pi_pdf_uncertainty.py

import canesm_LE_general as leg
import pandas as pd
import loadCanESM2data as lcd
import cccmautils as cutl
import loadmodeldata as lmd
import loadLE as le
import cccmacmaps as ccm
import matplotlib.lines as mlines
import collections as coll
import constants as con


printtofile=True
local=True
nresamp=1000 # number of times to resample PI (50-members each time)
doscatter=True

#fieldr='sic'; ncfieldr='sic'; compr='OImon'; 
##regionr='nh'; rstr='NH SIC'; rstrlong='Northern Hem SIC'; runits='%'; rkey='nhsic'
#regionr='bksmori'; rstr='BKS SIC'; rstrlong='Barents/Kara SIC'; runits='%'; rkey='bkssic'
#convr=1
#aconvr=100 # for agcm sims
#ylev=0.3 # for mean dots

#fieldr='sia'; ncfieldr='sianh'; compr='OImon'; 
#regionr='nh'; rstr='NH SIA'; rstrlong='Northern Hem SIA'; runits='m$^2$'; rkey='nhsia'
#convr=1
#aconvr=1 # for agcm sims
#ylev=0.3 # for mean dots

#fieldr='tas'; ncfieldr='tas'; compr='Amon'; 
#regionr='eurasiamori'; rstr='Eur SAT'; rstrlong='Eurasian SAT'; runits='$^\circ$C'; rkey='eursat'
#regionr='eurasiathicke'; rstr='EEur SAT'; rstrlong='East Eurasian SAT'; runits='$^\circ$C'; rkey='eeursat'
#convr=1
#aconvr=1 # for agcm sims
#ylev=0.3 # for mean dots

fieldr='zg50000.00'; ncfieldr='zg'; compr='Amon'; 
regionr='gt60n'; rstr='POL Z500'; rstrlong='Polar Z500'; runits='m'; rkey='gt60nz500'
#regionr='bksmori'; rstr='BKS Z500'; rstrlong='Barents/Kara Z500'; runits='m'; rkey='bksz500'
convr=1
aconvr=1/con.get_g() # for agcm sims
ylev=0.005 # for mean dots in pdf fig


#fieldr2='zg50000.00'; ncfieldr2='zg'; compr2='Amon'; 
#regionr2='bksmori'; rstr2='BKS Z500'; rstr2long='Barents/Kara Z500'; runits2='m'; rkey2='bksz500'
#convr2=1
#aconvr2=1/con.get_g() # for agcm sims
#ylev=0.005 # for mean dots in pdf fig


fieldr2='tas'; ncfieldr2='tas'; compr2='Amon'; 
regionr2='eurasiamori'; rstr2='Eur SAT'; rstr2long='Eurasian SAT'; runits2='$^\circ$C'; rkey2='eursat'
convr2=1
aconvr2=1 # for agcm sims
sear2='DJF'

sear='DJF'
timeselc='1979-01-01,1989-12-31'
timeselp='2002-01-01,2012-12-31'

lecol='red'
ocol='green'
picol = '0.8'
acol=ccm.get_linecolor('paperblue')

when='14:51:28.762886'; styearsR = [ 8.,  7.,  2.,  8.,  8.] # variable SIC styears
styearsE=[ 4.,  1.,  7.,  3.,  1.]; styearsN=[1.] #when for these: 17:01:16.908687


def load_pifield(fdict,seas,conv=1,subsampyrs=11,numsamp=50,
                 styear=None,anomyears=None,local=False,detrend=True,
                 verb=False,addcyc=False):
    """ TAKEN FROM load_canesmfield() in canesm_LE_composite.py

        loads subsampled CGCM data from specified simulation 
             (assumes a long control, e.g. piControl)

             number of total chunks will be determined by length of sim data
                      and numyrs (ntime / numyrs). First the simulation is chunked into
                      numyrs segments. Then 2 segments at a time are randomly chosen
                      (at least a decade apart) to generate anomalies. This is done 
                      numsamp times (e.g. 50)

              returns subsamp  (subsampled anomalies)
                      styears  (start index of chunking of long run)
                      anomyears (indices of anomaly differences)
    """
    casename='piControl'

    pidat = lcd.load_data(fdict,casename,local=local,conv=conv,verb=verb)
    piseadat = cutl.seasonalize_monthlyts(pidat,season=seas)

    if detrend:
        piseadat = cutl.detrend(piseadat,axis=0)

    # the data must be seasonalized before using this func.
    pisea,styear,anomyears = leg.subsamp_anom_pi(piseadat, numyrs=subsampyrs,numsamp=numsamp,
                                                 styear=styear,anomyears=anomyears)
    if addcyc:
        st=pisea[...,-1]
        pisea=np.dstack((pisea,st[...,None]))

    return pisea,styear,anomyears


def load_agcmfield(field,sims,seas,conv=1,region=None,subsampyrs=11,styears=None):
    """  TAKEN FROM load_agcmfield() in canesm_LE_composite.py

        loads subsampled agcm data from specified simulations

              number of total samples will be determined by length of all sim data
                      and numyrs (e.g. (ntime / numyrs)*numsims)

              returns subsamp
                      styears
    """
    threed=False

    simconv=conv
    if field=='tas': simfield='st'; simncfield='ST'
    elif field=='zg50000.00': simfield='gz50000'; simncfield='PHI'; simconv=1/con.get_g()
    elif field=='sia': simfield='sicn'; simncfield='SICN'; print '@@ danger, sia actually sicn average'
    elif field=='sic': simfield='sicn'; simncfield='SICN'
    elif field=='turb': simfield='turb'; simncfield='turb'; # the sim var names are placeholders
    else: print 'cannot addsims for ' + field

    
    if region!=None:
        simflddf = pd.DataFrame(lmd.loaddata((simfield,),sims,ncfields=(simncfield,), timefreq=seas, 
                                             region=region))*simconv
    else:
        # assume threed b/c no region given.
        threed=True
        simflddf = lmd.loaddata((simfield,),sims,ncfields=(simncfield,), timefreq=seas, 
                                region=region,rettype='ndarray')*simconv


    subsamp,styearsss = leg.subsamp_sims(simflddf,numyrs=subsampyrs,styears=styears,threed=threed)

    return subsamp,styearsss


def load_field(fdict,casename,timesel,seas,ftype='fullts',conv=1,local=False,verb=False):
    
    """ TAKEN FROM load_field() in canesm_le_composite.py

        returns [numens x space.flat] or [numens]

    """

    ledat = le.load_LEdata(fdict,casename,timesel=timesel, 
                           rettype='ndarray',conv=conv,ftype=ftype,local=local,verb=verb)

    # time needs to be first dimension
    try:
        if ledat.ndim==2:
            ledat = ledat.T
        elif ledat.ndim==3:
            ledat = np.transpose(ledat,(1,0,2))
        else:
            print 'Loaded data is not 2 or 3 dimensions. Do not understand.'
            raise Exception
    except:
        raise

    lesea = cutl.seasonalize_monthlyts(ledat,season=seas).mean(axis=0)  # numens x space.flat

    return lesea


def calc_pdf(dat, cisiglevel=0.05):

    pipdf_fitted,pimean,pisd,pixx = cutl.calc_normfit(dat)
    pidof = len(dat)-1
    pistder = pisd / np.sqrt(pidof+1)
    pici = sp.stats.t.interval(1-cisiglevel, pidof, loc=pimean, scale=pistder)
    picif = sp.stats.t.interval(1-cisiglevel, pidof, loc=pimean, scale=pisd)

    return pipdf_fitted, pimean, pixx


def test_significance(dat1, dat2, siglevel=0.05,verb=False):

    tstat, pval = sp.stats.ttest_ind(dat1,dat2)
    lstat, lpval = sp.stats.levene(dat1,dat2)
    if verb:
        print '  Mean1: ' + str(dat1.mean()) + ', Mean2: ' + str(dat2.mean())
        print '  TSTAT: ' + str(tstat) + ' PVAL: ' + str(pval)
        if pval<=siglevel:
             print '   The ensemble means are significantly different (' + str(1-siglevel) + ')'
        print '  LSTAT: ' + str(lstat) + ' PVAL: ' + str(lpval)
        if lpval<=siglevel:
             print '   The ensemble variances are significantly different (' + str(1-siglevel) + ')'

    return pval, lpval


# ########### Processing #############
fdictr = {'field': fieldr+regionr, 'ncfield': ncfieldr, 'comp': compr}
fdictr2 = {'field': fieldr2+regionr2, 'ncfield': ncfieldr2, 'comp': compr2}

piseardt={}; styeardt={}; anomyearsdt={}
pipdfdt={}; pimeandt={}; pixxdt={}
pisear2dt={}; slopedt={}; rvaldt={}; pvaldt={};sterrdt={}; yintdt={} 
for ii in range(0,nresamp):

    pisear,styear,anomyears = load_pifield(fdictr,sear,conv=convr,
                                           local=local,addcyc=False)
    piseardt[ii] = pisear
    styeardt[ii] = styear
    anomyearsdt[ii] = anomyears

    pipdf, pimean, pixx = calc_pdf(pisear)

    pipdfdt[ii] = pipdf
    pimeandt[ii] = pimean
    pixxdt[ii] = pixx

    # if scatter, do second field
    if doscatter:
        pisear2,styear,anomyears = load_pifield(fdictr2,sear2,conv=convr2,
                                                styear=styear,anomyears=anomyears,
                                                local=local,addcyc=False)
        pisear2dt[ii] = pisear2
        # scatter vals
        smm, sbb, srval, spval, sstd_err = sp.stats.linregress(pisear,pisear2)
        slopedt[ii] = smm
        rvaldt[ii] = srval
        pvaldt[ii] = spval
        sterrdt[ii] = sstd_err
        yintdt[ii] = sbb

piseardf=pd.DataFrame(piseardt)
pipdfdf=pd.DataFrame(pipdfdt)
pixxdf=pd.DataFrame(pixxdt)
pimeandf=pd.Series(pimeandt)
piflatpdf, piflatmean, piflatxx = calc_pdf(piseardf.values.flatten())

# Load AGCM sims
simsR=('R1','R2','R3','R4','R5')
arsear,styearsr = load_agcmfield(fieldr,simsR,sear,region=regionr,
                                 conv=aconvr,styears=styearsR)
arpdf, armean, arxx = calc_pdf(arsear)

simsE=('E1','E2','E3','E4','E5')
aesear,styearse = load_agcmfield(fieldr,simsE,sear,region=regionr,
                                 conv=aconvr,styears=styearsE)
aepdf, aemean, aexx = calc_pdf(aesear)

#    NSIDC
simsO=('NSIDC',)
osear,ostyearsr = load_agcmfield(fieldr,simsO,sear,region=regionr,
                                 conv=aconvr,styears=styearsN)
opdf, omean, oxx = calc_pdf(osear)


# Load LE (historical)
lecsear = load_field(fdictr, 'historical', timeselc, sear,
                     ftype='fullts', conv=convr,local=local)
lepsear = load_field(fdictr, 'historical', timeselp, sear,
                     ftype='fullts', conv=convr,local=local)
lesear = lepsear-lecsear
lepdf, lemean, lexx = calc_pdf(lesear)

if doscatter:
    arsear2,styearsr = load_agcmfield(fieldr2,simsR,sear2,region=regionr2,
                                     conv=aconvr2,styears=styearsR)

    aesear2,styearse = load_agcmfield(fieldr2,simsE,sear2,region=regionr2,
                                     conv=aconvr2,styears=styearsE)
    osear2,ostyearsr = load_agcmfield(fieldr2,simsO,sear2,region=regionr2,
                                 conv=aconvr2,styears=styearsN)

    lecsear2 = load_field(fdictr2, 'historical', timeselc, sear2,
                         ftype='fullts', conv=convr2,local=local)
    lepsear2 = load_field(fdictr2, 'historical', timeselp, sear2,
                         ftype='fullts', conv=convr2,local=local)
    lesear2 = lepsear2-lecsear2


    arsmm, arsbb, arsrval, arspval, arsstd_err = sp.stats.linregress(arsear,arsear2)
    aesmm, aesbb, aesrval, aespval, aesstd_err = sp.stats.linregress(aesear,aesear2)
    lesmm, lesbb, lesrval, lespval, lesstd_err = sp.stats.linregress(lesear,lesear2)
    osmm, osbb, osrval, ospval, osstd_err = sp.stats.linregress(osear,osear2)

    pismm, pisbb, pisrval, pispval, pisstd_err = sp.stats.linregress(pisear,pisear2)

print '====' 
print '====' + fieldr + ' ' + regionr + ' ' + sear
print '====R SIMS v E SIMS'
test_significance(arsear, aesear, verb=True)
print '====R SIMS v NSIDC SIMS'
test_significance(arsear, osear, verb=True)

print ''
print '====R SIMS v PI avg subsamp'
test_significance(arsear,piseardf.mean(axis=1), verb=True)
print '====E SIMS v PI avg subsamp'
test_significance(aesear,piseardf.mean(axis=1), verb=True)
print '====LE v PI avg subsamp'
test_significance(lesear,piseardf.mean(axis=1), verb=True)
print '====NSIDC v PI avg subsamp'
test_significance(osear,piseardf.mean(axis=1), verb=True)
print ''

print '====R SIMS v PI flatten (50*' + str(nresamp) + ')'
test_significance(arsear,piseardf.values.flatten(), verb=True)
print '====E SIMS v PI flatten (50*' + str(nresamp) + ')'
test_significance(aesear,piseardf.values.flatten(), verb=True)
print '====LE v PI flatten (50*' + str(nresamp) + ')'
test_significance(lesear,piseardf.values.flatten(), verb=True)
print '====NSIDC v PI flatten (50*' + str(nresamp) + ')'
test_significance(osear,piseardf.values.flatten(), verb=True)


# ########### PLOTTING ###################
legdt=coll.OrderedDict()
legdt['Preindustrial ' + str(nresamp) + ' 50-member samples'] = mlines.Line2D([],[],
                                                                              color=picol)
legdt['Preindustrial mean of ' + str(nresamp)] =  mlines.Line2D([],[],
                                                                color='k',linewidth=2)
legdt['Preindustrial mean of ' + str(nresamp*50)] =  mlines.Line2D([],[],
                                                                   color='k',linewidth=2,
                                                                   linestyle='--')
legdt['AGCM_variable'] = mlines.Line2D([],[],color=acol,linewidth=2)
legdt['AGCM_fixed'] = mlines.Line2D([],[],color=acol,linewidth=2,
                                    linestyle='--')
legdt['CGCM']=mlines.Line2D([],[],color=lecol,linewidth=2)
legdt['NSIDC']=mlines.Line2D([],[],color=ocol,linewidth=2)


fig,ax=plt.subplots(1,1)
fig.set_size_inches(9,8)
ax.plot(pixxdf.values, pipdfdf.values, color=picol,alpha=0.5)
ax.plot(pixxdf.mean(axis=1), pipdfdf.mean(axis=1), color='k', linewidth=2)
ax.plot(pimeandf.values, np.ones((pixxdf.values.shape[1]))*ylev,  
         linestyle='none',marker='.', color=picol)
ax.plot(pimeandf.mean(), ylev, linestyle='none',marker='.',color='k')
ax.plot(piflatxx, piflatpdf, color='k', linestyle='--',linewidth=2)

ax.plot(arxx, arpdf, color=acol,linewidth=3)
ax.plot(armean, ylev, linestyle='none',marker='s', color=acol,alpha=0.5)
ax.plot(aexx, aepdf, color=acol,linewidth=3,linestyle='--')
ax.plot(aemean, ylev, linestyle='none',marker='o', color=acol,alpha=0.5)

ax.plot(lexx, lepdf, color=lecol,linewidth=2)
ax.plot(lemean, ylev, linestyle='none', marker='^', color=lecol)

ax.plot(oxx, opdf, color=ocol,linewidth=2)
ax.plot(omean, ylev, linestyle='none', marker='^', color=ocol)

#ax.set_xlabel('Full PI sample mean: ' + str(pimeandf.mean()))
ax.set_ylabel('Density')
ax.set_xlabel('Change in ' + rstrlong + ' (' + runits + ')')

ax.legend((legdt.values()), (legdt.keys()),loc='upper left',
          fancybox=True,framealpha=0.5,frameon=False)
if printtofile:
    fig.savefig(fieldr + regionr + '_' + sear + '_' +\
                'pi' + str(nresamp) + 'resamp_AGCMer_LE_PDF.pdf')


if doscatter:


    print '-=-=-=-= regression vals -=-=-=-='
    print '-=-=-=-= ' + fieldr + ' ' + regionr + ' ' + sear +\
        ' v ' + fieldr2 + ' ' + regionr2 + ' ' + sear2
    print '        R SIMS slope,r,pval ' + str(arsmm),str(arsrval),str(arspval)
    print '        E SIMS slope,r,pval ' + str(aesmm),str(aesrval),str(aespval)
    print '        LE slope,r,pval ' + str(lesmm),str(lesrval),str(lespval)
    print '        PI slope,r,pval ' + str(pismm),str(pisrval),str(pispval)
    print '        NSIDC slope,r,pval ' + str(osmm),str(osrval),str(ospval)


    pisear2df=pd.DataFrame(pisear2dt)
    slopedf=pd.Series(slopedt)
    yintdf=pd.Series(yintdt)

    fig,ax=plt.subplots(1,1)
    fig.set_size_inches(9,8)
    ax.scatter(piseardf.values,pisear2df.values, marker='.', color=picol,alpha=0.5)

    axylims = ax.get_ylim()
    axxlims = ax.get_xlim()
    onex=np.linspace(axxlims[0],axxlims[1])
    
    for ii in range(0,len(slopedf.values)):
        ax.plot(onex,slopedf[ii]*onex + yintdf[ii], color='0.7',linewidth=1)

    ax.plot(onex,pismm*onex + pisbb, color='k',linewidth=2,linestyle='--')
    ax.plot(onex,slopedf.mean()*onex + yintdf.mean(), color='k',linewidth=2)
    ax.plot(onex,arsmm*onex + arsbb, color=acol,linewidth=2)
    ax.plot(onex,aesmm*onex + aesbb, color=acol,linewidth=2,linestyle='--')
    ax.plot(onex,lesmm*onex + lesbb, color=lecol, linewidth=2)
    ax.plot(onex,osmm*onex + osbb, color=ocol, linewidth=2)

    ax.set_xlabel('Change in ' + rstrlong + ' (' + runits + ')')
    ax.set_ylabel('Change in ' + rstr2long + ' (' + runits2 + ')')
    ax.set_ylim(axylims); ax.set_xlim(axxlims)
    ax.legend((legdt.values()), (legdt.keys()),loc='lower left',
              fancybox=True,framealpha=0.5,frameon=False)
    if printtofile:
        fig.savefig(fieldr + regionr + '_' + sear + '_' + fieldr2+regionr2+'_' +sear2+\
                    '_pi' + str(nresamp) + 'resamp_AGCMer_LE_SCATTER.pdf')


    plt.figure()
    slopeci=sp.stats.t.interval(1-0.05,len(slopedf.values)-1,
                                loc=slopedf.mean(),scale=slopedf.std())
    plt.axvspan(slopeci[0],slopeci[1],color='blue',alpha=0.1)
    plt.hist(slopedf.values,color=picol,alpha=0.7)
    plt.axvline(x=arsmm,color=acol,linewidth=2)
    plt.axvline(x=aesmm,color=acol,linewidth=2,linestyle='--')
    plt.axvline(x=lesmm,color=lecol,linewidth=2)
    plt.axvline(x=osmm,color=ocol,linewidth=2)

    plt.xlabel('slopes: ' + rstr + ' v ' + rstr2)
    if printtofile:
        plt.savefig(fieldr + regionr + '_' + sear + '_' + fieldr2+regionr2+'_' +sear2+\
                    '_pi' + str(nresamp) + 'resamp_SLOPEHIST.pdf')
    

# SAVE SOME OUTPUT
"""
******* This is for resamp= 1000 and nsamp=50 ******
************ EUR SAT

1. this first output tests against the solid black curve of PI,
  the average of all the sampled pdfs (avg of 1000 pdfs)

R SIMS v PI avg subsamp
==== testing input 1 vs input 2 ====
TSTAT: 0.949425595214 PVAL: 0.344739700599
LSTAT: 78.1725745675 PVAL: 3.93980817057e-14
The ensemble variances are significantly different (0.95)

E SIMS v PI avg subsamp
==== testing input 1 vs input 2 ====
TSTAT: 0.0684858870774 PVAL: 0.945538396429
LSTAT: 77.2108084012 PVAL: 5.16896427751e-14
The ensemble variances are significantly different (0.95)

2. the second output tests against the dashed black curve of PI,
  which is the full distribution of all 50,000 anomalies

R SIMS v PI flatten (50*1000)
==== testing input 1 vs input 2 ====
TSTAT: 1.10295407114 PVAL: 0.270052414469
LSTAT: 1.86544267023 PVAL: 0.172004087696

E SIMS v PI flatten (50*1000)
==== testing input 1 vs input 2 ====
TSTAT: 0.0742550921524 PVAL: 0.940807706367
LSTAT: 0.31666140677 PVAL: 0.573623479656


******* This is for resamp= 10000 and nsamp=50 ******

R SIMS v E SIMS
==== testing input 1 vs input 2 ====
TSTAT: 0.647565524008 PVAL: 0.518780140966
LSTAT: 0.243251494042 PVAL: 0.622970911577
R SIMS v PI avg subsamp
==== testing input 1 vs input 2 ====
TSTAT: 0.959612321708 PVAL: 0.339611949009
LSTAT: 80.6482833253 PVAL: 1.9720870637e-14
The ensemble variances are significantly different (0.95)
E SIMS v PI avg subsamp
==== testing input 1 vs input 2 ====
TSTAT: 0.0791961039654 PVAL: 0.93703813417
LSTAT: 79.8613461701 PVAL: 2.45467442474e-14
The ensemble variances are significantly different (0.95)


R SIMS v PI flatten (50*10000)
==== testing input 1 vs input 2 ====
TSTAT: 1.11050316472 PVAL: 0.266782799126
LSTAT: 1.73038241799 PVAL: 0.188362669839
E SIMS v PI flatten (50*10000)
==== testing input 1 vs input 2 ====
TSTAT: 0.0855281292414 PVAL: 0.931841567739
LSTAT: 0.264296082404 PVAL: 0.607184159031


****************** BKS Z500 *****************
******* This is for resamp= 100 and nsamp=50 ******

====R SIMS v E SIMS
  Mean1: 3.34624519573, Mean2: 4.08476507306
  TSTAT: -0.203966108758 PVAL: 0.838802946149
  LSTAT: 1.30148791711 PVAL: 0.256721855393

====R SIMS v PI avg subsamp
  Mean1: 3.34624519573, Mean2: -0.362034874386
  TSTAT: 1.3039819856 PVAL: 0.195294313572
  LSTAT: 52.4262093868 PVAL: 1.01754909141e-10
   The ensemble variances are significantly different (0.95)
====E SIMS v PI avg subsamp
  Mean1: 4.08476507306, Mean2: -0.362034874386
  TSTAT: 1.95193582793 PVAL: 0.0538000016487
  LSTAT: 60.1696440145 PVAL: 8.34303753016e-12
   The ensemble variances are significantly different (0.95)
====LE v PI avg subsamp
  Mean1: 20.9342897461, Mean2: -0.362034874386
  TSTAT: 9.1311157635 PVAL: 9.30117844593e-15
   The ensemble means are significantly different (0.95)
  LSTAT: 58.1727027078 PVAL: 1.57054953536e-11
   The ensemble variances are significantly different (0.95)

====R SIMS v PI flatten (50*100)
  Mean1: 3.34624519573, Mean2: -0.362034874386
  TSTAT: 1.38785266275 PVAL: 0.165243167144
  LSTAT: 0.025539764451 PVAL: 0.873035838143
====E SIMS v PI flatten (50*100)
  Mean1: 4.08476507306, Mean2: -0.362034874386
  TSTAT: 1.66757010635 PVAL: 0.095463123568
  LSTAT: 2.19780283627 PVAL: 0.138270032351
====LE v PI flatten (50*100)
  Mean1: 20.9342897461, Mean2: -0.362034874386
  TSTAT: 7.98484450166 PVAL: 1.72862927032e-15
   The ensemble means are significantly different (0.95)
  LSTAT: 1.51092221294 PVAL: 0.219055711487


****************** Polar (>60N) Z500 *****************
******* This is for resamp= 100 and nsamp=50 ******

====R SIMS v E SIMS
  Mean1: 4.34329642586, Mean2: 4.05086208953
  TSTAT: 0.124864173526 PVAL: 0.900886856615
  LSTAT: 1.23105032791 PVAL: 0.269918102382

====R SIMS v PI avg subsamp
  Mean1: 4.34329642586, Mean2: -0.292373281517
  TSTAT: 2.60305597301 PVAL: 0.0106742279736
   The ensemble means are significantly different (0.95)
  LSTAT: 65.771539419 PVAL: 1.47728131318e-12
   The ensemble variances are significantly different (0.95)
====E SIMS v PI avg subsamp
  Mean1: 4.05086208953, Mean2: -0.292373281517
  TSTAT: 2.82554660165 PVAL: 0.00572033369574
   The ensemble means are significantly different (0.95)
  LSTAT: 52.9011902239 PVAL: 8.69480715577e-11
   The ensemble variances are significantly different (0.95)
====LE v PI avg subsamp
  Mean1: 22.6614946398, Mean2: -0.292373281517
  TSTAT: 17.1831659206 PVAL: 2.49304911358e-31
   The ensemble means are significantly different (0.95)
  LSTAT: 75.1006068889 PVAL: 9.42967223238e-14
   The ensemble variances are significantly different (0.95)

====R SIMS v PI flatten (50*100)
  Mean1: 4.34329642586, Mean2: -0.292373281517
  TSTAT: 2.9180817548 PVAL: 0.0035374693358
   The ensemble means are significantly different (0.95)
  LSTAT: 0.893780887261 PVAL: 0.344500024223
====E SIMS v PI flatten (50*100)
  Mean1: 4.05086208953, Mean2: -0.292373281517
  TSTAT: 2.73830354628 PVAL: 0.00619736600903
   The ensemble means are significantly different (0.95)
  LSTAT: 0.572568927471 PVAL: 0.44927520812
====LE v PI flatten (50*100)
  Mean1: 22.6614946398, Mean2: -0.292373281517
  TSTAT: 14.4881870482 PVAL: 1.22760725958e-46
   The ensemble means are significantly different (0.95)
  LSTAT: 1.69412618173 PVAL: 0.193117335082


****************************************************


====sic bksmori DJF
====R SIMS v E SIMS
  Mean1: -4.13895896533, Mean2: -4.13896063321
  TSTAT: 6.92120265097e-06 PVAL: 0.999994491749
  LSTAT: 86.1572184431 PVAL: 4.37710753759e-15
   The ensemble variances are significantly different (0.95)

====R SIMS v PI avg subsamp
  Mean1: -4.13895896533, Mean2: -0.0114985260866
  TSTAT: -17.1139159282 PVAL: 3.35790952493e-31
   The ensemble means are significantly different (0.95)
  LSTAT: 79.3352918116 PVAL: 2.84306030468e-14
   The ensemble variances are significantly different (0.95)
====E SIMS v PI avg subsamp
  Mean1: -4.13896063321, Mean2: -0.0114985260866
  TSTAT: -425.713519836 PVAL: 6.46246744825e-162
   The ensemble means are significantly different (0.95)
  LSTAT: 89.5377488456 PVAL: 1.77770369851e-15
   The ensemble variances are significantly different (0.95)
====LE v PI avg subsamp
  Mean1: -5.8410614811, Mean2: -0.0114985260866
  TSTAT: -13.5356240796 PVAL: 3.65847108405e-24
   The ensemble means are significantly different (0.95)
  LSTAT: 86.5263352741 PVAL: 3.96371847757e-15
   The ensemble variances are significantly different (0.95)

====R SIMS v PI flatten (50*1000)
  Mean1: -4.13895896533, Mean2: -0.0114985260866
  TSTAT: -13.3277093499 PVAL: 1.87254388148e-40
   The ensemble means are significantly different (0.95)
  LSTAT: 4.05017086204 PVAL: 0.0441722207273
   The ensemble variances are significantly different (0.95)
====E SIMS v PI flatten (50*1000)
  Mean1: -4.13896063321, Mean2: -0.0114985260866
  TSTAT: -13.3316708812 PVAL: 1.77603935761e-40
   The ensemble means are significantly different (0.95)
  LSTAT: 88.4400990234 PVAL: 5.45308956409e-21
   The ensemble variances are significantly different (0.95)
====LE v PI flatten (50*1000)
  Mean1: -5.8410614811, Mean2: -0.0114985260866
  TSTAT: -18.8116225283 PVAL: 1.13442203656e-78
   The ensemble means are significantly different (0.95)
  LSTAT: 14.7388981125 PVAL: 0.000123624259492
   The ensemble variances are significantly different (0.95)
-=-=-=-= regression vals -=-=-=-=
-=-=-=-= sic bksmori DJF v zg50000.00 bksmori DJF
        R SIMS slope,r,pval -2.27291054962 -0.193605723514 0.177928875634
        E SIMS slope,r,pval nan 0.0 1.0
        LE slope,r,pval -1.52694237681 -0.28408601672 0.0455664758446
        PI slope,r,pval -3.12111933708 -0.407511964889 0.00331053112668


$$$$$$$$$$$$$$$$$$$$$$$$$ include NSIDC
SAMPLE=1000

====zg50000.00 bksmori DJF
====R SIMS v E SIMS
  Mean1: 3.34624519573, Mean2: 4.08476507306
  TSTAT: -0.203966108758 PVAL: 0.838802946149
  LSTAT: 1.30148791711 PVAL: 0.256721855393
====R SIMS v NSIDC SIMS
  Mean1: 3.34624519573, Mean2: 1.304501494
  TSTAT: 0.294518805923 PVAL: 0.76941305851
  LSTAT: 0.00354983436691 PVAL: 0.952694576802

====R SIMS v PI avg subsamp
  Mean1: 3.34624519573, Mean2: -0.112099637759
  TSTAT: 1.22193270617 PVAL: 0.224664126933
  LSTAT: 62.7222446738 PVAL: 3.76146015831e-12
   The ensemble variances are significantly different (0.95)
====E SIMS v PI avg subsamp
  Mean1: 4.08476507306, Mean2: -0.112099637759
  TSTAT: 1.85606291265 PVAL: 0.0664493304483
  LSTAT: 75.3362549404 PVAL: 8.81410661105e-14
   The ensemble variances are significantly different (0.95)
====LE v PI avg subsamp
  Mean1: 20.9342897461, Mean2: -0.112099637759
  TSTAT: 9.08858761728 PVAL: 1.14999498237e-14
   The ensemble means are significantly different (0.95)
  LSTAT: 72.2113860681 PVAL: 2.17438459097e-13
   The ensemble variances are significantly different (0.95)
====NSIDC v PI avg subsamp
  Mean1: 1.304501494, Mean2: -0.112099637759
  TSTAT: 0.516542520745 PVAL: 0.607439540702
  LSTAT: 78.717361952 PVAL: 2.15561939914e-12
   The ensemble variances are significantly different (0.95)

====R SIMS v PI flatten (50*1000)
  Mean1: 3.34624519573, Mean2: -0.112099637759
  TSTAT: 1.29135823287 PVAL: 0.196585450662
  LSTAT: 0.00675346412636 PVAL: 0.934504333045
====E SIMS v PI flatten (50*1000)
  Mean1: 4.08476507306, Mean2: -0.112099637759
  TSTAT: 1.56743448682 PVAL: 0.117019490347
  LSTAT: 2.4231127868 PVAL: 0.119563472043
====LE v PI flatten (50*1000)
  Mean1: 20.9342897461, Mean2: -0.112099637759
  TSTAT: 7.86021854275 PVAL: 3.91078957391e-15
   The ensemble means are significantly different (0.95)
  LSTAT: 1.70145391435 PVAL: 0.192103944905
====NSIDC v PI flatten (50*1000)
  Mean1: 1.304501494, Mean2: -0.112099637759
  TSTAT: 0.23666539358 PVAL: 0.812917353576
  LSTAT: 0.0123623716918 PVAL: 0.911469138564
-=-=-=-= regression vals -=-=-=-=
-=-=-=-= zg50000.00 bksmori DJF v tas eurasiamori DJF
        R SIMS slope,r,pval -0.0259499202434 -0.807961779808 1.32131111876e-12
        E SIMS slope,r,pval -0.018372879055 -0.48963119319 0.000307644171986
        LE slope,r,pval -0.0165286796574 -0.413836962376 0.00281317881451
        PI slope,r,pval -0.0177782325744 -0.649875789688 3.27492326874e-07
        NSIDC slope,r,pval -0.0163907086317 -0.55607007061 0.0950805453678


SAMPLE=1000

====zg50000.00 gt60n DJF
====R SIMS v E SIMS
  Mean1: 4.34329642586, Mean2: 4.05086208953
  TSTAT: 0.124864173526 PVAL: 0.900886856615
  LSTAT: 1.23105032791 PVAL: 0.269918102382
====R SIMS v NSIDC SIMS
  Mean1: 4.34329642586, Mean2: 0.453203404306
  TSTAT: 0.870099837881 PVAL: 0.387832725954
  LSTAT: 0.000546081317477 PVAL: 0.981436637394

====R SIMS v PI avg subsamp
  Mean1: 4.34329642586, Mean2: -0.0420948555995
  TSTAT: 2.4709697515 PVAL: 0.0152007628743
   The ensemble means are significantly different (0.95)
  LSTAT: 75.5874515631 PVAL: 8.20296027151e-14
   The ensemble variances are significantly different (0.95)
====E SIMS v PI avg subsamp
  Mean1: 4.05086208953, Mean2: -0.0420948555995
  TSTAT: 2.67501360614 PVAL: 0.00875775973691
   The ensemble means are significantly different (0.95)
  LSTAT: 62.6566227074 PVAL: 3.83865363406e-12
   The ensemble variances are significantly different (0.95)
====LE v PI avg subsamp
  Mean1: 22.6614946398, Mean2: -0.0420948555995
  TSTAT: 17.0999008301 PVAL: 3.5667870127e-31
   The ensemble means are significantly different (0.95)
  LSTAT: 90.4182185449 PVAL: 1.40967838773e-15
   The ensemble variances are significantly different (0.95)
====NSIDC v PI avg subsamp
  Mean1: 0.453203404306, Mean2: -0.0420948555995
  TSTAT: 0.246053836203 PVAL: 0.806509247192
  LSTAT: 41.9363746164 PVAL: 2.21228289594e-08
   The ensemble variances are significantly different (0.95)

====R SIMS v PI flatten (50*1000)
  Mean1: 4.34329642586, Mean2: -0.0420948555995
  TSTAT: 2.72542884967 PVAL: 0.00642403372391
   The ensemble means are significantly different (0.95)
  LSTAT: 0.579464241089 PVAL: 0.446525984601
====E SIMS v PI flatten (50*1000)
  Mean1: 4.05086208953, Mean2: -0.0420948555995
  TSTAT: 2.54407644225 PVAL: 0.0109596892491
   The ensemble means are significantly different (0.95)
  LSTAT: 0.845295664505 PVAL: 0.35789101817
====LE v PI flatten (50*1000)
  Mean1: 22.6614946398, Mean2: -0.0420948555995
  TSTAT: 14.1135108392 PVAL: 3.82862100909e-45
   The ensemble means are significantly different (0.95)
  LSTAT: 2.11633230683 PVAL: 0.145741449257
====NSIDC v PI flatten (50*1000)
  Mean1: 0.453203404306, Mean2: -0.0420948555995
  TSTAT: 0.137721445832 PVAL: 0.890461124062
  LSTAT: 0.0960458004409 PVAL: 0.756628735748
-=-=-=-= regression vals -=-=-=-=
-=-=-=-= zg50000.00 gt60n DJF v tas eurasiamori DJF
        R SIMS slope,r,pval -0.0310884060413 -0.606940319432 2.97219893946e-06
        E SIMS slope,r,pval -0.0240196543376 -0.433151275689 0.00167791876122
        LE slope,r,pval -0.0232146201281 -0.33317518497 0.0180638323556
        PI slope,r,pval -0.0114353689086 -0.2590476681 0.0692843640745
        NSIDC slope,r,pval -0.0192763401821 -0.480175036169 0.160137094547

"""