2017 Asia-Pacific Engineering and Technology Conference (APETC 2017) ISBN: 978-1-60595-443-1 Research of Tide Level Consistency Correction for Station Yang Wang, Chuanzhe Li, Mengjie Zhang, Jia Liu, Fuliang Yu, Jiyang Tian and Hanjiang Nie

ABSTRACT

For inconsistency phenomenon of tide level data series of tidal reach of downstream for Qinhuai River,e w take the annual highest tide level from 1947 to 2010 of Nanjing Xiaguan Station for example, analyze its wavelet to determine energy cycle of the series, and make consistency correction on the series with the use of the extracted trend term of each year for tide level data. Analyze the correlativity between the tide level datum of Qixiang estuary and Jiuxiang estuary intoh t e River from Nanjing Station and the Qinhuai East River, establish prediction model of tide level intoh t e Yangtze River estuary from the Qinhuai East River through regression analysis, and make use of the corrected tide level series to predict the high and low tidal levels into the Yangtze River estuary from the Qinhuai East River. The results show that this method corrects the rising trend of tide level data of many years for the measured data, the established regressiono m del can achieve better prediction accuracy.1

INTRODUCTION Nanjing, one of the national key flood control city, has increasingly high standard of flood control construction due to its special geogr aphical location, the Qinhuai River, as the mother river of Nanjing, research on it plays an important role in flood control construction, with the city development, the main stream reach of downstream of the Qinhuai River has also been fully integrated into the Nanjing center city area, the whole city area basically coincides with the watershed scope, thus mastering the characteristics of the Qinhuai River such as water level and water flow is significant to flood control construction of Nanjin. Qinhuai River basin is located at downstream of the Yangtze River which is in the southwest of Province, with a total area of 2658km 2, its downstream

Yang Wang1,a, Chuanzhe Li1,b*, Mengjie Zhang1,c, Jia Liu1,2,d, Fuliang Yu1,e, Jiyang Tian1,f and Hanjiang Nie1,g 1State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, Institute of Water Resources and Hydropower Research, No.1 Fuxing Road, Haidian District, Beijing 100038, China; 2State Key Laboratory of Hydrology-Water Resource and Hydraulic Engineering, Hohai University, Nanjing 210098, China; [email protected], [email protected],[email protected] [email protected],[email protected], [email protected], [email protected]

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outlet connects with the Yangtze River, flood water level and flow during flood season is largely influenced by tide level of the Yangtze River which directly affects flood drainage of the Qinhuai River, the historical data shows that in 23 years from 1969 to 1991, there are 7 years in which tide level of Nanjing Xiaguan for the Yangtze River is over 9m during flood season, with its high tide generally occurring in July and August [1-2]. The flood water of the Qinhuai River is poorly drained due to uplift of tidal bore, once rainfall annealing shall be ten days, resulting in long-term trend of arrival of high water level. Although rainfall of the Qinhuai River basin is not much in the few years, high water level also occurs inside due to high tide level of the Yangtze River. Thus it can be seen that the tide level data and its forecasts of the Qinhuai River is a crucial part of flood control construction in Nanjing. As we all know, when the construction planning of the relevant water conservancy project is carried out, we usually regard the environment arising from the required data such as water level, tide level and rainfall to be invariable, so that the series of hydrological features in our research is considered to be pure random variables, because the relevant consistency correspondingly exists in the consistency data series of its impact factor, it is convenient for our research [3]. But with the economic development of the coastal areas, especially leaps and bounds in the Yangtze River Delta Economic Zone, the human damage to the environment is very serious, especially renovation project of some watercourses and pollution seriously affect the underlying surface conditions of the basin [4-5]. By statistical analysis of annual maximum data of Nanjing Xiaguan Station, the annual highest tide level from 1947 to 2010 presents the obvious trend of rising, and is largely influenced by human activities. This article adopts the wavelet analysis method to identify the time-varying cycle of fluctuation energy of tide level data for Nanjing Xiaguan Station, and then adopts the series consistency correction of the extracted trend term to make consistency correction on tide level data for Xiaguan Station, and establish relevant formulas of tide level to calculate information of tide level into the Yangzte River estuary from the Qinhuai River.

DATA COLLECTION AND RESEARCH METHODS

Data Collection This article collects the annual highest tide level data from 1947 to 2010 for Nanjing Xiaguan Station to carry out the analysis, as shown in Figure 1 from which you can see the rising trend of the annual highest tide level until 2010 for Xiaguan Station.

2182 Figure 1. Annual highest tide level for Nanjing Xiaguan Station.

Research Methods

Wavelet analysis Wavelet analysis has been widely used in the field of scientific research at the present stage, from physics, mathematics to image processing and signal analysis, earthquake science, etc., as a mathematical microscope, wavelet analysis has a huge advantage [6] in multiscale analysis, especially analysis processing of non-stationary signal. The statistics shows that in 1993, Kumar and Foufoular-Gegious first applied wavelet analysis method to the field of hydrology, after a few years, this method has made considerable progress and development in hydrology, but application in the tidology research was not much, just compare it with the traditional method[7-8] and carry out wavelet analysis processing of tide, there was not much research [9] on how to make wavelet analysis based on the time series characteristics of tide, response to the variation tend of the system in different time scales and qualitative estimation of the future development trend of the system. The basic idea of wavelet analysis is to use a cluster wavelet function system to approximate to a signal or a function[10]. In wavelet analysis, the selection of the function is a key issue, wavelet function means a kind of function that features concussion and quickly decays to zero, which satisfies:    0dt)t( (1)   Wherein )t( is the base wavelet function, we can configure it to a cluster function system by change of its scale or shift on the corresponding time axis:  / 21  bt   at  )()( (2) ,ba a  )t( Wherein b,a is baby wavelet; a is scale factor which indicates cycle length; b is shift factor which reflects time shift, wherein  0aR,ba, . When the energy input is limited signal, namely,  2 )R(L)t(f , transform formula of continuous wavelet that takes formula (2) as baby wavelet is: 2/1-  bt f   (f(t)a)b,a(W dt) R a (3) )b,a(W In the formula (3), f is wavelet transform coefficient, f (t) is a signal or a  bx  bx  ( )  ( ) square integrable function, a is conjugate function of a , the meanings of a, b are the same as the formula (2), the corresponding wavelet variance is:

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 2  f db)ba,(W)a(Var   (4) Tide level time series are mostly discrete, if  )tk(f is represented as discrete wavelet function, transform formula of discrete wavelet is as follows: N 2/1-  b-tk f    (t)f(kta)b,a(W ) 1k a (5) In research of this article, we take into account discreteness of tide level data, select MexHat wavelet in many wavelet functions such as MexHat wavelet, Morlet wavelet and Wave wavelet as a function to analyze tide level time series, this because MexHat wavelet is second derivative of Guass, and compact support exists to be convenient for discrete wavelet transform, thus better reflecting local variations in discrete series [11-12]. MexHat wavelet function is as follows: t 2 1    2 )1()( ett 2 2 (6) Wherein t  。

Consistency correction method extracted based on the series trend It is generally believed that the time series mainly consist of trend term, cycle term and random factor term, the formula is expressed as follows:  tRtPtAtz )()()()( (7) Wherein tz )( represents the total time series, tA )( 、 tP )( 、 tR )( respectively represents trend term, cycle term and random factor term. In fact, the measured data series of tide level that we have researched can be seen as a comprehensive reflection of the above three terms, cycle term is inherent existence of time series, random factor term contains two parts, one is mutation item which is not obvious in tide level data that we have researched for Nanjing Xiaguan Station, the other is random fluctuation item which includes human activities influence and random fluctuation of series itself, the consistency correction purpose is to eliminate interference of random and cycle terms on trend term, and determine time series influenced by trend item [13], if tw )( represents the corrected time series, kA )( represents trend value of the k item of the series and tA )( represents trend value of the t item, tw )( can be expressed as follows:  tAkAtztw ))()(()()( (8) It can be seen that the key of consistency correction is to eliminate the impact of cycle variation and random fluctuation in time series on the trend, in general, after determining the primary cycle of time series, we can consider the primary cycle as the length to seek moving average series of the measured series, taking series after moving average can substantially eliminate the interference of the cycle term and random term[14], and then correct the measured data to the current annual level in accordance with the above formula after trend term of the time series is extracted after moving average. We use a polynomial to represent the trend item tA )( : )( 2   tatataatA n 210 n (9) aa Wherein n is the order of the polynomial, 0 n is undetermined coefficient.

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Tide level prediction for entrance along the river Some entrances into the Yangtze Estuary from the Qinhuai New River have no tide level stations for, some entrances have short measured data, in order to comprehensively predict the tide level information of each entrance along the river, regression analysis method is required to establish the formula of tide level into the entrance of Yangtze River from the Qinhuai New River. The general correlativity for tide level data of different stations is unknown, but if the two stations are located close, and have observational data of the same period, a certain regularity can often be obtained through the analysis, this is because the two might have the same relationship of physical causes, and their degree of correlation can be determined through correlation analysis of the data of the same period for the related station, and then conduct further research, the related close degree between the two research objects is expressed with correlation coefficient R, the formula is as follows:  yxxyn R   2  )( 2 2  yynxxn )( 2 (10) R value range is from 0 to 1, when R changes from 0 to 1, it indicates that correlativity between the two changes from weak correlation to significant correlation to high correlation, generally compare the calculated correlation R R coefficient R with the correlation coefficient critical value a , if it is less than a ,the R degree of correlation between the two is not high, if it is greater than a , the two have a good degree of correlation [15]. Regression analysis is a specific form to determine the correlation of two variables based on the correlation analysis after correlation direction and close degree of the two variables are determined, so that the value of correlation variable can be calculated through series data of a variable. Unary linear regression equation is as follows:  baxy (11) Wherein x is independent variable, y is dependent variable, a is regression coefficient, b is constant term. The key of regression analysis is to determine the a, b values of the regression equation, for the unary linear regression equation, the least square method can be used to inquire the a, b values [16], namely:  xayb (12)  yxxyn a  2 xn  x )( (13)

CASE STUDY Take the highest tide level data measured from 1947 to 2010 for Nanjing Xiaguan Station as an example to conduct case study. First select Mexhat wavelet to make wavelet analysis on the selected data, the wavelet variance diagram obtained is shown in Figure 2:

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Figure 2. Wavelet variance diagram of tide level data from 1947 to 2010 for Nanjing Xiaguan Station.

Wavelet variance diagram depicts the integral of wavelet variation coefficient to the time, changes distribution of energy during fluctuation can be seen which helps to determine the primary cycle in the tide level series, it can be seen from Figure 2: (1)There is a maximum value for tide level data of Xiaguan Station at location of time axis 2a, indicating tide level series of Xiaguan Station feature cycle variation of 2a. (2)There is also a great energy value for fluctuation of tide level data at the location of time axis 17a, indicating that the tide level series also feature a primary cycle of 17a. Ocean tide has a long cycle of 18.6a, but will be reduced due to the influence of factors such as seafloor topography and surface runoff when the tide reaches the position near the Yangtze River estuary, therefore, the primary cycle of 17a is basically in line with the actual situation. Conduct 17a moving average processing of tide level data for Nanjing Xiaguan Station through the determined 17a primary cycle, here the weight of high tide level data of each year is approximately the same, so directly take the arithmetic mean value of 17a data, the first data value is obtained from the data average of 17 years from 1947 to 1963, the result corresponding t = 9, the last data is obtained from the data average of 17 years from 1994to 2010, the result corresponding t = 56, the moving average results are shown in Figure 3:

Figure 3. Moving average process of the highest tide level for Nanjing Xiaguan Station.

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Before and after series that are after the moving average are 8 items less than the original series, fit the series after moving average with least square method, calculate as follows according to 2 of n taken in the formula (9) of fitting best principle: tA  t 2  t  7134.70278.00001.0)( (14) t=9，10，···，56. The highest tide level trend term from 1955 to 2002 is expressed by the formula (14), for the trend values of 14 terms of the original series that miss before and after, it can be obtained according to the following formula:  AtA )8()( t=1，2，3，···，7 （15）  56 )(A)t(A t=57，58， 59，···，64 (16) Consistency correction of the highest tide level series can be made for Nanjing Xiaguan Station by combing the formulas (14), (15) and (16) with the formula (8), the results are shown in Figure 4:

Figure 4. Comparison diagram before and after correction of the highest tide level for Xiaguan Station.

It can be seen from the diagram that correction amplitude of the highest tide level for Nanjing Xiaguan Station is relatively large in the early period, and the correction amplitude is relatively small in recent years, because the time and degree with impact of human activities undergone by the early data on the highest tide level are relatively large, and human activities interference undergone by recent data is relatively small, this result is in line with the requirements of the actual situation. The corrected results maintain the age change features of the original series, and it can be seen by adding the trend line that the trend term of the original data is on the rise, the corrected series trend line remains horizontal, indicating the correction process eliminates the interference of the cycle term random term. Finally, use the corrected data to predict the tide level into the Yangtze River entrance from the Qinhuai East River, Zhenjiang tide-gauge station is located at 80.15km downstream of Nanjing Xiaguan tide-gauge station, Qixiang estuary into the Yangtze River entrance from the Qinhuai East River is located at 32.55km downstream of Nanjing Xiaguan tide-gauge station, Jiuxiang estuary is located at 26.40km downstream of Nanjing Xiaguan tide-gauge station. Research the

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correlativity between Nanjing Station and Qixiang estuary as well as Nanjing Station and Jiuxiang estuary, establish correlation model of characteristic tide level for Nanjing Station and Qixiang estuary through characteristic tide level series of Nanjing Station and Qixiang estuary; similarly, establish correlation model of characteristic tide level for Nanjing Station and Jiuxiang estuary through characteristic tide level series of Nanjing Station and Jiuxiang estuary. Adopt daily characteristic tide level data of the main flood season ( from June 1 to August 31) of a total of four years from 2000 to 2003 for Nanjing Station, and locations of Zhenjiang station of Nanjing station and Qixiang estuary, Jiuxiang estuary into the Yangtze River entrance from the Qinhuai East River to conduct linear interpolation to obtain the daily characteristic tide level of the main flood season from 2000 to 2003 for the Yangtze River entrance and Jiuxiang estuary, and make correlation analysis on tide level of Nanjing Station and tide level of Jiuxiang estuary and Nanjing Station, which is shown as follows:

Figure 5. Correlativity of high tide level between Qixiang estuary and Nanjing Station.

Figure 6. Correlativity of high tide level between Jiuxiang estuary and Nanjing Station. Correlation equation of characteristic tide level of Qixiang estuary, Jiuxiang estuary into the Yangtze River entrance from the Qinhuai East River and Nanjing Station is obtained as follows through correlation analysis calculation: Zgqxh  8932.0 Zgxg  3166.0 (17) Zgjxh  9134.0 Zgxg  2611.0 (18) Wherein: Zgxg , Zgqxh are respectively high tide level of Nanjing station, high tide levels of Qixiang estuary and Jiuxiang estuary, tide level unit (Wusong datum level) is m.

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SUMMARY (1) When we research flood control of Qinhuai River basin located in Nanjing, we shall not only pay attention to upstream runoff generation and confluence, but also carry out research and make comprehensive analysis on tide level into the Yangtze Estuary due to its special geographical location, the uplift of tide level of Yangtze River in the watercourse has a great influence on upstream incoming water, so it is very necessary to obtain the correct tide level data to research the water level and flow for this tidal river reach. (2) The measured tide level of Nanjing Station has the uplift trend in the measured year, which is mainly due to the impact of human activities on the tide level, and by determining the intrinsic energy cycle of the data, with the moving average processing, and then through consistency method of the series, we can effectively eliminate the influence of cycle factor and random factor on the series, and more accurately extract the random term of each year. Unify the datum of different periods through the extracted random item to the status quo year, the tide level value inquired may reflect the measured year and future tide level changes to some extent, but the assumption of this method is that changes of tide level data in the near future remain stable. But in reality, a lot of tide level datum not only have trend changes in measured year, but also such changes will continue in the period ahead, in this case, even if the tide level datum are corrected to the status quo year, the resulting series only reflect the current trend of the tide level, and fail to reflect the future trend changes of the tide level, how to deal with consistency correction of the tide level data under the changes trend is an issue that needs further discussion. (3) Datum of many locations for tide level into the Yangtze River entrance from the Qinhuai River are not available, establish correlativity between the known tide-gauge station and unknown tide-gauge station through regression analysis, establish tide level correlation equation, predict the information on tide level into each entrance of the Yangtze River estuary from the Qinhuai East River, correlation of data between Nanjing Station and Qixiang estuary, Jiuxiang estuary is strong, with linear regression relation, the established tide level prediction equation is simple and accurate.

ACKNOWLEDGEMENTS This study was supported by the National Natural Science Foundation of China (Grant No. 51409270 and 51209225), the International Science and Technology Cooperation Program of China (Grant No. 2013DFG70990), the foundation of China Institute of Water Resources and Hydropower Research (1232), and the Open Research Fund Program of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering (2014490611).

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