應用ARIMAX及ANFIS模型於福山森林集水區逕流模擬之研究

Abstract

本研究嘗試以 2002 - 2011 年福山一號試驗集水區蒐集到的日雨量及日流量資料，建立降雨－逕流模型。選用的模型為 ARIMAX 模型和 ANFIS 模型，兩者皆很少用在森林集水區的研究。ARIMAX 模型依選擇建立的資料時間長度為 10 年、 5 年、 1 年，可分為 ARIMAX10、ARIMAX5¬、ARIMAX１ 三種模型；ANFIS 模型則依選擇建立的資料時間長度、隸屬函數種類、輸入變數個數可分為 ANFIS110 - ANFIS510、ANFIS15 - ANFIS55、ANFIS11 - ANFIS51 共 15 種模型；皆以 2012 年 1-6 月的流量為驗證對象。研究結果指出，選用 5 年資料時間長度建立的 ARIMAX5 模型已有好的模擬和驗證能力；增加資料時間長度到 10 年所建立的 ARIMAX10 模型反而模擬和驗證結果皆不佳。至於 ANFIS 模型，選用 10 年資料時間長度、四個輸入變數：Rt-1、Rt-2、Qt-1、Qt-2、隸屬函數為鐘型函數的 ANFIS310 模型，能同時在模擬和驗證得到不錯的結果，為最佳的 ANFIS 模型。 三種 ARIMAX 模型得到的 MAE 為0.004 - 0.012 m3/sec，RMSE 為 0.007 - 0.023 m3/sec，CE 為 86.2 - 93.1%。15 種 ANFIS 模型得到的 MAE 為0.001 - 0.007 m3/sec，RMSE 為 0.003 - 0.031 m3/sec，CE 為 74.3 - 98.6 %。顯示 ANFIS 模型的各項評鑑指標變動較 ARIMAX 模型大，ARIMAX 模型在平時低流量時的模擬結果較為穩定，不會像 ANFIS 模型可能出現異常偏差值；但是對豪雨或颱風時期的高流量模擬只能得到一個概略趨勢，無法像 ANFIS 模型仍可得到部分的精確模擬結果。未來的研究方向則可朝結合 ARIMAX 模型和 ANFIS 模型的混合模型發展。

Rainfall-runoff model is an important issue of hydrological field. In this study, rainfall-runoff models were investigated by applying ARIMAX (ARIMA with exogenous input) and ANFIS (adaptive network-based fuzzy inference system) model. To illustrate the applicapability and capability of these two models in forest watershed, Fushan experimental watershed No.1 was chosen as a case study area. Ten years of daily rainfall and flow data, from 2002 to 2011, were analyzed. There were three types of ARIMAX models developed by 10 years, 5 years and 1 year flow data individually, which are ARIMAX10, ARIMAX5 and ARIMAX1. In the other hand, 15 types of ANFIS model were developed by different data period, membership function and input variables, which are ANFIS110 - ANFIS510, ANFIS15 - ANFIS55 and ANFIS11 - ANFIS51. Results showed that ARIMAX5 model performed well in both simulating and verifying. Also, the best ANFIS model is ANFIS310 model, which was developed by 10 years data from 2002 to 2011, using four input variables: Rt-1, Rt-2, Qt-1, Qt-2 and bell-shaped membership function. ANFIS310 performed well in both simulating and verifying. Besides, the MAE of ARIMAX model is 0.004 - 0.012 m3/sec, RMSE is 0.007 - 0.023 m3/sec, and CE is 86.2 - 93.1%. The MAE of ANFIS model is 0.001 - 0.007 m3/sec, RMSE is 0.003 - 0.031 m3/sec, CE is 74.3 - 98.6 %。All the evaluation indexes of ANFIS model have a larger range than ARIMAX model, because ARIMAX are more stable in simulation and verification on lower flow period. However, ANFIS still can get accurate simulation and verification even on higher flow period, which ARIMAX can’t. In the future, a hybrid model of ARIMAX and ANFIS is a possible method to be applied.