We propose to approximate a model for repeated measures that incorporated random effects, correlated stochastic process and measurements error. The stochastic process used in this paper is the Integrated Ornstein-Uhlenbeck (IOU) process. We consider a Bayesian approach which is motivated by the complexity of the model, thus, we propose to approximate the IOU stochastic process into a continuous spatial model that constructed by convolving a very simple and independent, process with a kernel function. The goal of this approximation is to offer some advantages over specification through a spatial process of computing covariance, variogram, and extremal coefficient functions, also to add to the extremal coefficient plots the empirical estimates. This approximation is attractive because it facilitates calculations especially that contain a huge amount of data in addition it reduces the computational execution time, also it extends beyond simple stationary models.