Larger samples did have lower estimated bias and reduced standard deviation of the estimates, although when k is large even large samples can be biased. When using traditional simulation techniques, I found that the conditional likelihood estimator was consistently less biased than the other two estimators. When k was large, the moment estimator was the least biased and the most accurate. The five equations are combined to form one equation relating sediment thickness to water flow variables and parameters. For steady, critical water flow, the combined equation becomes a diffusion equation that is solved both numerically and analytically to replicate experimental data provided by Lisle et al.
Solutions compare well with the experimental data.
For unsteady, non-critical water flow, the full St. Venant equations and the combined equation are solved simultaneously using the Maccormack explicit finite difference scheme. In general, increases in bed slope and water depth increase the rate of dispersion of the slug while increases in friction have the reverse effect. The rate of translation increases with increasing water depth and decreases with increasing friction. Increasing the bed slope not only increases the rate of translation, in some cases it changes the direction of translation. In this work a Stochastic Spatial Traffic flow computer model was written specifically for the town of Arcata, California.