Investigation On Uncertainties Of Substance Exchanges Between Turbidity Currents And Surroundings And Their Influence On Modeling

Turbidity current is a common natural phenomenon which often occurs in reservoirs,submarine canyons and deep oceans.Layer-averaged mathematical model of turbidity current,which has become increasingly popular in the last decades,inevitably involve empirical formulae(such as empirical formulae for sediment erosion,water entrainment and sediment settling velocity).Among them,the accuracy of empirical formulae for sediment erosion and water entrainment has a significant impact on the numerical simulation of turbidity current.This is because the driving force of turbidity current is the density difference between turbidity current and the ambient fluid.Consequently,the rate of sediment erosion and ambient fluid entrainment will influence the density difference.However,it is not easy to collect sufficiently accurate data for high-quality calibration of empirical coefficients[N1,N2,A3 in sediment erosion Eq.(2.5),E1,E2 in water entrainment Eq.(2.17)]since turbidity current occurs in subaqueous environment.Inevitably,simulation results are subject to relatively high uncertainty.In this paper,Monte Carlo simulation method based on Bayesian theorem(Hereinafter referred to as the probability method)is applied to sample the empirical coefficient combinations of N1,N2,A3-N2 and E1-E2 in the two empirical formulae mentioned above,resulting in a large number of samples for empirical coefficients.These samples are fed into the layer-averaged four equation model and fully coupled three equation model.The impact of the empirical coefficient uncertainty on the simulation results are discussed through numerical case studies.Finally,a set of experimental turbidity currents is simulated by the fully coupled three equation model to further evaluate the uncertainties of empirical formulae.The following conclusions are made.1.Uncertainties of empirical coefficients:firstly,when A3= 4-7,there exists a maximum probability combination of N1-N2,which makes the correlation coefficient between calculated value and measured value of sediment erosion higher than that for the original Es93;secondly,the multiple interval for 25%,50%,75%,95%of total sample number relative to the maximvun probability N,-N2 value is the smallest when A3 = 4;For the water entrainment empirical formula,multiple interval for 95%of E1-E2 sample is greater than multiple interval of N1-N2 and A3-N2.It indicates that the uncertainty of water entrainment empirical formula is greater than that of the sediment erosion formula.2.Impact of empirical coefficient uncertainty on the four equation model:with 95%samples fed into the model,the gained multiple interval of hydraulic parameters(thickness,layer-averaged velocity and sediment concentration)increases with increasing distance and the multiple interval is the biggest with E1-E2 samples,compared with the corresponding hydraulic parameters calculated with maximum probability empirical coefficient value.It means that the impact of empirical formula uncertainty on the model increases with increasing distance.Simulation results using maximum probability N1-N2 or A3-N2 may underestimate thickness,overestimate velocity and concentration.Simulation results using maximum probability E1-E2 predict thickness and concentration well,but underestimate velocity.3.Impact of empirical coefficient uncertainty on the fully coupled model:the sensitivity of the coupled model to different empirical coefficient combinations is essentially the same as that of four equation model.With 25%N1-N2 or A3-N2 samples fed into the coupled model,the gained interval of the thickness,layer-averaged velocity,sediment concentration and bed deformation decreases with increasing distance.This indicates that the impact of sediment erosion uncertainty on the coupled model decreases with increasing distance.However,the impact of water entrainment uncertainty on the coupled model increases with increasing distance.Simulation results using maximum probability N1-N2 or A3-N2 may underestimate thickness,overestimate velocity,concentration,bed deformation and front position.Simulation results using maximum probability E1-E2 predict front position well,but may underestimate thickness and concentration,and overestimate velocity and bed deformation slightly.4.Evaluation of empirical formulae uncertainties with experimental turbidity currents by fully coupled model:by comparing with experimental data,the coupled model with maximum probability empirical coefficient may underestimate thickness and overestimate velocity,which is basically in consistent with Conclusion 3.Simulation results using maximum probability empirical coefficient may not fitting the measured data well,while the simulation results with 95%samples can cover most experimental data if the uncertainties are considered,.This exhibits that the probability method adopted in this paper is effective in the analysis of empirical coefficient uncertainty.