at the peak. [$E_{\rm peak}$]{} evolves from 1500 keV to 100 keV over the nominal duration of the pulse. \[Sim\_EP\_Fit\]](Sim_EP_Fit.pdf)

Spectral Lag and Pulse Width Evolution
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This simulation of the temporal evolution of spectral parameters allows us to compare it with certain other properties of observed pulses, such as the spectral lag and pulse-width evolution as a function of energy, as characterized in the initial pulse of GRB 130427A [@preece2014]. Because the simulations and the spectral fits share the same power law evolution model, the simulation reproduces the lag-width relation of the real data, when the lag is taken with respect to a fixed low energy channel. That is: the spectral lag increases as a function of increasing energy (@KocevskiLiang; see Figure \[Rob\_energy\_dep\_synthetic\_Suzanne\]). In addition, the pulse width decreases with increasing energy (@richaga; see Figure \[Rob\_FWHM\_Energy\]). Except for the factor of ten increase in the timescales associated with the simulations, these results are qualitatively consistent with the results presented in Figure 1 in @preece2014. One can visualize how this behavior arises by examining the joint temporal-spectral model as a contour plot. In Figure \[GRB130427A\_Horiz\_Contour\], we compare the fitted data from GRB130427A with the fitted data from our simulated pulse. 