desilets2006sp.m

Syntax:

scalingfactor = desilets2006sp(h,Rc)

Calculates the geographic scaling factor for cosmogenic-nuclide production for particular cutoff rigidity and atmospheric pressure according to the scheme in:

Desilets D., Zreda M., Prabu T., 2006. Extended scaling factors for in situ cosmogenic nuclides: New measurements at low latitude. Earth and Planetary Science Letters, v. 246, pp. 265-276.

The input arguments are h, atmospheric pressure (hPa), and Rc, cutoff rigidity (GV). Accepts vector arguments.

This function:

Converts atmospheric pressure $h$ (hPa) to atmospheric depth $x$ (g $\cdot$ cm$^{-2}$) by $x = 1.0197 h$.

Assigns cutoff rigidities below 2 GV a value of 2 GV.

Obtains the effective attenuation length in air $\Lambda_{eff,sp}$ via Equation (4) in the source paper:

$$\Lambda_{eff,sp} = \frac{1033-x}{g(1033,R_{C}) - g(x,R_{C})}$$ (26)

where $R_{C}$ is the cutoff rigidity (GV) and the function $g(x,R_{C})$ is:

$$g(x,R_{C}) = n\left[ 1 + \exp{\left(-\alpha R_{C}^{-k} \right)} \right]^{-1}x$$ (27)

$$+ \frac{1}{2} \left[ a_{0} + a_{1}R_{C} + a_{2}R_{C}^2\right] x^{2}$$ (28)

$$+ \frac{1}{3} \left[ a_{3} + a_{4}R_{C} + a_{5}R_{C}^2\right] x^{3}$$ (29)

$$+ \frac{1}{5} \left[ a_{6} + a_{7}R_{C} + a_{8}R_{C}^2\right] x^{4}$$ (30)

given constants:

$n$	$1.0177 \times 10^{-2}$
$\alpha$	$1.0207 \times 10^{-1}$
$k$	$-3.9527 \times 10^{-1}$
$a_{0}$	$8.5236 \times 10^{-6}$
$a_{1}$	$-6.3670 \times 10^{-7}$
$a_{2}$	$-7.0814 \times 10^{-9}$
$a_{3}$	$-9.9182 \times 10^{-9}$
$a_{4}$	$9.9250 \times 10^{-10}$
$a_{5}$	$2.4925 \times 10^{-11}$
$a_{6}$	$3.8615 \times 10^{-12}$
$a_{7}$	$-4.8194 \times 10^{-13}$
$a_{8}$	$-1.5371 \times 10^{-14}$

Obtains the altitude scaling factor $S_{alt}$:

$$S_{alt} = \exp{\left( \frac{1033-x}{\Lambda_{eff,sp}} \right)}$$ (31)

Obtains the latitude scaling factor $S_{lat}$ via Equation (6) in the source paper:

$$S_{lat} = 1 - \exp{\left( -\alpha R_{C}^{-k} \right) }$$ (32)

where $R_{C}$ is the cutoff rigidity, $\alpha = 10.275$, and $k = 0.9615$.

Finally, obtains the total scaling factor $S = S_{alt}S_{lat}$.

Accepts either scalars or vectors of equal sizes for all the input arguments. Returns either a scalar or a vector of the appropriate size.