The Spatial-temporal Statistics of Rain Rate Random Fields

Short Title: Spatial-Temporal Statistics of Rain. Abstract Rain rate near the ground can be interpreted as a collection of random variables forming a random field parameterised 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 rain rate as a function of location. However, increasingly interest is turning to second order statistics describing high-resolution rain rate 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 wide spread, slow moving and intense, convective rain event experienced by the South Eastern UK on 1/5/2001 are used to calculate the second order statistics of spatial-temporal log rain rate variation. It is demonstrated that log rain rate 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 rain rate model assuming that log rain rate is a homogeneous Gaussian random field. This model is developed further to yield closed form expressions for the second order statistics of the associated rain rate, specific attenuation and log specific attenuation random fields. 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.