عنوان مقاله [English]
Introduction: In the recent years, researchers interested on probabilistic forecasting of hydrologic variables such river flow.A probabilistic approach aims at quantifying the prediction reliability through a probability distribution function or a prediction interval for the unknown future value. The evaluation of the uncertainty associated to the forecast is seen as a fundamental information, not only to correctly assess the prediction, but also to compare forecasts from different methods and to evaluate actions and decisions conditionally on the expected values. Several probabilistic approaches have been proposed in the literature, including (1) methods that use resampling techniques to assess parameter and model uncertainty, such as the Metropolis algorithm or the Generalized Likelihood Uncertainty Estimation (GLUE) methodology for an application to runoff prediction), (2) methods based on processing the forecast errors of past data to produce the probability distributions of future values and (3) methods that evaluate how the uncertainty propagates from the rainfall forecast to the river discharge prediction, as the Bayesian forecasting system.
Materials and Methods: In this study, two different probabilistic methods are used for river flow prediction.Then the uncertainty related to the forecast is quantified. One approach is based on linear predictors and in the other, nearest neighbor was used. The nonlinear probabilistic ensemble can be used for nonlinear time series analysis using locally linear predictors, while NNPE utilize a method adapted for one step ahead nearest neighbor methods. In this regard, daily river discharge (twelve years) of Dizaj and Mashin Stations on Baranduz-Chay basin in west Azerbijan and Zard-River basin in Khouzestan provinces were used, respectively. The first six years of data was applied for fitting the model. The next three years was used to calibration and the remained three yeas utilized for testing the models. Different combinations of recorded data were used as the input pattern to streamflow forecasting.
Results and Discussion: Application of the used approaches in ensemble form (in order to choice the optimized parameters) improved the model accuracy and robustness in prediction. Different statistical criteria including correlation coefficient (R), root mean squared error (RMSE) and Nash–Sutcliffe efficiency coefficient (E) were used for evaluating the performance of models. The ranges of parameter values to be covered in the ensemble prediction have been identified by some preliminary tests on the calibration set. Since very small values of k have been found to produce unacceptable results due to the presence of noise, the minimum value is fixed at 100 and trial values are taken up to 10000 (k = 100, 200, 300,500, 1000, 2000, 5000, 10000). The values of mare chosen between 1 and 20 and delay time values γ are tested in the range [1,5]. With increasing the discharge values, the width of confidence band increased and the maximum confidence band is related to maximum river flows. In Dizaj station, for ensemble numbers in the range of 50-100, the variation of RMSE is linear. The variation of RMSE in Mashin station is linear for ensemble members in the range of 100-150. It seems the numbers of ensemble members equals to 100 is suitable for pattern construction. The performance of NNPE model was acceptable for two stations. The number of points excluded 95% confidence interval were equal to 108 and 96 for Dizaj and Mashin stations, respectively. The results showed that the performance of model was better in prediction of minimum and median discharge in comparing maximum values.
Conclusion: The results confirmed the performance and reliability of applied methods. The results indicated the better performance and lower uncertainty of ensemble method based on nearest neighbor in comparison with probabilistic nonlinear ensemble method. Nash–Sutcliffe model efficiency coefficient (E) for nearest neighbor probabilistic ensemble method in Dizaj and Mashin Stations during test period of model obtained 0.91 and 0.93, respectively.The investigation on the performance of models in different basins showed that the models have better performance in Zard river basin compared to Baranduz-Chaybasin. Furthermore the variation of discharge values during test period in Zard basin was lower in comparison of Baranduz-Chay basin. The real advantage of including streamflow forecasts requires detailed and specific investigations, but the preliminary results suggest the good potentiality of probabilistic NLP method. Using ensemble prediction method can help to decision makers in order to determine the uncertainty of prediction in water resources field.