Monthly and seasonal runoff estimation using time series, decision tree, and multivariable linear regression

One of the essential factors in the programming and management of water resources is predicting the amount of runoff. Increasing the accuracy in predicting runoff will increase the efficiency of programming and management; therefore, improving the modeling of discharge prediction is a requisite issue. The first aim of this study is to evaluate the efficiency of the multivariable linear regression, M5 decision tree, and time series in predicting the river runoff. The second aim is to analyze the modeling time step (monthly or seasonal) and the effects of model inputs (one delay steps variable against several delay steps variable) on the accuracy of the studied models.

Navrood watershed located in the west part of Gilan province is chosen for the study area in this research. Required data is collected from Kharjgil (1368-1398) and Kholian (1375-1397), including monthly river flow, rainfall, and temperature from Gilan regional water company. The amount of runoff is predicted in two approaches by the received data in monthly and seasonal time steps sing three models of multivariable linear regression, time series, and M5 decision tree. In the first approach, input variables to the model were river flow, rainfall, and temperature with three steps delay. In the second approach, the only variable was river flow with three steps delay. The model evaluation criteria in this research are the mean bias error (MBE), Nash-Sutcliffe efficiency (NSE), and coefficient of determination (R^2).

In the first approach and in monthly timestep, M5 decision tree is selected model with MBE-NSE equal to -0.04,0.80 (train) and 0.01,0.72 (test) in Kharjgil station, and -0.01,0.79 (train) and 0.00,0.86 (test) in Kholian station. In the seasonal time step, the criteria for the M5 decision tree in Kholian station are equal to 0.02,0.78 (train), -0.02,0.86 (test), and in Kholian station are -0.01,0.79 (train), 0.00,0.86 (test). This model was the best in this study for the first approach in the seasonal time step. The second approach has led to different findings considering both monthly and seasonal time steps. In the second approach, the criteria in monthly time step for time series model during train and test in Kharjgil station are respectively -0.05,0.47 and 0.10,0.52 and in Kholian are -0.02,0.63 and 0.2,0.49. The selected model criteria for seasonal time step considering train and test are -0.42,0.58 and 0.06,0.83 in Kharjgil station, and 0.09,0.40 and -0.10,0.62 in Kholian station. The time series model is selected in the second approach in the seasonal time step.

The findings of this research have shown that in both stations and time steps, the M5 decision tree model has shown a higher accuracy in prediction than the two other models in the first approach. Meanwhile, the decision tree model does not show accurate results in the second approach. Alternatively, compared to two other models in both stations and both time steps, the time series model had a higher accuracy. Findings of this research have emphatically shown that specific approaches in choosing the model's inputs can effectively influence the selected model and the accuracy of modeling.