Mean sea level (MSL) is rising worldwide, and correlated changes in ocean
tides are also occurring. This combination may influence future extreme sea
levels, possibly increasing coastal inundation and nuisance flooding events
in sensitive regions. Analyses of a set of tide gauges in Hong Kong reveal
complex tidal behavior. Most prominent in the results are strong
correlations of MSL variability to tidal variability over the 31-year period
of 1986–2016; these tidal anomaly correlations (TACs) express the
sensitivity of tidal amplitudes and phases (M2, S2, K1,
O1) to MSL fluctuations and are widely observed across the Hong Kong
region. At a few important harbor locations, time series of approximations
of the parameter δ-HAT, computed from combinations of the major
tidal constituents, are found to be highly sensitive to MSL variability,
which may further increase local flood levels under future MSL rise. Other
open-water locations in Hong Kong only show TACs for some individual tidal
constituents but not for combined tidal amplitudes, suggesting that the
dynamics in enclosed harbor areas may be partially frequency dependent and
related to resonance or frictional changes. We also observe positive
correlations of the fluctuations of diurnal (D1) tides to semidiurnal (D2) tides at most locations in the region, which may lead to further
amplified tidal ranges under MSL. It is demonstrated here that tidal changes
in the Hong Kong coastal waters may be important in combination with MSL
rise in impacting future total water levels.
Introduction
Ocean tides have long been thought of as a stationary process as they are
driven by the gravitational forcing of the Sun and Moon whose motions are
complex but highly predictable (Cartwright and Tayler, 1971). Yet, long-term
changes in the tides have been observed recently on regional (Ray, 2006; Jay, 2009; Zaron and Jay, 2014; Rasheed and Chua, 2014; Feng et al.,
2015; Ross et al., 2017) and global spatial scales (Woodworth, 2010;
Müller et al., 2011; Haigh et al., 2014; Mawdsley et al., 2014),
concurrent with long-term global mean sea level (MSL) rise (Church and
White, 2006, 2011). Since gravitational changes are not the reason for this, the
tidal changes are likely related to terrestrial factors such as changes in
water depth – which can alter friction (Arbic et al., 2009), coastal morphology,
and resonance changes in harbor regions (Cartwright, 1972; Bowen and Gray,
1972; Amin, 1983; Vellinga et al., 2014; Jay et al., 2011; Chernetsky et
al., 2010; Familkhalili and Talke, 2016) – or stratification changes induced
by increased upper-ocean warming (Domingues et al., 2008; Colosi and Munk,
2006; Müller, 2012; Müller et al., 2012), all of which are also
related to sea level rise.
Tides can also exhibit short-term variability correlated to short-term
fluctuations in MSL (Devlin et al., 2014, 2017a, b). These variabilities
may influence extreme water level events, such as storm surge or nuisance
flooding (Sweet and Park, 2014; Cherqui et al., 2015; Moftakhari et al.,
2015, 2017; Ray and Foster, 2016; Buchanan et al., 2017). Such short-term
extreme events are obscured when only considering long-term linear trends.
Any significant additional shorter-term positive correlation between tides
and sea level fluctuations may amplify this variability and would imply that
flood risk based only on the superposition of present-day tides and surge
onto a higher baseline sea level will be inaccurate in many situations. The
analysis of the correlations between tides and sea level at a local or
regional scale can indicate locations where tidal evolution should be
considered a substantial complement to sea level rise. Moreover, since
storm surge is a long-wave process, factors affecting tides can also alter storm
surge (Familkhalil and Talke, 2016; Arns et al., 2017). Hong Kong is often
subject to typhoons, with some recent storms yielding anomalously high storm
surges, so this issue is of critical interest if all such factors are
undergoing change.
Recent works surveyed tidal anomaly correlations (TACs) at multiple
locations in the Pacific; a TAC quantifies the sensitivity of tides to
short-term sea level fluctuations (Devlin et al., 2014,
2017a); they found that over 90 % of tide gauges analyzed exhibited some
measure of correlation in at least one tidal component. In a related work
(Devlin et al., 2017b), the combined TACs of the four largest tidal
components was calculated as a proxy for what can be described as changes in
the highest astronomical tide (δ-HAT), with 35 % of gauges
surveyed exhibiting a sensitivity of δ-HATs to sea level
fluctuations of at least ±50 mm under a 1 m sea level change
(∼5 %). A step-by-step description of the TAC and
δ-HAT methods, including the details of the calculations of the regressions
and statistics, can be found in the supplementary materials of Devlin et al. (2017a, b), and in this paper we summarize the meaning and
interpretations of the TACs and the δ-HATs in the Appendix.
A recent paper performed a similar analysis in the Atlantic Ocean, finding
comparable results to the Pacific (Devlin et al., 2019). Comparing all
worldwide locations found that the greatest (positive) δ-HAT
response was seen in Hong Kong (+650 mm m-1). A probability
distribution function analysis revealed that an extreme sea level exceedance
which includes tidal changes can be nearly double (+150 mm) that which
only considers MSL exceedance alone (+78 mm) over the past 50 years
(Devlin et al., 2017b). However, this approach did not consider water level
extremes due to nontidal or non-MSL factors, such as storm surge, which may
further complicate extreme water levels. Yet, even without storm surge
included, it was demonstrated that the nonstationarity of tides can be a
significant contributor to total (non-storm) water levels in this region and
warrants closer examination. Furthermore, tides and storm surge are both
long-wave processes and may be sensitive to the same forcing factors, so the
behavior of tides may be a possible instructor of the future behavior of
storm surge events.
Hong Kong and Pearl River Delta (PRD) regions contain many
densely populated areas with extensive coastal infrastructure and
significant and continuous recent land reclamation projects. Sea level rise
in the region has exhibited a variable rate in the region over the past
50 years (Li and Mok, 2012; Ip and Wai, 1990) but a common feature of all sea
level records in the South China Sea (SCS) is a steep increase in the late
1990s with a subsequent decrease in the early 2000s, followed by a sustained
increase to the present day. In addition to this variable MSL behavior,
there are also anomalous tidal events observed at gauges in semi-enclosed
harbor regions during the late 1990s and early 2000s (shown and discussed
below), corresponding to times of both rapidly changing sea level and
aggressive land reclamation. In this study, we perform a spatial and
temporal analysis of tidal sensitivity to MSL variations in Hong Kong using
the tidal anomaly correlation (TAC) method at 12 closely located tide gauges.
MethodsData sources
A set of 12 tide gauge records in the Hong Kong region was provided by the
Hong Kong Observatory (HKO) and the Hong Kong Marine Department (HKMD),
spanning from 12 to 63 years in length, including two gauges that are
“historical” (i.e., no longer operational). The longest record is the
North Point/Quarry Bay tide gauge, located in Victoria Harbour, established
originally in 1952 and relocated from North Point to Quarry Bay in 1986. The
datums were adjusted and quality controlled by HKO to provide a continuous
record (Ip and Wai, 1990). Another long and continuous record is located at
Tai Po Kau inside Tolo Harbour. Gauge locations in Hong Kong are shown in
Fig. 1, with the gauges from HKO indicated by green markers, gauges from
HKMD by light blue, and historical (nonoperational) gauges by red. Four of
six of the HKO gauges (Quarry Bay, Tai Po Kau, Tsim Bei Tsui, and Waglan
Island) are sea level pressure transducer types, and the other two
(Shek Pik and Tai Miu Wan) are pneumatic-type tide gauges. The Quarry Bay
gauge was recently updated from a float-type gauge (2017), and the Tai Po
Kau gauge was also updated from a float gauge in 2006, and all gauges
operated by the HK Marine Department were set up in 2004 as sea level
pressure transducers (https://www.hko.gov.hk/publica/pubsmo.htm, last access: 1 June 2019).
Tide gauge locations in Hong Kong used in this study. Green markers
indicate active gauges provided by the Hong Kong Observatory (HKO), light
blue markers indicate gauges provided by the Hong Kong Marine Department (HKMD), and red markers indicate historical gauges (once maintained by HKO) that are no longer operational.
Figure 2 shows the geographical setting of the South China Sea, with the
location of Hong Kong indicated by the red box. Table 1 lists the metadata
for all locations, including station name and station code, latitude, etc., and the ranges of the data records used in this study.
Location of Hong Kong in the South China Sea shown by the red box
with some major oceanographic features labeled. Depth is given by the color
bar in units of meters.
Metadata for all tide gauge locations, giving the station names and
station codes, latitude/longitude, year of the available records, and
the range of data analyzed.
StationLatitudeLongitudeStartEndNumber ofyearyearyears usedQuarry Bay (QB)22.27∘ N114.21∘ E1954201631 (1986–2016)Tai Po Kau (TPK)22.42∘ N114.19∘ E1963201631 (1986–2016)Tsim Bei Tsui (TBT)22.48∘ N114.02∘ E1974201631 (1986–2016)Chi Ma Wan (CMW)22.22∘ N114.00∘ E1963199736 (1963–1997)Cheung Chau (CHC)22.19∘ N114.03∘ E2004201612 (2004–2016)Lok On Pai (LOP)22.35∘ N114.00∘ E1981199918 (1981–1999)Ma Wan (MW)22.35∘ N114.06∘ E2004201612 (2004–2016)Tai Miu Wan (TMW)22.26∘ N114.29∘ E1996201620 (1996–2016)Shek Pik (SP)22.21∘ N113.89∘ E1999201617 (1999–2016)Waglan Island (WAG)22.17∘ N114.30∘ E1995201621 (1995–2016)Ko Lau Wan (KLW)22.45∘ N114.34∘ E2004201612 (2004–2016)Kwai Chung (KC)22.31∘ N114.12∘ E2004201612 (2004–2016)Tidal admittance calculations
Our investigations of tidal behavior use a tidal admittance method. The
tidal admittance is the unitless ratio of an observed tidal constituent to
the corresponding tidal constituent in the astronomical tide-generating
force expressed as a potential, V. This potential can then be divided by the acceleration due to gravity, g, to yield Zpot(t)=V/g, with units of length that can be compared to tidal elevations, Zobs(t). Yearly harmonic analyses are performed on both Zobs(t) and Zpot(t) at each
location using the R_T_TIDE package for
MATLAB (Leffler and Jay, 2009), a robust analysis suite based on
T_TIDE (Pawlowicz et al., 2002). The tidal potential is determined
based on the methods of Cartwright and Tayler (1971).
The result from a single harmonic analysis of Zobs(t) or Zpot(t) determines an amplitude, A, and phase, θ, at the central time of the analysis window for each tidal constituent, with error estimates. A moving analysis window (e.g., at mid-year) produces an annual time series of amplitude, A(t), and phase, θ(t), with the complex amplitude, Z(t), given by
Z(t)=A(t)eiθ(t).
The tidal admittance (A) and phase lag (P) are formed using Eqs. (2) and (3)
2A(t)=absZobs(t)Zpot(t),3P(t)=θobs(t)-θpot(t).
Nodal variabilities are typically present with similar strengths in both the
observed tidal record and in the tidal potential. Therefore, when the
observed data (harmonically analyzed in 1-year windows) are divided by the
potential (also analyzed in 1-year windows), nodal effects are mostly
constrained in the resulting admittance time series. This may not always
hold true in shallow-water areas (Amin, 1983) but does seem valid for the
locations and tides analyzed in Hong Kong. The harmonic analysis procedure
also provides an annual MSL time series. For each resultant dataset (MSL, A
and P), the mean and trend are removed from the time series to allow direct
comparison of their covariability. The magnitude of the long-term trends is
typically much less than the magnitude of the short-term variability, which
is more apparent in the datasets used here (Devlin et al., 2017a, b).
Tidal sensitivity to sea level fluctuations is quantified using tidal
anomaly correlations (TACs), the relationships of detrended tidal
variability to detrended MSL variability (see Appendix). With the use of the
TACs we determine the sensitivity of the amplitude and phase of individual
constituents (M2, S2, K1, O1) to sea level perturbations
at the yearly-analyzed scale. We also consider a proxy for the change in the
approximate highest astronomical tide (δ-HAT; see Appendix for
details). The approximation δ-HAT reflects the maximum tide-related
water level that would be obtained in a year from a combination of
time-dependent amplitudes and phases of the four largest tidal constituents
(M2, S2, K1, and O1) extracted by the admittance method,
typically ∼75 % of the full tidal range.
The detrended time series of the year-to-year change in the δ-HATs
are compared to detrended yearly MSL variability in an identical manner as
the TACs, and both are expressed in units of millimeter change in tidal
amplitude per 1 m fluctuation in sea level (mm m-1). These units
are adopted for convenience, though in practice the observed fluctuations
in MSL are on the order of ∼0.25 m. The phase TACs are
reported in units of degree change per 1 m fluctuation in sea level. The
TAC methodology can also be used to examine correlations between different
parts of the tidal spectrum. We additionally examine the sensitivity of
combined diurnal (D1: K1+O1) tidal amplitudes to
semidiurnal (D2: M2+S2) tidal amplitudes (D1/D2
TACs). The units of the D1/D2 TACs are dimensionless (i.e.,
mm mm-1) and statistics are calculated as above.
The use of a window of a year in a harmonic analysis may have an influence
on the value of the TAC or δ-HAT, e.g., calendar year (January–December) vs. water year (October–September). To provide a better estimate of the overall
correlations for all data we take a set of determinations of the
correlations using 12 distinct year definitions (i.e., 1-year windows
running from January–December, February–January, …, December–January). We take the
average of the set of significant determinations (i.e., p values of <0.05) as the magnitude of the TAC or δ-HAT. For an estimate of the confidence interval of the TAC or δ-HAT, the interquartile range
(middle 50 % of the set) is used.
For the very long record stations (e.g., Quarry Bay and Tai Po Kau), we only
consider the past 31 years for TAC and δ-HAT determinations (Table 1). The TAC values may change over time so we adopt a common epoch to
better match the rest of the Hong Kong tide gauge networks, which are
typically ∼12–31 years long. Finally, we highlight some
anomalous tidal events observed at certain Hong Kong gauges and discuss the
temporal evolution of the tidal characteristics in Hong Kong.
Results
The individual TACs for amplitude and phase in Hong Kong are discussed
first, followed by the δ-HATs and the D1/D2 TACs. In all
figures, significant positive results will be reported by red markers,
significant negative results by blue markers, and insignificant values are
shown as black markers. The relative size of the markers will indicate the
relative magnitude of the TAC or δ-HAT according to the legend scale on
each plot. All numerical results for the major amplitude TACs (M2,
S2, K1, and O1) are listed in Table 2, and the δ-HATs
and D1/D2 TACs are listed in Table 3. Phase TACs of the individual
constituents are reported in Table S1 of the Supplement.
Amplitude TACs for M2, S2, K1, and O1 for the
period of 1986–2016. All values given are in units of millimeter change in
tidal amplitude for a 1 m fluctuation in sea level (mm m-1).
Statistically significant positive values are given in bold text.
StationM2 TACS2 TACK1 TACO1 TACQuarry Bay (QB)+218±37+85±16+220±15+146±11Tai Po Kau (TPK)+267±42+98±17+190±68+100±25Tsim Bei Tsui (TBT)+7±80-10±15+32±22+24±22Chi Ma Wan (CMW)-58±11-7±5-18±8-37±10Cheung Chau (CHC)-63±20-22±35+69±48+50±92Lok On Pai (LOP)-81±24-18±8+8±32-24±12Ma Wan (MW)-68±4+1±25+52±4-62±21Tai Miu Wan (TMW)+22±59-1±9+10±22+38Shek Pik (SP)+62±29+11±18+70±4+28±17Waglan Island (WAG)+1±21+3±6+9±7-9±8Ko Lau Wan (KLW)-46±39-11±17+29±65+60±57Kwai Chung (KC)-90±46-10±29-91±226-202±161
The δ-HAT and D1/D2 TACs for the period of 1986–2016. The δ-HAT values given are in units of millimeter change in tidal amplitude for a 1 m fluctuation in sea level (mm m-1).
D1/D2 TACs are in unitless ratios (i.e., mm mm-1). Statistically significant values are given in bold text.
Stationδ-HATD1/D2Quarry Bay (QB)+665±82+1.08±0.05Tai Po Kau (TPK)+612±210+1.01±0.04Tsim Bei Tsui (TBT)+56±117+0.37±0.02Chi Ma Wan (CMW)-119±19+0.74±0.19Cheung Chau (CHC)-12±42+0.81±1.03Lok On Pai (LOP)-114±45+0.26±0.05Ma Wan (MW)-91±73+0.57±1.02Tai Miu Wan (TMW)+42±100+1.04±0.20Shek Pik (SP)+138±37+0.89±0.06Waglan Island (WAG)+3±31+1.11±0.17Ko Lau Wan (KLW)-66±47+1.31±0.62Tidal anomaly correlations (TACs)
The strongest positive M2 TACs are seen at Quarry Bay (+218±37 mm m-1) and at Tai Po Kau (+267±42 mm m-1) with a smaller positive TAC seen at Shek Pik (Fig. 3). In the waters west of
Victoria Harbour, all other gauges except Kwai Chung exhibit moderate
negative TACs. The semidiurnal phase TACs in Hong Kong (shown in the
Supplement, Fig. S1) show an earlier M2 tide under
higher MSL at Quarry Bay and Tai Po Kau and a later tide west of Victoria
Harbour. The S2 results in Hong Kong (Fig. 4) show that only Quarry
Bay and Tai Po Kau have significant amplitude TAC values (though smaller
than M2) and the S2-phase TACs in Hong Kong (Fig. S2) also show
an earlier tide at Quarry Bay and Tai Po Kau under higher MSL.
Tidal anomaly correlations (TACs) of detrended M2 amplitude to
detrended MSL in Hong Kong with the marker size showing the relative
magnitude according to the legend in units of mm m-1. Red/blue markers
indicate positive/negative TACs and black markers indicate TACs which are
not significantly different from zero.
Tidal anomaly correlations (TACs) of detrended S2 amplitude to
detrended MSL in Hong Kong with the marker size showing the relative
magnitude according to the legend in units of mm m-1. Red/blue markers
indicate positive/negative TACs and black markers indicate TACs which are
not significantly different from zero.
The diurnal TACs in Hong Kong generally exhibit a larger-magnitude and more
spatially coherent response than semidiurnal TACs. Like M2, the
strongest K1 values in Hong Kong (Fig. 5) are seen at Quarry Bay (+220±15 mm m-1) and Tai Po Kau (+190±68 mm m-1). The
O1 results in Hong Kong (Fig. 6) are like the M2 results showing
positive TACs at Quarry Bay (+146±11 mm m-1) and Tai Po Kau
(+100±25 mm m-1) and strongly negative TACs west of Quarry
Bay. However, unlike the semidiurnal constituents, the phase TACs for K1 are mostly insignificant in Hong Kong (Fig. S3) and O1 phase
TACs (Fig. S4) are only significant at Quarry Bay.
Tidal anomaly correlations (TACs) of detrended K1 amplitude to
detrended MSL in Hong Kong with the marker size showing the relative
magnitude according to the legend in units of mm m-1. Red/blue markers
indicate positive/negative TACs and black markers indicate TACs which are
not significantly different from zero.
Tidal anomaly correlations (TACs) of detrended O1 amplitude to
detrended MSL in Hong Kong with the marker size showing the relative
magnitude according to the legend in units of mm m-1. Red/blue markers
indicate positive/negative TACs and black markers indicate TACs which are
not significantly different from zero.
Combined tidal variability (δ-HATs) and tidal covariability
The TACs are widely observed in Hong Kong but the δ-HATs are
only of significance at particular locations (Fig. 7). Five stations
exhibit significant δ-HAT values with Quarry Bay and Tai Po Kau
having very large positive magnitudes (+665±85 mm m-1 and
+612±210 mm m-1, respectively) and Shek Pik having a lesser
magnitude of +138±47 mm m-1. Conversely, Ma Wan and Chi Ma
Wan exhibit moderate negative δ-HAT values (∼-100 mm m-1). The remainder of gauges (which are mainly open-water locations)
have statistically insignificant results for the combined tidal amplitudes,
even where some large individual TACs were observed. This shows that the
combined tidal amplitude effect as expressed by the δ-HATs is most
important in semi-enclosed harbors. The D1/D2 TACs are also
important in Hong Kong and are seen at almost every location. All
significant D1/D2 TACs results are positive (Fig. 8) and at
most locations the correspondence is nearly 1 to 1, indicating that a change
in D1 can yield a nearly identical magnitude change in D2, and
vice versa. Smaller magnitude relations are seen in the western areas of the
Hong Kong region.
The tidal anomaly correlation computed from the combination of the
four largest tidal constituent amplitudes (given by the detrended sum of
M2+S2+K1+O1) as a proxy for the change in the approximate highest astronomical tide (δ-HAT) relative to detrended MSL in Hong Kong with the marker size showing the relative magnitude according to the legend in units of mm m-1. Red/blue markers indicate positive/negative TACs and black markers indicate TACs which are not significantly different from zero.
The D1/D2 TACs; the relations of detrended diurnal tidal amplitude sum
(D1: K1+O1) to detrended semidiurnal tidal amplitude sum (D2: M2+S2) in Hong Kong with the marker size showing the relative magnitude according to the legend in dimensionless units.
Red/blue markers indicate positive/negative TACs and black markers indicate
TACs which are not significantly different from zero.
Anomalous tidal events at Hong Kong harbor locations
The overall temporal behavior of the tidal spectrum at enclosed harbor
locations in Hong Kong (Quarry Bay and Tai Po Kau) is especially
interesting. In Fig. 9, the time series of water level spectrum components
are shown for Quarry Bay and Tai Po Kau, presenting the D1 (K1+O1) band (Fig. 9a), the D2 (M2+S2) band (Fig. 9b), and mean sea
level (MSL) (Fig. 9c), given as normalized amplitudes with mean values shown in
the legends. The magnitude of MSL is given in relation to the Hong Kong
Chart Datum as defined by the Hong Kong Observatory. The Chart Datum is
defined as 0.146 m below the Hong Kong Principal Datum (HKPD). The HKPD
determined for the years 1965–1983 was approximately 1.23 m below MSL. The
HKPD has been recently redetermined using data from 1997–2015 to be 1.30 m
below MSL. Therefore, all MSL values reported here are given relative to the
HKPD for the epoch 1965–1985 (https://www.hko.gov.hk/contente.htm, last access: 1 March 2019).
Time series of water level spectrum components at Quarry Bay
(QB; blue) and Tai Po Kau (TPK; red) tide gauges in Hong Kong, showing the
D1 band (a), the D2 band (b), and mean sea level (MSL) (c). Components are plotted as a function of normalized amplitudes to show relative variability with mean values given in the legend.
Some very notable features of the tides are clear. At Quarry Bay, the early
part of the record shows nearly constant tidal amplitudes in D1, while
D2 amplitudes show a slight decrease, and MSL exhibits a slight
positive trend. In the late 1980s, however, both D1 and D2 increase until around the year 2003 at which time both tidal bands undergo
a rapid decrease in amplitude of ∼15 %, sustaining this
diminished magnitude for about 5 years before increasing nearly as
rapidly. The MSL record is also highly variable at Quarry Bay, with a nearly
zero trend during the increase in tides seen in the 1980s followed by a
strong increase from ∼1993–2000, and then a steep decrease
concurrent with the time of diminished tides before increasing again. The
gauge at Tai Po Kau shows a similar tidal behavior, although the timing and
magnitudes are different. The increase in D1 and D2 at Tai Po Kau
in the 1980s is much larger and peaks earlier than Quarry Bay, reaching a
maximum around 1996, and then decreasing around 1998, about 5 years
before the drop at Quarry Bay. Both locations experience an absolute minimum
around 2007 in D2 but the D1 minimum at TPK leads the Quarry Bay
minimum by a few years. These observed anomalies are only observed at these
two gauges; other locations in Hong Kong did not reveal similar behavior.
DiscussionSummary of observed tidal variability
This survey has identified several types of tidal variability in Hong Kong.
The individual TACs are significant at many Hong Kong locations, while the
TACs of the approximate δ-HATs appear to be more locally important,
as the strongest responses are mainly concentrated at specific locations
(e.g., Quarry Bay and Tai Po Kau). The M2 response (Fig. 3) is negative
at gauges just west of Quarry Bay and positive at Shek Pik, with a similar
pattern seen for the O1 TACs (Fig. 6). Conversely, the K1 TAC
results are generally positive (Fig. 5). At both Quarry Bay and Tai Po Kau,
the positive reinforcements of individual tidal fluctuations lead to very
large δ-HATs, though moderately negative δ-HATs are seen
near Quarry Bay at Chi Ma Wan and Ma Wan (Fig. 7). The spatial similarity in
the semi-enclosed center harbor regions suggest a connected mechanism; this
area is where most recent Hong Kong coastal reclamation projects have
occurred, including the construction of a new island for an airport,
shipping channel deepening, and other coastal morphology changes. Such
changes in water depth and coastal geometry strongly suggest a relation to
frictional or resonance mechanisms.
The D1/D2 TAC relations (Fig. 8) are a more regionally relevant
phenomenon, being significant nearly everywhere in Hong Kong. The majority
of significant D1/D2 TACs are positive with most being nearly
1 to 1 (i.e., a ∼1 mm change in D1 will yield a
∼1 mm change in D2), confirmed by the close similarity
of temporal tidal trends of the D1 and D2 tidal bands in Hong Kong
(Fig. 9). This aspect of tidal variability in Hong Kong may be related to the
dynamics near the Luzon Strait, where large amounts of baroclinic conversion
in both D1 and D2 tides may tend to couple the variabilities (Jan
et al., 2007, 2008; Lien et al., 2015; Xie et al., 2008, 2011, 2013). The
D1 and D2 internal tides may interact with each other as well as
with processes at other frequencies, such as at the local inertial
frequency, f, via parametric subharmonic instability (PSI) interactions
(McComas and Bretherton, 1977; MacKinnon and Winters, 2005; Alford, 2008;
Chinn et al., 2012), a form of resonant triad interactions (Craik, 1985).
The low-mode baroclinic energy can travel great distances, being enhanced
upon arrival at the shelf and leading to the further generation of
baroclinic energy. In the western part of Hong Kong, the D1/D2
relationships are less than 1 to 1 (∼0.33 to ∼0.25 at TBT and LOP, respectively). This may be partially influenced by
effects of the Pearl River, which discharges part of its flow along the
Lantau Channel. The flow of the river is highly seasonal and ejects a
freshwater plume at every ebb tide that varies with prevailing wind
conditions and with the spring–neap cycle (Pan et al., 2014). The plumes may
affect turbulence and mixing in the region and can dissipate tidal energy,
which may “decouple” the correlated response of D1 and D2 seen
in the rest of the Hong Kong coastal waters.
Effects of local dynamics on tidal variability
Hong Kong has had a long history of land reclamation to accommodate an
ever-growing infrastructure and population, including the building of a new
airport island (Chep Lap Kok); new land connections, channel deepening to
accommodate container terminals; and many bridges, tunnels, and “new
cities” built on reclaimed land. All of these may have changed the
resonance and/or frictional properties of the region. Tai Po Kau has also
had some land reclamation projects that have changed the coastal morphology
and may have modulated the tidal response. Both locations also show coherent
D1/D2 TACs, as well as having the largest positive δ-HATs,
and large tidal anomalies (Fig. 9). Other locations in Hong Kong did not
show such extreme variations so these variations appear to only be
amplified in harbor areas. Decreases in friction associated with sea level
rise may lead to larger tides and those changes may also be amplified by
the close correlations of D1 and D2 variability or local harbor
development, which may further decrease local friction. Hence, a small change
in friction due to a small sea level change may induce a significant change
in tidal constituents. The positive reinforcement of multiple tidal
constituent correlated with regional sea level adjustments may amplify the
risks of coastal inundation and coastal flooding, as evidenced by the gauges
that had the largest δ-HAT values.
Limitations of this study and future steps
The analysis of tides in the Hong Kong tide gauge network revealed new
dynamics and spatial connections in the area. However, some records are of
shorter length and/or have many gaps, making a full analysis of the area
problematic. For example, the Tsim Bei Tsui gauge covers a long period but
there are significant gaps in the record, which complicated our analysis.
This gauge is located within a harbor region (Deep Bay, bordered to the
north by Shenzhen, PRC, which has also grown and developed its coastal
infrastructure in past decades; therefore, one might expect similar dynamics
as was seen at Quarry Bay and Tai Po Kau. While there were moderately
significant D1/D2 correlations at Tsim Bei Tsui, no significant
TACs or δ-HATs were observed. The large anomalies seen at Quarry Bay
and Tai Po Kau around 2000 are suggested by the data at Tsim Bei Tsui but
some data are missing around this time, making any conclusions speculative.
The Deep Bay region is ecologically sensitive, being populated by extensive
mangrove forests which may be disturbed by rapidly changing sea levels
(Zhang et al., 2018), so accurate determination of future sea levels is of
utmost importance to the vitality of these important ecosystems. Future
studies considering highly accurate digital elevation models will employ
simple analytical models as well as high-resolution three-dimensional
numerical ocean models to simulate the changing impacts on coastlines under
a variety of sea level, tidal forcing, and anthropogenic change scenarios
(historical and future) to better understand the tidal dynamics in Hong
Kong, and to try to separate the relative importance of local and regional
effects. Lastly, we briefly mention the instrumental changes at two of the
HKO gauges. The Quarry Bay gauge was recently updated from a float-type gauge (2017) and the Tai Po Kau gauge was also updated from a float
gauge in 2006. Neither of these times correspond to any obvious anomalies in
the tidal admittance records (the large changes at Tai Po Kau predate this
by a few years at least, and are consistent before and after the gauge
change) so we conclude that the instrumental changes were not a factor in
the observed variability.
Conclusions
This study has presented new information about the tidal variability in Hong
Kong, based on observations of a set of closely located tide gauges in Hong
Kong. The TACs, D1/D2 relations, δ-HATs, and the anomalous
events in tidal amplitudes seen at the Quarry Bay and Tai Po Kau gauges show
an amplified tidal response to MSL fluctuations in these harbor regions as
opposed to more open-water locations, where individual TACs were sometimes
significant but the δ-HAT changes were less significant. The reason
for the observed behavior may be due to changing friction or resonance
induced by coastal engineering projects that are only significant at highly
local (i.e., individual harbor) scales. Alternatively, the observed behavior
could be related to regional South China Sea changes due to climate change
(such as increased upper-ocean warming and/or regional stratification and
internal tide generation). It is difficult to separate the local engineering
changes from regional climatic changes without closer investigations.
However, even without exact knowledge of the relevant mechanisms, these
anomalies do suggest that a pronounced change in tidal properties occurred
around the year 2000 in Hong Kong, with the effect being most pronounced at
gauges in semi-enclosed harbors. Overall, the tidal variability in Hong Kong
documented here may have significant impacts on the future of extreme sea
level in the region, especially if the strong positive reinforcements hold
or increase in coming decades. Short-term inundation events, such as
nuisance flooding, may be amplified under scenarios of higher sea levels
that lead to corresponding changes in the tides, which may amplify small
changes in water levels and/or reductions in friction due to harbor
improvements. The δ-HAT and D1/D2 TAC results illustrate
that the tidal variability in multiple constituents may be additive and may
reinforce MSL changes at some locations, which may further aggravate coastal
flooding under MSL future rise. Since tides and storm surge are both
long-wave processes, the locations of strong tidal response may also
experience an exaggerated storm surge in the near future.
Code availability
All code employed in this study was developed using
MATLAB, version R2011B. All code and methods can be provided upon request.
Data availability
The data used in this study from the Hong Kong Observatory
(HKO; http://www.hko.gov.hk, last access: 1 June 2019) and the Hong Kong Marine
Department (HKMD; http://www.mardep.gov.hk/en/home.html, last access: 1 June 2019) were
provided upon request, with discussion of intentions of use, and with permission from
the appropriate agency supervisors. Data used from the University of Hawaii
Sea Level Center (UHSLC; http://www.uhslc.soest.hawaii.edu, last access: 1 June 2019) are publicly available.
Tidal admittances are constructed as described above, employing the use of
the tidal potential and Eqs. (2) and (3) to constrain the nodal variation
present in the observed tidal amplitudes and phases. Our primary interest in
this paper is the interannual to decadal variations and not the long-term
trends in mean values. Therefore, we first remove the long-term trends and
mean values using the MATLAB “detrend” function. The detrended time series
of residual variations in A and P, and the residual variations in MSL, can
now be examined for coherence, using scatter plots, cross correlations, and
regression statistics. We define the tidal anomaly correlation (TAC) as the
slope between detrended tidal properties (amplitude and phase) and detrended
MSL, expressed as the millimeter change in tidal amplitude per meter of sea
level rise (mm m-1). The same approach is used with the phase
difference time series to provide phase anomaly trends, with the trends
expressed as degree change in tidal phase per meter of sea level rise (deg m-1). The errors of the TAC determinations are defined as the 95 %
confidence interval (CI) of the linear trend determination. Trends are
deemed significant if the signal-to-noise ratio (SNR) of the linear trend to
the associated error is greater than 2.0.
Approximate change in the highest astronomical tide (δ-HAT)
We also construct a proxy quantity as an approximate change in the
highest astronomical tide (δ-HAT) using an extension of the TAC
method. To do this, we combine the tidal admittance amplitudes of the
(typically) four largest astronomical tides (M2, S2, K1, and
O1) then detrend the resultant combined time series as above. Next, we
perform a similar scatter plot and regression approach against the detrended
MSL time series as was done with the TACs. The benefit of this approach is
to give a clear picture of the overall changes in tides related to sea level
changes. Some locations may show that the variability in multiple tidal
constituents partially cancel each other (e.g., semidiurnal tides may
have a large positive tendency compared to MSL variability while diurnal
tides may have a large negative tendency, resulting in an offsetting of
variabilities under MSL changes, and a smaller overall magnitude
δ-HAT), while other locations may show a reinforced variability (e.g.,
both diurnal and semidiurnal tides have positive tendencies compared to MSL
changes, resulting in an amplified δ-HAT). Thus, the accurate
interpretation of the δ-HAT is that it reflects the maximum
tide-related water level that would be obtained in a given analysis period
(here, 1 year) from a chosen set of time-dependent amplitudes extracted
from the admittance method.
Two details about the δ-HAT parameter should be noted here. First,
only the amplitude of the tidal admittance can be combined in this manner,
as combining the phase variability in multiple frequencies may be inaccurate
at worst and at best is not very helpful. Second, we acknowledge that the
use of the term “δ-HAT” may be somewhat confusing as previous
literature about tidal analysis uses the term “Highest Astronomical Tide” (HAT) to denote the highest water level that can be expected to occur under
average meteorological conditions due purely to astronomical forcing in a
given epoch. This typical period is 19 years, which considers the full nodal
cycle. This definition of HAT does not reflect the highest possible water level at a
given location, since storm surge or other non-average meteorological
conditions may amplify water levels far above this level on a shorter timescale than a 19-year determination can reveal. The intention behind our
chosen nomenclature of the “approximate change in the highest astronomical
tide” (δ-HAT) attempts to expand on this concept by considering the
full tidal variability (not strictly true since the four largest tides are
only about 75 % of the full tidal range but these tidal components are
nearly always stable in 1-year analyses, so it is a dependable and easily
comparable metric) at timescales shorter than a nodal period
(∼19 years), but longer than a storm surge (∼2–5 d) or other meteorological anomalies. Furthermore, our interest is
the changes in tidal components that is not due to astronomy or to
meteorology. Rather, we show possible changes to tide-related water level
modifications due to MSL modifications, which may be important on seasonal
to decadal timescales, induced by mechanisms associated with global climate
change (e.g., steric sea level rise due to ice melt, thermal sea level rise
due to upper-ocean warming) or to more local effects (such as rapid harbor
modifications or land reclamation that adjusts tidal resonance at a
particular location).
The changes shown by the δ-HATs are important to consider since a
full understanding of the changes in all components and timescales of the
tides may better instruct future coastal planning and engineering. The
δ-HAT method used here can give important information about possible
future water level inundation in coastal locations that are not
storm related, such as nuisance flooding (or sometimes called “sunny day
flooding”). These may be obscured by longer-term analyses of the classical
HAT (i.e., 19 years) if changes are more rapid (i.e., year to year or
season to season). However, it should also be reiterated that a good
understanding of changes in tides due to changing background water levels
may also be instructive for future storm-surge-related inundation at a
location; both tides and storms are long-wave processes so changes in one
aspect of water level variability (i.e., a large positive δ-HAT) may
also indicate future increase in storm surge levels at the same location.
The supplement related to this article is available online at: https://doi.org/10.5194/os-15-853-2019-supplement.
Author contributions
ATD worked on all analyses, figures, tables, the majority of
writing, and complied the paper. JP provided editing, insight,
guidance, and direction to this study. HL provided critical insight and
helpful input.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
This work is supported by The National Basic Research
Program of China (2015CB954103), the National Natural Science Foundation of
China (project 41376035), the General Research Fund of Hong Kong Research
Grants Council (RGC) (CUHK 14303818), and the talent startup fund of Jiangxi
Normal University. The authors also thank the Hong Kong Observatory. In
addition to sharing their data archive, they were also a part of the
discussions that led to this paper.
Review statement
This paper was edited by John M. Huthnance and reviewed by two anonymous referees.
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