Application of cross-wavelet–linear programming–Kalman filter and GIUH methods in rainfall–runoff modeling

  • Fatemeh Mohammadi
  • Ahmad Fakheri Fard
  • Mohammad Ali GhorbaniEmail author
Original Article


The existence of high uncertainty and nonlinearity of rainfall and runoff relationships makes it difficult to simulate the process. In this study, cross-wavelet transform, Kalman Filter, and Linear Programming methods (KF–LP–CW), and also a combination of cross-wavelet model and geomorphologic unit hydrograph (GIUH–CW) and GIUH based on Nash models (GIUH-Nash–CW) were used to analyze nine compound events of rainfall–runoff of the Sufi Chai watershed, Iran. In this study, by applying the phase difference between rainfall and runoff signals, effective rainfall hyetograph components were modified to minimize the simulation error which was added to model as pseudo-lag time (PLT). By applying cross-wavelet method phase differences, all of the errors in the simulation, such as loss of infiltration, evaporation, and human and instrument measurement errors, are included in the effective precipitation hyetograph and involve the displacement of the effective rainfall components. In this paper, the use of phase difference diagrams and its application in the simulation of compound events is discussed. Other applications of phase differences diagrams are being studied. The calculated unit hydrograph of the linear programming method was used as the Kalman filter measurement model. In addition, the convolutional integral as a transfer function was used in three methods. Using the four evaluation criteria, in terms of the Modified Nash–Sutcliff coefficient (Ej), the results showed that the KF–LP–CW method compared to the other three methods in both calibration steps (0.96) and Verification (0.82) is more suitable. In the case of time to peak estimation, the model performance was more successful than for the base time and peak discharge, respectively.


Compound event Cross-wavelet GIUH Kalman filter Rainfall–runoff 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Fatemeh Mohammadi
    • 1
  • Ahmad Fakheri Fard
    • 1
  • Mohammad Ali Ghorbani
    • 1
    • 2
    Email author
  1. 1.Department of Water EngineeringTabriz UniversityTabrizIran
  2. 2.Engineering FacultyNear East UniversityNicosiaTurkey

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