3586 
JOURNAL OF CLIMATE 
Volume 27 
1910 1930 1950 1970 1990 2010 
Time [yr] 
; 
99.9 
99 
98 
95 
90 
80 
70 : 
60 
50 
40 : 
30 
20 
10 
5 
2 
1 
0.1 
Hourly Surge Trend [mm/yr] 
Fig. 2. Comparison of the statistics of daily surges based on 
hourly observations (black) and the skew surge record (colored 
and dotted) over the common period from 1918 to 2008 at the tide 
gauge of Cuxhaven. (a) Annual percentiles and (b) linear trends of 
annual percentiles as a correlation plot. The gray lines mark the 
SEs of each trend. 
linear trends (Fig. 2b). The figure clearly demonstrates 
that the percentiles derived from both data sources show 
virtually the same characteristics in terms of both vari 
ability (Fig. 2a) and linear trends (Fig. 2b). The highs 
and lows in the resulting time series are of similar 
characteristic: that is, they show the same temporal de 
velopment and also match in magnitude. This is further 
confirmed by the correlations in Table 1, which are all 
larger than 0.94 for the four upper percentiles (which are 
hereafter investigated in detail). 
We investigate storminess by computing annual and 
seasonal [October-March for the cold season (winter); 
April-September for the warm season (summer)] 
95th, 98th, 99th, and 99.9th percentiles of daily surges. 
Since no gaps are present in the record, there are no re 
strictions for the analysis of linear trends. We quantify 
long-term changes by applying the ordinary least squares 
Table 1. Pearson correlation coefficients between daily skew 
surges and daily nontidal residuals (i.e„ surges based on hourly 
measurements) over the period 1918-2008. Significant correlations 
(f test) are marked in boldface. 
Daily skew surges 
95th 
98th 
99th 99.9th 
Daily nontidal residuals 
0.96 
0.96 
0.94 0.98 
regression (OLS). The significance of linear trends is as 
sessed using standard errors (SEs) considering serial 
correlation of the time series by reducing the number of 
degrees of freedom as suggested by Santer et al. (2000). It 
may happen in time series of extreme events that the 
trends are largely biased by outliers. In such cases, robust 
regression methods such as the Theil-Sens slope (Gilbert 
1987) are more appropriate. We have compared the re 
sults from a range of methods and could not find any 
differences in the trend estimates. This is mainly attrib 
uted to the fact that the time series considered here are 
long and that there are no obvious outliers in the record. 
Hence, we decided to proceed in the analysis with the 
common OLS method. 
With respect to our second aim (i.e., comparing storm 
surges with the variability of large-scale atmospheric 
circulation patterns), we make use of three additional 
datasets: 
1) The NAO index provided by Jones et al. (1997): The 
NAO index is a proxy describing large-scale atmo 
spheric circulation over the North Atlantic region. It 
is calculated by the differences of pressure anomalies 
taken from stations in southern Iceland and Gibraltar, 
Spain. The updated index was downloaded from 
the webpage of the University of East Anglia, United 
Kingdom (http://www.cru.uea.ac.uk/cru/data/nao/). 
2) 20CRv2 wind and pressure fields (Compo et al. 
2011): 20CRv2 is the newest generation of global 
reanalysis products covering a long period from 1871 
to 2010. By assimilating daily SLP observations into 
a state-of-the-art climate model with monthly mean 
sea surface temperatures and sea ice as boundary 
conditions, 20CRv2 provides an ensemble of 56 
equally likely best estimates of the atmospheric state 
at a given time step with a temporal resolution of 
6 h and on a global grid with a resolution of 2°. For 
the present investigations, we have downloaded daily 
data from the webpage of the National Oceano 
graphic and Atmospheric Administration (NOAA), 
Boulder, Colorado (http://www.esrl.noaa.gov/psd/data/ 
gridded/data.20thC_ReanV2.htm; http://portal.nersc. 
gov/project/20C_Reanalysis/). Both each individual 
ensemble member and the ensemble mean are analyzed.