Development of an Objective Low Flow Identification Method Using Breakpoint Analysis
Abstract
:1. Introduction
2. Data
3. Methods
3.1. Breakpoint Approach to Low Flow Identification
3.2. Breakpoint Algorithm Selection
3.3. Objective Threshold Approach Description
- 1.
- Determination of the number (n) of points in the daily flow series needed to calculate the breakpoint based on the lower FDC range (by default: below the 35th percentile, as described further in the Results section):Q: {Q ∈ R + | Q ≤ Q35}
- 2.
- Implementation of the Fisher–Jenks algorithm to define the breakpoint [52] by minimizing deviation of each class from the class mean, while maximizing the deviation of each class from the means of the other classes:
- a.
- Order flow data series in increasing order and assigning weights (w):w: i ∈ {1,…,n}
- b.
- Compute the diameter matrix Di,j to store the distance between all pairs of n observations, such that:1 ≤ i ≤ j ≤ n
- c.
- Populate the error matrix with variance of n observations when classified into two classes (one class for atmospheric driven resources, representing mean flow conditions (FDC part above breakpoint), and second for the drought conditions and baseflow (FDC part below breakpoint)):
- d.
- Locate the optimal partition from the error matrix by maximizing inter-class variance and minimizing intra-class variance:
- 3.
- Application of the defined breakpoint (Qt) as the low flow threshold for further analysis of low flow distribution, streamflow droughts, or for water management systems at the alert point, according to the following relation:
- Qt—threshold flow determined by Fisher-Jenks algorithm,
- Qlf—flow identified as low flow.
4. Results
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Van Loon, A.F.; Gleeson, T.; Clark, J.; Van Dijk, A.I.J.M.; Stahl, K.; Hannaford, J.; Di Baldassarre, G.; Teuling, A.J.; Tallaksen, L.M.; Uijlenhoet, R.; et al. Drought in the Anthropocene. Nat. Geosci. 2016, 9, 89–91. [Google Scholar] [CrossRef] [Green Version]
- Tokarczyk, T. Classification of low flow and hydrological drought for a river basin. Acta Geophys. 2013, 61, 404–421. [Google Scholar] [CrossRef]
- Yevjevich, V. An Objective Approach to Definitions and Investigations of Continental Hydrologic Droughts. Colorado State University. 1967. Available online: https://mountainscholar.org/bitstream/handle/10217/61303/HydrologyPapers_n23.pdf (accessed on 15 May 2022).
- Stahl, K.; Vidal, J.-P.; Hannaford, J.; Tijdeman, E.; Laaha, G.; Gauster, T.; Tallaksen, L.M. The challenges of hydrological drought definition, quantification and communication: An interdisciplinary perspective. Proc. Int. Assoc. Hydrol. Sci. 2020, 383, 291–295. [Google Scholar] [CrossRef]
- Van Loon, A.F. Hydrological drought explained. WIREs Water 2015, 2, 359–392. [Google Scholar] [CrossRef]
- Van Lanen, H.A.J.; Wanders, N.; Tallaksen, L.M.; Van Loon, A.F. Hydrological drought across the world: Impact of climate and physical catchment structure. Hydrol. Earth Syst. Sci. 2013, 17, 1715–1732. [Google Scholar] [CrossRef] [Green Version]
- Van Loon, A.F.; Van Lanen, H.A.J. A process-based typology of hydrological drought. Hydrol. Earth Syst. Sci. 2012, 16, 1915–1946. [Google Scholar] [CrossRef] [Green Version]
- Wong, W.K.; Beldring, S.; Engen-Skaugen, T.; Haddeland, I.; Hisdal, H. Climate Change Effects on Spatiotemporal Patterns of Hydroclimatological Summer Droughts in Norway. J. Hydrometeorol. 2011, 12, 1205–1220. [Google Scholar] [CrossRef]
- Fleig, A.K.; Tallaksen, L.M.; Hisdal, H.; Demuth, S. A global evaluation of streamflow drought characteristics. Hydrol. Earth Syst. Sci. 2006, 18, 535–552. [Google Scholar] [CrossRef] [Green Version]
- Hisdal, H.; Stahl, K.; Tallaksen, L.M.; Demuth, S. Have streamflow droughts in Europe become more severe or frequent? Int. J. Climatol. 2001, 21, 317–333. [Google Scholar] [CrossRef]
- Hisdal, H. Hydrological drought characteristics. Dev. Water Sci. 2004, 48, 139–198. [Google Scholar]
- Smakhtin, V.U. Low flow hydrology: A review. J. Hydrol. 2001, 240, 147–186. [Google Scholar] [CrossRef]
- Grosser, P.F.; Schmalz, B. Low Flow and Drought in a German Low Mountain Range Basin. Water 2021, 13, 316. [Google Scholar] [CrossRef]
- Cammalleri, C.; Vogt, J.; Salamon, P. Development of an operational low-flow index for hydrological drought monitoring over Europe. Hydrol. Sci. J. 2016, 62, 346–358. [Google Scholar] [CrossRef] [Green Version]
- Holmes, S. Overwiev of Drought and Hydrologic Conditions in the United States and Southern Canada: Water Years 1986–1990; US Department of The Interior, US Geological Survey: Washington, DC, USA, 1992. [Google Scholar]
- Sutanto, S.J.; Van Lanen, H.A.J. Streamflow drought: Implication of drought definitions and its application for drought forecasting. Hydrol. Earth Syst. Sci. 2021, 25, 3991–4023. [Google Scholar] [CrossRef]
- Floriancic, M.G.; van Meerveld, I.; Smoorenburg, M.; Margreth, M.; Naef, F.; Kirchner, J.W.; Molnar, P. Spatio-temporal variability in contributions to low flows in the high Alpine Poschiavino catchment. Hydrol. Process. 2018, 32, 3938–3953. [Google Scholar] [CrossRef]
- Van Loon, A.F.; Van Huijgevoort, M.H.J.; Van Lanen, H.A.J. Evaluation of drought propagation in an ensemble mean of large-scale hydrological models. Hydrol. Earth Syst. Sci. 2012, 16, 4057–4078. [Google Scholar] [CrossRef] [Green Version]
- Gustard, A.; Demuth, S. Manual of Low-flow. Estimation and Prediction. Oper. Hydrol. Rap. 2008, 50, 138. [Google Scholar]
- Hisdal, H.; Tallaksen, L.M. Drought Event Definition. Tech. Rep. 2000, 6, 45. [Google Scholar]
- Sung, J.H.; Chung, E.-S. Development of streamflow drought severity–duration–frequency curves using the threshold level method. Hydrol. Earth Syst. Sci. 2014, 18, 3341–3351. [Google Scholar] [CrossRef] [Green Version]
- Zelenhasić, E.; Salvai, A. A method of streamflow drought analysis. Water Resour. Res. 1987, 23, 156–168. [Google Scholar] [CrossRef]
- Svensson, C.; Kundzewicz, W.Z.; Maurer, T. Trend detection in river flow series: 2. Flood and low-flow index series/Détection de tendance dans des séries de débit fluvial: 2. Séries d’indices de crue et d’étiage. Hydrol. Sci. J. 2005, 50, 6. [Google Scholar] [CrossRef] [Green Version]
- Madsen, H.; Rosbjerg, D. On the modelling of extreme droughts. AHS Publ. Ser. Proc. Rep. Int. Assoc. Hydrol. Sci. 1995, 231, 377–386. [Google Scholar]
- Vogel, R.M.; Stedinger, J.R. Generalized storage-reliability-yield relationships. J. Hydrol. 1987, 89, 303–327. [Google Scholar] [CrossRef]
- Yang, T.; Zhou, X.; Yu, Z.; Krysanova, V.; Wang, B. Drought projection based on a hybrid drought index using Artificial Neural Networks: A New drought index and drought projection in tarim river basin. Hydrol. Process. 2015, 29, 2635–2648. [Google Scholar] [CrossRef]
- Yahiaoui, A.; Touaïbia, B.; Bouvier, C. Frequency analysis of the hydrological drought regime. Case of oued Mina catchment in western of Algeria. Rev. Nat. Technol. 2009, 1, 3–15. [Google Scholar]
- Van Lanen, H.A.J.; Kundzewicz, W.Z.; Tallaksen, L.M.; Hisdal, H.; Fendekova, M.; Prudhomme, C. Indices for Different Types of Droughts and Floods at Different Scales; Water and Global Change, Technical Report no. 11. 2008. Available online: https://www.academia.edu/15920058/INDICES_FOR_DIFFERENT_TYPES_OF_DROUGHTS_AND_FLOODS_AT_DIFFERENT_SCALES (accessed on 15 May 2022).
- Kjeldsen, T.R.; Lundorf, A.; Rosbjerg, D. Use of a two-component exponential distribution in partial duration modelling of hydrological droughts in Zimbabwean rivers. Hydrol. Sci. J. 2000, 45, 285–298. [Google Scholar] [CrossRef]
- Hisdal, H.; Tallaksen, L.M.; Frigessi, A. Handling non-extreme events in extreme value modelling of streamflow droughts. In FRIEND 2002: Regional Hydrology: Bridging the Gap between Research and Practice; IAHS Publication: Wallingford, UK, 2002; Volume 274, pp. 281–288. [Google Scholar]
- Pyrce, R. Hydrological Low Flow Indices and Their Uses; Watershed Science Centre: Peterborough, ON, USA, 2004. [Google Scholar]
- Raczyński, K.; Dyer, J. Simulating low flows over a heterogeneous landscape in southeastern Poland. Hydrol. Process. 2021, 35, e14322. [Google Scholar] [CrossRef]
- Wanders, N.; Wada, Y.; Van Lanen, H.A.J. Global hydrological droughts in the 21st century under a changing hydrological regime. Earth Syst. Dyn. 2015, 6, 1–15. [Google Scholar] [CrossRef] [Green Version]
- Ryu, J.H.; Lee, J.H.; Jeong, S.; Park, S.K.; Han, K. The impacts of climate change on local hydrology and low flow frequency in the Geum River Basin, Korea. Hydrol. Process. 2011, 25, 3437–3447. [Google Scholar] [CrossRef]
- Milly, P.C.D.; Betancourt, J.; Falkenmark, M.; Hirsch, R.M.; Kundzewicz, Z.W.; Lettenmaier, D.P.; Stouffer, R.J. Stationarity Is Dead: Whither Water Management? Science 2008, 319, 573–574. [Google Scholar] [CrossRef]
- WMO. Manual on Low-Flow Estimation and Prediction: Operational Hydrology Report No. 50; WMO: Geneva, Switzerland, 2008. [Google Scholar]
- Jones, R.N.; Chiew, F.H.S.; Boughton, W.C.; Zhang, L. Estimating the sensitivity of mean annual runoff to climate change using selected hydrological models. Adv. Water Resour. 2006, 29, 1419–1429. [Google Scholar] [CrossRef] [Green Version]
- Dyer, J.; Mercer, A.; Raczyński, K. Identifying spatial patterns of hydrologic drought over the southeast US using retrospective National Water Model simulations. Water 2022, 14, 1525. [Google Scholar] [CrossRef]
- NOAA. The National Water Model. 2022. Available online: https://water.noaa.gov/about/nwm (accessed on 15 May 2022).
- Lahmers, T.M.; Hazenberg, P.; Gupta, H.; Castro, C.; Gochis, D.; Dugger, A.; Yates, D.; Read, L.; Karsten, L.; Wang, Y.-H. Evaluation of NOAA National Water Model Parameter Calibration in Semi-Arid Environments Prone to Channel Infiltration. J. Hydrometeorol. 2021, 22, 2939–2969. [Google Scholar] [CrossRef]
- Raczyński, K.; Dyer, J. Multi-annual and seasonal variability of low-flow river conditions in southeastern Poland. Hydrol. Sci. J. 2020, 65, 2561–2576. [Google Scholar] [CrossRef]
- Tsakiris, G.; Nalbantis, I.; Vangelis, H.; Verbeiren, B.; Huysmans, M.; Tychon, B.; Jacquemin, I.; Canters, F.; Vanderhaegen, S.; Engelen, G.; et al. A System-based Paradigm of Drought Analysis for Operational Management. Water Resour. Manag. 2013, 27, 5281–5297. [Google Scholar] [CrossRef]
- Tomaszewski, E. Multiannual and Seasonal Dynamics of Low Flows in Rivers of Central Poland; Wydawnictwo Uniwersytetu Łódzkiego: Łódź, Poland, 2012. [Google Scholar]
- Higginbottom, T.P.; Symeonakis, E. Identifying Ecosystem Function Shifts in Africa Using Breakpoint Analysis of Long-Term NDVI and RUE Data. Remote Sens. 2020, 12, 1894. [Google Scholar] [CrossRef]
- Horion, S.; Prishchepov, A.V.; Verbesselt, J.; de Beurs, K.; Tagesson, T.; Fensholt, R. Revealing turning points in ecosystem functioning over the Northern Eurasian agricultural frontier. Glob. Chang. Biol. 2016, 22, 2801–2817. [Google Scholar] [CrossRef]
- Scott, D.T.; Gomez-Velez, J.D.; Jones, N.C.; Harvey, J.W. Floodplain inundation spectrum across the United States. Nat. Commun. 2019, 10, 5194. [Google Scholar] [CrossRef]
- Dodds, W.K.; Clements, W.H.; Gido, K.; Hilderbrand, R.H.; King, R.S. Thresholds, breakpoints, and nonlinearity in freshwaters as related to management. J. N. Am. Benthol. Soc. 2010, 29, 988–997. [Google Scholar] [CrossRef]
- Tomaszewski, E. Defining the threshold level of hydrological drought in lake catchments. Limnol. Rev. 2011, 11, 81–88. [Google Scholar] [CrossRef]
- Raczyński, K. Threshold levels of streamflow droughts in rivers of the Lublin region. Ann. Univ. Mariae Curie-Sklodowska Sect. B Geogr. Geol. Mineral. Petrogr. 2015, 30, 117–129. [Google Scholar] [CrossRef] [Green Version]
- Tokarczyk, T. Low Flow as Indicator of Hydrological Drought; Instytut Meteorologii i Gospodarki Wodnej: Warszawa, Poland, 2010. [Google Scholar]
- Sarailidis, G.; Vasiliades, L.; Loukas, A. Analysis of streamflow droughts using fixed and variable thresholds. Hydrol. Process. 2019, 33, 414–431. [Google Scholar] [CrossRef]
- Rey, S.J.; Stephens, P.; Laura, J. An evaluation of sampling and full enumeration strategies for Fisher Jenks classification in big data settings. Trans. GIS 2017, 21, 796–810. [Google Scholar] [CrossRef]
- Guédon, Y. Exploring the latent segmentation space for the assessment of multiple change-point models. Comput. Stat. 2013, 28, 2641–2678. [Google Scholar] [CrossRef]
- Truong, C.; Oudre, L.; Vayatis, N. Selective review of offline change point detection methods. Signal Process. 2020, 167, 107299. [Google Scholar] [CrossRef] [Green Version]
- Celisse, A.; Marot, G.; Pierre-Jean, M.; Rigaill, G.J. New efficient algorithms for multiple change-point detection with reproducing kernels. Comput. Stat. Data Anal. 2018, 128, 200–220. [Google Scholar] [CrossRef]
- Arlot, S.; Celisse, A.; Harchaoui, Z. A Kernel Multiple Change-point Algorithm via Model Selection. J. Mach. Learn. Res. 2019, 20, 1–56. [Google Scholar]
- Korkas, K.; Fryzlewicz, P. Multiple change-point detection for non-stationary time series using Wild Binary Segmentation. Stat. Sin. 2017, 27, 287–311. [Google Scholar] [CrossRef] [Green Version]
- Alodah, A.; Seidou, O. Assessment of Climate Change Impacts on Extreme High and Low Flows: An Improved Bottom-Up Approach. Water 2019, 11, 1236. [Google Scholar] [CrossRef] [Green Version]
- Keogh, E.; Chu, S.; Hart, D.; Pazzani, M. An online algorithm for segmenting time series. In Proceedings of the 2001 IEEE International Conference on Data Mining, San Jose, CA, USA, 29 November–2 December 2001; pp. 289–296. [Google Scholar] [CrossRef]
- BenYahmed, Y.; Bakar, A.A.; RazakHamdan, A.; Ahmed, A.; Abdullah, S.M.S. Adaptive sliding window algorithm for weather data segmentation. J. Theor. Appl. Inf. Technol. 2015, 80, 322–333. [Google Scholar]
- Shobha, N.; Asha, T. Monitoring Weather based Meteorological Data: Clustering approach for Analysis. In Proceedings of the International Conference on Innovative Mechanisms for Industry Applications, Bengaluru, India, 21–23 February 2017; pp. 75–81. [Google Scholar] [CrossRef]
- Sinaga, K.P.; Yang, M.-S. Unsupervised K-Means Clustering Algorithm. IEEE Access 2020, 8, 80716–80727. [Google Scholar] [CrossRef]
- Murtagh, F.; Contreras, P. Algorithms for hierarchical clustering: An overview. WIREs Data Min. Knowl. Discov. 2012, 2, 86–97. [Google Scholar] [CrossRef]
- Murtagh, F.; Legendre, P. Ward’s Hierarchical Agglomerative Clustering Method: Which Algorithms Implement Ward’s Criterion? J. Classif. 2014, 31, 274–295. [Google Scholar] [CrossRef] [Green Version]
n | nu | Qm | std | Cv | IQR | |
---|---|---|---|---|---|---|
mean | 527.7 | 0.554 | 0.079 | 0.014 | 0.252 | 0.022 |
std | 333.8 | 0.353 | 0.231 | 0.039 | 0.196 | 0.062 |
var | 111438.8 | 0.125 | 0.053 | 0.002 | 0.038 | 0.004 |
Cv | 0.633 | 0.637 | 2.917 | 2.825 | 0.779 | 2.831 |
IQR | 665 | 0.703 | 0.032 | 0.007 | 0.133 | 0.011 |
Relation | Qobj–Median | Qobj–Qp | Median–Qp |
---|---|---|---|
FDC range | 20% | ||
statistics | −54.0508 | −59.3941 | 4.6209 |
p-value | 0.0000 | 0.0000 | 0.0000 |
FDC range | 25% | ||
statistics | −51.2043 | −58.6077 | 4.4995 |
p-value | 0.0000 | 0.0000 | 0.0000 |
FDC range | 30% | ||
statistics | −39.3186 | −44.1184 | 4.0386 |
p-value | 0.0000 | 0.0000 | 0.0001 |
FDC range | 35% | ||
statistics | −22.8904 | −25.4409 | 4.0794 |
p-value | 0.0000 | 0.0000 | 0.0000 |
FDC range | 40% | ||
statistics | 8.5917 | 13.9009 | 3.4002 |
p-value | 0.0000 | 0.0000 | 0.0007 |
FDC range | 45% | ||
statistics | 38.5965 | 41.6176 | 3.2249 |
p-value | 0.0000 | 0.0000 | 0.0013 |
FDC range | 50% | ||
statistics | 49.8975 | 50.6962 | 3.1834 |
p-value | 0.0000 | 0.0000 | 0.0015 |
μ | m | σ | β2 | Skp | nσ1 | nσ2 | nσ3 | |
---|---|---|---|---|---|---|---|---|
Qobj | 59.64 | 62.05 | 16.03 | 2.635 | −1.315 | 76.76 | 94.49 | 97.45 |
Q10 | 32.40 | 36.45 | 8.816 | 3.979 | −2.012 | 85.62 | 92.74 | 96.49 |
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Raczyński, K.; Dyer, J. Development of an Objective Low Flow Identification Method Using Breakpoint Analysis. Water 2022, 14, 2212. https://doi.org/10.3390/w14142212
Raczyński K, Dyer J. Development of an Objective Low Flow Identification Method Using Breakpoint Analysis. Water. 2022; 14(14):2212. https://doi.org/10.3390/w14142212
Chicago/Turabian StyleRaczyński, Krzysztof, and Jamie Dyer. 2022. "Development of an Objective Low Flow Identification Method Using Breakpoint Analysis" Water 14, no. 14: 2212. https://doi.org/10.3390/w14142212
APA StyleRaczyński, K., & Dyer, J. (2022). Development of an Objective Low Flow Identification Method Using Breakpoint Analysis. Water, 14(14), 2212. https://doi.org/10.3390/w14142212