# Event-based Sediment Yield Modeling using Artificial Neural Network

## Authors

- First Online:

- Received:
- Accepted:

DOI: 10.1007/s11269-007-9170-3

- Cite this article as:
- Rai, R.K. & Mathur, B.S. Water Resour Manage (2008) 22: 423. doi:10.1007/s11269-007-9170-3

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## Abstract

In the present study, a back propagation feedforward artificial neural network (ANN) model was developed for the computation of event-based temporal variation of sediment yield from the watersheds. The training of the network was performed by using the gradient descent algorithm with automated Bayesian regularization, and different ANN structures were tried with different input patterns. The model was developed from the storm event data (i.e. rainfall intensity, runoff and sediment flow) registered over the two small watersheds and the responses were computed in terms of runoff hydrographs and sedimentographs. Selection of input variables was made by using the autocorrelation and cross-correlation analysis of the data as well as by using the concept of travel time of the watershed. Finally, the best fit ANN model with suitable combination of input variables was selected using the statistical criteria such as root mean square error (RMSE), correlation coefficient (CC) and Nash efficiency (CE), and used for the computation of runoff hydrographs and sedimentographs. Further, the relative performance of the ANN model was also evaluated by comparing the results obtained from the linear transfer function model. The error criteria viz. Nash efficiency (CE), error in peak sediment flow rate (EPS), error in time to peak (ETP) and error in total sediment yield (ESY) for the storm events were estimated for the performance evaluation of the models. Based on these criteria, ANN based model results better agreement than the linear transfer function model for the computation of runoff hydrographs and sedimentographs for both the watersheds.

### Keywords

Automated Bayesian RegularizationANNEvent-basedRunoffSediment yieldSedimentographSmall watersheds### List of notations and abbreviation

*t*_{i}Target output at node

*i**a*_{i}Network output at node

*i*- N
Number of observation

- \( \overline{X} _{{k + 1}} \)
Weight factor at iteration (

*k*+ 1)- \( \overline{g} \)
\( = \nabla f{\left( {\overline{X} _{{_{k} }} } \right)} = \) error gradient vector

*Y*_{norm}Normalized dimensionless variable

*Y*_{i}Observed value of variable

*Y*_{min}Minimum value of variable

*Y*_{max}Maximum value of variable

*O*_{(i)}Output at

*i*th hidden node*O*_{n}Net output at

*i*th hidden node*Q*_{t}Direct runoff at time

*t**Q*(*t − r*)Direct runoff at lag-

*r**S*_{t}Sediment flow at time

*t**S*_{O}Observed sediment flow

*S*_{C}Computed sediment flow

- \( \overline{S} _{{\text{O}}} \)
Mean of observed sediment flow

*E*_{D}Sum of square error

*E*_{W}Sum of square network weights

*F*Objective function

*λ*Parameter of objective function

*η*Parameter of objective function

*S*(*t − p*)Sediment flow at lag-

*p**R*_{t}Rainfall intensity at time

*t**R*(*t − q*)Rainfall intensity at lag-

*q*- p, q, r
integer

*n*Chosen step size

*k*Lag

- CE
Nash efficiency

- EPS
Error in peak sediment flow rate

- ETP
Error in time to peak

- ESY
Error in sediment yield

- RMSE
Root mean square error

- CC
Correlation coefficient