Variable

Identification

a

Filtered gridcell temperatures (page 17)

AA

Working matrix used for SVD on several occasions (page 16 for proxies; page 18-19 for weighted TPCs); page 19 set equal to beta: dim= mkeep x nfilter).

aint

Dummy on page 3 (nmax0xmaxproxy]

Reconstructed temperature matrix (page 21)

alon1, alon2, alat1, alat2

0, 360, -90,90 (page 4). Parameters for gridcell subdomain

anew

Matrix: Annual/seasonal average of TPCs from monthly calculation – page 11;

Mean (dateave) then removed on page 13;

Divide by standard deviation (sd) on bottom of page 13.

annmean

calibration mean of gridcell annual average (annual) (p12)

annual

gridcell annual average in calibration period (from anom; sigma) [check] (p 12)

anom

Gridcell temperature data

anom0

Matrix (page 26(

aprox

Matrix of proxy time series (read in on page 14); mean subtraced and then divided by standard deviation (page 14)

aver0

Dummy on page 3 – nmax0 x maxproxy

Set equal to anom0-nean (page 27)

b0

Time series of weighted average of proxies (page 18); fresh calculation on page 19 for time seires of weighted average of proxies

beta

Matrix of coefficients (dim nproxy x neofs) (page 19)

corrglob, corrnhem

Page 30

corrgp

Vector of length iabv – page 29

dateave

TPCs with calibratin mean removed (page 12)

flnm

Vector of file names for individual proxy time series

globc

Calculated from aint – page 28. an average

globv

Calculated from aver0 – page 28. an average

iabv

=ispat (# of time series) - 1082

ifilter

.ne.2 – train with first eofs; 1 – use specified subset of eofs; 2 – use rule N criterion applied to proxies (set at 0 – page 4)

igood

Logical vector to select gridcell subdomain. Seems to be selector for 1082 gridcells

ikeep

Index for proxy in step [check] page 19

imonte

1 – compute bootstrap confidence intervals

index0

Page 27

ioption

1 – go to 1111; 2- 2222; 3- 3333; 4 – 4444; 5 – 5555

ipc

40 (page 4)

ipcmax

40

iproxy

input manually from prompt. Following options 

      0 - all proxies + long histor data'
      1 - proxy data only'
      2 - long histor data only' 

iseason

0 – all seasons; 1 – cold season; 2 – warm season (base case 0 – page 4)

iset

"records to be used" given that earliest proxy sampling year is nlow. Input manually from prompt. This enables the quirky selections attested in SI.  Following options:

0 -  fixed set dating back to specified year

1 -  all available for any given year

ispat

# of gridcells in a selected subdomain (p. 8)

istart

First year of proxy record

iteofs

0 (page 4)

itermax

1000

itrainmin0; itrainmax0

Calibration (“training”) period

itype

0 (page 4)

iunif

weights on proxies:    0 - pre-specified  ;  1 - uniform

iverif

0 – use verification periods specified above; 1 - ?

ivermin; ivermax

1854, 1901

iwhich

1:neofs (page 4)

iwhich

Index of RPCs to retain

iy0

= iyearmax-nlow+1 (page 28)

iyearmax; iyearmin

1993, 1902

iymax

= ivermax-nlow+1 (page 28)

iymin

 = ivermin-nlow+1 (page 28)

m0

Number of retained proxies (page 16)

max0

Mmax+20 (1102)

maxlong

240

maxmonth

1680

maxproxy

450

maxstat

1082. # of gridcells

mean

Vector of gridcell means (anom) – page

mkeep

#of retained proxies in step (page 14; also page 19)

mmax

=maxstat (1082)

n0

79 (page 16)

neofmax

40 (=ipc) page 17

neofs

keep first how many pcs for training (1<pcs< min(ipc,maxproxy)
      	-1 for automatic rule N application. Then set ifilter = 2;  neofs = ipc
       	0 for specified subset. SEt ifilter = 1. 

		Then keep first how many pcs for training (1<pcs<min(ipc,maxproxy))
       	read (5,*) neofs. Then manually input eif #s until done. 

	nfilter is number of eofs. 

	iwhich[i] is item #

	k>=1 use eofs 1,...k  

	nfilter is set equal to neofs in method

nfilter`

=neofs (10) (page 4); calculated in 2222 loop (page 4)

nhigh

1980 (page 4?]

nkeep

Time series of # of retained proxies (page 19)

nlarge

8000

nlow

500 [page 4?] this seems strange

nmax0

1500

nmax1

1104

nmax2

150

nome

Vector of proxy identifications (read in page 14 from multiproxy.dat)

np1

60 (page 16) - used in pseudo-Preisendorfer method to determine how many RPCs

np2

40 (page 16)

np3

M0/2 (page 16) – half the number of proxiesi n step

nproxy

number of retained proxies in a step (page 14)

nretain

Number of retained PCs (page 16) from decomposition of proxies

ntotal

40 (=ipc ,page 17)

ntrain

1980-1902+1=79; length of calibration period

ntrnmax

80

pccalib

Rescaled RPCs (page 20)

proxave

Average of proxy in calbration period (aprox)

rpc

Reconstructed pc (page 20)

rpckeep

Retained RPCs (page 20)

S

Working eigenvalues from decomposition Used on several occasions: monthly gridcell temperatures (set to S0); proxies (page 16)

S0

Page 10 – eigenvalues from gridcell PC decomposition (monthly)

sd

Standard deviation of temperature PCs (page 12)

sdprox

Detrended standard deviation of aprox

sigma

Standard deviations from monthly gridcells in calibration period (anom)(page 9)

sigma0

Detrended standard deviation of annualized gridcell temperatures (page 12)

SS

Eigenvalues from SVD on weighted TPCs (page 19)

standard

From anom- page 9; ???

Standardized temperature PCs (page 12)

tpc

Reflated TPCs (page 17)

uu

Left matrix from svd on weighted TPCs (page 19)

varcalgp

Vector of length iabv -Page 29

varclaglob, varcalnhem

Page 30

varrawgp0

Vector of length iabv Page 29

varverglob, varvernhem

Page 30

weight

Vector of Cos(latitude) – page 9

weight0

Vector of proportion of TPC eigenvalues to sum of retained TPC eigenvalues (page 18)

weightprx

Vector of proxy weights (read in page 14 from multiproxy.dat)

work0

Working vector only. Vector of length nfilter. B0 *  UU* *diag(SS)     (1xn) * (nxp) * (pxp).  

Used again in matrix calclation on page 20

x0

VV*work0  (p x p) * (p x 1) (page 19)

Used again in matrix calclation on page 20