  The Stokes-Einstein (SE) relation has three commonly used variants:
D~1/{\tau}, D~T/{\tau} and D~T/{\eta}. In this work, the consistency of the
original SE relation and its three variants in supercooled water is examined by
molecular dynamics simulation with the TIP5P and Jagla water models,
respectively. It is found that the original SE relation remains valid even when
the three variants are all invalid in the simulated temperature ranges:
D~1/{\tau} and D~T/{\tau} follow the fractional forms D~(1/{\tau}){\zeta} and
D~(T/{\tau}){\zeta} with a crossover temperature, at which the
wavevector-dependent exponent {\zeta} changes its value; D~T/{\eta} is
equivalent to the original SE relation only when the effective hydrodynamic
radius a is a constant, which is however found to decrease with decreasing
temperature T. Therefore, care should be taken when employing its variants to
judge the validity of the original SE relation in supercooled water.
