Rainrate near the ground can be interpreted as a collection of random variables forming a random field parameterized by three coordinates: two spatial coordinates and one temporal. Interest among the radio propagation community has been focused on the first order statistics of these random variables, principally on the average annual probability distribution of rainrate as a function of location. However, increasingly interest is turning to second order statistics describing high-resolution rainrate variation in both time and space. This information is important for the design of fade countermeasures and for efficient spectrum management. In this paper radar data from a widespread, slow moving and intense, stratiform rain event experienced by the southeastern UK on May 1, 2001, are used to calculate the second order, spectral, statistics of spatial-temporal log rainrate variation. It is demonstrated that log rainrate is self-similar in all three coordinates and that symmetry exists between the spatial and temporal variation. These data are used to develop an isotropic, spatial-temporal log rainrate model assuming that log rainrate is a homogeneous, Gaussian, random field. This model is developed further to yield closed form expressions for the mean and covariance of the random fields associated with rainrate, with specific attenuation and the logarithm of specific attenuation. Furthermore, expressions for the temporal covariance of the rain attenuation experienced by pairs of radio links are developed, and these expressions are tested against measured rain attenuation data from an experimental link.