of 10 Hz. The mean wind speed (010C, MetOne Instruments Inc., Grants Pass, OR, USA), air temperature and humidity (HMP45C, Campbell Scientific, Inc., Logan, UT, USA), and wind direction (020C, MetOne Instruments Inc., Grants Pass, OR, USA) are observed at four levels from 2 to 20 meters. The gradient data are obtained from the finite difference between the two levels of 4 meters and 16 meters. The observational data were collected from July 1 to July 31, 2022. More information concerning the Naiman station can be found in Li et al. (2015) and Wei et al. (2021).

The Dezhou station is located at Pingyuan county meteorological bureau in Shandong Province. The underlying surface is typical flat farmland in North China Plain. The station is equipped with a set of instruments at the height of 2.8m, including a three-dimensional sonic anemometer (IRGASON, Campbell Scientific, Inc., USA) orienting towards North, a continuous particle measuring instrument E-sampler (Met One, Inc.), and a high-frequency sampling extinction coefficient measuring instrument (CS120A, Campbell Scientific, Inc., USA). The The sampling frequency of wind speed is 10 Hz, and that of PM_2.5 density is 1 Hz. The gradient data is acquired from a near-surface observation of a GPS low-altitude electronic sonde (XHD-403, Institute of Atmospheric Physics of the Chinese Academy of Sciences). The sonde collects data every 10 meters, and the averaged finite difference within 100 meters from the land surface is calculated as the gradient of each meteorological parameter. Observations are repeated every 3 hours from December 27, 2018 to January 24, 2019, and the data are interpolated to match the sampling frequency of other instruments. There is a comprehensive introduction on the Dezhou station and the methodology of the measurement of PM_2.5 density in Ren et al. (2020).

The raw turbulence observational data were pre-processed using the EddyPro software (Advanced 7.0.9, LI-COR Biosciences, Inc., USA), including error flags, despiking (Vickers and Mahrt, 1997), double coordinate rotation (Wilczak et al., 2001), and detrending. The turbulent fluxes are also corrected to eliminate the influence of tilt, time lag, and WPL terms within the software and the following reconstructions. The averaging time span of data processing is 1 hr for the data from Tianjin and 30 min for the data from Naiman and Dezhou. This allows for a comprehensive comparison of the characteristics of atmospheric turbulence under different conditions, and the calculations in the following sections use the same time spans.