DAILY AIR TEMPERATURE AND PRESSURE SERIES ... - BALTEX

DAILY AIR TEMPERATURE AND PRESSURE SERIES FOR STOCKHOLM (1756–1998) 195
following equation was used to convert the observed height (H obs )ofthemercury
column (in sw.inch) to the true height in sw.inch (H sw. inch ):
H sw. inch = f · (H obs − 25.3) + 25.3 ,
(3a)
where
(
f = 1 + a ) (
π · r 2 )
i
= 1 +
A π · (Ri 2 − ro 2) . (3b)
In Equation (3b), a = area of upper mercury surface, A = area of lower
mercury surface, r i = inner radius of glass tube, r o = outer radius of glass tube
and R i = inner radius of mercury container. The inner and outer radii of the glass
tube were measured in the X-ray image (Figure 10), and were found to be 3 mm
and 4 mm respectively. The entire mercury container can unfortunately not be seen
in the image because it is covered by a brass shield which cannot be removed. R i
can therefore not be determined from the X-ray image. One can only say that R i
can take any value between about 13 and 28 mm. This corresponds to values of the
factor f in Equation (3) between 1.06 and 1.01. We decided to use R i = 28 mm, i.e.
the maximum possible radius, giving f = 1.01, because it is likely that Ekström
wanted to minimize the influence of level changes of the lower mercury surface.
We applied Equation (3a) with f = 1.01 to all observed barometer values
1756–1858 and then we converted these values to mm. This seems to be relevant
for all cases when the Ekström barometer was used. If another barometer was used
some short periods (which certainly happened, see Section 5.5.), another correction
might have been more appropriate for these periods. With no explicit information
available about any possibly different barometers, however, we found no reason to
make other choices of correction.
5.3.3. Reduction to 0 ◦ C and Conversion to hPa
Reduction to 0 ◦ C, for the period 1756–1858, and at the same time conversion to
pressure in hPa was made using the standard equation:
p 0 = g 45 · ρ 0 · H T,mm · (1 − γ · T)· 10 −5 , (4)
where p 0 = air pressure reduced to 0 ◦ CinhPa,g 45 = 9.80665 m · s −2 (normal
gravity acceleration), ρ 0 = 13.5951 · 10 3 kg · m −3 (density of mercury at 0 ◦ C),
H T,mm = corrected length of the mercury column (in mm) at temperature T (in
◦ C), γ = 1.82 · 10 −4 K −1 (thermal expansion coefficient of mercury) ⋆ and T =
barometer temperature (in ◦ C).
We assumed that the Ekström barometer was correct at 0 ◦ C. This assumption
is arbitrary, but it is the common case for modern barometers. If we introduced a
⋆ The thermal expansion coefficient of brass (1.9 · 10 −5 K −1 ) was omitted because the maximum
error of omitting this coefficient for the short brass scale on the Ekström barometer is about
±0.03 hPa, which is negligible in this context.