A Comparison between MLR, MARS, SVR and RF Techniques: Hydrological Time-series Modeling

Pankaj Kumar, Abhinav Kumar Singh


Pan evaporation modeling is an essential part of water resources management and water budget governance. The study's objective was to examine the suitability of regression and tree-based techniques for estimating pan evaporation from climatic variables. Multiple linear regression (MLR), multivariate adaptive regression splines (MARS), support vector machine (SVM) and random forest (RF) techniques are employed for weekly pan evaporation modeling for the Ranichauri station situated in the Mid-Himalayan region of Uttarakhand, India. The determination of the most appropriate inputs among climatic variables to map evaporation was done by regression approaches. The data was divided into two parts: the first three years of data used for calibration and the remainder of the one-year data used for model validation. Statistical indices such as root mean square error (RMSE), Nash Sutcliffe coefficient of efficiency (NSE), and coefficient of determination (R2) were used to assess the performance of weekly pan evaporation estimating models. Based on scatter plots, the results are under-predicted and over-predicted for the weekly pan evaporation values. The results showed that the values of the RMSE values ranged from 0.542 to 0.689, the NSE values ranged from 0.953 to 0.974, and the highest R2value was found for the SVR model for the testing period. Therefore, the SVR model was found to be superior and can be applied to predict weekly pan evaporation values for the Ranichauri site.


Doi: 10.28991/HEF-2022-03-01-07

Full Text: PDF


Pan Evaporation; MLR; MARS; SVM; Random Forest; Hydrology.


Penman, H. L. (1948). Natural evaporation from open water, hare soil and grass. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 193(1032), 120–145. doi:10.1098/rspa.1948.0037.

Stephens, J. C., & Stewart, E. H. (1963). A comparison of procedures for computing evaporation and evapotranspiration. Publication, 62, 123-133.

Kim, S. J., Ko, S. H., Kwak, R., Posner, J. D., Kang, K. H., & Han, J. (2012). Multi-vortical flow inducing electrokinetic instability in ion concentration polarization layer. Nanoscale, 4(23), 7406. doi:10.1039/c2nr32467a.

Kisi, O. (2015). Pan evaporation modeling using least square support vector machine, multivariate adaptive regression splines and M5 model tree. Journal of Hydrology, 528, 312–320. doi:10.1016/j.jhydrol.2015.06.052.

Wang, L., Niu, Z., Kisi, O., Li, C., & Yu, D. (2017). Pan evaporation modeling using four different heuristic approaches. Computers and Electronics in Agriculture, 140, 203–213. doi:10.1016/j.compag.2017.05.036.

Resnick, K., Nelson, M. (2011). Reflections from the 2009 NEWWA/EPA Water Resources Symposium: Water Resiliency - Adapting Water Supply to Changing Climate, Land Use, and Regulation. Journal of the New England Water Works Association, 125(3), 244.

Tezel, G., & Buyukyildiz, M. (2016). Monthly evaporation forecasting using artificial neural networks and support vector machines. Theoretical and Applied Climatology, 124(1-2), 69–80. doi:10.1007/s00704-015-1392-3.

Bruton, J. M., McClendon, R. W., & Hoogenboom, G. (2000). Estimating daily pan evaporation with artificial neural networks. Transactions of the American Society of Agricultural Engineers, 43(2), 491–496. doi:10.13031/2013.2730.

Sudheer, K. P., Gosain, A. K., & Ramasastri, K. S. (2002). A data-driven algorithm for constructing artificial neural network rainfall-runoff models. Hydrological Processes, 16(6), 1325–1330. doi:10.1002/hyp.554.

Kişi, Ö. (2006). Daily pan evaporation modelling using a neuro-fuzzy computing technique. Journal of Hydrology, 329(3–4), 636–646. doi:10.1016/j.jhydrol.2006.03.015.

Doǧan, E., Işik, S., & Sandalci, M. (2007). Estimation of daily evaporation using artificial neural networks. Teknik Dergi/Technical Journal of Turkish Chamber of Civil Engineers, 18(2), 4119–4131.

Kim, S., & Kim, H. S. (2008). Neural networks and genetic algorithm approach for nonlinear evaporation and evapotranspiration modeling. Journal of Hydrology, 351(3–4), 299–317. doi:10.1016/j.jhydrol.2007.12.014.

Piri, J., Amin, S., Moghaddamnia, A., Keshavarz, A., Han, D., & Remesan, R. (2009). Daily Pan Evaporation Modeling in a Hot and Dry Climate. Journal of Hydrologic Engineering, 14(8), 803–811. doi:10.1061/(asce)he.1943-5584.0000056.

Moghaddamnia, A., Gosheh, M. G., Nuraie, M.., Mansuri, M. A., Han, D., & Schmitter, E. (2010). Performance evaluation of LLR, SVM, CGNN and BFGSNN models to evaporation estimation. In WSEAS International Conference. Proceedings. Mechanical Engineering Series (Vol. 5). World Scientific and Engineering Academy and Society.

Kumar, P., D., K., Jaipaul, & Tiwari, A. K. (2012). Evaporation Estimation Using Artificial Neural Networks and Adaptive Neuro-Fuzzy Inference System Techniques. Pakistan Journal of Meteorology, 8(16), 81–88.

Samui, P. (2012). Determination of ultimate capacity of driven piles in cohesionless soil: A Multivariate Adaptive Regression Spline approach. International Journal for Numerical and Analytical Methods in Geomechanics, 36(11), 1434–1439. doi:10.1002/nag.1076.

Kumar, P., Kumar, D., & Panwar, R. (2016). Evaporation estimation from climatic factors. Mausam, 67(4), 897–902. doi:10.54302/mausam.v67i4.1417.

Fan, J., Yue, W., Wu, L., Zhang, F., Cai, H., Wang, X., Lu, X., & Xiang, Y. (2018). Evaluation of SVM, ELM and four tree-based ensemble models for predicting daily reference evapotranspiration using limited meteorological data in different climates of China. Agricultural and Forest Meteorology, 263, 225–241. doi:10.1016/j.agrformet.2018.08.019.

Yaseen, Z. M., Al-Juboori, A. M., Beyaztas, U., Al-Ansari, N., Chau, K. W., Qi, C., Ali, M., Salih, S. Q., & Shahid, S. (2020). Prediction of evaporation in arid and semi-arid regions: a comparative study using different machine learning models. Engineering Applications of Computational Fluid Mechanics, 14(1), 70–89. doi:10.1080/19942060.2019.1680576.

Bhardwaj, S., Chandrasekhar, E., Padiyar, P., & Gadre, V. M. (2020). A comparative study of wavelet-based ANN and classical techniques for geophysical time-series forecasting. Computers and Geosciences, 138. doi:10.1016/j.cageo.2020.104461.

Friedman, J. H. (1991). Multivariate Adaptive Regression Splines. The Annals of Statistics, 19(1), 1-67. doi:10.1214/aos/1176347963.

Zhang, Y., Zhao, Z., & Zheng, J. (2020). CatBoost: A new approach for estimating daily reference crop evapotranspiration in arid and semi-arid regions of Northern China. Journal of Hydrology, 588, 125087. doi:10.1016/j.jhydrol.2020.125087.

Kisi, O., & Parmar, K. S. (2016). Application of least square support vector machine and multivariate adaptive regression spline models in long term prediction of river water pollution. In Journal of Hydrology 534, 104–112. doi:10.1016/j.jhydrol.2015.12.014.

Rezaie-balf, M., Naganna, S. R., Ghaemi, A., & Deka, P. C. (2017). Wavelet coupled MARS and M5 Model Tree approaches for groundwater level forecasting. Journal of Hydrology, 553, 356–373. doi:10.1016/j.jhydrol.2017.08.006.

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. doi:10.1016/j.jhydrol.2019.124371.

Vapnik, V. (1992). Principles of risk minimization for learning theory. Advances in neural information processing systems, NeurIPS Proceedings, 4, 831–838.

Breiman, L. Random Forests. Machine Learning 45, 5–32 (2001). doi:10.1023/A:1010933404324.

Prasad, A. M., Iverson, L. R., & Liaw, A. (2006). Newer classification and regression tree techniques: Bagging and random forests for ecological prediction. In Ecosystems 9,(2), 181–199. doi:10.1007/s10021-005-0054-1.

Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning. Springer Series in Statistics, Springer New York, NY, United States. doi:10.1007/978-0-387-84858-7.

Sadler, J. M., Goodall, J. L., Morsy, M. M., & Spencer, K. (2018). Modeling urban coastal flood severity from crowd-sourced flood reports using Poisson regression and Random Forest. Journal of Hydrology, 559, 43–55. doi:10.1016/j.jhydrol.2018.01.044.

Srivastava, R., Tiwari, A. N., & Giri, V. K. (2019). Solar radiation forecasting using MARS, CART, M5, and random forest model: A case study for India. Heliyon, 5(10). doi:10.1016/j.heliyon.2019.e02692.

Stefánsson, A., Končar, N., & Jones, A. J. (1997). A note on the gamma test. Neural Computing and Applications, 5(3), 131–133. doi:10.1007/BF01413858.

Zick, S. E. (2020). Quantifying extreme precipitation forecasting skill in high-resolution models using spatial patterns: A case study of the 2016 and 2018 Ellicott City floods. Atmosphere, 11(2), 136. doi:10.3390/atmos11020136.

Keshtegar, B., Piri, J., & Kisi, O. (2016). A nonlinear mathematical modeling of daily pan evaporation based on conjugate gradient method. Computers and Electronics in Agriculture 127, 120–130. doi:10.1016/j.compag.2016.05.018.

Zounemat-Kermani, M., Seo, Y., Kim, S., Ghorbani, M. A., Samadianfard, S., Naghshara, S., Kim, N. W., & Singh, V. P. (2019). Can decomposition approaches always enhance soft computing models? Predicting the dissolved oxygen concentration in the St. Johns River, Florida. Applied Sciences, Switzerland, 9(12). doi:10.3390/app9122534.

Kreklow, J., Tetzlaff, B., Burkhard, B., & Kuhnt, G. (2020). Radar-based precipitation climatology in germany-developments, uncertainties and potentials. Atmosphere, 11(2), 217. doi:10.3390/atmos11020217.

Kumar, P., Singh, R., Sharma, A., Singh, G., Kumar, D., & Singh, A. K. (2021). Comparison of Different Interpolation Techniques for Mean Areal Rainfall Estimation of Uttarakhand using Geographical Information System. Journal of the New England Water Works Association, 135(3), 43–50.

Hutengs, C., & Vohland, M. (2016). Downscaling land surface temperatures at regional scales with random forest regression. Remote Sensing of Environment, 178, 127–141. doi:10.1016/j.rse.2016.03.006.

Kenney, T. (2021). Obituaries: Guy Manning Foss. Journal of the New England Water Works Association, 135(1), 89–89.

Yaseen, Z. M., Sulaiman, S. O., Deo, R. C., & Chau, K.-W. (2019). An enhanced extreme learning machine model for river flow forecasting: State-of-the-art, practical applications in water resource engineering area and future research direction. Journal of Hydrology, 569, 387–408. doi:10.1016/j.jhydrol.2018.11.069.

Full Text: PDF

DOI: 10.28991/HEF-2022-03-01-07


  • There are currently no refbacks.

Copyright (c) 2022 Pankaj Kumar