The Lagrangian and Eulerian descriptions of the flow in a double gyre, eddy-resolving numerical simulation are compared in the context of exploring the use of drifter arrays to describe ocean circulation. The parameterization of the unresolved scales of motion in large-scale numerical ocean models is analyzed through a combination of Lagrangian and Eulerian simulated fields. Here, in Part I, the Lagrangian and Eulerian description of the flow is presented with special emphasis on the description of the eddy diffusivity field. In Part II, the limitations that coarse spatial resolution imposes on the advective–diffusive equation are tested by comparing the evolution of a passive tracer field in high- and low-resolution numerical models. The number of “buoy days” used in the numerical experiment is similar to what is expected to be launched in the Atlantic Ocean during WOCE/TOGA surface velocity program. The parameters that determine the model ocean circulation were chosen such that the mean and eddy kinetic energy levels are comparable to observations in the upper ocean. The diffusivity fields presented here are obtained from two different statistical approaches, namely, from the shear of the velocity field and from the application of Taylor's Lagrangian diffusion theory. This theory relates the absolute dispersion of tagged particles to the diffusive power of the turbulent velocity field in statistically homogeneous and stationary turbulent flows. By using a combination of Lagrangian and Eulerian statistics, it is observed that with a large number of particles the mean Eulerian velocities and velocity variances can be estimated well from the Lagrangian trajectories. The estimation of Lagrangian statistics (i.e., dispersion rates with respect to the center of mass, Taylor diffusivities, etc.) depends significantly on the region in which they are computed. The estimation of the spatial distribution of the diffusivity function from the trajectories of the particles released in the eddy-resolving numerical model reproduce the most important large-scale characteristics observed in the analysis of drifters and floats in the ocean: anisotropy of the horizontal components of the diffusivity matrix with zonal values usually being larger than meridional diffusivities, and an inhomogeneous diffusivity field, with large values in those regions where the eddy kinetic energy is larger. Central gyre statistics are typically well defined both in terms of the theory and within the drifter densities used. In the western boundary layer Lagrangian statistics are not robust, not because of sample size problems but due to the breakdown of the assumptions behind single particle calculations. Regimes where this occurs have ratios of the local advective time scale to the Lagrangian decorrelation time scale greater than one and are therefore typically nonstationary.