post-processing of GEOCARBSULFvolc simulation results

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c program gcsv_ppdf.f

c 5/30/10 JJP

c f77 -o /Users/jjpark/bin/gcsv_ppdf gcsv_ppdf.f

c program to read variance reduction matrices for gcsfdata_export/search

c reads relative variance residual for CO2-proxy datafit to ndat*10000

c geocarb model runs

GEOCARBSULFvolc carbon-cycle simulation code

Google Drive JParkCodes folder gcsv10_export.f

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c program gcsv10_export.f

c fortran version of bob berner's GEOCARBSULF BASIC code

c gcsv10 stands for GeoCarbSulfVolc algorithm for 2010

c THIS CODE CAN READ EITHER THE 2006/7 proxy-CO2 data file

c OR THE 2010 DATA FILE.

c 8/17/2010 -- confirmed the VNV parameter as 4, though Berner asked for 5,

c as motivated by Aaron Taylors thesis -- but other Taylor source is vnv=3

c this code developed in MacOS 10.4, using gcc compiler,

c takes 90minutes to run on a 2006-vintage Macbook Pro with 2 GHz Intel Core Duo processor

c takes 45minutes to run on a 2009-vintage Macbook Pro with 2.53 GHz Intel Core 2 Duo processor

c -- looped over range of input parameters, set up to fit proxy data for CO2 ppm

c 11/22/06 JJP

c proxy data has uncertainties that are sometimes large. To make the data-fitting robust,

c compute chi-squared using an uncertainty in the log-domain.

c xf77 -o /Users/jjpark/bin/gcsv10_export gcsv10_export.f /Users/jjpark/Plotxy/plotlib.a

c

c code uses plotit, a standalone fortran/C plotting subroutine in Xwindows

c this code can be found on JPark's website http://earth.geology.yale.edu/~jjpark/Code/plotit.tar

c instructions for PLOTIT at http://earth.geology.yale.edu/~jjpark/Code/plotit.html

c

c code updated from the code used for the paper

c

c Royer, D. L., Berner, R. A., and Park, J., 2007, Climate sensitivity constrained by carbon

c dioxide concentrations over the last 420 million years: Nature, v.446, p.530-532.

c

c and used for this paper

c

c Park, J., and D. L. Royer, Geologic constraints on the glacial amplification of Phanerozoic

c climate sensitivity, American J. Science, V.311, 2011, P. 1-26, DOI 10.2475/01.2011.01

c

c there are many test computations in Park and Royer (2011) that were effected

c with modified versions of this gcsv10_export.f code

c

c Output of this code is written to two files

c outoutout.dat is a simple table of CO2proxy data values averaged in 10My intervals

c out_gcsv10.dat is a large ASCII file (>50 Mb) that contains the GEOCARB carbon-cycle simulations

c for all parameter choices. This allows the user to examine the statistical behavior of the

c carbon-cycle simulations offline this code (e.g. in gcsv_ppdf.f)

c

c code converted from BASIC to run grid search over parameters

c Newton-Raphson damping applied here, to avoid NaN.

c divergent transition over 380-350My is interpolated better,

c correcting earlier convergence error

c the code reads a file proxydata.txt that contains proxy CO2 PPM data

c the GEOCARBSULF carbon-cycle model is computed at time steps of 1-My from 570Ma to present

c the proxy data ranges only from 420Ma to the present

c

c Five nested loops comprise the heart of the code, from outermost to innermost

c DeltaT = temp increase with CO2 doubling

c ACT = dimensionless activation-energy for silicate weathering

c FERT = plant CO2-fertilization coefficient

c LIFE = liverwort-based weathering factor -- less than vascular plants

c GYM = gymnosperm-based weathering factor (1=angiosperm weathering parameter)

c gymnosperms (e.g. conifers) might be better at weathering than angiosperms

c

c for each choice of parameters, we compute the carbon flux balance between terms

c that depend on silicate weathering (fBBS) and carbon burial/degassing (fB),

c each normalized with common factors derived by Bob Berner many years ago

c The carbon-cycle balance depends on CO2 level,

c because the weathering of silicates accelerates with warmer temps induced by greenhouse gases

c

c the code solves for the CO2 level that achieves the balance of carbon fluxes

c The CO2-dependent parameter fB is calculated at each time step from carbon and

c carbon isotope mass balance and values of all other parameters, based on

c geological and biological data, that affect the carbon cycle. Then the value of

c RCO2 (CO2 concentration normalized to the mean value for the past 1 million

c years = 250 ppm) is calculated by inversion from a complex expression for fB based on the

c greenhouse effect, CO2 fertilization of plant weathering, solar evolution, and

c changes in land temperature).

c

c for detailed exposition of the theoretical GEOCARB models, see

c

c Berner, R. A., The Phanerozoic Carbon Cycle: CO2 and O2, 150pp. Oxford University Press, 2004.

c

c and a collection of GEOCARB and GEOCARBSULF papers published over the past decade by

c Berner and Colleagues.

c

c Berner, R. A., 2006a, GEOCARBSULF: A combined model for Phanerozoic atmospheric O2 and CO2:

c Geochimica et Cosmochimica Acta, v.70, p.5653-5664.

c

c Berner, R. A., 2006b, Inclusion of the weathering of volcanic rocks in the GEOCARBSULF model:

c American Journal of Science, v.306, p.295-302, doi:10.2475/052006.01.

c

c Berner, R. A., 2008, Addendum to Inclusion of the weathering of volcanic rocks in the

c GEOCARBSULF model (Berner, R. A., 2006, v.306, p.295-302) American Journal of Science,

c v.308, p.100-103, doi:10.2475/01.2008.04.

c

c Berner, R. A., 2009, Phanerozoic atmospheric oxygen: New results using the GEOCARBSULF Model:

c American Journal of Science, v.309, p.603-606, doi:10.2475/07.2009.03.

c

c The code computes the aggregate data fit of GEOCARBSULF for each choice

c of the combined parameters, expressed as the fractional variance residual when expressed

c in the log domain without uncertainty weighting.

c description of the proxy data can be found in

c

c Royer et al, CO2 as a primary driver of Phanerozoic climate, GSA Today, March 2004.

c

Reminder for the Fortran plotting subroutine PLOTIT

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plotit.tar

information README at

plotit.html

Disclaimer and Free Software Statement

The computer codes that I post to the JParkCodes blog are provided as free software.

You can redistribute the codes and/or modify them under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 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 may obtain a copy of the GNU General Public License

along with these program at the link above. If not active, see http://www.gnu.org/licenses/.

grn_propzon.f -- code to compute greensfunctions for zonally-symmetric earth models.

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c program grn_propzon -- three-component gfcts
c for zonally-symmetric earth models
c f77 -o /Users/jjpark/bin/grn_propzon grn_propzon.f /Users/jjpark/Ritz/jlib.a
c xf77 -o /Users/jjpark/bin/grn_propzon grn_propzon.f /Users/jjpark/Plotxy/plotlib.a /Users/jjpark/Ritz/jlib.a
c the code reads a special compressed hybrid eigenvector file
c produced by program propzon.
c This routine does a coupling calculation in frequency intervals, storing all
c hybrid singlets in a central interval of the coupling bandwidth.
c the trick is to read the coupling partners for each block, calculate
c receiver and source scalars, then read the eigenvectors one by one.

As with the spherical-earth greensfunction code, this code creates waveforms for a source-receiver geometry stored in the SAC header of a common seismic data file. Unlike the sph-earth code, the output is tied to geographic coordinates (east/north), not radial/transverse. The code syndat.f takes the greensfunctions and sums with a source mechanism to form synthetic seismograms.

sample input:

0 --> # of point to compute, 0=same number as in the data file
ffc.lhz --> data file for source-receiver-station info
gzB0.05_ffc --> filename root for greenfct files, code will append ".lhz" ".lhe" ".lhn"
../Vary/ymodel10_B0.05.zon20 --> input file of hybrid singlets, computed with zonchn.f
/Users/jjpark/Mineos/Models/premiss --> earth model (isotropic PREM in this case)
/Users/jjpark/Mineos/sphnl --> N,L file of spheroidal mode parameters
/Users/jjpark/Mineos/sphe --> direct-access Fortran file of spheroidal modal eigenfunctions
/Users/jjpark/Mineos/tornl --> N,L file of toroidal mode parameters
/Users/jjpark/Mineos/tore --> direct-access Fortran file of toroidal modal eigenfunctions
stop

zonsubs.f -- the subroutines needed to make zonchn.f work

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This set of subroutines serves zonchn.f, see the earlier post. The first routine yread reads the parameters of the zonally symmetric model example file here

1 1 ! useless parameters for option I never implemented
0.0 0.05 0.0 0.0 0.0 A,B,C,D,E relative perts to the Backus anisotropy parameters for azim anisotropy with an axis of symmetry.
1 152 181 ! lithosphere in model premiss
10 ! k=10 wavenumber on the sphere

Some relevant passages of code are the following:

c angint is original theta integral for cos{(l+1/2)\theta} structure
c angint2 uses 3-j tricks to speed up the calculation
c angint2X uses 3-j tricks, but for either spherical cap or equatorial band
c angint2XX is s=20 expansion of equatorial band model, no discontinuites
c call angint2(l1,l2,ls(kii),angi)
call angint2X(l1,l2,ls(kii),angi)
c call angint2XX(l1,l2,ls(kii),angi)


c combine isotropic and anisotropic parts, use b,c,e & a,d
c **************************** note that code can incorporate only
c ***************************** one aspherical wavenumber, despite
c ***************************** the do loops
c NOTE: some lines have alternate versions for phi and theta as axis of sym
if(ick.eq.3) then ! tor-tor
do j=1,nom
coup(j)=coup(j)
x +angi(3,j)*(c*ysc(1,1)+e*ysc(2,1)) ! anisotropic
c x -angi(5,j)*e*ysc(3,1)-angi(6,j)*c*ysc(1,1) ! anisotropic-phi
x +angi(5,j)*e*ysc(3,1)-angi(6,j)*c*ysc(1,1) ! anisotropic-theta
x +angi(2,j)*d*ysc(3,1)+angi(3,j)*d*ysc(2,1) ! isotropic
end do

comment or uncomment the phi and theta terms as you wish, but dont comment both or uncomment both.

zonchn.f -- code to couple free oscillations for a zonally symmetric earth model

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zonchn.f is a code to couple together free oscillations of Earth for a set of highly restricted aspherical earth models. The models are zonally symmetric, dependent only on co-latitude. The code has subroutines that integrate the modes against two types of models (1) a model that depends on a single wavenumber k, and (2) a model that is an equatorial band or a symmetric spherical cap. The first model type was used to examine the wavenumber behavior of surface-wave coupling, and the second type simulates the interaction of surface waves with a sharp boundary. The paper that describes the code's workings is

Park, J., The sensitivity of seismic free oscillations to upper mantle anisotropy I. Zonal symmetry, J. Geophys. Res., v98, 19933-19949, 1993.

Zonal symmetry in the model allows the coupling to vanish for all free-oscillation singlets with differing azimuthal numbers m, m'. In this manner, if there are two modes nSl and n'Sl' with a total of 2l'+1+2l+1 = 2(l+l'+1) singlets, the coupling problem splits apart into (for l'>l) 2l+1 2x2 coupling matrices, and l'-l uncoupled singlets. As a result of this symmetry, zonchn can readily accept a large number of modes in a narrow frequency band without breaking the computer memory or the CPU. The general scheme is to march up in frequency in steps of df and Df: All modes in a half-bandwidth Df about some fiducial frequency fo are coupled, but only those hybrid modes in a narrower bandwidth df about fo are saved. The code increases fo by 2*df and iterates up to some cutoff frequency. The user specifies how many overtones n are included. The uploaded version of zonchn.f has been tested with 0.2.le.f.le.20 mHz and df=0.1 mHz, Df=0.5 mHz and n-max=5.

The code depends on a set of subroutines in the file zonsubs.f, which are posted next in this blog.

The code reads from an input file "phzonchn" that contains

print *,'open(15,file=phzonchn,form=formatted)'
open(15,file='phzonchn',form='formatted')
call yread
print *,'output chain file '
read(15,102)namchn
print *,namchn
102 format(80a)
print *,'initial open of output file in append mode (0=no) '
read(15,*) iappend
print *,'iappend= ',iappend
print *,'enter inner freq halfwidth, outer freq halfwidth (mHz)'
c outer band is modes that couple, inner band contains modes that are saved
read(15,*) hfin,hfout
print *,hfin,hfout
print *,'enter freq band for hybrid modes (mHz)'
read(15,*) fb1,fb2
print *,fb1,fb2
fb1=dmax1(fb1,0.25d0)
print *,'enter max overtone branch to consider'
read(15,*) nbrmax

The option of writing the output file in "append" mode is an artifact of slow computers of the 1990s, in which one might need to stop and restart a long computation. I doubt that the user will need this option in 2009, though my test calculation required the greater part of an hour to complete.

example for phzonchn:

ymodel10_B0.05 --> aspherical model file
ymodel10_B0.05.zon20 --> output file of hybrid modes (linear comb of sph-earth modes, new frequencies)
0 --> dont open output file in append mode (usual case)
0.1 0.5 --> inner band contains modes that are saved, outer band is modes that couple (mHz)
0.2 20 --> frequency band to compute (mHz)
5 --> max number of overtones
/Users/jjpark/Mineos/Models/premiss --> earth model (isotropic PREM in this case)
/Users/jjpark/Mineos/sphnl --> N,L file of spheroidal mode parameters
/Users/jjpark/Mineos/sphe --> direct-access Fortran file of spheroidal modal eigenfunctions
/Users/jjpark/Mineos/tornl --> N,L file of toroidal mode parameters
/Users/jjpark/Mineos/tore --> direct-access Fortran file of toroidal modal eigenfunctions


The model file is based on the A,B,C,D,E Backus parameterization of hexagonally-symmetric anisotropy. A and D are isotropic P and S wavespeed perturbations (peak2peak variation: A=0.05 implies 5%). B is the 2\phi azimuthal Vp term, C is the 4\phi azimuthal Vp term, and E is the 2\phi azimuthal Vs term. The input, as explained in the post for zonsubs.f iare the values of the ABCDE and the wavenumber k of a corrugation in colatitude. The code does not allow the user to choose the equatorial band model on input. You must change a subroutine call and recompile the code. I may fix this soon, as it is cumbersome. Similarly, there is a slight alteration in the coupling formulas that switches the cases for an anisotropic symmetry axis w-hat aligned with theta-hat, or with phi-hat, that is, with colatitude and longitude, respectively. Due to symmetry restrictions, only w-hat parallel to theta-hat or phi-hat is allowed by this code. No tilted axes of symmetry, no general azimuthal angle.