Review and Assessment of gap-filling methods from tide-gauges: Maxima missing at the Esbjerg, Denmark station, before 1910.

Information on extremes of the sea-level is obtained from tide-gauge
records.  Such records may have gaps.

Estimates of potential changes in the size and/or frequency of sea-level
extremes are hampered by long gaps, or when just the high extremes are
missing due, e.g. to equipment failure.

Methods used for filling such gaps can be based on having multiple
records from gauges near each other; but what to do if there is
only one record? This problem can typically occur when old tide-gauge
records are used -- the use of multiple recorders at the same place is
more wide-spread today. However, especially older and therefore longer
records hold the key to obtaining long-baseline insights into the temporal
evolution of extreme tides and thus impacts of e.g. climate change.

In this work, we review and assess methods for gap filling. We asses using
the 'known truth' method, i.e. by applying realistic gaps to complete
gauge records and reconstructing and then comparing errors calculated as
the diffrence between modelled and actual values.  We compare a simple
harmonic model fit method to various spline methods as well as Neural
network and deep learning approches.  We also test a hybrid method
which uses not just tide-gauge data but also air pressure readings
from a meteorological station near the tide-gauge.

We then attempt to fill in the missing maxima of the Esbjerg, Denmark
hourly tide-gauge record since 1889. Particularly, before 1910 the maxima
above 300 cm are missing (Bijl, et al., 1999), and we try to fill these in.