Water and Irrigation Management

Water and Irrigation Management

Reconstruction of missing daily streamflow data using Multiple Imputation by Chained Equations in Kajo river

Document Type : Research Paper

Authors
Fatemeh Ganji Gohari 1
Hamid Nazaripour 1
Mohammadreza Poodineh 1
Mohsen Hamidianpour 1
Alireza Ghaemi 1
Reza Teimouri 2
1 Department of Physical Geography, Faculty of Geography and Environmental Planning, University of Sistan and Baluchestan, Zahedan, Iran.
2 Department of Water Engineering, Faculty of Water and Soil Engineering, Gorgan University of Agricultural Sciences and Natural Resources, Gorgan, Iran.
10.22059/jwim.2026.408919.1280
Abstract
Missing values in hydrology studies are a common challenge for hydrologists, especially in statistical analyses that require complete datasets. This research evaluates the performance of the Multiple Imputation by Chained Equations (MICE) method in predicting and reconstructing daily river flow values. The study area is the Kajo River basin in southeastern Iran, and the statistical period covers the hydrological years from 1972-1973 to 2021-2022. To investigate and validate the effectiveness of the MICE approach in managing missing flow data, complete historical daily flow records from the hydrological years 2011–2012 to 2021–2022 were used. Subsequently, the MICE method along with Multiple Linear Regression (MLR) was applied to reconstruct all missing daily flow values. The best-performing estimation methods were evaluated using criteria such as the adjusted coefficient of determination (Adj R2), residual standard error (RSE), and mean absolute percentage error (MAPE). The findings indicated that the Classification and Regression Trees (CART) method combined with MLR outperformed other tested methods, achieving the highest  value and the lowest RSE and MAPE values. The RSE and MAPE values for the CART-MLR method at the Pirsehrab station are 0.472 and 0.583, respectively, and at the Chandokan station are 0.475 and 0.588, respectively.
Keywords
Missing Data
Streamflow
Multiple Imputation
MICE
CART
Subjects
  1. Adeloye, A.J. (1996). An opportunity loss model for estimating the value of streamflow data for reservoir planning. Water Resources Management, 10 (1), 45-79.
  2. Ahmat Zainuri, N., Aziz Jemain, A., & Muda, N. (2015). A comparison of various imputation methods for missing values in air quality data. Sains Malaysiana, 44 (3), 449-456.
  3. Ahn, K.H. (2021). Streamflow estimation at partially gaged sites using multiple-dependence conditions via vine copulas. Hydrology and Earth System Sciences, 25 (8), 4319-4333.
  4. Aryanmanesh, J., Nazaripour, H., Mahmoodi, P., & Khosravi, P. (2024). Reconstruction of Missing Daily Streamflow Data using the MissForest Algorithm in Southern Baluchestan Basin, Iran. J Watershed Manage Res., 15(2), 49-64.
  5. Bertsimas, D., Pawlowski, C., & Zhuo, Y.D. (2018). From predictive methods to missing data imputation: an optimization approach. Journal of Machine Learning Research, 18 (2018), 1-39.
  6. Breiman, L., et al. (1984). Classification and regression trees. New York: Wadsworth Publishing.
  7. Campozano, L., et al. (2014). Evaluation of infilling methods for time series of daily precipitation and temperature: the case of the Ecuadorian Andes. Maskana, 5 (1), 99-115.
  8. Carey, A.M., & Paige, G.B. (2016). Ecological site-scale hydrologic response in a semiarid rangeland watershed. Rangeland Ecology and Management, 69 (6), 481-490.
  9. Chhabra, G., Vashisht, V., & Ranjan, J. (2017). A comparison of multiple imputation methods for data with missing values. Indian Journal of Science and Technology, 10 (19), 1-7.
  10. De’ath, G., & Fabricius, K.E. (2000). Classification and regression trees: a powerful yet simple technique for ecological data analysis. Ecology, 81 (11), 3178-3192.
  11. Devineni, N., et al. (2013). A tree-ring-based reconstruction of Delaware River basin streamflow using hierarchical Bayesian regression. Journal of Climate, 26 (12), 4357-4374.
  12. Donders, A.R.T., et al. (2006). Review: a gentle introduction to imputation of missing values. Journal of Clinical Epidemiology, 59 (10), 1087-1091.
  13. Dong, Y., & Peng, C.-Y.J. (2013). Principled missing data methods for researchers. SpringerPlus, 2 (1), 1-17.
  14. Erdal, H.I., & Karakurt, O. (2013). Advancing monthly streamflow prediction accuracy of CART models using ensemble learning paradigms. Journal of Hydrology, 477 (2013), 119-128.
  15. Feizi, H., & Sattari, M. T. (2026). Streamflow Forecasting Based on PatchTST, LSTM, and Ensemble Learning Approaches. Water Resources Management, 40(1), 44.
  16. Gao, Y. (2017). Dealing with missing data in hydrology - data analysis of discharge and groundwater time-series in Northeast Germany. Germany: Freie Universität Berlin.
  17. Gill, M.K., et al. (2007). Effect of missing data on performance of learning algorithms for hydrologic predictions: implications to an imputation technique. Water Resources Research, 43 (7), 1-12.
  18. Gires, A., Tchiguirinskaia, I., & Schertzer, D. (2021). Infilling missing data of binary geophysical fields using scale invariant properties through an application to imperviousness in urban areas. Hydrological Sciences Journal, 66 (7), 1197-1210.
  19. Hamzah, F.B., et al. (2020). Imputation methods for recovering streamflow observation : a methodological review. Cogent Environmental Science, 6 (1), 21.
  20. Hamzah, F.B., et al. (2021). A comparison of multiple imputation methods for recovering missing data in hydrological studies. Civil Engineering Journal, 7 (9), 1608-1619.
  21. Hamzah, F. B., Mohamad Hamzah, F., Mohd Razali, S. F., & El-Shafie, A. (2022). Multiple imputations by chained equations for recovering missing daily streamflow observations: A case study of Langat River basin in Malaysia. Hydrological Sciences Journal, 67(1), 137-149.
  22. Harvey, C.L., Dixon, H., & Hannaford, J. (2012). An appraisal of the performance of data-infilling methods for application to daily mean river flow records in the UK. Hydrology Research, 43 (5), 618-637.
  23. Heitjan, D.F., & Rubin, D.B. (1990). Inference from coarse data via multiple imputation with application to age heaping. Journal of the American Statistical Association, 85 (410), 304-314.
  24. Islam Khan, S., & Hoque, A.S.M.L. (2020). SICE: an improved missing data imputation technique background and related works. Journal of Big Data, 7 (1), 37.
  25. Jamil, J.M. (2012). Partial least squares structural equation modelling with incomplete data: an investigation of the impact of imputation methods. The University of Bradford.
  26. Johnston, C.A. (1999). Development and evaluation of infilling methods for missing hydrologic and chemical watershed monitoring data. Virginia Polytechnic Institute and State University.
  27. Kamaruzaman, I.F., Wan Zin, W.Z., & Mohd Ariff, N. (2017). A comparison of method for treating missing daily rainfall data in Peninsular Malaysia. Malaysian Journal of Fundamental and Applied Sciences, 13 (4), 375-380. (Special Issue on Some Advances in Industrial and Applied Mathematics).
  28. Karakurt, O., et al. (2013). Comparing ensembles of decision trees and neural networks for one-day-ahead stream flow predict. Scientific Research Journal, 1 (15), 43-54.
  29. Kim, S.U., & Lee, K.S. (2009). Regional low flow frequency analysis using Bayesian regression and prediction at ungauged catchment in Korea. KSCE Journal of Civil Engineering, 14 (1), 87-98.
  30. Little, R.J.A., & Rubin, D.B. (2002). Statistical analysis with missing data, hlm. 2nd Edisi. Hoboken, New Jersey: John Wiley & Sons, Inc.
  31. Mispan, M.R., et al. (2015). Missing river discharge data imputation approach using artificial neural network. ARPN Journal of Engineering and Applied Sciences, 10 (22), 10480-10485.
  32. Mohamad Hamzah, F., Mohd Yusoff, S.H., & Jaafar, O. (2019). L-moment-based frequency analysis of high-flow at the Sungai Langat, Kajang, Selangor, Malaysia. Sains Malaysiana, 48 (7), 1357-1366. L-Moment-Based.
  33. Müller, K.-R., et al. (1997). Predicting time series with support vector machines. In: W. Gerstner, et al., (eds) Artificial Neural Networks — ICANN’97. ICANN 1997. Lecture Notes in Computer Science. Berlin Heidelberg: Springer.
  34. Mwale, F.D., Adeloye, A.J., & Rustum, R. (2012). Infilling of missing rainfall and streamflow data in the Shire River basin, Malawi - A self organizing map approach. Physics and Chemistry of the Earth, 50-52 (2012), 34-43.
  35. Nekoeeyan, M. A., Radmanesh, F., & Ahmadi, F. (2022). Prediction of Monthly Streamflow Using Shannon Entropy and Wavelet Theory Approaches (Case study: Maroon River). Water and Irrigation Management, 12(1), 15-31. 
  36. Nor, S.M.C.M., et al. (2020). A comparative study of different imputation methods for daily rainfall data in east-coast Peninsular Malaysia. Bulletin of Electrical Engineering and Informatics, 9 (2), 635-643.
  37. Norazizi, N.A.A., & Deni, S.M. (2019). Comparison of Artificial Neural Network (ANN) and other imputation methods in estimating missing rainfall data at Kuantan Station. Soft Computing in Data Science, 5th International Conference, SCDS 2019, hlm, Singapore. Iizuka, Japan: Springer, 298-308.
  38. Plaia, A., & Bondì, A.L. (2006). Single imputation method of missing values in environmental pollution data sets. Atmospheric Environment, 40 (38), 7316-7330.
  39. Rahman, N.F.A., et al. (2015). Semi distributed hydro climate model; The Xls2NCascii program approach for weather generator. ARPN Journal of Engineering and Applied Sciences, 10 (15), 6619-6622.
  40. Regonda, S.K., et al. (2013). Short-term ensemble streamflow forecasting using operationally-produced single-valued streamflow forecasts-A Hydrologic Model Output Statistics (HMOS) approach. Journal of Hydrology, 497 (2013), 80-96.
  41. Schenker, N., & Taylor, J.M.G. (1996). Partially parametric techniques for multiple imputation. Computational Statistics and Data Analysis, 22 (4), 425-446.
  42. Schmitt, P., Mandel, J., & Guedj, M. (2015). A comparison of six methods for missing data imputation. Journal of Biometrics & Biostatistics, 6 (1), 1-6.
  43. Semiromi, M.T., & Koch, M. (2019). Reconstruction of groundwater levels to impute missing values using singular and multichannel spectrum analysis: application to the Ardabil Plain, Iran. Hydrological Sciences Journal, 64 (14), 1711-1726.
  44. Su, Y.-S., et al. (2011). Multiple imputation with diagnostics (mi) in R: opening windows into the black box. Journal of Statistical SoftwareSoftware, 45 (2), 31.
  45. Tencaliec, P., et al. (2015). Reconstruction of missing daily streamflow data using dynamic regression models. Water Resources Research, American Geophysical Union, 51 (12), 9447-9463.
  46. Tencaliec, P. (2017). Developments in statistics applied to hydrometeorology: imputation of streamflow data and semiparametric precipitation modeling. Universite Grenoble Alpes.
  47. Tyralis, H., Papacharalampous, G., & Langousis, A. (2019). A brief review of random forests for water scientists and practitioners and their recent history in water resources. Water, 11 (5), 1-37.
  48. van Buuren, S. (2007). Multiple imputation of discrete and continuous data by fully conditional specification. Statistical Methods in Medical Research, 16 (3), 219-242.
  49. van Buuren, S., & Groothuis-Oudshoorn, K. (2011). Mice : Multivariate Imputation by Chained Equations in R. Journal of Statistical Software, 45 (3), 1-67.
  50. Van Loon, A.F., & Laaha, G. (2015). Hydrological drought severity explained by climate and catchment characteristics. Journal of Hydrology, 526, 3-14.
  51. Vezza, P., et al. (2010). Low flows regionalization in north-western Italy. Water Resources Management, 24 (14), 4049-4074.
  52. White, I.R., & Wood, A.M. (2011). Multiple imputation using chained equations : issues and guidance for practice. Statistics in Medicine, 30 (4), 377-399.
  53. Widaman, K.F. (2006). Missing Data: what to do with or without them. Monographs of the Society for Research in Child Development, 71 (1), 210-211.
  54. Zhao, Y., & Long, Q. (2016). Multiple imputation in the presence of high-dimensional data. Statistical Methods in Medical Research, 25 (5), 2021-2035.
  55. Zvarevashe, W., Krishnannair, S., & Sivakumar, V. (2019). Analysis of rainfall and temperature data using ensemble empirical mode decomposition. Data Science Journal, 18 (1), 1-9.
Water and Irrigation Management
Volume 16, Issue 1
Spring 2026
Pages 141-162