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doi: 10.1515/popore-2016-0018vol. 37, no. 3, pp. 337–360, 2016
Pol. Polar Res. 37 (3): 337–360, 2016
Surface currents in the Porsanger fjord
in northern Norway
Malgorzata STRAMSKA1,2 *, Andrzej JANKOWSKI1 and Agata CIESZYŃSKA2
1 Institute of Oceanology, Polish Academy of Sciences, Powstańców Warszawy 55,
Sopot 81-712, Poland
2 Department of Earth Sciences, Szczecin University, Mickiewicza 16, Szczecin 70-383, Poland
<mstramska@wp.pl> <jankowsk@iopan.gda.pl> <cieszynska.agata@gmail.com>
* corresponding author
Abstract: We describe surface currents in the Porsanger fjord (Porsangerfjorden) located
in the European Arctic in the vicinity of the Barents Sea. Our analysis is based on surface
current data collected in the summer of 2014 using High Frequency (WERA, Helzel
Messtechnik GmbH) radar system. One of our objectives was to separate out the tidal
from the nontidal components of the currents and to determine the most important tidal
constituents. Tides in the Porsanger fjord are substantial, with tidal range on the order
of about 3 m. Tidal analysis attributes to tides about 99% of variance in sea level time
series recorded in Honningsvaag. The most important tidal component in sea level data
is the M2 component, with amplitude of ~90 cm. The S2 and N2 constituents (ampli-
tude of ~20 cm) also play a significant role in the semidiurnal sea level oscillations.
The most important diurnal component is K1 with amplitude of about 8 cm. The most
important tidal component in analyzed surface currents records is the M2 component.
The second most important component is the S2. Our results indicate that in contrast
to sea level, only about 10–30% of variance in surface currents can be attributed to
tidal currents. This means that about 70–90% of variance is due to wind-induced and
geostrophic currents.
Key words: Arctic, northern Norway, fjords, coastal processes, tides, ocean observing
systems.
Introduction
Fjords are elongated, deep, and narrow bays surrounded by mountains and
sea cliffs. They constitute an interface between the land and the ocean. On one
hand, they are influenced by the physical and chemical properties of the oceanic
boundary currents. A buoyancy-driven estuarine exchange controls the transport
of saltier seawater into the fjords. On the other hand, fjords act as export chan-
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Malgorzata Stramska et al.
338
nels for the fresh water runoff from land into the ocean and this can potentially
affect the shelf hydrography and biogeochemical properties of oceanic waters.
Processes such as geostrophic control, tidal and local wind driven currents can
play a significant role in these interactions.
The Porsanger fjord is located at about 25.0–26.5°E and 70.0–71.0°N
(Fig. 1a). It is approximately 100 km long, 15–10 km wide, has a maximum
depth of more than 230 m, and extends in the southwest direction from the
northern tip of Norway in the coastal region of the Barents Sea (Fig. 1b). It
has been proposed in the past that if the fjord width significantly exceeds
the first baroclinic radius of deformation it should be classified as a broad
fjord (Cushman-Roisin et al. 1994). In broad fjords, the Coriolis effect leads
to upwelling and downwelling responses that are contained within the defor-
mation radius along each side of the fjord that behave like separate coastal
regions. Cushman-Roisin et al. (1994) have evaluated the Porsanger fjord using
this criterion. In their calculations, they have assumed the latitude of 70.5°N
(f = 1.37 x 10-4 s
-l), mean depth of H = 200 m, mean width of L = 18 km,
and that a homogeneous upper layer of density ρ1 = 1022 kg m-3 and depth
Hl = 50 m is located on top of the deep-water layer with average density
ρ2 = 1024 kg m-3 and H2 = 150 m. From these assumptions they have derived
the reduced gravity g’ = g(ρ2 – ρ1)/ρ2 = 0.02 m s-2 and the baroclinic radius of
deformation R = (g’ Hl H2 /H)1/2/f = 6.3 km. Thus, according to Cushman-Roisin
et al. (1994), the width of the Porsanger fjord is approximately three times
the deformation radius, and the fjord can be classified as an intermediate size.
Since the freshwater input from land to fjords is a major factor controlling their
hydrography including water circulation, Svendsen (1995) suggested a classifica-
tion of fjords based on the ratio of water runoff to the surface area of a fjord. This
allows one to classify fjords into three broad categories: (i) fjords with relatively
small freshwater runoff where wind stress is a key forcing mechanism for the water
circulation, (ii) fjords with relatively large runoff, where density currents domi-
nate the hydrography, (iii) fjords with intermediate water runoff. The Porsanger
fjord has been classified as a fjord with relatively low runoff, but in the spring/
summer season freshwater runoff can significantly influence its hydrography.
Based on topography, the Porsanger fjord (Fig. 1b) can be divided into three
different zones: inner (0–30 km), middle (30–70 km), and outer (70–100 km).
The inner zone is separated from the remainder of the fjord by the 60-m deep
sill, situated approximately 30 km from the inland end (head) of the fjord.
The middle part of the fjord starts outside of this sill, and is separated from
the outer zone by an island (Tamsøya) located about 70 km from the head of the
fjord. The outer zone ends with a deep sill (180 m), therefore it is well con-
nected with the coastal water masses of the Barents Sea. This is in contrast to
the inner part of the fjord, which has quite limited exchange with the open sea
and is undergoing strong cooling during most of the year. In this inner zone, the
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Surface currents in the Porsanger fjord 339
environment is very different from the rest of the fjord and holds a unique arctic
ecosystem (Eilertsen and Frantzen 2007). The Porsanger fjord is stratified from
May to October due to seasonal river runoff and surface heating (Svendsen 1995).
In this paper, we describe surface currents in the outer zone of the Porsanger
fjord. Our analysis is based on data collected in the summer of 2014. Our interest
in this fjord comes from the fact that this is a region of high climatic sensitivity.
For example, it has been documented that sea surface temperature (SST) has
increased in this area of the Barents Sea at a rate of 0.04°C to 0.05°C per year
(Jakowczyk and Stramska 2014). According to Good et al. (2007), the globally
averaged SST trend (calculated for 20 years of AVHRR Pathfinder data from
January 1985 to December 2004) is only about 0.018°C to 0.017°C per year,
thus trends in the coastal region of the Barents Sea are stronger than the global
average. In addition, significant changes in the ecosystem of the Porsanger fjord
have been observed in recent years (Sivertsen and Bjørge 2015). One of our
long-term goals is to develop an improved understanding of the ongoing changes
and interactions between the Porsanger fjord and the large-scale atmospheric
and oceanic conditions in the Barents Sea.
In order to derive a better understanding of the ongoing changes, one must
first improve the knowledge of the basic physical processes that shape the
environment of the fjord. The present study is the first step in this direction.
One of our objectives is to evaluate the importance of tidal and non-tidal forc-
ing on surface currents. In particular, we will estimate what contribution to
the total variance of surface currents can be attributed to tidal and non-tidal
variability and we will show which tidal components contribute significantly
to the observed surface currents.
Fig. 1. Location of the Porsanger fjord in the northern Europe (a) and its bathymetry (b). Positions
of the HF radars are indicated by exes.
ab
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Data sets and methods
The basic data set used in this paper includes vector components of surface
currents measured using high frequency (HF) radar system (e.g., Helzel et al.
2010, 2011) operating in the Porsanger fjord from June 10, 2014 (year day 161)
to October 11, 2014 (year day 284). HF radar systems are unique in their ability
to monitor surface patterns of ocean currents, and to provide synoptic current
maps over extended periods of time. These systems are now widely accepted
by the oceanographic community as an efficient tool and are routinely used by
many U.S. and European oceanographic research organizations (see for example
the Southern California Coastal Ocean Observing System at www.sccoos.org).
The performance of HF radars has been extensively tested by comparisons with
moored ADCPs, ship mounted ADCPs, drifters and models (e.g., Carbajal and
Pohlmann 2004; Chapman et al. 1997; Kaplan et al. 2005; Kohut and Glenn
2003; Kokkini et al. 2014; Ohlmann et al. 2007; Shay et al. 2008; Parks et al.
2009; Robinson and Wyatt 2011). For example, comparisons of ADCP and WERA
(Wellen Radars) estimates of surface currents at the observation network in the
German Bight showed that the standard deviation between the two estimates
was less than 0.1 ms-1 and the bias was -0.004 ms-1. Chapman et al. (1997)
pointed out that, since HF radar noise is random, standard errors decrease as
the length of the time series increases.
WERA system applied in this study has been developed at the University of
Hamburg in 1996, and demonstrated robust accuracy and reliability at numer-
ous installation sites (e.g., Helzel et al. 2010, 2011; Kokkini et al. 2014). In
our experiment, WERA system was used in a phased-array mode, advanta-
geous in fjord environment where spatial and temporal variability of surface
currents is relatively high. An in-depth overview of HF radars can be found
for example in Paduan and Graber (1997). We will only summarize here the
most important aspects, for completeness. In our application, the system used
4 transmit and 12 receive antennas, HF frequencies were set to about 26 MHz
and the nominal bandwidth was 250 kHz. The method uses the observations of
Doppler (i.e. frequency) shift between the transmitted and received radiowave
signals to infer the total sea surface velocity. The knowledge about Bragg scat-
tering is applied to remove the influence of sea surface waves and to calculate
the horizontal velocity of the current. Bragg scattering, geometric resonance
phenomenon, leads to a much stronger signal at the receiver from the Bragg-
resonant sea surface waves than from any other constituent of the sea surface
wave field. Recall that, according to the deep-water theory for gravity waves,
wind driven ocean waves with wavelengths comparable to the electromagnetic
wavelengths in the HF band move at a precisely known speed depending only
on the wavelength itself. Removal of that speed from the total speed determined
from the Doppler shift of the backscattered radiowaves results in estimates of the
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Surface currents in the Porsanger fjord 341
ocean current velocity. This implies, that the measurements of surface currents
with HF radars are restricted to the depth of the Bragg-resonant wind-waves.
These waves decay exponentially with depth from the sea surface. Therefore,
radar-derived ocean currents in our experiment represent the surface water layer
approximately 0.5 m deep.
Another critical aspect of surface current mapping with HF radars is the fact
that each instrument (radar) produces a map of ocean current velocity compo-
nents along radial lines emanating from the radar site. At least two radar sites
are needed to derive full velocity vectors of the currents. The installation in the
Porsanger fjord included two transmit (Tx) and receive (Rx) sites positioned at
about 27 km from each other. Radar stations were located in Repvaag (70.76°N,
25.69°E) and Nordvaagen (70.97°N, 26.02°E), as indicated in Fig. 2. The region
monitored by the radars is located in the outer zone of the the Porsanger fjord.
The positions of several pixels that will be referred to in the Results sections
are indicated in Fig. 2 by numbers 1–7 as well as symbols A1, A2, A3 and M.
The two-dimensional surface current velocity vectors have been computed by
combining the radial velocity components obtained from the two radar stations
in the area of signal overlap, using software provided by the manufacturer (Hel-
zel Messtechnik GmbH). The processing steps involved in WERA HF radars
data processing are described in detail in the literature (e.g., Barth et al. 2010;
Stanev et al. 2014).
After the transformation of the measurements from radar coordinates
(i.e. range and azimuth) to Cartesian grid, the spatial resolution of the current
vector field was 0.75 km, as shown in Figs 2 and 3. Surface current maps have
been provided every half an hour. The HF radar measurement is sensitive to
weather conditions, ionospheric reflection, sea-surface conductivity as well as
noise from interference, which leads to gaps in the time series after removal of
erroneous data. The percentage of high quality data during our experiment in
each grid point is shown in Fig. 3a. Note that in the central region about 90%
or more good data have been obtained. Near the boundaries of the monitored
area the record exhibits a radial decrease in data return, thus reducing data
availability in distant areas. Preliminary data processing has been performed
on full resolution 30-minute data record by the WERA software. During this
process the quality control has been performed on raw data. After the final data
processing, the 2D flow data are referred to as total vectors and contain u (east–
west) and v (north–south) velocity components at each grid point. The missing
current components have been interpolated in space by the WERA software to
fill in small data gaps (one or two records missing). After this interpolation
the number of missing data slightly increased as shown in Fig. 3b. In addition
to values of surface current vector components, the processed HF radar data
set includes estimates of the accuracy for each component (e.g., Stanev et al.
2014). This accuracy estimate includes the influence of the geometry between
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Fig. 2. Spatial grid used for the HF radar measurements. HF radar stations were deployed in
Nordvaagen and Repvaag. The letters A1, A2, A3, and M indicate the locations discussed in the
text. Time series of surface current data from these pixels are presented in Results and interpretation
section. Numbers 1–7 indicate stations S included in the diagram shown in Fig. 16. Sea level
and meteorological data were recorded in Honningsvaag (from the Norwegian Meteorological
Institute and the Norwegian Mapping Authority, Hydrographic Service).
Fig. 3. Availability of HF radar-measured current vectors during the time period of June 10, 2014
to October 11, 2014, (a) percentage of data return when both vector components were recorded,
(b) percentage of data return when interpolated data for one vector component are additionally
included in the estimate.
ab
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Surface currents in the Porsanger fjord 343
the radar sites and random errors. The accuracy of 99% of recorded u and v
component data was below 0.04 ms-1 and 0.035 ms-1 at pixels discussed in this
paper. Harmonic analysis described below was done on uninterpolated, subsam-
pled data sets with hourly resolution and we have focused on the region where
data coverage shown in Fig. 3a was 90% or more. Before this analysis, a small
number of outliers that differed from average values by more than 3 standard
deviations was removed.
Additional data sets have also been used. Sea level data were provided by
the Norwegian Hydrographic Service through their websites (http://kartverket.no
and http://vannstand.no). We have carried out tidal analysis using the 19-year
long time series (1996–2014) of sea level data from Honningsvaag (70.980°N,
25.972°E). Meteorological data from Honningsvaag with hourly resolution cov-
ering the time period from June to October 2014 were obtained from the Nor-
wegian Meteorological Institute (http://www.yr.no). The geographical location
of Honningsvaag is shown in Fig. 2.
In order to derive an understanding of the temporal and spatial patterns of
surface currents in the Porsanger fjord, we have carried out tidal analysis of
sea level and surface current data. The purpose of this analysis was to separate
out the tidal from the nontidal components of the currents and to determine the
most important tidal constituents. The underlying assumption of tidal analysis is
that tidal oscillations can be broken down into a collection of simple sinusoids.
Although the real ocean is generally not in equilibrium with tidal forcing, tidal
amplitudes are small compared with the total ocean depth in many regions. In
such a scenario, the dynamics are nearly linear, the forced response contains
only those frequencies present in the forcing, and specialized analysis techniques
can be used to take advantage of the deterministic nature of tidal processes.
For our calculations, we have used the method based on a least-squares fit
coupled with nodal modulation for the constituents that can be resolved over
the length of a given data record. The method has been described in detail
by Foreman (1977, 1978). The computer codes with manuals are available at
www.pac.dfo-mpo.gc.ca/science/oceans/tidal-marees/index-eng.html. Two sets
of harmonic tidal analyses were performed. In the first case, the analysis was
carried out for the 19-year long time series of sea level (1996–2014). In the
second case, the tidal analysis was completed for surface currents. In this case,
the data from our field measurements covering the time period from June 10
to October 11, 2014 have been used.
Errors in the tidal current analysis can result from two major sources. These
are the contamination of the harmonic analysis results due to current oscillations
not associated with tides and measurement errors in the current data. However,
these measurement errors are random in nature rather than systematic, therefore
their effect on the harmonic analysis results should be substantially reduced
over the record lengths (123 days) used in our analysis. One phenomenon that
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potentially can have some influence on our results are inertial oscillations, that
at the latitudes (~71°N) of our study area have period of 12.67 hours, similar to
N2 semi-diurnal tidal constituent. The intensity of inertial oscillations depends on
fluctuations in the surface wind. Because individual inertial events have a rela-
tively short duration and occur at random phase with one another, the effect on
the results of tidal current analysis is most likely reduced. However it is possible
that our estimate of the N2 tidal current component is somewhat overestimated.
In addition to tidal harmonic analysis, we have carried out spectral analysis.
Autospectra of physical variables have been determined using standard signal
processing techniques (Bloomfield 2000; Bendat and Piersol 2010). We applied
a Fourier transform to the autocovariance and to the crosscovariance functions
to obtain power spectra and squared coherence of scalar variables. The standard
error is 34% in these power spectral estimates. The squared coherence above
0.28 is statistically significant at 95% confidence level. Additionally, vector time
series, i.e. surface currents and residuals, have been resolved into clockwise
(CW) and counterclockwise (CCW) components, and rotary spectra, have been
estimated following Gonella (1972). In this case, the individual time series were
divided into subsamples consisting of 512 data points, and power spectra were
averaged. Before these calculations all data gaps were linearly interpolated, and
series with gaps longer than four hours were discarded.
Continuous records of surface currents allowed us to estimate the net transport
of surface water out from the inner part of the Porsanger fjord during our experi-
ment. This has been done using data recorded at pixels indicated by numbers
1–7 (Fig. 2). First, each current vector has been decomposed into the component
parallel to the transect line and another component perpendicular to the transect
line. Next, the time series of the current vector components perpendicular to
the transect segments have been used to estimate daily average water transport
through each of the sectors limited by pixels 1 through 7. Finally, using the
trapezoidal approach, total net daily transport of water has been estimated. In
these calculations, we have assumed that the surface layer is 1-m deep.
Results and interpretation
Example maps of current vectors recorded by the HF radar system are
presented in Fig. 4. The direction and magnitude of surface currents varies
significantly during a day. Our goal is to analyze these complex patterns moni-
tored at high spatial and temporal resolution with HF radars. We will start with
describing a background information that can be derived from long time series
of sea level observations. The results from tidal analysis of the 19-year long
time series (1996–2014) of sea level data from Honningsvaag are summarized
in Table 1. For brevity, only the 7 most important tidal components have been
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Surface currents in the Porsanger fjord 345
listed in Table 1, but the analysis allowed us to extract 70 components. Figure 5
shows a subset of sea level time series corresponding to the time period covered
by our in situ experiment (June 10 to October 11, 2014, year days 161–284).
The upper panel (Fig. 5a) displays the measured data, the middle panel (Fig. 5b)
the modeled tide, and the bottom panel (Fig. 5c) the residual sea level variability.
Fig. 4. Example maps showing spatial patterns and temporal variability of surface currents observed
during our experiment. This example is for day 184 (July 3, 2014). The lowest sea level on day 184
was recorded at 1 am and 1 pm.
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Table 1
The most important semidiurnal and diurnal tidal constituents estimated
from the 19-year long time series of sea level data in Honningsvaag.
Constituent Amplitude (cm) Period (hours) Phase
M2 90.1 12.42 80.7
S2 25.0 12.00 122.4
N2 19.5 12.66 53.2
L2 1.9 12.19 120.2
K1 8.2 23.93 241.2
O1 2.5 25.82 76.7
P1 2.5 24.07 239.2
Fig. 5. Subset of time series of sea level recorded in Honningsvaag. This subset covers the time
period from June 10, 2014 (year day 161) to October 11, 2014 (year day 284). (a) The measured sea
level (referenced to the lowest astronomical tide observed at this station). (b) The predicted water
level variability due to tides. The predicted tidal level is based on the 70 harmonic components
obtained from our tidal analysis of the 19 years (1996–2014) of sea level data. The most important
components are listed in Table 1. (c) The residual sea level estimated as the difference between
the measured and the modeled sea level.
a
b
c
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Surface currents in the Porsanger fjord 347
Since we have used the data referenced to the lowest astronomical tide, the
measured time series are positive numbers. The reconstruction (Fig. 5b) is based
on the 70 tidal components determined in the tidal analysis. About 99% of the
total variance in the measured time series shown in Fig. 5a is accounted for by
the tidal model. The residuals (Fig. 5c) have been estimated as the difference
between the measured and the modeled sea level. The residual sea level cor-
responds to the non-tidal variations in the water level, e.g., due to wind stress
or air pressure effects. However, since our reconstruction used limited number
(70) of tidal constituents to fit the data, it is also possible that the calculated
residuals contain some minor tidal variations not accounted for by the predictive
model. We note that the largest residual sea level (about 40 cm) was observed
on year day 270.
Figure 6 shows schematically the respective contribution of the six most
important diurnal and semidiurnal tidal constituents to the sea level variability
in Honningsvaag. Tidal forcing is predominantly semi-diurnal, and the largest
constituent is the “principal lunar semidiurnal” indicated by symbol M2 with
amplitude of about 90 cm (see Table 1). In addition, we note that the S2 (prin-
cipal solar semidiurnal) and N2 (larger lunar elliptic semidiurnal) components
have amplitudes of about 20 cm, while the most important diurnal constituents
have amplitudes of only a few centimeters.
The results from tidal analysis are also presented as diagrams in Fig. 7.
Figure 7a shows the reconstructed time series of sea level and Fig. 7b the
Fig. 6. Relative contribution of the most important tidal components to sea level variability
in Honningsvaag.
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Fig. 7. Diagrams illustrating variability of sea level (in cm) in Honningsvaag during the time period
from June 10 (year day 161) to October 11, 2014 (year day 284) due to (a) tides (reconstructed)
and (b) non-tidal contribution (residuals). Note the systematic time shift of the maximum
and minimum sea level in panel a.
residual sea levels. Note that hours of each day are shown on the vertical scale
and consecutive day numbers are indicated on the horizontal scale of each
plot in Fig. 7. This figure allows us to observe how the daily maximum and
minimum sea levels shift progressively in time. For example, on day 161 the
maximum sea level has been observed at 1–2 am and 1–2 pm. Subsequently,
we can observe that the timing of the maximum and minimum sea level gradu-
ally shifted during the following days. The tidal amplitude reached for example
relatively high values on days 226 and 254, while at other times (days 187, 216)
it was much smaller. The highest positive values of residuals are observed on
days 270–271 and 170–171, while negative residuals are noted for example on
days 281–283 and 235. In order to derive better understanding of the possible
factors influencing the magnitudes of the residual sea level variability, we plotted
in Fig. 8 time series of meteorological data collected at Honningsvaag airport.
Air temperature during our experiment varied mostly between 2 and 15°C,
with unusually warm days 187 and 191 (July 6 and 10), when air temperature
exceeded 25°C. Wind speed (see Figs 8 and 9) was below 7.5 ms-1 most of
the time (80%) with some episodes when it exceeded 12.5 m s-1 (5% of the
time). Wind direction most often varied between north-west to north-east, while
the easterly winds were rare (Fig. 9). Comparison of meteorological data with
sea level residuals at Honningsvaag station shows that there is an inverse rela-
tionship between the sea level residuals and the barometric pressure (Fig. 9d).
The correlation coefficient between hourly sea level residuals and barometric
pressure is R = -0.74, scatter plot is not shown. The largest residual sea level
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Surface currents in the Porsanger fjord 349
Fig. 8. Meteorological data recorded at Honningsvaag: (a) air temperature, (b) wind speed, (c) wind
direction (in meteorological convention, 360 indicates wind from North), and (d) atmospheric
pressure at sea level and time series of residual sea level. Note, that in situations when the true
wind direction oscillated between small and large angles (~50 to 360 degrees) we have added
360 degrees to plot wind direction at small angles in order to make Fig. 8c more readable. This
means that, for example, 400 degrees in Fig. 8c indicates the true wind direction of 40 degrees.
Fig. 9. Frequency distribution of (a) wind speed and (b) wind direction at Honningsvaag station
during our experiment (from June 10 to October 11, 2014).
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of about 40 cm was detected on day 270 (September 27, 2014), when the air
pressure attained the lowest value observed during our experiment (975 hPa).
This relationship between the barometric pressure and sea level is most likely
so evident, because sea level station at Honningsvaag is situated in a harbor
that is well sheltered from winds. Therefore topographic effects related to wind
are minimized at this site.
We will now discuss surface currents, mostly focusing on data representing
the pixels highlighted in Fig. 2 (points A1, A2, A3, M, and transect with sta-
tions 1–7). Note that the current observed at any time in the ocean is a superpo-
sition of tidal and non-tidal components. Tidal current is the periodic horizontal
flow of water accompanying the rise and fall of the tide. Nontidal currents include
all flows not associated with the tidal movement, for example quasi-permanent
geostrophic currents or temporary currents forced by changing meteorological
conditions. For instance, inertial ocean currents can play a significant role at our
study area, since winds are variable in this region and we observed few events
with relatively high winds. Recall, that the inertial currents are the oscillations
in water that was set in motion and is moving over a rotating earth. The prime
generator of ocean inertial motions is change in wind velocity, but details of
the motion depend also on topography and ocean density structure, e.g., Mayer
et al. (1981). In their simplest form, inertial oscillations are circular motions with
the rotation being clockwise in the northern hemisphere. They occur intermit-
tently, as a response to individual wind events, and decay rapidly within a few
cycles. The period of inertial oscillations depends on the latitude. The so-called
“inertial latitudes” are latitudes where the inertial period is equal to one of the
tidal constituents (e.g., Wunsch 1975). For the semi-diurnal tidal constituents
the inertial latitudes range between 70° and 90°. The period of inertial oscil-
lation in our study region is similar to the semidiurnal period of the dominant
tidal forcing (N2 constituent). At stations A1, A2, and A3, the inertial period
equals 12.67 hours.
We will focus now our attention on the results of tidal analysis carried out for
HF data recoded at pixels 1–7, A1, A2, A3, and M. Example results of analysis
for pixels A1 and A3 are shown as time series of measured (Figs 10a and 10c),
tidal (Figs 10b and 10e) and non-tidal (Figs 10c and 10f) surface currents. In
our analysis, we have estimated the 36 most important tidal constituents. Tidal
u and v components of up to about +/- 0.3 ms-1 have been observed (Figs 10b
and 10e). The magnitudes of the residual current components are generally up
to about +/- 0.4 ms-1 (Figs 10c and 10f). Figure 11 summarizes the results of
tidal analysis for surface currents recorded at pixels S1–S7, see Fig. 2 for posi-
tions. Figures 11a and 11b show reconstruction of tidal current components u
and v, respectively. Figures 11c and 11d demonstrate u and v components of
the residual currents. About 10–30% of the total variance in the measured time
series is accounted for by the tidal model. Note that in the offshore locations,
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Surface currents in the Porsanger fjord 351
where the direction of current is not restricted by topography, the tidal currents
are rotary. This means that as the current flows, its direction is turning during the
entire tidal period through all points of the compass. The speed of the current
also changes. Since at our example locations the tidal forcing is predominantly
semi-diurnal, current speed usually has two maxima and two minima (at about
halfway between the maxima) during the day. The rotary tidal currents can be
depicted as the elliptical patterns referred to as current ellipses. The relative
importance of the most significant tidal components K1, M2, S2, N2, and L2 at
sites A1, A2, A3, and M are compared in Fig. 12. These tidal current ellipses
show the length of the semi-major axis and the length of the semi-minor axis.
The semi major axis represents the maximum amplitude of the tidal current
constituent, while its inclination denotes the angle between the direction of the
maximum tidal flow and the true East, in degrees counterclockwise. As can be
seen in Fig. 12 and in Table 2, the M2 semidiurnal lunar constituent has the
largest amplitude at all sites. The second largest constituent at all points is S2.
Even if 36 major tidal constituents were separated in our tidal current recon-
struction, only the M2 constituent will be discussed now since this is the dominant
component. In Fig. 13, we present the spatial distribution of the M2 tidal ellipses.
Fig. 10. Example time series of surface currents at pixels A1 and A3: (a and d) observations,
(b and e) tidal currents (reconstructed), and (c and f) residual currents estimated as the difference
between measured and reconstructed surface currents. Red and blue color indicate u and v current
components, respectively.
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cf
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Malgorzata Stramska et al.
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The dimensions of these tidal current ellipses, i.e. the semi-major and the semi-
minor axes, are exaggerated in comparison to the spatial scale of the map, in order
to obtain ellipses that are plainly visible to the reader. The grid points on the map
are located 750 m apart. The dimensions of selected ellipses can be compared in
Table 2. As seen in Fig. 13, at some locations (X4, A3), the tidal currents can be
reversing. This means that the tidal flow alternates between approximately opposite
directions with a short period of little or no tidal current. During the tidal flow in
each direction, the current speed varies from zero to a maximum.
Example rotary spectra for observed surface currents and residual currents
are shown in Fig. 14. For convenience, the spectra are plotted as a function of
period, expressed in days. This example presents spectra obtained for station A1.
The main features of rotary spectra estimated at other locations were similar (not
Fig. 11. Diagrams for sea currents observed at transect indicated in Fig. 2. The horizontal scale
indicates pixel numbers 1–7 and the vertical scale shows time in days from the start (day 161)
to the end of our experiment (day 284). Panels a and b present reconstruction of tidal current
components u and v, respectively. Panels c and d illustrate u and v components of residual
currents, respectively.
a
c
b
d
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Surface currents in the Porsanger fjord 353
Fig. 12. Tidal ellipses illustrating the relative contribution of the most important tidal components
to tidal currents at pixels A1, A2, A3, and M (see Fig. 2 for pixel positions).
Fig. 13. Spatial distribution of M2 ellipses. The dimensions of selected ellipses are given in Table 2.
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Malgorzata Stramska et al.
354
Table 2
Summary of the results from the tidal analysis of surface currents.
Clockwise rotation is indicated by the minus sign for the semi-minor axis,
inclination is the angle between east and the major axis of the ellipse.
STATION A1, depth ~ 170 m
Constituent Phase
(degrees) Major (m/s) Minor (m/s) Inclination
(degrees)
M2 323.5 0.046 -0.010 46.7
S2 189.0 0.032 -0.013 122.3
N2 245.5 0.013 0.002 32.3
L2 180.4 0.022 -0.004 145.2
K1 119.8 0.026 -0.002 171.2
STATION A2, depth ~ 200 m
Constituent Phase
(degrees) Major (m/s) Minor (m/s) Inclination
(degrees)
M2 335.2 0.065 -0.008 43.6
S2 227.2 0.031 -0.013 54.5
N2 292.8 0.017 -0.001 32.4
L2 175.7 0.015 -0.006 155.5
K1 295.6 0.026 -0.006 2.5
STATION A3, depth ~ 200 m
Constituent Phase
(degrees) Major (m/s) Minor (m/s) Inclination
(degrees)
M2 335.1 0.068 -0.003 49.6
S2 227.3 0.029 -0.012 62.4
N2 312.4 0.015 -0.000 33.1
L2 213.7 0.009 0.001 131.9
K1 298.7 0.024 -0.005 15.4
STATION M, depth ~ 210 m
Constituent Phase
(degrees) Major (m/s) Minor (m/s) Inclination
(degrees)
M2 332.4 0.039 -0.002 68.2
S2 217.2 0.015 -0.012 100.6
N2 310.5 0.010 0.001 80.7
L2 232.7 0.008 0.001 137.2
K1 301.2 0.021 0.000 6.7
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Surface currents in the Porsanger fjord 355
shown). As can be seen on Fig. 14a, the most prominent peak for surface currents
time series is observed at semidiurnal frequency. It is impossible to separate differ-
ent tidal current constituents that are contributing to this peak in Fig. 14. This is
because our observational time series were recorded at too low (hourly) temporal
resolution to resolve these time scales through spectral analysis. In Fig. 14a, the
peak for the diurnal variability is much smaller than the semidiurnal peak, in
agreement with the results from harmonic analysis. If we compare Figs 14a and
b, we note that the diurnal peak has been removed by the harmonic analysis. The
semidiurnal peak is still present in the residual time series (Fig. 14b), although it
is significantly smaller than in Fig. 14a, and is basically restricted to CW rotation.
This shows that our harmonic tidal analysis has disassociated, at least to some
degree, semidiurnal inertial currents from semidiurnal tidal currents.
In addition, we note that significant variance in the power spectrum is allocated
to periods longer than diurnal, which is also seen in Fig. 15. Figure 15 compares
power spectral densities for sea level and wind speed recorded in Honningsvaag,
and current speed at station A1. In each case, the power spectrum has been nor-
malized to the total variance of the respective time series. The plots show that
relatively larger portion of the total variance is attributed to the diel and semidi-
urnal variability of sea level, than in the surface current speed time series. The
corresponding maxima in the power spectrum for surface current speed are much
less pronounced than in the power spectrum for sea level. Power spectra for wind
and current speed indicate that proportionally more variance is attributed to time
scales longer than a day, in comparison to the sea level data.
Figure 15b summarizes the results of the cross-spectral analysis between
selected pairs of variables. Red line indicates the squared coherence between
the wind and the current speed and blue line indicates the squared coherence
Fig. 14. Example rotary power spectra at location A1: (a) HF radar recorded current velocities,
(b) current residuals. The red line indicates clockwise rotation and the black line indicates
counterclockwise rotation.
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Malgorzata Stramska et al.
356
between the sea level and the current speed, respectively. The coherence above
0.28 is statistically significant at 95% level (Bloomfield 2000; Bendat and Piersol
2011). In case of an ideal linear system the coherence would be one. We can
see that the coherence between the wind speed and the current speed is above
the critical level for periods longer than about 2.5 days and indicates that these
variables are significantly correlated at synoptic time scales. In contrast, the sea
level and the current speed are not significantly correlated at time scales longer
than ~3.5 days, although there is a significant correlation at time scale of ~2–3
days. This can likely be related to atmospheric pressure variability. These results
support the notion that adding to the complexity of the surface currents in the
Porsanger fjord is the temporal and spatial variability of the wind’s influence.
Strong nontidal surface flows driven by wind stress are a very important contri-
bution to the observed variability of surface currents.
Continuous observations of surface currents allowed us to estimate the aver-
age transport of surface waters across transect indicated by pixels S1–S7. The
results are displayed in Fig. 16. Figure 16a shows time series of daily averaged
transport estimated at each segment of the transect, as well as the total transport
integrated between pixels S1 and S7. Figure 16b illustrates spatial distribution
of water transport, expressed as m3 of water transported during a day through
1 m of transect, on a 2D diagram. There are events when more surface water
during the day is transported into than out of the fjord. The export of surface
water from the fjord is more efficient on the south-eastern side of the fjord.
However, on average the total daily transport of surface water out of the fjord is
positive, and during our experiment it was estimated at about 32.106 m3 per day
Fig. 15. (a) Comparison of the normalized power spectral density for wind speed, sea level, and
surface current speed. Power spectra are normalized to the total variance. (b) Squared coherence
between sea level and current speed (blue line) and between wind speed and current speed
(red line) at location A1. The coherence >0.283 is significant at 95% confidence level.
a b
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Surface currents in the Porsanger fjord 357
assuming surface water layer 1-m thick. Obtaining an estimate of the total water
transport at different water depths would require information about 3D flow in
the fjord that is not available from the HF radar data.
Summary
In this paper, we provided detailed information about surface currents in
the Porsanger fjord. Tides are quite considerable, with tidal range on the order
of about 3 m. Tidal analysis attributes to tides about 99% of variance in sea
level time series recorded in Honningsvaag. The most important tidal component
Fig. 16. Estimated daily averaged net transport of surface water across the transect shown in Fig. 2.
(a) Time series of water transport at each of the segments of the transect and the total transport
integrated across the transect line, and (b) 2-D diagram summarizing water transport.
a
b
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Malgorzata Stramska et al.
358
based on sea level data is the M2 component (amplitude of ~90 cm). The S2
and N2 components (amplitude of ~20 cm) also play a significant role in the
semidiurnal sea level oscillations. The most important diurnal component is K1
with amplitude of about 8 cm.
Tidal analysis has led us to the conclusion that the most important tidal
component in surface currents is the M2 component. The second most impor-
tant is the S2 component. Our results indicate that in contrast to sea level, only
about 10–30% of variance in surface currents can be attributed to tidal currents.
This means that about 70–90% of variance can be credited to wind-induced and
geostrophic currents. In particular, it is obvious that surface currents respond
to the significant variability of wind including strong wind events. As a result,
surface currents contain the component associated directly with wind forcing
as well as the inertial component.
Our data did not allow us to achieve the necessary frequency resolution and
to strictly separate the inertial oscillations from tidal variations. However, our
results indicate that most of the variance in the time series of surface currents
is allocated to time scales longer than diurnal. This indicates that surface cur-
rents in the fjord can have a significant component related to Ekman forcing.
Because of the complicated interactions involving wind field (variable in
time and spatially) and topography of the fjord, we underline the need for
further investigation of currents in this region using a coastal model. We plan
to adapt such model and to further investigate various scales of ocean current
variability observed with the HF radar system.
Finally, our data allowed us to estimate time series of surface water transport
out of the fjord area monitored by the HF radar system. These results confirmed
the general expectations that, on average, transport of surface waters out of the
fjord dominates in this region. This transport has to be compensated by the
inflow of oceanic waters at greater depth, as well as by the transport of fresh
water from rivers and land runoff. Better understanding of the water budget
will be possible through a modeling study.
Acknowledgements. — We are grateful to Thomas Helzel and his staff from Helzel
Messtechnik GmbH for their support with all aspects of HF radar system operations.
Many thanks to Knut Yngve Børsheim, Hans Kristian Strand, and Henrik Søiland from
Institute of Marine Research for their help with the field logistics. We are grateful
to Jagoda Białogrodzka, Dariusz Ficek, Mateusz Jakowczyk, Daniel Materka, Roman
Majchrowski, Roman Marks, Marek Świrgoń, Marzena Wereszka, and Tomasz Żmójdzin
for their participation in the NORDFLUX field experiment in 2014. The authors are
grateful to all the persons involved in the programs providing free access to the data sets
used in this study. The sea level data were provided by the Norwegian Hydrographic
Service. Meteorological data from Honningsvaag were made available by the Norwe-
gian Meteorological Institute. This work was funded by the Norway Grants through the
Polish-Norwegian Research Programme operated by the National Centre for Research
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Surface currents in the Porsanger fjord 359
and Development NCBR contract No. 201985 Application of in situ observations, high
frequency radars, and ocean color, to study suspended matter, particulate carbon, and
dissolved organic carbon fluxes in coastal waters of the Barents Sea. Partial funding
for MS and AJ comes also from the statutory funds at IO PAN. We would also like to
thank Daniel C. Conley and an anonymous reviewer for their detailed and constructive
comments which helped to improve this paper.
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Received 14 April 2016
Accepted 11 July 2016
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