The International Height Reference System (IHRS) can be realised by geopotential numbers derived from a regional gravimetric (quasi)geoid model and ellipsoidal heights determined by a satellite technique like GNSS. One method to compute the gravimetric model is to use a stochastic kernel modification to combine a satellite-derived Earth Gravitational Model (EGM) with regional terrestrial gravity data, for instance the least squares modification of Stokes’ formula. Often degree variance models are used to model the a priori errors and the signal variation, for instance the bandlimited white noise or reciprocal distance models. A potential problem here is that the stochastic modification might give too high weight to the terrestrial gravity data for low to medium spherical harmonic degrees, leading to that the satellite-only EGM is changed for degrees where the GOCE and GRACE derived EGM is clearly superior to the regional terrestrial gravity data. The main purpose of this contribution is to study the above type of systematic error that might be generated by stochastic kernel modification. This is investigated empirically over a case study area covering Sweden. It is shown that the bandlimited white noise model with a low standard uncertainty introduces a significant systematic errror of about 0.050 gpu over Sweden. By using coloured noise instead, or the Wong and Gore kernel modification, this systematic bias can be avoided in the realisation of IHRS.