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Nonstationary statistical approach for designing LNWLs in inland waterways: a case study in the downstream of the Lancang River

  • Jiangyan Zhao
  • Ping Xie
  • Mingyang Zhang
  • Yan-Fang Sang
  • Jie Chen
  • Ziyi Wu
Original Paper
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Abstract

Conventional methods to design the lowest navigable water level (LNWL) in inland waterways are usually based on stationary time series. However, these methods are not applicable when nonstationarity is encountered, and new methods should be developed for designing the LNWL under nonstationary conditions. Accordingly, this article proposes an approach to design the LNWL in nonstationary conditions, with a case study at the Yunjinghong station in the Lancang River basin in Southwest China. Both deterministic (trends, jumps and periodicities) and stochastic components in the hydrological time series are considered and distinguished, and the rank version of the von Neumann’s ratio (RVN) test is used to detect the stationarity of observed data and its residue after the deterministic components are removed. The stationary water level series under different environments are then generated by adding the corresponding deterministic component to the stationary stochastic component. The LNWL at the Yunjinghong station was estimated by this method using the synthetic duration curve. The results showed that the annual water level series at the Yunjinghong station presented a significant jump in 2004 with an average magnitude decline of − 0.63 m afterwards. Furthermore, the difference of the LNWL at certain guaranteed rate (90%, 95% and 98%) was nearly − 0.63 m between the current and past environments, while the estimated LNWL under the current environment had a difference of − 0.60 m depending on nonstationarity impacts. Overall, the results clearly confirmed the influence of hydrological nonstationarity on the estimation of LNWL, which should be carefully considered and evaluated for channel planning and design, as well as for navigation risk assessment.

Keywords

Lowest navigable water level Inland waterways Synthetic duration curve Hydrological nonstationarity Lancang River 

1 Introduction

Inland waterways play a vital role in promoting economic development, due to their considerable capacity for the low-cost transport of goods. Especially in China, there are numerous rivers and lakes throughout the mainland, and they offer abundant water resources for the development of inland waterways (Paul et al. 2009; Yan et al. 2017b). However, navigation on these inland waterways has faced some troubles caused by the limited runoff and the low water levels (as described in “Appendix 1”) during dry seasons (Linde et al. 2016). Transport vessels have to reduce their loads and even stop navigating to avoid the risk of grounding (Samuelides et al. 2009; Hawkes et al. 2010; Mazaheri et al. 2016). These situations increase the costs of transport and will be unfavorable for the development of the navigation industry (Jonkeren et al. 2011).

To optimize the capacity of inland navigation, many researches have considered both ship loading variations and channel dredging to provide the largest ship draft and the best available navigable depth. Generally, declining water levels will reduce ship clearances in channels and increase the demand for dredging (Kling et al. 2003). While it was not always possible or desirable to increase channel depths, it may be necessary to either lighten the current ship loading maximum or use a new type of ships in order to meet the underkeel safety margin requirement (Grambsch 2002).

Among these methods, designing, building and outfitting new ships or dredging channels are both time-consuming and costly, and are therefore insufficient to compensate for the losses resulting from recurrent low water levels. Eloot and Söhngen (2014) considered the impact of tide and water level changes as well as other factors on the design of channels to meet the requirement of navigable depth and to assess the restrictions on vessels caused by low water levels. In order to ensure continuous water levels and the minimum required navigable water level, Wagenpfeil et al. (2010) created a model to adjust the amount of pumping and discharge. However, navigable hydrological conditions were not thoroughly considered, especially in the context of a changing environment.

Because the available water depth is one of the most critical factors for efficient inland navigation, the concept of navigable depth (or nautical depth) has been accepted for defining a safe and effective channel bottom criterion. The requirement of water depth is that these vessels can safely navigate through the channel with a suitable under keel clearance (UKC) over the fluid mud (Herbich et al. 2015; Mcanally et al. 2015), where the UKC is the difference between the ship draft and the lowest safe channel depth, as defined by United States Army Corps of Engineers (USACE 2006). In China, the lowest navigable water level (LNWL) is designed using the synthetic duration curve, as the primary method, with the duration-frequency method utilized as a secondary method. Both the LNWL and the lowest safe channel depth can reflect the navigable capacity of a channel, and they can convert to each other with no essential differences. However, these methods for the design of the LNWL are mainly based on stationary hydrological time series; they are not applicable for nonstationary hydrological time series due to the change of environment (Parry et al. 2007; Blöschl et al. 2007; Sivapalan and Blöschl 2015) that can result in changes in the frequency distribution of hydrological events (e.g., floods, droughts, etc.) (Milly et al. 2008; Schiermeier 2011; Sang et al. 2017), as well as occurrences of different forms and degrees of hydrological variations (Villarini et al. 2009; Vogel et al. 2011). Therefore, an approach for dealing with the nonstationary hydrological time series is needed in determining LNWLs.

Generally, studies of nonstationary hydrological frequency analysis methods can be divided into two main classes (Liang et al. 2017). The first uses nonstationary frequency analysis models to estimate the hydrological design values (Strupczewski et al. 2001; Alila and Mtiraoui 2002; Singh et al. 2005; Villarini et al. 2009). However, these methods require the complex calculation of model parameters, generally associated with considerable estimation errors. In addition, the design standards (e.g., exceedance probability, return period, etc.) for stationary frequency analysis cannot be used when adopting distribution functions varying with time for this first class of methods. Thus, exceedance probability, return period or the other design standards need to be carefully defined in a changing environment (Yan et al. 2017a). The second class of methods involves converting the hydrological time series from nonstationary to stationary in order to apply conventional stationary frequency analysis methods (Xie et al. 2005; Hu et al. 2015; Gado and Nguyen 2016; Liang et al. 2017). These methods have been widely used in frequency analysis of nonstationary annual runoff or of extreme flow with the goals of estimating flood or drought risk. However, they have not been used in frequency analysis for nonstationary water levels, which could have a great influence on navigation safety.

Accordingly, a nonstationary approach is proposed for LNWL design. This method is developed based on the concept of detecting and decomposing different components in hydrological time series, and then composing these components in annual time series (Xie et al. 2005), and thus it is categorized with the second class of methods defined above. Specifically, the stationary daily water level series is composed by multiplying the observed daily water level by a ratio scaling index. The ratio scaling index is defined as the ratio of the reconstructed stationary annual water level and the observed annual water level for each year. This approach allows the use of conventional methods to design the LNWL. The synthetic duration curve is used here to estimate the LNWL based on the composed daily water level series. The article is organized as follows. Section 2 describes the study area and data, and then the methodology for designing nonstationary LNWLs is presented in Sect. 3. The results and discussion are presented in Sect. 4, followed by conclusions and suggestion for future work in Sect. 5. These sections are followed by two appendices that describe specific terminology and methods used for detecting deterministic components, respectively.

2 Study area and data

The Lancang River, with a length of 4880 km, is the upper section of the Lancang-Mekong River, which is the largest river in Southeast Asia and has a drainage area of approximately 795 000 km2 (Campbell 2009). From its source to its outlet on the China–Myanmar border, the river plunges 4700 m through the high gorges of Tibet and Yunnan Province, which is more than 90% of its entire drop in elevation (Fan et al. 2015). The Lancang River is an important navigable river for Yunnan Province, and it also plays a significant role in international waterway transport linking China and Indochina Peninsula countries; the Lancang-Mekong River is regarded as an international golden waterway. The river thus has special international meaning for the economic development of Yunnan Province and for the Association of Southeast Asian Nations (ASEAN). However, the physical conditions of hydrological cycles and of the water level profile in the Lancang River basin have changed under the influence of global climate change and especially high-intensity human activities, including cascade hydropower development (Lauri et al. 2012; Tang et al. 2014; Räsänen et al. 2017). The observed water level series present variability and changes, which means that the assumption of stationary observations is not fulfilled. Especially at the Yunjinghong hydrological station, the main control station in the dowstream of the Lancang River, the streamflow regimes are affected not only by climate change but also by upstream dams.

There now are six large dams located in the mainstream of the Lancang River, namely Gongguoqiao, Xiaowan, Manwan, Dachaoshan, Nuozhadu and Jinghong (Fig. 1). The Manwan Dam, completed in 1992, and the five other large dams completed subsequently are presented in Table 1. The six dam reservoirs have an accumulated total storage of approximately 43.2 km3 (Li et al. 2017), accounting for 78.5% of the annual runoff at Yunjinghong station (55.0 km3 per year from 1955 to 2014).
Fig. 1

Location of the Yunjinghong hydrological station and the major dams

Table 1

Characteristics of the major dams in Lancang River basin

Dam

Year started

Year completed

Total storage (km3)

Catchment area (km2)

Manwan

1986

1992

0.92

114,500

Dachaoshan

1992

2003

0.93

121,000

Xiaowan

2002

2010

14.56

113,300

Jinghong

2003

2009

1.23

149,100

Nuozhadu

2004

2014

22.40

144,700

Gongguoqiao

2007

2011

3.16

97,300

For the design of the LNWL, water level variations should be considered, including its response to hydropower development and its influence on navigation safety. In this study, the daily water level data measured at the Yunjinghong station (national vertical datum 1985 in China) during the 1955–2014 are chosen to design the LNWL in the downstream section of the Lancang River.

3 Approach for designing nonstationary LNWLs

Hydrological time series include deterministic components, which show nonstationary characteristics (Papoulis and Pillai 2002; Salas 1993). Since conventional methods for the design of LNWLs in inland waterways are based on stationary data, they are not applicable when the requirement of stationarity cannot be satisfied. Thus, the initial problem for designing the nonstationary LNWL is to detect deterministic components in water level series. In this paper, the Mann–Kendall test, the Brown–Forsythe test and the Fourier series method (as described in “Appendix 2”) are chosen to detect trends, jumps and periodicities, respectively. The stationary series are then constructed by composing the stationary stochastic component and the deterministic component for any selected year. Since the deterministic component is a constant, the composed series are stationary with constant mean value (Milly et al. 2015). By utilizing this method, the LNWL can be determined using a synthetic duration curve.

3.1 Preliminary assumption

Hydrological time series can be decomposed into deterministic and stationary stochastic parts. Such decomposition allows the application of statistical tools based on stationarity in the characterization of the stationary stochastic components of observed time series (Milly et al. 2015).

Here it is assumed that annual hydrological time series \(X_{t}\) is composed of deterministic (\(Y_{t}\)) and stochastic (\(S_{t}\)) components (Yevjevich 1972; Guttman and Plantico 1989; Xie et al. 2005; Stojković et al. 2017). This is also called an additive model and can be expressed as:
$$X_{t} = Y_{t} + S_{t}$$
(1)
where \(Y_{t}\) includes three different types of trend, jump and periodicity (Maidment 1993), all with nonstationarity, while \(S_{t}\) is usually considered to be stationary.

3.2 Detection of hydrological components

In order to decompose the nonstationary hydrological series into deterministic and stationary stochastic components, these deterministic components should be detected and removed from the observed series to gain stationary stochastic parts. The ranked version of the von Neumann’s ratio (RVN) (Bartels 1982) is used to judge whether an observed series contains a time invariant mean (Machiwal and Jha 2012), which indicates the stationarity of the series. If a series is not stationary, the stationarity of its residue obtained by removing the assumed deterministic components must be tested. The test statistic RVN is given as:
$$RVN = {{\sum\limits_{i = 1}^{n - 1} {(R_{i} - R_{i + 1} )^{2} } } \mathord{\left/ {\vphantom {{\sum\limits_{i = 1}^{n - 1} {(R_{i} - R_{i + 1} )^{2} } } {\sum\limits_{i = 1}^{n} {(R_{i} - \bar{R})^{2} } }}} \right. \kern-0pt} {\sum\limits_{i = 1}^{n} {(R_{i} - \bar{R})^{2} } }}$$
(2)
where \(\bar{R}{ = }\frac{1}{n}\sum\nolimits_{i = 1}^{n} {R_{i} }\); \(R_{i}\) is the rank of the ith observation and \(n\) is the length of samples.

Here the \(N(2,4/T)\) distribution can be used as an approximation of RVN (where \(N\) represents a normal distribution; 2 and \(4/T\) represent the mean and variance, respectively). The time series is nonstationary if the value of RVN is bigger than the value of \((2{ + }2U_{{1{ - }\alpha /2}} /\sqrt n )\) or smaller than the value of \((2{ - }2U_{{1{ - }\alpha /2}} /\sqrt n )\), where \(U_{1 - \alpha /2}\) is the critical value of standard normal distribution with the specification of the significance level \(\alpha\). Otherwise, the time series is stationary.

If the observed hydrological series is not stationary, the trend is detected by using the nonparametric Mann–Kendall test (Naghettini 2017). If the null hypothesis of no trend is rejected at the significance level of \(\alpha\), the trend is assumed to be linear (A nonlinear trend can be transformed into a linear trend by mathematical transformation), expressed as:
$$Y_{t} = A + Bt$$
(3)
where A and B are two coefficients whose values can be estimated using the least squares method.
Meanwhile, the Brown–Forsythe test (Brown and Forsythe 1974) is used to determine the occurrence of the jump point, which retains the virtue of simplicity and reduces the limitations for data samples. If a significant jump exists, the whole series is divided into two parts, with the data length of \(n_{1}\) and \(n_{2}\):
$$Y_{t} = \left\{ {\begin{array}{*{20}l} {0,} \hfill & {t = 1,2, \ldots ,n_{1} } \hfill \\ {b,} \hfill & {t = n_{1} + 1,n_{1} + 2, \ldots ,n} \hfill \\ \end{array} } \right.$$
(4)
where \(b\) is a constant.
The hydrological series is expressed as:
$$X_{t} = \left\{ {\begin{array}{*{20}l} {S_{t} ,} \hfill & {t = 1,2, \ldots ,n_{1} } \hfill \\ {b + S_{t} ,} \hfill & {t = n_{1} + 1,n_{1} + 2, \ldots ,n} \hfill \\ \end{array} } \right.$$
(5)
where the value of \(b\) is equal to the difference of the mean magnitude between the two parts of the series.
If only trend or jump are detected to be significant by the above tests, the corresponding deterministic component is removed from the observed series. When both of them are significant, the Nash efficiency coefficient is introduced to make a comprehensive judgement. The Nash efficiency coefficient is calculated as:
$$R^{2} = 1 - \frac{{\sum\nolimits_{i = 1}^{n} {(Q_{obs,i} - Q_{sim,i} )}^{2} }}{{\sum\nolimits_{i = 1}^{n} {(Q_{obs,i} - \bar{Q}_{obs} )}^{2} }}$$
(6)
where \(Q_{obs,i}\) (i = 1, …, n) represents the observed hydrological series \(X_{t}\); \(\bar{Q}_{obs}\) represents the mean of the observed hydrological series \(\bar{X}\); and \(Q_{sim,i}\) (i = 1, …, n) is the sum of the assumed deterministic component and the mean of the stochastic component. The deterministic component with a greater efficiency coefficient is then chosen as the variation form.
After removing the trend and jump components, the RVN test is used to identify whether the residual component is stationary. If not, the periodic component is detected using the Fourier series (Machiwal and Jha 2012), and the period \(T\) can be determined. Here the periodic component is expressed as:
$$Y_{t} = A + B\sin \frac{2\pi }{T}(t - t_{0} )$$
(7)
where A and B are two coefficients; \(t_{0}\) is the initial phase, and \(t_{0} \in [ - \pi ,\pi ]\).

A and B can be calculated using the least squares method with each assumed \(t_{0}\), and their values are chosen by applying the Nash efficiency coefficient, which quantifies the similarity between \(Y_{t}\) and the residue obtained by removing the trend or jump component of the observed series.

3.3 Design of the LNWL

The synthetic duration curve method and the guaranteed rate-frequency method are usually used to design the LNWL with stationary water level series. The former method first sorts all the values of daily average water level from large to small, and then calculates the cumulative guaranteed rate corresponding to the water level at each degree. The synthetic duration curve is then drawn and the corresponding LNWL can be determined for the designed guaranteed rate. In a changing environment, water level series are no longer stationary, and so the synthetic duration curve cannot be used to calculate the values of the LNWL with the observed data. Under such circumstances, a good option would be to draw the synthetic duration curves corresponding to different conditions, so that the LNWL can be estimated for different environments. In this study, the stationary series is reconstructed for a certain time by means of an additive model based on hydrological component analysis. The LNWL is then calculated using the synthetic duration curve for different conditions. The framework for the design of the nonstationary LNWL is shown in Fig. 2.
Fig. 2

Framework for the design of the LNWL with nonstationarity

The approach for the design of the LNWL consists of the following eight steps:
  • Step i: Detect the trend and jump components For an annual water level series, its trend and jump components are detected by using the Mann–Kendall test and the Brown–Forsythe test, respectively. Further, the Nash efficiency coefficient is used to make comprehensive judgement of trend and jump. The deterministic component with greater efficiency coefficient is chosen as the form of variation;

  • Step ii: Detect the periodic component If the residual component is nonstationary after removing the trend or jump in step i, the Fourier series method is used to detect the periodicity of the residual series, and then the periodic component can be determined;

  • Step iii: Gain stationary stochastic component According to the additive model, the hydrological series \(X_{t} (t = 1,2, \ldots ,n)\) includes a deterministic component \(Y_{t} (t = 1,2, \ldots ,n)\) and stochastic component \(S_{t} (t = 1,2, \ldots ,n)\). The deterministic component is removed, so as to gain the stationary component \(S_{t}\):
    $$S_{t} = X_{t} - Y_{t}$$
    (8)
  • Step iv: Compose stationary annual water level series The crux of gaining the stationary annual water level series is to determine the deterministic component \(Y_{{t_{0} }}\) for each year \(t_{0}\). The stationary annual water level series \(X_{{t,t_{0} }}\) corresponding to the environment of the year \(t_{0}\) is composed through the numerical formula as:
    $$X_{{t,t_{0} }} = Y_{{t_{0} }} + S_{t} = Y_{{t_{0} }} + (X_{t} - Y_{t} )$$
    (9)
    where \(t = 1,2, \ldots ,n\); n is the length of the annual water level series.
  • Step v: Calculate ratio scaling index of water level for each year \(t_{0}\) The stationary annual water level series \(X_{{t,t_{0} }}\) for different environments are generated using the above steps. The ratio of the stationary annual water level and the observed annual water level for each year \(t_{0}\) is calculated as:
    $$K_{t} = X_{{t,t_{0} }} /X_{t}$$
    (10)
    where \(K_{t}\) is the ratio scaling index.
  • Step vi: Determine stationary daily water level series The observed daily water level in each year \(t_{0}\) is multiplied by \(K_{{t_{0} }}\), which is the ratio scaling index for the corresponding year. The stationary daily water level series is then generated with the above calculations.

  • Step vii: Draw synthetic duration curves for daily water levels All values of the daily average water level are first sorted from large to small in the statistical years, and then the cumulative guaranteed rate is calculated corresponding to the water level at each degree. The synthetic duration curve is then drawn based on those cumulative guaranteed rates.

  • Step viii: Design the LNWL According to the synthetic duration curve, the water level is estimated to satisfy the requirement of guaranteed rate. Thus, the designed LNWL can be determined by using the synthetic duration curve.

4 Results and discussion

4.1 Detecting the components of annual water level series

The variability of water levels at the Yunjinghong Station from 1955 to 2014 are shown in Fig. 3, where the Y-axis is expressed in terms of the modulus coefficient in dimensionless form, that is, \(Y_{t} = X_{t} /\bar{X}\), where \(\bar{X} = (\sum\nolimits_{t = 1}^{n} {X_{t} } )/n\). The maximum and the minimum of original daily water levels are 552.08 m and 533.52 m, respectively, so the range of water level changes is 18.56 m, which means the water level fluctuations are relatively large.
Fig. 3

Interannual and interdecadal variations of water levels at the Yunjinghong station for 1955–2014

The stationarity of annual water level series is first judged using the RVN test with the following equation:
$$RVN = 1.29 < (2 - 2U_{1 - \alpha /2} /\sqrt n ) = 1.49$$
(11)
where the test is taken under the significance level of α = 0.05, and \(U_{1 - \alpha /2}\) is the significant critical value following a standard Normal distribution. Here the \(RVN\) is smaller than the critical value as presented in Eq. (11), which means the time series is nonstationary with a probability of 95%.
The deterministic component can be detected. The trend is detected using the Mann–Kendall test, and the standardized test statistic \(U_{MK}\) is calculated as:
$$|U_{MK} | = | - 0.91| = 0.91 < U_{1 - \alpha /2} = 1.96$$
(12)
According to this result, the trend is not significant for this time series. In addition, the jump component is detected using the Brown–Forsythe test. Considering the fact that the samples are too small when the time point is too close to the two end-points of the sub-series, the sliding starting point is the tenth of the samples and the ending point is n-10 (n is the length of samples). The largest value of F, which is the statistic of the Brown–Forsythe test, is calculated as:
$$F_{\hbox{max} } = 28.28 > F_{\alpha } = 4.48$$
(13)
where \(F_{\hbox{max} }\) is bigger than the theoretical value \(F_{\alpha }\) with the specification of the significance level \(\alpha { = }0.05\). This result shows that the jump is significant for this time series.
Overall, the jump is significant for the hydrological series, while the trend is not. The result shows that the mean of the annual water levels at the Yunjinghong station jumped down in 2004, as shown in Fig. 4 (the Y-axis is expressed using the modulus coefficient in dimensionless form, that is, \(Y_{t} = X_{t} /\bar{X}\), where \(\bar{X} = (\sum\nolimits_{t = 1}^{n} {X_{t} } )/n\)).
Fig. 4

Jump variation of annual water levels at the Yunjinghong station for 1955–2014

The mean of the sub-series before and after the jump point 2004 is calculated, and the jump function is:
$$y_{t} = \left\{ {\begin{array}{*{20}l} {536.77} \hfill & {1956 \le t \le 2004} \hfill \\ {536.14} \hfill & {t > 2004} \hfill \\ \end{array} } \right.$$
(14)
where the measurement of \(y_{t}\) is in meters.
The difference of the mean magnitude after and before the jump point 2004 is regarded as the jump component:
$$Y_{t} = \left\{ {\begin{array}{*{20}l} 0 \hfill & {1956 \le t \le 2004} \hfill \\ { - 0.63} \hfill & {t > 2004} \hfill \\ \end{array} } \right.$$
(15)
The jump component is first removed from the water level series, and then the RVN test is taken for the residual component. The result is:
$$\left\{ {\begin{array}{*{20}l} {RVN = 1.57 > (2 - 2U_{1 - \alpha /2} /\sqrt n ) = 1.49} \hfill \\ {RVN = 1.57 < (2 + 2U_{1 - \alpha /2} /\sqrt n ) = 2.51} \hfill \\ \end{array} } \right.$$
(16)

According to the RVN test, the residual component is stationary, which can be regarded as the stationary stochastic component. Thus, the periodicities would not need to be considered.

4.2 Design of the LNWL

The existence of a jump point in 2004 means the sub-series between 1955–2004 and 2005–2014 may correspond to two environments: one with the deterministic component 0 named as the past environment, and the other with the deterministic component − 0.63 m considered as the current environment. Since the length of the second period is not long enough to be used in the design of the LNWL, the stationary annual water level series are composed for the above two environments through Eq. (9). This step ensures that the reconstructed stationary series has the same length as the original series. Further, in order to determine the stationary daily water level series, the ratio of the stationary annual water level and the original annual water level for each statistical year is calculated. The observed daily water level is then multiplied by the ratio scaling index for the corresponding year. The stationary daily water level series is generated through Steps (v–vi). It can be found that the reconstructed stationary daily water level for the current environment is generally lower than that for the past environment, as indicated in Fig. 5. The daily water level for the past environment fluctuates around its mean of 536.77 m, while that for the current one fluctuates around its mean of 536.14 m. It is consistent with the difference of the deterministic components corresponding to the above two environments.
Fig. 5

Stationary daily water level series for different environments for 1955–2014

According to the stationary daily water level series for different environments, the LNWL is determined using the synthetic duration curve (Fig. 6) introduced in Steps (vii–viii). Although the conventional method for the LNWL design could not be directly applied to the nonstationary observed water level series, the synthetic duration curve for observed nonstationary daily water levels is also drawn so as to compare the difference of the designed LNWL between different environments and assumptions. Furthermore, Table 2 shows the results of the designed LNWL for different environments and assumptions, with guaranteed rates of 90%, 95% and 98%.
Fig. 6

Diagram of synthetic duration curves for different environments and assumptions (Not considering nonstationarity means the observed nonstationary daily water levels were directly used to draw the synthetic duration curve, while past environment and current environment mean the stationary water level series are first constructed based on the corresponding deterministic component, and then their synthetic duration curves are drawn. These synthetic duration curves are enlarged with the guaranteed rate from 90 to 100%.)

Table 2

Results of designing the lowest navigable water level (m)

LNWL for different environments and assumptions

Guaranteed rate

90%

95%

98%

Past environment

534.90

534.77

534.65

Current environment

534.27

534.14

534.03

Not considering nonstationarity

534.85

534.75

534.64

Difference between current and past environment

− 0.63

− 0.63

− 0.62

Difference between the current with and without considering nonstationarity

− 0.58

− 0.61

− 0.61

When considering the nonstationarity of water levels, the stationary water level series can be constructed for different environments based on the corresponding deterministic components. The difference of the deterministic component is − 0.63 m after and before the jump point 2004 as presented in Eq. (15), which is consistent with the results in Table 2. It can be seen that the difference of the LNWL for the same guaranteed rate (90%, 95%, 98% respectively) between the current environment and the past one is nearly − 0.63 m. Moreover, when the observed water level series is directly used to calculate the LNWL using a synthetic duration curve, the difference of the LNWL under the current conditions between considering nonstationarity or not is approximately − 0.60 m. This may have a negative influence on navigation safety since the standard water depth of the channel is only 2.0 m.

4.3 Exploration of physical causes

Water levels between 1955–2004 and 2005–2014 are compared using a Tukey-boxplot (Sheskin 2011) as shown in Fig. 7. The results illustrate that the median of water levels for the current period is smaller than that for the past one, as are the maximum and the minimum values. In addition, Fig. 7 also shows a reduction of the water level fluctuations for 2005–2014 compared to those for 1955–2004.
Fig. 7

Tukey-boxplot for water level for different periods

The physical causes of the jump point in 2004 in the annual water levels at the Yunjinghong station and other characteristics of water level variation are analyzed from the following two aspects: regional precipitation change and cascade hydropower development.

The annual precipitation of the region influencing the Yunjinghong station from 1961 to 2014 is shown as Fig. 8. The Y-axis is expressed in terms of the modulus coefficient in dimensionless form, that is, \(Y_{t} = X_{t} /\bar{X}\), where \(\bar{X} = (\sum\nolimits_{t = 1}^{n} {X_{t} } )/n\). Further, the stationarity of the annual precipitation is tested using the test statistic RVN. It can be calculated as:
$$\left\{ {\begin{array}{*{20}l} {RVN = 2.11 > 2 - 2U_{1 - \alpha /2} /\sqrt n = 1.47} \hfill \\ {RVN = 2.11 < 2 + 2U_{1 - \alpha /2} /\sqrt n = 2.53} \hfill \\ \end{array} } \right.$$
(17)
where the test is taken under the significance level of α = 0.05, and \(U_{1 - \alpha /2}\) is the significant critical value following a standard Normal distribution.
Fig. 8

Annual precipitation and its mean values for Yunjinghong station for 1955–2014

The result of the RVN test shows that the annual precipitation series is stationary. The previous study showed that the annual precipitation in the Lancang River basin decreased by 10–20% in 2003, which was a particularly dry year for the whole Mekong River basin (He et al. 2006; Li and He 2008). However, since the annual precipitation series is stationary, it can be concluded that the annual precipitation did not result for the jump in the water level series.

The cascade hydropower development in the Lancang River is considered next. On one hand, the operation of these water conservancy projects regulates runoff and affects water levels in the river, which make a reduction of the water level fluctuations for 2005–2014 as shown in Fig. 7; on the other hand, these projects also greatly change the river’s shape and alter water levels and navigation conditions. There are six large dams constructed in the mainstream of Lancang River (Fig. 1), and these dams have different influences on water processes due to their storage capacities and catchment areas. Considering the jump point is 2004, it can be concluded that the construction of Xiaowan, Jinghong and Nouzahdu contributed greatly to the water level variation, since these three dams began to be constructed in 2002, 2003 and 2004, respectively. Especially, the storage capacity of the Nouzhadu dam ranks the highest among these six dams as presented in Table 2. Although the Dachaoshan dam began to run in 2003, the reservoir does not have multi-year regulation performance. Thus, the annual water level is still mainly affected by the construction of water conservancy projects.

4.4 Impacts of water level variation on navigation safety

The LNWL is the minimum water level that allows standard ships or fleets to navigate safely, and it is an important indicator to determine whether a ship has a risk of grounding. To prevent a ship from bottoming out, there are certain UKCs, including the ship squat and the safety margin for bottoming (Sergent et al. 2015; Liu and Liu 2016), as shown in Fig. 9. In general, if the value of the UKC increases, the ship navigation safety will be improved while the capacity of the waterways will be reduced. Therefore, the UKC needs to be maintained at a reasonable value to balance the relationship between navigation safety and a waterway’s capacity. The navigation standards and norms provide the UKC corresponding to the degree of channels as well as the scale of import and export channels at ports. The largest ship draft corresponding to the water level or water depth can thus be calculated. When the actual draft is greater than the largest calculated draft, the ship will ground. Since the ship draft is determined by ship’s own weight and cargo volume, people usually avoid the risk of grounding by reducing their ship’s capacity during dry seasons, which is not beneficial for the development of commercial navigation.
Fig. 9

Relationship between water level, ship draft and UKC (Liu and Liu 2016)

The purpose of designing the LNWL is to balance the relationship between navigation safety and ship capacity. In other words, it aims to maximize the shipping economy while ensuring navigation safety. The LNWL is based on the water level of the channel as the main data basis, and the designed water level is determined to satisfy the requirement of the guaranteed rate for each type of waterways. Therefore, when there is hydrological variation, the water level conditions for different periods are quite varied, which will affect the design of the LNWL. As shown in Table 3, the statistical parameters under two environments (i.e., the past and the current) are compared. The results show that both the variance coefficient and the skew coefficient of water level did not change, but the mean value was different between the past and the current. This indicates a decrease in the mean magnitude of the water level, which could have adverse effects on navigation. Therefore, it is necessary to consider the specific conditions of the channel and its navigation when analyzing the availability of a navigable water level.
Table 3

Comparison of statistical parameters of water level under different environments

Environmental conditions

Statistical parameters

Mean

Variance coefficient

Skew coefficient

Past

542.8050

0.0099

0.0028

Current

542.1624

0.0099

0.0028

For a ship with a certain cargo volume, a lower water level means a greater risk of grounding. Currently, the channel from Jinghong to the boundary (No. 243) between China and Myanmar meets the fifth navigation standards. The channel scale is 2.0 m × 40 m × 300 m (water depth × bottom width × bending radius), and it is navigable for 300-ton ships. In general, the draft of a 300-ton ship is about 1.3 m. As the results indicate in the Sect. 4.2, when the guaranteed rate is between 90 and 98%, the designed water level for the current environment considering nonstationarity is less than that without considering nonstationarity. The difference between these two is approximately − 0.60 m, which accounts for around 46% of the ship draft. Therefore, the water level variation is a very important factor that cannot be ignored for navigation safety.

In “Lancang-Mekong River Commercial Vessel Passage Agreement” (2001), the LNWL at the Yunjinghong station is determined as 534.69 m for the guaranteed rate of 95%. According to Table 2 and Fig. 6, when the LNWL is 534.69 m, the guaranteed rate for the current environment will be less than 90%. Therefore, if the hydrological nonstationarity is ignored, the designed water level cannot meet the guaranteed rate requirement. This would make the shipping engineering design, water depth maintenance and other activities based on the LNWL become unreasonable and unreliable.

5 Conclusions

In this study, we proposed a nonstationary statistical approach for the design of LNWL in inland waterways based on hydrological component analysis. With this approach, the stationary series can be generated to design the LNWL for different environments. Compared to conventional methods, which directly handle the observed hydrological data, the proposed nonstationary statistical approach is able to provide more reasonable design parameters in a changing environment.

This nonstationary statistical approach was applied to design the LNWL in the downstream of the Lancang River. Results indicate that the LNWL is 534.90 m, 534.77 m and 534.65 m with guaranteed rates of 90, 95 and 98% in the past environment, respectively, while it is 534.27 m, 534.14 m, and 534.03 m in the current condition, respectively. The LNWL for the current environment with and without the assumption of nonstationarity were compared. Results show that in the current environment, the LNWL considering nonstationarity is about 0.60 m less than that without considering nonstationarity. This difference equals to approximately 46% of the draft of standard ships (300 tons) in the downstream of the Lancang River, which cannot be ignored when estimating the maximum ship capacity.

In summary, the approach proposed in this paper can be used in inland navigation to calculate the minimum navigable water levels in different places and environments. Further research should be performed to deal with the changing environment rather than only considering water level variations. This would provide a more reasonable reference for channel planning and design, and navigation safety assessment.

Notes

Acknowledgements

The authors gratefully acknowledged the valuable hydrological data and information provided by the Hydrology Bureau of Yunnan Province. This study was financially supported by the National Natural Science Foundation of China (Nos. 51579181, 91547205, 91647110, 51779176), and the Youth Innovation Promotion Association CAS (No. 2017074).

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Water Resources and Hydropower Engineering ScienceWuhan UniversityWuhanChina
  2. 2.Collaborative Innovation Center for Territorial Sovereignty and Maritime RightsWuhanChina
  3. 3.Intelligent Transportation Systems Research CenterWuhan University of TechnologyWuhanChina
  4. 4.National Engineering Research Center for Water Transport SafetyWuhan University of TechnologyWuhanChina
  5. 5.Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources ResearchChinese Academy of SciencesBeijingChina

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