IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 53, NO. 3, AUGUST 2011 773 Engineering Lightning Return Stroke Models Incorporating Current Reflection From Ground and Finitely Conducting Ground Effects Vernon Cooray and Valdimir A. Rakov, Fellow, IEEE Abstract—A return stroke model that incorporates a reflected wave from ground without introducing any current discontinuities at the return stroke front is introduced. The incident current is treated using current generation concepts and the reflected current using current dissipation concepts. It is shown that the effect of the reflected current wave is to cause flattening of close electric field waveforms within about 10 μs. Additionally, it is shown how a return stroke model could be utilized to study the effect of ground conductivity on the return stroke current. The results show that the peak time derivative of current in lightning strokes terminating on poorly conducting ground is significantly lower than in the case of highly conducting ground. The model is also used to predict the spatial variation of return stroke velocity. The results show that the return stroke velocity increases initially, reaches a peak, and then decays with increasing height. Index Terms—Finite ground conductivity, lightning, lightning current, lightning electromagnetic pulse (LEMP), lightning mod- els, return stroke. I. INTRODUCTION R ESEARCHERS use various concepts to describe and model lightning return strokes. In one type of models, the current propagation (CP) models (also known as transmis- sion line type models and lumped current source models), the return stroke channel acts as a guiding structure for the CP, with the driving source being at the ground. The models belonging to this category are the transmission line model [1] and the modi- fied transmission line models [2], [3]. The input parameters of these models are the channel base current, return stroke veloc- ity, and a function that describes the attenuation of the current amplitude with height. Return stroke can also be described by current generation (CG) models (also known as traveling cur- rent source type models or distributed current source models). A pictorial description of the CG concept is given in Fig. 1(a). In CG models, the neutralization of the leader charge during the return stroke phase gives rise to the return stroke current. Ac- cording to these models, as the return stroke front passes through Manuscript received November 13, 2009; revised April 4, 2010 and June 22, 2010; accepted September 9, 2010. Date of publication April 7, 2011; date of current version August 18, 2011. V. Cooray is with the Division for Electricity, Uppsala University, Uppsala S-75121, Sweden (vernon.cooray@angstrom.uu.se). V. A. Rakov is with the Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32603 USA (e-mail: rakov@ece.ufl.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TEMC.2011.2113350 a given point on the leader channel, the collapse of the corona sheath results in the injection of a corona current into the central core of the return stroke. Once in the core, the corona current is assumed to travel to ground at the speed of light. The total return stroke current (as depicted by the curve to the right of the figure) is the sum of such elementary current components gen- erated by corona sources distributed along the channel. Since the corona current is turned on by the return stroke front, the return stroke current is zero above the return stroke front [point A in Fig. 1(a)]. At any given time t, the return stroke front is located at a height which is equal to vt, where v is the average speed of the return stroke front. Models belonging to CG type are introduced by Heidler [4], Diendorfer and Uman [5], and Cooray [6] among others. In all these models, the corona current is generally described by an exponential function with a certain decay time constant. With such a corona current, the input parameters of CG models could be any three of the following: channel base current, spatial variation of the return stroke speed, distribution of the charge deposited by the return stroke along the channel, and the spatial variation of the decay time constant of the corona current. Once three of these parameters are specified, the fourth parameter can be estimated using first principles. Recently, based on the theory of pulse propagation along transmission lines in the presence of corona, a third procedure to describe return strokes, which in fact is the mirror image of CG models, was introduced by Cooray [7]. Models based on the new concept are called current dissipation (CD) models. A pictorial description of the CD model concept is shown in Fig. 1(b). As mentioned earlier, in CG models the corona currents generated by the neutralization of the corona sheath travel downward and the cumulative effects of these corona currents generate the return stroke current. In CD models, the return stroke is initiated by a current pulse injected into the core of the leader channel at ground level. This injected current pulse travels upward with a speed equal to that of light in free space [waveform 1 to the right in Fig. 1(b)]. The propagation of this pulse along the central core initiates the neutralization of the corona sheath leading to the release of corona currents into the central core. In contrast to CG models in which corona currents travel downward, these corona currents travel upward along the core. The speed of propagation of the corona pulses upward along the core is also equal to the speed of light, and their polarity is opposite to that of the injected current pulse. Thus, the current waveform generated by the sum of corona currents (waveform 2 to the right) travels upward with speed of light. Point B is the front of these current waveforms. 0018-9375/$26.00 © 2011 IEEE