The tropical Pacific Ocean surface current system can be characterized by a strong degree of nonstationarity due to the fast response time of equatorial and near-equatorial dynamics. The ocean-atmospheric dynamics create longitudinally coherent zonal flow (zonal length scales lx~60¿) with strong meridional shear (ly~1¿ in latitude) in the large-scale mean and an energetic mesoscale (O(100 km)) component. Parameterization of the effects of the mesoscale field depends on the separation of the large-scale mean from the observed velocity. In this paper the focus is placed on the key issue: separating the flow into large-scale mean and mesoscale eddy components in order to compute meaningful eddy diffusivity estimates in flow regimes that demonstrate strong currents and strong shear. Large gradients in the large-scale mean have precluded diffusivity estimation by traditional binning techniques. In this first of two publications, a method is developed for using Lagrangian data to estimate the diffusivity addressing the inhomogeneity of the mean flow. The spatially dependent estimate of the mean field is computed with a least squares bicubic smoothing spline interpolation scheme with an optimized roughness parameter which guarantees minimum energy in the fluctuation field at low frequencies. Numerical simulations based on a stochastic model of a turbulent shear flow are used to validate our approach in a conceptually simple but realistic scenario. The technique is applied to near-surface drifter observations obtained from 1979--1996 from two dynamically distinct time-space regions of the tropical Pacific Ocean. The first region, in the South Equatorial Current, is characterized by a linear zonal shear mean flow and an approximately exponential autocovariance structure in the residuals. The velocity residuals have velocity variance of s⁁2=130 cm2 s-2 for both components, and horizontal diffusivities are &kgr;⁁u≈7¿107 cm2 s-1 and &kgr;⁁v≈3¿107 cm2 s-1. No significant interannual variations of the estimates are detected, but residual trends in the estimators arise from intraseasonal variations in the velocity field during the 3-month season. The second region, in the North Equatorial Countercurrent and the North Equatorial Current, has a mean flow with a strong zonal shear and a weak northward velocity. The autocovariance is approximately exponential for the zonal component, while the meridional component has a negative lobe at about 10 days, probably due to the presence of instability waves. The variance is 380 cm2 s-2 for the zonal component and 360 cm2 s-2 for the meridional component, while the horizontal diffusivities are &kgr;⁁u≈15¿107 cm2 s-1 and &kgr;⁁v≈4¿107 cm2 s-1. Strong intraseasonal variability requires a maximum time window of 2 months for approximate stationarity to hold for the covariance calculations. ¿ 1998 American Geophysical Union