Abstract
The Lowest navigable water level (LNWL) is an important indicator used for navigation design to balance the relationship between navigation safety and economic benefits of a waterway. However, it is a challenge of accurately estimating LNWLs due to the nonstationary characteristics of observed water level data series. In this study, a comprehensive framework was developed for handling this issue. In this framework, inter-annual variabilities in both the mean and variance of water level series were described by decomposing original series and were eliminated by composing new series. Intra-annual variability was determined by detecting indicators describing intra-annual water level distributions. Considerations of inter- and intra-annual variabilities were combined by designing annual water level processes for the past and current environments. Shipping risks during both annual and multi-annual periods were considered in the framework as well. The framework was demonstrated in estimating LNWLs at the Gaodao and Shijiao stations in the North River basin, southern China. The recommended LNWLs at the Gaodao station were 22.32 m for 95% guaranteed rate and 21.84 m for 98% guaranteed rate; LNWLs at the Shijiao station were 0.27 m for 95% guaranteed rate and 0.15 m for 98% guaranteed rate. The impact of variance variability on estimations of LNWLs was also evaluated. Results indicated that the recommended LNWLs would have errors of 0.11 ~ 0.48 m at the Gaodao station and 0.03 ~ 0.04 m at the Shijiao station if the variance variability was not considered. The proposed framework was then compared with Nonstationary synthetic duration curve (NSDC) method, and results illustrated that the duration curves plotted by NSDC method were unreasonable, leading to inaccurate design values. Overall, the developed framework is more reasonable and suitable for designing LNWLs of waterways where the variabilities of the water levels at different time scales are different or where the historical water level data contain various variations .
Similar content being viewed by others
Data Availability
The authors gratefully acknowledged the valuable hydrological data and information provided by the Hydrology Bureau of Guangdong Province, China. The data that support the findings of this study are available from the corresponding author upon reasonable request.
Code availability
The code is available from the corresponding author upon reasonable request.
References
Afifi AA, Azen SP (1972) Statistical analysis, a computer oriented approach. Academic Press, Harcourt Brace Jovanonich Publishers, New York, p 366
Ahn KH, Palmer RN (2016) Use of a nonstationary copula to predict future bivariate low flow frequency in the Connecticut river basin. Hydrol Process 30(19):3518–3532. https://doi.org/10.1002/hyp.10876
Bartels R (1982) The rank version of von Neumann’s ratio test for randomness. J Am Stat Assoc 77(377):40–46
Bras RL, Rodriguez-Iturbe I (1993) Random functions and hydrology. Dover Publications, New York
Brown MB, Forsythe AB (1974) Robust tests for the equality of variances. J Am Stat Assoc 69(346):364–367
Cai SY, Lei XH, Meng XY, Yi J, Mahalingam S, Gao XZ, Hamed VN (2018) Ecological flow analysis method based on the comprehensive variation diagnosis of Gini coefficient. J Intell Fuzzy Syst 34(2):1025–1031. https://doi.org/10.3233/jifs-169396
Cannon AJ (2010) A flexible nonlinear modelling framework for nonstationary generalized extreme value analysis in hydroclimatology. Hydrol Processes. https://doi.org/10.1002/hyp.7506
Christodoulou A, Christidis P, Bisselink B (2020) Forecasting the impacts of climate change on inland waterways. Transp Res Part d: Transp Environ 82:102159. https://doi.org/10.1016/j.trd.2019.10.012
Cleveland RB, Cleveland WS, Mcrae JE, Terpenning I (1990) Stl: a seasonal trend decomposition procedure based on loess. J off Stat 6(1):3–73
Cui T, Tian FQ, Yang T, Wen J, Khan MYA (2020) Development of a comprehensive framework for assessing the impacts of climate change and dam construction on flow regimes. J Hydrol 590:125358. https://doi.org/10.1016/j.jhydrol.2020.125358
Dai SB, Yang SL, Cai AM (2008) Impacts of dams on the sediment flux of the Pearl River, southern China. CATENA 76(1):36–43. https://doi.org/10.1016/j.catena.2008.08.004
Du JK, Wu XS, Wang ZL, Li J, Chen XH (2020) Reservoir-Induced Hydrological Alterations Using Ecologically Related Hydrologic Metrics: Case Study in the Beijiang River. Water, China. https://doi.org/10.3390/w12072008
Feng Y, Shi P, Qu S, Mou SY, Chen C, Dong FC (2020) Nonstationary flood coincidence risk analysis using time-varying copula functions. Sci Rep 10(1):3395. https://doi.org/10.1038/s41598-020-60264-3
Gado TA, Nguyen VTV (2016a) An at-site flood estimation method in the context of nonstationarity IA Simulation Study. J Hydrol 535:710–721. https://doi.org/10.1016/j.jhydrol.2015.12.063
Gado TA, Nguyen VTV (2016b) An at-site flood estimation method in the context of nonstationarity II. Statistical analysis of floods in Quebec. J Hydrol 535:722–736. https://doi.org/10.1016/j.jhydrol.2015.12.064
Gau HS, Chen TC, Chen JS, Liu CW (2007) Time series decomposition of groundwater level changes in wells due to the Chi-Chi earthquake in Taiwan: a possible hydrological precursor to earthquakes. Hydrol Process 21:510–524. https://doi.org/10.1002/hyp.6257
Gumbel EJ (1954) Applications of the circular normal distribution. J Am Stat Assoc 49(266):267–297. https://doi.org/10.1080/01621459.1954.10483505
Guttman NB, Plantico MS (1989) On an additive model of daily temperature climates. J Clim 2(10):1207–1209. https://doi.org/10.1175/1520-0442(1989)002%3c1207:OAAMOD%3e2.0.CO;2
He W, Lian JJ, Zhang J, Yu XD, Chen S (2019) Impact of intra-annual runoff uniformity and global warming on the thermal regime of a large reservoir. Sci Total Environ 658:1085–1097. https://doi.org/10.1016/j.scitotenv.2018.12.207
Hu YM, Liang ZM, Singh VP, Zhang XB, Wang J, Li BQ, Wang HM (2018) Concept of equivalent reliability for estimating the design flood under non-stationary conditions. Water Resour Manag 32:997–1011. https://doi.org/10.1007/s11269-017-1851-y
Hu YM, Liang ZM, Jiang XL, Bu H (2015) Non-stationary hydrological frequency analysis based on the reconstruction of extreme hydrological series. Proc Int Assoc Hydrol Sci. https://doi.org/10.5194/piahs-371-163-2015
Inc S (2003) Statistica: The Small Book. Statsoft Inc., Tulsa, p 144
Jawitz JW, Mitchell J (2011) Temporal inequality in catchment discharge and solute export. Water Resour Res. https://doi.org/10.1029/2010WR010197
Jiang C, Xiong L, Xu CY, Guo SL (2015) Bivariate frequency analysis of nonstationary low-flow series based on the time-varying copula. Hydrol Process 29:1521–1534. https://doi.org/10.1002/hyp.10288
Jiang C, Xiong LH, Yan L, Dong QJ, Xu CY (2019) Multivariate hydrologic design methods under nonstationary conditions and application to engineering practice. Hydrol Earth Syst Sci 23:1683–1704. https://doi.org/10.5194/hess-23-1683-2019
Jonkeren O, Jourquin B, Rietveld P (2011) Modal-split effects of climate change: the effect of low water levels on the competitive position of inland waterway transport in the river Rhine area. Transp Res Part A Policy Pract 45(10):1007–1019. https://doi.org/10.1016/j.tra.2009.01.004
Jonkeren O, Rietveld P, Ommeren JV, Linde AT (2014) Climate change and economic consequences for inland waterway transport in Europe. Reg Environ Change 14:953–965. https://doi.org/10.1007/s10113-013-0441-7
Kendall MG (1955) Rank correlation methods. Griffin, London
Kling GW, Hayhoe K, Johnson LB, Magnuson JJ, Polassky S, Robinson SK, Shuter BJ et al (2003) Confronting climate change in the great lakes region: impacts on our communities and ecosystems. https://www.researchgate.net/publication/248822899
Lee AFS, Heghinian SM (1977) A shift of the mean level in a sequence of independent normal random variable: a Bayesian approach. Technometrics 19(4):503–506. https://doi.org/10.1080/00401706.1977.10489592
Li GF, Xiang XY, Guo CX (2016) Analysis of nonstationary change of annual maximum level records in the Yangtze river estuary. Adv Meteorol 2016:1–14. https://doi.org/10.1155/2016/7205723
Li M, Zhang T, Feng P (2019a) A nonstationary runoff frequency analysis for future climate change and its uncertainties. Hydrol Process 33(21):2759–2771. https://doi.org/10.1002/hyp.13526
Li R, Tang CY, Li X, Jiang T, Shi YP, Cao YJ (2019b) Reconstructing the historical pollution levels and ecological risks over the past sixty years in sediments of the Beijiang River, South China. Sci Total Environ 649:448–460. https://doi.org/10.1016/j.scitotenv.2018.08.283
Liang ZM, Yang J, Hu YM, Wang J, Li BQ, Zhao JF (2017) A sample reconstruction method based on a modified reservoir index for flood frequency analysis of non-stationary hydrological series. Stoch Env Res Risk Assess 32:1561–1571. https://doi.org/10.1007/s00477-017-1465-1
Linde F, Ouahsine A, Huybrechts N, Sergent P (2017) Three-dimensional numerical simulation of ship resistance in restricted waterways: effect of ship sinkage and channel restriction. J Waterw Port Coast Ocean Eng 143(1):1–11. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000353
Liu Y, Hao YH, Fan YH, Wang TK, Liu YC, Jim-Yeh TC (2014) A nonstationary extreme value distribution for analysing the cessation of karst spring discharge. Hydrol Process. https://doi.org/10.1002/hyp.10013
López-Moreno JI, Vicente-Serrano SM, Zabalza J, Beguer’ia S, Lorenzo-Lacruz J, Azorin-Molina C, Morán-Tejeda E (2013) Hydrological response to climate variability at different time scales: a study in the Ebro basin. J Hydrol. https://doi.org/10.1016/j.jhydrol.2012.11.028
Lu XX, Zhang SR, Xie SP, Ma PK (2007) Rapid channel incision of the lower Pearl River (China) since the 1990s as a consequence of sediment depletion. Hydrol Earth Syst Sci 11:1897–1906. https://doi.org/10.5194/hess-11-1897-2007
Luo Y, Liu S, Fu SL, Liu JS, Wang GQ, Zhou GY (2008) Trends of precipitation in Beijiang River Basin, Guangdong Province, China. Hydrol Process 22:2377–2386. https://doi.org/10.1002/hyp.6801
Machiwal D, Jha MK (2012) Hydrologic time series analysis: Theory and practice. Springer, Netherlands
Magilligan FJ, Graber BE (1996) Hydroclimatological and geomorphic controls on the timing and spatial variability of floods in New England, USA. J Hydrol 178:159–180. https://doi.org/10.1016/0022-1694(95)02807-2
Magilligan FJ, Nislow KH (2005) Changes in hydrologic regime by dams. Geomorphol 71(1):61–78. https://doi.org/10.1016/j.geomorph.2004.08.017
Maidment DR (1993) Handbook of hydrology. McGraw-Hill, New York
Mann HB (1945) Nonparametric tests against trend. Econometrica 13:245–259. https://doi.org/10.2307/1907187
Masaki Y, Hanasaki N, Takahashi K, Hijioka Y (2014) Global-scale analysis on future changes in flow regimes using Gini and Lorenz asymmetry coefficients. Water Resour Res 50(5):4054–4078. https://doi.org/10.1002/2013WR014266
Milly PCD, Betancourt J, Falkenmark M, Hirsch RM, Zbigniew W, Lettenmaier DP, Stouffer RJ (2008) Stationarity is dead: Whither water management? Sci 319:573–574. https://doi.org/10.1126/science.1151915
Milly PCD, Betancourt J, Falkenmark M, Hirsch RM, Kundzewicz ZW, Lettenmaier DP, Stouffer RJ et al (2015) On critiques of “stationarity is dead: Whither water management?” Water Resour Res 51(9):7785–7789. https://doi.org/10.1002/2015WR017408
Ministry of Development of the People’s Republic of China, General Administration of Quality Supervision & Inspection and Quarantine of the People’s Republic of China (2014) Navigation standard in inland river (GB50139-2014). China Plan Press, Beijing
Montanari A, Koutsoyiannis D (2014) Modeling and Mitigating Natural Hazards: Stationarity is Immortal! Water Resour Res. https://doi.org/10.1002/2014WR016092
Oztanriseven F, Nachtmann H (2017) Economic impact analysis of inland waterway disruption response. Eng Econ 62(1):73–89. https://doi.org/10.1080/0013791X.2016.1163627
Palleiro L, Rodríguez-Blanco ML, Taboada-Castro MM (2014) Hydrological response of a humid agroforestry catchment at different time scales. Hydrol Process 28(4):1677–1688. https://doi.org/10.1002/hyp.9714
Ren K, Huang S, Huang Q, Wang H, Leng GY (2018) Environmental flow assessment considering inter- and intra-annual streamflow variability under the context of non-stationarity. Water 10:1737. https://doi.org/10.3390/w10121737
Rootzen H, Katz RW (2013) Design life level: quantifying risk in a changing climate. Water Resour Res 49:5964–5972. https://doi.org/10.1002/wrcr.20425
Rosner A, Vogel RM, Kirshen PH (2014) A risk-based approach to flood management decisions in a nonstationary world. Water Resour Res 50(3):1928–1942. https://doi.org/10.1002/2013WR014561
Salas JD, Obeysekera J (2014) Revisiting the concepts of return period and risk for nonstationary hydrologic extreme events. J Hydrol Eng 19:554–568. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000820
Sarhadi A, Burn DH, Ausín MC, Wiper MP (2016) Time-varying nonstationary multivariate risk analysis using a dynamic Bayesian copula. Water Resour Res 52:2327–2349. https://doi.org/10.1002/2015WR018525
Sheskin D (2011) Handbook of Parametric and Nonparametric Statistical Procedures. CRC Press, USA
Shi WL, Yu XZ, Liao WG, Wang Y, Jia BZ (2013) Spatial and temporal variability of daily precipitation concentration in the Lancang River basin, China. J Hydrol 495:197–207. https://doi.org/10.1016/j.jhydrol.2013.05.002
Shiau JT, Wu FC (2007) Pareto-optimal solutions for environmental flow schemes incorporating the intra-annual and interannual variability of the natural flow regime. Water Resour Res. https://doi.org/10.1029/2006WR005523
Singh KP, Sinclair RA (1972) Two distribution method for flood frequency analysis. J Hydraulics Division 98(1):29–44
Singh VP, Wang SX, Zhang L (2005) Frequency analysis of nonidentically distributed hydrologic flood data. J Hydrol 307(1–4):175–195. https://doi.org/10.1016/j.jhydrol.2004.10.029
Stojković M, Kostić S, Plavšić J, Prohaska S (2017) A joint stochastic-deterministic approach for long-term and short-term modelling of monthly flow rates. J Hydrol 544:555S. https://doi.org/10.1016/j.jhydrol.2016.11.025
Strupczewski WG, Kaczmarek Z (2001) Non-stationary approach to at-site flood frequency modelling II. Weighted least squares estimation. J Hydrol 248:143–151. https://doi.org/10.1016/S0022-1694(01)00398-5
Strupczewski WG, Singh VP, Feluch W (2001a) Non-stationary approach to at-site flood frequency modelling I. Maximum likelihood estimation. J Hydrol 248:123–142. https://doi.org/10.1016/S0022-1694(01)00397-3
Strupczewski WG, Singh VP, Mitosek HT (2001b) Non-stationary approach to at-site flood frequency modelling III. Flood analysis of Polish rivers. J Hydrol 248:152–167. https://doi.org/10.1016/S0022-1694(01)00399-7
Tu X, Singh VP, Chen XH, Chen L, Zhang Q, Zhao Y (2015) Intra-annual distribution of streamflow and individual impacts of climate change and human activities in the Dongijang river basin, China. Water Resour Manag 29(8):2677–2695. https://doi.org/10.1007/s11269-015-0963-5
Valle D, Kaplan D (2019) Quantifying the impacts of dams on riverine hydrology under non-stationary conditions using incomplete data and Gaussian copula models. Sci Total Environ 677:599–611. https://doi.org/10.1016/j.scitotenv.2019.04.377
Villarini G, Smith JA, Serinaldi F, Bales JD, Bates PD, Krajewski WF (2009) Flood frequency analysis for nonstationary annual peak records in an urban drainage basin. Adv Water Resour 32(8):1255–1266. https://doi.org/10.1016/j.advwatres.2009.05.003
Vinnikov KY, Robock A (2002) Trends in moments of climatic indices. Geophys Res Lett 29(2):1027. https://doi.org/10.1029/2001GL014025
Vogel RM, Yaindl C, Walter M (2011) Nonstationarity: flood magnification and recurrence reduction factors in the United States. J Am Water Resour Assoc 47(3):464–474. https://doi.org/10.1111/j.1752-1688.2011.00541.x
Wang D, Ding H, Singh VP, Shang XS, Liu DF, Wang YK, Zeng XK et al (2015) A hybrid wavelet analysis–cloud model data-extending approach for meteorologic and hydrologic time series. J Geophys Res Atmos 120:4057–4071. https://doi.org/10.1002/2015JD023192
Wang Y, Chen X, Borthwick AGL, Li TH, Liu HH, Yang SF, Zheng CM et al (2020) Sustainability of global golden inland waterways. Nat Commun 11:1553. https://doi.org/10.1038/s41467-020-15354-1
Waylen P, Woo MK (1982) Prediction of annual floods generated by mixed processes. Water Resour Res 18(4):1283–1286. https://doi.org/10.1029/WR018i004p01283
Willems JJ, Busscher T, Woltjer J, Arts J (2018) Co-creating value through renewing waterway networks: a transaction-cost perspective. J Transp Geogr 69:26–35. https://doi.org/10.1016/j.jtrangeo.2018.04.011
Wu CH, Huang GR, Yu HJ, Chen ZJ, Ma JG (2014) Impact of climate change on reservoir flood control in the upstream area of the Beijiang river basin, South China. J Hydrometeorol 15(6):2203–2218. https://doi.org/10.1175/JHM-D-13-0181.1
Xie P, Wu ZY, Sang YF, Gu HT, Zhao YX, Singh VP (2018) Evaluation of the significance of abrupt changes in precipitation and runoff process in China. J Hydrol 560:451–460. https://doi.org/10.1016/j.jhydrol.2018.02.036
Yan L, Xiong LH, Liu DD, Hu TS, Xu CY (2016) Frequency analysis of nonstationary annual maximum flood series using the time-varying two-component mixture distributions. Hydrol Process 31(1):69–89. https://doi.org/10.1002/hyp.10965
Yang YP, Zhang MJ, Liu WL, Wang JJ, Li XX (2019) Relationship between waterway depth and low-flow water levels in reaches below the three Gorges dam. J Waterw Port Coast Ocean Eng 145(1):04018032. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000482
Yao LL, Libera DA, Kheimi M, Sankarasubramanian A, Wang DB (2020) The roles of climate forcing and its variability on streamflow at daily, monthly, annual, and long-term scales. Water Resour Res. https://doi.org/10.1029/2020WR027111
Yevjevich V (1972) Stochastic processes in hydrology. Water Resources Publications, Fort Collins, Colorado, USA
Zhao JY, Xie P, Zhang MY, Sang YF, Chen J, Wu ZY (2018) Nonstationary statistical approach for designing LNWLs in inland waterways: a case study in the downstream of the Lancang River. Stoch Env Res Risk Assess 32:3273–3286. https://doi.org/10.1007/s00477-018-1606-1
Zheng F, Tao R, Maier HR, See LM, Savic D, Zhang TQ, Chen QW et al (2018) Crowdsourcing methods for data collection in geophysics: state of the art, issues, and future directions. Rev Geophys. https://doi.org/10.1029/2018RG000616
Funding
This study was financially supported by the National Natural Science Foundation of China (No. 51579181, 91547205, and 41971040); the Research Council of Norway (No. 274310), and the Youth Innovation Promotion Association CAS (No. 2017074).
Author information
Authors and Affiliations
Contributions
Ping Xie developed the main ideas. Lu Wang implemented the algorithms of the methods. Ping Xie collected the data used in the case study. Ping Xie, Chong-Yu Xu and Yan-Fang Sang provided funding for this study. Lu Wang wrote the original draft of the manuscript. Chong-Yu Xu, Yan-Fang Sang and Jie Chen supervised this study, reviewed and edited the original draft. Tao Yu validated the results of this study.
Corresponding authors
Ethics declarations
Conflict of interest
We confirm that this work is original and has not been published elsewhere, nor is it currently under consideration for publication elsewhere. All authors have read and approved the manuscript being submitted, and agree to its submittal to this journal, and have no conflicts of interest to disclose. The work described in this paper was supported financially by the National Natural Science Foundation of China (grant numbers 51579181, 91547205, and 41971040), and the Research Council of Norway (grant number 274310). The hydrological data and information of the study site were provided by the Hydrology Bureau of Guangdong Province, China.
Consent for publication
We confirm that this work is original and has not been published elsewhere, nor is it currently under consideration for publication elsewhere. All authors have read and approved the manuscript being submitted and agree to its publication in this journal.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wang, L., Xie, P., Xu, CY. et al. A framework for determining lowest navigable water levels with nonstationary characteristics. Stoch Environ Res Risk Assess 36, 583–608 (2022). https://doi.org/10.1007/s00477-021-02058-1
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00477-021-02058-1