In this paper, some abnormal or rogue wave events registered in the North Sea by means of the surface elevation measurements are reconstructed with the help of theoretical models for water waves and numerical simulations of wave evolution. Time series of surface elevation, which are measured at a single point, provide incomplete information about the waves. The registered time series are used to restore the wave dynamics under reasonable assumptions. Different frameworks associated with the relation between the surface elevation and the fluid velocity fields are considered, and different numerical models are used to simulate the wave dynamics in time and space. It is shown that for some abnormal or rogue wave records the result of the extreme event reconstruction is robust. In particular, the verification of approximate approaches versus the fully nonlinear numerical simulation is performed. The reconstructed rogue wave is generally less steep than the measured one. Possible reasons for this discrepancy are suggested.