Application of Bayesian Model Averaging (BMA) Approach for Estimating Evapotranspiration in Gorganrood-Gharesoo Basin, Iran

Document Type : Original Research

Authors
Department of Irrigation and Reclamation Engineering, University College of Agriculture and Natural Resources, University of Tehran, 31587-77871 Karaj, Islamic Republic of Iran.
Abstract
Accurate estimation of Evapotranspiration (ET), as a key component in the hydrological cycle, is essential in agricultural water management. In the current study, an approach based on the Bayesian Model Averaging (BMA) was used to combine eight ET empirical models, namely, Blaney-Criddle, Makkink, Penman, FAO-Penman-Monteith, Priestly-Taylor, Thornthwaite, Turc and Wang to improve the accuracy of ET estimations compared to individual models. The results of eight models and 247 combinations of them (without replacement) were compared to the results of the Water Balance (WB) model as the reference of comparison. This study was performed using warm season (April-September) data of 2005-2014 from Gorganrood-Gharesoo Basin, north of Iran. The performance of the eight models and all possible combinations were evaluated based on four statistical metrics i.e. Root Mean Square Error (RMSE), Kling-Gupta (KGE), Coefficient of Determination (R2), and Bias. Then, the best-performing combination, (BMA-Best), was determined. Based on the WB method, the BMA-Best combination had better performance than the single models according to most of the metrics. In a few cases in which individual models showed slightly better performance than BMA-Best combination, the differences were not statistically significant. On average, the BMA-Best combination increased the R2 by more than 50% and decreased RMSE by more than 70%. According to results of the current study, BMA provides a more reliable estimation of ET and it is recommended for use rather than the individual models. Moreover, the BMA-best combination mostly consisted of energy-based ET models, suggesting that these models have a better performance in climatic conditions of the study area.

Keywords

Subjects


1. Alexandris, S., Stricevic, R., and Petkovic, S. 2008. Comparative analysis of reference evapotranspiration from the surface of rainfed grass in central Serbia, calculated by six empirical methods against the Penman-Monteith formula. European Water, 21(22), 17-28.
2. Allen, R. G., Pereira, L. S., Raes, D., and Smith, M. 1998. Crop evapotranspiration-Guidelines for computing crop water requirements-FAO Irrigation and drainage paper 56. Fao, Rome, 300(9), D05109.
3. Bakhtiari, B., Ghahreman, N. and Afzali Goruh, Z.(2020) Instruments and methods of observation in agrometeorology. University of Tehran Press.206pp (In Persian)
4. Bastiaanssen, W. G., Molden, D. J., and Makin, I. W. 2000. Remote sensing for irrigated agriculture: examples from research and possible applications. Agricultural water management, 46(2), 137-155. https://doi.org/10.1016/S0378-3774(00)00080-9.
5. Blaney, H.F. and Criddle, W.D. 1950. Determining Requirements Water in Irrigated Areas from Climatological and Irrigation Data. Washington Soil Conservation Service, 48.
6. Box, G. E., and Cox, D. R. 1964. An analysis of transformations. Journal of the Royal Statistical Society. Series B (Methodological), 211-252.
7. Chen, Y., Yuan, W., Xia, J., Fisher, J. B., Dong, W., Zhang, X. and Feng, J. 2015. Using Bayesian model averaging to estimate terrestrial evapotranspiration in China. Journal of Hydrology, 528, 537-549. https://doi.org/10.1016/j.jhydrol.2015.06.059.
8. Chun, Y. N. 1989. An empirical model for estimating evapotranspiration from catchments. IAHS Publ, 177, 265-270.
9. Dong, L., Xiong, L., and Yu K. 2013. Uncertainty analysis of multiple hydrologic models using the Bayesian Model Averaging Method, Journal of Applied Mathematics, https://doi.org/10.1155/2013/346045
10. Duan, Q., and Phillips, T. J. 2010. Bayesian estimation of local signal and noise in multimodel simulations of climate change. Journal of Geophysical Research: Atmospheres, 115(D18). http://dx.doi.org/10.1029/2009JD013654.
11. Duan, Q., Ajami, N. K., Gao, X., and Sorooshian, S. 2007. Multi-model ensemble hydrologic prediction using Bayesian model averaging. Advances in Water Resources, 30(5), 1371-1386. http://dx.doi.org/10.1016/j.advwatres.2006.11.014.
12. Ellison, A. M. 2004. Bayesian inference in ecology. Ecology letters, 7(6), 509-520. http://dx.doi.org/10.1111/j.1461-0248.2004.00603.x.
13. European Commission.2015. Guidance document on the application of water balances for supporting the implementation of the WFD. ISBN 978-92-79-52021-1doi: 10.2779/352735
14. Fernandez, C., Ley, E., and Steel, M. F. 2001. Model uncertainty in cross country growth regressions. Journal of applied Econometrics, 16(5), 563-576. https://doi.org/10.1002/jae.623.
Gao, G. 2010. Changes of evapotranspiration and water cycle in China during the past decades. PhD. Thesis, University of Gothenburg. http://hdl.handle.net/2077/21737
16. Hao, Y., Baik, J., and Choi, M. 2019.Combining generalized complementary relationship models with the Bayesian Model Averaging method to estimate actual evapotranspiration over China. https://doi.org/10.1016/j.agrformet.2019.107759
17. Hinn, M., Gronau, Q.F.,van den Berg, D., and Wagenmakers E. 2020. A conceptual introduction to bayesian model averaging. Advances in Methods and Practices in Psychological Science ,3(2), 200 –215
18. Karongo, S. K., and Sharma, T. C. 1997. An evaluation of actual evapotranspiration in tropical East Africa. Hydrological processes, 11(5), 501-510. https://doi.org/10.1002/(SICI)1099-1085(199704)11:5%3C501::AID-HYP456%3E3.0.CO;2-T
19. Li, Y., Andersen, H. E., and McGaughey, R. 2008. A comparison of statistical methods for estimating forest biomass from light detection and ranging data. Western Journal of Applied Forestry, 23(4), 223-231. https://doi.org/10.1093/wjaf/23.4.223.
20. Liu B, Hu Q, Wang W P, Zeng X F, Zhai J Q. 2011. Variation of actual evapotranspiration and its impact on regional water resources in the Upper Reaches of the Yangtze River. Quaternary international, 244(2), 185-193. https://doi.org/10.1016/j.quaint.2011.02.039
21. Madadgar, S., and Moradkhani, H. 2014. Improved Bayesian multi-modeling: Integration of copulas and Bayesian model averaging. Water Resources Research, 50(12), 9586-9603. https://doi.org/10.1002/2014WR015965.
22. Makkink, G. F. 1957. Testing the Penman formula by means of lysimeters. Journal of the Institution of Water Engineerrs, 11, 277-288.
23. Najafi, M. R., Moradkhani, H., and Jung, I. W. 2011. Assessing the uncertainties of hydrologic model selection in climate change impact studies. Hydrological processes, 25(18), 2814-2826. http://dx.doi.org/10.1002/hyp.8043.
24. Olson, R., Fan, Y. and Evans, J. P. 2016. A simple method for Bayesian model averaging of regional climate model projections: Application to southeast Australian temperatures, Geophys. Res.Lett., 43, 7661–7669, doi: 10.1002/2016GL069704.
25. Penman, H. L. 1948. Natural evaporation from open water, bare soil and grass. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 193(1032), 120-145.
26. Priestley, C. H. B., and Taylor, R. J. 1972. On the assessment of surface heat flux and evaporation using large-scale parameters. Monthly weather review, 100(2), 81-92.
27. Raftery, A. E., Gneiting, T., Balabdaoui, F., and Polakowski, M. 2005. Using Bayesian model averaging to calibrate forecast ensembles. Monthly weather review, 133(5), 1155-1174. http://dx.doi.org/10.1175/MWR2906.1.
28. Raneesh, K. Y., and Thampi, S. G. 2013. Bias correction for RCM predictions of precipitation and temperature in the Chaliyar River Basin. Journal of Climatology & Weather Forecasting, 1-7. http://dx.doi.org/10.4172/2332-2594.1000105.
29. Sloughter, J. M. L., Raftery, A. E., Gneiting, T., and Fraley, C. 2007. Probabilistic quantitative precipitation forecasting using Bayesian model averaging. Monthly Weather Review, 135(9), 3209-3220. https://doi.org/10.1175/MWR3441.1.
30. Sun, H.; Yang, Y.; Wu, R.; Gui, D.; Xue, J.; Liu, Y.; Yan, D. 2019.Improving Estimation of Cropland Evapotranspiration by the Bayesian Model Averaging Method with Surface Energy Balance Models. Atmosphere, 10, 188
31. Teuling, A. J., Hirschi, M., Ohmura, A., Wild, M., Reichstein, M., Ciais, P., ... and Wohlfahrt, G. 2009. A regional perspective on trends in continental evaporation. Geophysical Research Letters, 36(2). https://doi.org/10.1029/2008GL036584.
32. Tucker, C. J. 1979. Red and photographic infrared linear combinations for monitoring vegetation. Remote sensing of Environment, 8(2), 127-150. https://doi.org/10.1016/0034-4257(79)90013-0.
33. Turc, L. 1961. Estimation of irrigation water requirements, potential evapotranspiration: a simple climatic formula evolved up to date. Ann. Agron, 12(1), 13-49. Thornthwaite, C. W. 1948. An approach toward a rational classification of climate. Geographical review, 38(1), 55-94.
34. Wang, K., Wang, P., Li, Z., Cribb, M., and Sparrow, M. 2007. A simple method to estimate actual evapotranspiration from a combination of net radiation, vegetation index, and temperature. Journal of Geophysical Research: Atmospheres, 112(D15). https://doi.org/10.1029/2006JD008351.
35. Wang, Q. J., Schepen, A., and Robertson, D. E. 2012. Merging seasonal rainfall forecasts from multiple statistical models through Bayesian model averaging. Journal of Climate, 25(16), 5524-5537.http://dx.doi.org/10.1175/JCLI-D-11-00386.1.
36. Water Resources Atlas, Gorganrood-Gharesoo River basin. 2009. Ministry of energy, Iran water Resources Company,. Tehran, Iran.
37. Zhao, L., Xia, J., Xu, C. Y., Wang, Z., Sobkowiak, L., and Long, C. 2013. Evapotranspiration estimation methods in hydrological models. Journal of Geographical Sciences, 23(2), 359-369. https://doi.org/10.1007/s11442-013-1015-9.