A dynamic relaxation technique is examined to update a spectral model. The technique consists of constraining selected time dependent model variables towards their predetermined space–time estimates, while the remaining variables evolve unconstrained. The scheme involves gradual assimilation of data and thus is essentially free from data insertion shocks generally associated with data assimilation schemes. The scheme can also be used to update the model variables consistent with the observed estimates of diabatic forcings. The spectral formulation is particularly suited to relax the current estimates of model variables towards their observed estimates scale-by-scale. The scheme has been applied to initialize model variables by relaxing vorticity, divergence and total mass (surface pressure) fields through one to three observation periods using an 11-layer model with T-42 spectral resolution. In addition, the moisture field and diabatic heating rates have been relaxed consistent with the observed ... Abstract A dynamic relaxation technique is examined to update a spectral model. The technique consists of constraining selected time dependent model variables towards their predetermined space–time estimates, while the remaining variables evolve unconstrained. The scheme involves gradual assimilation of data and thus is essentially free from data insertion shocks generally associated with data assimilation schemes. The scheme can also be used to update the model variables consistent with the observed estimates of diabatic forcings. The spectral formulation is particularly suited to relax the current estimates of model variables towards their observed estimates scale-by-scale. The scheme has been applied to initialize model variables by relaxing vorticity, divergence and total mass (surface pressure) fields through one to three observation periods using an 11-layer model with T-42 spectral resolution. In addition, the moisture field and diabatic heating rates have been relaxed consistent with the observed ...