Combined distribution of ice thickness and speed based on local measurements at the Norströmsgrund lighthouse 2000-2003

Abstract

Fatigue caused by ice-induced vibrations (IIV) is an important design consideration for offshore structures exposed to drifting sea ice. The occurrence of IIV is promoted by, but not limited to, certain combinations of ice thickness and ice drift speed, which makes them fundamental input parameters for structure fatigue life estimation. To that end, this work identifies and analyses the frequency of combined ice thicknesses and ice drift speeds during all recorded ice-structure interaction events at the Norströmsgrund lighthouse during 2000-2003. The ice drift speed measurements were performed manually at the lighthouse, leading to bias towards multiples of 0.05 m/s. The ice thickness measurements by EM antenna underestimates ridge keel depth. The current approach gave a total of above 25 days of ice condition measurements. The cumulative distributions for ice thickness and speed were estimated. Given drifting ice conditions, the probability of encountering ice thicker than 0.8 m was 0.34, i.e. the probability of encountering thicker ice than most of the level ice in the area. A relatively frequent combination of ice conditions was ice thickness between 0.1 and 0.6 m and ice drift speed between 0.05 and 0.15 m/s, occurring with a probability of 0.29.

Full text

Combined distribution of ice thickness and speed based on local
measurements at the Norströmsgrund lighthouse 2000-2003
Vegard Hornnes1, Knut Vilhelm Høyland1, Joshua Dennis Turner1, Ersegun Deniz
Gedikli1,2, Morten Bjerkås3
1 Department of Civil and Environmental Engineering, Norwegian University of Science and
Technology,
Høgskoleringen 7A, 7491 Trondheim, Norway
vegard.hornnes@ntnu.no
2 Department of Ocean and Resources Engineering, University of Hawaii at Manoa,
Honolulu, USA
3 DIMB Consult AS,
Ellefsens vei 3, 7020 Trondheim, Norway
Fatigue caused by ice-induced vibrations (IIV) is an important design consideration for
offshore structures exposed to drifting sea ice. The occurrence of IIV is promoted by, but not
limited to, certain combinations of ice thickness and ice drift speed, which makes them
fundamental input parameters for structure fatigue life estimation. To that end, this work
identifies and analyses the frequency of combined ice thicknesses and ice drift speeds during
all recorded ice-structure interaction events at the Norströmsgrund lighthouse during 2000 –
2003. The ice drift speed measurements were performed manually at the lighthouse, leading to
bias towards multiples of 0.05 m/s. The ice thickness measurements by EM antenna
underestimates ridge keel depth. The current approach gave a total of above 25 days of ice
condition measurements. The cumulative distributions for ice thickness and speed were
estimated. Given drifting ice conditions, the probability of encountering ice thicker than 0.8 m
was 0.34, i.e. the probability of encountering thicker ice than most of the level ice in the area.
A relatively frequent combination of ice conditions was ice thickness between 0.1 and 0.6 m
and ice drift speed between 0.05 and 0.15 m/s, occurring with a probability of 0.29.
25th IAHR International Symposium on Ice
Trondheim, 23 - 25 November 2020

1. Introduction
Drifting sea ice can cause severe IIVs of offshore structures. One example is the Kemi-I
lighthouse situated in the Bay of Bothnia, which eventually collapsed after a period of heavy
vibrations caused by ice actions during the winter of 1973/74 (Määttänen, 1975). To ensure
safe and reliable structures, the potential IIVs caused by ice conditions in an area must therefore
be considered during design (ISO, 2019). IIVs can be divided into three regimes: intermittent
crushing, frequency lock-in and continuous brittle crushing (ISO, 2019). The occurrence of
each type of IIV will depend on the local ice conditions as well as parameters such as the
structural flexibility (Hendrikse and Nord, 2019). Notably, frequency lock-in can lead to
significant vibrations close to the natural frequencies of the structure and is therefore a concern
when it comes to structural fatigue (Hendrikse and Koot, 2019).
For offshore wind turbines, fatigue load caused by wind and waves is a major design concern
(Igwemezie et al., 2019), making it important to consider the addition of possible fatigue loads
from ice. Different models have been developed to understand the impact of IIVs on structural
fatigue, such as by Hendrikse and Nord (2019). The application of the model for an offshore
wind project is described by Hendrikse and Koot (2019). In short, the model attempts to find
the combinations of ice drift speed and ice thickness that lead to frequency lock-in for a
structure. Then, the probability of occurrence of the relevant ice conditions can be used to
determine the vibration cycles and the contribution to fatigue. A parallel can be drawn to
structural reliability analyses based on wave conditions, which rely on simultaneous
distributions of significant wave height and wave period (Vanem, 2016). Consequently,
accurate statistics of local ice conditions in an area are necessary in order to determine the
fatigue contribution from ice interactions.
A relevant source of statistics on local ice conditions were recorded through the ‘Low Level
Ice Forces’ (LOLEIF) and the ‘Measurements on Structures in Ice’ (STRICE) projects. During
the years 2000 – 2003, extensive full-scale measurements of ice thickness and ice drift speed
were carried out at the Norströmsgrund lighthouse (Haas and Jochmann, 2003).
Norströmsgrund is located in the Bay of Bothnia in the Northern Baltic sea (N65°6.6′
E22°19.3′), in a transition zone between land-fast and drift ice (Bjerkås, 2006, Ervik et al.,
2019). The ice condition measurements at Norströmsgrund are advantageous in that they
provide a temporal distribution of the conditions experienced by the structure, and that possible
influences from the structure on the ice speed are included. The probability of occurrence of
ice conditions at Norströmsgrund can thus be used as input for fatigue modelling. In addition,
the statistics can provide a starting point for connecting local ice conditions and met-ocean
data, in order to predict local ice conditions in other areas (Bjerkås and Gedikli, 2019, Turner
et al., 2020).
2. Data and data analysis
The following outlines how the local measurements of ice thickness and speed were carried
out during the LOLEIF/STRICE projects.
2.1. Ice drift speed
The ice drift velocity was estimated manually by the personnel stationed on the lighthouse
during ice-structure interactions (Fransson, 2008). A video screen showing the ice was marked
corresponding to a 10x10 m2 grid, and the ice speed and direction was estimated by tracking
distinct ice features through the grid. The manual measurement method resulted in a discrete
distribution of speed values with at most two significant digits per value. The measurements
were performed infrequently and irregularly, with gaps in time between measurements ranging

from minutes to hours. No clear pattern in the timing of the measurements was observed. A
measurement was often made when the load recording started and after significant shifts in
speed, but this was not always the case, see Samardžija (2018) and Ervik et al. (2019).
2.2. Ice thickness
The ice thickness measurements at the Norströmsgrund lighthouse were carried out with
several different combination of instruments during the four-year period (Haas and Jochmann,
2003). An upward-looking sonar (ULS) as well as a Geonics EM31 electromagnetic ice
thickness sensor (EM) was employed in 2000 to measure the subsurface profile of the ice, while
a laser distance meter measured the elevation above the surface. The laser distance meter was
replaced by a sonic distance meter in 2003. The ULS was placed 6 – 7 m below mean water
level, about 5 m southeast of the lighthouse. The EM sensor and laser distance meter were
mounted on a rig extending 10 m away from the lighthouse, approximately 2 m above the mean
water level. The ice thickness measurement frequency varied between 0.1 – 1 Hz. Note that the
ice thickness was not always recorded due to instrument issues.
The EM measurements averaged the ice thickness over a certain footprint of some metres in
diameter (Haas and Jochmann, 2003). For ridges, the EM most probably measured the
thickness of the consolidated layer and some part of the rubble depending on their
conductivities, which is affected by their salinities and the macroporosity (Ervik et al., 2019).
As a result, the EM measurements underestimated the ridge keel depth. In contrast, the ULS
always measured the deepest point on the ice keel, making it more accurate for ridge thickness.
Haas and Jochmann (2003) found that EM measurements underestimated the keel depth by as
much as 50%, but that EM and ULS measurements agreed well for level ice. Bjerkås (2006)
multiplied the EM keel depths with 3.16 in order to reach similar values as measured by ULS.
In what follows, no correction will be made for possible underestimation of keel depth by EM.
In order to maintain a consistent measurement method between 2000 – 2003, this work focuses
on the ice thickness measured through EM only.
2.3. Data structure
Measurements of loads, ice thickness, speed and other parameters were recorded and saved in
a total of 519 time series known as events, with durations ranging from 10 minutes to 24 hours.
Importantly, the measurements of ice speed were only recorded simultaneously with load
measurements, primarily during ice-structure interactions. The loads were recorded when
observers noticed interesting ice interactions with the lighthouse (Bjerkås et al., 2003). That is,
the ice-structure interactions governed the collection of ice condition data. As such, the
selection of recorded ice conditions during events will be inherently skewed towards conditions
which produce ice-structure interactions.
2.4. Data analysis
A MATLAB routine was used to search through and extract recorded measurements from the
519 events. Errors in the dataset were removed. Subsequently, the collected data were
processed as outlined in the following.
2.4.1. Stepwise interpolation
Because of variations in the measurement frequency of ice thickness and speed and the poor
temporal resolution of the speed measurements, the parameters were interpolated as illustrated
in Figure 1 within each event. The interpolation was not carried out outside the duration of the
events. Stepwise interpolation schemes were preferred over alternatives like linear
interpolation in order to avoid generating thickness and speed values that did not necessarily

occur. The values were interpolated every second, effectively standardizing the measurement
frequency to 1 Hz. Additionally, a comparison between the previous neighbour interpolation
and nearest neighbour interpolation was carried out in order to investigate the resulting speed
frequency distributions.
Figure 1. Example of a speed time series, showing measured speeds (crosses) along with
stepwise interpolation methods (lines) between measurements.
2.4.2. Parameter constraints
To focus the analysis on conditions which may contribute to structural fatigue, only drifting
ice with a certain ice thickness is considered. Static ice with a drift speed of 0 m/s is removed,
as well as ice thinner than 0.1 m. The purpose of setting an ice thickness criterion is to eliminate
false positives from open water, which restricts the analysis to conditions where sea ice has
been confirmed to occur. Only common measurements that fulfil both parameter constraints
simultaneously are considered for the analysis.
3. Results
Figure 2 shows the frequency of all local ice thickness and ice speed values that were recorded
during the interaction events of the LOLEIF/STRICE campaigns, without interpolation and
parameter constraints. A mean thickness of 0.86 m was measured during events, with a
standard deviation of 0.77 m and where the most frequently measured thicknesses were in the
interval 0.05 – 0.10 m. The frequency distribution shows a decreasing trend for thicknesses
above 0.4 m, with the exception of local peaks at 0.7 m, 1.4 m and 1.9 m. The measurements
contained fluctuations on the order of ± 0.05 m for level ice, giving a baseline uncertainty.
The measured speed shown in Figure 2 has a mean of 0.12 ± 0.09 m/s, with a mode of 0.1 m/s.
The values contain at most two significant digits, and only 48 unique speed values were
recorded in total. The frequency distribution contains prominent peaks for multiples of 0.1 m/s,
with less prominent peaks at values such as 0.15 and 0.25 m/s. These peaks point to a
significant underlying bias in the speed measurements towards multiples of 0.05 m/s. Although
they follow the underlying trend of decreasing frequency with increasing speed, the
prominence of the peaks are large outliers from the apparent underlying distribution.

Figure 2. The frequency of measured ice thickness values (left, bin width 0.05 m) and non-
zero ice speed values (right, bin width 0.01 m/s) recorded during the events of the
LOLEIF/STRICE campaigns.
The previous neighbour and nearest neighbour interpolation methods result in similar speed
frequency distributions. The relative difference between the two interpolation methods is below
± 0.1 for the most frequently occurring intervals. Because of the overall small difference in the
resulting distribution for speed, the previous neighbour interpolation was utilized for the
combined distribution for consistency.
Implementing previous neighbour interpolation and the parameter constraints results in the
frequency distributions of ice thickness and speed shown in Figure 3. The mean thickness is
0.76 ± 0.70 m with a mode in the interval 0.10 – 0.15 m. Compared to the frequency distribution
of the measured results (cf. Figure 2), the ice thickness has notably less prominent peaks at
higher thicknesses, and the distribution is more evenly decreasing.
Figure 3. The frequency of interpolated ice thickness values (left, bin width 0.05 m) and ice
speed values (right, bin width 0.01 m/s) that simultaneously fulfil the parameter constraints.
The mean speed after interpolation is 0.10 ± 0.08 m/s, and the mode is in the interval 0.10 –
0.11 m/s. The bias in the speed data is still present, although occurrences of 0.15 m/s and 0.25
m/s are relatively less frequent.
After interpolation, the frequency distribution of thickness and speed can be considered an
estimate of the occurrence of each parameter in seconds, as the measurement frequency is
standardized to 1 Hz. The result is thickness and speed data within the parameter constraints
for a total of about 25 days and 5 hours between 2000 – 2003. In comparison, the total event

duration is about 94 days and 16 hours across the four years. Most of the removed data was
static ice, making up a total duration of above 52 days. Interpolation results in about 79 days
of ice thickness measurements during events, where the ice was thicker than 0.1 m for roughly
67 days and 18 hours.
Figure 4 shows the interpolated thickness distribution per year, while Table 1 summarizes the
mean, standard deviation and mode per year. 2003 is an outlier, with a large mean thickness
and a frequency distribution skewed towards thicker ice compared to other years. This is,
however, not reflected in the modes, as 2003 also contains a significant number of
measurements between 0.10 – 0.15 m. These measurements were primarily recorded during
the final weeks of the measurement campaign in April. If the final full week of measurements
is not included, the mean thickness for 2003 is 1.23 ± 0.85 m with a mode between 0.45 – 0.50
m.
Figure 4. Interpolated ice thickness distributions per year for drifting ice, with bin widths 0.1
m. The bin heights are normalized by probability, summing to 1.
Table 1. Ice thickness means, standard deviations, and modes in total and per year for measured
and interpolated ice thickness distributions with parameter constraints. The modes are the most
frequent interval with interval widths of 0.05 m.
Year
Measured ice thickness
Interpolated ice thickness
Mean ± st. dev. [m]
Mode [m]
Mean ± st. dev. [m]
Mode [m]
Total
0.86 ± 0.77
0.05-0.10
0.76 ± 0.70
0.10-0.15
2000
0.69 ± 0.57
0.25-0.30
0.84 ± 0.62
0.25-0.30
2001
0.57 ± 0.51
0.20-0.25
0.46 ± 0.45
0.15-0.20
2002
0.67 ± 0.62
0.30-0.35
0.70 ± 0.59
0.30-0.35
2003
1.03 ± 0.85
0.05-0.10
1.06 ± 0.87
0.10-0.15

3.1. Combined distribution
The combined distribution of drifting ice thickness and speed is illustrated in Figure 5. The
biased speed distribution affects the combined distribution, resulting in separate thickness
distributions for certain speed values. The most frequently occurring combination is between
0.15 – 0.20 m and 0.03 – 0.04 m/s. The joint cumulative histogram of the ice thickness and
speed is shown in Figure 5c, and can be used to estimate the probability of certain ice
conditions. The most frequent combinations occurred for ice thicknesses in the interval 0.1 –
0.6 m and speeds in the interval 0.05 – 0.15 m/s with a total probability of 0.29. The thickness
distribution had a long tail, resulting in a 0.34 probability of encountering ice thicker than 0.8
m. Multiplying the probabilities from the cumulative histogram with the total duration of 25
days and 5 hours gives approximate time durations that the conditions in question were
encountered at the lighthouse. For example, drifting ice thicker than 0.8 m was encountered an
estimated total duration of 8 days and 20 hours between 2000 – 2003.
(a)
(b) (c)
Figure 5. Figures showing the combined distribution of ice thickness and ice drift speed. (a)
shows a bivariate frequency distribution of the two parameters with bin widths of 0.05 m x
0.01 m/s. (b) shows a heatmap of the frequency distribution in (a), where the colour of each
field shows the probability of each combination of parameters, normalized over the visible
bins. The heatmap has bin widths of 0.2 m x 0.02 m/s. (c) shows the same distribution as a joint
cumulative histogram, with bin widths of 0.1 m x 0.02 m/s.

4. Discussion
After interpolation, the frequency distributions of ice thickness and speed can be interpreted as
temporal distributions of ice conditions at the lighthouse, because the parameters are
interpolated to every second. The frequency of a given combination of ice thickness and speed
will equal an estimate of its total duration. The duration can then be divided by the total
measurement time over four years to find the probability of occurrence of the conditions in
question. Note that the durations will be a lower bound estimate, as the measurements and
interpolation are limited only to the recorded events, with a total duration of 94 days and 16
hours over the four years. Despite this, much of the drifting ice encountered during the
campaign periods are likely recorded in events. Drifting ice often caused ice-structure
interactions, and recording these interactions was the focus of the campaign.
The significant bias in the speed data towards multiples of 0.05 m/s is likely caused by rounding
to one or two significant figures, as the speed was manually estimated. Some information is
lost when the values are rounded, which makes it difficult to recover the underlying
distribution. The bias makes the combined distribution less accurate for small speed intervals,
effectively reducing the resolution from which useful data can be extracted.
Some relevant ice thickness measurements by EM of drifting ice in the Bay of Bothnia are
summarized by Ronkainen et al. (2018) and can be used for comparison to the measurements
at Norströmsgrund. In 2003, several ice thickness measurement campaigns were carried out by
using a helicopter-borne EM instrument (HEM), described by Haas (2004). The analysis of the
dataset done by Ronkainen et al. (2018) focused on drifting ice, where they found a mean ice
thickness of 1.39 m and a mode of 0.5 – 0.6 m on the 21st of February, east in the Bay of
Bothnia. They also found that 63.1% of the drift ice was deformed. Haas et al. (2009) found a
generally good agreement between HEM measurements and ground-based measurements
using a Geonics EM31 instrument, which was also used at Norströmsgrund.
Except for the large mode at 0.1 – 0.2 m, the ice thickness distribution at Norströmsgrund
follows a similar trend as the HEM measurements in 2003, with a local peak at 0.5 – 0.6 m and
a gradual decline with a very long tail in the distribution. Importantly, the seasonal
development of ice thickness will impact the Norströmsgrund statistics, as these were recorded
over more than two months, while the HEM data is from a single day. Excluding the thin ice
during the last week of measurements in April, the mean thickness at Norströmsgrund (1.23
m) is close to the mean thickness through HEM (1.39 m). Additionally, Ronkainen et al. (2018)
writes that there was less ice in the west side of the Bay and a greater presence of coastal leads,
which will reduce the mean ice thickness at Norströmsgrund compared to the helicopter
measurements. Note that the frequency distribution of ice thickness at Norströmsgrund will
depend on the ice speed, while the ice can be assumed static relative to the helicopter during
HEM measurements.
Drift ice thicker than 0.8 m was encountered 35% of the time during events at Norströmsgrund,
much of which was deformed ice. According to Määttänen and Kärnä (2011), the level ice
thickness was less than 0.6 m in the area during the measurement years. Li et al. (2016) found
a mean annual maximum ice thickness of 0.61 m between 2000 – 2003 based on Freezing
Degree Days calculations, with 2003 being the most severe year with 0.71 m. The severity of
the winter in 2003 is reflected in the long tail of the thickness distribution that year (see Figure
4d). Ronkainen et al. (2018) points out that 2003 was very windy, which likely contributed to
the large amount of ridging.

Note that the temporal distribution of ice thickness at Norströmsgrund may be affected by the
structure itself, but the magnitude of this effect is unknown. For example, when the driving
forces on an ice floe are insufficient for limit stress failure to occur, the floe may get stuck on
the lighthouse. The thickness of the stuck floe will continue to be measured for some time,
increasing its relative frequency in the data.
5. Conclusions
The recorded ice thicknesses and ice drift speeds at Norströmsgrund during the
LOLEIF/STRICE campaigns in the years 2000 – 2003 were extracted and analysed. By
interpolating per second, the varying measurement frequencies were corrected, and a joint
temporal frequency distribution of drift ice at the lighthouse was estimated. The joint
distribution can provide input to fatigue modelling and as a basis for transferring local ice
conditions to other areas. However, ridge keel depth was underestimated by EM measurements.
In addition, the accuracy of the combined distribution was affected by significant underlying
bias in the ice speed data. Establishing a more accurate local speed distribution is a target for
further research.
The drift ice thickness distribution in 2003 followed a similar trend to helicopter EM
measurements that year, with the addition of a large mode for thin ice measured late in the
season. A significant fraction of the drift ice encountered was thicker than level ice, which is
important to consider for distributions of local ice thickness. The influence of the structure on
the local ice drift and resulting thickness distribution was not quantified but is highly relevant
for fatigue simulations based on local ice conditions and should be investigated further.
Acknowledgments
The authors wish to extend their gratitude to Ilija Samardžija, Torodd S. Nord, Hayo Hendrikse,
and other partners on the FATICE project who provided helpful feedback on the methods and
findings in this work.
The authors also wish to acknowledge the support to the FATICE project from the
MarTERA partners, the Research Council of Norway (RCN), German Federal Ministry of
Economic Affairs and Energy (BMWi), the European Union through European Union’s
Horizon 2020 research and innovation programme under grant agreement No 728053-
MarTERA and the support of the FATICE partners.
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