  We study the impact of catastrophic errors occurring in the photometric
redshifts of galaxies on cosmological parameter estimates with cosmic shear
tomography. We consider a fiducial survey with 9-filter set and perform photo-z
measurement simulations. It is found that a fraction of 1% galaxies at
z_{spec}~0.4 is misidentified to be at z_{phot}~3.5. We then employ both chi^2
fitting method and the extension of Fisher matrix formalism to evaluate the
bias on the equation of state parameters of dark energy, w_0 and w_a, induced
by those catastrophic outliers. By comparing the results from both methods, we
verify that the estimation of w_0 and w_a from the fiducial 5-bin tomographic
analyses can be significantly biased. To minimize the impact of this bias, two
strategies can be followed: (A) the cosmic shear analysis is restricted to
0.5<z<2.5 where catastrophic redshift errors are expected to be insignificant;
(B) a spectroscopic survey is conducted for galaxies with 3<z_{phot}<4. We find
that the number of spectroscopic redshifts needed scales as N_{spec} \propto
f_{cata}\times A where f_{cata}=1% is the fraction of catastrophic redshift
errors (assuming a 9-filter photometric survey) and A is the survey area. For
A=1000 {deg}^2, we find that N_{spec}>320 and 860 respectively in order to
reduce the joint bias in (w_0,w_a) to be smaller than 2\sigma and 1\sigma. This
spectroscopic survey (option B) will improve the Figure of Merit of option A by
a factor \times 1.5 thus making such a survey strongly desirable.
