Series expansion of the Modified Einstein Procedure

This study improves total sediment load calculations based on depth-integrated and point sediment measurements. A new procedure uses a Series Expansion of the Modified Einstein Procedure (SEMEP) to remove the empiricism found in the Modified Einstein Procedure (MEP). The solution calculates the Rouse number (Ro) based on a median particle size found in suspension and the bed sediment discharge load is determined directly from the measured concentration.Depth-integrated concentration measurements are tested using SEMEP. Based on an evaluation of the ratio of measured to total sediment discharge the results indicate that when u*/o is greater than 5, SEMEP will perform accurately, with a coefficient of determination (R2) of 0.99, concordance correlation coefficient (rho c) of 0.98 and mean absolute percent error (MAPE) of 5%. The Bureau of Reclamation Automated Modified Einstein Procedure (BORAMEP) is also tested and resulted in a R2 of 0.65, rhoc of 0.74 and MAPE of 18%.The ratio of suspended sediment to total sediment discharge as a function of u*/o and relative submergence is determined using SEMEP. It is found that when u* /o is less than 0.2, sediment is not transported. When u*/o is between 0.2 and 0.5, sediment moves as bed load when u*/o is between 0.5 and 2 the sediment transport occurs as mixed load and when u */o is greater than 2, sediment moves as suspended load.For point velocity and concentration measurements are also used to test SEMEP. Results indicate that deeper rivers give a better estimate of total sediment discharge (qt) compared to shallow rivers. When the ratio of the measured depth to the bed particle size is greater than 1,000, the comparison between SEMEP and measurements of qt are quite accurate with an MAPE less than 25%.In summary, the results indicate that SEMEP performs accurately (error less than 25%) when the value of u*/o is greater than 5 (or Ro less than 0.5). SEMEP calculations are acceptable, but less accurate when u*/o is between 2 to 5 (1.25>Ro<0.5). Both SEMEP and MEP should not be used when u*/o is less than 2.