Partial Autocorrelation Functions of Water Level in Flood Modelling

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Table 1 shows the statistical parameters of calibration and validation data. The maximum value of calibration period was larger than that of the validation range while the minimum value was less than that of validation. Thus, extrapolation problems may not exist in this data set. The skewness in both calibration and validation data sets are not drastically different. At the forecasting station, the autocorrelation and partial autocorrelation functions of water level with corresponding confidence limits were estimated up to 20 lags as shown in Fig. 4. The ACF for many successive lags was quite high in the water level series as a signal of high persistence. The PACF indicates a significant correlation up to lag 4. Thereafter, correlations fell within the confidence limits. In this case, five delay water levels at times (t-1) to (t-5) were considered as inputs.

The cross correlations between water levels and rainfalls during flood season were also determined to estimate the degree to which two variables are correlated. It was found that the water level was less correlated with its at-site rainfall although the positive relation was shown up to 8 previous rainfalls. The CCFs of five antecedent rainfalls are 0.16, 0.17, 0.16, 0.15, and 0.13, respectively, and considered as predictor variables. The number of input was directly determined by the number of lagged values to be used for forecasting of the next value. The general function of input-output relations for both SMLR and ANN models are as follows:

Case – 1 Ht to Ht+4 = f [ Ht-1,Ht-2, Ht-3, Ht-4, Ht-5]

Case – 2 Ht to Ht+4 = f [Ht-1,Ht-2, Ht-3, Ht-4, Ht-5, Rt-1, Rt-2, Rt-3, Rt-4, Rt-5]

Where t = time (day), H = water level and R = rainfall

The output water levels (H) at time ...

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...while the predicted values marginally agreed with the observed ones in Aug 2008 and 2011. Overall, their performances are not very different in terms of R2. It was found that both models slightly under predicted the high floods in rising limb while over predicted the falling limbs, caused by the effects of antecedent water levels. The models could not fully capture the underlying mechanism of the rising and falling rates of high floods. In the case of extreme events, the MAPE is 1.5% for SMLR and 1.4% for ANN models. Minimum and maximum percent errors ranged between 0.09% and 7.4% in the SMLR models while 0.05% and 6.7% in the ANN models, respectively. Thus, particularly ANN models have a lower error range than the SMLR in predicting high floods. It seems that ANN models better generalize the variability of high floods in the observation period than SMLR models.

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