  Sub-mm observations of protoplanetary disks now approach the acuity needed to
measure the turbulent broadening of molecular lines. These measurements
constrain disk angular momentum transport, and furnish evidence of the
turbulent environment within which planetesimal formation takes place. We use
local magnetohydrodynamic (MHD) simulations of the magnetorotational
instability (MRI) to predict the distribution of turbulent velocities in low
mass protoplanetary disks, as a function of radius and height above the
mid-plane. We model both ideal MHD disks, and disks in which Ohmic dissipation
results in a dead zone of suppressed turbulence near the mid-plane. Under ideal
conditions, the disk mid-plane is characterized by a velocity distribution that
peaks near v \simeq 0.1cs (where cs is the local sound speed), while supersonic
velocities are reached at z > 3H (where H is the pressure scale height).
Residual velocities of v \approx 0.01cs persist near the mid-plane in dead
zones, while the surface layers remain active. Anisotropic variation of the
linewidth with disk inclination is modest. We compare our MHD results to
hydrodynamic simulations in which large-scale forcing is used to initiate
similar turbulent velocities. We show that the qualitative trend of increasing
v with height, seen in the MHD case, persists for forced turbulence and is
likely a generic property of disk turbulence. Percent level determinations of v
at different heights within the disk, or spatially resolved observations that
probe the inner disk containing the dead zone region, are therefore needed to
test whether the MRI is responsible for protoplanetary disk turbulence.
