Accurate water level forecasts are essential for flood warning. This study adopts a data-driven approach based on the adaptive network-based fuzzy inference system (ANFIS) to forecast the daily water levels of the Lower Mekong River at Pakse, Lao People's Democratic Republic. ANFIS is a hybrid system combining fuzzy inference system and artificial neural networks. Five ANFIS models were developed to provide water level forecasts from 1 to 5 days ahead, respectively. The results show that although ANFIS forecasts of water levels up to three lead days satisfied the benchmark, four-and five-lead-day forecasts were only slightly better in performance compared with the currently adopted operational model. This limitation is imposed by the auto-and cross-correlations of the water level time series. Output updating procedures based on the autoregressive (AR) and recursive AR (RAR) models were used to enhance ANFIS model outputs. The RAR model performed better than the AR model. In addition, a partial recursive procedure that reduced the number of recursive steps when applying the AR or the RAR model for multi-step-ahead error prediction was superior to the fully recursive procedure. The RAR-based partial recursive updating procedure significantly improved three-, four-and five-lead-day forecasts. Our study further shows that for long lead times, ANFIS model errors are dominated by lag time errors. Although the ANFIS model with the RAR-based partial recursive updating procedure provided the best results, this method was able to reduce the lag time errors significantly for the falling limbs only. Improvements for the rising limbs were modest. À Á T is the regression vector that consists of previous values of measured outputs, where p is the order of the recursive regressive model. The gain, K t , determines how much the current prediction error Figure 1. Schematic of ANFIS architecture (Jang, 1993) Figure 8. A comparison of performance between Naïve, URBS and ANFIS: (a) COE, (b) MPAE, (c) MAE and (d) RMSE Figure 9. A comparison of AR a , RAR a , AR b and RAR b updating procedures
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