In Europe the monitoring of ozone doses to growing crops is based on measurement of AOT40, the annual accumulated excess ozone concentration over a threshold of 40 ppb, aggregated over the growing season. To show the extent of ozone pollution it is desirable to construct maps of AOT40. However, data are limited and there is large inter-annual variation, so what is to be mapped is very variable, and our knowledge of it is limited. This paper describes a spatially referenced random effects model which appears able to describe many features of the data and our uncertainty about them. The problem of translating this or similar models into a map faithfully representing our knowledge is considered, as are some questions it raises about decision-makers' and the public's need for and use of technical models.