Identification of Major Drought Events based on Mean Du-

Major drought events were found in this study using the technique described in section 3.4.3. These benchmark events are required for the future analysis of possible consequences of climate change on agricultural droughts. The drought clustering algorithm was applied to every ensemble realization to find the spatio-temporal evolution of all drought events during the reconstruction period from 1951-2010. For every event, drought characteristics such as mean duration (D), total magnitude (M), and mean areal extent (A), among others, were evaluated using the procedure illustrated in section 3.4.4. The ensemble average of these characteristics, i.e. ˆD, ˆM, and ˆA are depicted in Figure 3.10. The corresponding uncertainty of these characteristics is presented in Table 3.1.

Figure 3.10: Area under drought, duration, and magnitude of the eight largest events in Germany since 1950 based on the ensemble hSMIi.

The eight largest drought events identified during the last 60 years in Germany are the following periods: 1962-1965, 1971-1974, 1975-1978, 1959-1960, 1953-1954, 1991-1993, 2005, and 1995-1997. It is worth noting that the event from 2003-2005, appears in this overall ranking in the 7th position. Vidal et al. (2010) also

noticed this fact and concluded that 2003 hardly appears as a benchmark event in France. This is a rather controversial conclusion because in this year the highest temperatures during the last 500 years were recorded (Luterbacher et al., 2004).

In Germany alone, great losses in the agricultural sector (COPA-COGECA, 2003) were reported. A likely explanation for this paradox is provided in section 3.5.7.

Table 3.1: Uncertainty of characteristics of major drought events in Germany since 1950. Uncertainty of the characteristics and mean±standard deviation.

Period Duration Area Magnitude

[month] [%] [% area× month × 10³ ] 1953-1954 8.0 ± 0.2 70.8 ± 3.0 24.6 ± 1.0

1959-1960 12.0 ±0.2 59.2 ± 2.3 36.3 ± 0.7 1962-1965 14.5 ±0.9 41.5 ± 1.5 36.8 ± 2.0 1971-1974 14.8 ±4.6 43.1 ± 5.0 36.7 ± 12.9 1975-1978 12.4 ±0.8 43.5 ± 4.9 36.5 ± 1.9 1988-1991 5.9 ± 0.2 22.7 ± 2.0 11.1 ± 1.1 1991-1993 9.3 ± 1.5 29.3 ± 4.2 20.7 ± 3.6 1995-1997 8.5 ± 2.3 24.7 ± 6.7 11.8 ± 3.2 2003-2005 7.6 ± 0.5 32.1 ± 4.5 17.1 ± 1.6 2005-2007 5.6 ± 1.0 24.7 ± 3.4 11.5 ± 2.2

The three drought characteristicsD,M, andAdepicted in Figure 3.10, are highly correlated with each other. The Pearson correlation coefficient between D and M, is the highest, and equal to 0.97, whereas those between (D and A) and (M and A) are 0.80 and 0.87, respectively. This indicates that this triplet has low dimensionality. In fact, the first eigenvector of the correlation matrix of this triplet alone explains 92% of the total variance.

Using the k-means cluster analysis, three main groups of drought events were distinguished, 1) events with a large areal extent and duration, i.e. events 1962-1965, 1971-1974, 1975-1978, and 1959-1960; 2) events with the largest areal extent and moderate duration, i.e. 1953-1954; and 3) events with moderate areal extent and duration, i.e. 1991-1993, 2003-2005, and 1995-1997. Based on the ensemble SMI mean (SMI), the event from 1971-1974 exhibited the longest duration, and the event from 1953-1954 covered the largest area. The events from 1962-1965 and 1971-1974 reached the two largest magnitudes.

The absolute ranking of these extreme drought events is rather difficult due to the parameter uncertainty as illustrated in Table 3.2. This table presents an estimate of the probability to order every event into the eight top ranks using a linear, equal-weighted, normalized indicator composed of D and A, as an example. The results presented in this table indicate that the maximum probability of finding

3.5. Results and Discussion

Table 3.2: Probability of finding a drought event in any of the top eight ranks.

Here, only the eight largest events in Germany since 1950 were selected.

The sum of the likelihood is not necessarily one due to the truncation of the table up to only the eighth rank. Values in bold represent the largest likelihood based on the ensemble simulations.

Event Ranking likelihood

1 2 3 4 5 6 7 8

1953-1954 0.04 0.31 0.56 0.09 1959-1960 0.34 0.51 0.15

1962-1965 0.43 0.48 0.08 0.01

1971-1974 0.67 0.03 0.19 0.10 0.01

1975-1978 0.02 0.06 0.36 0.56

1991-1993 0.59 0.09 0.08

1995-1997 0.07 0.53 0.29

2003-2005 0.03 0.10 0.23 0.59

an event in one of the top ranks is not greater than 0.67. The ranking of a given event spans at least over three categories. Low ranking events tend to have a much larger ranking spread than the top ones, though.

The size of the ensemble also played a very important role to estimate the proba-bility of finding an event in a given rank (1−α), whereαdenotes the false positive rate. Figure 3.11, for example, shows the probability of not identifying the event from 1971-1974 as the largest since 1951. This figure clearly shows that the vari-ance of the false positive rate is strongly dependent on the ensemble size. These results were obtaining by bootstrapping the 200 ensemble simulations without re-placement and limiting the number of realizations to 1000 for a given sample size.

This figure showed also that the first two moments of α tend to stabilize with ensemble sizes larger than 50. Consequently, it is safe to conclude that small en-semble sizes would lead to misleading results. An enen-semble with 200 members, as realized in this study would lead to safer results. These Monte Carlo realizations clearly highlighted the role of parametric uncertainty in identifying the benchmark drought events which should be handled carefully.

The spatial distribution of severity (S_d) based on SMI at the peak of the eight largest drought events is shown in Figure 3.12. It can be observed from this figure that each event has its own peculiarities with respect to the spatial distribution of the affected areas. The drought event during December 1954 has the largest areal coverage, with 93.5% of the German territory under water stress, whereas the event during April 1996 had the lowest coverage with 46.5%. The latter drought event at its peak was particularly concentrated on the north-west part of Germany.

The event of 1976, with its peak in August, had spread over whole Germany with an exception of the Alpine Foreland. The latter areas endured the highest severity during August 2003.

Figure 3.11: Sensitivity of the false positive rate (α) to ensemble size. In this example, α denotes the probability of rejecting the null hypothesis that the event from 1971-1974 ranks 1st among all drought events from 1950 to 2010. The size of the bootstrapping realizations was 1000.

Figure 3.12: Severity at the peak of the eight largest drought events from 1951-01-01 to 21951-01-010-12-31 based on the ensemble mean SMI.

3.5. Results and Discussion

3.5.7 Uncertainty of Large Events Occurring in Summer and