An implicit finite difference model for predicting flood routing is applied to the lower Columbia River, where tidal forcing causes flow reversals interacting with upstream dam flow during small river flow periods. The model is one-dimensional, unsteady, including lateral inflow and variable bed friction for different channel sections. A comparison of stages at six stations was made for a sensitivity analysis. The analysis used a total of 2209 hours of simulated river stages. Downstream boundary changes of ±0.5 feet and ±2.0 feet were made to the Astoria tide stages. Model simulations showed that 70% of the tide difference appears at Vancouver and Portland, 80% at St. Helens, 85% at Longview, 93% at Wauna and 95% at Skamokawa. Varying the upstream boundary condition (Bonneville Dam discharges) by ±10% and ±25% were markedly different from the downstream boundary changes. Upstream, where the tide influence is weakest, the tidal cycle is more likely to be "washed out" by the higher flows of the Columbia. Also these changes fluctuated with the tide cycle. Downstream stations did not show such differences because of the larger cross section areas of the Columbia River nearer the mouth and the proximity to the downstream boundary condition. The river system was calibrated in a downstream to upstream direction and used a total of 606 hours of observed river stages. Three periods with distinct river flow conditions were used in the calibration. Regression analyses of the computed residual values for each of the stations gave correlation coefficients (r²) less than 0.360. However, cross correlations between residual and computed stages showed that the two series were highly sinusoidally correlated for all stations. A spectral estimation of the residuals exhibited very strong peaks at frequencies of 0.081 hr ¹ (12.3 hrs), 0.042 hr¹ (24.0 hrs) and subsequent harmonics of these frequencies. The residual components are strongly associated with the tidal cycle.http://archive.org/details/analysisofnumeri00koehLieutenant, National Oceanic and Atmospheric AdministrationApproved for public release; distribution is unlimited.