Images are widely used to visualise physical processes. Models may be developed which attempt to replicate those processes and their effects. The technique of coupling model output to images, which is here called "image-model coupling", may be used to help understand the underlying physical processes, and better understand the limitations of the models. An information theoretic framework is presented for image-model coupling in the context of communication along a discrete channel. The physical process may be regarded as a transmitter of images and the model as part of a receiver which decodes or recognises those images. Image-model coupling may therefore be interpreted as image recognition. Of interest are physical processes which exhibit "memory". The response of such a system is not only dependent on the current values of driver variables, but also on the recent history of drivers and/or system description. Examples of such systems in geophysics include the ionosphere and Earth's climate. The discrete channel model is used to help derive expressions for matching images and model output, and help analyse the coupling.