HESS Hydrology and Earth System Sciences HESS Hydrol. Earth Syst. Sci. 1607-7938 Copernicus Publications Göttingen, Germany 10.5194/hess-16-255-2012 A spatial neural fuzzy network for estimating pan evaporation at ungauged sites Chung C.-H. 1 Chiang Y.-M. 1 Chang F.-J. 1 Department of Bioenvironmental Systems Engineering, National Taiwan University, Taipei 10617, Taiwan 25 01 2012 16 1 255 266 Copyright: © 2012 C.-H. Chung et al. 2012 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://hess.copernicus.org/articles/16/255/2012/hess-16-255-2012.html The full text article is available as a PDF file from https://hess.copernicus.org/articles/16/255/2012/hess-16-255-2012.pdf

Evaporation is an essential reference to the management of water resources. In this study, a hybrid model that integrates a spatial neural fuzzy network with the kringing method is developed to estimate pan evaporation at ungauged sites. The adaptive network-based fuzzy inference system (ANFIS) can extract the nonlinear relationship of observations, while kriging is an excellent geostatistical interpolator. Three-year daily data collected from nineteen meteorological stations covering the whole of Taiwan are used to train and test the constructed model. The pan evaporation (<i>E</i><sub>pan</sub>) at ungauged sites can be obtained through summing up the outputs of the spatially weighted ANFIS and the residuals adjusted by kriging. Results indicate that the proposed AK model (hybriding ANFIS and kriging) can effectively improve the accuracy of <i>E</i><sub>pan</sub> estimation as compared with that of empirical formula. This hybrid model demonstrates its reliability in estimating the spatial distribution of <i>E</i><sub>pan</sub> and consequently provides precise <i>E</i><sub>pan</sub> estimation by taking geographical features into consideration.

 References Allen, R. G., Pereira, S. L., Raes, D., and Smith, M.: Crop evapotranspiration, Guidelines for computing crop water requirements, Irrigation and Drainage Paper No. 56, FAO, Rome, 1998. Antar, M. A., Elassiouti, I., and Allam, M. N.: Rainfall-runoff modelling using artificial neural networks technique: a Blue Nile catchment case study, Hydrol. Process., 20, 1201–1216, 2006. Chang, F. J. and Chang, Y. T.: Adaptive neuro-fuzzy inference system for prediction of water level in reservoir, Adv. Water Res., 29, 1–10, 2006. Chang, F. J., Chang, L. C., Kao, H.-S., and Wu, G.-R.: Assessing the effort of meteorological variables for evaporation estimation by self-organizing map neural network, J. Hydrol., 384, 118–129, 2010. Chang, L. C. and Chang, F. J.: Intelligent control for modelling of real-time reservoir operation, Hydrol. Process., 15, 1621–1634, 2001. Chang, Y. T., Chang, L.C., and Chang, F. J.: Intelligent control for modeling of real-time reservoir operation, part II: artificial neural network with operating rule curves, Hydrol. Process., 19, 1431–1444, 2005. Chen, S. H., Lin, Y. H., Chang, L. C., and Chang, F. J.: The strategy of building a flood forecast model by neuro-fuzzy network, Hydrol. Process., 20, 1525–1540, 2006. Chen, Y. C.: Rainfall network design using kriging and entropy, Hydrol. Process., 22, 340–346, <a href="http://dx.doi.org/10.1002/hyp.6292">https://doi.org/10.1002/hyp.6292</a>, 2008. Chen, Y. H. and Chang, F. J.: Evolutionary Artificial Neural Networks for Hydrological Systems Forecasting, J. Hydrol., 367, 125–137, 2009. Chiang, Y. M. and Chang, F. J.: Integrating hydrometeorological information for rainfall-runoff modelling by artificial neural networks, Hydrol. Process., 23, 1650–1659. 2009. Choudhury, B. J., Ahmed, N. U., Idso, S. B., Reginato, R. J., and Daughtry, C. S. T.: Relations between evaporation coefficients and vegetation indices studied by model simulations, Remote Sens. Environ., 50, 1–17, 1994. Cressie, N.: The originas of Kriging, Math. Geol., 22, 239–252, 1990. Daly, C.: Guidelines for assessing the suitability of spatial climate data sets, Int. J. Climatol., 26, 707–721, 2006. Donohue, R. J., McVicar, T. R., and Roderick, M. L.: Assessing the ability of potential evaporation formulations to capture the dynamics in evaporative demand within a changing climate, J. Hydrol., 386, 186–197, 2010. Gonzalez-Camacho, J. M., Cervantes-Osornio, R., Ojeda-Bustamante, W., and Lopez-Cruz, I.: Forecasting reference evapotranspiration using artificial neural networks, Ingenieria Hidraulica En Mexico, 23, 127–138, 2008. Hutchinson, M. F.: Interpolating mean rainfall using thin plate smoothing splines, Int. J. Geogr. Inf. Syst., 9, 385–403, 1995. Jang, J. S. R.: ANFIS – Adaptive-network-based fyzzy inference system, IEEE T. Syst. Man Cybernet., 23, 665–685, 1993. Journel, A. G. and Huijbregts, C. J.: Mining Geostatistics, Academic Press, 1981. Kanevsky, M., Arutyunyan, R., Bolshov, L., Demyanov, V., and Maignan, M.: Artificial neural networks and spatial estimations of Chernobyl fallout, Geoinformatics, 7, 5–11, 1996. Keskin, M. E. and Terzi, O.: Artificial neural network models of daily pan evaporation, J. Hydrol. Eng.-ASCE, 11, 65–70, 2006. Kim, G. and Barros, A. P.: Quantitative flood forecasting using multisensor data and neural networks, J. Hydrol., 246, 45–62, 2001. Kisi, O.: Daily pan evaporation modelling using a neuro-fuzzy computing technique, J. Hydrol., 329, 636–646, 2006. Kisi, O. and Ozturk, O.: Adaptive neurofuzzy computing technique for evapotranspiration estimation, J. Irrig. Drain. Eng.-ASCE, 133, 368–379, 2007. Koike, K., Matsuda, S., and Gu, B.: Evaluation of interpolation accuracy of neural kriging with application to temperature-distribution analysis, Math. Geol., 33, 421–448, 2001. Legleiter, C. J.: Spatial prediction of river channel topography by kriging, Earth Surf. Proc. Land., 33, 841–867, <a href="http://dx.doi.org/10.1002/esp.1579">https://doi.org/10.1002/esp.1579</a>, 2008. McVicar, T. R., Van Niel, T. G., Li, L. T., Hutchinson, M. F., Mu, X. M., and Liu, Z. H.: Spatially Distributing Monthly Reference Evapotranspiration and Pan Evaporation Considering Topographic Influences, J. Hydrol., 338, 196–220, 2007. Neuman, S. P. and Jacobson, E. A.: Analysis of nonintrinsic spatial varibility by residual kriging with application to regional groundwater levels, J. Int. Assoc. Math. Geol., 16, 499–521, 1984. Penman, H. L.: Natural evaporation from open water, bare soil and grass, Proc. Roy. Soc. B, 193, 120–145, <a href="http://dx.doi.org/10.1098/rspa.1948.0037">https://doi.org/10.1098/rspa.1948.0037</a>, 1948. Schultz, C., S. Myers, J. Hipp, and C. Young .: Nonstationary Bayesian kriging: a predictive technique to generate corrections for detection, location, and discrimination, Bull. Seism. Soc. Am., 88, 1275–1288, 1998. Schuurmans, J. M., Bierkens, M. F. P., Pebesma, E. J., and Uijlenhoet, R.: Automatic prediction of high-resolution daily rainfall fields for multiple extents: The potential of operational radar, J. Hydrometeorol., 8, 1204–1224, 2007. Shu, C. and Ouarda, T. B. M. J.: Regional flood frequency analysis at ungauged sites using the adaptive neuro-fuzzy inference system, J. Hydrol., 349, 31–43, 2008. Smith, M., Allen, R., and Pereira, L.: Revised FAO methodology for crop water requirement, Land and Water Development Division, FAO, Rome, 1997. Trajkovic, S., Todorovic, B., and Stankovic, M.: Forecasting of reference evapotranspiration by artificial neural networks, J. Irrig. Drain. Eng.-ASCE, 129, 454–457, 2003. Xu, C. Y. and Singh, V. P.: Dependence of evaporation on meteorological variables at different time scales and intercomparsion of estimation methods, Hydrol. Process., 12, 429–442, 1998. Xu, C. Y., Gong, L., Jiang, T., Chen, D., and Singh, V. P.: Analysis of spatial distribution and temporal trend of reference evapotranspiration and pan evaporation in Changjiang (Yangtze River) catchment, J. Hydrol., 327, 81–93, 2006. Yeh, H. F., Lee C.-H., Chen, J.-W., and Chang, K.-L.: Evaluation of pan coefficients for estimating reference evapotranspiration in southern Taiwan, J. Taiwan Agr. Eng., 54, 27–35, 2008.