Introduction
Ocean variability covers a wide range of temporal and spatial scales, from
seconds to tens of thousands of years and from millimeters to tens of
thousands of kilometers. Obviously, even the most advanced ocean models
cannot resolve this wide range of scales, and thus they use sub-grid
parameterizations to account for such phenomena. Modeling of oceanic dynamics
is often based on forcing from point measurements and on long-term-mean
measurements (e.g., monthly averages). In addition, models are often
calibrated (tuned) and validated against these long-term-mean point
measurements. Such calibration and validation is performed under the
assumption that these measurements represent the spatial grid resolution of
the ocean model.
One key variable of ocean dynamics is ocean currents. There are various ways
to measure ocean currents, particularly ocean surface currents. Point
measurement tools include rotor-based devices and the acoustic Doppler
current profiler (ADCP). Various types of drifters and floats can be used to
approximate the currents. Satellite data that measure the sea surface height
can be used to estimate geostrophic currents; these provide, on a daily
basis, global-scale surface current maps with resolutions of a few
kilometers. Coastal radar (CODAR, see details below) systems are increasingly
used to measure surface currents at finer spatial (from a few hundred meters)
and temporal (half an hour and more) scales. Such rich and detailed data can
be used to analyze the statistical properties of surface currents.
The Weibull distribution was previously used to characterize the probability
density function (PDF) of altimeter-based surface currents
e.g.,, and global maps
of the shape and scale parameters of the Weibull distribution were
constructed. A detailed statistical analysis of CODAR-based surface currents
from the northern tip of the Gulf of Elat (Aqaba) was performed by some of us
; it was found that the shape
and scale parameters of the Weibull distribution significantly vary in this
small area of 6 km × 10 km (Fig. b, d). Using a variant
of a simple Ekman layer model, this spatial variability was attributed to the
temporal variability of the local winds.
(a) Southeastern China–Taiwan region. The white rectangle
indicates the region of Nan-Wan Bay. (b) Northern Red Sea region.
The white rectangle indicates the northern part of the Gulf of Elat.
(c) The bathymetry of Nan-Wan Bay, marked by the white rectangle in
(a). The white rectangle indicates the approximate regions covered
by the CODAR stations. (d) The bathymetry of the northern Gulf of
Elat, marked by the white rectangle in (b). The white rectangle
indicates the approximate regions covered by the CODAR stations.
The first goal of the present study was to verify whether the spatial
variability of the statistical properties of the surface currents in the Gulf
of Elat, reported in , also exists
in a quite different environment such as Nan-Wan Bay of Taiwan
(Fig. a, c). There are several differences between the Gulf of
Elat and Nan-Wan Bay: (i) Nan-Wan Bay is open to the ocean from three sides,
while the Gulf of Elat is a semi-enclosed basin (with one open boundary);
(ii) Nan-Wan Bay is directly connected to the world ocean (the South China
Sea), while the Gulf of Elat is connected to the world ocean (the Indian
Ocean) via two straits, to and from the Red Sea; (iii) the water depth in
Nan-Wan Bay (in the study area, Fig. c) is relatively shallow
compared with the depth of the Gulf of Elat (in the study area,
Fig. d); and (iv) the currents of Nan-Wan Bay have a strong
tidal component, while those of the Gulf of Elat do not. We find that the
level of variability in these two different basins is similar. We note that
the specific choice of Nan-Wan Bay and the Gulf of Elat is primarily because
high quality continuous CODAR data were available to us for analysis for
these two locations; it is possible that comparison of CODAR data from other
locations (which unfortunately was not available to us) would result in
additional conclusions.
The second goal of the present study was to identify and quantify the surface
currents' temporal asymmetry (i.e., the ratio between the time during which
the current speed increases and the total time) in both Nan-Wan Bay and the
Gulf of Elat. The asymmetry and other statistical characteristics of surface
currents may be used to test and validate the performance of oceanic models.
We found that the surface currents in Nan-Wan Bay are significantly
asymmetric, while those of the Gulf of Elat are symmetric. We show here that
the asymmetry of Nan-Wan Bay's currents is rooted in the strong tides of the
bay, while the absence of asymmetry in the Gulf of Elat is associated with
the relatively weak tidal signal in this gulf.
The paper is organized as follows. We first describe the research area of
Nan-Wan Bay (Sect. ) and the Gulf of Elat
(Sect. ). We next describe the CODAR data, the
statistical methods used to evaluate the parameters of the currents PDFs, the
detiding procedure, and the measure for current temporal asymmetry
(Sect. ). We then compare the statistical properties of
Nan-Wan Bay with those of the Gulf of Elat (Sect. ). The
results regarding the temporal asymmetry of the currents and their relation
to the tides are discussed in Sect. . A summary then follows
(Sect. ).
Study regions
Nan-Wan Bay
Nan-Wan (“wan” is Chinese for “bay”) Bay is located in the southernmost
part of Taiwan (Fig. a, c). It is bounded by western
(Mou-Bi-Tou) and eastern (O-Luan-Bi) capes where the distance between them is
∼ 14 km. The bay is surrounded by the Taiwan Strait (from the west),
the South China Sea (from the southwestern direction), the Luzon Strait (from
the south), and the Pacific Ocean (from the east). The bay includes some
seamounts that partially block it. The eastern side of the bay includes a
shallow continental shelf (≈ 5 km wide); the western side of the
bay has a very small continental shelf. The curved (parallel to the coast)
channel is partially bounded by the southern seamount.
Nan-Wan is subject to monsoonal winds; these blow from the southwestern
direction during summer and from the northeastern direction during late fall,
winter, and early summer. Thus, during winter, the strong monsoon winds blow
downhill to the south from the mountains of Nan-Wan towards the bay. During
the fall, wind-driven currents are weak compared to the tidally driven
currents, yet wind-driven currents are strong during a few typhoon events.
The north-flowing Kuroshio Current is adjacent to Taiwan from the east, but
still, its influence on Nan-Wan Bay is not significant compared to the
tidally driven currents. The tidal current speed at spring tides exceeds
2 m s-1
.
The semidiurnal and diurnal tidal components of the currents in Nan-Wan Bay
are approximately equal in their magnitude
but are modulated by the
spring–neap tidal cycle. The temperature hardly drops around the neap tides,
while during the spring tides, the temperature can suddenly drop by several
degrees for several hours due to strong tidally magnified upwelling. Such a
temperature drop can reach 10 ∘C. For example, on 24 November 1988,
the sea surface temperature dropped suddenly (within a few hours) by
10 ∘C (from 24 to 14 ∘C), leading to a massive fish kill. A
similar event occurred during July 2008.
The Gulf of Elat
The study region is located at the northern terminus of the Gulf of
Elat/Aqaba, in the northeastern region of the Red Sea; it is a nearly
rectangular, deep (∼ 700 m; Fig. d), and semi-enclosed
basin. A desert mountain range surrounds the Gulf of Elat and steers the
persistent northerly wind along its main axis
.
Several components affect the water circulation/currents in the gulf: winds,
tides, and the thermohaline circulation. The semidiurnal peak, forced by the
flux of water through the Straits of Tiran, dominates the weak diurnal tidal
component . The surface current in the
study region often exhibits a complex (although spatially coherent) pattern,
including eddies that cover a large part of the domain
.
The gulf is almost blocked from the cold and dense water of the world ocean
due to the shallow sill (137 m) between the Indian Ocean and the Red Sea
(Bab el Mandeb) and the shallow sill (240 m) between the Red Sea and the
Gulf of Elat (Straits of Tiran) . Thus, the
water column in the gulf exhibits weak stratification and winter deep water
formation caused by surface cooling and evaporation
. During February
and March, temperature and salinity are almost uniform down to a depth of a
few hundred meters (and sometimes down to the bottom); new stratification
begins to form in March
. The gulf is
stratified in summer when an upper (∼ 200 m) warm layer overlies a
homogeneous deeper layer .
The wind in the Elat region is northerly (with a small easterly component)
during most of the year
.
Strong southerly winds occur rarely during the winter, usually during
southern storms. There is a strong diurnal cycle associated with the diurnal
breeze cycle in the summer . On
average, the wind is stronger during summer.
Methods
HF-radar-based currents
High frequency (HF) radar systems for surface current measurements
, like the SeaSonde
and Wellen Radar
WERA;, have become
popular in recent years and have mainly been used to study coastal
circulation. These systems usually operate at a frequency of ∼ 24 MHz
or lower, covering distances from several tens of kilometers up to more than
a hundred kilometers, at a resolution of a few kilometers.
Many articles have described in detail the theory behind the HF radar surface
current measurements e.g.,. Briefly, surface gravity waves reflect
radio waves that were transmitted by the HF radar, and these are again
detected by the radar. Surface currents can be measured based on the Bragg
resonance of the surface waves with the transmitted radio waves. The received
spectrum is not identical to the transmitted spectrum due to the Doppler
shift caused by the radial component of the phase shift of incoming and
outgoing waves. Waves that are superimposed onto a current lead to a further
shift in the spectral peaks. This additional shift allows the extraction of
the radial component of the current. It is possible to calculate the surface
velocity field based on two radar sites that measure the radial velocity of a
patch of water from two different angles.
CODAR systems have been used to measure surface current fields both in
Nan-Wan (Fig. a) and in the Gulf of Elat see,
e.g.,. There are two CODAR stations in Nan-Wan
(indicated by the red dots in Fig. a) operated at 24–27 MHz;
a third CODAR station has been operated since June 2014 and is not included
here. The CODARs produce current fields with a spatial resolution of 1.5 km
and a temporal resolution of 1 h. The CODAR measurements in the Gulf of Elat
are conducted by two 42 MHz SeaSonde HF radar systems that were installed in
the gulf in August 2005. They measure currents at a temporal resolution of
half an hour and a spatial resolution of about 300 m. Below we analyze 1
year of surface current fields for both Nan-Wan (from 1 March 2013) and the
Gulf of Elat (from 1 October 2005). The surface current fields were filtered
and interpolated to fill spatial gaps in the observation see,
e.g.,.
There were many missing days of Nan-Wan Bay data from September to
November 2013, and we thus do not present the results of these fall months.
Consequently, the presented annual mean results underestimate the effect of
the fall season.
Current field of Nan-Wan Bay as estimated by the CODAR. (a)
Snapshot from 19:00 on 7 March 2013. (b) Annual mean current field.
(c) Winter (DJF) mean current field. (d) Summer (JJA) mean
current field. The filled red circles indicate the locations of the CODAR
stations. The “x” indicates the location of the sample time series shown in
Fig. a.
The Weibull distribution
In a previous study , some of us
analyzed the parameters of the Weibull distribution describing the PDF of the
surface currents in the Gulf of Elat. It was found that these parameters
exhibit a large spatial variability that changes seasonally. Here we applied
the same procedure to the Nan-Wan CODAR surface current measurements. We thus
only briefly describe the parameter estimation procedure, and the interested
reader can find more details in .
(a) A sample of speed time series from Nan-Wan Bay (blue)
spanning 12 July to 1 August 2013, from 120∘ E, 21.87∘ N
(indicated by the “x” in Fig. ) and its corresponding detided
time series (red). (b) The tidal component of the current speed time
series shown in (a). (c) The probability density function
(PDF) of the current speed time series (filled blue circles) of JJA 2013
(part of which is shown in a), its best Weibull distribution fit
(red curve), and the Weibull PDF for k=1. (d) Same as (c)
in a semi-log presentation.
Summary of the statistical results of Nan-Wan Bay. Left column: the
shape k parameter of the Weibull distribution; middle column: the scale
λ parameter of the Weibull distribution; right column: mean current
speed (in cm s-1). The first, second, and third rows summarize the
annual (1 March 2013 to 1 March 2014), winter (DJF of 2013–2014), and summer
(JJA 2013) results.
The Weibull distribution was suggested as an appropriate PDF of wind
e.g., and
surface current e.g.,
speed. While it is possible that other distributions may be more appropriate
models for current speeds, we restricted ourselves to the Weibull
distribution to allow comparison with previous results.
The Weibull PDF has two parameters, the scale and shape parameters, λ
and k, and is given by
f(x;λ,k)=kλxλk-1e-(x/λ)k,
where x is a Weibull random variable. λ and k are greater than
zero. Given a data set (in our case, the time series of surface current
speed), it is possible to estimate k using either (i) the different
statistical moments, or (ii) the hazard function seefor more
details, or (iii) the maximum likelihood
estimator of the Weibull distribution. Once the shape parameter, k, is
found, it is possible to estimate the scale parameter, λ, for
example, by using the relation between λ and the mean of the time
series. The different methods yielded similar results, and we thus present
below only the results that are based on the different moment estimation
see.
A typical current speed time series from Nan-Wan Bay (from the location
marked by “x” in Fig. ) is shown in
Fig. a. The corresponding PDF and the Weibull fit are
shown in Fig. c, d. The estimated shape parameter is
k≈2, indicating that this specific PDF is close to the Rayleigh
distribution. For comparison, we also plotted the Weibull distribution with
k=1, which corresponds to the exponential distribution. Unlike the PDF of
the data, this PDF decreases monotonically and indicates a higher probability
of high current speed values.
The asymmetry ratio, A (Eq. ), of the Nan-Wan
Bay current speed time series for the (a) 1 h time interval (lag)
for annual time series, (b) 7 h time interval for annual time
series, (c) 1 h time interval for winter time series, and
(d) 1 h time interval for summer time series. The 0.5 value is
indicated by the black contour line.
Detiding
To study the effect of tides on the CODAR currents, we implemented the
algorithm of . We decomposed
the current speed time series into the tidal component and detided time
series. An example of such a time series from Nan-Wan Bay is shown in
Fig. a, b. It is clear that the tidal component
dominates the current time series, as reported by previous studies on Nan-Wan
Bay .
Temporal asymmetry
To measure the temporal asymmetry of the current speed time series, we
computed the ratio between the increasing speed time steps and the total
number time steps. This and similar measures were used to quantify the
asymmetry of the temperature time series
. The asymmetry measure,
A, of the current speed time series si (i=1…N where N is the
length of the time series) can be expressed as
A(τ)=1N-Nτ∑i=1N-NτΘ(si+Nτ-si),
where τ=NτΔt is the asymmetry time interval, Δt is the
measurement temporal resolution, Nτ is the number of time steps to
compose the asymmetry time interval, and Θ(x) is a step function that
is 1 for x>0 and 0 otherwise. Thus, when the number of positive increments
is equal to the number of negative increments, A=0.5. A>0.5 (A<0.5)
indicates that the current speed increases (decreases) gradually and
decreases (increases) rapidly. 2A-1 indicates by how much the number of
positive increments exceeds the negative ones; for example, if A=0.55,
there are 10 % more positive increments than negative increments. It is
possible to measure the asymmetry over a different time interval τ. When
the time series is asymmetric and periodic, the asymmetry
measure (Eq. ) will change sign when τ exceeds half of
the period of the time series.
Same as Fig. for the Gulf of Elat. No
significant asymmetry is observed.
We used a surrogate data test to assess the significance of the asymmetry
results. Specifically, we randomly shuffled the time series and then measured
the asymmetry A(τ). If the original asymmetry lies outside the error bar
of the surrogate data (e.g., outside the range of the mean ±1 SD), the
asymmetry of the original time series may be considered significant.
Results
We first calculated the mean surface current field for each grid point in the
study area of Nan-Wan Bay (Fig. ). Consistent with previous
studies in the region
, the surface currents are strong and exhibit
cyclonic circulation, with the center located close to middle of the line
connecting the capes of Nan-Wan Bay (Fig. b). The currents are
much stronger during the summer (Fig. d) than during the winter
(Fig. c). The mean current speed (in the research area) is
80 cm s-1 in the summer and 60 cm s-1 in the winter
(Table ). Moreover, as is reflected in Fig. ,
the mean zonal velocity during the summer is more than 4 times greater than
the winter one (Table ), pointing to an eastward current
south of the cyclonic eddy. The current speed is relatively weak in the
northern part of the domain and largest in the eastern part of the domain
(Fig. c, f, i), possibly due to the Kuroshio Current.
Summary of the surface current statistics of Nan-Wan Bay. The table
includes the shape parameter k of the Weibull distribution, the scale
parameter λ (cm s-1) of the Weibull distribution, the mean
zonal current u (cm s-1), the mean meridional current v
(cm s-1), and the mean current speed u2+v2 (cm s-1).
The mean ± 1 standard deviation is given for the annual, winter, and
summer periods.
Parameter
Annual
Winter
Summer
k
1.78 ± 0.09
1.66 ± 0.11
2.21 ± 0.03
λ
74.1 ± 12.2
67.4 ± 10.8
90.6 ± 18.7
u
32.6 ± 15.8
16 ± 14.4
67.1 ± 25.1
v
-2.16 ± 9.32
-9 ± 7.56
2.27 ± 16.8
u2+v2
65.9 ± 10.8
60.3 ± 9.77
80.43 ± 16.7
The asymmetry ratio of the Nan-Wan Bay current speed time series,
for the annual (upper panels), winter (middle panels), and summer (bottom
panels) time series, and for the tidal (left panels) and detided (right
panels) time series. The 0.5 value is indicated by the black contour line.
We next examined the shape and scale parameters of the Weibull fit to the
surface current of Nan-Wan Bay (Fig. ). As expected, the
spatial pattern of the scale parameter, λ, is similar to the pattern
of the current speed (the second column of Fig. vs. the
third column). Interestingly, the shape parameter of the Weibull
distribution, k (first column of Fig. ), exhibits large
spatial and seasonal variability. While the k parameter is maximal in the
northwestern region during the winter, it is maximal in the southeastern
region during the summer, suggesting a different dynamics during these two
seasons, probably related to tides, as these also exhibit strong seasonal
variations. Moreover, the k parameter is much larger during the summer
(k≈2.21) than during the winter (k≈1.66,
Table ), and exhibits large spatial variability in both
seasons (from 1.8 to 2.8 during the summer and from 1.5 to 2 during the
winter). This is probably related to the tides that are stronger during the
fall and summer periods; more accurately, the spatial mean standard
deviations of the tidal component were 21.5, 25.5, 30.85, 23.6, and
18.9 cm s-1 for the annual, summer, fall, winter, and spring periods,
respectively (note that the fall value is less reliable due to lack of data).
A comparison of the results shown in Fig. with the ones
from the Gulf of Elat Fig. 3 of
indicates a similar range of spatial and seasonal variability. Yet the
surface currents in the Gulf of Elat are much weaker than those in Nan-Wan
Bay and the value of the shape parameter, k, is lower there. We thus
conclude that the spatial and seasonal variability of the surface currents'
statistical parameters is not unique to Elat and, indeed, is also present in
the quite different region and environment of Nan-Wan Bay. We stress here
that we observed the spatial variability, both in Nan-Wan Bay and the Gulf of
Elat, in a relatively small region on the order of 10 × 10 10 km.
Encouraged by the apparent asymmetry of the surface speed (see the black
arrows in Fig. a), we next studied the temporal
asymmetry of the surface current field, both in Nan-Wan Bay and the Gulf of
Elat, following Eq. (). The asymmetry measure may be used
to test the performance of ocean models as it also quantifies nonlinear
aspects of the underlying process. Figure a depicts the
Nan-Wan Bay asymmetry measure, A(τ), of the annual time series for a
1 h time interval. First, we found large spatial variability in A(τ),
in which it is less than 0.5 in parts of the northern side of the basin and
larger than 0.5 on the southern side of the domain. This indicates that
statistically the current speed increases gradually and decreases more
rapidly in the southern part of the domain, in contrast to the current
surface increase/decrease in extensive regions on the northern side of the
basin. The asymmetry range is 0.48<A<0.52, indicating up to 4 %
positive/negative steps compared to negative/positive steps. Second, we
randomly shuffled the time series of each grid point, calculated the
asymmetry measure A, and found the mean value ±1 SD of A=0.5±0.003. This indicates that the reported asymmetry is significant, being well
outside these error bars. Third, for a time lag of τ=7 h
(Fig. b), we found that the asymmetry changes sign for
extensive parts of the domain. This suggests that the asymmetry is linked to
tides that have a semidiurnal periodicity for which the asymmetry should
change sign for a time lag that is half the period. Fourth, the asymmetry
during the summer (Fig. d) was found to be much stronger
than the winter one (Fig. c), again suggesting that the
asymmetry is influenced by the tides, as the tidal signal is stronger during
the summer than during the winter. In the summer, A exceeds 0.54,
indicating that in the southern part of the domain, there are at least
8 % more positive increments of the surface currents than negative ones.
Finally, the pattern of the annual asymmetry field
(Fig. a) was found to be similar to the summer one
(Fig. d).
We performed a similar asymmetry analysis for the Gulf of Elat's surface
currents (Fig. ). Here, however, we did not find
significant asymmetry as A fluctuated very closely around 0.5 with an
asymmetry similar to a randomly shuffled time series. This absence of
asymmetry is associated with the weak tidal signal in the Gulf of Elat.
To verify the hypothesis that the tides underlie the observed asymmetry in
Nan-Wan Bay, we decomposed the surface current time series, at every grid
point in the domain, into tidal and detided components. In
Fig. a, b, we present this decomposition, which
indicates a large and apparently asymmetric tidal component. We then
calculated the asymmetry of the tidal and detided components of the surface
currents (Fig. ). While the detided signals exhibit
hardly any asymmetry (Fig. b, d, f), the tidal
component is highly asymmetric (Fig. a, c, e), even
more than the original time series. Also, here the asymmetry during the
summer is much stronger than the winter one. The range of asymmetry during
the summer is 0.44<A<0.56, indicating that the relative number of
positive/negative increments in the tidal component of the surface currents
can reach 12 %. We thus conclude that the observed asymmetry in Nan-Wan
Bay (both spatial and temporal as shown in Fig. ) is due
to the asymmetry of the tides in the region.
Summary
We analyzed the statistical properties of CODAR-based surface current fields
in Nan-Wan Bay, Taiwan, and compared them to the statistical properties of
CODAR-based surface current fields from the Gulf of Elat, Israel. The study
area of both areas is on the order of 10 × 10 km. We fitted the PDFs
of the surface currents to the Weibull distribution and found large spatial
and seasonal variability of the Weibull distribution parameters (the shape
k and scale λ parameters) in both basins, in spite of the many
differences between the two regions. In addition, we also analyzed the
temporal asymmetry of the surface current time series and found that Nan-Wan
Bay's currents are asymmetric, while those of the Gulf of Elat are not. The
asymmetry in Nan-Wan Bay is stronger in the summer. By analyzing the
asymmetry of the tidal component of the currents, we associated the observed
asymmetry with the tides.
Many previous studies have reported on the asymmetry of tidal currents,
mainly in estuaries and coastal regions e.g.,. The tidal
asymmetry is influenced by, among other factors, the bathymetry of the basin.
The spatial differences in the asymmetry may be related to differences in the
bathymetry of the basin, to the regional variability of the flow pattern, and
to the asymmetry between flood-ebb tidal currents
; we hope to explore these possibilities
in the near future. In addition, the asymmetry of satellite-based surface
current data may be studied in the future as the temporal and spatial
resolutions of these altimetry-based data constantly increase with time. Our
results indicate large spatial variability of the statistical properties of
surface currents, even in regions of a few kilometers. Thus, regional ocean
modeling verification as well as the estimation of kinetic energy that can be
extracted using ocean currents should be performed by using a sufficiently
fine spatial resolution. In addition, the statistical characteristics of the
various regions should be used as a benchmark for model performance.