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Brian Jackson added In_panel_b_the_Gamma___.tex
over 8 years ago
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In panel (b), the $\Gamma_{\rm obs}$ density monotonically increases as $\Gamma_{\rm obs}$ increases since devils with larger $\Gamma_{\rm act}$-values are more likely to be observed (Equation \ref{eqn:recovery_bias}), and they're likely to be observed with yet wider profiles. By contrast, in panel (c), the density peaks at a moderate value of $P_{\rm obs}$, falling off to either side. Few devils are observed with $P_{\rm obs} \approx P_{\rm max}$ because nearly central ($b \approx 0$) would be required, which are unlikely. Looking at the other side of the peak from small $P_{\rm obs}$, devils with larger $P_{\rm act}$ are more likely to be detected. Since we require $\Gamma_{\rm obs} \le \Gamma_{\rm max}$, those devils are confined to a finite range of $b$ and therefore a minimum value of $P_{\rm obs} \ge P_{\rm act} \left( \Gamma_{\rm act}/\Gamma_{\rm max} \right)^2$, often greater than $P_{\rm min}$.
Figure \ref{fig:uniform_actual_distribution_to_observed_distribution} clearly contradicts results from real dust devil surveys, such as \cite{Jackson_2015} who found many fewer dust devils with larger $P_{\rm obs}$-values than those with smaller values. The obvious conclusion is that the underlying distribution of detected dust devils is not uniform in $P_{\rm obs}$.
