Earth's large-scale topography and lower-mantle structure are linked to past tectonic motions and mantle flow, making it possible to gain insights in the properties of the solid Earth from time-dependent global convection models driven by tectonic reconstructions. Recent work suggests that the amplitude of residual topography, obtained by subtracting models of isostatic topography from total topography, may be up to ~1000 m at spherical harmonic degree two (wavelength ~13 300 km) and > 200 m at spherical harmonic degree 12 (wavelength ~3000 km). The amplitude of dynamic topography and the structure of the lower mantle predicted by time-dependent forward mantle flow models both depend on the physical assumption and on model parameters. Here, I investigate the consequence of using the Boussinesq, extended Boussinesq or truncated anelastic liquid approximation (TALA) in time-dependent flow models for predicting present-day mantle structure and dynamic topography; I characterize the sensitivity of the spectral distribution of dynamic topography amplitude to the boundary conditions and model set-up for the computation of dynamic topography; and I investigate the sensitivity of model results to parameters including the depth- and temperature dependence of viscosity, the model initial age and the density of the basal layer. Extended Boussinesq and TALA models are preferred to Boussinesq models that overpredict the volume of lower-mantle slabs and the amplitude of long-wavelength dynamic topography. The correlation between dynamic and residual topography models for spherical harmonic degrees 1-3 generally ranges between 0.4 and 0.5. The flow models better predict the geographical location of large low shear velocity provinces than that of lower-mantle slabs, which cover smaller areas in map view. I show that preserving shallow lateral viscosity variations in the computation of dynamic topography increases the amplitude of dynamic topography for wavelengths > 6000 km. Parameter trade-offs exist to fit both deep and surface constraints. The best-fitting model cases considered either a moderately dense basal layer (approximately 2 per cent denser than ambient mantle) or weak temperature- and pressure dependence of lower-mantle viscosity. The fit to present-day constraints does not significantly deteriorate when extending the reconstruction of mantle flow from 200 to 410 Ma, reflecting that seismic tomography models capture the history of mantle convection over the last 200-250 Myr, and suggesting that palaeogeographically constrained mantle flow models should be compared to time-dependent surface geological constraints.