The phenomenon of evaporation affects the distribution of water in the hydrological cycle and plays a key role in agriculture and water resource management. We propose a self-organizing map neural network (SOMN) to assess the variability of daily evaporation based on meteorological variables. The daily meteorological data sets from a climate gauge were collected as inputs to the SOMN and then were classified into a topology map based on their similarities to investigate their multi-collinear relationships to assess their effort in the evaporation. To accurately estimate the daily evaporation based on the input pattern, the weights that connect the clustered centers in a hidden layer with the output were trained by using the least square regression method. In addition, we compared the results with those of back propagation neural network (BPNN), modified Penman and Penman–Monteith formulas. The results demonstrated that the topological structures of SOMN could give a meaningful map to present the clusters of meteorological variables and the networks could well estimate the daily evaporation. By comparing the performances of these models in estimating daily and long-term (monthly or yearly) cumulative evaporation, the SOMN provides the best performance.