Context :

Aims : We present the Stagger -grid , a comprehensive grid of time-dependent , three-dimensional ( 3D ) , hydrodynamic model atmospheres for late-type stars with realistic treatment of radiative transfer , covering a wide range in stellar parameters .
This grid of 3D models is intended for various applications besides studies of stellar convection and atmospheres per se , including stellar parameter determination , stellar spectroscopy and abundance analysis , asteroseismology , calibration of stellar evolution models , interferometry , and extrasolar planet search .
In this introductory paper , we describe the methods we applied for the computation of the grid and discuss the general properties of the 3D models as well as of their temporal and spatial averages ( here denoted \left \langle 3 \mathrm { D } \right \rangle models ) .

Methods : All our models were generated with the Stagger -code , using realistic input physics for the equation of state ( EOS ) and for continuous and line opacities .
Our \sim 220 grid models range in effective temperature , T _ { \mathrm { eff } } , from 4000 to 7000 \mathrm { K } in steps of 500 \mathrm { K } , in surface gravity , \log g , from 1.5 to 5.0 in steps of 0.5 dex , and metallicity , \left [ \mathrm { Fe } / \mathrm { H } \right ] , from -4.0 to +0.5 in steps of 0.5 and 1.0 \mathrm { dex } .

Results : We find a tight scaling relation between the vertical velocity and the surface entropy jump , which itself correlates with the constant entropy value of the adiabatic convection zone .
The range in intensity contrast is enhanced at lower metallicity .
The granule size correlates closely with the pressure scale height sampled at the depth of maximum velocity .
We compare the \left \langle 3 \mathrm { D } \right \rangle models with currently widely applied one-dimensional ( 1D ) atmosphere models , as well as with theoretical 1D hydrostatic models generated with the same EOS and opacity tables as the 3D models , in order to isolate the effects of using self-consistent and hydrodynamic modeling of convection , rather than the classical mixing length theory ( MLT ) approach .
For the first time , we are able to quantify systematically over a broad range of stellar parameters the uncertainties of 1D models arising from the simplified treatment of physics , in particular convective energy transport .
In agreement with previous findings , we find that the differences can be rather significant , especially for metal-poor stars .

Conclusions :