deletions | additions       diff --git a/subsection_Converting_Between_the_Observed__.tex b/subsection_Converting_Between_the_Observed__.tex  index afab0d6..f3d97a8 100644  --- a/subsection_Converting_Between_the_Observed__.tex  +++ b/subsection_Converting_Between_the_Observed__.tex 
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\label{eqn:convert_from_actual_to_observed_density}  \rho(P_{\rm obs}, \Gamma_{\rm obs}) = \int_{b = 0}^{b_{\rm max}} f\ \rho(P_{\rm act}(b), \Gamma_{\rm act}(b))\ \dfrac{2b\ db}{b_{\rm max}^2} = \int_{b = 0}^{\frac{1}{2} \sqrt{\Gamma_{\rm obs}^2 - \Gamma_{\rm min}^2}} f\ \rho(P_{\rm act}(b), \Gamma_{\rm act}(b))\ \left( \Gamma_{\rm obs}^2 - \Gamma_{\rm min}^2 \right)^{-1}\ 4b\ db.  \end{equation}  Figure \ref{fig:uniform_actual_distribution_to_observed_distribution} shows the result for a uniform distribution for underlying values, $\rho(P_{\rm act}, \Gamma_{\rm act}) = \left( P_{\rm max} - P_{\rm min} \right)^{-1}\ \left( \Gamma_{\rm max} - \Gamma_{\rm min} \right)^{-1}$ and compares it to a simulated dust devil survey (blue circles). Figure \ref{fig:uniform_actual_distribution_to_observed_distribution} indicates a tendency to observed  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 $P_{\rm obs}$.