Derivation of error estimates for Ca ii H. Bottom: formation heights in the original (red) and modified HSRA model (black). The blue line gives the formation height from phase differences. Middle: rms fluctuations induced by random Doppler shifts (black). The red line shows an average profile. Top: temperature rms using the original (black) and modified HSRA model (red). Their ratio is given by the blue line with the axis on the right-hand side.