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LSDCRNParameters.cpp
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//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// LSDCRNParameters.cpp
//
// Land Surface Dynamics Cosmogenic Radionuclide Parameters Object
//
// This keeps track of paramters used to calculate the evolution of
// in situ cosmogenic nuclides.
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//
// An object within the University
// of Edinburgh Land Surface Dynamics group topographic toolbox
// for calculating concntration of environmental tracers, CRNs, TCN, fallout
// nuclides
//
// Developed by:
// Simon M. Mudd
// Martin D. Hurst
// David T. Milodowski
// Stuart W.D. Grieve
// Declan A. Valters
// Fiona Clubb
//
// Copyright (C) 2013 Simon M. Mudd 2013
//
// Developer can be contacted by simon.m.mudd _at_ ed.ac.uk
//
// Simon Mudd
// University of Edinburgh
// School of GeoSciences
// Drummond Street
// Edinburgh, EH8 9XP
// Scotland
// United Kingdom
//
// This program is free software;
// you can redistribute it and/or modify it under the terms of the
// GNU General Public License as published by the Free Software Foundation;
// either version 2 of the License, or (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY;
// without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
// See the GNU General Public License for more details.
//
// You should have received a copy of the
// GNU General Public License along with this program;
// if not, write to:
// Free Software Foundation, Inc.,
// 51 Franklin Street, Fifth Floor,
// Boston, MA 02110-1301
// USA
//
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
#include <fstream>
#include <math.h>
#include <iostream>
#include <vector>
#include <map>
#include "TNT/tnt.h"
#include "LSDStatsTools.hpp"
#include "LSDCRNParameters.hpp"
using namespace std;
using namespace TNT;
#ifndef LSDCRNParameters_CPP
#define LSDCRNParameters_CPP
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// the LSDCRNParameters object
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
// function to set CRN parameters
void LSDCRNParameters::create()
{
version = "1.0";
S_t = 1;
neutron_S_t = 1;
// from Vermeesh 2007
lambda_10Be = 456e-9; // in yr-1
lambda_26Al = 980e-9; // in yr-1
lambda_14C = 121e-6; // in yr-1
lambda_36Cl = 230e-8; // in yr-1
// from Vermeesh 2007
P0_10Be = 5.11; // in a/g/yr
P0_26Al = 30.31; // in a/g/yr
P0_14C = 5.86; // in a/g/yr
P0_36Cl = 55.45; // in a/g/yr
P0_21Ne = 20.29; // in a/g/yr
P0_3He = 97.40; // in a/g/yr
// in g/cm^2
Gamma[0] = 160;
Gamma[1] = 738.6;
Gamma[2] = 2688;
Gamma[3] = 4360;
// dimensionless
F_10Be[0] = 0.9724;
F_10Be[1] = 0.0186;
F_10Be[2] = 0.004;
F_10Be[3] = 0.005;
// dimensionless
F_26Al[0] = 0.9655;
F_26Al[1] = 0.0233;
F_26Al[2] = 0.005;
F_26Al[3] = 0.0062;
// dimensionless
F_14C[0] = 0.83;
F_14C[1] = 0.0691;
F_14C[2] = 0.0809;
F_14C[3] = 0.02;
// dimensionless
F_36Cl[0] = 0.903;
F_36Cl[1] = 0.0447;
F_36Cl[2] = 0.05023;
F_36Cl[3] = 0.0;
}
// this function gets the parameters used to convert elevation to
// pressure
void LSDCRNParameters::load_parameters_for_atmospheric_scaling(string path_to_data)
{
cout.precision(8);
// first load the levels
levels.push_back(1000);
levels.push_back(925);
levels.push_back(850);
levels.push_back(700);
levels.push_back(600);
levels.push_back(500);
levels.push_back(400);
levels.push_back(300);
// the dimensions of the data
int n_levels = 8;
int NRows = 73;
int NCols = 145;
Array2D<double> new_slp(NRows,NCols,0.0);
Array2D<double> new_meant(NRows,NCols,0.0);
// now load the mean sea level pressure
string filename = "NCEP2.bin";
filename = path_to_data+filename;
//cout << "Loading mean sea level, file is: " << endl << filename << endl;
ifstream ifs_data(filename.c_str(), ios::in | ios::binary);
if( ifs_data.fail() )
{
cout << "\nFATAL ERROR: the data file \"" << filename
<< "\" doesn't exist" << endl;
exit(EXIT_FAILURE);
}
double temp;
//cout << "The size of a double is: " << sizeof(temp) << endl;
for (int i=0; i<NCols; ++i)
{
for (int j=0; j<NRows; ++j)
{
ifs_data.read(reinterpret_cast<char*>(&temp), sizeof(temp));
new_slp[j][i] = temp;
//cout << "new_slp["<<j+1<<"]["<<i+1<<"]: " << new_slp[j][i] << endl;
}
}
for (int i=0; i<NCols; ++i)
{
for (int j=0; j<NRows; ++j)
{
ifs_data.read(reinterpret_cast<char*>(&temp), sizeof(temp));
new_meant[j][i] = temp;
//cout << "new_meant100["<<j+1<<"]["<<i+1<<"]: " << new_meant[j][i] << endl;
}
}
// now get the indices
vector<double> temp_lat(NRows,0.0);
for (int i=0; i<NRows; ++i)
{
ifs_data.read(reinterpret_cast<char*>(&temp), sizeof(temp));
temp_lat[i] = temp;
//cout << "Lat["<<i+1<<"]: " << temp_lat[i] << endl;
}
vector<double> temp_long(NCols,0.0);
for (int i=0; i<NCols; ++i)
{
ifs_data.read(reinterpret_cast<char*>(&temp), sizeof(temp));
temp_long[i] = temp;
//cout << "Long["<<i+1<<"]: " << temp_long[i] << endl;
}
ifs_data.close();
// now the data with levels
filename = "NCEP_hgt.bin";
filename = path_to_data+filename;
//cout << "Loading hgt, file is: " << endl << filename << endl;
ifstream ifs_data2(filename.c_str(), ios::in | ios::binary);
if( ifs_data2.fail() )
{
cout << "\nFATAL ERROR: the data file \"" << filename
<< "\" doesn't exist" << endl;
exit(EXIT_FAILURE);
}
// get the gm heights
vector< Array2D<double> > vec_hgt_gm_array;
for (int lvl = 0; lvl < n_levels; lvl++)
{
Array2D<double> current_hgt_array(NRows,NCols,0.0);
for (int i=0; i<NCols; ++i)
{
for (int j=0; j<NRows; ++j)
{
ifs_data2.read(reinterpret_cast<char*>(&temp), sizeof(temp));
current_hgt_array[j][i] = temp;
//cout << "new_slp["<<lvl<<"]["<<j+1<<"]["<<i+1<<"]: " << current_hgt_array[j][i] << endl;
}
}
//cout << "new_slp["<<j+1<<"]["<<i+1<<"]: " << new_slp[j][i] << endl;
vec_hgt_gm_array.push_back(current_hgt_array.copy());
}
// now the gp heights
vector< Array2D<double> > vec_hgt_gp_array;
for (int lvl = 0; lvl < n_levels; lvl++)
{
Array2D<double> current_hgt_array(NRows,NCols,0.0);
for (int i=0; i<NCols; ++i)
{
for (int j=0; j<NRows; ++j)
{
ifs_data2.read(reinterpret_cast<char*>(&temp), sizeof(temp));
current_hgt_array[j][i] = temp;
//cout << "new_slp["<<lvl<<"]["<<j+1<<"]["<<i+1<<"]: " << current_hgt_array[j][i] << endl;
}
}
//cout << "new_slp["<<j+1<<"]["<<i+1<<"]: " << new_slp[j][i] << endl;
vec_hgt_gp_array.push_back(current_hgt_array.copy());
}
ifs_data2.close();
// now update the data elements
NCEPlat = temp_lat;
NCEPlon = temp_long;
meanslp = new_slp.copy();
meant1000 = new_meant.copy();
gp_hgt = vec_hgt_gp_array;
gm_hgt = vec_hgt_gp_array;
//cout << "Size lat: " << NCEPlat.size() << " size long: " << NCEPlon.size() << endl;
//cout << "size slp:" << meanslp.dim1() << " " << meanslp.dim2() << endl;
//cout << "size t1000: " << meant1000.dim1() << " " << meant1000.dim2() << endl;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// This function sets a number of paramters that are used for acalucaltion
// of scaling and error propigation
//
// They are constants used in the CRONUS caluclator, and have been ported
// from make_al_be_consts_v22.m written by Greg Balco
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDCRNParameters::set_CRONUS_data_maps()
{
//cout << "Line 278, creating the CRONUS data maps" << endl;
map<string,double> temp_map;
// 10Be decay: this is specific to the CRONUS calculator
temp_map["l10"] = -log(0.5)/1.387e6; // Chmeleff/Korschinek value
// Al-26 decay constant -- value compatible with Nishiizumi standards
temp_map["l26"] = 9.83e-7;
//cout << "Creating CRONUS data maps, lambda 10: " << temp_map["l10"]
// << " and lambda 26: " << temp_map["l26"] << endl;
// Note that the uncertainty is not used in exposure-age or erosion-rate
// calculators. Here only for development purposes
double dldt = -log(0.5)*(1/(1.387e6*1.387e6));
temp_map["dell10"] = sqrt((dldt*1/(0.012e6*0.012e6)));
temp_map["dell26"] = 2.5e-8;
//Effective attenuation length for spallation in rock
// Commonly accepted value: 160 g/cm2
// For discussion see Gosse and Phillips (2000)
temp_map["Lsp"] = 160.0;
// Fsp - fraction of total production by spallation rather than muons
// For use with Lal/Stone scaling scheme in exposure age calculation
// For details, see Stone (2000)
// This aspect of Stone(2000) is de-emphasized in version 2. These constants
// are only in use for historical comparisons and quick initial guesses for
// the exposure age and erosion rate solvers.
// Note that they are probably incorrect WRT Be-10 restandardization. Don't
// use these for anything important.
temp_map["Fsp10"] = 0.978;
temp_map["Fsp26"] = 0.974;
// Be-10 standardization info.
// Standards comparison/conversion lookup table
temp_map["Be_std_07KNSTD"] = 1.0000;
temp_map["Be_std_KNSTD"] = 0.9042;
temp_map["Be_std_NIST_Certified"] = 1.0425;
temp_map["Be_std_LLNL31000"] = 0.8761;
temp_map["Be_std_LLNL10000"] = 0.9042;
temp_map["Be_std_LLNL3000"] = 0.8644;
temp_map["Be_std_LLNL1000"] = 0.9313;
temp_map["Be_std_LLNL300"] = 0.8562;
temp_map["Be_std_NIST_30000"] = 0.9313;
temp_map["Be_std_NIST_30200"] = 0.9251;
temp_map["Be_std_NIST_30300"] = 0.9221;
temp_map["Be_std_NIST_30600"] = 0.9130;
temp_map["Be_std_NIST_27900"] = 1;
temp_map["Be_std_S555"] = 0.9124;
temp_map["Be_std_S2007"] = 0.9124;
temp_map["Be_std_BEST433"] = 0.9124;
temp_map["Be_std_BEST433N"] = 1;
temp_map["Be_std_S555N"] = 1;
temp_map["Be_std_S2007N"] = 1;;
// Same for Al-26. A zero placeholder is
// also allowed.
temp_map["Al_std_KNSTD"] = 1.0;
temp_map["Al_std_ZAL94"] = 0.9134;
temp_map["Al_std_SMAL11"] = 1.021;
temp_map["Al_std_0"] = 1.0;
temp_map["Al_std_ZAL94N"] = 1.0;
temp_map["Al_std_ASTER"] = 1.021;
temp_map["Al_std_Z92-0222"] = 1;
// Reference production rates at SLHL for spallation according to various
// scaling schemes. Letter codes De, Du, Li, and St refer to
// scaling schemes of Desilets et al. (2006), Dunai (2001), Lifton (2006),
// and Stone (2000) respectively. The final letter code Lm refers to the
// paleomagnetically corrected version of the Lal 1991/Stone 2000 scaling
// factors.
// These reference production rates are derived using the current version of
// get_al_be_age.m.
// Al-26 and Be-10 production rates are linked by the production ratio,
// not determined independently. This is because there are not very
// many geological-calibration sites for Al-26. See the calibration data
// sets and the accompanying paper for more information.
// This reflects the v 2.1 air pressure upgrade.
// Also the update to 07KNSTD in version 2.2.
// Be-10 production rates. Brent's values. Greg agrees.
temp_map["P10_ref_St"] = 4.49;
temp_map["delP10_ref_St"] = 0.39;
temp_map["P10_ref_Lm"] = 4.39;
temp_map["delP10_ref_Lm"] = 0.37;
temp_map["P10_ref_De"] = 4.41;
temp_map["delP10_ref_De"] = 0.52;
temp_map["P10_ref_Du"] = 4.43;
temp_map["delP10_ref_Du"] = 0.52;
temp_map["P10_ref_Li"] = 4.87;
temp_map["delP10_ref_Li"] = 0.48;
// Al-26 production rates are derived from Be-10 production rates
double R2610 = 6.1*1.106; // Update assumed production ratio
temp_map["P26_ref_St"] = temp_map["P10_ref_St"]*R2610;
temp_map["delP26_ref_St"] = temp_map["delP10_ref_St"]*R2610;
temp_map["P26_ref_Lm"] = temp_map["P10_ref_Lm"]*R2610;
temp_map["delP26_ref_Lm"] = temp_map["delP10_ref_Lm"]*R2610;
temp_map["P26_ref_De"] = temp_map["P10_ref_De"]*R2610;
temp_map["delP26_ref_De"] = temp_map["delP10_ref_De"]*R2610;
temp_map["P26_ref_Du"] = temp_map["P10_ref_Du"]*R2610;
temp_map["delP26_ref_Du"] = temp_map["delP10_ref_Du"]*R2610;
temp_map["P26_ref_Li"] = temp_map["P10_ref_Li"]*R2610;
temp_map["delP26_ref_Li"] = temp_map["delP10_ref_Li"]*R2610;
// Muon interaction cross-sections. All follow Heisinger (2002a,b).
// Note that the energy-dependence-of-muon-interaction-cross-section
// exponent alpha is treated as model-dependent -- it's internal to
// P_mu_total.m and can't be passed.
temp_map["Natoms10"] = 2.006e22;
temp_map["Natoms26"] = 1.003e22;
// Be-10 interaction cross-sections
// Restandardized by ETH-07KNSTD factor for version 2.2.1.
temp_map["k_neg10"] = (0.704 * 0.1828 * 0.0043)/1.096;
temp_map["delk_neg10"] = (0.704 * 0.1828 * 0.0003)/1.096;
temp_map["sigma190_10"] = (0.094e-27)/1.096;
temp_map["delsigma190_10"] = (0.013e-27)/1.096;
temp_map["Be10_Natoms_times_sigma190"] = 1.7205e-6;
temp_map["Be10_Natoms_times_delsigma190"] = 2.37938e-7;
temp_map["Be10_Natoms_sigma_modified_for_fast"] = 3.361886e-8;
//cout << "LINE 405, be10 prod: " << temp_map["Be10_Natoms_sigma_modified_for_fast"] << endl;
// Al-26 interaction cross-sections
temp_map["k_neg26"] = 0.296 * 0.6559 * 0.022;
temp_map["delk_neg26"] = 0.296 * 0.6559 * 0.002;
temp_map["sigma190_26"] = 1.41e-27;
temp_map["delsigma190_26"] = 0.17e-27;
temp_map["Al26_Natoms_times_sigma190"] = 1.41423e-5;
temp_map["Al26_Natoms_times_delsigma190"] = 1.7051e-6;
temp_map["Al26_Natoms_sigma_modified_for_fast"] = 2.76347e-8;
// Paleomagnetic records for use in time-dependent production rate schemes
// Derived from Nat Lifton's compilation of paleomagnetic data from
// various sources. See Lifton et al. (2006) and Pigati and Lifton (2005).
// Load the magnetic field data
// load PMag_Mar07
// Relative dipole moment and time vector
// al_be_consts.M = MM0;
// al_be_consts.t_M = t_M;
// These start at 7500 yr -- time slices are 7500,8500,9500,10500,11500
// in order to use data from Yang et al; subsequent time slices are
// 12000:1000:800000 for SINT800 data; final two time points are 801000
// and Inf.
// Cutoff rigidity blocks for past 6900 yr.
// TTRc and IHRC are lon x lat x time blocks of Rc values for the past
// 6900 years.
// Both are derived by Nat Lifton from the magnetic field reconstructions of
// Korte and Constable.
// TTRC has cutoff rigidity obtained by trajectory tracing -- these are for
// the Lifton and Desilets scaling factors. IHRc has cutoff rigidity
// obtained by finding magnetic inclination and horizontal field strength
// from the field model, then applying Equation 2 of Dunai(2001).
// al_be_consts.TTRc = TTRc; % data block
// al_be_consts.IHRc = IHRc; % data block
// al_be_consts.lat_Rc = lat_Rc; % lat and lon indices for Rc data block
// al_be_consts.lon_Rc = lon_Rc;
// al_be_consts.t_Rc = t_Rc; % time vector for Rc data block
// Effective pole positions and field strengths inferred from K and C field
// reconstructions for last 7000 yr. These are used in the
// paleomagnetically-corrected implementation of the Lal SF. They are for
// the same times as the RC slices in the data block above. Again,
// generated by Nat Lifton -- hence KCL = Korte-Constable-Lifton.
// al_be_consts.MM0_KCL = MM0_KCL;
// al_be_consts.lat_pp_KCL = lat_pp_KCL;
// al_be_consts.lon_pp_KCL = lon_pp_KCL;
// Solar variability from Lifton et al. 2005
// Has been averaged and resampled to the same time slices as everything
// else.
// al_be_consts.S = S;
// al_be_consts.SInf = 0.95; % Long-term mean S value;
// set the data member map
CRONUS_data_map = temp_map;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// This function retrieves the Stone production reference values for 10Be and
// 26Al
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
vector<double> LSDCRNParameters::get_Stone_Pref()
{
// first check to see if CRONUS data maps are set
if(CRONUS_data_map.find("l10") == CRONUS_data_map.end())
{
cout << "You haven't set the CRONUS data map. I'm doing that for you now!" << endl;
set_CRONUS_data_maps();
}
vector<double> Stone_pref(2,0.0);
Stone_pref[0] = CRONUS_data_map["P10_ref_St"];
Stone_pref[1] = CRONUS_data_map["P26_ref_St"];
return Stone_pref;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// This function wraps the CRONUS muon production function
// It returns a vector with elements
// Muon_production[0] = 10Be fast
// Muon_production[1] = 26Al fast
// Muon_production[2] = 10Be neg
// Muon_production[3] = 26Al neg
// 14/10/2014
// SMM
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
vector<double> LSDCRNParameters::calculate_muon_production_CRONUS(double z, double h)
{
vector<double> Muon_production(4,0.0);
P_mu_total(z,h);
Muon_production[0] = CRONUS_muon_data["P_fast_10Be"];
Muon_production[1] = CRONUS_muon_data["P_fast_26Al"];
Muon_production[2] = CRONUS_muon_data["P_neg_10Be"];
Muon_production[3] = CRONUS_muon_data["P_neg_26Al"];
return Muon_production;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// This function sets CRONUS muon production paramteters
//
// Calculates the production rate of Al-26 or Be-10 by muons
// as a function of depth below the surface z (g/cm2) and
// site atmospheric pressure h (hPa).
//
// out.phi_vert_slhl muons/cm2/s/sr
// out.R_vert_slhl muons/g/s/sr
// out.R_vert_site muons/g/s/sr
// out.phi_vert_site muons/cm2/s/sr
// out.phi muons/cm2/yr
// out.R muons/g/yr
// out.P_fast atoms/g/yr
// out.P_neg atoms/g/yr
// out.Beta nondimensional
// out.Ebar GeV
// out.H g/cm2
// out.LZ g/cm2
//
// This uses the scheme in Heisinger and others (2002, 2 papers). The
// vertically traveling muon flux is scaled to the site elevation using
// energy-dependent attenuation lengths from Boezio et al. (2000). See the
// hard-copy documentation for detailed citations and a full discussion of
// the calculation.
//
// Note that some constants are internal to the function. The only ones that
// get passed from upstream are the ones that a) are nuclide-specific, or b)
// actually have quoted uncertainties in Heisinger's papers.
// The fraction of muons that are negative is internal; so is the
// energy-dependence exponent alpha.
//
// Original Written by Greg Balco -- UW Cosmogenic Nuclide Lab
// balcs@u.washington.edu
// March, 2006
// Part of the CRONUS-Earth online calculators:
// http://hess.ess.washington.edu/math
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDCRNParameters::P_mu_total(double z,double h)
{
map<string,double> temp_data_map;
//cout << "CHECKING MUON FLUX, Line 504 " << endl;
// first check to see if CRONUS data maps are set
if(CRONUS_data_map.find("l10") == CRONUS_data_map.end())
{
cout << "You haven't set the CRONUS data map. I'm doing that for you now!" << endl;
set_CRONUS_data_maps();
}
// calculator the atmospheric depth in g/cm2
double H = (1013.25 - h)*1.019716;
//cout << "Atmospheric depth is: " << H << " g/cm^2" << endl;
// find the vertical flux at SLHL
double a = 258.5*(pow(100,2.66));
double b = 75*(pow(100,1.66));
// this is equation (1) From Heisinger 2002a and (3) from Heisinger 2002b
double phi_vert_slhl = (a/((z+21000.0)*((pow((z+1000),1.66)) + b)))
*exp(-5.5e-6* z);
// The above expression is only good to 2e5 g/cm2. We don't ever consider production
// below that depth. The full-depth scheme appears in the comments below.
// ------ begin full-depth flux equations -------
//phiz_1 = (a./((z+21000).*(((z+1000).^1.66) + b))).*exp(-5.5e-6 .* z);
//phiz_2 = 1.82e-6.*((121100./z).^2).*exp(-z./121100) + 2.84e-13;
//out(find(z<200000)) = phiz_1(find(z<200000));
//out(find(z>=200000)) = phiz_2(find(z>=200000));
// ------ end full-depth flux equations -------
// find the stopping rate of vertical muons at SLHL
// this is done in a subfunction Rv0, because it gets integrated later.
double R_vert_slhl = Rv0(z);
// find the stopping rate of vertical muons at site
double R_vert_site = R_vert_slhl*exp(H/LZ(z));
//cout << "LZ(" << z << "): " << LZ(z) << endl;
//cout << "R_vert_slhl: " << R_vert_slhl << " R_vert_site: " << R_vert_site << endl;
// find the flux of vertical muons at site
// integrate
// ends at 200,001 g/cm2 to avoid being asked for an zero
// range of integration --
// get integration tolerance -- want relative tolerance around
// 1 part in 10^4.
double tol = phi_vert_slhl*1e-4;
double phi_vert_site = integrate_muon_flux(z, H, tol);
//=====================
// I THINK below here is an error in Balco's code
// The below equation uses a which is calculated above,
// but in balco's code a is then used as an index, so the below
// equation takes the index value rather than the precalculated
// value of a
//=======================
// invariant flux at 2e5 g/cm2 depth - constant of integration
// calculated using commented-out formula above
double phi_200k = (a/((2.0e5+21000.0)*((pow((2.0e5+1000.0),1.66)) + b)))
*exp(-5.5e-6 * 2.0e5);
//double test_balco_error = (1.0/((2.0e5+21000.0)*((pow((2.0e5+1000.0),1.66)) + b)))
// *exp(-5.5e-6 * 2.0e5);
phi_vert_site = phi_vert_site + phi_200k;
// find the total flux of muons at site
// angular distribution exponent
double nofz = 3.21 - 0.297*log((z+H)/100.0 + 42.0) + 1.21e-5*(z+H);
// derivative of same
double dndz = (-0.297/100.0)/((z+H)/100.0 + 42.0) + 1.21e-5;
// caluculate phi in muons/cm2/s
double phi_temp = (phi_vert_site*2* M_PI) / (nofz+1.0);
// convert to muons/cm2/yr
double phi = phi_temp*60.0*60.0*24.0*365.0;
// find the total stopping rate of muons at site in muons/g/s
double R_temp = (2*M_PI/(nofz+1.0))*R_vert_site
- phi_vert_site*(-2*M_PI*(1/((nofz+1.0)*(nofz+1.0))))*dndz;
// convert to negative muons/g/yr
double this_R = R_temp*0.44*60.0*60.0*24.0*365.0;
// Now calculate the production rates.
// Depth-dependent parts of the fast muon reaction cross-section
double Beta = 0.846 - 0.015 * log((z/100.0)+1.0)
+ 0.003139 * (log((z/100.0)+1.0)*log((z/100.0)+1.0));
double Ebar = 7.6 + 321.7*(1 - exp(-8.059e-6*z))
+ 50.7*(1-exp(-5.05e-7*z));
// internally defined constants
double aalpha = 0.75;
double sigma0_Be10 = CRONUS_data_map["sigma190_10"]/(pow(190.0,aalpha));
double sigma0_Al26 = CRONUS_data_map["sigma190_26"]/(pow(190.0,aalpha));
// fast muon production
double P_fast_Be10 = phi*Beta*(pow(Ebar,aalpha))
*sigma0_Be10*CRONUS_data_map["Natoms10"];
double P_fast_Al26 = phi*Beta*(pow(Ebar,aalpha))
*sigma0_Al26*CRONUS_data_map["Natoms26"];
//cout << "Phi: " << phi << " Beta " << Beta << " Ebar: " << Ebar << endl
// << "aalpha: " << aalpha << endl
// << " prod10: " << CRONUS_data_map["Be10_Natoms_sigma_modified_for_fast"] << endl
// << " prod26: " << CRONUS_data_map["Al26_Natoms_sigma_modified_for_fast"] << endl;
//double P2_10Be = phi*Beta*(pow(Ebar,aalpha))*
// CRONUS_data_map["Be10_Natoms_sigma_modified_for_fast"];
//double P2_26Al = phi*Beta*(pow(Ebar,aalpha))*
// CRONUS_data_map["Al26_Natoms_sigma_modified_for_fast"];
//cout << "Pfast10be: " << P_fast_Be10 << " P2: " << P2_10Be << endl;
//cout << "Pfast26Al: " << P_fast_Al26 << " P2: " << P2_26Al << endl;
// negative muon capture
double P_neg_Be10 = this_R*CRONUS_data_map["k_neg10"];
double P_neg_Al26 = this_R*CRONUS_data_map["k_neg26"];
//cout << "Sig0: " << sigma0_Be10 << " Pfast: " << P_fast_Be10 << " P_neg: " << P_neg_Be10 << endl;
temp_data_map["phi_vert_slhl"] = phi_vert_slhl;
temp_data_map["R_vert_slhl"] = R_vert_slhl;
temp_data_map["phi_vert_site"] = phi_vert_site;
temp_data_map["R_vert_site"] = R_vert_site;
temp_data_map["phi"] = phi;
temp_data_map["R"] = this_R;
temp_data_map["Beta"] = Beta;
temp_data_map["Ebar"] = Ebar;
temp_data_map["P_fast_10Be"] = P_fast_Be10;
temp_data_map["P_fast_26Al"] = P_fast_Al26;
temp_data_map["P_neg_10Be"] = P_neg_Be10;
temp_data_map["P_neg_26Al"] = P_neg_Al26;
temp_data_map["H"] = H;
temp_data_map["LZ"] = LZ(z);
CRONUS_muon_data = temp_data_map;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// This function wraps the P_mu_tot function and replaces the 10Be and
// 26Al production rates
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDCRNParameters::P_mu_total_return_nuclides(double z,double h,
double& Be10_total_mu, double& Al26_total_mu)
{
// get the muon roduction
P_mu_total(z,h);
double p10 = CRONUS_muon_data["P_fast_10Be"]+CRONUS_muon_data["P_neg_10Be"];
double p26 = CRONUS_muon_data["P_fast_26Al"]+CRONUS_muon_data["P_neg_26Al"];
Be10_total_mu = p10;
Al26_total_mu = p26;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// this subfunction does the integration of muon sotpping to get the total
// muon flux
//
// NOTE: THIS IS RATE LIMITING
// Will probably need to come back and try to speed up.
// The best way is to retain previously calculated balues, so at new
// node spacings only the intermediate values are recalculated.
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
double LSDCRNParameters::integrate_muon_flux(double z, double H, double tolerance)
{
// we just use a simple simpsons rule but we keep fining the grid until there
// is no difference in the solution
int n_nodes = 101;
double start_z = z;
double end_z = 2.0e5+1.0;
double spacing = (end_z-z)/double(n_nodes-1);
double a,b, intermediate;
double fa,fb,fi,sum, last_sum;
double integral_difference;
// get the inital guess
b = start_z;
fb = Rv0(b)*exp(H/LZ(b));
sum = 0;
for(int i = 1; i< n_nodes; i++)
{
// locations of spacings
a = b;
b = a+spacing;
intermediate = (b+a)/2.0;
//cout << "z["<<i<<"]: " << a << " i+1/2: " << intermediate << " i+1: " << b << endl;
// functions evaluated at spacings
fa = fb;
fi = Rv0(intermediate)*exp(H/LZ(intermediate));
fb = Rv0(b)*exp(H/LZ(b));
sum+= ((b-a)/6.0)*(fa+4.0*fi+fb);
}
last_sum = sum;
//cout << "LINE 660, integrating muon flux, initial guess: " << last_sum << endl;
double log_error_ratio = 0.5;
double node_multiplier;
// now loop until the error tolerance is reached
do
{
// this implements and adaptive spacing between nodes, determined by the
// ratio between the error and the tolerance in an attempt to speed up
// the integration
node_multiplier = 1.0+log_error_ratio;
// increase the density of the nodes
n_nodes = int(double(n_nodes)*node_multiplier);
//cout << "Looping for simpsons, n_nodes: " << n_nodes << endl;
spacing = (end_z-z)/double(n_nodes-1);
//cout << "Nodes: " << n_nodes << " and spacing: " << spacing << endl;
b = start_z;
fb = Rv0(b)*exp(H/LZ(b));
sum = 0;
for(int i = 1; i< n_nodes; i++)
{
// locations of spacings
a = b;
b = a+spacing;
intermediate = (b+a)/2.0;
// functions evaluated at spacings
fa = fb;
fi = Rv0(intermediate)*exp(H/LZ(intermediate));
fb = Rv0(b)*exp(H/LZ(b));
sum+= ((b-a)/6.0)*(fa+4.0*fi+fb);
}
// compare this integral with the last one
integral_difference = fabs(last_sum-sum);
log_error_ratio = log(integral_difference/tolerance);
//cout << "log error_ratio: " << log_error_ratio << endl;
// reset the last sum
last_sum = sum;
//cout << "this sum: " << last_sum << endl;
} while(integral_difference>tolerance);
// now return the integral
return last_sum;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// this subfunction returns the stopping rate of vertically traveling muons
// as a function of depth z at sea level and high latitude.
// Modified from Greg Balco's CRONUS calculator
// z is the depth below the surface in g/cm^2
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
double LSDCRNParameters::Rv0(double z)
{
double a = exp(-5.5e-6*z);
double b = z + 21000.0;
double c = pow((z + 1000.0),1.66) + 1.567e5;
double dadz = -5.5e-6 * exp(-5.5e-6*z);
double dbdz = 1.0;
double dcdz = 1.66*(pow((z + 1000),0.66));
double out = -5.401e7*(b*c*dadz-a*(c*dbdz+b*dcdz))/(b*b*c*c);
return out;
// full depth calculation appears in comments below
// testing indicates this isn't really necessary
//R_1 = -5.401e7 .* (b.*c.*dadz - a.*(c.*dbdz + b.*dcdz))./(b.^2 .* c.^2);
//f = (121100./z).^2;
//g = exp(-z./121100);
//dfdz = (-2.*(121100.^2))./(z.^3);
//dgdz = -exp(-z./121100)./121100;
//R_2 = -1.82e-6.*(g.*dfdz + f.*dgdz);
//out(find(z<200000)) = R_1(find(z<200000));
//out(find(z>=200000)) = R_2(find(z>=200000));
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//
// this subfunction returns the effective atmospheric attenuation length for
// muons of range Z
// z is the depth in g/cm^2
//
// Original by Greg Balco as part of the CRONUS calculator
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
double LSDCRNParameters::LZ(double z)
{
//define range/momentum relation
// table for muons in standard rock in Groom and others 2001
// units are range in g cm-2 (column 2)
//momentum in MeV/c (column 1)
vector<double> data_for_LZ_range;
vector<double> data_for_LZ_momentum;
data_for_LZ_momentum.push_back(4.704e1);
data_for_LZ_range.push_back(8.516e-1);
data_for_LZ_momentum.push_back(5.616e1);
data_for_LZ_range.push_back(1.542e0);
data_for_LZ_momentum.push_back(6.802e1);
data_for_LZ_range.push_back(2.866e0);
data_for_LZ_momentum.push_back(8.509e1);
data_for_LZ_range.push_back(5.698e0);
data_for_LZ_momentum.push_back(1.003e2);
data_for_LZ_range.push_back(9.145e0);
data_for_LZ_momentum.push_back(1.527e2);
data_for_LZ_range.push_back(2.676e1);
data_for_LZ_momentum.push_back(1.764e2);
data_for_LZ_range.push_back(3.696e1);
data_for_LZ_momentum.push_back(2.218e2);
data_for_LZ_range.push_back(5.879e1);
data_for_LZ_momentum.push_back(2.868e2);
data_for_LZ_range.push_back(9.332e1);
data_for_LZ_momentum.push_back(3.917e2);
data_for_LZ_range.push_back(1.524e2);
data_for_LZ_momentum.push_back(0.945e2);
data_for_LZ_range.push_back(2.115e2);
data_for_LZ_momentum.push_back(8.995e2);
data_for_LZ_range.push_back(4.418e2);
data_for_LZ_momentum.push_back(1.101e3);
data_for_LZ_range.push_back(5.534e2);
data_for_LZ_momentum.push_back(1.502e3);
data_for_LZ_range.push_back(7.712e2);
data_for_LZ_momentum.push_back(2.103e3);
data_for_LZ_range.push_back(1.088e3);
data_for_LZ_momentum.push_back(3.104e3);
data_for_LZ_range.push_back(1.599e3);
data_for_LZ_momentum.push_back(4.104e3);
data_for_LZ_range.push_back(2.095e3);
data_for_LZ_momentum.push_back(8.105e3);
data_for_LZ_range.push_back(3.998e3);
data_for_LZ_momentum.push_back(1.011e4);
data_for_LZ_range.push_back(4.920e3);
data_for_LZ_momentum.push_back(1.411e4);
data_for_LZ_range.push_back(6.724e3);
data_for_LZ_momentum.push_back(2.011e4);
data_for_LZ_range.push_back(9.360e3);
data_for_LZ_momentum.push_back(3.011e4);
data_for_LZ_range.push_back(1.362e4);
data_for_LZ_momentum.push_back(4.011e4);
data_for_LZ_range.push_back(1.776e4);
data_for_LZ_momentum.push_back(8.011e4);
data_for_LZ_range.push_back(3.343e4);
data_for_LZ_momentum.push_back(1.001e5);
data_for_LZ_range.push_back(4.084e4);
data_for_LZ_momentum.push_back(1.401e5);
data_for_LZ_range.push_back(5.495e4);
data_for_LZ_momentum.push_back(2.001e5);
data_for_LZ_range.push_back(7.459e4);
data_for_LZ_momentum.push_back(3.001e5);
data_for_LZ_range.push_back(1.040e5);
data_for_LZ_momentum.push_back(4.001e5);
data_for_LZ_range.push_back(1.302e5);
data_for_LZ_momentum.push_back(8.001e5);
data_for_LZ_range.push_back(2.129e5);
// deal with zero situation
if(z < 1)
{
z = 1.0;
}
double log_z = log(z);
//cout << "z is:" << z << " and log z is: " << log_z << endl;
// obtain momenta
// use log-linear interpolation
int n_momentum_dpoints = int(data_for_LZ_momentum.size());
vector<double> log_momentum;
vector<double> log_range;
for(int i = 0; i<n_momentum_dpoints; i++)
{
log_momentum.push_back(log(data_for_LZ_momentum[i]));
log_range.push_back(log(data_for_LZ_range[i]));
//cout << "Momentum: " << log_momentum[i] << " range: " << log_range[i] << endl;
}
double P_MeVc = exp(interp1D_ordered(log_range,log_momentum,log_z));
//cout << "log_z: " << log_z << " interp: "
// << interp1D_ordered(log_range,log_momentum,log_z) << " P_MeVc: " << P_MeVc << endl;
// obtain attenuation lengths
double out = 263.0 + 150*(P_MeVc/1000.0);
return out;
}
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
// This sets the parameters to those used by Granger and Smith 2000
//=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
void LSDCRNParameters::set_Granger_parameters()
{
//S_t = 1;
// from Vermeesh 2007
// 10Be from Chmeleff/Korschinek 10Be decay constant;
lambda_10Be = 500e-9; // in yr-1
lambda_26Al = 980e-9; // in yr-1
lambda_14C = 121e-6; // in yr-1
lambda_36Cl = 230e-8; // in yr-1
// from Vermeesh 2007
// These are calibrated to the Stone scaling
// Also linke to the nishizumii standards
// These come with Cosmocalc version 2.0
// http://www.ucl.ac.uk/~ucfbpve/cosmocalc/updates.html
P0_10Be = 4.30; // in a/g/yr
P0_26Al = 31.10; // in a/g/yr
P0_14C = 15.21; // in a/g/yr
P0_36Cl = 58.95; // in a/g/yr
P0_21Ne = 18.23; // in a/g/yr
P0_3He = 121.59; // in a/g/yr
// in g/cm^2
Gamma[0] = 160;
Gamma[1] = 738.6;
Gamma[2] = 2688;
Gamma[3] = 4360;