This is the first part of a two-part investigation that applies nonstationary time series analysis methods and the St. Venant equations to the problem of understanding juvenile salmonid access to favorable shallow-water habitat in a tidal river. Habitat access is a function of river stage, tidal range, and the distribution of bed elevation. Part 1 models nonstationary tidal properties: species amplitudes and phases and tidal range. Part 2 models low-frequency river stage in the Lower Columbia River and reconstructs historical water levels, using the tidal model from part 1. To incorporate the nonstationary frictional effects of variable river discharge into the tidal model, we decompose the tidal wave into tidal species and calculate daily tidal range. Our one-dimensional tidal model is based on analytic wave solutions to the linearized St. Venant equation and uses six coefficients per tidal species to represent the upstream evolution of the frictionally damped tidal wave. The form of the coefficients is derived from the St. Venant equations, but their values are determined objectively from the data. About 50 station-years of surface elevation data collected (1981--2000) below Bonneville Dam (235 km from the ocean) were processed with a wavelet filter bank to retrieve time series of tidal species properties. A min-max filter was used to estimate daily tidal range. Tidal range, diurnal, and semidiurnal amplitudes were predicted with mean root mean square errors <30 mm, which is significantly more accurate than predictions obtained from harmonic analysis. Thus despite the compact form of our solution, we model nonstationary fluvial tidal properties with a high level of accuracy.