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Comment on “An unexpected pattern of distinct weekly periodicities in climatological variables in Germany” by Dominique Bäumer and Bernhard Vogel

2008; American Geophysical Union; Volume: 35; Issue: 5 Linguagem: Inglês

10.1029/2007gl031279

1944-8007

Harrie‐Jan Hendricks Franssen,

Climate variability and models

[1] Bäumer and Vogel [2007] (hereinafter referred to as BV07) presented a statistical analysis of sunshine duration, cloud cover, temperature and precipitation data, and found for all these weather elements a significant dependence on the weekday. The analysis was carried out for 12 meteorological stations spread over Germany, for the period 1991–2005. Here data since 1864 (precipitation) or 1901 (sunshine duration) from the Swiss stations Zurich and Lugano are analyzed. In addition, the data from the period 1991–2005 were used in a Monte Carlo analysis to investigate whether pure random effects could generate a weekly cycle as documented by BV07. The following points will be addressed in the data analysis: [2] I. If, as BV07 argue, a human-induced weekly cycle of meteorological variables exists, a similar cycle (probably with a smaller or larger amplitude) should also exist before 1991, as the air composition before 1991 (especially after 1950) was also strongly influenced by human activities, possibly even with higher aerosol numbers. The historical data of Zurich and Lugano were checked for such a cycle. [3] II. If the weekly cycle that BV07 found is due to a new mechanism that had a significant impact only from 1991 onwards, the individual weekdays should show much smaller deviations from the overall mean in the period before 1991 as compared with the period after. It is therefore tested to what extent the deviations for individual weekdays for the period 1991–2005 are statistically significant, using as a basis the overall period 1864–2005 (or 1901–2005 in case of sunshine duration). [4] III. Data on sunshine duration and precipitation amount exhibit important spatial auto-correlation, due to the typical length scale of extra-tropical cyclones and anticyclones and since the main variables that influence convective precipitation (lapse rate, humidity) show a strong spatial auto-correlation. Because the German time series that BV07 analyzed are expected to be spatially auto-correlated, and because also the weather variables measured in Zurich will have spatial autocorrelation with the German data, Lugano was included in this analysis. The weather on the Southern side of the Alpes tends to be poorly correlated with the German weather (between Zurich and Lugano the linear correlation was +0.02 for sunshine duration and +0.27 for precipitation). A further consideration is that Lugano is strongly affected by emissions of pollutants and aerosols from the Po Plateau in Northern Italy (e.g., Milano), so that the mechanisms that BV07 postulate as possible causes for the weekly cycle are also present here. [5] IV. A Monte Carlo analysis was used to test if random effects could explain important deviations that were observed by BV07 and that are also found in this study (for precipitation in Zurich and sunshine duration in Lugano). The Monte Carlo analysis was also used to test whether random effects could explain a weekly cycle as observed by BV07. [6] Meteorological data since 1864 (precipitation) and 1901 (sunshine duration) from Zurich and Lugano, located on the Northern and Southern side of the Swiss Alpes respectively, were analyzed. The observational data were measured, quality checked and stored by the Swiss Federal Office of Meteorology and Climatology MeteoSwiss. For the period 1991–2005 (the period analyzed by BV07), average precipitation amounts and sunshine duration were calculated for each weekday, and the anomaly with respect to the overall 15-years mean was determined. To assess the significance of the observed deviations in the 1991–2005 period, blocks of 15-years precipitation averages were calculated for the period 1864–1998 (i.e., 1864–1878, 1879–1893, etcetera). In addition, within each of these 15 year blocks, the average precipitation per weekday (Sunday, Monday, etcetera) and the deviation of this average with respect to the 15-years average were determined. In total 63 (9 blocks of fifteen years × 7 weekdays) anomalies were obtained (hereinafter P). For sunshine duration, data since 1901 were available and seven blocks of 15 years were analyzed (1901–1915, …, 1991–2005), using the same procedure described above for precipitation amounts, which yielded 49 (7 × 7) 15-years blocks with anomalies (hereinafter S). Although earlier measurements of precipitation and, particularly, sunshine duration (Campbell-Stokes) were probably associated with larger measurement errors, this is unlikely to affect the analysis, as each measurement (and each weekday) is impacted by this in a similar manner, and it does not generate systematically more sunshine or less precipitation for a certain weekday. [7] In order to investigate further the significance of a weekly cycle in observed precipitation amounts for the period 1991–2005 in Zurich and sunshine duration for the same period in Lugano, a small stochastic experiment was performed. The observed data from the 1st of January 1991 until the 31st of December 2005 were randomly re-arranged, neglecting temporal auto-correlation, by drawing a random number between 0 and 1 for each day, and ordering the data set according the values of the random numbers. The purely randomly ordered data should not show a weekly cycle or significant anomalies for a certain weekday now, but still reproduce exactly the experimental data series. This experiment was repeated 100 times, and in each experiment the anomaly from the overall mean was calculated for each weekday. In addition, for the precipitation in Zurich it was analyzed how many weekly cycles were found in the 100 experiments: an experiment was considered to exhibit a weekly cycle comparable to Figure 3a of BV07 if at least four consecutive weekdays all had either an above-average or a below-average precipitation rate and the other weekdays all had an opposite anomaly with respect to the mean. [8] The discussion of the results is organized around points I, II, III, IV as formulated in the section 1. [9] I. Before 1991, neither for Zurich nor for Lugano, the precipitation and sunshine duration exhibited a weekly cycle as observed by BV07. For instance, considering the most recent three fifteen year periods (1954–1998 for precipitation, 1961–2005 for sunshine duration), for only eight out of 28 cases (2 stations × 2 variables × 7 days) the kind of anomaly for a certain weekday (above or below overall mean) was consistent over the three periods (without a week cycle one would expect due to randomness seven cases). See Tables 1 and 2 with the data for Zurich. [10] II. The analysis of the 63 P values for Zurich, gives an average standard deviation for P of 5.8%. If we assume P to be normally distributed, a P value that differs more than two standard deviations from the mean is statistically significant (significance always at the 95% level). The assumed normal distribution slightly overestimates the number of statistically significant anomalies because the true statistical distribution for the anomalies is, for several reasons, not normal with longer tails. One P value for the period 1991–2005 (corresponding to Saturday precipitation) has a statistically significant anomaly (+18.0%). See also Table 1. The standard deviation of S for Zurich was 1.8%. None of the weekdays in the period 1991–2005 showed a statistically significant anomaly from the mean; in fact, all anomalies were within one standard deviation of S. See also Table 2. The standard deviation of P for Lugano was 6.8%. All the P values for the period 1991–2005 are within two standard deviations of P. The standard deviation of S for Lugano was 1.7%. Three S values for the 1991–2005 period for Lugano deviated by more than twice the standard deviation: the Saturday sunshine duration showed a deviation of +4.1%, and also Sunday (+3.5%) and Thursday (−3.9%) had large deviations. In all, from the 28 analyzed P and S values (2 stations × 2 variables × 7 days) four values were statistically significantly different from the overall mean. One would expect 1.4 statistically significant anomalies (due to random effects) out of 28 (5% of the 28 analyzed P and S values), and the chance of finding at least 4 anomalies due to randomness is 4.9%. However, note that the assumed normal distribution overestimates the number of significant anomalies. In addition, three of the four anomalies that were found to be statistically significant (the sunshine duration in Lugano) had a sign opposite to what BV07 found. Nevertheless, the found statistically significant anomalies were investigated in more detail (section 3, IV). [11] III. For the period 1991–2005, Lugano showed a completely different weekly cycle as compared to the German stations analyzed by BV07. No systematic cycle was observed, and, for instance, the Saturday was in Lugano the most sunny weekday, whereas for the German stations it was the least sunny weekday. [12] IV. The statistically significant anomalies were investigated in more detail with the Monte Carlo experiment described in section 2. For Saturday precipitation in Zurich (the statistically largest anomaly, and the only one in correspondence with BV07) it was found that for 16 out of the 100 random experiments the average P was larger than for the experimental data (P > 9.3%), for realization #40 P was even 12.1%. Moreover, for 65 out of 100 realizations at least one of the seven P values was larger than 10%, and for 9 out of 100 realizations a similar or larger P value than in the observation set (18%) was found (maximum +20.3% for Monday precipitation in realisation #90). This illustrates that a purely random ordering of the observed precipitation amounts also yields important anomalies from the mean, and that none of the observed weekday precipitation anomalies in Zurich is statistically significant. The only statistically significant anomaly that was found before (see point II), is related with the underlying point distribution of precipitation observed in Zurich for 1991–2005. This underlying point distribution gave rise to larger P values (probably due to higher extreme precipitation events) than the ones observed before 1991. In addition, it was found that 21 out of the 100 random experiments (21%) showed a weekly cycle according to the definition given in section 2, even though temporal autocorrelation was neglected in this Monte Carlo experiment. The Monte Carlo experiment was also done for the sunshine duration data of Lugano, as three statistically significant anomalies were found (see section 3, II). Surprisingly, around half of the stochastic realizations, had for a certain weekday a larger anomaly than the largest anomaly observed in the time series (4.1%). None of the three observed sunshine duration anomalies is statistically significant and also in this case the underlying point distribution gave rise to larger anomalies. [13] In order to investigate whether the weekly cycle in meteorological variables as found by BV07 for the period 1991–2005 in Germany, is statistically significant, the analysis was extended to Zurich and Lugano for the period 1864–2005. Both Lugano and Zurich never showed a persistent weekly cycle for precipitation and sunshine duration for the investigated period. In addition, only 4 of the calculated 28 anomalies for the period 1991–2005 (2 stations × 2 variables × 7 weekdays) were statistically significant (statistically 1.4 anomalies are expected). Only one of the four statistically significant anomalies had the same sign as observed by BV07. The anomalies were analyzed further in a Monte Carlo study. The stochastic simulation experiments suggest that none of the anomalies was significant; even the largest anomaly (the anomaly of Saturday precipitation in Zurich of 18.0%) occurred in 9% of the experiments due to purely random effects. In addition, for 21% of the stochastic experiments a weekly cycle in precipitation in Zurich is found due to random effects. The fact that BV07 reported a significant weekly periodicity could be due to the fact that the meteorological variables involved have a strong spatial auto-correlation. BV07 neglected this spatial auto-correlation while assessing the statistical significance of the merged time series. Of course, a (very) weak weekly periodicity in meteorological variables like temperature and sunshine duration could exist; however, the current contribution suggests that the periodicity found by BV07 is probably not statistically significant. 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