A sequential synthesis inversion method is described to estimate CO<sub>2</sub> sources from continuous atmospheric data. The sequential method makes the problem computationally feasible. The method is assessed using four-hourly synthetic concentration data generated from known sources. Multi-year mean sources and seasonal cycles are estimated with comparable quality as those from a traditional inversion of monthly mean data. Interannual variations in the estimated sources are closer to those of the known sources using the four-hourly data rather than monthly data. The computational cost of the basis function simulations can be reduced by generating responses that are only six months long. This does not significantly degrade the inversion results compared to using responses that are 12 months in length.