  We study Milky Way kinematics using a sample of 18.8 million main-sequence
stars with r<20 and proper-motion measurements derived from SDSS and POSS
astrometry, including ~170,000 stars with radial-velocity measurements from the
SDSS spectroscopic survey. Distances to stars are determined using a
photometric parallax relation, covering a distance range from ~100 pc to 10 kpc
over a quarter of the sky at high Galactic latitudes (|b|>20 degrees). We find
that in the region defined by 1 kpc <Z< 5 kpc and 3 kpc <R< 13 kpc, the
rotational velocity for disk stars smoothly decreases, and all three components
of the velocity dispersion increase, with distance from the Galactic plane. In
contrast, the velocity ellipsoid for halo stars is aligned with a spherical
coordinate system and appears to be spatially invariant within the probed
volume. The velocity distribution of nearby ($Z<1$ kpc) K/M stars is complex,
and cannot be described by a standard Schwarzschild ellipsoid. For stars in a
distance-limited subsample of stars (<100 pc), we detect a multimodal velocity
distribution consistent with that seen by HIPPARCOS. This strong
non-Gaussianity significantly affects the measurements of the velocity
ellipsoid tilt and vertex deviation when using the Schwarzschild approximation.
We develop and test a simple descriptive model for the overall kinematic
behavior that captures these features over most of the probed volume, and can
be used to search for substructure in kinematic and metallicity space. We use
this model to predict further improvements in kinematic mapping of the Galaxy
expected from Gaia and LSST.
