  We investigate the impact of $1/f$ noise on cosmology for an intensity
mapping survey with SKA1-MID Band\,1 and Band\,2. We use a Fisher matrix
approach to forecast constraints on cosmological parameters under the influence
of $1/f$ noise, adopting a semi-empirical model from an earlier work, which
results from the residual $1/f$ noise spectrum after applying a component
separation algorithm to remove smooth spectral components. Without $1/f$ noise,
the projected constraints are $4\%$ on $w_0$, $1\%$ on $h$, $2\%$ on $b_{\rm
HI}$ using Band\,1+\emph{Planck}, and $3\%$ on $w_0$, $0.5\%$ on $h$, $2\%$ on
$b_{\rm HI}$ using Band\,2+\emph{Planck}. A representative baseline $1/f$ noise
degrades these constraints by a factor of $\sim1.5$ for Band\,1+\emph{Planck},
and $\sim1.2$ for Band\,2+\emph{Planck}. On the power spectrum measurement,
higher redshift and smaller scales are more affected by $1/f$ noise, with
minimal contamination comes from $z\lesssim1$ and $\ell\lesssim100$. Subject to
the specific scan strategy of the adopted $1/f$ noise model, one prefers a
correlated in frequency with minimised spectral slope, a low knee frequency,
and a large telescope slew speed in order to reduce its impact.
