Numerical Phase Errors in Broadband Simulations of Lightning Electromagnetic Fields over Lossy Ground

Reliable interpretation of broadband lightning fields requires numerical phase errors to be distinguished from propagation effects. We examine this problem over 1–450 kHz using an axisymmetric finite-difference time-domain model with a modified transmission-line return-stroke current model with exponential decay, finite radial support, and a rational surface-admittance boundary. Matched discrete, continuous local-admittance, and Sommerfeld halfspace references test different aspects of the response. At fixed spatial resolution, reducing the high-band time step by a factor of four increases the maximum uncorrected surface radial-field phase difference from 43.64° to 62.26°. Combined source-endpoint and horizontal Yee corrections reduce these values to 3.03° and 0.76°, respectively. The source correction compensates a common temporal phase, whereas the Yee correction compensates a range-accumulated numerical phase; only the latter remains in within-band relative propagation. Frequency differences converge to the analytic derivative of the same finite record, but proximity to a continuous reference alone does not establish derivative accuracy. Continuous-reference residuals are below 0.10 dB and 0.87° at eligible samples, and periodic waveforms at 50 km range and 125 m height differ from the Sommerfeld reference by approximately 0.20% in relative L2 norm. Direct Heidler-current calculations further show that similar lossy-ground and perfectly conducting-ground peaks can coexist with appreciable same-time waveform differences. These results link phase treatment to waveform interpretation and provide a numerical baseline for lightning-field propagation above homogeneous ground.