Criteria for selecting 500 μm-risers. Plotted is a SPIRE colour diagram related to the MBB model. The plot is a result of a Monte Carlo simulation in which we start with a single-temperature modified blackbody with the flux S₅₀₀ = 30 mJy. The mock SEDs are generated to account for different fixed T_d and β illustrating temperature-redshift degeneracy. Plotted against all possible colours are simulated sources with T_d = 45 K and β = 1.8 (upper panel) and T_d = 38 K and β = 1.8 (lower panel). Left: colour-redshfit plot. Red lines represent redshift tracks rising from right to left. The coloured background indicates the average redshift in these colour-colour spaces. Blue lines define the 95% confidence limit region. A correction factor due to modelled effect of CMB heating on colours is applied. However, our simulations show that we do not expect a major contribution from that effect at sources lying below z ~ 7; right: different chi-square fitting values reflected on SPIRE colour-colour ratios. For our final 500 μm-risers selection we kept only those sources whose chi-square resides inside the 95% confidence limit region (χ² < 3.84).