  We present and compare several methods to mitigate time-correlated (1/f)
noise within the HI intensity mapping component of the MeerKAT Large Area
Synoptic Survey (MeerKLASS). By simulating scan strategies, the HI signal,
foreground emissions, white and correlated noise, we assess the ability of
various data processing pipelines to recover the power spectrum of HI
brightness temperature fluctuations. We use MeerKAT pilot data to assess the
level of 1/f noise expected for the MeerKLASS survey and use these measurements
to create realistic levels of time-correlated noise for our simulations. We
find the time-correlated noise component within the pilot data to be between 10
and 20 times higher than the white noise level at the scale of k = 0.04 Mpc^-1.
Having determined that the MeerKAT 1/f noise is partially correlated across all
the frequency channels, we employ Singular Value Decomposition (SVD) as a
technique to remove both the 1/f noise and Galactic foregrounds but find that
over-cleaning results in the removal of HI power at large (angular and radial)
scales; a power loss of 40 per cent is seen for a 3-mode SVD clean at the scale
of k = 0.04 Mpc^-1. We compare the impact of map-making using weighting by the
full noise covariance (i.e. including a 1/f component), as opposed to just a
simple unweighted binning, finding that including the time-correlated noise
information reduces the excess power added by 1/f noise by up to 30 per cent.
