Calculation of watershed flow concentration based on the grid drop concept

The grid drop concept is introduced and used to develop a micromechanism-based methodology for calculating watershed flow concentration. The flow path and distance traveled by a grid drop to the outlet of the watershed are obtained using a digital elevation model （DEM）. Regarding the slope as an uneven carpet through which the grid drop passes, a formula for overland flow velocity differing from Manning＇s formula for stream flow as welt as Darcy＇s formula for pore flow is proposed. Compared with the commonly used unit hydrograph and isochronal methods, this new methodology has outstanding advantages in that it considers the influences of the slope velocity field and the heterogeneity of spatial distribution of rainfall on the flow concentration process, and includes only one parameter that needs to be calibrated. This method can also be effectively applied to the prediction of hydrologic processes in un-gauged basins.

Nash Model Parameter Uncertainty Analysis by AM-MCMC Based on BFS and Probabilistic Flood Forecasting

A hydrologic model consists of several parameters which are usually calibrated based on observed hy-drologic processes. Due to the uncertainty of the hydrologic processes, model parameters are also uncertain, which further leads to the uncertainty of forecast results of a hydrologic model. Working with the Bayesian Forecasting System (BFS), Markov Chain Monte Carlo simulation based Adaptive Metropolis method (AM-MCMC) was used to study parameter uncertainty of Nash model, while the probabilistic flood forecasting was made with the simu-lated samples of parameters of Nash model. The results of a case study shows that the AM-MCMC based on BFS proposed in this paper is suitable to obtain the posterior distribution of the parameters of Nash model according to the known information of the parameters. The use of Nash model and AM-MCMC based on BFS was able to make the probabilistic flood forecast as well as to find the mean and variance of flood discharge, which may be useful to estimate the risk of flood control decision.

Discussion of Muskingum method parameter X

The parameter X of the Muskingum method is a physical parameter that reflects the flood peak attenuation and hydrograph shape flattening of a diffusion wave in motion. In this paper, the historic process that hydrologists have undergone to find a physical explanation of this parameter is briefly discussed. Based on the fact that the Muskingum method is the second-order accuracy difference solution to the diffusion wave equation, its numerical stability condition is analyzed, and a conclusion is drawn： X ≤ 0.5 is the uniform condition satisfying the demands for its physical meaning and numerical stability. It is also pointed out that the methods that regard the sum of squares of differences between the calculated and observed discharges or stages as the objective function and the routing coefficients C0, C1 and C2 of the Muskingum method as the optimization parameters cannot guarantee the physical meaning of X.