# calc_CosmicDoseRate

##### Calculate the cosmic dose rate

This function calculates the cosmic dose rate taking into account the soft- and hard-component of the cosmic ray flux and allows corrections for geomagnetic latitude, altitude above sea-level and geomagnetic field changes.

##### Usage

```
calc_CosmicDoseRate(depth, density, latitude, longitude, altitude,
corr.fieldChanges = FALSE, est.age = NA, half.depth = FALSE,
error = 10, ...)
```

##### Arguments

- depth
numeric (

**required**): depth of overburden (m). For more than one absorber use`c(depth_1, depth_2, ..., depth_n)`

- density
numeric (

**required**): average overburden density (g/cm^3). For more than one absorber use`c(density_1, density_2, ..., density_n)`

- latitude
numeric (

**required**): latitude (decimal degree), N positive- longitude
numeric (

**required**): longitude (decimal degree), E positive- altitude
numeric (

**required**): altitude (m above sea-level)- corr.fieldChanges
logical (

*with default*): correct for geomagnetic field changes after Prescott & Hutton (1994). Apply only when justified by the data.- est.age
numeric (

*with default*): estimated age range (ka) for geomagnetic field change correction (0-80 ka allowed)- half.depth
logical (

*with default*): How to overcome with varying overburden thickness. If`TRUE`

only half the depth is used for calculation. Apply only when justified, i.e. when a constant sedimentation rate can safely be assumed.- error
numeric (

*with default*): general error (percentage) to be implemented on corrected cosmic dose rate estimate- ...
further arguments (

`verbose`

to disable/enable console output).

##### Details

This function calculates the total cosmic dose rate considering both the soft- and hard-component of the cosmic ray flux.

**Internal calculation steps**

(1) Calculate total depth of all absorber in hg/cm^2 (1 hg/cm^2 = 100 g/cm^2)

$$absorber = depth_1*density_1 + depth_2*density_2 + ... + depth_n*density_n$$

(2)
If `half.depth = TRUE`

$$absorber = absorber/2$$

(3) Calculate cosmic dose rate at sea-level and 55 deg. latitude

a) If absorber is > 167 g/cm^2 (only hard-component; Allkofer et al. 1975): apply equation given by Prescott & Hutton (1994) (c.f. Barbouti & Rastin 1983)

$$D0 = C/(((absorber+d)^\alpha+a)*(absober+H))*exp(-B*absorber)$$

b) If absorber is < 167 g/cm^2 (soft- and hard-component): derive D0 from Fig. 1 in Prescott & Hutton (1988).

(4) Calculate geomagnetic latitude (Prescott & Stephan 1982, Prescott & Hutton 1994)

$$\lambda = arcsin(0.203*cos(latitude)*cos(longitude-291)+0.979* sin(latitude))$$

(5) Apply correction for geomagnetic latitude and altitude above sea-level. Values for F, J and H were read from Fig. 3 shown in Prescott & Stephan (1982) and fitted with 3-degree polynomials for lambda < 35 degree and a linear fit for lambda > 35 degree.

$$Dc = D0*(F+J*exp((altitude/1000)/H))$$

(6) Optional: Apply correction for geomagnetic field changes in the last 0-80 ka (Prescott & Hutton 1994). Correction and altitude factors are given in Table 1 and Fig. 1 in Prescott & Hutton (1994). Values for altitude factor were fitted with a 2-degree polynomial. The altitude factor is operated on the decimal part of the correction factor.

$$Dc' = Dc*correctionFactor$$

**Usage of depth and density**

(1) If only one value for depth and density is provided, the cosmic dose
rate is calculated for exactly one sample and one absorber as overburden
(i.e. `depth*density`

).

(2) In some cases it might be useful to calculate the cosmic dose rate for a
sample that is overlain by more than one absorber, e.g. in a profile with
soil layers of different thickness and a distinct difference in density.
This can be calculated by providing a matching number of values for
`depth`

and `density`

(e.g. `depth = c(1, 2), density = c(1.7, 2.4)`

)

(3) Another possibility is to calculate the cosmic dose rate for more than
one sample of the same profile. This is done by providing more than one
values for `depth`

and only one for `density`

. For example,
`depth = c(1, 2, 3)`

and `density = 1.7`

will calculate the cosmic dose rate
for three samples in 1, 2 and 3 m depth in a sediment of density 1.7 g/cm^3.

##### Value

Returns a terminal output. In addition an '>RLum.Results-object is returned containing the following element:

data.frame summary of all relevant calculation results.

list used arguments

call the function call

The output should be accessed using the function get_RLum

##### Note

Despite its universal use the equation to calculate the cosmic dose rate provided by Prescott & Hutton (1994) is falsely stated to be valid from the surface to 10^4 hg/cm^2 of standard rock. The original expression by Barbouti & Rastin (1983) only considers the muon flux (i.e. hard-component) and is by their own definition only valid for depths between 10-10^4 hg/cm^2.

Thus, for near-surface samples (i.e. for depths < 167 g/cm^2) the equation of Prescott & Hutton (1994) underestimates the total cosmic dose rate, as it neglects the influence of the soft-component of the cosmic ray flux. For samples at zero depth and at sea-level the underestimation can be as large as ~0.1 Gy/ka. In a previous article, Prescott & Hutton (1988) give another approximation of Barbouti & Rastins equation in the form of

$$D = 0.21*exp(-0.070*absorber+0.0005*absorber^2)$$

which is valid for depths between 150-5000 g/cm^2. For shallower depths (< 150 g/cm^2) they provided a graph (Fig. 1) from which the dose rate can be read.

As a result, this function employs the equation of Prescott & Hutton (1994) only for depths > 167 g/cm^2, i.e. only for the hard-component of the cosmic ray flux. Cosmic dose rate values for depths < 167 g/cm^2 were obtained from the "AGE" programm (Gruen 2009) and fitted with a 6-degree polynomial curve (and hence reproduces the graph shown in Prescott & Hutton 1988). However, these values assume an average overburden density of 2 g/cm^3.

It is currently not possible to obtain more precise cosmic dose rate values for near-surface samples as there is no equation known to the author of this function at the time of writing.

##### Function version

0.5.2 (2018-01-21 17:22:38)

##### How to cite

Burow, C. (2018). calc_CosmicDoseRate(): Calculate the cosmic dose rate. Function version 0.5.2. In: Kreutzer, S., Burow, C., Dietze, M., Fuchs, M.C., Schmidt, C., Fischer, M., Friedrich, J. (2018). Luminescence: Comprehensive Luminescence Dating Data Analysis. R package version 0.8.6. https://CRAN.R-project.org/package=Luminescence

##### References

Allkofer, O.C., Carstensen, K., Dau, W.D., Jokisch, H., 1975. Letter to the editor. The absolute cosmic ray flux at sea level. Journal of Physics G: Nuclear and Particle Physics 1, L51-L52.

Barbouti, A.I., Rastin, B.C., 1983. A study of the absolute intensity of muons at sea level and under various thicknesses of absorber. Journal of Physics G: Nuclear and Particle Physics 9, 1577-1595.

Crookes, J.N., Rastin, B.C., 1972. An investigation of the absolute intensity of muons at sea-level. Nuclear Physics B 39, 493-508.

Gruen, R., 2009. The "AGE" program for the calculation of luminescence age estimates. Ancient TL 27, 45-46.

Prescott, J.R., Hutton, J.T., 1988. Cosmic ray and gamma ray dosimetry for TL and ESR. Nuclear Tracks and Radiation Measurements 14, 223-227.

Prescott, J.R., Hutton, J.T., 1994. Cosmic ray contributions to dose rates for luminescence and ESR dating: large depths and long-term time variations. Radiation Measurements 23, 497-500.

Prescott, J.R., Stephan, L.G., 1982. The contribution of cosmic radiation to the environmental dose for thermoluminescence dating. Latitude, altitude and depth dependences. PACT 6, 17-25.

##### See Also

##### Examples

```
# NOT RUN {
##(1) calculate cosmic dose rate (one absorber)
calc_CosmicDoseRate(depth = 2.78, density = 1.7,
latitude = 38.06451, longitude = 1.49646,
altitude = 364, error = 10)
##(2a) calculate cosmic dose rate (two absorber)
calc_CosmicDoseRate(depth = c(5.0, 2.78), density = c(2.65, 1.7),
latitude = 38.06451, longitude = 1.49646,
altitude = 364, error = 10)
##(2b) calculate cosmic dose rate (two absorber) and
##correct for geomagnetic field changes
calc_CosmicDoseRate(depth = c(5.0, 2.78), density = c(2.65, 1.7),
latitude = 12.04332, longitude = 4.43243,
altitude = 364, corr.fieldChanges = TRUE,
est.age = 67, error = 15)
##(3) calculate cosmic dose rate and export results to .csv file
#calculate cosmic dose rate and save to variable
results<- calc_CosmicDoseRate(depth = 2.78, density = 1.7,
latitude = 38.06451, longitude = 1.49646,
altitude = 364, error = 10)
# the results can be accessed by
get_RLum(results, "summary")
#export results to .csv file - uncomment for usage
#write.csv(results, file = "c:/users/public/results.csv")
##(4) calculate cosmic dose rate for 6 samples from the same profile
## and save to .csv file
#calculate cosmic dose rate and save to variable
results<- calc_CosmicDoseRate(depth = c(0.1, 0.5 , 2.1, 2.7, 4.2, 6.3),
density = 1.7, latitude = 38.06451,
longitude = 1.49646, altitude = 364,
error = 10)
#export results to .csv file - uncomment for usage
#write.csv(results, file = "c:/users/public/results_profile.csv")
# }
```

*Documentation reproduced from package Luminescence, version 0.8.6, License: GPL-3*