Modelling and observational uncertainties in the derived ξ and N_H parameters of typical ionised outflows in AGN (NGC 5548). The modelling uncertainties, shown in solid blue lines, correspond to the deviation between the parameter values derived by the Cloudy, SPEX, and XSTAR photoionisation codes as described in Sect. 7. The observational uncertainties, shown in dashed red lines, correspond to the statistical errors of the fitted parameters at 1σ confidence level for 100 ks (upper dashed line) and 1 Ms (lower dashed line) simulated observations with each instrument. The left column panels indicate the uncertainties in the ξ parameter, and the right column panels show the uncertainties in the N_H parameter. The photoionisation calculations and spectral simulations were carried out for a PIE plasma ionised by the AGN1 SED (see Fig. 1), with log ξ ranging between 1.0 and 3.0 with an increment of 0.5, N_H = 1 × 10²² cm^-2 and σ_v = 200 km s^-1.