al_be_erosion_one.m

Syntax:

retstr = al_be_erosion_one(ins)

The MATLAB web server calls this function when the erosion rate data input form is submitted. It takes as input a structure containing string variables, which is supplied by the MATLAB web server. It returns a text string consisting of an output HTML document containing the results of the erosion rate calculation. The documentation for the MATLAB web server describes this process in more detail.

The input structure ins contains the following fields. These have the same names as the data-entry fields in the HTML input form.

ins.sample_name	Sample name
ins.str_lat	Latitude
ins.str_long	Longitude
ins.str_alt	Either elevation in meters or pressure in hPa
ins.aa	Flag that indicates how to interpret the str_alt variable. Has three possible values: `std' if the elevation value is in meters and the standard atmosphere approximation is to be used; `ant' if the elevation value is in meters and the Antarctic atmosphere approximation is to be used; and `pre' if the elevation value is in hPa.
ins.str_thick	Sample thickness in cm
ins.str_rho	Sample density, g $\cdot$ cm$^{-3}$
ins.str_othercorr	Shielding correction. The shielding correction can be calculated using skyline.m
ins.str_N10	$^{10}$Be concentration, atoms $\cdot$ g $^{-1} \cdot$ yr$^{-1}$
ins.str_delN10	standard error of $^{10}$Be concentration
ins.str_N26	$^{26}$Al concentration, atoms $\cdot$ g $^{-1} \cdot$ yr$^{-1}$
ins.str_delN26	standard error of $^{26}$Al concentration

The majority of this function consists of routines that check the input data to make sure it is in the expected form and is within expected bounds, and convert string variables to numerical values. After the data checking is complete, the function then assembles the data sets needed for the $^{26}$Al and $^{10}$Be exposure age calculations, loads the data file containing values for physical constants, and passes data to the function get_al_be_erosion.m, which actually carries out the erosion rate calculation and returns the result. Finally, this function assembles the output data, generates the required plots, and inserts the output data into the output HTML template.

The only actual calculation that takes place inside this function is the calculation of the uncertainty in the $^{26}$Al $^{10}$Be ratio. Denote the $^{26}$Al/$^{10}$Be ratio by $R_{26/10}$ and its $1\sigma$ uncertainty by $\sigma R_{26/10}$. Assuming linear, uncorrelated uncertainties:

$$\left( \sigma R_{26/10} \right) ^{2} = \left(\frac{\sigma N_{26}}{N_{10}} \right)^{2} + \sigma N_{10}^2 \left( \frac{-N_{26}}{N_{10}^2} \right)^{2}$$ (3)

where $N_{i}$ is the concentration of nuclide $i$ and $\sigma N_{i}$ is its $1\sigma$ analytical uncertainty.