Skip to main content
SpringerLink
Log in

Rainfall-Runoff Simulation in Ungauged Tributary Streams Using Drainage Area Ratio-Based Multivariate Adaptive Regression Spline and Random Forest Hybrid Models

  • Original Paper
  • Published:
Pure and Applied Geophysics Aims and scope Submit manuscript

Abstract

For various reasons, it is not always possible to obtain adequate and reliable long-term streamflow records in a river basin. It is known that streamflow records are even shorter when the stations located on tributary channels are of the interest. Hence, it is necessary to develop dependable streamflow estimation models for the tributary streams that play a key role in the micro-hydrology of the basin. In this study, rainfall-runoff models are developed to estimate the daily streamflow in ungauged tributary streams. Precipitation and streamflow in the most similar gauging station on the main channel and lagged values up to three days before on the same tributary station are used as the input variables of the allocated models. To select the most similar gauging station, a similarity index criterion is developed and used in the analysis. Then, two scenarios based on the streamflow or the corresponding set of direct runoff and base-flow in the same station are used. By applying multivariate adaptive regression spline (MARS) and random forest (RF) methods, several rainfall-runoff models are developed and evaluated based on determination coefficient, mean absolute percentage error, root mean square error, relative peak flow, scatter plot and time series plot. Alternatively, the MARS and RF models are combined with a drainage area ratio (DAR) model to produce the DAR-MARS and DAR-RF models. It is concluded that the direct runoff in the mainstream is more effective on the streamflow of the tributary station, while the integration of models with DAR enhanced the capabilities of the models in estimation of extreme values in the streamflow time series.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Data Availability

The data used in this study can be provided by the corresponding author through a reasonable and formal request.

References

  • Abbasi, M., Farokhnia, A., Bahreinimotlagh, M., & Roozbahani, R. (2021). A hybrid of Random Forest and Deep Auto-Encoder with support vector regression methods for accuracy improvement and uncertainty reduction of long-term streamflow prediction. Journal of Hydrology, 597, 125717.

    Article  Google Scholar 

  • Adnan, R. M., Liang, Z., Heddam, S., Zounemat-Kermani, M., Kisi, O., & Li, B. (2020). Least square support vector machine and multivariate adaptive regression splines for streamflow prediction in mountainous basin using hydro-meteorological data as inputs. Journal of Hydrology, 586, 124371.

    Article  Google Scholar 

  • Adnan, R. M., Yuan, X., Kisi, O., & Anam, R. (2017). Improving accuracy of river flow forecasting using LSSVR with gravitational search algorithm. Advances in Meteorology, 20, 17.

    Google Scholar 

  • Al-Sudani, Z. A., Salih, S. Q., & Yaseen, Z. M. (2019). Development of multivariate adaptive regression spline integrated with differential evolution model for streamflow simulation. Journal of Hydrology, 573, 1–12.

    Article  Google Scholar 

  • Araza, A., Hein, L., Duku, C., Rawlins, M. A., & Lomboy, R. (2020). Data-driven streamflow modelling in ungauged basins: regionalizing random forest (RF) models. bioRxiv.

  • Arsenault, R., & Brissette, F. P. (2014). Continuous streamflow prediction in ungauged basins: The effects of equifinality and parameter set selection on uncertainty in regionalization approaches. Water Resources Research, 50(7), 6135–6153.

    Article  Google Scholar 

  • Asquith, W.H., Roussel, M.C., & Vrabel, J. (2006). Statewide analysis of the drainage-area ratio method for 34 streamflow percentile ranges in Texas. US Geological Survey. Scientific Investigations Report 2006-5286.

  • Belabid, N., Zhao, F., Brocca, L., Huang, Y., & Tan, Y. (2019). Near-real-time flood forecasting based on satellite precipitation products. Remote Sensing, 11(3), 252.

    Article  Google Scholar 

  • Bhandari, S., Thakur, B., Kalra, A., Miller, W. P., Lakshmi, V., & Pathak, P. (2019). Streamflow forecasting using singular value decomposition and support vector machine for the upper Rio Grande River Basin. JAWRA Journal of the American Water Resources Association, 55(3), 680–699.

    Article  Google Scholar 

  • Bitew, M. M., Gebremichael, M., Ghebremichael, L. T., & Bayissa, Y. A. (2012). Evaluation of high-resolution satellite rainfall products through streamflow simulation in a hydrological modeling of a small mountainous watershed in Ethiopia. Journal of Hydrometeorology, 13(1), 338–350.

    Article  Google Scholar 

  • Breiman, L. (2001). Random forests. Machine Learning, 45(1), 5–32.

    Article  Google Scholar 

  • Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (2008). Time series analysis, forecasting and control (4th ed.). Wiley. ISBN 9780470272848.

    Google Scholar 

  • Burn, D. H., & Boorman, D. B. (1993). Estimation of hydrological parameters at ungauged catchments. Journal of Hydrology, 143(3–4), 429–454.

    Article  Google Scholar 

  • Camici, S., Ciabatta, L., Massari, C., & Brocca, L. (2018). How reliable are satellite precipitation estimates for driving hydrological models: A verification study over the Mediterranean area. Journal of Hydrology, 563, 950–961.

    Article  Google Scholar 

  • Emerson, D. G., Vecchia, A. V., & Dahl, A. L. (2005). Evaluation of drainage-area ratio method used to estimate streamflow for the Red River of the North Basin, North Dakota and Minnesota. US Geological Survey. Scientific Investigations Report 2005-5017.

  • Farmer, W. H., & Vogel, R. M. (2013). Performance-weighted methods for estimating monthly streamflow at ungauged sites. Journal of Hydrology, 477, 240–250.

    Article  Google Scholar 

  • Fathian, F., Mehdizadeh, S., Sales, A. K., & Safari, M. J. S. (2019). Hybrid models to improve the monthly river flow prediction: Integrating artificial intelligence and non-linear time series models. Journal of Hydrology, 575, 1200–1213.

    Article  Google Scholar 

  • Friedman, J. H. (1991). Multivariate adaptive regression splines (with discussion). The Annals of Statistics, 19(1), 1–141.

    Google Scholar 

  • Ghoddusi, H., Creamer, G. G., & Rafizadeh, N. (2019). Machine learning in energy economics and finance: A review. Energy Economics, 81, 709–727.

    Article  Google Scholar 

  • Hastie, T., Tibshirani, R., & Friedman, J. (2009). The elements of statistical learning. Springer.

    Book  Google Scholar 

  • Heddam, S., & Kisi, O. (2018). Modelling daily dissolved oxygen concentration using least square support vector machine, multivariate adaptive regression splines and M5 model tree. Journal of Hydrology, 559, 499–509.

    Article  Google Scholar 

  • Jiang, D., & Wang, K. (2019). The role of satellite-based remote sensing in improving simulated streamflow: A review. Water, 11(8), 1615.

    Article  Google Scholar 

  • Jiang, L., & Bauer-Gottwein, P. (2019). How do GPM IMERG precipitation estimates perform as hydrological model forcing? Evaluation for 300 catchments across Mainland China. Journal of Hydrology, 572, 486–500.

    Article  Google Scholar 

  • Kashani, M. H., Ghorbani, M. A., Dinpashoh, Y., & Shahmorad, S. (2016). Integration of Volterra model with artificial neural networks for rainfall-runoff simulation in forested catchment of northern Iran. Journal of Hydrology, 540, 340–354.

    Article  Google Scholar 

  • Kneis, D., Chatterjee, C., & Singh, R. (2014). Evaluation of TRMM rainfall estimates over a large Indian river basin (Mahanadi). Hydrology and Earth System Sciences, 18(7), 2493–2502.

    Article  Google Scholar 

  • Kumar, A., Ramsankaran, R. A. A. J., Brocca, L., & Muñoz-Arriola, F. (2021). A simple machine learning approach to model real-time streamflow using satellite inputs: Demonstration in a data scarce catchment. Journal of Hydrology, 595, 126046.

    Article  Google Scholar 

  • Mehr, A. D., & Kahya, E. (2017). A Pareto-optimal moving average multigene genetic programming model for daily streamflow prediction. Journal of Hydrology, 549, 603–615.

    Article  Google Scholar 

  • Mehr, A. D., Safari, M. J. S., & Nourani, V. (2021). Wavelet packet-genetic programming: A new model for meteorological drought hindcasting. Teknik Dergi, 32(4), 11029–11050.

    Google Scholar 

  • Mohammadi, B., Linh, N. T. T., Pham, Q. B., Ahmed, A. N., Vojteková, J., Guan, Y., Abba, S. I., & El-Shafie, A. (2020). Adaptive neuro-fuzzy inference system coupled with shuffled frog leaping algorithm for predicting river streamflow time series. Hydrological Sciences Journal, 65(10), 1738–1751.

    Article  Google Scholar 

  • Mohammadi, B., Safari, M. J. S., & Vazifehkhah, S. (2022). IHACRES, GR4J and MISD-based multi conceptual-machine learning approach for rainfall-runoff modeling. Scientific Reports, 12(1), 1–21.

    Article  Google Scholar 

  • Nayak, P. C., Sudheer, K. P., & Jain, S. K. (2007). Rainfall-runoff modeling through hybrid intelligent system. Water Resource Research, 43, 7.

    Article  Google Scholar 

  • Razavi, T., & Coulibaly, P. (2016). Improving streamflow estimation in ungauged basins using a multi-modelling approach. Hydrological Sciences Journal, 61(15), 2668–2679.

    Article  Google Scholar 

  • Ries, K. G. & Friesz, P. J. (2000). Methods for estimating low-flow statistics for Massachusetts streams. US Geological Survey. Scientific Investigations Report 4135.

  • Safari, M. J. S. (2019). Decision tree (DT), generalized regression neural network (GR) and multivariate adaptive regression splines (MARS) models for sediment transport in sewer pipes. Water Science and Technology, 79(6), 1113–1122.

    Article  Google Scholar 

  • Safari, M. J. S. (2020). Hybridization of multivariate adaptive regression splines and random forest models with an empirical equation for sediment deposition prediction in open channel flow. Journal of Hydrology, 590, 125392.

    Article  Google Scholar 

  • Safari, M. J. S., Arashloo, S. R., & Mehr, A. D. (2020). Rainfall-runoff modeling through regression in the reproducing kernel Hilbert space algorithm. Journal of Hydrology, 587, 125014.

    Article  Google Scholar 

  • Samadianfard, S., Kargar, K., Shadkani, S., Hashemi, S., Abbaspour, A., & Safari, M. J. S. (2022). Hybrid models for suspended sediment prediction: Optimized random forest and multi-layer perceptron through genetic algorithm and stochastic gradient descent methods. Neural Computing and Applications, 34(4), 3033–3051.

    Article  Google Scholar 

  • Samuel, J., Coulibaly, P., & Metcalfe, R. A. (2011). Estimation of continuous streamflow in Ontario ungauged basins: Comparison of regionalization methods. Journal of Hydrologic Engineering, 16(5), 447–459.

    Article  Google Scholar 

  • Shiri, J. (2018). Improving the performance of the mass transfer-based reference evapotranspiration estimation approaches through a coupled wavelet-random forest methodology. Journal of Hydrology, 561, 737–750.

    Article  Google Scholar 

  • Su, F., Hong, Y., & Lettenmaier, D. P. (2008). Evaluation of TRMM multisatellite precipitation analysis (TMPA) and its utility in hydrologic prediction in the La Plata Basin. Journal of Hydrometeorology, 9(4), 622–640.

    Article  Google Scholar 

  • Tan, S. B., Chua, L. H., Shuy, E. B., Lo, E. Y. M., & Lim, L. W. (2008). Performances of rainfall-runoff models calibrated over single and continuous storm flow events. Journal of Hydrologic Engineering, 13(7), 597–607.

    Article  Google Scholar 

  • Tang, X., Zhang, J., Gao, C., Ruben, G. B., & Wang, G. (2019). Assessing the uncertainties of four precipitation products for SWAT modeling in Mekong River Basin. Remote Sensing, 11(3), 304.

    Article  Google Scholar 

  • Tongal, H., & Booij, M. J. (2018). Simulation and forecasting of streamflows using machine learning models coupled with base flow separation. Journal of Hydrology, 564, 266–282.

    Article  Google Scholar 

  • TSMS (2021), Turkish State Meteorological Service. www.mgm.gov.tr.

  • Waseem, M., Ajmal, M., & Kim, T. W. (2015). Ensemble hydrological prediction of streamflow percentile at ungauged basins in Pakistan. Journal of Hydrology, 525, 130–137.

    Article  Google Scholar 

  • Vaheddoost B., & Aksoy H. (2019). Evaluation of base flow index in stream flows of the Lake Urmia Basin using one parameter digital filter method. The 1st International and 4th National Congress on Iranian Irrigation and Drainage, November 13–14. Urmia University, Urmia, Iran.

  • Yang, X., Magnusson, J., Rizzi, J., & Xu, C. Y. (2018). Runoff prediction in ungauged catchments in Norway: Comparison of regionalization approaches. Hydrology Research, 49(2), 487–505.

    Article  Google Scholar 

  • Yao, D., Yang, J., & Zhan, X. (2013). A novel method for disease prediction: Hybrid of random forest and multivariate adaptive regression splines. Journal of Computers, 8(1), 170–177.

    Article  Google Scholar 

  • Yilmaz, A. G., & Muttil, N. (2014). Runoff estimation by machine learning methods and application to the Euphrates Basin in Turkey. Journal of Hydrologic Engineering, 19(5), 1015–1025.

    Article  Google Scholar 

  • Yilmaz, M. U., & Onoz, B. (2019). Evaluation of statistical methods for estimating missing daily streamflow data. Teknik Dergi, 30(6), 9597–9620.

    Google Scholar 

  • Yilmaz, M. U., & Onoz, B. (2020). A comparative study of statistical methods for daily streamflow estimation at ungauged Basins in Turkey. Water, 12(2), 459.

    Article  Google Scholar 

  • Yilmaz, M. U., & Onoz, B. (2022). Development of ensemble approaches based on performance of statistical methods for daily streamflow estimation. Hydrological Sciences Journal. https://doi.org/10.1080/02626667.2022.2072735

    Article  Google Scholar 

  • Zelelew, M. B., & Alfredsen, K. (2014). Transferability of hydrological model parameter spaces in the estimation of runoff in ungauged catchments. Hydrological Sciences Journal, 59(8), 1470–1490.

    Article  Google Scholar 

  • Zhao, W., Sánchez, N., Lu, H., & Li, A. (2018). A spatial downscaling approach for the SMAP passive surface soil moisture product using random forest regression. Journal of Hydrology, 563, 1009–1024.

    Article  Google Scholar 

  • Zhou, J., Peng, T., Zhang, C., & Sun, N. (2018). Data pre-analysis and ensemble of various artificial neural networks for monthly streamflow forecasting. Water, 10(5), 628.

    Article  Google Scholar 

Download references

Acknowledgements

The authors express their gratitude to the General Directorate of State Hydraulic Works of Turkey (DSI in Turkish acronym) and the Turkish State Meteorological Service (MGM in Turkish acronym) for providing the data used in this study. We also want to thank the Editor and anonymous reviewers who helped us in enhancing the scientific quality of the article.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Bursa Technical University, Bursa, Turkey

    Babak Vaheddoost

  2. Department of Civil Engineering, Yasar University, Izmir, Turkey

    Mir Jafar Sadegh Safari

  3. Department of Civil Engineering, Kirklareli University, Kirklareli, Turkey

    Mustafa Utku Yilmaz

Authors
  1. Babak Vaheddoost
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mir Jafar Sadegh Safari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mustafa Utku Yilmaz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mir Jafar Sadegh Safari.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vaheddoost, B., Safari, M.J.S. & Yilmaz, M.U. Rainfall-Runoff Simulation in Ungauged Tributary Streams Using Drainage Area Ratio-Based Multivariate Adaptive Regression Spline and Random Forest Hybrid Models. Pure Appl. Geophys. 180, 365–382 (2023). https://doi.org/10.1007/s00024-022-03209-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00024-022-03209-3

Keywords

Search

Navigation