Brian Jackson edited Figure_ref_fig_n_Pobs_from_uniform_n__.tex  almost 9 years ago

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Figure \ref{fig:n-Pobs_from_uniform_n-Pact} shows how significantly the miss distance effect modifies the observed distribution of pressure depths as compared to the underlying distribution. Well away from the $P_{\rm max}$, the distribution $n(P_{\rm obs})$ follows a $P_{\rm obs}^{-2}$ power-law, similar to what has been observed in several studies. However, the lack of devils with $P_{\rm act} > P_{\rm max}$ means that eventually the distribution declines toward zero.  As a check of this result, we conducted a Monte-Carlo simulation of dust devil encounters, similar to that in \citet{Lorenz_2014}. We modeled 100,000 dust devils with a uniform distribution of $P_{\rm act}$ between $P_{\rm min}$ and $P_{\rm max}$ and assumed a fixed value for $\Gamma_{\rm act}$. For each devil, we chose a random closest encounter distance as $b = \sqrt{\Phi}\ b_{\rm max}$, where $\Phi$ is a random variable uniformly distributed between 0 and 1. Figure \ref{fig:n-obs_MC-pred} compares the result from the numerical simulation to the prediction from Equation \ref{eqn:n-Pobs_from_uniform_n-Pact}