Tweek-atmospherics (tweeks), along with radio transmission by VLF radio stations, are used to study the lower ionosphere. The new single-position method for determining of electron density in the lower ionosphere by multimodal tweek-atmospherics is studied upon the numerical simulations. The electron density profile model in the nighttime atmospherics (tweeks) approach aims to more closely represent the physical profile of the D-layer nighttime ionosphere. It corresponds to a layer of constant electron density at least 8...10 km thick and a much lower electron density below it. The influence of five main variable parameters on the sought-for electron density for realistic natural values of the parameters was numerically studied. The main influence has been shown to be exerted by the difference in the effective reflection heights of the first and second harmonics of tweek-atmospheric. It is shown that the scope of applicability of this method can be expanded taking into account the different scale of the contribution of variable parameters. It is shown that failure to correctly account for the polarization of the tweeks could result in the true electron concentration being about 25% of the calculated one.