  A calibration of the mixing-length parameter in the local mixing-length
theory (MLT) is presented for the lower part of the convection zone in
pure-hydrogen atmosphere white dwarfs. The parameterization is performed from a
comparison of 3D CO5BOLD simulations with a grid of 1D envelopes with a varying
mixing-length parameter. In many instances, the 3D simulations are restricted
to the upper part of the convection zone. The hydrodynamical calculations
suggest, in those cases, that the entropy of the upflows does not change
significantly from the bottom of the convection zone to regions immediately
below the photosphere. We rely on this asymptotic entropy value, characteristic
of the deep and adiabatically stratified layers, to calibrate 1D envelopes. The
calibration encompasses the convective hydrogen-line (DA) white dwarfs in the
effective temperature range 6000 < Teff (K) < 15,000 and the surface gravity
range 7.0 < log g < 9.0. It is established that the local MLT is unable to
reproduce simultaneously the thermodynamical, flux, and dynamical properties of
the 3D simulations. We therefore propose three different parameterizations for
these quantities. The resulting calibration can be applied to structure and
envelope calculations, in particular for pulsation, chemical diffusion, and
convective mixing studies. On the other hand, convection has no effect on the
white dwarf cooling rates until there is a convective coupling with the
degenerate core below Teff ~ 5000 K. In this regime, the 1D structures are
insensitive to the MLT parameterization and converge to the mean 3D results,
hence remain fully appropriate for age determinations.
