Optimization of Precipitation Monitoring Network via Robust Empirical Orthogonal Function Analysis with QR Column Pivoting
Publication: Journal of Hydrologic Engineering
Volume 29, Issue 3
Abstract
The design of optimal precipitation station configuration (network) is pivotal for obtaining accurate spatiotemporal data in a cost-efficient manner in terms of high operation, management and maintenance costs of stations, and missing data completion. In the present study, historical spatiotemporal precipitation data of 18 stations located in the Upper Euphrates watershed basin are initially exposed to empirical orthogonal function (EOF) analysis to exploit the general intrinsic low dimensionality of the precipitation phenomenon. Along with the basic EOF analysis, robust and mean-centered versions are also developed to improve the prediction accuracy of spatiotemporal precipitation data and optimize the number of stations in the watershed basin. Importantly, for the first time, robust EOF (R-EOF) analysis has been carried out in a hydrological predictive study. The matrix that contains the obtained modes (EOFs) is fed into the QR factorization with a column pivoting algorithm and sparse precipitation gauge locations are identified. The assessment of the model using the Nash–Sutcliffe coefficient of efficiency (CE), root mean square error (RMSE), and mean absolute error (MAE) metrics reveals that the complete dimensional state space can be reconstructed effectively, and its future evolution can be predicted accurately even with a small number of observation stations. Remarkably, the spatiotemporal precipitation data for the entire field can be reconstructed using only four, five, 10, or 12 stations, utilizing robust mean-centered (R-MC-EOF), robust (R-EOF), mean-centered (MC-EOF), and standalone EOF models. These models demonstrate high performance with CE values of 0.96, 0.94, 0.84, and 0.81 and RMSE values of 2.2, 3.8, 5.7, and 6.8 mm, respectively. Notably, both the R-EOF and MC-EOF models outperformed their standalone counterparts in terms of model performance. When a sufficient amount of spatiotemporal data is available, the optimal number and locations of precipitation gauges can be easily determined using the QR with a column pivoting algorithm. This algorithm is user friendly and can be implemented in popular programming environments such as Python, MATLAB, and R. Due to the limited budgets and/or low accessibility conditions, challenging basin topography, and bad weather conditions, not many areas are extensively equipped with instruments to measure the precipitation; thus, high-resolution data is not always available. Acquiring reliable and accurate data is critical for water resources management, flood and drought warning, irrigation networks, hydrological (e.g., watershed, rain-runoff) modeling, and urban and environmental planning. This renders the proposed methodology very crucial in obtaining high-fidelity spatiotemporal data.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
We sincerely thank the Türkiye Meteorological Service for providing precipitation data.
References
Altunkaynak, A. 2005. “Significant wave height prediction by using a spatial model.” Ocean Eng. 32 (8–9): 924–936. https://doi.org/10.1016/j.oceaneng.2004.10.012.
Altunkaynak, A. 2008. “Estimation of streamflow by slope regional dependency function.” Hydrol. Earth Syst. Sci. 12 (4): 1121–1127. https://doi.org/10.5194/hess-12-1121-2008.
Altunkaynak, A. 2009. “Streamflow estimation using optimal regional dependency function.” Hydrol. Process. 23 (25): 3525–3533. https://doi.org/10.1002/hyp.7446.
Altunkaynak, A. 2015. “Prediction of significant wave height using spatial function.” Ocean Eng. 106 (Sep): 220–226. https://doi.org/10.1016/j.oceaneng.2015.06.028.
Altunkaynak, A. 2019. “Predicting water level fluctuations in lake van using hybrid season-neuro approach.” J. Hydrol. Eng. 24 (8): 04019021. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001804.
Altunkaynak, A., and T. A. Nigussie. 2015. “Prediction of daily rainfall by a hybrid wavelet season-neuro technique.” J. Hydrol. 529 (Part 1): 287–301. https://doi.org/10.1016/j.jhydrol.2015.07.046.
Altunkaynak, A., and M. Özger. 2005. “Spatial significant wave height variation assessment and its estimation.” J. Waterw. Port Coastal Ocean Eng. 31 (6): 277. https://doi.org/10.1061/(ASCE)0733-950X(2005)131:6(277).
Aziz, M. K., F. Yusof, Z. M. Daud, Z. Yusop, and M. A. Kasno. 2016. “Optimal design of rain gauge network in Johor by using geostatistics and particle swarm optimization.” Int. J. Geomater. 11 (25): 2422–2428. https://doi.org/10.21660/2016.25.5137.
Balov, N., and A. Altunkaynak. 2020. “Spatio-temporal evaluation of various global circulation models in terms of projection of different meteorological drought indices.” Environ. Earth Sci. 79 (6): 126. https://doi.org/10.1007/s12665-020-8881-0.
Bayat, B., M. Nasseri, and E. Delmelle. 2021. “Uncertainty-based rainfall network design using a fuzzy spatial interpolation method.” Appl. Soft Comput. 106 (Jul): 107296. https://doi.org/10.1016/j.asoc.2021.107296.
Bowden, G. J., H. R. Maier, and G. C. Dandy. 2012. “Real-time deployment of artificial neural network forecasting models: Understanding the range of applicability.” Water Resour. Res. 48 (10). https://doi.org/10.1029/2012WR011984.
Brunton, B. W., L. A. Johnson, J. G. Ojemann, and J. N. Kutz. 2016. “Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition.” J. Neurosci. Methods 258 (Jan): 1–15. https://doi.org/10.1016/j.jneumeth.2015.10.010.
Brunton, S. L., and J. N. Kutz. 2019. Data-driven science and engineering machine learning, dynamical systems, and control. Cambridge, UK: Cambridge University Press.
Candes, E. J., X. Li, Y. Ma, and J. Wright. 2011. “Robust principal component analysis?” J. ACM 58 (3): 1–37. https://doi.org/10.48550/arXiv.0912.3599.
Dai, Q., M. Bray, L. Zhuo, T. Islam, and D. Han. 2017. “A scheme for rain gauge network design based on remotely sensed rainfall measurements.” J. Hydrometeorol. 18 (2): 363–379. https://doi.org/10.1175/JHM-D-16-0136.1.
Donigan, A. S., and J. T. Love. 2003 “Sediment calibration procedures and guidelines for watershed modeling.” In Vol. 4 of Proc., Water Environment Federation, 728–747. Beckley, WV: Water Environment Federation.
Hirsh, S. M., K. D. Harris, J. N. Kutz, and B. W. Brunton. 2020. “Centering data improves the dynamic mode decomposition.” SIAM J. Appl. Dyn. Syst. 19 (3): 1920–1955. https://doi.org/10.1137/19M1289881.
Kutz, J. N. 2013. Data driven modeling & scientific computation. Oxford, UK: Oxford University Press.
Lorenz, C., and H. Kunstmann. 2012. “The hydrological cycle in three state-of-the-art reanalyses: Intercomparison and performance analysis.” J. Hydrometeor. 13 (5): 1397–1420. https://doi.org/10.1175/JHM-D-11-088.1.
Manohar, K., B. W. Brunton, M. J. Kutz, and S. L. Brunton. 2018. “Data-driven sparse sensor placement for reconstruction: Demonstrating the benefits of exploiting known patterns.” IEEE Control Syst. Mag. 38 (3): 63–86. https://doi.org/10.1109/MCS.2018.2810460.
Mishra, A. K. 2009. “Developments in hydrometric network design: A review April.” Rev. Geophys. 47 (2). https://doi.org/10.1029/2007RG000243.
Moriasi, D. N., J. G. Arnold, M. W. Van Liew, R. L. Bingner, R. D. Harmel, and T. L. Veith. 2007. “Model evaluation guidelines for systematic quantification of accuracy in watershed simulations.” Trans. ASABE 50 (3): 885–900. https://doi.org/10.13031/2013.23153.
Nash, J. E., and J. V. Sutcliffe. 1970. “River flow forecasting through conceptual models part I: A discussion of principles.” J. Hydrol. 10 (3): 282–290. https://doi.org/10.1016/0022-1694(70)90255-6.
Qi, Z., G. Kang, C. Chu, Y. Qiu, Z. Xu, and Y. Wang. 2017. “Comparison of SWAT and GWLF model simulation performance in humid south and semi-arid north of China.” Water 9 (8): 567. https://doi.org/10.3390/w9080567.
Saeidifarzad, B., V. Nourani, M. T. Aalami, and K. W. Chau. 2014. “Multi-site calibration of linear reservoir based geomorphologic rainfall-runoff models.” Water 6 (9): 2690–2716. https://doi.org/10.3390/w6092690.
Scherl, I., B. Strom, J. K. Shang, O. Williams, B. L. Polagye, and S. L. Brunton. 2020. “Robust principal component analysis for modal decomposition of corrupt fluid flows.” Phys. Rev. Fluids 5 (5): 054401. https://doi.org/10.1103/PhysRevFluids.5.054401.
Schmid, P. J. 2010. “Dynamic mode decomposition of numerical and experimental data.” J. Fluid Mech. 656: 5–28.
Solomatine, D. P., and D. L. Shrestha. 2009. “A novel method to estimate model uncertainty using machine learning techniques.” Water Resour. Res. 45 (12). https://doi.org/10.1029/2008WR006839.
Wang, K., Q. Guan, N. Chen, D. Tong, C. Hu, Y. Peng, X. Dong, and C. Yang. 2017. “Optimizing the configuration of precipitation stations in a space-ground integrated sensor network based on spatial-temporal coverage.” J. Hydrol. 548 (May): 625–640. https://doi.org/10.1016/j.jhydrol.2017.03.033.
Wang, K., J. Yang, Y. Peng, Q. Wu, and C. Hu. 2020. “Multiobjective optimization of sensor placement for precipitation station monitoring network design.” J. Hydrol. Eng. 25 (9): 04020039. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001954.
Wang, K.-H., and A. Altunkaynak. 2012. “Comparative case study of rainfall-runoff modeling between SWMM and fuzzy logic approach.” J. Hydrol. Eng. 17 (2): 283–291. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000419.
Yildirim, B., C. Chryssostomidis, and G. E. Karniadakis. 2009. “Efficient sensor placement for ocean measurements using low dimensional concepts.” Ocean Modell. 27 (3–4): 160–173. https://doi.org/10.1016/j.ocemod.2009.01.001.
Yürekli, K. 2015. “Impact of climate variability on precipitation in the Upper Euphrates–Tigris Rivers Basin of Southeast Turkey.” Atmos. Res. 154 (Mar): 25–38. https://doi.org/10.1016/j.atmosres.2014.11.002.
Information & Authors
Information
Published In
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Nov 3, 2022
Accepted: Dec 18, 2023
Published online: Feb 29, 2024
Published in print: Jun 1, 2024
Discussion open until: Jul 29, 2024
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.