We have modeled the distribution of $\delta ^{18}$O in atmospheric CO$_2$ with a new comprehensive global three-dimensional model. We have focused in this study on the seasonal cycle and the meridional gradient in the atmosphere. The model has been compared with a data set of $\delta ^{18}$O-CO$_2$, which merges measurements made by different laboratories, with allowance for recently elucidated calibration biases. The model compares well with the seasonal cycle of CO$_2$, but advances the measured $\delta ^{18}$O-CO$_2$ seasonal cycle by two months. The calculated seasonal amplitude is typically 2/3 of the measured value, but the sensitivity to uncertainties in the input parameter set is such that a range of amplitudes over a factor of 3 is accommodated. Unlike the case for the amplitude, the sensitivity analyses demonstrate that the modeled phase of the seasonal cycle and the north-south gradient are practically unaffected by uncertainty in the parameter set. The north-south gradient comes, on the one hand, from the disequilibrium of the $\delta ^{18}$O-CO$_2$ isofluxes at every grid point and, on the other hand, from rectification gradients, a covariance of the varying $\delta ^{18}$O-CO$_2$ source with the atmospheric transport. The model exhibits a very strong rectification gradient that can lead to a misinterpretation of the measurements compared to the model. We therefore restrict comparison to the latitudinal means of only ocean grid cells with measurements from stations sampling the marine boundary layer. Assimilation and respiration are the determining factors of the seasonal cycle and the north-south gradient of $\delta ^{18}$O-CO$_2$. In a number of sensitivity studies we have explored the range of possible processes affecting the simulated seasonal cycle and hemispheric gradient. None of these processes contributed significantly to improve the model-observation mismatch. The contribution of assimilation and respiration to the total signal does change significantly in the sensitivity studies, but, because of feedback processes, they change in such a way that the overall response of the model is only marginally altered. In particular, prescribing $\delta ^{18}$O-H$_2$O soil values to monthly means of rain does not significantly change the modeled signal, either in the seasonal cycle or in the meridional gradient. This highlights the need to accurately model assimilation and respiration in order to understand $\delta ^{18}$O in atmospheric CO$_2$.