Statistical Modeling and Trend Detection of Extreme Sea Level Records in the Pearl River Estuary

Sea level rise has become an important issue in studies of global climate change. The Fifth Assessment Report of the IPCC noted that the mean rate of global average sea level rise was 1.7 0.2 mm yr^-1 between 1901 and 2010, 2.0 0.3 mm yr^-1 between 1971 and 2010, and even higher after 1993 (IPCC, 2013). The Pearl River Delta is an urban agglomeration with an extremely high population density and a fast-growing economy, and its location on the coast of China makes it vulnerable to sea level rise and extreme climate. In Hong Kong and Macau, for example, many coastal building lots originated from land reclamations after the 1910s, with flat terrain and very low elevations inside the dykes (Nissim, 2012). At the same time, the Pearl River Delta is in the sphere of influence of South China Sea and western North Pacific typhoons. As extreme meteorological and environmental phenomena, typhoons and storm surges have attracted considerable attention locally (e.g., Wang et al., 2012; Feng et al., 2013).

There is a long tradition of using extreme value theory (EVT) in studies of climate extremes. In earlier decades, a generalized extreme value distribution was applied in statistical modeling of the so-called "block maxima" of climate series, such as the annual maximum temperature or daily precipitation (Gumbel, 1958), which is still widely used today in estimating return levels of extreme events (e.g., Zhou et al., 2009). Later, the peaks-over-threshold model was developed to model all exceedances above a specific high threshold (Coles, 2001; Katz et al., 2005). Meanwhile, time-dependent trends of extreme events can be introduced by parametric changes in nonstationary EVT models (Nogaj et al., 2006; Brown et al., 2008; Ding et al., 2011; Wang et al., 2015a, 2015b). Ordinary parametric trend estimation methods, such as least-squares regression, are not recommended for extreme events, mainly because they require the time series to be normally distributed, which is likely to be violated for extreme events (Qian et al., 2015). Therefore, nonparametric trend detection methods, such as the nonparametric Mann-Kendall test (Mann, 1945; Kendall, 1975), which require only that the data be independent, are widely used. However, if the distributional assumptions——the generalized Pareto (GP) distribution, for example——are fulfilled, parametric tests are suggested to be the most powerful for extreme-value data (Zhang et al., 2004; Zhai et al., 2005; Madsen et al., 2014).

The historical mean sea level (MSL) changes in Macau and adjacent waters were evaluated in a recent study (Wang et al., 2016a, b). But rising sea level and coastal storm surges are two different phenomena with significant impacts on natural systems and human society (Park et al., 2011). Therefore, there is a need to detect historical changes in extreme sea level records. Whether or not the intensity and frequency of these extremes are amplified against the background of global sea level rise, for instance, is a noteworthy question (Meehl et al., 2000; Goddard et al., 2015; Wahl and Chambers, 2015). This paper applies the peaks-over-threshold model of EVT to statistically model and estimate secular parametric trends of extreme sea level records in the Pearl River Estuary (PRE), which, to the best of the authors' knowledge, has not been attempted previously.

Macau and Hong Kong are located on two sides of the PRE, which makes their tide gauge stations representative for describing sea level change in the estuary (Fig. 1). Three data sources of tide gauge measurements are included in this study. First, tidal data in Macau, spanning from 1 January 1925 to 31 December 2010, are provided by the Macao Meteorological and Geophysical Bureau (http://www.smg.gov.mo/smg/c_index.htm). For analysis of extremes in sea level, the daily parameter higher high water (HHW) height is utilized; while for analysis of extremes in tidal residuals, hourly records are utilized. Second, daily records of Hong Kong data can be freely downloaded from the Hong Kong Observatory website (http://www.hko.gov.hk/cis/dailyTide_e.htm?stn=QUB), including daily MSL and HHW. MSL data during 1 January 1954 to 31 December 2014 at Hong Kong station are utilized; while for HHW at this site, data after 1 January 1965 are used, as there are many missing values before this time. Third, hourly data from Hong Kong spanning from 1 January 1962 to 31 December 2014 are obtained from the University of Hawaii Sea Level Center (http://uhslc.soest.hawaii.edu/data/?rq#uh635a).

Figure 1.  Land-sea contrast map of the PRE and the locations of Macau (Porto Interior) and Hong Kong (Quarry Bay) tide gauge stations.

During their operational periods, the Macau and Hong Kong tide gauge stations have been relocated twice and once, respectively. Details, including tide gauge station names, locations, and operating periods, are listed in Table 1. Figure 1 provides their latest locations. The Macao Meteorological and Geophysical Bureau has been responsible for homogenization of the time series. The Hong Kong data are a combination of the North Point and the Quarry Bay records. (Ding et al., 2001) assumed an offset of 1.02 cm. However, we decided not to adopt this assumption, for two reasons. First, it is still subject to debate. This offset was not accepted in another study (Wong et al., 2003), who suggested that the tide gauge data from the two stations should be regarded as belonging to the same series. Second, (Ding et al., 2001) also noted an offset of 13.87 cm in 1957, and the fact that this regime shift may actually exist implies that their method of determining offsets may be questionable. Figure 2 provides a comparison of annual MSL at Macau and Hong Kong. An obvious decadal high MSL appears around the 1950s at Macau. More importantly, the global MSL also experienced a similar regime shift from the 1950s to the early 1970s (Wang et al., 2016a).

Figure 2.  Annual MSL rise: the observed increasing trend of MSL in Macau (Hong Kong) during 1925-2010 (1954-2014) is 1.3 mm yr^-1 (1.4 mm yr^-1).

Figure 3.  Computed 18.6-year nodal modulations (rate f multiplies corresponding mean tidal amplitude) to the hourly tidal series of Hong Kong. The red, blue, green and purple lines denote the O₁, K₁, M₂ and K₂ tidal constituents, respectively, while the dashed black line represents the sum.

Settlement monitoring of tide gauge stations at Hong Kong has been conducted by the Civil Engineering Department of Hong Kong since 1954, and the tide gauge data have been adjusted for the effect of settlement by the Hong Kong Observatory according to the leveling measurements (Ding et al., 2001; Wong et al., 2003). Unfortunately, there is no such monitoring and adjustment at Macau. However, there is an alternative approach to recovering vertical land movement. As absolute sea level can be measured by satellite altimetry, vertical land movement can be derived from the difference between altimetry and tide gauge data. This method has been widely used in previous studies (e.g., Ray et al., 2010). Appling this method to compare satellite altimetry data and the Macau tide gauge measurements, (Wang et al., 2016c) estimated that the rate of vertical land movement at Macau is -0.153 mm yr^-1, accumulating only 1.53 cm of subsidence over a span of one century; they therefore concluded that Macau has virtually no vertical motion.

Quality control involved visual checks of the hourly and daily values, month by month, of both the original gauge records and the computed tidal residuals. Values with spurious jumps and time shifts were removed. Tidal constituents were estimated year by year using the MATLAB t-tide package developed by (Pawlowicz et al., 2002). This software package makes use of classical harmonic analysis for tidal records of not more than one year, with allowance for satellite corrections. Tidal predictions based on the estimated tidal constituents were produced and subtracted from the tide gauge records, thereby creating tidal residuals.

It has long been recognized that the 18.6-year nodal tidal cycle has significant effects on long-term sea level changes (Kaye and Stuckey, 1973; Gratiot et al., 2008). The satellite correction function of the t-tide package was not used in this study. Instead, the 18.6-year nodal modulations to tidal constituents should be estimated directly (Foreman and Neufeld, 1991), as we have time series longer than 18.6 years. The ratio f between the nodal amplitude and its corresponding mean amplitude can be estimated by the equilibrium equation of nodal amplitude modulation given (Pugh, 1996). Based on the results of year-by-year tidal constituent estimation and recommendations in previous studies (Shaw and Tsimplis, 2010; Liu et al., 2015), nodal modulations of four tidal constituents, two diurnal (O₁ and K₁) and two semi-diurnal (M₂ and K₂), were taken into consideration in this procedure. Constant parameters of the equilibrium equation of the chosen tidal constituents are given in Table 2, which is modified from Table 4:3 of (Pugh, 1996). Mean amplitudes of the four chosen tidal constituents at Macau and Hong Kong are listed as well. The computed 18.6-year nodal modulations to the hourly tidal series of Hong Kong are shown in Fig. 3. The situation at Macau is similar and is not shown. Serial correlations (autocorrelations) of detrended annual mean tidal residuals are demonstrated (Fig. 4). The influence of the 18.6-year nodal cycle appears as a strong negative correlation at around 9 years' lag, and positive correlation at one full cycle away, in both Macau and Hong Kong, provided that residuals are extracted from tides with nodal modulations. Finally, statistical models based on EVT, which will be introduced in the next section, were applied to the sea level records and tidal residuals with and without accounting for the 18.6-year nodal modulation, respectively.

Figure 4.  Serial correlations (autocorrelations) of detrended annual mean tidal residuals for (a) Macau before the 18.6-year nodal modulation, (b) Macau after the 18.6-year nodal modulation, (c) Hong Kong before the 18.6-year nodal modulation, and (d) Hong Kong after the 18.6-year nodal modulation. The sample autocorrelation function (ACF) was calculated and plotted by the MATLAB function "autocorr". Two lags were assumed, beyond which the theoretical ACF is effectively 0. The blue horizontal lines indicate two standard deviations, i.e., the 95% confidence interval, approximately.

In this study, the peaks-over-threshold model is applied to model extreme sea level records in Macau and Hong Kong. The annual frequency of extreme HHW records exceeding a high threshold is modeled by a Poisson distribution, and its intensity (the HHW height amount that is above the threshold for defining an extreme event) is modeled by a GP distribution. The method based on EVT is the same as that employed by (Wang et al., 2015a) and (Wang et al., 2016b) in their study of climatic extremes, from which the following text is derived with minor modifications.

The probability mass function of the Poisson distribution is given by \begin{equation} P(k)=\dfrac{\lambda^k e^{-\lambda}}{k!} ,k=0,1,2,\cdots, (1)\end{equation} where Λ is the Poisson parameter, and k is the number of events in a given year. A GP distribution is given by \begin{equation} F(x;\xi,\sigma_u,u)=1-\left[1+\xi\dfrac{x-u}{\sigma_u}\right]^{-1/\xi},x>u,1+\xi\dfrac{x-u}{\sigma_u}>0 , (2)\end{equation} where \(\xi\) stands for the shape parameter, and σ_u>0 denotes the scale parameter depending on the selected threshold u. A geometric distribution that can model the duration of an extreme event is given by \begin{equation} G(k)=(1-p)^{k-1}p ,k=1,2,\cdots,(3) \end{equation} with the reciprocal of the parameter p being the mean. Parameter estimation in the peaks-over-threshold model is done by maximum likelihood methods.

If all records in the observed period are fitted into the above distributions, this is the stationary model. To allow for estimating trends in extreme sea level characteristics, the peaks-over-threshold model has to be extended to be nonstationary. Parameters of the aforementioned distributions within a given year are fixed, but shift from one year to the next. Mathematically, for each year x in the record period, the Poisson parameter is given as Λ=Λ(x), the GP scale parameter is given as σ_u=σ_u(x), and the geometric parameter is given as p=p(x). The shape parameter of the GP distribution is kept fixed, since changes in this parameter are rarely observed and difficult to model (Wang et al., 2015a). For the geometric model, trends are obtained through a generalized linear model (GLM) framework. In the Poisson-GP model, trends are introduced through a GLM framework in the Poisson model and through covariate effects in the GP scale parameter. P-values of the likelihood ratio test are used to indicate significant trends below a certain level, usually taken as 5% (Furrer et al., 2010).

A covariate means that the extreme behavior of one series is related to that of another. Specifically, series σ_u(x) is related to Λ(x) in the nonstationary Poisson-GP model. Using the notation \(\rm GP(\xi,\sigma_u)\) to denote the GP distribution, the severity (the magnitude of the excess over the threshold) of an extreme event is given as \begin{equation} Z_t\sim{\rm GP}[\xi,\sigma_u(t)] ,(4) \end{equation} where \begin{equation} \sigma_u(t)=\beta_0+\beta_1\lambda(t) ,(5) \end{equation} in which Λ(t) denotes the Poisson parameter (the annual exceedances of extreme sea level records) in year t. While β₀ and β₁ are parameters for a linear model, presented as an example here. There is a unity structure of extreme value parameters that can be written in the form \begin{equation} \theta(t)=h({X}^{\rm T}{\beta}) , (6)\end{equation} where θ denotes an extreme value parameter (either the Poisson parameter Λ or the geometric parameter p in this study), β is a vector of the parameters, X is a model vector, and h is usually referred to as the inverse-link function. There is a similarity between the class of model implied by Eq. (6) and the conventional GLM. The main difference is that the conventional GLM family is restricted to distributions that are within the exponential family of distributions, while the standard extreme value models generally fall outside of this family. More details regarding this GLM framework can be found in Chapter 6 of (Coles, 2001).

Historical records of Hong Kong's Tropical Cyclone Warning Signals in recent decades are used to identify changes in tropical cyclones that influence the PRE. There are five basic signals, from low-level to high-level, Nos. 1, 3, 8, 9 and 10. The lowest signal, No. 1, means "A tropical cyclone is centered within about 800 km of Hong Kong and may affect the territory". Signal No. 8 means "Gale or storm force wind is expected or blowing generally in Hong Kong near sea level, with a sustained wind speed of 63-117 km h^-1 from the quarter indicated. Gusts may exceed 180 km h^-1, and the wind condition is expected to persist". The tropical cyclone plotting map and detailed meanings of all signals can be found in a pamphlet published by the (Hong Kong Observatory, 2012). Two involved parameters——total tropical cyclone warning hours and frequency of high-level (No. 8 and above) warning signals——are freely available from http://gb.weather.gov.hk/informtc/historical_tc/fttcwc.htm.

Before defining and modeling extreme sea levels, the linear trends of annual MSL in the PRE are estimated by least-squares regression. The annual MSL is simply averaged from daily MSL records. The Kolmogorov-Smirnov (KS) test (Massey, 1951; Lilliefors, 1967), as well as the Anderson-Darling (AD) test (Anderson and Darling, 1952; Stephens, 1974), supports the fulfillment of the normal distribution assumption for the series in both Macau and Hong Kong. We therefore estimate the linear trend using an ordinary least-squares regression. The results are shown in Fig. 2, which presents increasing trends for both tide gauge sites. The increasing trends in Macau and Hong Kong are 1.3 mm yr^-1 and 1.4 mm yr^-1, respectively. Both are statistically significant at the 0.01 significance level.

To quantify past changes and project future impacts of climate extremes, accurate definitions are important (Qian et al., 2011; Yan et al., 2011; Wang et al., 2016c). Choosing a threshold based on EVT, we have to strike a balance between a relatively high threshold so that Eq. (2) of the GP distribution is not violated, and a relatively low threshold so that we can have enough samples of extremes to be modelled (Li et al., 2005). Here, we utilize the parameter stability plot proposed by (Coles, 2001) to choose the threshold. The parameter stability plot involves plotting the parameter estimates from the GP distribution against a range of values of threshold u. According to (Coles, 2001), if a GP distribution is a reasonable model for excesses of a threshold u₀, then excesses of a higher threshold u should also follow a GP distribution. Consequently, estimates of the GP shape parameter \(\xi\) and scale parameter σ_u should be stable (constant) above the u₀ at which the GP model becomes valid. Sampling variability means that the estimates of these quantities will not be exactly constant, but they should be stable after allowance for their sampling errors. In practice, the scale parameter has to be modified to make it independent from the threshold during this process. Before plotting the parameter stability plot, the range of thresholds to be tested, i.e., the x-axis of Fig. 5, is roughly determined by the mean, the maxima, the standard deviation, and some typical percentiles calculated from the raw records at each tide gauge station.

Figure 5.  Parameter stability plots for choosing thresholds for extremes in original sea level records. Modified parameter σ_u and shape parameter \(\xi\) estimates (error bars: confidence intervals) against threshold values for (a, b) Macau and (c, d) Hong Kong.

Figure 5 then further narrows down the range for threshold choices. From this figure, we can conclude that the range for Macau is 3.30-3.40 m, and for Hong Kong it is 2.75-2.85 m, where both stable modified scale and shape parameters can be observed. Finally, sensitivity tests of every threshold between these ranges are conducted. The test interval is 0.01 m, which is also the effective value of tide gauge measurements. The test tool is the function gpd.fit and gpd.diag in the R-package "ismev" (Heffernan et al., 2009), which provides functions to support the computations carried out by (Coles, 2001). These functions revisit the goodness-of-fit of the GP model. A threshold of 3.36 m for Macau and 2.84 m for Hong Kong, respectively, can be chosen through these sensitivity tests (figures not shown). Similar procedures are applied to the tidal residuals and the chosen thresholds are 3.18 for Macau and 2.56 for Hong Kong. The same thresholds are adopted for residuals before and after the 18.6-year nodal modulation (Table 3).

Once the thresholds are chosen, the intensity and frequency of extreme sea level records can be computed. Fitting parameters of the peaks-over-threshold model can be obtained by maximum likelihood estimations (Table 3). This is the stationary model, by which realistic modeling can be recommended for daily HHW records at both Macau and Hong Kong (Fig. 6). It is usually more convenient to interpret extreme value models in terms of quantiles and return levels. Both the quantile plots and return level plots suggest that the fitting of the GP model is convincing. Meanwhile, the return levels and corresponding return periods predicted by the GP model can provide practical references for risk assessment. Some typical values for Macau and Hong Kong are listed in Table 4.

Figure 6.  (a) Quantile plot and (b) return level plot for the GP distribution fitted to original sea level records in Macau. (c) Frequency of extremes in original sea level records in Macau fitted to the Poisson distribution. (d-f) As in (a-c), but for records in Hong Kong.

The chosen thresholds are relatively high, so that Eq. (2) is not violated. The threshold of 3.36 m for Macau is the 99.65th percentile of 30 258 HHW observations with missing values excluded. A total of 99 extreme records are obtained, with an expectation of 1.15 records per year, which is also the Poisson parameter Λ (Table 3). In Fig. 6c, the observations (circles) show a maximum of five occurrences per year, and zero time per year has the maximum probability. However, the Poisson model (red line) predicts a maximum probability of one occurrence per year. We learned from the sensitivity tests described above that to make the predicted occurrence of maximum probability agree with observations, a higher threshold, which can result in Λ being smaller than 1, is needed. However, at the same time this will result in some loss of extreme samples for modeling. The situation in Hong Kong is similar to that in Macau. The threshold of 2.84 m for Hong Kong is the 99.5th percentile of 17 874 HHW observations with missing values excluded. A total of 85 extreme records are obtained, with an expectation of 1.7 records per year. The maximum occurrence can be up to seven times in one year (Fig. 6f).

The peaks-over-threshold model applied to the original sea level records (i.e., daily HHW) discussed above does not include the modeling of extreme event duration using the geometric model. This is because the continuity of extremes in the original sea level records is rather low. For example, a threshold of 3.36 m results in a longest duration of only 3 days, with very low probability in extreme HHW at Macau. Therefore, the extremes in the original sea level records are handled as daily events. However, the situation is different for tidal residuals. Stationary models for tidal residuals before and after the 18.6-year nodal modulation are given in Figs. 7a-d and Figs. 7e-h, respectively. Figure 8 is the same as Fig. 7 but for models of tidal residuals at Hong Kong. In tidal residuals without nodal modulation at Macau, for instance, the threshold of 3.18 m is the 99.57th percentile of 31 272 records. A total of 66 extreme records are obtained, with an expectation of 0.786 records per year. The mean length of extremes is 2.12 days, which is actually the reciprocal of the geometric parameter p in Table 3. Therefore, the total number of days with extreme high tidal residuals is about 140. These 140 days have to be clustered into 66 extreme events due to their relatively high continuity, which can be seen in Fig. 7d. A similar situation is found in tidal residuals before and after the 18.6-year nodal modulation, and at both Macau and Hong Kong (Figs. 7-8).

Figure 7.  (a) Quantile plot and (b) return level plot for the GP distribution fitted to daily extremes in tidal residuals without the 18.6-year nodal modulation in Macau. (c) Frequency and (d) duration of extremes in tidal residuals without nodal modulation in Macau fitted to the Poisson and geometric distributions, respectively. (e-h) As in (a-d), but for tidal residuals after the 18.6-year nodal modulation.

Figure 8.  As in Fig. 7, but for Hong Kong.

In a recent study of sea level extremes on the coast of China, (Feng and Tsimplis, 2014) revealed that tidal residual maxima are determined predominantly by tropical cyclones, while tides and tropical cyclones determine the spatial distribution of sea level maxima. The different extreme behavior in the original sea level records and tidal residuals may be contributed by the modulations of tides on storm surges. That is, the upthrow effect of storm surges on sea level can normally persist for several days, but its continuity can be broken by the sinusoidal fluctuation of tides, particularly by the diurnal and semidiurnal constituents. Accordingly, the statistical models for the original sea level records and tidal residuals are different.

When comparing the upper and lower panels in Fig. 7 (or Fig. 8), particularly for the observed (circles) frequency and duration of extremes in tidal residuals, one may deduce that the 18.6-year nodal modulation exerts a significant influence on hydrological extreme events. As the mean Λ and p are close in tidal residuals before and after the nodal modulation (Table 3), the differences in the observed distribution of frequency and duration imply that the impact of the 18.6-year nodal cycle on extreme tidal residuals is mainly on an interannual to interdecadal timescale (Feng and Tsimplis, 2014). These effects on long-term changes of extremes in tidal residuals can be further demonstrated in the other nonstationary models.

Figure 9.  Trends (red lines) of (a) intensity and (b) frequency of extreme sea level records in Macau during 1925-2010 estimated by the GP and Poisson distributions, respectively. The stems represent observed annual values. (c, d) As in (a, b), but for records in Hong Kong.

There are evident decadal variations in the intensity and frequency of extremes in sea level records in the PRE (stems in Fig. 9). In the longer series in Macau, for example, high values for both intensity and frequency occur during the 1950s and the 1990s-2000s, which is consistent with the MSL in Fig. 2 (black line). Parametric trends are introduced through covariate effects in the GP scale parameter and through a GLM framework in the Poisson model (solid red lines in Fig. 9). Meanwhile, p-values for significance tests can be computed as well (Table 5). However, none of the parameters (intensity and frequency) of daily HHW extremes in either Macau or Hong Kong has a significant increasing or decreasing trend.

Parametric trends of extremes in tidal residuals differ from trends of extremes in original sea level records at Macau, as shown in Fig. 10. The increasing parametric trends of both frequency and duration of extremes in tidal residuals without nodal modulations at Macau are significant at the 0.05 significance level, while only the increasing trend of duration is significant for extremes in tidal residuals with nodal modulations (Table 5). The overall result of trends of extremes in tidal residuals in Hong Kong (Fig. 11) is consistent with the trends of extremes in original sea level records: none of the parameters presents a significant trend in recent decades (Table 5). Moreover, effects of the 18.6-year nodal cycle on extreme tidal residuals and interannual to interdecadal variability are now evident, when the left and right panels of Fig. 10 (or Fig. 11) are compared.

Figure 10.  Trends (red lines) of (a) intensity, (b) frequency and (c) duration of extremes in tidal residuals without the 18.6-year nodal modulation in Macau during 1925-2010, estimated by the GP, Poisson and geometric distributions, respectively. The stems represent observed annual values. (d-f) As in (a-c), but for tidal residuals after the 18.6-year nodal modulation.

Figure 11.  As in Fig. 10, but for Hong Kong.

Figure 12.  (a) Total duration (hours) of display of tropical cyclone warning signals and their linear trend, and (b) frequency of display of high-level (No. 8 and above) tropical cyclone warning signals and their parametric trend when fitted into a Poisson distribution in Hong Kong during 1956-2014.

Possible causes of extreme changes in sea level records and tidal residuals are of interest for a better understanding of the changing climate. Herein, we analyze the long-term changes of two potentials: tidal amplitudes and tropical cyclones. The annual mean amplitudes of the major tidal constituents we considered above (O₁, K₁, M₂ and K₂) are found to violate the normal distribution in both the KS and AD tests. Detection of their linear trends may hence not be suitable here. In the time series of annual amplitudes (not shown), an evident shift around 1970 can be found in most of the tidal constituents of concern, which can also be recognized in the MSL of Fig. 2. The mean tidal amplitudes before and after 1970 are listed in Table 6. It is found that the mean amplitude of all major constituents except K₂ decreases by approximately 20%. Such evident change cannot be found in the mean amplitudes of tidal constituents at Hong Kong with shorter series since the 1960s.

The secular trend of tropical cyclones that influence Hong Kong, in terms of total tropical cyclone warning hours and frequency of high-level (No. 8 and above) warning signals, is computed. The KS and AD tests suggest that the total tropical cyclone warning hours fulfill the normal distribution assumption, while the frequency of high-level warning signals does not. The record of high-level warning signals is a series of extreme event frequency. We therefore detect trends with a least-squares regression for the former and with a parametric trend in the Poisson model for the latter. The results are shown in Fig. 8. A decreasing trend is found in the total hours with warning signals display, but it is not significant at the 0.05 significance level. The correlation coefficient for the significance test is -0.1924, with 57 degrees of freedom during 1956-2014. A decreasing parametric trend of -0.008 is detected from the nonstationary Poisson model. A p-value of 0.0487 further demonstrates that the frequency of high-level tropical cyclone warning signals decreases significantly at the 0.05 significance level during the observation period.

This study investigates changes in sea level records and their extremes in the PRE using tide gauge measurements in Macau and Hong Kong. Linear regressions of annual mean tide records in Macau during 1925-2010 and in Hong Kong during 1954-2014 suggest linear trends of 1.3 mm yr^-1 and 1.4 mm yr^-1 at these two stations, respectively, which are slightly weaker than the global average level of increase given by (IPCC, 2013). Similar to the global average situation, the sea level in the region is rising at an accelerated rate (Shi et al., 2008; You et al., 2012). Taking Macau as an example, it rose 1.3 mm yr^-1 over 1925-2010 and jumped to 4.2 mm yr^-1 over 1970-2010. However, it is also noteworthy that decadal oscillations——specifically, the decadal low levels during the mid-1960s and 1970s (Fig. 2)——have contributed to this acceleration. Less attention is being paid to these multiscale natural fluctuations in sea level (Karamperidou et al., 2013).

So, we basically see agreement in the rising trend of MSL in the PRE. However, there is debate regarding storm surge disaster estimation and impact assessment. For example, (Hallegatte et al., 2013) suggested that two cities on the Pearl River Delta, Guangzhou and Shenzhen, have the first and fifth highest risk of future flood losses of major coastal cities in the world, while (Feng et al., 2013) argued that this was overestimated, mainly because storm surge disasters do not increase year by year, so a linear relationship between average annual losses and gross domestic product is logically wrong. (Feng et al., 2013) further pointed out that the linear superposition method of predicting the return period of extreme sea levels (e.g., Wang et al., 2011) is not reasonable.

Through a series of sensitivity tests, the threshold for defining extremes in original sea level records is determined to be 3.36 m for Macau and 2.84 m for Hong Kong, which are the local 96.65th and 95.5th percentiles, respectively. Realistic modeling of the peaks-over-threshold model can be observed with these threshold choices. In the meantime, return periods of extreme sea level records can be obtained from the GP model, which can be consulted for risk assessment and management. The peaks-over-threshold model applied to the original sea level records does not include the modeling of extreme event length, as the continuity of extremes in these data is rather low. The geometric distribution is added to model the duration of extremes in tidal residuals that present strong continuity. The different extreme behavior in original sea level records and tidal residuals may be due to the modulation of tides on storm surges. Meanwhile, it is found that the 18.6-year nodal modulation has evident influence on the variability of tidal residual extremes, generally on interannual to interdecadal timescales. This is demonstrated in both stationary (Figs. 7-8) and nonstationary (Figs. 10-11) modeling.

Parametric trends are estimated through the nonstationary EVT model. However, the p-values suggest that none of the extreme sea level parameters in Macau (1925-2010) and Hong Kong (1965-2014) presents a significant trend. Previous studies have also noted that there are significant correlations between climate warming and sea level rise in the PRE (Chen et al., 2008), while variation in maximum high sea levels in the area is not related to climate warming (Chen et al., 2011). Long-term changes in tidal amplitudes may be a factor influencing the extremes; but, as the annual tidal amplitudes in recent decades, e.g., since the 1960s, show no significant change, reduced storm surges caused by tropical cyclones in the PRE (Fig. 12) may be the major contributor to the nonsignificant trends of extremes in sea level as well as tidal residuals (Table 5), against the background of increased MSL (Fig. 2). For the longer-term record since the 1920s at Macau, the regime shift of tidal amplitudes around 1970 (Table 6) can explain the discrepancy of extreme trends in original sea level records and tidal residuals; that is, no significant trend in the former, but a significant increase in the latter (Table 5 and Figs. 9-10). However, why the extremes in original sea level records show no significant trend against the background of increased MSL is unclear. Further studies may address this question, as well as possible causes for the reduction in tropical cyclones that influence the PRE.