Paper Title
Developing a New Total Sediment Transport Formula via Polynomial Best Subset Regression

The aim of this study is to derive a new total sediment load formula which is more accurate and which has less application constraints than the well-known formulae of the literature. There are many sediment transport formulas in the literature but most of them are derived from small data sets of natural rivers or experimental designs. Each formulation has its own restrictions, which depends on the original dataset of that study. None of them have gained universal acceptance. To achieve this aim, a wide range of dataset is compiled which includes both experimental lab(flume) data and Natural river data so that a very large range (of parameters) has been achieved. Then this dataset is used to generate a new formula.Five most known total sediment transport formulae, which are approved by American Society of Civil Engineers (ASCE) are used for benchmarking. The dimensionless parameters of these widely used formulae are used as inputs in a new regression approach. The new approach is called Polynomial Best subset regression (PBSR) analysis. The aim of the PBRS analysis is fitting and testing all possible combinations of the input variables and selecting the best subset. All the input variables with their second and third powers are included in the regression to test the possible relation between the explanatory variables and the dependent variable. While selecting the best subset a multistep approach is used that depends on significance values and the Multicollinearity degrees of inputs. According to proposed formulae, the sediment transport phenomenon is deeply related to velocity of water (U), slope (S), depth (H), shear velocity (U*), sediment size (d50) and specific gravity (Gs). The new formula is compared to others in a holdout dataset and detailed performance investigations are conducted for field and lab datasets within this holdout data. Different goodness of fit statistics are used as they represent different perspectives of the model accuracy. After the detailed comparisons are figure out, PBSR is the most accurate equation that is also applicable on both flume and river data. Especially, on field dataset the prediction performance of the proposed formula outperformed the benchmark formulations. Index Terms - River Hydrology, Sediment Transport, Total Sediment Load, Polynomial Best Subset Regression (PBSR)