The quality of water level time series data strongly varies with periods of
high- and low-quality sensor data. In this paper we are presenting the
processing steps which were used to generate high-quality water level data
from water pressure measured at the Time Series Station (TSS) Spiekeroog. The
TSS is positioned in a tidal inlet between the islands of Spiekeroog and
Langeoog in the East Frisian Wadden Sea (southern North Sea). The processing
steps will cover sensor drift, outlier identification, interpolation of data
gaps and quality control. A central step is the removal of outliers. For this
process an absolute threshold of 0.25 m 10 min

Left: Time Series Station Spiekeroog in the tidal inlet between the
East Frisian islands Spiekeroog and Langeoog. Right: schematic of the Time
Series Station Spiekeroog with attached sensors; T: temperature sensor; C:
conductivity sensor; P: pressure sensor, ADCP: acoustic Doppler current
profiler, MST: Multispectral Transmissometer.

The Time Series Station (TSS) Spiekeroog measures different time series data
in the East Frisian Wadden Sea. The station is positioned in the tidal inlet
between the East Frisian islands Spiekeroog and Langeoog
(Fig.

Time series are often analysed for hindcast of events and trends in the past

The pressure sensor of the TSS Spiekeroog is installed in a tube
approximately 1.5 m above the sea floor (Fig.

Pressure sensors used between 2002 and 2012 at the Time Series Station Spiekeroog (FS: full scale).

Data were pre-processed and stored on the TSS. The pre-processing includes the conversion from measured currents to pressure data and binning of the measurement data to 1 min. In regular intervals the data were copied to a land-based computer. From this system the data were exported at an interval of 10 min for the time interval from 2003 to 2012 as monthly files.

The data used in this paper are available at PANGAEA
(

Flag codes

The data processing method is divided into four steps. For these steps
meta-information about the time series, measurement station and nearby
measurements is required. These steps are the following:

Subtraction of a trend

Removal of outliers

Calculation of supporting points and interpolation of missing data

Quality control of processed data

At first the time series of the water level data are divided into different
sections. The divisions depend on the maintenance of the pressure sensor.
Figure

Measured water pressure data (blue) at the Time Series Station Spiekeroog before the validation and times of sensor maintenance (red vertical lines).

If a strong decreasing trend is detected (Fig.

During this step the transition from pressure data to water level data will
also be performed for which the Gibbs Sea Water (GSW) Oceanographic Toolbox
(V3.01, 11 May 2011) for MATLAB (R2014b, The MathWorks) was used. The toolbox
is based on the International Thermodynamic Equation of SeaWater – 2010
(TEOS-10,

The next step of the data processing is to remove outliers. Outliers occur
for example during sensor maintenance. To detect probable outliers the speed
of water level change (gradient) between two adjacent data points is
calculated. For this, the distribution of the gradients is presented in the
histogram of Fig.

The histogram is showing the gradient between two adjacent data
points. Vertical lines indicate the 0.25 m 10 min

The removed outliers and gaps of the original time series represent missing
information making it more difficult to interpret the data set especially
since many methods for the analysis of time series require evenly sampled
data

The subfigures show the validation process for the year 2008. Top: the time series before the validation (blue) and sensor maintenance (red vertical lines) are shown. Middle: the time series (blue) and outliers (red) after the first two steps of the validation. Bottom: the time series after the interpolation (blue) and the comparison data of Neuharlingersiel (red) are shown.

Comparison between the two data sets is drawn in two ways. The first is a comparison of the two curves to deduce the similarities in the water level range of the tide and differences at high and low water. This provides a possible offset and scale factor. The second is a cross correlation (MATLAB R2014b, function xcorr) analysis to find out the time lag between the two measurement sites. With this information it is possible to calculate auxiliary supporting points for the interpolation.

Tides can be described as a combination of cosine using a spline interpolation (MATLAB R2014b, function interp1 with spline method) the missing data points can be interpolated with a high certainty of achieving trustworthy data. For gaps longer than a tidal cycle (12.5 h) the prior calculated supporting points are used to avoid greater over and under estimation.

Finally, to ensure the quality of the processed data a Fourier harmonic
analysis and a storm flood analysis were performed. The Fourier harmonic
analysis intends to show that it is possible to find all the main tidal
frequencies and the difference between the original and the processed data.
The storm flood analysis searches for severe short-term rises in the water
level data. The German Hydrographic Institute (BSH, “Bundesamt für
Schifffahrt und Hydrographie”) has published values for different magnitudes
of storm floods at the German North Sea Coast

The different processing steps were applied to the whole time series
presented in Fig.

Examples of the results of the first four processing steps for data from 2008
are shown in Fig.

All three curves show data for 2 weeks in June 2007. The blue line shows the data after the removal of a trend and outliers and the red curve the interpolated data at the TSS Spiekeroog. The green curve shows data from Neuharlingersiel.

Figure

The middle graph in Fig.

The bottom graph of Fig.

Figure

Fast Fourier Transformation (FFT) of the original (red) and
processed (black) water level at Time Series Station Spiekeroog.

In Fig.

Storm flood analysis of the water level data from the Time Series Station Spiekeroog (top) and Neuharlingersiel (bottom). Green marker: weak storm flood; red marker: severe storm flood; black marker: very severe storm flood.

In the first processing step a piecewise linear trend or mean was subtracted.
While it is easier to identify outliers by this way, it makes the data set
more difficult to analyse for long-term sea level changes. The manual of the
utilized pressure sensors states that the sensor degradation is

Water levels of storm floods above the mean high tide in Neuharlingersiel and at the Time Series Station Spiekeroog between 2005 and 2011. Water level between 1.5 and 2.5 m characterise a weak storm flood, between 2.5 and 3.5 m characterise a severe storm flood and values above 3.5 m indicate a very severe storm flood.

A comparison between the time series data from Spiekeroog and
Neuharlingersiel reveals that both are in good agreement. Constant values
below

The Fourier analysis has shown two pronounced differences between the original and processed data. The first is the high peak at the beginning of the curve with a frequency of 0 representing the mean of the original data. The second difference is the strength of the tidal peaks. For the original time series data these peaks are not as distinct as for the processed data. These differences result from the previous processing steps and illustrate their usefulness.

Discrepancies in the storm flood events between the TSS Spiekeroog and Neuharlingersiel originate from the different positions of the measurement sites. During storm floods the wind blew from northern or western directions forcing the water into the harbour of Neuharlingersiel where it can accumulate and lead to increased water levels. The water level is also increasing at the measurement station but here it is not possible for the water to pile up resulting in lower water levels than at Neuharlingersiel.

Processing water level data resulted in a relevant long-term data set. Here it
should be emphasised that:

From 99.96 % of the time series data only a linear trend was subtracted which leads to no difference in the ratio between the values.

During the removal of outliers no values during extreme events were deleted. This was concluded derived from a comparison of storm floods between the Time Series Station Spiekeroog and Neuharlingersiel.

The calculation of supporting points has yielded a mean 20 min time lag between the TSS Spiekeroog and Neuharlingersiel. This is greater than comparable data from the BSH and needs further analysis.

The interpolated data follow the same trend as the measured data at the TSS Spiekeroog.

A spectral analysis has shown that all major tidal frequencies can be found. Also during the storm flood analysis six events were found for the Time Series Station and eight for Neuharlingersiel. The difference comes from the different positions of the measurement stations.

The second is that although the time series is now without gaps the interpolated data can be wrong. A possibility to circumvent part of these prerequisites would be to install another device for the measurement of the water level. This device should then use a different method for measuring sea level changes, e.g., based on radar signals from an above-water installation.

As mentioned before, the TSS Spiekeroog was serviced multiple times per year.
During these times the measurement equipment was cleaned or exchanged for
new or re-calibrated sensors. In Tables

Maintenance times of the water level pressure sensor between December 2002 and January 2009. Dates marked with a “*” were not used during the trend removal.

Maintenance times of the water level pressure sensor between April 2009 and November 2012. Dates marked with a “*” were not used during the trend removal.

Special thanks to Axel Braun and Waldemar Siewert for the maintenance on the station during the whole year and all weather conditions as well as for Helmo Nikolai for servicing the institute boats. The authors are grateful to Rainer Reuter for the concept and construction of the Time Series Station Spiekeroog.

Part of the data was acquired during the project BioGeoChemistry of Tidal Flats (DFG, grant no. FOR 432). Edited by: F. Schmitt