Develepment of Cross wavelet- kalman filter isochrones lines model to analyze compound rainfall-runoff events

Document Type : Research Paper


1 Water Engr. Dept. Faculty of Agriculture, University of Tabriz, Iran

2 Water Engr. Dept. Faculty of Agriculture, University of Tabriz

3 Mathematical Dept. Faculty of Mathematical Sciences. University of Tabriz


Hydrological modeling plays a valuable role in watershed management. In order to advance this important, in this study, a combination of linear programming, cross-wavelet transform and Kalman filter as a control model for the analysis of nine compound rainfall and runoff events were used in Sufi Chay Basin. The results were compared with modified time area unit hydrograph, and e geomorphologic unit hydrograph. Finally, using the evaluation criteria used in the research, the final performance of these methods was investigated and analyzed. it was revealed that the modified time area method has a relatively weaker performance than the other two methods, which is due to the assumptions used in drawing the isochrones lines. The LP-CW-KF method showed the best performance among the studied methods, which simulated the compound events in the calibration and validation stage with a mean squared error of 2.47 and 2.7, respectively. On average, in all the events and the three studied methods, the mean absolute relative error (MARE) was 0.069 in the time to peak, 0.131 in the peak discharge and 0.125 in the base time. Therefore, on average, all methods showed a better performance in estimating time to peak.


  1. عبداللهی س. (1390). تخمین دبی جریان روزانه رودخانه کارون با استفاده از آنالیز موجک متقاطع. پایان نامه کارشناسی ارشد مهندسی آب، دانشگاه تبریز.
  2. Adamowski J and Sun K (2010). Development of a coupled wavelet transform and neural network method for flow forecasting of no perennial rivers in semiarid watersheds. Hydrology. 390: 85-91.
  3. Antonios A and Constantine E.V (2003). Wavelet Exploratory Analysis of the FTSE ALL SHARE Index. Economics Letters University of Durham UK.
  4. Bateni M., Eslamian, S. S., Mousavi, S. F. and Hosseinipour E.Z. (2012). Application of a Localization Scheme in Estimating Groundwater Level using Deterministic Ensemble Kalman Filter, EWRI/ASCE 10th Symposium on Groundwater Hydrology, Quality and Management, USA.
  5. Cheng H and Sun Z (1996). Application of wavelet packets theory in maneuver target tracking. National Aerospace and Electronics Conference. 1: 157-162.
  6. Chou C.M and Wang R.Y (2004). Application of wavelet-based multi model Kalman filters to real-time flood forecasting. Hydrology process. 18: 987-1008.
  7. Guasti Lima F and Assaf Neto A (2012). Combining wavelet and kalman filters for financial time series forecasting, International Finance and Economics. 12: 47.
  8. Hong L., Chen G and Chui C.K (1998). A filter-bank-based Kalman filtering technique for wavelet estimation and decomposition of random signals. Analog Digit Signal Processing, 45(2): 237-241.
  9. Jury M.R., Enfield D.B and Melice J.L (2002). Tropical monsoons around Africa: stability of El Nino-southern oscillation associations and links with continental climate. Geophysical Research. 107: 10-29.
  10. Labat D., Ababou R and Mangin A (2000). Wavelet analysis in karstic hydrology. 2nd Part: Rainfall–runoff cross–wavelet analysis. Earth and Planetary Science. 329: 881-887.
  11. Lee Y. H. and Singh V. P(1999). Tank model using kalman filter, hydrologic engineering. 4: 344-349.
  12. Moradkhani H and Sorooshian S (2008). General Review of Rainfall-Runoff Modeling: Model Calibration, Data Assimilation, and Uncertainty Analysis, in Hydrological Modeling and Water Cycle, Coupling of the Atmospheric and Hydrological Models. Water Science and Technology Libra ry. 63: 1-23.
  13. Nayak P.C., Venkatesh B., Krishna B and Jain Sharad K (2013). Rainfall-runoff modeling using conceptual, data driven, and wavelet based computing approach. Hydrology. 493: 57-67.
  14. Nourani V, Hosseini Baghanam A, Adamowski J and Gebremichael M (2013). Using self-organizing maps and wavelet transforms for space–time pre-processing of satellite precipitation and runoff data in neural network based rainfall–runoff modeling. Hydrology. 476: 228-243.
  15. Shoaib M Y., Shamseldin A and Melville B (2014). Comparative study of different wavelet based neural network models for rainfall–runoff modeling. Hydrology. 515: 47-58.
  16. Singh V. P., Corradini C and Melone F (1985). Comparision of some methods of deriving the instantaneous unit hydrograph, Nordic hydrology. 16(1): 1-10.
  17. Todini E (1978). Mutually interactive state parameter (MISP) estimation. Application of Kalman Filter. Chapman Conference. University of Pittsburgh, Pittsburgh. 15: 135-151.