Flooding in Delta Areas Under Changing Climate: Response of Design Flood Level to Non-Stationarity in Both Inﬂow Floods and High Tides in South China

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Article Flooding in Delta Areas under Changing Climate: Response of Design Flood Level to Non-Stationarity in Both Inﬂow Floods and High Tides in South China

Yihan Tang 1,3, Qizhong Guo 2, Chengjia Su 1,3 and Xiaohong Chen 1,3,* 1 Center for Water Resources and Environment, Sun Yat-sen University, Guangzhou 510275, China; [email protected] (Y.T.); [email protected] (C.S.) 2 Department of Civil and Environmental Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, USA; [email protected] 3 Guangdong Engineering Technology Research Center of Water Security Regulation and Control for Southern China, Sun Yat-sen University, Guangzhou 510275, China * Correspondence: [email protected]; Tel.: +86-20-84114575

Received: 30 March 2017; Accepted: 22 June 2017; Published: 11 July 2017

Abstract: Climate change has led to non-stationarity in recorded floods all over the world. Although previous studies have widely discussed the design error caused by non-stationarity,most of them explored basins with closed catchment areas. The response of flood level to nonstationary inflow floods and high tidal levels in deltas with a dense river network has hardly been mentioned. Delta areas are extremely vulnerable to floods. To establish reliable standards for flood protection in delta areas, it is crucial to investigate the response of flood level to nonstationary inflow floods and high tidal levels. Pearl River Delta (PRD), the largest delta in South China, was selected as the study area. A theoretical framework was developed to quantify the response of flood level to nonstationary inflow floods and the tidal level. When the non-stationarity was ignored, error up to 18% was found in 100-year design inflow floods and up to 14% in 100-year design tidal level. Meanwhile, flood level in areas that were ≤22 km away from the outlets mainly responded to the nonstationary tidal level, and that ≥45 km to the nonstationary inflow floods. This study will support research on the non-stationarity of floods in delta areas.

Keywords: non-stationarity; ﬂood level; delta ﬂood; Pearl River Delta

1. Introduction Since the early twentieth century, climate change has altered hydrological cycles all over the world. Flood records are no longer stationary [1–5]. In particular, delta areas have experienced intensified flooding due to the combined impacts of the inflow floods from the upstream watershed and the rising high tidal level induced by sea-level rise (SLR). Meanwhile, livable climate and convenient sea transportation have contributed to increasing population and economy in delta areas around the world [6,7]. Thus, delta zones have become extremely vulnerable to floods. It is important to understand the response of flood level to nonstationary inflow floods and high tidal levels in delta areas, especially ones with a dense river network. There were some previous studies discussing the variation in design tidal levels under the impact of SLR. Trends in recording series, as well as the correlation between these trends and other climate factors, were explored using sophisticated extreme value analysis methodology [8]. To calculate reliable at-site frequency of the increasing tidal level, many previous researchers generated a stationary series before carrying out frequency analysis. Some restored the stationary time series by removing the increment caused by SLR [9–11], while some tried to generate stationary samples by duplicating the characteristics of historical tidal processes, which were assumed to be stationary [12]. Other researchers assumed that the rate of high tidal levels was time-dependent, and conducted frequency analysis on the recorded series with a time-correlated variable [8–13].

Water 2017, 9, 471; doi:10.3390/w9070471 www.mdpi.com/journal/water Water 2017, 9, 471 2 of 16 Water 2017, 9, 471 2 of 16

Design[12]. Other flood researchers levels assumed in delta that areas the were rate of also high analyzed tidal levels by was statistical time-dependent, methods and in conducted past studies. Jointfrequency distribution analysis was on the the most recorded widely series used with approach a time-correlated to statistically variable estimate[8–13]. flood levels in delta areas, whichDesign was flood simultaneously levels in delta areas affected were by also multiple analyzed forcing by statistical factors methods like rainstorms, in past studies. storm Joint surges, upstreamdistribution floods, was and the high most tides.widely Toused take approach non-stationarity to statistically caused estima byte flood environmental levels in delta changes areas, into which was simultaneously affected by multiple forcing factors like rainstorms, storm surges, concern, joint distribution incorporated the nonstationary characteristics of changing factors into upstream floods, and high tides. To take non-stationarity caused by environmental changes into marginalconcern, distribution joint distribution functions. incorporated However, the in nonsta this way,tionary both characteristics the difficulty of changing of parameter factors estimation into and themarginal uncertainty distribution of results functions. were Ho significantlywever, in this increased way, both [14 the]. Anotherdifficulty commonlyof parameter used estimation method for deltaand flood the protection uncertainty is of to results first calculate were significantly two design increased flood levels,[14]. Another under commonly the impact used of either method the for inflow floodsdelta or theflood high protection tidal level, is to and first choose calculate the highertwo design one asflood the levels, design under value the [15 impact]. This methodof either isthe simple and convenient,inflow floods but or the itneglects high tidal the level, interconnection and choose the betweenhigher one inflow as the floodsdesign andvalue high [15]. tides.This method Thisis simple research and aimsconvenient, to estimate but it the neglects response the ofinterconnection flood level to thebetween impact inflow of inflow floods floods and high and downstreamtides. tidal level,This when research the time aims series to ofestimate these two the factors response are bothof flood nonstationary. level to the Toachieve impact of thisinflow purpose, floods Pearl and River Deltadownstream (PRD) in South tidal China level, when was selected the time as series the studyof these area. two This factors paper are isboth arranged nonstationary. as follows. To achieve In Section 2, this purpose, Pearl River Delta (PRD) in South China was selected as the study area. This paper is a brief introduction of the study area, dataset and methodology is provided. In Section3, the response of the arranged as follows. In Section 2, a brief introduction of the study area, dataset and methodology is floodprovided. level to the In nonstationarySection 3, the response inflow floodsof the flood and the level high to the tidal nonstationary level is estimated, inflow andfloods its and spatial the high pattern is discussed.tidal level Conclusions is estimated, are made and initsSection spatial4 pattern. The investigation is discussed. in Conclusions PRD can be usedare made as reference in Section for estimations4. The of theinvestigation flood level response in PRD can in other be used delta as areas reference with similarlyfor estimations complicated of the environmentalflood level response conditions. in other delta areas with similarly complicated environmental conditions. 2. Study Area and Methods 2. Study Area and Methods 2.1. Study Area and Dataset 2.1. Study Area and Dataset Pearl River Delta, which covers an area of 39,380 km2, is the largest delta in South China (Figure1). It has a humidPearl River subtropical Delta, which climate. covers The an monsoon area of 39,380 period km in2 this, is the area largest lasts fromdelta Aprilin South to September.China Due(Figure to the terrain1). It has altitude, a humid the subtropical dense river climate. network The monsoon develops period from inthe this northwest area lasts from to the April southeast. to WaterSeptember. flow in PRD Due comesto the terrain from West altitude, River the and dense North river River,network and develops all the from water the in northwest the delta to flows the into southeast. Water flow in PRD comes from West River and North River, and all the water in the delta Pearl River Estuary through multiple outlets. Based on its source of inflow floods water, PRD area can flows into Pearl River Estuary through multiple outlets. Based on its source of inflow floods water, be furtherPRD area divided can be into further a West divided River into sub-delta, a West River and sub-delta, a North Riverand a sub-delta.North River Floods sub-delta. in twoFloods upstream in rivertwo basins upstream mainly river occur basins between mainly June occur and between August. June Meanwhile, and August. extreme Meanwhile, tides extreme in the estuary, tides in inducedthe by typhoonsestuary, induced or storm by surges, typhoons mainly or storm occur surges, around mainly September occur around [16]. September [16].

Figure 1. Map of Pearl River Delta and locations of gauge stations: (a) location of Pearl River Delta Figure 1. Map of Pearl River Delta and locations of gauge stations: (a) location of Pearl River Delta on on the map of China; (b) gauge stations of upstream rivers; (c) a closer view of Pearl River Delta. the map of China; (b) gauge stations of upstream rivers; (c) a closer view of Pearl River Delta.

PRD is the megaregion where Macao is located [17]. In 2014, the population of cities in PRD surpassed that of Chicago and it was ranked in the top 30 in the world [18]. In 2015, the total income Water 2017, 9, 471 3 of 16

Water 2017, 9, 471 3 of 16 of only two cities in PRD, i.e., Guangzhou and Foshan, reached $20.6 million [19]. With its fast growth in economyPRD andis the population, megaregion PRD where is extremely Macao is vulnerablelocated [17]. to In flood 2014, risk. the population of cities in PRD surpassedIn this research, that of Chicago recorded and peak it was flood ranked volumes in the top in the 30 in flood the world season, [18]. i.e., In from 2015, June the total to August, income in Wuzhouof only and two Shijiao cities werein PRD, used. i.e., So Guangzhou were the high and tidal Foshan, levels reached in seven $20.6 outlet million stations [19]. (Figure With1 ,its Table fast1 ). Allgrowth the data in wereeconomy collected and population, during the PRD period is extremely from 1958 vulnerable to 2011. to flood risk. In this research, recorded peak flood volumes in the flood season, i.e., from June to August, in Wuzhou and Shijiao were used.Table So 1. Gaugewere the stations high and tidal trend levels detection. in seven outlet stations (Figure 1, Table 1). All the data were collected during the period from 1958 to 2011. River Basin No. Gauge Station Channel Name Mann–Kendall Table 1. Gauge stations and trend detection. 0 Gaoyao - - West River River Basin 1No. WuzhouGauge Station Channel - Name Mann–Kendall Upward (z = 1.66) 0 Gaoyao - - North RiverWest River 2 Shijiao - No (z = 0.38) 1 Wuzhou - Upward (z = 1.66) North River 32 Sanshakou Shijiao Humen- No (z No= 0.38) (z = 1.43) 43 NanshaSanshakou JiaomenHumen No (z No = 1.43) (z = −0.37) 5 Wanqinshaxi4 Nansha HongqimenJiaomen No (z = No −0.37) (z = 1.57) Pearl River Delta Outlets 65 HengmenWanqinshaxi Hongqimen Hengmen No Upward (z = 1.57) (z = 2.96) Pearl River Delta Outlets7 Denglongshan6 Hengmen ModaomenHengmen Upward Upward (z = 2.96) (z = 1.96) 87 HuangjinDenglongshan Modaomen Jitimen Upward Upward (z = 1.96) (z = 2.65) 8 Huangjin Jitimen Upward (z = 2.65) 9 Xipaotai Hutiaomen Upward (z = 2.44) 9 Xipaotai Hutiaomen Upward (z = 2.44) | | > Note:Note: When When |Z| 11.65,.65, thethetrend trend is is 90% 90% significant. significant. 2.2. Methodology 2.2. Methodology InIn this this research, research, a methodology a methodology was was developed developed to estimate to estimate the impactthe impact of the of nonstationary the nonstationary inflow floodsinflow and floods the high and tidal the high level tidal on flood level level. on flood First, level. a time-varying First, a time-varying moments (TVM)moments model (TVM) was model applied to evaluatewas applied the to design evaluate inflow the floodsdesign frominflow the floods upstream from the river upstream basins andriver the basins high and tidal the levels high aroundtidal thelevels delta around estuaries. the Then,delta estuaries. the influence Then, of the the influence nonstationary of the nonstationary inflow floods inflow and the floods high and tidal the level high on floodtidal level level was on estimatedflood level through was estimated a one-dimensional through a one-dimensional hydrodynamic hydrodynamic model using the model TVM-estimated using the designTVM-estimated inflow floods design and the inflow high floods tidal level and as the its high inputs. tidal Four level scenarios as its wereinputs. created Four byscenarios combining were the nonstationarycreated by inflowcombining floods the and nonstationary the high tidal inflow level, andfloods then and the the nonstationary high tidal waterlevel, leveland inthen PRD the was estimatednonstationary under water these scenarios.level in PRD The was whole estimated schedule unde ofr thisthese combined scenarios. methodology The whole schedule is shown of this in the flowchartcombined presented methodology in Figure is 2shown. All the in partsthe flowchart that are considered presented nonstationaryin Figure 2. All are the highlighted parts that in are blue. considered nonstationary are highlighted in blue.

FigureFigure 2. Flow2. Flow chart chart of the of methodology.the methodology. Parts Parts highlighted highlight in blueed in considered blue considered non-stationarity non-stationarity in time series. in time series.

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2.2.1. Time-Varying Moments Estimating Nonstationary Inflow Floods and High Tidal Levels The time-varying moments method, which has been widely applied in the statistical estimation of nonstationary peak flood volume, was used in this investigation to calculate the nonstationary design value of inflow floods and high tidal level [20]. In this method, to incorporate the non-stationarity, the first two moments of the time series were initially assumed to have trends that are either linear (L) or parabolic (P) [21,22]. Four conditions were generated by assembling the L or P trend in the first two moments, labeled A to D [22]: (1) when only the first moment, i.e., the mean of the time series, is time-dependent, whether the trend is L or P, the condition is named A; (2) when only the second moment, i.e., the standard deviation of the time series, is time-dependent, whether the trend is L or P, the condition is named B; (3) when both the mean and the standard deviation have time-dependent trends in, and the standard deviation is a product of, the mean and a constant value, i.e., the coefficient of variation (Cv), the condition is named C; (4) when both the first two moments have trends, but they are not directly correlated, the condition is named D. By combining Scenarios A–D and two types of trends, i.e., L and P, eight time-trend models were generated. All models are listed in Table2, where m0 represents the mean of the nonstationary time series that is defined in relation to both the mean of a stationary time series, m, and time, t. Likewise, σ0 denotes the nonstationary standard deviation and is considered to be associated with both the stationary standard deviation σ and time, t. In all functions, am, aσ, bm, and bσ denote the constants.

Table 2. Time trend models of the ﬁrst two moments.

Probability Time-Varying Time Trend Model m σ Distribution Function Model 0 0 AL P3-AL m = m + amt σ = σ 0 0 BL P3-BL m = m σ = σ + aσt 0 0 CL P3-CL m = m + amt σ = Cv·m 0 0 DL P3-DL m = m + amt σ = σ + aσt P3 0 2 0 AP P3-AP m = m + amt + bmt σ = σ 0 0 2 BP P3-BP m = m σ = σ + aσt + bσt 0 2 0 CP P3-CP m = m + amt + bmt σ = Cv·m 0 2 0 2 DP P3-DP m = m + amt + bmt σ = σ + aσt + bσt Note: P3 denotes the Pearson type III.

According to studies carried out in the 1990s, Pearson type III performs the best among all commonly used probability distribution functions for either the flood flow or the high tidal level in PRD [23–30]. Therefore, Pearson type III was selected as the probability density function (PDF) used in design value estimation in this research. Based on the eight time trend models, parameters of Pearson type III were all defined to be time-dependent variables. All these parameters were estimated by the maximum likelihood method, where t was used as a variable. The goodness of fit of PDFs, i.e., Pearson type III with parameters of different time trend models, was tested by the Akaike Information Criterion (AIC).

2.2.2. One-Dimensional River Network Hydrodynamic Model The one-dimensional hydrodynamic model has been widely used in flood level estimation. It is comparatively more accurate in representing the cross-sectional area of channels and requires only a small amount of field data to set up the model. Also, it can be quickly set up, and the computation is fast [31]. Therefore, the one-dimensional hydrodynamic model was chosen as the basic tool to estimate the flood level in this research. Water 2017, 9, 471 5 of 16 momentum balance equation as the governing equations. The implicitly weighted four-point Preissmann scheme [33] was used to solve these governing equations. The model set the time-step as 10 min, and a space lag from 500 to 2500 m. In all, the model includedWater 2017, 1969, 471 channels and 144 nodes (Figure 3). The upstream inflow from Gaoyao (West River)5 and of 16 Shijiao (North River), as well as the tidal levels in seven outlets (Figure 1, Table 1), were set as its boundaries,1. Model Setup and the and recorded Input Data data in these stations were used as the input to run the model. Conducting simultaneous field survey over a large basin like PRD region is extremely time-consumingThe one-dimensional and expensive. hydrodynamic Meanwhile, model alth usedough inlarge-scale the present field study measurement was developed has been from carriedthe one out created by the by Guangdong the Center forHydraulic Water Resources Bureau ever andy five Environment years, the (2015),data are and beyond the whole our access. model Owingwas set to up the in limitations Fortran [ 32of]. survey This data, model this adopted research the applied Saint-Venant the topographic continuity data equation collected and in the floodlongitudinal season momentumof 1998 to develop balance equationa 1D model. as the All governing topographic equations. maps were The implicitlyobtained weightedfrom the Guangdongfour-point Preissmann Hydraulic schemeBureau, [in33 a] wasmeasuring used to scale solve of these 1:5000. governing The hourly equations. flood flow and water level were Thesimultaneously model set the detected time-step at 40 as stations 10 min, during and a a space typical lag flood from in 500 PRD. to 2500Data m.collected In all, from the model 12:00 p.m.included on 25 196 June channels 1998 to and 12:00 144 p.m. nodes on (Figure 28 June3). 1998 The upstreamat hydrological inflow stations from Gaoyao in Gaoyao (West and River) Shijiao and wereShijiao used (North to drive River), the asmodel well and as the calibrate tidal levels the parameters. in seven outlets The fluvial (Figure water1, Table level1), at were each setsampling as its frequencyboundaries, was and linearly the recorded interpol dataated in to these the model stations time-step. were used as the input to run the model.

Figure 3. Overview of the simplified one-dimensional hydrodynamic model of PRD. Figure 3. Overview of the simpliﬁed one-dimensional hydrodynamic model of PRD.

Conducting simultaneous field survey over a large basin like PRD region is extremely time-consuming and expensive. Meanwhile, although large-scale field measurement has been carried out by the Guangdong Water 2017, 9, 471 6 of 16

Hydraulic Bureau every five years, the data are beyond our access. Owing to the limitations of survey data, this research applied the topographic data collected in the flood season of 1998 to develop a 1D model. All topographic maps were obtained from the Guangdong Hydraulic Bureau, in a measuring scale of 1:5000. The hourly flood flow and water level were simultaneously detected at 40 stations during a typical flood in PRD. Data collected from 12:00 p.m. on 25 June 1998 to 12:00 p.m. on 28 June 1998 at hydrological stations in Gaoyao and Shijiao were used to drive the model and calibrate the parameters. The fluvial water level at each sampling frequency was linearly interpolated to the model time-step. 2. Model Validation The hydrodynamic model was validated before estimating the flood level at PRD stations. The coefficient of riverbed roughness was first set between 0.016 and 0.035 [33]. Next, after the model had been running for Water 2017, 9, 471 6 of 16 30 days, the parameters were updated by the results obtained on day 30. The aforementioned procedures were repeated2. moreModel than Validation 10 times before the simulation results stabilized. The model parameters were finally set when the differenceThe hydrodynamic between themodel simulation was validated results before of estimating day 1 and the day flood 30 remainedlevel at PRD within stations. 1%. The To assesscoefficient the performance of riverbed roughness of the was model, first set measured between 0.016 and and model-estimated 0.035 [33]. Next, after amplitudes the model for eight constituentshad were been compared running for in six30 days, stations, the parameters i.e., Makou, were Sanshui, updated Tianhe, by the results Baijiao, obtained Xiaheng, on andday 30. Shaluowei, The and aforementioned procedures were repeated more than 10 times before the simulation results the result was shown in Figure4. Difference bands were both plotted at ±0.025 and ±0.05 m, with an overall stabilized. The model parameters were finally set when the difference between the simulation RMSE of 6.87results cm. of For day each 1 and of day these 30 remained six stations, within recorded 1%. and estimated flood levels were also compared. The average absoluteTo assess errors the performance in the six stationsof the model, were me belowasured 0.05and model-estimated m, with a minimum amplitudes of 0.001 for eight m at Baijiao. To further measureconstituents the modelwere compared efficiency, in ansix indexstations, (α )i.e., was Makou, applied, Sanshui, was calculated Tianhe, Baijiao, by the Xiaheng, following and equations: Shaluowei, and the result was shown in Figure 4. Difference bands were both plotted at ±0.025 and ±0.05 m, with an overall RMSE0 of 6.87 cm. For each of these six stations, recorded and estimated Z − Z0 flood levels were also compared.ri = The average× 100% absolute(i = errors1, 2, 3,in the . . . ,six 72 stations) were below 0.05 m, (1) with a minimum of 0.001 m at ZBaijiao.0 To further measure the model efficiency, an index (α) was applied, was calculated by the following (equations: 0 (5 ≤ r ) i Ai = (2) = × 100% (i = 1, 2, 3, …, 72) (1) 1 (ri < 5) 0 5 72 =∑ A (2) α = 1i=1 i ×5100%, (3) 72∑ α = × 100%, (3) 0 where Z is the estimated ﬂood level; Z0, the recorded ﬂood level; and i, the number of hours. When where is the estimated flood level; , the recorded flood level; and i, the number of hours. α ≥ 75%, the simulation of the model was predicted to be valid. The value of α is 95% in Makou, 83% When α 75%, the simulation of the model was predicted to be valid. The value of α is 95% in in Sanshui,Makou, 90% in 83% Tianhe, in Sanshui, 92% 90% in Baijiao,in Tianhe, 81% 92% in Baijiao, Xiaheng, 81% andin Xiaheng, 92% inand Shaluowei. 92% in Shaluowei. All α Alls are above 80%, and theαs modelare above has 80%, been and the proved model tohas be been valid. proved to be valid.

Figure 4. ComparisonFigure 4. Comparison of harmonic of harmonic constituent constituent amplitudes, amplit withudes, differencewith difference bands bands located located at 0.025at 0.025 and 0.05 m. and 0.05 m.

Water 2017, 9, 471 7 of 16

3. Results and Discussion Water 2017, 9, 471 7 of 16 3.1. Non-Stationarity in the Inﬂow Floods and the Downstream Tidal Level 3. Results and Discussion

3.1.1. Increasing3.1. Non-Stationarity Inflow Floods in the Inflow Floods and the Downstream Tidal Level Trends in the inflow floods of PRD were estimated by Mann–Kendall method [34,35]. As is shown 3.1.1. Increasing Inflow Floods in Table1, inflow floods from West River had significantly increased since 1958. Since 1950, global warming andTrends atmosphere in the inflow circulation floods of abnormities PRD were esti havemated led by to Mann–Kendall fewer but more method intense [34,35]. tropical As is cyclones shown in Table 1, inflow floods from West River had significantly increased since 1958. Since 1950, in Westglobal River warming [36–38]. and Meanwhile, atmosphere the circulation extreme abnormit precipitationsies have led (over to fewer 99 percentile) but more intense in West tropical River have increasedcyclones by more in West than River 45 mm [36–38]. since Meanwhile, 1959 [39]. the As extr a result,eme precipitations the flood flow (over in 99 lower percentile) West in River West became significantlyRiver have higher increased in the by flood more season than 45 [ 40mm]. since 1959 [39]. As a result, the flood flow in lower West BasedRiver on became the trend significantly test results, higher designin the flood flood season in West [40]. River was estimated by TVM, and CL was detected toBased be the on best-fitthe trend time-trend test results, design model flood for thein West increasing River was inflow estimated floods by TVM, (Table and2 ).CL Thirty-year was detected to be the best-fit time-trend model for the increasing inflow floods (Table 2). Thirty-year simple moving mean and standard deviation of annual peak flood flow series in West River was simple moving mean and standard deviation of annual peak flood flow series in West River was analyzedanalyzed and displayed and displayed in Figure in Figure5. Since5. Since the the firstfirst two moments moments of ofthe the flood flood series series both had both linear had linear trends,trends, the results the results of AIC of AIC test test were were proven proven to to be be reliable.reliable.

Figure 5. Trends in the first two moments of Wuzhou: (a) simple moving mean; (b) simple moving Figurestandard 5. Trends deviation. in the ﬁrst two moments of Wuzhou: (a) simple moving mean; (b) simple moving standard deviation.

The 100-, 50-, and 20-year design ﬂood ﬂow in West River in 2050 were then estimated. To compare the design volumes with and without taking non-stationarity into consideration, the relative difference E was calculated as follows: X − X E = T 0 × 100%, (4) X0 Water 2017, 9, 471 8 of 16

where XT denotes the nonstationary design value, and X0 denotes the stationary one. The gap between a 100-year and a 20-year XT is ∆XT, and the difference between a 100-year and a 20-year X0 is ∆X0. Both ∆XT and ∆X0 were calculated and compared. The greater the value of ∆XT or ∆X0, the steeper the slope of the upper tail (and the greater the pressure in flood protection. (The “upper tail” here specifically refers to the part of the flood frequency curve with an exceedance probability lying between 1% and 5%.) Results showed that by ignoring the increasing tendency, the 100-year peak flood flow was underestimated by 17.51% (9825 m3/s) (Table3). Meanwhile, the relative underestimation ( E) was augmented when the exceeding probability reached 5%, i.e., by 17.91% (9417 m3/s) for the 50-year 3 3 flood, and by 18.52% (8809 m /s) for the 20-year flood. In addition, ∆XT (9553 m /s) was larger than 3 ∆X0 (8537 m /s), indicating that non-stationarity in the flood had contributed to a steeper upper tail.

Table 3. Comparison of design ﬂood.

T = 100 T = 50 T = 20 Station Unit XT X0 E (%) XT X0 E (%) XT X0 E (%) Wu-zhou m3/s 65,926 56,101 17.51 61,990 52,573 17.91 56,373 47,564 18.52 Heng-men 2.93 2.68 9.33 2.83 2.57 10.12 2.69 2.42 11.16 Denglong-shan 3.00 2.63 14.07 2.88 2.50 15.20 2.70 2.31 16.88 m Huang-jin 3.65 3.20 14.06 3.50 3.00 16.67 3.28 2.73 20.15 Xipao-tai 3.18 3.34 −4.79 3.06 3.12 −1.92 2.90 2.83 2.47 Note: T is the return period.

3.1.2. Varied High Tidal Level High tidal levels in seven outlets were tested, and tidal levels in all outlets but Nansha had upward tendencies. Somehow, only the tendencies in Hengmen, Denglongshan, Huangjin, and Xipaotai reached a significance of 90% (Table1). Rising sea-level rise at the Pearl River Estuary pushed up the high tidal levels, and severe sand excavation and channel regulation from the 1980s to the early 21st century around the upstream of Nansha neutralized the rising trend [41]. Nonstationary estimations were carried out in the six outlets that had significant trends. In each station, best-fit models was detected, and the nonstationary design value was compared with the stationary one (Tables2 and3). Results showed that, whether the return period was 100, 50, or 20 years, design levels were all underestimated in Hengmen, Denglongshan, and Huangjin, and the increase in the return period had led to a greater underestimation, which was displayed in the value of E. Meanwhile, the 100-, 50-, and 20-year Es ranged from 9.33% (0.25 m) to 11.16% (0.27 m) in Hengmen, 14.07% (0.37 m) to 16.88% (0.39 m) in Denglongshan, and 14.06% (0.45 m) to 20.15% (0.55 m) in Huangjin. Both XT and Es decreased along the coastline from the southwest to the northeast, i.e., from Huangjin and Denglongshan to Hengmen. Furthermore, since ∆XT reached 0.24 m in Hengmen, 0.30 m in Denglongshan, and 0.37 m in Huangjin, it is easy to conclude that the slope of upper tail was steeper in the southwest (Huangjin) than in the northeast (Hengmen). The direction of the ocean current affected the impact of SLR on the tidal level. Based on this criteria, Wu [42] divided the PRD outlets into three groups. In the first group, to which Huangjin belonged, high tides in outlet were mainly influenced by the current from the Indian Ocean. In the second group, to which Denglongshan belonged, high tidal levels were affected by a substantial impact of ocean currents from both the Pacific Ocean and the Indian Ocean. In the third group, to which Hengmen belonged, high tidal levels were solely influenced by the Pacific Ocean current. The surrounding environment of all these outlet stations affected the ocean current impact as well. Take Huangjin as an example: since it was located in a bay surrounded by tiny islands, the tidal vibration affected by the current impact was amplified. In Hengmen, conversely, the tidal vibration induced by the current effect was reduced, due to the land lying to the east of Pearl River Estuary [42,43]. Water 2017, 9, 471 9 of 16 tidal vibration affected by the current impact was amplified. In Hengmen, conversely, the tidal Watervibration2017, 9induced, 471 by the current effect was reduced, due to the land lying to the east of Pearl River9 of 16 Estuary [42,43].

3.2. Response of the Design Flood Level to Nonstationary InflowInflow Floods and the High Tidal LevelLevel Design floodflood levels in 22 stations were estimated under six scenarios, combining nonstationary inflowinflow floodsfloods and nonstationary high tidal level (Table 4 4,, Figure Figure6 ).6). The The design design flood flood level level estimated estimated with these nonstationary inputs was called the nonstationary floodflood level, whereas the one without considering non-stationaritynon-stationarity waswas named named the thestationary stationary flood flood level level. For. For all 22all stations,22 stations,nonstationary nonstationaryand theandstationary the stationary flood flood levels levelswere were compared compared under under Scenarios Scenarios 1 and 1 4.and 4.

Figure 6. Locations of the 22 gauging stations in Pearl River Delta.

Table 4. Scenarios employed. Return Period Scenario Return Period Scenario Flood Flow Extreme Tidal Level 1 Flood100a Flow Extreme100a Tidal Level 1 2 100a100a 50a 100a 2 3 50a100a 100a 50a 3 4 50a50a 50a 100a 4 50a 50a 3.2.1. Response of Flood Level at a Single Spot 3.2.1.In Response 21 out of of Flood22 stations, Level atthe a Singlenonstationary Spot flood level was higher than the stationary. Only in HengshanIn 21 out was of the 22 stations, stationary the floodnonstationary level higher. flood levelThis wasis because higher thanHengshan the stationary was located. Only in just Hengshan 18 km wasaway the fromstationary the outlet flood at level Xipaotai,higher. and This its isflood because level Hengshan was highly was affected located byjust the 18nonstationary km away from design the outlettidal level at Xipaotai, in Xipaotai. and Due its flood to the level result was in highly Table affected1, the nonstationary by the nonstationary design tidal design level tidal in Xipaotai level in Xipaotai.was lower Due than to the resultstationary in Table one.1, theTherefore, nonstationary the stationary design tidalflood levellevel inin XipaotaiHengshan was was lower higher than than the stationarythe nonstationary one. Therefore, one. the stationary flood level in Hengshan was higher than the nonstationary one. To further assess the response of flood level to the nonstationary inflow floods and high tidal level in PRD, the 22 stations were divided into three groups by the K-means clustering method, based WaterWater2017 2017, 9,, 4719, 471 10 of10 16 of 16

To further assess the response of flood level to the nonstationary inflow floods and high tidal onlevel theabsolute in PRD, differencethe 22 stations between were their dividednonstationary into threeand groupsstationary by the ﬂood K-means levels (Tableclustering5). Among method, the threebased groups, on the Group absolute 1 had difference the highest between mean their value, nonstationary and Group and 3 the stationary lowest. Ifflood a station levels belonged(Table 5). to theAmong same group the three under groups, both Group scenarios, 1 had it wasthe highest marked me inan blue value, (Table and5 ).Group 3 the lowest. If a station belonged to the same group under both scenarios, it was marked in blue (Table 5). Table 5. K-means clustering results. Table 5. K-means clustering results. Scenario Number Group 1 Group 2 Group 3 Scenario Group 1 Baijiao,Group Ganzhu, 2 Lanshi, Group 3 Number Baiqing, Da’ao, Lianyao, Banshawei, Fengmamiao, Nanhua, Rongqi, 1 Baiqing, Da’ao,Makou, Lianyao, Sanshui, Baijiao, Ganzhu, Lanshi, Banshawei,Hengshan, Fengmamiao, Jiangmen, Sanduo, Tianhe, 1 Makou, Sanshui,Zhuyin, Zhuyin, Zhuzhou Nanhua, Rongqi, Sanduo, Hengshan,Ma’an, Jiangmen, Sanshanjiao Ma’an, Xiaolan, Zidong Zhuzhou Tianhe, Xiaolan, Zidong Sanshanjiao Baijiao, Baiqing, Da’ao, Baijiao, Baiqing, Da’ao, Banshawei,Banshawei, Fengmamiao, Fengmamiao, Lianyao, Sanduo, Ganzhu, Lanshi, Makou, 4 Ganzhu, Lanshi, Makou, Jiangmen, Hengshan, Nanhua, 4 Lianyao, Sanduo,Sanshui, Sanshui, Zhuzhou, Ma’an, Rongqi, Xiaolan Jiangmen, Hengshan, Nanhua, Ma’an, Rongqi, Xiaolan Sanshanjiao, Tianhe Zhuzhou, Zhuyin,Zhuyin, Zidong Zidong Sanshanjiao, Tianhe

Under both scenarios, five stations, i.e., Baiqing, Da’ao, Lianyao, Zhuyin, and Zhuzhou, Under both scenarios, five stations, i.e., Baiqing, Da’ao, Lianyao, Zhuyin, and Zhuzhou, belonged belonged to the first group. These five stations were located between 25 and 42 km away from the todelta the first outlets, group. and These their fiveflood stations levels were similarl locatedy between affected 25by andthe high 42 km tidal away levels. from Meanwhile, the delta outlets, the andresponses their flood in levelsBanshawei, were similarlySanshanjiao, affected and byFeng themamiao high tidal stations levels. were Meanwhile, the lowest the under responses both in Banshawei,scenarios. Sanshanjiao,The distance and between Fengmamiao these stations stations an wered their the outlets lowest was under within both the scenarios. area of 15–33 The distance km. betweenOutlets these of these stations stations, and theiri.e., Wanqingshaxi outlets was within and Sa thenshanjiao, area of 15–33exhibited km. no Outlets significant of these trend stations, in the i.e., Wanqingshaxihigh tidal level. and Sanshanjiao, exhibited no significant trend in the high tidal level. WhenWhen the the scenario scenario changed changed from from 1 to 1 4,to stations 4, statio locatedns located in the in Westthe West River River sub-delta, sub-delta, i.e., Makou, i.e., Baijiao,Makou, Jiangmen, Baijiao, Jiangmen, Nanhua, andNanhua, Tianhe, and fell Tianhe, from groupsfell from with groups higher with mean higher values mean to values ones with to ones lower meanwith values. lower Meanwile,mean values. the Meanwile, stations in the the stations North Riverin the sub-delta, North River i.e., Zidongsub-delta, and i.e., Sanduo Zidong stations, and jumpedSanduo from stations, the group jumped with from lower the mean group (Group with lower 2) to themean group (Group with 2) a to higher the group one (Group with a 1).higher Alteration one in(Group geometries 1). Alteration in the upstream in geometries river channel in the increased upstream the river flood channel flow distribution increased ratiothe flood in the flow North Riverdistribution sub-delta. ratio Under in the Scenario North 1,River the flow sub-delta. distribution Under ratio Scenario in Sanshui, 1, the i.e.,flow the distribution income of ratio the North in RiverSanshui, sub-delta, i.e., the was income 0.7% (300of the m 3North/s), higher River thansub-delta, under was Scenario 0.7% (300 4 (Table m3/s),3). higher In other than words, under the increaseScenario in the4 (Table upstream 3). In flood other flow words, in the the North increase River in the sub-delta upstream was flood greater flow under in the Scenario North 4,River while thesub-delta increment was of greater income under flood Scenario flow in the4, while West the River increment sub-delta of droppedincome flood by 300 flow m in3/s. the West River sub-delta dropped by 300 m3/s. 3.2.2. Response of the Flood Level along the River Channel 3.2.2. Response of the Flood Level along the River Channel The flood level in each station along the same river channel was connected into a flood line, and the 100-yearThe flood nonstationary level in each flood station line along was comparedthe same river with channel the stationary was connected one in twointo representativea flood line, and the 100-year nonstationary flood line was compared with the stationary one in two river channels (Figures6 and7). Makou–Zhuyin channel was located in the West River sub-delta, representative river channels (Figures 6 and 7). Makou–Zhuyin channel was located in the West where there were five stations along the way, i.e., Makou, Tianhe, Jiangmen, Da’ao, and Zhuyin. River sub-delta, where there were five stations along the way, i.e., Makou, Tianhe, Jiangmen, Da’ao, Sanshui–Sanshanjiao channel was located in the North River sub-delta, and Sanshui, Sanduo, and and Zhuyin. Sanshui–Sanshanjiao channel was located in the North River sub-delta, and Sanshui, Sanshanjiao were located along the river channel from the delta income to the outlet. Sanduo, and Sanshanjiao were located along the river channel from the delta income to the outlet.

Figure 7. Cont.

Water 2017, 9, 471 11 of 16

Figure 7. Flood line difference in river channels: (a) difference in Makou–Zhuyin Channel; Figure(b) relative 7. Flood difference line difference in Makou–Zhuyin in river channels: Channel; (a) difference(c) difference in Makou–Zhuyin in Sanshui–Sanshanjiao Channel; Channel; (b) relative difference(d) relative in difference Makou–Zhuyin in Sanshui–Sanshanjiao Channel; (c) difference Channel. in Sanshui–Sanshanjiao Channel; (d) relative difference in Sanshui–Sanshanjiao Channel. In either channel, the nonstationary flood line was higher than the stationary one, and the absoluteIn either gap channel, between thetwo nonstationaryflood lines gradually flood line narrowed was higher from the than delta the incomes stationary to one,the outlets and the absolute(Figure gap7a,b). between The relative two flooddifference lines E graduallyin the two narrowedchannels varied from thedramatically delta incomes in the tospot the 60 outlets km (Figureaway7 a,b).from Thethe relativeoutlet (Figure difference 7c,d).E Whenin the it two came channels around varied the area dramatically that was 60 in km the away spot 60from km the away fromoutlet, the outletE kept (Figure dropping7c,d). along When the it Sanshui–Sanshanjiao came around the area channel, that was while 60 kmit increased away from sharply the outlet, in E keptMakou–Zhuyin dropping along channel. the Sanshui–SanshanjiaoIn Sanshui–Sanshanjiao channel, channel while, since it increased the high sharplytidal level in Makou–Zhuyinin the outlet channel.displayed In Sanshui–Sanshanjiao no significant upward channel, trend since (Table the 1) high, the tidal increase level inin the the outlet design displayed flood line no significantmainly upwardresponded trend to (Table the upstream1), the increase floods’ in increment. the design Thus, flood the line impact mainly of respondedthe nonstationary to the upstream inflow floods floods’ decreased smoothly along the channel solely due to the reduction in the elevation. On the contrary, increment. Thus, the impact of the nonstationary inflow floods decreased smoothly along the channel however, the increment of the 100-year tidal level reached 14.07% in the outlet of Makou–Zhuyin solely due to the reduction in the elevation. On the contrary, however, the increment of the 100-year channel (Table 3). Affected by the interactive impact of increasing inflow floods and high tidal level, tidal level reached 14.07% in the outlet of Makou–Zhuyin channel (Table3). Affected by the interactive the relative difference between flood lines increased in the area that was 60 km away from impact of increasing inflow floods and high tidal level, the relative difference between flood lines the outlet. increasedBoth in the the absolute area that and was the 60 kmrelative away difference from the between outlet. the nonstationary and stationary flood lineBoth declined the absolute sharply andin Jiangmen, the relative caused difference by the flo betweenw distribution the nonstationary ratio variation and in stationary its upstream, flood linei.e., declined the node sharply where inTianhe Jiangmen, and Nanhua caused parted. by the A flow large distribution portion of ratiothe flood variation flow (45.53%) in its upstream, from i.e.,Makou the node went where through Tianhe Tianhe, and located Nanhua 13 km parted. away from A large Jiangmen. portion However, of the flood the width–depth flow (45.53%) ratio from Makouin Tianhe went was through only half Tianhe, that locatedin Makou 13 [44]. km awayTherefore, from the Jiangmen. relative However,gap between the nonstationary width–depth and ratio instationary Tianhe was flood only level half in that Tianhe in Makou increased. [44]. Nevertheless, Therefore, the th relativee width–depth gap between ratio nonstationaryin Jiangmen isand stationary2.4 times flood that level in Tianhein Tianhe [44]. increased. Thus, the Nevertheless,relative gap between the width–depth the nonstationary ratio in Jiangmenand the stationary is 2.4 times thatdesign in Tianhe level [in44 Jiangmen]. Thus, the was relative narrowed gap abruptly between from the nonstationary Tianhe. and the stationary design level in Jiangmen was narrowed abruptly from Tianhe.

Water 2017, 9, 471 12 of 16 Water 2017, 9, 471 12 of 16

3.3.3.3. Leading Leading Factors Factors of of Non-Statio Non-Stationaritynarity and and the the Flood Flood Level Level Response Response NonstationaryNonstationary flood flood levels levels underunder different different scenarios scenarios were were further further calculated calculated and andcompared. compared. To compareTo compare the theresponse response of the of the flood flood level level to tononstati nonstationaryonary inflow inflow floods floods and and that that to to the the nonstationary nonstationary tidaltidal level, level, index index X X was was developed developed and and calculated calculated by by the the following following equation: equation:

||/ || |Z=1 − Z3|/Z1= |Z1 −, Z3| (5) X = ||/ =|| , (5) |Z1 − Z2|/Z1 |Z1 − Z2| where (i = 1, 2, 3) is the nonstationary design flood level simulated under scenario i. When where0.5Z, ithe(i = flood 1, 2, 3)level is the in nonstationary PRD mainly designresponded flood to level the simulatednonstationary under high scenario tide, i.whereas When X when≤ 0.5 , the flood 5, the level flood in level PRD mainly mainly responded responded to to the the nonstationary nonstationary inflow high tide,floods. whereas when X ≥ 5, the floodIn level general, mainly X in responded each station tothe was nonstationary positively correlated inflow floods. to the distance between this station and the deltaIn general, outlet X(Figurein each 8). station Xs of was stations positively that correlatedwere less tothan the 22 distance km away between from this the station PRD andoutlet the were delta alloutlet below (Figure 0.5. 8Meanwhile,). Xs of stations when that the were distances less than between 22 km stations away from and thethe PRDdelta outlet outlet were were all more below than 0.5. 45Meanwhile, km, all Xs when were the above distances 5. It betweencan be deducted stations and that the in deltaPRD, outlet in stations were more that thanare more 45 km, than all X 45s werekm awayabove from 5. It canthe beoutlets, deducted the thatflood in level PRD, was in stations mainly that influenced are more by than the 45 nonstationary km away from inflow the outlets, floods. the Furthermore,flood level was flood mainly levels influenced in stations by the that nonstationary are located within inflow floods.22 km Furthermore,of the delta outlets flood levels were instrongly stations affectedthat are locatedby the nonstationary within 22 km of high the delta tidal outlets level. were strongly affected by the nonstationary high tidal level.

Figure 8. Cont.

Water 2017, 9, 471 13 of 16 Water 2017, 9, 471 13 of 16

FigureFigure 8. XXss ofof stations stations in in Pearl Pearl River River Delta: Delta: (a) stations (a) stations with Xwith≥ 5; X (b )≥stations 5; (b) stations with X ≤ with0.5; (Xc) stations 0.5; (withc) stations 0.5 < Xwith< 5.0.5 X 5.

AsAs for for the the flood flood level in stations lying between 22–45 22–45 km km from from delta outlets, their their response response to to eithereither nonstationary nonstationary inflow inflow floods floods did did not not increase increase when when they they became became farther farther away away from from the the delta delta outlets.outlets. Take Take Zhuzhou, Zhuzhou, for for example; example; though though it it is is located located 39 39 km km away away from from the the outlet, outlet, its its XX waswas the the samesame as as that that of Banshawei, which which was was 33 km aw awayay from the outlet. Since Since the the impact impact of of extreme tidestides decreased whenwhen thethe distance distance between between the the station station and and delta delta outlets outlets increased, increased,X in X Zhuzhou in Zhuzhou was wassupposed supposed to be to higher be higher than than that inthat Banshawei. in Bansha Onwei. the On other the other hand, hand, however, however, Zhuzhou Zhuzhou was much was muchfarther farther away fromaway the from entrance the entrance of PRD of than PRD Banshawei than Banshawei (Figure8 ).(Figure Therefore, 8). Therefore, the impact the of upstreamimpact of upstreamchange decreased change decreased to a greater to extent a greater in Zhuzhou extent in than Zhuzhou in Banshawei. than in Banshawei. Moreover, theMoreover, outlet of the Zhuzhou outlet ofhad Zhuzhou a more severe had upwarda more tendency severe thanupward Banshawei tendency (Table than1). Thus, Banshawei the non-stationarity (Table 1). ofThus, the highthe non-stationaritytidal level in the of outlet the high of Zhuzhou tidal level exerted in the a outl moreet severeof Zhuzhou impact exerted on the a flood more level severe in Zhuzhou.impact on the floodAlthough level in Zhuzhou. Rongqiwas located 2 km farther from the delta outlet than Xiaolan [44], X in Rongqi wasAlthough the same asRongqi in Xiaolan was located (Figure 28 km). Simply farther accordingfrom the delta to the outlet distance than betweenXiaolan [44], stations X in and Rongqi the wasdelta the outlets, same Xasin in RongqiXiaolan was (Figure supposed 8). Simply to be a higherccording than to inthe Xiaolan. distance However, between stations the estimated and theX deltawas inconsistentoutlets, X in with Rongqi our assumption.was supposed This to wasbe higher due to th thean impact in Xiaolan. of a dense However, river networkthe estimated and the X wasdirections inconsistent of the with development our assumption. of river This channels was due [37, 44to]. the Rongqi impact was of a located dense onriver a rivernetwork way and almost the directionsparallel to of the the latitude. development Since the of channelriver channels was in accordance[37,44]. Rongqi with was the directionlocated on of thea river reduction way almost of the parallelelevation, to flowthe latitude. speed in Since this channel the channel slowed was down. in ac Meanwhile,cordance with the the region direction where of Rongqi the reduction was located of thehad elevation, a higher density flow speed of river in this networks channel than slow othered spotsdown. in Meanwhile, PRD, and the the complexity region where of river Rongqi channels was locatedfurther weakenedhad a higher the density impact ofof nonstationaryriver networks high than tidal other levels, spots whose in PRD, effect and decreased the complexity from the of outlets river channelsto the incomes. further Based weakened on X sthe in Zhuyinimpact andof nonstationary Sanshanjiao, ithigh was tidal concluded levels, thatwhose the effect estimated decreased water fromlevel inthe Sanshanjiao outlets to the was incomes. more affected Based byon non-stationarity Xs in Zhuyin and in theSanshanjiao, upstream floodit was flow. concluded Somehow, that their the estimateddistance to water the delta level outlets in Sanshanj was almostiao was the more same, affected i.e., 25 by km non-stat for Zhuyinionarity and in 24 the km upstream for Sanshanjiao. flood flow.As was Somehow, mentioned their in distance Section 3.1.1to the, there delta was outlets an increasewas almost in the the upstream same, i.e., flow 25 km in thefor NorthZhuyin River and 24sub-delta km for withSanshanjiao. the rising As input was flood mentioned flow in in the Section West River. 3.1.1, Meanwhile, there was an Sanshanjiao increase in was the closer upstream to the flowincome in stationthe North than River Zhuyin. sub-delta The impact with ofthe nonstationary rising input inflow flood floodsflow in was the thus West maintained. River. Meanwhile, Likewise, Sanshanjiaoalthough the was distances closer from to the Lanshi income and Ma’anstation to than their Zhuyin. outlets were The both impact 27 km, of Lanshinonstationary had an Xinflowmuch floodshigher thanwas thatthus ofmaintained. Ma’an. Since Likewise, Ma’an was although located atthe the distances downstream from of Lanshi a node whereand Ma’an the flood to their from outletsboth Makou were both and Sanshui27 km, Lanshi joined, had the variancean X much in thehigher upstream than that flood of changeMa’an. exertedSince Ma’an little was impact. located The atdistance the downstream between the of stationa node andwhere the the income flood station from both was theMakou main and cause. Sanshui joined, the variance in the upstream flood change exerted little impact. The distance between the station and the income station was the main cause.

Water 2017, 9, 471 14 of 16

4. Conclusions Here, the response of flood level in a dense river network to nonstationary inflow floods and high tidal level was studied. Pearl River Delta (PRD) in South China was selected as the study area. Non-stationarity in inflow floods and tidal level was first evaluated by statistical methods such as that of Mann–Kendall, and the design value was further calculated by the time-varying moment method. The flood level estimated with nonstationary input was calculated under six scenarios in a one-dimensional hydrodynamic network model. The flood level estimated with nonstationary inputs was compared with that with stationary inputs, and the response of the flood level to non-stationarity was studied. The methodology utilized in this research for estimating the flood level response to non-stationarity can be used as a reference to investigate the design flood level change in other deltas with a dense river network. It was found that the flood level response was highly affected by nonstationary inflow floods and the high tidal level induced by environmental changes. In PRD, not considering the non-stationarity in incoming flood flow would have resulted in an 18% underestimation of the 100-year flood level, and an underestimation up to 14% (0.37 m) in the 100-year tidal levels among the multiple outlets. The underestimation of incoming flood flow or downstream high tidal level would have further caused underestimation of flood level along river channels. This situation will not only challenge the existing standard for the local flood protection but also lead to a higher degree of loss in both economy and life. For deltas that have endured intense environmental changes just like PRD, the design flood level needs to be updated by taking the non-stationarity of hydrological inputs into account. In this paper, the spatial pattern of the flood level response was discovered. The flood level in places located 25–42 km away from the outlets in the West River sub-delta responded the most to the non-stationarity in both inflow floods and high tidal level. Meanwhile, in the North River sub-delta, places lying 15–33 km away from delta outlets had the minimum response to the nonstationary inflow floods and the high tidal level. Due to the change in the geometries of upstream river channel, the North River sub-delta had a greater distribution ratio of inflow floods. This resulted in a greater increase in the flood level in the North River sub-delta, with a rise in the nonstationary flood and tidal level of a smaller return period. The site in the West River sub-delta situated 60 km away from the outlet was an anomalous spot since the at-site flood level merely responded to the non-stationarity. Based on the leading factor that the flood level responded to, PRD was divided into three regions. In general, regions within 22 km of delta outlets responded the most to the increasing tidal level induced by sea level rise, and spots that were located more than 45 km away from outlets were more affected by increasing inflow floods than by increasing high tidal levels. Stations that were located 22–45 km away from the delta outlets were influenced by both the sea level rise and the inflow increase. As for these stations, distance to the income stations, river network density, and the directions of river channels could all affect the extent of flood level response to the mutual impact of the nonstationary inflow floods and high tidal level. How these factors affect the water levels and their extents at different stations remains to be studied further. Meanwhile, the boundary of the incoming flood impact or that of the tidal level in other deltas can be detected in the same way.

Acknowledgments: The research was financially supported by the National Natural Science Foundation of China (Grant No. 91547202, 51210013, 51479216, 51379223, 51479217), the Chinese Academy of Engineering Consulting Project (2015-DA-07-04-03), the Public Welfare Project of Ministry of Water Resources (Grant No. 200901043-03), and the Project for Creative Research from Guangdong Water Resources Department (Grant No. 2016-07, 2016-01). Author Contributions: Yihan Tang and Xiaohong Chen conceived and designed the experiments; Chengjia Su performed the experiments; Yihan Tang analyzed the data with the help of Qizhong Guo; Yihan Tang, Xiaohong Chen and Chengjia Su contributed data and analysis tools; Yihan Tang wrote the paper with the help of Qizhong Guo and Xiaohong Chen. Conflicts of Interest: The authors declare no conflict of interest. Water 2017, 9, 471 15 of 16

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