Summary: This paper compares two methods built on a hierarchical Bayesian foundation and designed for modeling hourly ozone concentrations over the eastern United States. One, a dynamic linear state space model (DLM), that has been proposed earlier [G. Huerta et al., J. R. Stat. Soc., Ser. C 53, No. 2, 231–248 (2004; Zbl 1111.62372)], lies in a very contemporary setting where two historical paths to temporal process models, the Kalman filter and the dynamic system with random perturbations, converge. The other, which we call the Bayesian spatial predictor (BSP), is a Bayesian alternative to the purely spatial method of kriging. The DLM as a dynamic system model has parameters that are states of the process which generate the ozone and change with time. More specifically, the model includes a time-varying site invariant mean field as well as time-varying coefficients for 24 and 12 hour diurnal cyclic components. The resulting model’s great flexibility comes at the cost of complexity, forcing the use of an MCMC approach and very time-consuming computations. Thus, the size of the DLM’s spatial domain of applicability has to be restricted and the number of monitoring sites that can be treated limited. The paper’s assessment of the DLM reveals other difficulties that point to the need to consider a less flexible competitor, a Bayesian spatial predictor (BSP). The two methods are compared in a variety of ways and overall conclusions given. In particular, the conclusions point to the BSP as the more practical alternative for spatial prediction.