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Fig. 5.5 Relation between significant wave height, H s in m and 100 m wind speed in m/s in the
German Bight from three years of hourly data (2004-2006) at FINO1. The two curves indicate
the temporal development of H s for storm ''Britta'' on November 1, 2006 (full curve) and for
storm ''Erwin'' on January 8, 2005 (dotted curve). Arrows indicate the direction of this
development
5.1.2 Fetch and Stability Dependent Wave Formation
The preceding subchapter has shown that the development of waves is decisive for
the sea surface roughness. The calculation of oceanic wave heights from local
wind speeds has a long and well-established history in oceanic and atmospheric
sciences (see, e.g., Sverdrup and Munk 1947 ; Neumann 1953 ). Although the local
wind speed and the local structure of the MABL are supposed to have an important
influence, there are other factors determining the wave height. Wave heights
additionally depend on the length of the fetch and on the duration of high wind
speeds over these fetches. Further on, the wave height also depends on non-
atmospheric conditions like the, e.g., simulations with the wave ocean model
(WAM; Hersbach and Janssen 1999 ) have shown for infinite duration and deep
water that for a wind speed of 30 m/s, the significant wave height increases from
about 10 m for 50 km fetch to nearly 12 m for 100 km fetch and more than 15 m
for 400 km fetch.
A closer analysis of development of wind-driven wave heights in the German
Bight can be found in Emeis and Türk ( 2009 ). In this study wind speed, friction
velocity and significant wave height data from the FINO1 platform in the southern
German Bight 45 km off the coast for the years 2004-2006 have been evaluated
and related to each other. The wave height is usually expressed in terms of a
significant wave height, H s . H s is often defined as the average height (trough to
crest) of that third of waves out of all waves which have the largest wave heights.
The maximum wave height is 1.6-1.7 times the significant wave height (Kumar
et al. 1999 ). Toba ( 1978 ) has given a relation between the friction velocity, u * , and
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