deletions | additions       diff --git a/subsection_Converting_Between_the_Observed__.tex b/subsection_Converting_Between_the_Observed__.tex  index 1b6fcad..72b23a7 100644  --- a/subsection_Converting_Between_the_Observed__.tex  +++ b/subsection_Converting_Between_the_Observed__.tex 
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\begin{equation}  \label{eqn:convert_from_actual_to_observed_density}  \rho(\Gamma_{\rm obs}, P_{\rm obs}) = \int_{b = 0}^{b(\Gamma_{\rm obs}, P_{\rm obs})} f\ \rho(\Gamma_{\rm act}(b), P_{\rm act}(b))\ \dfrac{2b\ db}{b_{\rm max}^2}\\  = A_{\rm max}^{-1}\ \upsilon\ \kappa\ b_{\rm max}^{-2} \int_{b = 0}^{\left( \Gamma_{\rm obs}/2 \right) \sqrt{\left( P_{\rm obs} - P_{\rm min} \right)/P_{\rm min}}} \Gamma_{\rm act} \left( \dfrac{P_{\rm act} - P_{\rm min}}{P_{\rm min}} \right)^{1/2} \left( \Gamma_{\rm act}/{\rm act}(b)/{\rm  m} \right)^{2/3}\ \rho( \Gamma_{\rm act}(b), P_{\rm act}(b))\ 2b\ db, \end{equation}  where $\kappa = 40\ {\rm s}$. Figure \ref{fig:uniform_actual_distribution_to_observed_distribution} shows the result for a uniform distribution for underlying values, $\rho(\Gamma_{\rm act}, P_{\rm act}) = \left( P_{\rm max} - P_{\rm min} \right)^{-1}\ \left( \Gamma_{\rm max} - \Gamma_{\rm min} \right)^{-1}$ and compares it to a simulated dust devil survey (blue circles).