elevation_from_airmass

pycraf.atm.elevation_from_airmass(airmass)

Airmass derived from elevation using extrapolation by Maddalena & Johnson.

Parameters:

airmassQuantity

Airmass [dimless]

Returns:

elevQuantity

Elevation [deg]

Notes

For low elevations, the well-known 1/sin-law breaks down. Maddalena & Johnson (2006) propose the following extrapolation for El (in degrees):

\[\begin{split}\textrm{AM} = \begin{cases} -0.02344 + \frac{1.0140}{ \sin\left(\mathrm{El} + \frac{5.18}{\mathrm{El} + 3.35}\right)}\qquad\mathrm{for~}\mathrm{El}<32\\ \frac{1}{\sin\mathrm{El}}\qquad\mathrm{for~}\mathrm{El}\geq32 \end{cases}\end{split}\]

which was simply inverted:

\[\begin{split}\mathrm{El} = \begin{cases} \frac{B}{2} + \frac{1}{40}\sqrt{400 B^2 + 2680 B - 3799} - 1.675\qquad\mathrm{for~}\mathrm{AM}\leq1.88708 \\ \sin^{-1}\frac{1}{\mathrm{AM}}\qquad\mathrm{for~}\mathrm{AM}>1.88708 \end{cases}\end{split}\]

where

\[B \equiv \sin^{-1}\left(\frac{1.0140}{\mathrm{AM} + 0.02344}\right)\]