Context : Radiation from accretion discs in cataclysmic variable stars ( CVs ) provides fundamental information about the properties of these close binary systems and about the physics of accretion in general .
Of particular interest are dwarf-nova outburst cycles during which variations of the disc properties allow a detailed study of the physical processes in accretion flows .

Aims : The detailed diagnostics of accretion disc structure can be achieved by including in its description all the relevant heating and cooling physical mechanism , in particular the convective energy transport that , although dominant at temperatures \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \mathchar 536 $ } \hss } \raise 2.0 pt% \hbox { $ \mathchar 316 $ } } 10 ^ { 4 } K , is usually not taken into account when calculating spectra of accretion discs .
The disc ’ s self-consistently calculated structure and emission allow testing models of dwarf-nova outbursts and accretion-disc models in general .

Methods : We constructed a radiative transfer code coupled with a code determining the disc ’ s hydrostatic vertical structure .

Results : We have obtained for the first time model spectra of cold , convective accretion discs .
As expected , these spectra are mostly flat in the optical wavelengths with no contribution from the UV , which in quiescence must be emitted by the white dwarf .
The disc structures obtained with our radiative-transfer code compare well with the solutions of equations used to describe the dwarf-nova outburst cycle according to the thermal-viscous disc instability model thus allowing the two to be combined .
For high-temperature radiative discs our spectra are compatible with models obtained with Hubeny ’ s code TLUSTY .

Conclusions : Our code allows calculating the spectral evolution of dwarf nova stars through their whole outburst cycle , providing a new tool for testing models of accretion discs in cataclysmic variables .
We show that convection plays an important role in determining the vertical disc structure and substantially affects emitted spectra when , as often the case , it is effective at optical depths \tau \sim 1 .
The emergent spectrum is independent of the parameters of the convection model .
We confirm that , as required by the disc instability model , quiescent discs in dwarf novae must be optically thick in their outer regions .
In general , no emission lines are present in the absence of external irradiation .