DAILY AIR TEMPERATURE AND PRESSURE SERIES ... - BALTEX

DAILY AIR TEMPERATURE AND PRESSURE SERIES FOR STOCKHOLM (1756–1998) 207
collected during the last decade and many individuals have been very helpful
in different ways. We thank in particular: Bengt Dahlström, Haldo Vedin, Hans
Alexandersson, Peter Svensson and Krister Boqvist (all at the SMHI), Christer
Wijkström (Royal Swedish Academy of Sciences), Olle Amelin (Office for History
and Science, Uppsala University), Inga Elmqvist (Stockholm Observatory
Museum), Maria Brunskog (Stockholm City Museum), Ingvar Johansson (Swedish
Institute for Wood Technology Research) and Birgitta Björling (Dept. of Meteorology,
Stockholm University). Lars Bärring’s thorough review comments helped at
lot to improve the paper. Financial support before IMPROVE started was given
by Carl Mannerfelts fond, Andréefonden and Axel Lagrelius’ fond för geografisk
forskning.
Appendix
This appendix gives a description of how the -values and f cl factors in Equation
(1) were obtained.
MODEL FOR THE DIURNAL TEMPERATURE CYCLE
To determine the -values to be used in Equation (1) we used ninety years (1869–
1958) of hourly temperature observations from Uppsala as a basis, as we consider
the diurnal temperature cycle in Uppsala to be representative for Stockholm if its
amplitude is scaled with respect to the climatic difference and its phase is adjusted
for the small time difference between the longitudes (1 min 44 s).
Here we are interested only in the deviations of instantaneous temperatures from
the average daily mean temperatures, and not of absolute temperatures. The diurnal
cycle of these deviations is abbreviated DC. In order to avoid small irregularities
in the DC curves, which may be due to micro-climatic conditions specifically related
to conditions at Uppsala, they were smoothed using Fourier series with four
harmonics.
For each month, m (1 ≤ m ≤ 12), the DC for Stockholm can be expressed as
where
DC m (h) =
4∑
n=1
A (S)
m,n = f m · A (U)
m,n .
A (S)
m,n
(2π · cos n
)
· h ·
24 + ω m,n , (A.1a)
(A.1b)
In these equations, h is the hour (CET decimal hour, 0 ≤ h ≤ 24), A is the amplitude
of each harmonic (with the superscripts (S) and (U) denoting Stockholm and
Uppsala). The amplitudes A (U)
m,n and phase angles ω m,n (the latter with the appropriate
phase shift) were determined from the Uppsala data. The scaling factor, f m ,