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Context. Synthetic model atmosphere calculations are still the most commonlyused tool when determining precise stellar parameters and stellar chemicalcompositions. Besides three-dimensional models that consistently solve forhydrodynamic processes, one-dimensional models that use an approximation forconvective energy transport play the major role.  Aims. We use modern Balmer-line formation theory as well as spectral energydistribution (SED) measurements for the Sun and Procyon to calibrate the modelparameter {\alpha} that describes the efficiency of convection in our 1Dmodels. Convection was calibrated over a significant range in parameter space,reaching from F-K along the main sequence and sampling the turnoff and giantbranch over a wide range of metallicities. This calibration was compared totheoretical evaluations and allowed an accurate modeling of stellaratmospheres.  Methods. We used Balmer-line fitting and SED fits to determine the convectiveefficiency parameter {\alpha}. Both methods are sensitive to the structure andtemperature stratification of the deeper photosphere.  Results. While SED fits do not allow a precise determination of theconvective parameter for the Sun and Procyon, they both favor valuessignificantly higher than 1.0. Balmer-line fitting, which we find to be moresensitive, suggests that the convective efficiency parameter {\alpha} is$\approx$ 2.0 for the main sequence and quickly decreases to $\approx$ 1.0 forevolved stars. These results are highly consistent with predictions from 3Dmodels. While the values on the main sequence fit predictions very well,measurements suggest that the decrease of convective efficiency as stars evolveto the giant branch is more dramatic than predicted by models.

Calibrating the {\alpha} parameter of convective efficiency using observed stellar properties