  L\'{e}vy flight models whose jumps have infinite moments are mathematically
used to describe the superdiffusion in complex systems. Exponentially tempering
the Levy measure of L\'{e}vy flights leads to the tempered stable L\'{e}vy
processes which combine both the $\alpha$-stable and Gaussian trends; and the
very large jumps are unlikely and all their moments exist. The probability
density functions of the tempered stable L\'{e}vy processes solve the tempered
fractional diffusion equation. This paper focuses on designing the high order
difference schemes for the tempered fractional diffusion equation on bounded
domain. The high order difference approximations, called the tempered and
weighted and shifted Gr\"{u}nwald difference (tempered-WSGD) operators, in
space are obtained by using the properties of the tempered fractional calculus
and weighting and shifting their first order Gr\"{u}nwald type difference
approximations. And the Crank-Nicolson discretization is used in the time
direction. The stability and convergence of the presented numerical schemes are
established; and the numerical experiments are performed to confirm the
theoretical results and testify the effectiveness of the schemes.
