Environmental Engineering Reference
In-Depth Information
of weekly variation in ozone was demonstrated with ozone data from the EPA's
air quality system (www.epa.gov/ttn/airs/airsaqs/detaildata/downloadaqsdata.htm).
CASTNET sites and CMAQ grid cells at Abington, CT (ABT147) and Shenan-
doah National Park, VA (SHN418) were chosen for purposes of illustration. ABT is
downwind of the New York City urban area. SHN is a high altitude site (elev.
1,073 m).
2.3. Low pass filter (KZ)
A low-pass filter (iterative moving average where high frequencies are damped and
low frequencies are unaltered) was used to define the trend (KZ(k = 3 iterations,
q = 182 days) and intra-day (original − KZ(k = 3 iterations, q = 1 h)) time scales
(Zurbenko, 1986; Rao and Zurbenko, 1994). An advantage of the KZ over other
linear filters is its ease of application when some observations are missing: missing
values are ignored and a mean is computed from whatever values are present.
Endpoints of time series (as well as the edges of gaps) are not properly filtered and
are therefore clipped when presented.
2.4. Wavelet filter
The KZFT(q,k,w) wavelet is a Fourier transform (FT) version of the KZ
(Zurbenko and Porter, 1998). The KZFT is given by:
where q is the half-window size and k is the number of iterations, Τ is a frequency
of interest, and 'i' is (−1)
1/2
. The real part of the filtered time series, Υ(Y
t
), is a
bandpass component centered at frequency Τ, and |(Y
t
)| is the instantaneous
amplitude of Y(t).
Cross-correlations do not adequately describe relationships among different
periodic processes. Any two time series with seasonal (or diurnal) variation will
tend to be highly correlated when adjusted for phase difference. As such, it's
better to compare amplitudes and phases. Consider the following conceptual
model for seasonal variation:
where Q
se
is seasonal variation in a process Q at time t, A
t
is the amplitude of
seasonal variation at time t, p is the period (1 year) and ph
t
is the phase at time t.
Seasonal phase is calculated from (Bloomfield, 2000):
