  Cosmology has entered an era where the experimental limitations are not due
to instrumental sensitivity but instead due to inherent systematic
uncertainties in the instrumentation and data analysis methods. The field of HI
intensity mapping (IM) is still maturing, however early attempts are already
systematics limited. One such systematic limitation is 1/f noise, which largely
originates within the instrumentation and manifests as multiplicative gain
fluctuations. To date there has been little discussion about the possible
impact of 1/f noise on upcoming single-dish HI IM experiments such as BINGO,
FAST or SKA. Presented in this work are Monte-Carlo end-to-end simulations of a
30 day HI IM survey using the SKA-MID array covering a bandwidth of 950 and
1410 MHz. These simulations extend 1/f noise models to include not just
temporal fluctuations but also correlated gain fluctuations across the receiver
bandpass. The power spectral density of the spectral gain fluctuations are
modelled as a power-law, and characterised by a parameter $\beta$. It is found
that the degree of 1/f noise frequency correlation will be critical to the
success of HI IM experiments. Small values of $\beta$ ($\beta$ < 0.25) or high
correlation is preferred as this is more easily removed using current component
separation techniques. The spectral index of temporal fluctuations ($\alpha$)
is also found to have a large impact on signal-to-noise. Telescope slew speed
has a smaller impact, and a scan speed of 1 deg s$^{-1}$ should be sufficient
for a HI IM survey with the SKA.
