  Aims: Develop and validate tools to estimate residual noise covariance in
Planck frequency maps. Quantify signal error effects and compare different
techniques to produce low-resolution maps.
  Methods: We derive analytical estimates of covariance of the residual noise
contained in low-resolution maps produced using a number of map-making
approaches. We test these analytical predictions using Monte Carlo simulations
and their impact on angular power spectrum estimation. We use simulations to
quantify the level of signal errors incurred in different resolution
downgrading schemes considered in this work.
  Results: We find an excellent agreement between the optimal residual noise
covariance matrices and Monte Carlo noise maps. For destriping map-makers, the
extent of agreement is dictated by the knee frequency of the correlated noise
component and the chosen baseline offset length. The significance of signal
striping is shown to be insignificant when properly dealt with. In map
resolution downgrading, we find that a carefully selected window function is
required to reduce aliasing to the sub-percent level at multipoles, ell >
2Nside, where Nside is the HEALPix resolution parameter. We show that
sufficient characterization of the residual noise is unavoidable if one is to
draw reliable contraints on large scale anisotropy.
  Conclusions: We have described how to compute the low-resolution maps, with a
controlled sky signal level, and a reliable estimate of covariance of the
residual noise. We have also presented a method to smooth the residual noise
covariance matrices to describe the noise correlations in smoothed, bandwidth
limited maps.
