  We present the first grid of mean three-dimensional (3D) spectra for
pure-hydrogen (DA) white dwarfs based on 3D model atmospheres. We use CO5BOLD
radiation-hydrodynamics 3D simulations instead of the mixing-length theory for
the treatment of convection. The simulations cover the effective temperature
range of 6000 < Teff (K) < 15,000 and the surface gravity range of 7 < log g <
9 where the large majority of DAs with a convective atmosphere are located. We
rely on horizontally averaged 3D structures (over constant Rosseland optical
depth) to compute <3D> spectra. It is demonstrated that our <3D> spectra can be
smoothly connected to their 1D counterparts at higher and lower Teff where the
3D effects are small. Analytical functions are provided in order to convert
spectroscopically determined 1D effective temperatures and surface gravities to
3D atmospheric parameters. We apply our improved models to well studied
spectroscopic data sets from the Sloan Digital Sky Survey and the White Dwarf
Catalog. We confirm that the so-called high-log g problem is not present when
employing <3D> spectra and that the issue was caused by inaccuracies in the 1D
mixing-length approach. The white dwarfs with a radiative and a convective
atmosphere have derived mean masses that are the same within ~0.01 Msun, in
much better agreement with our understanding of stellar evolution. Furthermore,
the 3D atmospheric parameters are in better agreement with independent Teff and
log g values from photometric and parallax measurements.
