


\section{Introduction}

As part of the efforts to reduce the vulnerability to flooding, it is of paramount importance to have available flooding charts that spell out the risk of flooding for a given location. This risk is typically expressed as the flooding levels associated with various return periods, e.g. the 100 year flooding level. In Norway the concerns about flooding events are primarily connected with two types of flooding: On the one hand, in rivers and lakes, which are mainly related to melting snow; and on the other, along the coast, which are mainly due to a combination of offshore storm surges and tides. In this chapter the attention is limited to coastal areas. Specifically, the extreme value statistics of sea levels measured at three stations along the Norwegian coastline will be investigated: Oslo, Heimsj{\o} and Honningsvåg, see Figure~\ref{datamap}. This provides an excellent opportunity to compare the performance of the following four methods for extreme value estimation: The Annual Maxima (AM) method (Chapter~\ref{chap:aevt}), the Peaks-Over-Threshold (POT) method (Chapter~\ref{chap:pot}), the ACER method (Chapter~\ref{chap:acer}), and also the Revised Joint Probabilities (RJP) method \citep{tava89,tawn92} (see also \cite{batstone09} for modifications of the RJP method). Since the RJP method has not been discussed previously in this book, it will be explained in some detail here. This chapter largely follows the work presented by \cite{sknabr13jcr}.

 
\begin{figure}[!htb]
\centering
\includegraphics[scale=0.75]{EWL/Figures/datasets_map.pdf}%
\caption{Map with locations of the sea level measuring stations considered in this paper.}%
\label{datamap}%
\end{figure}



\section{Data Sets}

The data sets used in this chapter are water level measurements and tidal predictions for three locations on the Norwegian coast. Water level measurements are collected by automated equipment, while the tidal predictions are based on standard numerical models.

There is one data set from the south of Norway, Oslo. Tidal variations are not as large an influence on the water level here as it is further north. The location is referred to as \textit{surge-dominant}\index{water level!surge-dominant}. The total height of sea levels are also lower here than further north. There is one data set from the middle of Norway, Heimsj{\o}, and one from the far north, Honningsvåg. The sea levels are much more influenced by tides here; the locations are \textit{tide-dominant}\index{water level!tide-dominant}. The data sets are not in the public domain, but were provided by the Norwegian Hydrographic Service, a division of the Norwegian Mapping Authority.

The sea level measurements are done either hourly or every 10 minutes. For the 10 minute data, hourly measurements have been extracted for use with the POT, RJP and ACER methods. There are several reasons for this: Firstly, the RJP method uses tidal predictions which were provided as hourly sea levels. Secondly, many locations have hourly data for older periods and ten minute measurements for the recent years. In order to use both data sets, values every hour are extracted from the more frequent observations. Thirdly, the literature used in the theoretical studies have hourly measurements. Methodological comparisons are therefore made simpler. 

If not otherwise noted, all references to the height of the sea level are in centimeters relative to a mean sea level. All return periods are, if not otherwise noted, given in years. 


\subsection*{ Oslo}\index{water level measurements!Oslo}

For the measurement station in Oslo, there are available hourly measured sea levels from December 10, 1914, to December 31, 1991, and 10 minute interval data from October 1, 1991, to September 16, 2010, which was the cut-off date for our analyses. These data are uncorrected for post-glacial rebound, which is an important factor in the Oslo area. To correct for this, 4 mm/year have been added to data points for years after 1988 and the same amount has been subtracted per year before 1988, according to the formula $currentValue +0.4\cdot(currentYear-1988)$. This was found in a previous report \citep{Hansen2000}, and is based on the fact that 1988 was the base year to calculate mean sea level (MSL) in Oslo.

For the same periods, tidal sea level predictions are available. These are based on a numerical model, the details of which are not publicly available. 




\subsection*{ Heimsj{\o}}\index{water level measurements!Heimsjø}

Heimsj{\o} is located on the coast of S{\o}r-Tr{\o}ndelag, and the measurement station is found at latitude $63^{\circ} 26'$ N and longitude $09^{\circ} 07'$ E. Data are available as hourly measurements from November 1, 1928, to December 31, 1990, and as 10-minute interval measurements from November 1, 1990, to September 16, 2010. Tide predictions are also available for the same periods. 



\subsection*{ Honningsvåg}\index{water level measurements!Honningsvåg}

Honningsvåg is found at the very north of Norway, in Finnmark. The location of the measurement station is latitude $70^{\circ} 59'$ N and longitude $25^{\circ} 59'$ E. Measured values exist in hourly form from from June 5, 1970, to December 31, 1988, and as 10 minute data from June 1, 1988, to September 16, 2010. Corresponding tidal predictions are also available.


\input{EWL/am}


\input{EWL/pot}


\input{EWL/rjp}


\input{EWL/acer}


\input{EWL/discussion}




