In Varrio Research Station the flowering date of Bilberry has been followed since 1981. On average Bilberry flowers on 16 June (day number 167 in the calendar year), although variation among the dates is considerable, between 31 May and 2 July (Fugure 1, see also the original data).
It is also notable in the flowering observations that during the past 27 years there has not been any trend for earlier flowering, for instance as an effect of climate change.
When studying the effect of temperature on the duration of certain phenological phases, for instance with
Downy birch the duration from bud burst burst to full leaf (see Pohjonen 2008), it is essential to define what is the initial stage s1 and what is the final stage s2. In the case of Bilberry only the final stage s2, the flowering date, has been been recorded but no earlier stages. It is therefore assumed that the onset of Bilberry development coincides with the disappearance of snow. This in turn has been recorded in Varrio Research Station (Figure 2), as part of the regular weather monitoring of Finnish Meteorological Office, since 1975 (see also the original data)
On average the snow disappears in Varrio Nature Reserve measurement point on 18 May (day number 138). The earliest date has been 27.4.1990 and the latest 14.6.1982. There is a slight downwards trend in the graph, telling that snow disappears somewhat earlier than in the 1970. The trend, however, is not statistically significant.
By defining the snow disappearance as initial stage (s1) and flowering as the final stage (s2) for each year
|Figure 3. Duration of phenological
phase from disappearance of snow
1981 … 2008, the duration s2 – s1 in calendar days follows. On average, it takes 28.5 Calendar Days for Bilberry from snow disappearance to flowering. The shortest period (in 2007) was 14 days and the longest (in 2004) 47 days. The variance (STDPA) in the data set is 9.53 days and Coefficient of Variation 33.4 per cent.
There is a slight upward trend in the data, telling that in the later years it has taken somewhat longer for Bilberry to flower as calculated from the disappearance of the snow. The trend, however, has no statistical significance.
By applying the standard Degree Days calculation with baseline temperature of 5 degrees, that is used in Finland, the following measures result:
Average duration 80.7 DD-units
Range 21.3 – 144 DD units
Standard deviation 34.6 DD units
Coefficient of Variation 42.9 per cent
The Coefficient of Variation with Calendar Days (33.4%) is lower than with Degree Days (43.9%). This tells that with Bilberry the standard concept of Degree Days does not work. For prediction purposes use of Calendar Days gives more accurate results than use of Degree Days. An obvious reason is that the baseline temperature of 5 degrees is too high for Bilberry.
Therefore, is there more ambient baseline temperature b for the development of Bilberry, lower than 5 degrees? This can be studied with the help of Coefficient of Variation. Let us maintain the normalization condition for the development rate M(x) where x is the average daily temperature. Thus
M(6) = 1, and
M(b) = 0
The general equation for the development rate thus becomes (Eq. 1)
(2) M(x) = (x – b) / (6 – b)
where b is the baseline temperature. Standard Degree Days come from the same equation. When baseline temperature is 5 degrees, M(x) = x – 5. It is notable that Calendar Days also come from the same equation. When baseline temperature approaches minus indefinite, M(x) approaches 1 at all temperatures, which tells that development rate is 1 every day, irrespective of temperature.
Next, let us vary the baseline temperature, calculate a new measure DDb for Degree Days (over baseline temperature b), and study how the Coefficient of variation changes along with the baseline temperature. The following measures result:
Baseline temperature, b -2.22 degrees
Average duration 30.5 DDb units
Range 8.7 – 48.1 DDb units
Standard deviation 7.97 DDb units
Coefficient of Variation 26.1 per cent
|Figure 4. Minimum Coefficient of
Variation for optimum baseline
temperature with Bilberry
By reducing it the Coefficent of Variation drops fast. The Coefficient of Variation related to Calendar Days (33.4%) is bypassed at around 3 degrees. This tells that DD-calculation is better than Calendar Day calculation only with baseline temperatures under 3 degrees. The Coefficient of Variation minimizes in a negative baseline temperature of -2.22 degrees (Figure 4).