Intelligent flow discharge computation in a rectangular channel with free overfall condition

The free overfall is a simple and widely used device for measuring discharge in open irrigation channels and agricultural research projects. However, the direct measurement of discharge can be difficult and time-consuming with care needed to minimize potential inaccuracies of empirical equations applied to site-specific conditions. Thus, in the present study four standalone algorithms of Isotonic Regression (ISO), Least Median of Square Regression (LMS), M5Prime (M5P) and REPT and four novel hybrid algorithms of rotation forest (ROF) combined with those four standalone models (i.e., ROF-ISO, ROF-LMS, ROF-M5P and ROF-REPT) were applied for the intelligent prediction of discharge per unit width for the free overfall condition in rectangular channels. This was accomplished via six data sets (355 data) collected from the published literature including end depth, Manning's roughness coefficient, channel width, bed slope and unit discharge. The dataset was partitioned in a 70:30 ratio randomly, 70% (248 data) of data used for model development while 30% (107 data) applied for model validation. Also, four different input combinations were constructed to identify the most effective prediction method. Furthermore, results were validated using several visually based (line graph, scatter plot, violin plot and Taylor diagram) and quantitative-based [root mean square error (RMSE), Nash–Sutcliffe efficiency (NSE), Willmott’s index of agreement, Legates and McCabe coefficient of efficiency (LM)] approaches. Results of the sensitivity analysis revealed that end depth had the highest effect on the results, while channel width was least influential. Results also showed that the best input combination incorporated all four input parameters. According to the results, ROF-REPT had the best performance with RMSE of 0.0035 (m3/s/m), NSE of 0.990, WI of 0.997% and LM of 0.905% followed by ROF-M5P REPT, M5P, ROF-LMS, ISO and LMS.