3.4 The Soil Moisture Index
3.5.7 Uncertainty of Large Events Occurring in Summer and Winter 69
As mentioned before, the ranking of drought events based on ensemble character-istics (D, M, and A) does not allow the identification of their impact at a given point in time from their onset, nor to differentiate them according to their level of incidence in a particular season. The drought intensity proposed in Eq. 3.6 en-ables estimating the transient evolution of a drought event from its onset, and by so doing, it allows quantifying how fast a drought event covered a given area and by what magnitude. Panel (a) in Figure 3.13 shows the results of plotting drought intensity versus duration from the onset (d) of a given event for the ten largest events since 1950. Panel (b) in the same figure depicts the results obtained by ranking the drought intensities of all events at various durations from their onsets (e.g. 3, 6, ... months). The classification of an event into summer or winter was estimated with the procedure illustrated in section 3.4.3 (Eq. 3.6). The ensemble SMI mean (i.e. SMI) was used instead of individual realizations for both analyses because the former is an unbiased estimate of the SMI, and thus leads to a robust estimate of the evolution of the drought intensity.
(a) (b)
Figure 3.13: Panel (a): Drought intensity evolution for the 10 largest drought events since 1950. Panel (b): Major drought events for a given du-ration and season of occurrence. The numbers denote the follow-ing events: 1: 1953-1954, 2: 1959-1960, 3: 1962-1965, 4: 1971-1974, 5: 1975-1978, 6: 1988-1991, 7: 1991-1993, 8: 1995-1997, 9: 2003-2005, 10: 2005-2007.
Based on the results described above and shown in Figure 3.13, it was found that at 3 month duration, summer events have much larger drought intensity than the
corresponding ones in winter. At 6 and 9 months duration, the opposite happens.
The events with more than a 9 month duration mostly reach their higher intensities during summer as compared to winter ones. However, droughts having a duration of 30 months or more are more intense during winter months. The event 1953-1954 not only exhibits the largest intensities at 6 and 9 month durations during winter months (Nov-Apr), but also the largest intensity in summer at 12 months duration.
The event 2003-2005 is, according to these results, the summer event with the largest intensity at 6 months duration. Among the 10 largest drought events in Germany during last 60 years, the 1953-1954 event had the largest intensity peaking within a relatively short period of time (less than 12 months). This event, however, lasted for only one and a half years. Four drought events, namely, 1962-1965, 1971-1974, 1975-1978, and 1991-1993, spanned over the period of more than 30 months (i.e. two and a half years). According to this analysis, the decade of 1970 could be regarded as the most severe drought period in Germany. The drought events 1962-1965 and 1971-1974 clearly exhibited more than one peak over their whole life span. The analysis also indicated that most of the historical drought events in Germany have their peaks during 6 to 12 months of duration.
The empirical bivariate density function between the average drought area (A) and the total magnitude (M) was constructed to analyze the uncertainty in overall drought characteristics (D, M, and A) based on the ensemble realizations. The large number of model runs also allowed to assess the uncertainty in time evolution of these characteristics. The four most intense drought events with 6 months and at least 30 months duration after its onset were selected to illustrate this procedure, namely: the events 1953-1954 and 2003-2005 for shorter duration, and the events 1975-1978 and 1962-1965 for longer duration, respectively (Figure 3.14). It is worth noting that the events 1953-1954 and 2003-2005 are classified as winter and summer events, respectively, at 6 months duration (Figure 3.13 (b)). Likewise, the events 1975-1978 and 1962-1965 peaked in winter and summer, respectively. Droughts that are peaking within a relatively short time (up to 6 months) from their onset are quite relevant because they have large repercussion on socio-economic activities.
Based on the ensemble results, the density function for each event was estimated independently with a bivariate Gaussian kernel smother algorithm. The estima-tion of the bandwidths in both direcestima-tions was carried out in a similar way as presented in section 3.4.2. The results of this analysis are depicted in the top pan-els (a) to (d) of Figure 3.14, which clearly supports the research hypothesis that the parametric uncertainty of soil moisture has a strong implication for drought characterization. Most events exhibit multimodal behavior which is the combined result of the uncertainty of the model parametrization and drought identification (e.g. clustering, threshold).
Events having shorter durations and peaking in winter (1953-1954) appear to be more certain than those peaking in summer (2003-2005) as can be noted by the larger spread of the respective distribution (Figure 3.14 (a) and (b)). Consequently,
3.5. Results and Discussion
(a) (b) (c) (d)
Figure 3.14: Top: Bivariate density functions between drought area and total drought magnitude of four major events. Panels (a) and (b) depict the most intense drought events with 6 months duration after its onset in winter and summer, respectively. Panels (c) and (d) correspond to the most intense drought events having a drought duration of at least 30 months, in winter and summer, respectively. Bottom: Predictive uncertainty and evolution of the area under drought for the selected events.
the probability density values for the summer event are lower than those of the winter event. However, at longer durations no conclusive comparison could be drawn from this analysis because longer events experience various seasons over many years. The time evolution of the area under droughtA(t) for each events, as depicted in bottom panels of Figure 3.14, also supports the assertion that a single model realization would lead, very likely to a high rate of false alarms for drought monitoring.
3.5.8 Uncertainty of the Severity-Area-Duration Curves
SAD curves obtained with the ensemble SMI mean (SMI) for the eight largest drought events in Germany at duration 3, 6, 9, and 12 months are depicted in panel (a-d) of Figure 3.15. From this analysis, the event from 1975-1978 appears to be the most severe and extensive event at durations ranging from 3 to 9 months. Based on this measure, the 2003-2005 event, however, hardly appears as a benchmark event at longer durations and area coverage. The event from 1953-1954 is quite severe at 3 and 6 months, but not at longer durations. The apparent contradiction of these results, can be clarified with the individual evolution graphs presented in Figure 3.13.
SAD curves have often been used to rank drought events (Andreadis et al., 2005;
(a) (c) (e)
(b) (d)
Figure 3.15: Panels (a) to (d): Ensemble averaged Severity-Area-Duration (SAD) curves of eight major drought events for 3, 6, 9, and 12 months du-ration since 1950 over Germany. Panel (e) depicts the predictive uncertainty of the SAD curves obtained for the event 2003-2005. In this panel, lines in red denote the ensemble mean.
Sheffield et al., 2009). Due to parametric uncertainty, however, they exhibit large variability as shown in panel (e) of Figure 3.15. This, again, corroborate our hypothesis that a single model run would lead to unsatisfactory conclusions and event ranking. These results indicate that the SAD variability increases as the area under drought and duration increase. The variability of the SAD curve with a 12-month duration is almost twice as much as that for 3 months. The variability of SAD curves for summer events is higher than that estimated for winter at any duration.