15 May 2014 
DANGENDORF ET AL. 
3587 
3) Pressure readings from homogenized station records 
[European and North Atlantic Daily to Multidecadal 
Climate Variability Project (EMULATE); Ansell 
et al. 2006]: These data will be used to compare the 
storm surge record with homogeneous SLP observa 
tions covering the past approximately 160 yr on a 
large scale (see section 3 for more details). 
The third objective of our study is to compare the 
long-term behavior of surges with that of reanalysis wind 
fields. In a shallow shelf sea such as the North Sea, the 
variability is clearly dominated by the wind stress: that 
is, the downward transfer of the momentum from the air 
into the water. Surges in the southeastern North Sea are 
caused by atmospheric disturbances over the ocean and 
can be accurately predicted in the region by the use of 
simplified statistical-empirical wind surge formulas 
(Muller-Navarra and Giese 1999). The model used here 
describes surges S(t) by a number of functions gj with 
coefficients cij and residuals e(f), 
S{t)= ¿«,g,(0 + e(0. (1) 
;=o 
whereas here six functions of g ; - based on quadratic and 
cubic wind stress and SLP fluctuations are linearly fitted 
with the least squares method to the surges. The func 
tions are given by 
So = 1 ’ 
(2) 
gi = f 2 cos(/3). 
(3) 
g 2 =f sin(/3). 
(4) 
g 3 = / 3 cos(/3). 
(5) 
g 4 =f sin(/3), and 
(6) 
g 5 = p — 1015 hPa, 
(7) 
where g 0 is a constant term, gi and g 2 are the quadratic 
wind stress, g 3 and g 4 are the cubic wind stress, and g 5 is 
the static response of the water column to SLP changes. 
The variables / and /3 represent the wind speed and di 
rection, respectively. 
We use the empirical relationship to analyze (i) 
whether the increasing trends in the 20CRv2 data, 
detected by Donat et al. (2011b), are reflected in the 
statistical connection between winds, SLP, and surges 
and (ii) whether the predicted surges differ (on decadal 
and longer time scales) from the observations. To do so, 
we apply the wind surge formulas to daily wind and SLP 
Fig. 3. (a) Correlation plot for observed and modeled surges at 
the tide gauge of Cuxhaven over the period from 1950 to 2010. The 
black crosses represent the result by using the ensemble mean as 
input data, while the gray dots give the minimum and maximum 
range as a result of evaluating each ensemble member itself, (b) 
Coefficient of determination (i.e., squared correlation coefficient) 
and RMSE for each ensemble member and the ensemble mean 
(gray shaded). 
data from the 20CRv2 и and v winds and mean SLP 
(MSLP) from the nearest grid point at 54°N, 8°E. Since 
surges measured in Cuxhaven are the cumulative re 
sponse to changes in the wind field over the North Sea, 
we have also tested whether using additional grid point 
time series in the regression model (by using a stepwise 
regression) may improve the results. No grid point time 
series was able to increase the model performance sig 
nificantly. Hence, we decided to use only one grid point 
for the analysis. Regression coefficients are estimated 
for the period from 1950 to 2010, a period for which the 
20CRv2 was proven to be of good quality (Compo et al. 
2011; Krueger et al. 2013b). 
Figure 2 shows the results of the cross validation be 
tween observed and predicted surges. The model is able 
to reproduce the observations during the validation 
period from 1950 to 2010, as demonstrated by a high 
correlation of 0.91 and a small root-mean-square error 
(RMSE) of 13.9 cm for the ensemble mean (Fig. 3a). The 
RMSE is close to those of hydrodynamic models applied 
in the region (e.g., Weisse and Pliip 2006), which also 
300 
250 
200 
150 
и 
о 
<ч -100 
-150 
-200 
10 20 30 40 50 EM 
Ensemble Member 
- 250 - 200 - 150-100 =50 0 50 100 150 200 250 300 
Observed Surges [cm] 
_ .828 
I 
>, .826 
u 
.§ .824 
ш 822 - Coefficient of Determination 
- RMSE 
h 14.06 
h 14.02 I 
13.98 I 
13.94 “