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[1] In the first part of this paper, the rigorous theory describing the electromagnetic field radiated by a lightning return stroke over a two-layered conducting ground was presented and the exact expressions for the lightning electromagnetic fields were developed and discussed. In this part of the paper, the theory along with its time domain numerical evaluation algorithm is used for the assessment of the validity of simplified approaches proposed in the literature for the vertical electric and horizontal magnetic field components. The simplified approaches are based on the concept of ground surface impedance and its corresponding attenuation function. It is shown that the results obtained using the simplified approaches are in excellent agreement with exact results in both near (50 m) and intermediate (1000 m) distance range. However, since the vertical electric and azimuthal magnetic field components are not appreciably affected by the ground finite conductivity, they can also be evaluated assuming the ground as a perfectly conducting ground. On the other hand, the horizontal electric field above a horizontally stratified ground is very much affected by the ground electrical parameters. Its waveform is characterized by an early negative excursion due to the currents flowing into the ground followed by a late time positive excursion which is due to the elevation of the observation point from the ground level. The magnitude of the negative peak is sharper for subsequent return strokes than first return strokes and is higher for lower conducting grounds. A new formula is proposed for the evaluation of the horizontal electric field at a given height above the air-ground interface. The formula can be viewed as the generalization of the Cooray-Rubinstein formula for the case of a two-layer ground. We show that the new formula is able to reproduce in a satisfactory manner the horizontal electric field above a two-layer ground. The proposed formulation is, however, less accurate at distances as close to 10 m from the channel base and for very poor ground conductivity (0.0001 S/m).

[1] In this paper we review simplified analytical expressions derived by Wait using the concept of attenuation function for the analysis of the propagation of lightning-radiated electromagnetic fields over a mixed propagation path (vertically stratified ground). Two different formulations proposed by Wait that depend on the relative values of ground surface impedances are discussed. It is shown that both formulations give nearly the same results for the time domain electric field. However, depending on the values of the normalized surface impedance for each ground section, the use of one of the two formulations is computationally more efficient. The accuracy of the Wait formulations was examined taking as reference full-wave simulations obtained using the finite difference time domain technique. It is shown that Wait's simplified formulas are able to reproduce the distant field peak and waveshape with a good accuracy.Citation: Shoory, A., A. Mimouni, F. Rachidi, V. Cooray, and M. Rubinstein (2011), On the accuracy of approximate techniques for the evaluation of lightning electromagnetic fields along a mixed propagation path, Radio Sci., 46, RS2001,

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[1] The formulation describing the electromagnetic field radiated by a lightning return stroke over a two-layered conducting ground is presented in this paper. The derivation of the Green's functions required to solve the problem is first discussed in detail, and the expressions for the lightning electromagnetic fields are determined. Afterward, an efficient method for the numerical evaluation of the electromagnetic field is proposed. The proposed method is based on a suitable modification of a previously developed model for the evaluation of the fields in the presence of a lossy but homogeneous soil. Particular attention is devoted to the soil reflection coefficient properties, both from a physical and from a mathematical point of view. In part 2 of the paper, the developed approach and numerical algorithms will be used to evaluate the effect of the soil stratification on the radiated fields and to perform the validity assessment of simplified approaches proposed in the literature.