Interpolations of missing monthly mean temperatures in the Karasjok series

Transcription

1 Interpolations of missing monthly mean temperatures in the Karasjok series Øyvind ordli (P.O. Box 43, OSLO, ORWAY) ABSTRACT Due to the HistKlim project the sub daily data series from Karasjok was digitised and quality controlled. The present report discusses some problems with missing values in the period where many interpolations had to be done in order to fill the gaps. The uncertainties of the interpolations were assessed for daily as well as for monthly values. In the database, however, only interpolated monthly values were accepted. The standard error of the interpolations of the monthly mean temperatures varies with the month of the year. The errors are much larger in winter than in summer, about 1 o C during winter and 0.2 o C or less during the season April September (AMJJAS). If the data coverage in a month is 50 % the uncertainties are reduces by 71 % compared with a situation were all values in the month are missing. o. 24 Oslo, 2 ovember 2009

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3 1 introduction In the period there are two major problems with the Karasjok series. The first one is the question about the calibration of the minimum thermometer and the second one is the many gaps in the series. The calibration problems are in short discussed by Høgåsen (1996) and in more detail by ordli (2008) where calibration methods were suggested. These were later adopted for the official series stored in met.no s data base. The problem with the many gaps is the subject for the present report. The observer, who was the vicar of the parish, had to travel long distances as there were churches or chapels also outside the Karasjok village. Thus, the duties of the observer could not easily be combined. The gaps are more frequent in summer than in winter, so apparently he must have visited the remote places most frequently during summer. During the 19 th century the neighbouring stations to Karasjok are situated far away. The nearest one, Kautokeino, is of little use for interpolations as also this series has many gaps, unfortunately at the same intervals as Karasjok. At the station Alta, however, observations have been carried out without interruption during the whole period. The station is located in the innermost part of Alta Fjord but has continental climate during winter, in particular due to the drainage of cold air from the inland areas down the Alta valley. In order to use the station for gap filling the Alta series was digitised for the period Previously only the monthly means have been digitised. 2 Methods and results Simple linear regression analysis was carried out on daily mean values at Alta (predictor) and Karasjok (predictand). Thus, in principle all gaps could be filled for the Karasjok series by use of the regression equations, one for each month. The results and uncertainties in the interpolations are given in table1 and in figure 1. Table 1 Regression equations: Daily mean temperature at Karasjok, T dk, (predictand) and daily mean temperature at Alta, T da, (predictor), the regression correlation, R, and the standard error of the estimate SE. Month Regression equ. R SE January T dk = * T da February T dk = * T da March T dk = * T da April T dk = * T da May T dk = * T da June T dk = * T da July T dk = * T da August T dk = * T da September T dk = * T da October T dk = * T da ovember T dk = * T da December T dk = * T da Occasionally also full months are missing in the Karasjok series. On monthly bases all orwegian series are digitised and ready for use in regression analysis. A multiple regression analysis was thus established with all of the nearest stations, but this analysis did not give significantly better results than using Alta alone. Therefore the regressions done on daily values with Alta as the only predictor were also used for the interpolation of full months. 3

4 The uncertainties in the monthly means, s M, at Karasjok will depend on the number of days in the month that are missing, n i. Let s di and s dk be the uncertainty of the daily values at Karasjok, the s di being the uncertainties of the interpolated values and s dk the measured values. Then the uncertainty of the monthly mean is given by (1) SM ni sdi ( ni ) sdk where is the number of days in the month and i is the number of missing days in the month. If we only want to consider the uncertainties in the interpolations equation (1) takes the form: ni (2) S M sdi When the whole month is missing and = n i we see that equation (2) takes the well known form of the uncertainty of a mean value: sdi (3) S M Following table 1 and equation (1) the uncertainties in the monthly means due to interpolations depend on the months of the year and the number of missing values. For 8 missing days the uncertainty is reduced by 50 %. The reduction of uncertainty due to increasing number of existing daily values in each month is shown graphically in figure 1. Standard deviation ( C) Uncertainties in monthly mean interp. for Karasjok umber of days interpolated jan feb mar apr mai jun jul aug sep okt nov des Figure 1. Uncertainty in the interpolations as a function of the number of missing values in each month 4

5 The figure depict interesting differences between the months showing much larger uncertainties during the winter months than during spring, summer and autumn. In the months AMJJAS the standard error of the mean values never exceeds 0.4 o C, whereas this limit is exceed already with 4 missing days in December and January and with 5 missing days in ovember and December. The missing values are mainly concentrated during summer as shown in table 2. Outside the period there are some missing values at the end of WW II, where the population of Finnmark County was evacuated and houses burned down. Table 2 The problematic period in the Karasjok series. The white fields mark the months with complete data coverage, whereas the magenta fields mark the months that are completly missing. The partly missing months is marked with yellow colour. A figure is giving the number of existing daily means. Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct ov Dec Conclusions The standard error of the interpolations of the daily mean temperatures varies with the month of the year. The errors are much larger in winter than in summer, about 5 o C during winter and 2 o C or less during the months AMJJAS. For the monthly means this amounts to about 1 o C during winter and less than 0.2 o C in AMJJAS for missing values of the whole month. 4 References Høgåsen, S. 1996: Stasjonshistorie for Karasjok. DMI-klima, rapport nr. 9/96, Oslo, 21 pp. ordli, Ø. 2008: Om korreksjon av minimumstemperatur brukt I Karasjok Den norske kulderekorden frå met.no.report, o.19/2008 Climate, 14 pp. 5