22 
Negative Surges in the Southern Baltic Sea 
3.3. Long-term statistics 
The Gumbel method is well suitable for evaluat 
ing the probability of low sea levels in the Baltic 
Sea. In Gumbel distributions, extreme-value 
events are distributed asymmetrically (Fig. 3.3. a) 
The Gumbel probability curve, which has a posi 
tively skewed shape (skewed to the left), de 
scribes a double exponential distribution. 
The number of years used as a basis in comput 
ing the Gumbel probability for low water events 
is T >5 years. 
The following probability of non-exceedance 
W(x) can be used as design basis for the occur 
rence of a low sea water event with the maximum 
value x: 
W(x) = e‘ y y-a (x-b) x = cy+a 
Hence it follows: 
W(x) = e -‘ a<x ' b> 
Probabilities according to the Gumbel method 
are computed by means of the above conditional 
equations y = a(x-b) and x = ay+b using annual 
extreme water levels. They are updated annually. 
The recurrence intervals T (x) are defined as re 
ciprocal annual probabilities of occurrence: 
T(x) = 1 -W(x) 
X 
Fig. 3.3. a Gumbel distributions 
Table 3.3. Gumbel probability of low sea levels in m below mean sea level (MSL=5 m) computed in 2007/2008 for 
recurrence intervals T (years) 
Gauge/T in years 
5 
10 
20 
50 
100 
Flensburg 
1.58 
1.76 
1.93 
2.15 
2.31 
Schleimünde 
1.43 
1.59 
1.74 
1.94 
2.08 
Eckernförde 
1.41 
1.55 
1.69 
1.88 
2.01 
Kiel 
1.41 
1.57 
1.72 
1.91 
2.06 
Neustadt 
1.37 
1.54 
1.70 
1.90 
2.06 
Travemünde 
1.40 
1.55 
1.70 
1.90 
2.04 
Wismar 
1.38 
1.55 
1.70 
1.90 
2.05 
Warnemünde 
1.21 
1.34 
1.47 
1.64 
1.76 
Stralsund 
1.04 
1.15 
1.26 
1.40 
1.50 
Sassnitz 
0.93 
1.05 
1.17 
1.32 
1.43 
Greifswald 
1.06 
1.18 
1.29 
1.44 
1.54 
Swinoujscie 
0.97 
1.07 
1.17 
1.29 
1.39 
Kotobrzeg 
0.85 
0.96 
1.06 
1.19 
1.28