We investigate the dynamics of particulate matter, nitrogen oxides, and ozone concentrations in Hong Kong. Using fluctuation functions as a measure for their variability, we develop several simple data models and test their predictive power. We discuss two relevant dynamical properties, namely, the scaling of fluctuations, which is associated with long memory, and the deviations from the Gaussian distribution. While the scaling of fluctuations can be shown to be an artifact of a relatively regular seasonal cycle, the process does not follow a normal distribution even when corrected for correlations and non-stationarity due to random (Poissonian) spikes. We compare predictability and other fitted model parameters between stations and pollutants.

1.
World Health Organization, see https://www.who.int/air-pollution/news-and-events/how-air-pollution-is-destroying-our-health for “How Air Pollution Is Destroying Our Health” (2019).
2.
A.
Ukhov
,
S.
Mostamandi
,
A.
da Silva
,
J.
Flemming
,
Y.
Alshehri
,
I.
Shevchenko
, and
G.
Stenchikov
, “
Assessment of natural and anthropogenic aerosol air pollution in the Middle East using MERRA-2, CAMS data assimilation products, and high-resolution WRF-Chem model simulations
,”
Atmos. Chem. Phys.
20
,
9281
9310
(
2020
).
3.
Y.
Tian
,
X.
Pan
,
T.
Nishizawa
,
H.
Kobayashi
,
I.
Uno
,
X.
Wang
,
A.
Shimizu
, and
Z.
Wang
, “
Variability of depolarization of aerosol particles in the megacity of Beijing: Implications for the interaction between anthropogenic pollutants and mineral dust particles
,”
Atmos. Chem. Phys.
18
,
18203
18217
(
2018
).
4.
C.
Varotsos
and
D.
Kirk-Davidoff
, “
Long-memory processes in ozone and temperature variations at the region 60° S-60° N
,”
Atmos. Chem. Phys.
6
,
4093
4100
(
2006
).
5.
S. T.
Rao
,
H.
Luo
,
M.
Astitha
,
C.
Hogrefe
,
V.
Garcia
, and
R.
Mathur
, “
On the limit to the accuracy of regional-scale air quality models
,”
Atmos. Chem. Phys.
20
,
1627
1639
(
2020
).
6.
M.
Massah
and
H.
Kantz
, “
Confidence intervals for time averages in the presence of long-range correlations, a case study on earth surface temperature anomalies
,”
Geophys. Res. Lett.
43
,
9243
, https://doi.org/10.1002/2016GL069555 (
2016
).
7.
L.
Li
,
J.
Qian
,
C.-Q.
Ou
,
Y.-X.
Zhou
,
C.
Guo
, and
Y.
Guo
, “
Spatial and temporal analysis of air pollution index and its timescale-dependent relationship with meteorological factors in Guangzhou, China, 2001–2011
,”
Environ. Pollut.
190
,
75
81
(
2014
).
8.
T.
Plocoste
,
R.
Calif
, and
S.
Jacoby-Koaly
, “
Temporal multiscaling characteristics of particulate matter PM10 and ground-level ozone O3 concentrations in Caribbean region
,”
Atmos. Environ.
169
,
22
35
(
2017
).
9.
C.
Varotsos
,
J.
Ondov
, and
M.
Efstathiou
, “
Scaling properties of air pollution in Athens, Greece and Baltimore, Maryland
,”
Atmos. Environ.
39
,
4041
4047
(
2005
).
10.
A.
Chelani
, “
Long-memory property in air pollutant concentrations
,”
Atmos. Res.
171
,
1
4
(
2016
).
11.
T.
Graves
,
R.
Gramacy
,
N.
Watkins
, and
C.
Franzke
, “
A brief history of long memory: Hurst, Mandelbrot and the road to ARFIMA, 1951–1980
,”
Entropy
19
(
9
),
437
(
2017
).
12.
H.
Rust
, “
Interactive comment on ‘Long-memory processes in global ozone and temperature variations’ by C. Varotsos and D. Kirk-Davidoff
,”
Atmos. Chem. Phys. Discuss.
6
,
S1182
S1185
(
2006
).
13.
M.
Efstathiou
and
C.
Varotsos
, “
On the altitude dependence of the temperature scaling behaviour at the global troposphere
,”
Int. J. Remote Sens.
31
,
343
349
(
2010
).
14.
D.
Maraun
,
H.
Rust
, and
J.
Timmer
, “
Tempting long-memory-on the interpretation of DFA results
,”
Nonlinear Process. Geophys.
11
,
495
503
(
2004
).
15.
C.
Varotsos
,
M.
Efstathiou
, and
A.
Cracknell
, “
On the scaling effect in global surface air temperature anomalies
,”
Atmos. Chem. Phys.
13
,
5243
5253
(
2013
).
16.
E.
Alessio
,
A.
Carbone
,
G.
Castelli
, and
V.
Frappietro
, “
Second-order moving average and scaling of stochastic time series
,”
Eur. Phys. J. B
27
,
197
200
(
2002
).
17.
P.
Abry
and
D.
Veitch
, “
Wavelet analysis of long-range-dependent traffic
,”
IEEE Trans. Inf. Theory
44
,
2
15
(
1998
).
18.
Y. X.
Huang
,
F. G.
Schmitt
,
Z. M.
Lu
, and
Y. L.
Liu
, “
An amplitude-frequency study of turbulent scaling intermittency using empirical mode decomposition and Hilbert spectral analysis
,”
EPL
84
,
40010
(
2008
).
19.
Y.
Zhou
,
Y.
Leung
, and
J.-M.
Ma
, “
Empirical study of the scaling behavior of the amplitude–frequency distribution of the Hilbert–Huang transform and its application in sunspot time series analysis
,”
Physica A
392
,
1336
1346
(
2013
).
20.
C. K.
Peng
,
S. V.
Buldyrev
,
S.
Havlin
,
M.
Simons
,
H. E.
Stanley
, and
A. L.
Goldberger
, “
Mosaic organization of DNA nucleotides
,”
Phys. Rev. E
49
,
1685
(
1994
).
21.
C.
Heneghan
and
G.
McDarby
, “
Establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic processes
,”
Phys. Rev. E
62
,
6103
(
2000
).
22.
M.
Hoell
and
H.
Kantz
, “
The relationship between the detrendend fluctuation analysis and the autocorrelation function of a signal
,”
Eur. Phys. J. B
88
,
327
(
2015
).
23.
P. G.
Meyer
and
H.
Kantz
, “
Inferring characteristic timescales from the effect of autoregressive dynamics on detrended fluctuation analysis
,”
New J. Phys.
21
,
033022
(
2019
).
24.
P. G.
Meyer
and
H.
Kantz
, “
A simple decomposition of European temperature variability capturing the variance from days to a decade
,”
Clim. Dyn.
53
,
6909
6917
(
2019
).
25.
P. G.
Meyer
,
M.
Anvari
, and
H.
Kantz
, “
Identifying characteristic time scales in power grid frequency fluctuations with DFA
,”
Chaos
30
,
013130
(
2020
).
26.
H.-C.
Lu
, “
The statistical characters of PM10 concentration in Taiwan area
,”
Atmos. Environ.
36
,
491
502
(
2002
).
27.
L.
Chen
,
K. E.
Bassler
,
J. L.
McCauley
, and
G. H.
Gunaratne
, “
Anomalous scaling of stochastic processes and the Moses effect
,”
Phys. Rev. E
95
,
042141
(
2017
).
28.
B.
Morel
, “
Statistical distributions for air pollution applied to the study of the particulate problem in Santiago
,”
Atmos. Environ.
33
,
2575
2585
(
1999
).
29.
F.
Costabile
,
G.
Bertoni
,
F.
Desantis
,
F.
Wang
,
H.
Weimin
,
L.
Fenglei
, and
I.
Allegrini
, “
A preliminary assessment of major air pollutants in the city of Suzhou, China
,”
Atmos. Environ.
40
,
6380
6395
(
2006
).
30.
H. D.
Kahn
, “
Note on the distribution of air pollutants
,”
J. Air Pollut. Control Assoc.
23
,
973
(
1973
).
31.
G.
Williams
,
B.
Schäfer
, and
C.
Beck
, “
Superstatistical approach to air pollution statistics
,”
Phys. Rev. Res.
2
,
013019
(
2020
).
32.
K.
Shi
, “
Detrended cross-correlation analysis of temperature, rainfall, PM10 and ambient dioxins in Hong Kong
,”
Atmos. Environ.
97
,
130
135
(
2014
).
33.
P. K.
Louie
,
L.
Zhong
,
J. A.
Zheng
, and
A. K.
Lau
, “
A special issue of atmospheric environment on ‘Improving regional air quality over the Pearl River Delta and Hong Kong: From science to policy’
,”
Atmos. Environ.
76
,
1
2
(
2013
).
34.
R. J.
Hyndman
and
G.
Athanasopoulos
,
Forecasting: Principles and Practice
(
OTexts
,
2018
).
35.
M. S.
Taqqu
and
V.
Teverovsky
, “On estimating the intensity of long-range dependence in finite and infinite variance time series,” in A Practical Guide to Heavy Tails: Statistical Techniques and Applications, edited by R. Adler, R. Feldman, and M. Taqqu (Birkhäuser, 1998), pp. 177–218.
36.
M.
Hoell
,
H.
Kantz
, and
Y.
Zhou
, “
Detrended fluctuation analysis and the difference between external drifts and intrinsic diffusionlike nonstationarity
,”
Phys. Rev. E
94
,
042201
(
2016
).
37.
J.
Beran
,
Y.
Feng
,
S.
Ghosh
, and
R.
Kulik
,
Long-Memory Processes
(
Springer
,
2016
).
38.
F.
Hooge
, “
1/f noise
,”
Physica B+C
83
,
14
23
(
1976
).
39.
S.
Porter-Hudak
, “
An application of the seasonal fractionally differenced model to the monetary aggregates
,”
J. Am. Stat. Assoc.
85
,
338
344
(
1990
).
40.
K.
Hu
,
P.
Ch. Ivanov
,
Z.
Chen
,
P.
Carpena
, and
H. E.
Stanley
, “
Effect of trends on detrended fluctuation analysis
,”
Phys. Rev. E
64
,
011114
(
2001
).
41.
X.
Fan
,
K.-C.
Lam
, and
Q.
Yu
, “
Differential exposure of the urban population to vehicular air pollution in Hong Kong
,”
Sci. Total Environ.
426
,
211
219
(
2012
).
42.
C.
Beck
and
E. G.
Cohen
, “
Superstatistics
,”
Physica A
322
,
267
275
(
2003
).
43.
M.
Hoell
and
H.
Kantz
, “
The fluctuation function of the detrended fluctuation analysis–Investigation on the AR(1) process
,”
Eur. Phys. J. B
88
,
126
(
2015
).
44.
J.
Allen
, “
Short term spectral analysis, synthesis, and modification by discrete Fourier transform
,”
IEEE Trans. Acoust. Speech Signal Process.
25
,
235
238
(
1977
).
45.
E.
Sejdić
,
I.
Djurović
, and
J.
Jiang
, “
Time–frequency feature representation using energy concentration: An overview of recent advances
,”
Digit. Signal Process.
19
,
153
183
(
2009
).
46.
Hong Kong Environmental Protection Department
(2020). “Environmental Protection Interactive Centre,” https://cd.epic.epd.gov.hk/EPICDI/air/station/?lang=en.

Supplementary Material

You do not currently have access to this content.