  Based on detailed 2D numerical radiation hydrodynamics (RHD) calculations of
time-dependent compressible convection, we have studied the dynamics and
thermal structure of the convective surface layers of solar-type stars. The RHD
models provide information about the convective efficiency in the
superadiabatic region at the top of convective envelopes and predict the
asymptotic value of the entropy of the deep, adiabatically stratified layers.
This information is translated into an effective mixing-length parameter alpha
suitable to construct standard stellar structure models. We validate the
approach by a detailed comparison to helioseismic data.
  The grid of RHD models for solar metallicity comprises 58 simulation runs
with a helium abundance of Y=0.28 in the range of effective temperatures 4300K
< Teff < 7100K and gravities 2.54 < logg < 4.74. We find a moderate,
nevertheless significant variation of alpha between about 1.3 for F-dwarfs and
1.75 for K-subgiants with a dominant dependence on Teff. In the close
neighbourhood of the Sun we find a plateau where alpha remains almost constant.
The internal accuracy of the calibration of alpha is estimated to be +/- 0.05
with a possible systematic bias towards lower values. An analogous calibration
of the convection theory of Canuto & Mazzitelli gives a different temperature
dependence but a similar variation of the free parameter.
  For the first time, values for the gravity-darkening exponent beta are
derived independently of mixing-length theory: beta=0.07...0.10.
  We show that our findings are consistent with constraints from stellar
stability considerations and provide compact fitting formulae for the
calibrations.
