Contrary to the popular notion that radar can measure rainfall, we demonstrate that both the physics of the radar measurement process as well as the processing of radar data can have significant effects on inferred statistics of rainfall. Only the following effects were considered: (1) the radar beam averaging scheme, (2) the nonlinear transformations inherent in estimation of rainfall based on radar observations, and (3) the coordinate transformation from a polar to a Cartesian grid. The statistics included the following: mean, variance, spatial covariance, and a certain scaling parameter. We limited our considerations to spatial aspects of the problem. The methodology used in this paper is based on analysis of two radar rainfall estimation algorithms and a numerical Monte Carlo simulation. A series of simple experiments allows us to consider the above effects individually and collectively. In the experiments, the true rainfall process is simulated using a variety of statistical models. Its statistics are compared to those obtained after the radarlike processing has been applied. The models used to simulate the rainfall field include point process models, which conceptualize mesoscale rainfall organization according to marked Poisson processes, a random cascade model, and an iterated random pulse model, which is a combination of the above two models. ¿ American Geophysical Union 1996