We analyze long-term time series of daily average PM10 concentrations in Chengdu city. Detrended fluctuation analysis of the time series shows long range correlation at one-year temporal scale. Spectral analysis of the time series indicates 1/
The adverse effects of PM10 have been recognized in environmental sciences. Besides the reduction of visibility, the direct impact on human health via inhalation is an important issue [
As asked by Nagel [
However, why do the complex structures of PM10 concentrations evolution exhibit scale-invariant?
As an introduction to the concept, self-organized criticality (SOC) has been proposed by Bak et al. [
In this work, at first, long range correlation,
Chengdu city is located in western Sichuan Basin of China. Sichuan Basin covers 260,000 km2, generally at low altitudes of about 500 m. These lower lying areas are surrounded by mountains and a plateau higher than 4 km. The unique geographical environment directly affects meteorological condition of pollutant diffusion and increases the frequency of calm wind at Chengdu. At Chengdu city, the average annual frequency of calm wind, namely, wind speed being 0~0.2 m/s, is 46%. So the local pollution sources play a more significant role in air quality of Chengdu [
There are eight automatic monitoring stations at Chengdu city. The daily average concentrations of pollutants are made at each station. These concentrations are further averaged over the stations to provide the daily average values of pollutant to represent the daily average air quality of Chengdu city. In this work, the examined data set is daily average PM10 concentrations data from 2001 to 2011 in Chengdu city, as shown in Figure
The daily average PM10 concentrations data from 2001 to 2011 in Chengdu city. The data lengths all are 4018 (days).
Detrended fluctuation analysis (DFA), which was proposed by Peng et al. [
A DFA exponent
The power spectrums have been used in investigating the
In some natural phenomena, cumulative magnitude-frequency distributions exhibit power-law scaling. It is regarded as the typical “critical” dynamical behavior of SOC systems [
In the study, a general sandpile model for PM10 pollution has been established with a nondimensional formalism.
The model is defined on a square lattice of size
Driving mechanism: at a given time, as a consequence of pollution source emission at some site
Redistribution and relaxation mechanism: when the amounts of PM10 pollutants at some site
This rule will be circulating running in accordance with the above method until a new stable configuration is reached, namely, all
These rules represent the movements and transformation process of PM10 under calm condition. When PM10 pollutants diffuse, the site of pollution source will reserve partial pollutants, which are set to one-fifth of its original value. At the same time, owing to precipitation, adsorption, and chemical action, some PM10 pollutants will be lost during transportation and diffusion. In our model, we presume that 4% of PM10 pollutants will be lost when they topple to the four adjacent neighbor sites. So the model is local and nonconservative.
Temporal degradation mechanism: PM10 pollutants will decay with time owing to self-purification of atmospheric environment. We simplify this process and presume that degradation of PM10 follows the first level of decaying kinetics. So when a new stable configuration is reached after each relaxation rule, PM10 pollutants at all sites will decay to
After all lattice sites are stable, another grain of sand is added.
If PM10 evolution is an example of a SOC process, the avalanche size distribution will follow power-law distribution. In a nondimensional formalism, we select
Figure
DFA of the study data. The dots are values of
On the power spectrum plot shown in Figure
The power spectrum plot for the study data. The black lines are power law
Figure
The number (
In order to investigate the robustness of the scale invariance in PM10 concentrations, the same analysis is performed at the different time intervals, shown in Figure
The number (
The number (
The SOC state is stationary in the sense that over long timescales, the average height
The simulations are performed for 50 × 50 lattice sizes. The average height
Plot of average height
When reaching the nonequilibrium steady state, extensive data collection has been made for
Avalanche size distribution for the PM10 pollution sand model when
There are no unequivocal determining criteria to ascertain whether evolution of some natural phenomenon is governed by SOC. One accustomed approach is to compare characteristic measures of some natural phenomenon to those obtained from a known SOC system.
To motivate comparisons between PM10 pollution and SOC sandpile, we firstly take a qualitative description of the complexity in PM10 pollution system which could give rise to SOC dynamics. PM10 pollution system contains many components such as pollutant sources, atmospheric pollutants components, solar radiation, wind speed, temperature, atmospheric self-purification, topographical feature, and other meteorologic factors. Each component has a certain influence on the average PM10 concentration each day. When all the components are considered together, they interact and correlate with each other on vastly different timescales. One group of comparatively fast radical chemical reactions relaxes on timescales of fractions of seconds up to hours, while another group the rather slow processes (e.g., the movement of PM10 pollutants) relaxes on timescales of days up to years or even longer. Thus, PM10 pollution system is a complex system composed of a series of interconnected components. These components have some complex pattern of influence on the daily average PM10 concentration, which result in the fluctuations of PM10 concentrations in long term.
We make an analogy between the sandpile and PM10 evolution. PM10 pollutants form mainly as a result of first and (or) secondary pollutants produced from the emission of air pollution sources. The driving force is the continuously PM10 pollutants emission in atmospheric environment, which serve as the grains continuously dropped on a pile. We can define the superposition of local PM10 pollutants concentration which represents the chain of forces in sandpile. When the amounts of microscopic condensed PM10 pollutants reach some threshold magnitude, the pollutants masses can be transported on microscopic scales by diffusion or convection. They reach a new location, where the local PM10 pollutants concentration is lower and can be diluted. If the local PM10 pollutants concentration in the neighborhood is also high, the amount of condensed pollutants will increase. Once the system reaches some critical point, any small perturbation, in principle, can trigger a chain reaction like the avalanches in atmospheric system. The normal atmospheric environmental capability serves as the critical state. If the local PM10 pollutants concentration is higher than the same critical value, pollutants are assembled and precipitated in the atmosphere. Thus, the system will adapt itself by removing these dissidents to maintain the critical state just as the sandpile adapts itself by avalanching to reach its constant angle of repose. Therefore, we can define the fluctuations of PM10 concentrations as avalanches events in a SOC sandpile. At the critical state, long range correlation,
The micromechanisms of PM10 concentrations evolution are very complex. Some microscopic physical and chemical mechanisms are still uncertain. For example, how do photochemical reaction rate change with first and (or) secondary pollutants? How do the components of pollutants affect mass transport and chemical reaction at gas and solid two phases? Based on this traditional “reductionism” science perspective, the origin of robust scale-invariant in PM10 concentrations evolution can be quite hard to understand. However, when we turn sight to “holism” science perspective, the satisfactory understanding is achieved to this problem. Considering the similarities between sandpile system and PM10 evolution, a simplified sandpile model for PM10 pollution with a nondimensional formalism is put forward. This model mechanism only includes the emission of PM10 pollutants, the movements and transformation of PM10, and temporal degradation process of PM10. The high correspondence of the results to observations indicates that the model provides an effective parameterization of the key physical process that governs PM10 concentrations evolution.
It is important to note that the power system organizes itself to an operating point near to, but not at, a critical value. This could make the system quite robust in different time intervals. One consequence is that the measured frequency of occurrence of small events can be used to estimate the frequency of occurrence of large events. For example, the recurrence interval for serious air pollution can be estimated from the frequency of smaller air pollution.
Based on DFA, power spectrum, and statistical analysis, we have identified long range correlation,
The work is supported by the National Natural Science Foundation of China (no. 41105118) and Hunan Provincial Natural Science Foundation of China (13JJB012).