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\subsection*{Combining the $P_{\rm act}/\Gamma_{\rm act}$ Biases and Distortions}  Now we investigate these same biases and distortions when both $P_{\rm act}$ and $\Gamma_{\rm act}$ are allowed to vary. In this case, the recovery bias $f = f(P_{\rm act}, \Gamma_{\rm act})$ and represents a bias in two dimensions. We can cast it as before, by comparing the area occupied by the measurable portion of a dust devil with $P_{\rm act}$ and $\Gamma_{\rm act}$ to that largest measurable area for a devil. In principle, though, the latter area does not necessarily correspond to a devil with $P_{\rm act} = P_{\rm max}$ and $\Gamma_{\rm act} = \Gamma_{\rm max}$ since the profile depth and width can be physically coupled in a way that does not allow that combination to occur for a devil. For example, since profiles are ultimately determined from time-series data, the inferred widths are related to the velocity at which a dust devil is advected. Several previous studies (refs) have observed their deepest profiles near mid-day, and if wind speeds are fastest at that time of day, the deepest profiles may actually be some of the narrowest. For  the time being, however, though,  we will assume the parameters are uncoupled, giving \begin{equation}\label{eqn:full_bias_uncoupled}  f(P_{\rm act}, \Gamma_{\rm act})_{\rm uncoupled} = \left( \dfrac{\Gamma_{\rm act}}{\Gamma_{\rm max}} \right)^2 \left( \dfrac{P_{\rm act} - P_{\rm min}}{P_{\rm max} - P_{\rm min}} \right).  \end{equation}  Figure \ref{fig:} shows how this bias maps along the two dimensions.