KiDS-1000 catalogue: Redshift distributions and their calibration

We present redshift distribution estimates of galaxies selected from the fourth data release of the Kilo-Degree Survey over an area of similar to 1000 deg(2) (KiDS-1000). These redshift distributions represent one of the crucial ingredients for weak gravitational lensing measurements with the KiDS-1000 data. The primary estimate is based on deep spectroscopic reference catalogues that are re-weighted with the help of a self-organising map (SOM) to closely resemble the KiDS-1000 sources, split into five tomographic redshift bins in the photometric redshift range 0.1 < z(B) <= 1.2. Sources are selected such that they only occupy that volume of nine-dimensional magnitude-space that is also covered by the reference samples ('gold' selection). Residual biases in the mean redshifts determined from this calibration are estimated from mock catalogues to be less than or similar to 0.01 for all five bins with uncertainties of similar to 0.01. This primary SOM estimate of the KiDS-1000 redshift distributions is complemented with an independent clustering redshift approach. After validation of the clustering-z on the same mock catalogues and a careful assessment of systematic errors, we find no significant bias of the SOM redshift distributions with respect to the clustering-z measurements. The SOM redshift distributions re-calibrated by the clustering-z represent an alternative calibration of the redshift distributions with only slightly larger uncertainties in the mean redshifts of similar to 0.01-0.02 to be used in KiDS-1000 cosmological weak lensing analyses. As this includes the SOM uncertainty, clustering-z are shown to be fully competitive on KiDS-1000 data.