Nonoverlapping Block Stratified Random Sampling Approach for Assessment of Stationarity
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Volume 26, Issue 7
Abstract
Assessment of stationarity in any hydroclimatic time series is a vital task for hydrologic design and climate change assessments. Methods that rely on the presence of statistically significant trends or change points to derive inferences about stationarity may fail to check for all the time-invariant characteristics of time series. An approach that uses nonoverlapping stratified random sampling blocks of time series and nonparametric tests is proposed and evaluated in this study to assess stationarity. Chronologically continuous data from contiguous blocks are evaluated using two-sample and multisample nonparametric tests for the assessment of distributional, median and variance similarity, invariance of statistical moments, and autocorrelation at several lags. Explicit methods for the evaluation of different characteristics of time series are also developed to assess the two forms (viz., weak and strict) of stationarity. The multiple test evaluations are weighted using the analytical hierarchy process (AHP) to draw conclusions about stationarity. The proposed approach is tested using several real-world and synthetically generated hydroclimatic data sets through extensive simulations. Stationarity assessments derived from nonparametric trend and unit root tests have been compared to those from the approach developed. Results from this study point to the correct identification of weak and strict stationarity in real-world hydroclimatic time series compared to similar evaluations from unit root and trend tests. The robustness of the approach is also confirmed by an accurate assessment of the stationarity of several synthetic time series representing various hydroclimatic processes at different time scales. The proposed approach is a conceptually simple and superior alternative to trend and unit root tests since it provides a comprehensive assessment of stationarity using multiple nonparametric tests.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available in a repository or online following funder data retention policies. The annual maximum streamflow time series for the stream gauges in their respective river basins in India can be accessed from the relevant publications available on the web portal of the Central Water Commission (CWC), Ministry of Jal Shakti, Government of India: http://cwc.gov.in/hydro_16-17 (accessed June 2020). The annual total precipitation time series can be retrieved from the India Water Portal https://www.indiawaterportal.org/met_data/ (accessed June 2020). The mean monthly streamflow data for two stations in the US state of Florida were downloaded from the USGS website: https://waterdata.usgs.gov/nwis/ (accessed June 2020). The temperature data set was obtained from the National Climatic Data Center (NCDC) web portal: https://www.ncdc.noaa.gov/ushcn/introduction (accessed June 2020). The long-term series of annual temperature and precipitation observed at Radcliffe Meteorological Station in Oxford, UK, was retrieved from the University of Oxford website: https://www.geog.ox.ac.uk/research/climate/rms/monthly-annual.html (accessed September 2020). The CoSMoS toolbox (MATLAB version) for generating synthetic time series can be retrieved at https://www.mathworks.com/matlabcentral/fileexchange/73051-cosmos (accessed December 2020).
Acknowledgments
The authors thank the agencies Central Water Commission (CWC), USGS, National Climatic Data Center (NCDC), India Water Portal, and the University of Oxford for disseminating data on their respective web portals, which were collected and analyzed in this study. The manuscript benefited from the insightful and constructive comments of Francesco Serinaldi. The authors thank Simon Papalexiou for recommending the CoSMoS toolbox for the generation of synthetic time series tested in this work. The authors are thankful to the reviewers for their objective criticism of the manuscript.
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Journal of Hydrologic Engineering
Volume 26 • Issue 7 • July 2021
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© 2021 American Society of Civil Engineers.
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Received: Sep 27, 2020
Accepted: Feb 16, 2021
Published online: Apr 16, 2021
Published in print: Jul 1, 2021
Discussion open until: Sep 16, 2021
ASCE Technical Topics:
- Business management
- Climate change
- Climates
- Decision making
- Ecosystems
- Engineering fundamentals
- Environmental engineering
- Hydrologic engineering
- Hydrologic properties
- Hydrology
- Mathematics
- Parameters (statistics)
- Practice and Profession
- Statistics
- Time series analysis
- Vegetation
- Water and water resources
- Water stratification
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