Fourth Study Conference on BALTEX Scala Cinema Gudhjem

- 82 -
Variability of Ångström Coefficients during Summer in Estonia
Hilda Teral 1 , Hanno Ohvril 1 , Nels Laulainen 2
1 Institute of Environmental Physics, University of Tartu, ohvril@ut.ee
2 Pacific Northwest National Laboratory, Richland, USA
1. The Ångström formula
Generalizing his own and colleagues’ experimental results,
Anders Ångström (1888–1981), (1929, 1930) proposed the
use of certain quantities α and β for a description of the
spectral variability of atmospheric columnar aerosol optical
thickness δAER (λ):
δAER (λ) = β (λ) – α , (1)
where λ is in µm. Physically it is more correct to normalize
λ with a certain wavelength λ0, following Ångström’s
approach, λ0 = 1 µm = 1000 nm (Shifrin, 1995):
− α
⎛ ⎞
⎜ λ
δ
⎟
AER
( λ)
= β . (2)
⎜ ⎟
⎝
λ
0 ⎠
A basic wavelength λ0 allows application of a power-law
dependence to a dimensionless variable λ/λ0 and to interpret
the coefficient β as the atmospheric columnar aerosol optical
thickness at a wavelength λ0 :
( )
β = δAER
λ0
. (3)
Thus, β is known as the Ångström turbidity coefficient. The
other Ångström coefficient, α, is linked with the size distribution
of aerosol particles. It is significant, that (in the case
of spherical particles and the Junge size distribution), the
Ångström’s formula was confirmed theoretically [Junge,
1955; Ångström, 1964].
Concerning α, its maximum value, α = 4, corresponds to
molecular (Rayleigh) scattering. For different conditions in
the real atmosphere, Ångström himself (1929) found it to
have a value between 1.0 and 1.5. As an exception of this
rule he noted hazy days of the summer 1912, when the
eruption of Mt Katmai caused decrease of α down to 0.5–
0.7. Thirty years later Ångström concluded “that α varies
within a comparatively small range and that under average
conditions, at a rather variety of stations, it has a value close
to 1.3 ± 0.2 [Ångström, 1961].
For the determination of the Ångström turbidity coefficient
β only one measurement of spectral irradiance, at λ = 1000
nm, is needed. A symbol β1000 is then used (Martinez-Lozano
et al., 1998). For the determination of both coefficients,
α and β, spectral transmittancies of the “aerosol layer” at
two wavelengths are needed. Usually these coefficients are
determined by a linear fit to
ln δAER (λ) = ln β – α ln λ (4)
and they enable a good general description of aerosol
particles and an indication of their size [Molineaux and
Ineichen, 1996]. However, it should be noted that the
Ångström formula is only a convenient approximation, not
necessarily valid over all spectral ranges and atmospheric
conditions (Martinez-Lozano et al., 1998). In this work we
try to assess the applicability of the Ångström formula in
Estonia and the variability of the Ångström coefficients.
2. AERONET sunphotometer at Toravere
The installation of an AERONET (AErosol RObotic
NETwork) autonomous sunphotometer Cimel CE 318-1
(generously provided by B. Holben, NASA Goddard
Space Flight Center) at Toravere (58°15′, 26°27′, 70 ASL)
in the spring of 2002, allowed Estonian atmospheric
phycisists, in addition to traditional broadband actinometry,
to start regular spectral investigations. The sunphotometer
made measurements of direct solar beam in
seven spectral bands (340, 380, 440, 500, 670, 870, 1020
nm) when only the solar disc was free of clouds.
A program of automatic data processing includes the calculation
of Aerosol Optical Thicknesses (AOT) δAER (λ),
which appear, corresponding to different quality levels, on
the AERONET homepage (http://aeronet.gsfc.nasa.gov/).
Level 1.0 contains unscreened data. Data at Level 1.5 are
automatically screened. Level 2.0 is quality assured, which
means pre-, and (NB!), postinstallation field calibration at
NASA and manual inspection.
Summer 2002 Level 2.0 data include 68 observational
days (in June 16, July 24, August 28, days, respectively).
The total number of measurement series, at all seven
wavelengths, was 1602. Actually AERONET measurements
were continued in September, but this is a transitional
month in Estonia, when the weather conditons
change, and the behaviour of the AOT is more
complicated.
3. Evaluation of applicability of the Ångström
formula
If the parameters ln δAER (λ) and ln λ lie on a straight line
(4), the Ångström formula is suitable for a general description
of the corresponding aerosol particles.
R
Correlation coefficients for the Ångström formula, 340-1020
nm, summer 2002, Toravere, Estonia
-1.01
-1.00
-0.99
-0.98
-0.97
-0.96
-0.95
-0.94
-0.93
151
June
182
July
Julian day
213
August
244
Figure 1. Coefficients of correlation R (note that they
are negative) characterizing the fit of the Ångström
formula at Toravere, Estonia, in summer 2002. Each point
corresponds to a measurement series of 7 spectral bands in
range 340–1020 nm. In total 1602 points (series) are
shown. Julian day is counted from 1 to 365.