最近学习了一下泰勒图的做法，对2001年泰勒的文章进行了简单学习，说一点自己的理解：
泰勒图一般是用来评估多个模式对观测数据的模拟能力，包括标准差、中心型均方根误差、相关系数这三部分，这三部分可以构建一个三角关系。相关系数是用来量化模式之间的相似性，但是它有缺点，无法量化变化幅度。比如，当两个空间场变化极其相似，但是变化程度有量级差异，如果不看均方根误差而只看相关系数，那么很容易出现问题。标准差可以看出来模式相对于观测的离散程度。
在ncl的脚本中，官网提供了现成的代码给我们绘制泰勒图，只需要提供模式和观测之间的相关系数，以及模式与观测之间的标准差的比率，就可以画出。因为代码中用到的是标准差比率，根据文章中提到的三角关系，我们图中最终得到的是标准化后的样本标准差和标准化后的中心型均方根误差，这样得到的图更加清晰明了。
如果要对模式进行优选，就可以根据自己的需求，设定标准化后的标准差的范围（标准化后的中心型均方根误差类似），还可以对相关系数进行显著性检验等等。
下面是官网提供的泰勒图代码：
function taylor_diagram (wks:graphic ,RATIO[*][*]:numeric, CC[*][*]:numeric \
,rOpts:logical)
;--------------------------------------------------------------------
; This version of taylor_diagram supports "paneling"
; It requires NCL version 4.2.0.a034 because it uses "gsn_create_legend"
;--------------------------------------------------------------------
;
; Generate a Taylor Diagram:
; Generate Multiple Aspects of Model Performance in a Single Diagram
; Taylor, K. E., J. Geophys. Res., 106, D7, 7183-7192, 2001
;
; An example:
; http://www.grida.no/climate/ipcc_tar/wg1/fig8-4.htm
;
; This expects one or more datasets. The left dimension
; is the number of datasets. The rightmost is the number of pts.
;
; Markers are at:
; http://www.ncl.ucar.edu/Document/Graphics/Resources/gs.shtml
;
; By default, the function can handle up to 10 variable comparisons..
; To expand ... modify the 'Colors' and 'Markers' attributes.
; The user can change / add some default settings.
;
; The defaults that the user can modify:
;
; rOpts = True
; ; 'made-up' resources
; rOpts@Colors = (/ "blue" , "red", "green", "cyan", "black" \
; , "turquoise", "brown", "yellow"/)
; rOpts@Markers = (/ 2, 3, 6, 14, 9, 12, 7, 4/) ; Marker Indices
; rOpts@markerTxOffset = 0.0175 ; offset for text above marker
; rOpts@stnRad = (/ 1. /) ; (/ 0.50, 0.75, 1.5 /)
; rOpts@centerDiffRMS = False ; True mean draw additional radii from REF
; rOpts@caseLabelsFontHeightF = 0.05
; rOpts@varLabelsFontHeightF = 0.013
; rOpts@varLabelsYloc = 0.65
; rOpts@legendWidth = 0.015
; rOpts@legendHeight = 0.030*nCase
; rOpts@taylorDraw = True
; rOpts@taylorFrame = True
;
; ; standard NCL resources
; rOpts@tiMainString = "Taylor" ; not using title makes plot bigger
; rOpts@gsMarkerSizeF = 0.0085 ; marker size
; rOpts@gsMarkerThicknessF = 1.0
; rOpts@txFontHeightF = 0.0125 ; text size
; rOpts@tiMainFontHeightF = 0.0225 ; tiMainString size
;
; It returns to the user a graphic object containing the
; Taylor background and plotted x/y pts.
; This graphic object contains a simple Taylor background appropriate
; for standardized data and the markers for the datasets.
; ==================================================================
; This version allows paneling:
; The 'cumbersome' "dum" variables were added by
; Adam Phillips to allow paneling via "gsn_add_?".
; ==================================================================
begin
dimR = dimsizes(RATIO)
nCase = dimR(0) ; # of cases [models]
nVar = dimR(1) ; # of variables
; x/y coordinates for plotting
X = new ( (/nCase,nVar/) , typeof(RATIO) )
Y = new ( (/nCase,nVar/) , typeof(RATIO) )
do nc=0,nCase-1
angle = acos( CC(nc,:) ) ; array operation
X(nc,:) = RATIO(nc,:)*cos( angle )
Y(nc,:) = RATIO(nc,:)*sin( angle )
end do
xyMin = 0.
xyOne = 1.00
xyMax = 1.65
xyMax_Panel = xyMax+ 0.10 ; paneling purposes
if (rOpts .and. isatt(rOpts,"txFontHeightF")) then
FontHeightF = rOpts@txFontHeightF ; user wants to specify size
else
FontHeightF = 0.0175
end if
; ----------------------------------------------------------------
; Part 1:
; base plot: Based upon request of Mark Stevens
; basic x-y and draw the 1.0 observed and the outer curve at 1.65
; ----------------------------------------------------------------
rxy = True
rxy@gsnDraw = False
rxy@gsnFrame = False
rxy@vpHeightF = 0.65
rxy@vpWidthF = 0.65
rxy@tmYLBorderOn = False
rxy@tmXBBorderOn = False
rxy@tiYAxisString = "Standardized Deviations (Normalized)"
rxy@tiYAxisFontHeightF= FontHeightF ; default=0.025
rxy@tmXBMode = "Explicit"
rxy@tmXBValues = (/0.0,0.25,0.50,0.75,1.00,1.25,1.5/) ; major tm
; default "OBS" or "REF"
;rxy@tmXBLabels = (/"0.00","0.25","0.50","0.75","REF" ,"1.25","1.50"/)
rxy@tmXBLabels = (/" ","0.25","0.50","0.75","REF" ,"1.25","1.50"/)
if (rOpts .and. isatt(rOpts,"OneX") ) then ; eg: rOpts@OneX="1.00"
;rxy@tmXBLabels = (/"0.00","0.25","0.50","0.75",rOpts@OneX,"1.25","1.50"/)
rxy@tmXBLabels = (/" ","0.25","0.50","0.75",rOpts@OneX,"1.25","1.50"/)
end if
rxy@tmXBMajorLengthF = 0.015 ; default=0.02 for a vpHeightF=0.6
rxy@tmXBLabelFontHeightF = FontHeightF
rxy@tmXBMinorOn = False
rxy@trXMaxF = xyMax_Panel
rxy@tmYLMode = "Manual"
rxy@tmYLMinorOn = False
rxy@tmYLMajorLengthF = rxy@tmXBMajorLengthF
rxy@tmYLLabelFontHeightF = FontHeightF
rxy@tmYLMode = "Explicit"
rxy@tmYLValues = (/0.0, .25,0.50, 0.75, 1.00, 1.25, 1.5/) ; major tm
rxy@tmYLLabels = (/"0.00","0.25","0.50","0.75","1.00","1.25","1.50"/)
;rxy@tmYLLabels = (/" ","0.25","0.50","0.75","1.00","1.25","1.50"/)
rxy@trYMaxF = xyMax_Panel
rxy@tmYRBorderOn = False
rxy@tmYROn = False ; Turn off right tick marks.
rxy@tmXTBorderOn = False
rxy@tmXTOn = False ; Turn off right tick marks.
rxy@xyDashPatterns = (/ 0 /) ; line characteristics (dash,solid)
rxy@xyLineThicknesses = (/ 2./) ; choose line thickness
rxy@gsnFrame = False ; Don't advance the frame.
; create outer 'correlation axis'
npts = 200 ; arbitrary
xx = fspan(xyMin,xyMax,npts)
yy = sqrt(xyMax^2 - xx^2 ) ; outer correlation line (xyMax)
sLabels = (/"0.0","0.1","0.2","0.3","0.4","0.5","0.6" \ ; correlation labels
,"0.7","0.8","0.9","0.95","0.99","1.0" /); also, major tm
cLabels = stringtofloat(sLabels)
rad = 4.*atan(1.0)/180.
angC = acos(cLabels)/rad ; angles: correlation labels
if (rOpts .and. isatt(rOpts,"tiMainString")) then
rxy@tiMainString = rOpts@tiMainString
;rxy@tiMainOffsetYF = 0.015 ; default 0.0
if (isatt(rOpts,"tiMainFontHeightF")) then
rxy@tiMainFontHeightF = rOpts@tiMainFontHeightF
else
rxy@tiMainFontHeightF = 0.0225 ; default 0.025
end if
end if
;;if (rOpts .and. isatt(rOpts,"gsnCenterString")) then
;; rxy@gsnCenterString = rOpts@gsnCenterString ; only gsn_csm_xy
;;end if
taylor = gsn_xy(wks,xx,yy,rxy) ; Create and draw XY plot.
rsrRes = True
rsrRes@gsLineThicknessF = rxy@xyLineThicknesses(0) ; line thickness
rsrRes@gsLineDashPattern = 0 ; solid line pattern
; draw x and y to xyMax
dum0 = gsn_add_polyline(wks,taylor,(/0., 0. /),(/0.,xyMax/), rsrRes)
dum1 = gsn_add_polyline(wks,taylor,(/0.,xyMax/),(/0., 0. /), rsrRes)
xx = fspan(xyMin, xyOne ,npts) ; draw 1.0 standard radius
yy = sqrt(xyOne - xx^2)
rsrRes@gsLineDashPattern = 1 ; dashed line pattern
rsrRes@gsLineThicknessF = rxy@xyLineThicknesses(0) ; line thickness
dum2 = gsn_add_polyline(wks,taylor,xx,yy, rsrRes)
delete(xx)
delete(yy)
if (rOpts .and. isatt(rOpts,"stnRad") ) then
rsrRes@gsLineThicknessF = 1 ; rxy@xyLineThicknesses(0)
nStnRad = dimsizes(rOpts@stnRad)
dum3 = new(nStnRad,graphic)
do n=0,nStnRad-1
rr = rOpts@stnRad(n)
xx = fspan(xyMin, rr ,npts)
yy = sqrt(rr^2 - xx^2)
dum3(n) = gsn_add_polyline(wks,taylor,xx,yy, rsrRes)
end do
taylor@$unique_string("dum")$ = dum3
delete(xx)
delete(yy)
end if
getvalues taylor ; get style info from taylor
"tmYLLabelFont" : tmYLLabelFont ; use for correlation axis
"tmYLLabelFontHeightF" : tmYLLabelFontHeightF
end getvalues
; ----------------------------------------------------------------
; Part 2:
; Correlation labels
; ----------------------------------------------------------------
radC = xyMax ; for correlation labels
xC = radC*cos(angC*rad)
yC = radC*sin(angC*rad)
; added to get some separation
xC = xC + 0.020*cos(rad*angC)
yC = yC + 0.060*sin(rad*angC)
txRes = True ; text mods desired
txRes@txFontHeightF = FontHeightF ; match YL
txRes@tmYLLabelFont = tmYLLabelFont ; match YL
txRes@txAngleF = -45.
if (.not.isatt(rOpts,"drawCorLabel") .or. rOpts@drawCorLabel) then
dum4 = gsn_add_text(wks,taylor,"Correlation",1.30,1.30,txRes)
taylor@$unique_string("dum")$ = dum4
end if
txRes@txAngleF = 0.0
txRes@txFontHeightF = FontHeightF*0.50 ; bit smaller
;;dum0 = gsn_add_text(wks,taylor,"OBSERVED",1.00,0.075,txRes)
plRes = True
plRes@gsLineThicknessF = 2.
txRes@txJust = "CenterLeft" ; Default="CenterCenter".
txRes@txFontHeightF = FontHeightF ; match YL
;txRes@txBackgroundFillColor = "white"
tmEnd = 0.975
radTM = xyMax*tmEnd ; radius end: major TM
xTM = new( 2 , "float")
yTM = new( 2 , "float")
dum5 = new(dimsizes(sLabels),graphic)
dum6 = dum5
do i=0,dimsizes(sLabels)-1 ; Loop to draw strings
txRes@txAngleF = angC(i)
dum5(i) = gsn_add_text(wks, taylor, sLabels(i),xC(i),yC(i),txRes) ; cor label
xTM(0) = xyMax*cos(angC(i)*rad) ; major tickmarks at
yTM(0) = xyMax*sin(angC(i)*rad) ; correlation labels
xTM(1) = radTM*cos(angC(i)*rad)
yTM(1) = radTM*sin(angC(i)*rad)
dum6(i) = gsn_add_polyline(wks,taylor,xTM,yTM,plRes)
end do
; minor tm locations
mTM = (/0.05,0.15,0.25,0.35,0.45,0.55,0.65 \
,0.75,0.85,0.91,0.92,0.93,0.94,0.96,0.97,0.98 /)
angmTM = acos(mTM)/rad ; angles: correlation labels
radmTM = xyMax*(1.-(1.-tmEnd)*0.5) ; radius end: minor TM
dum7 = new(dimsizes(mTM),graphic)
do i=0,dimsizes(mTM)-1 ; manually add tm
xTM(0) = xyMax*cos(angmTM(i)*rad) ; minor tickmarks
yTM(0) = xyMax*sin(angmTM(i)*rad)
xTM(1) = radmTM*cos(angmTM(i)*rad)
yTM(1) = radmTM*sin(angmTM(i)*rad)
dum7(i) = gsn_add_polyline(wks,taylor,xTM,yTM,plRes)
end do
; added for Wanli
if (rOpts .and. isatt(rOpts,"ccRays") ) then
angRL = acos(rOpts@ccRays)/rad ; angles: radial lines
rlRes = True
rlRes@gsLineDashPattern= 2 ; line pattern
rlRes@gsLineThicknessF = 1 ; choose line thickness
if (isatt(rOpts,"ccRays_color")) then
rlRes@gsLineColor = "LightGray"
end if
dum8 = new(dimsizes(angRL),graphic)
do i=0,dimsizes(angRL)-1
xRL = xyMax*cos(angRL(i)*rad)
yRL = xyMax*sin(angRL(i)*rad)
dum8(i) = gsn_add_polyline(wks,taylor,(/0, xRL /),(/0, yRL /),rlRes)
end do
taylor@$unique_string("dum")$ = dum8
end if
; ----------------------------------------------------------------
; Part 3:
; Concentric about 1.0 on XB axis
; ----------------------------------------------------------------
if (rOpts .and. isatt(rOpts,"centerDiffRMS") \
.and. rOpts@centerDiffRMS) then
respl = True ; polyline mods desired
respl@xyLineThicknessF = 1.0 ; line thickness
respl@xyLineDashPattern = 2 ; short dash lines
respl@gsLineColor = "Black" ; line color
if (isatt(rOpts,"centerDiffRMS_color")) then
respl@gsLineColor = "LightGray"
end if
dx = 0.25
ncon = 4 ; 0.75, 0.50, 0.25, 0.0
npts = 100 ; arbitrary
ang = fspan(180,360,npts)*rad
dum9 = new(ncon,graphic)
do n=1,ncon
rr = n*dx ; radius from 1.0 [OBS] abscissa
xx = 1. + rr*cos(ang)
yy = fabs( rr*sin(ang) )
if (n.le.2) then
dum9(n-1) = gsn_add_polyline(wks,taylor,xx,yy,respl)
end if
if (n.eq.3) then
n3 = floattointeger( 0.77*npts )
dum9(n-1) = gsn_add_polyline(wks,taylor,xx(0:n3),yy(0:n3),respl)
end if
if (n.eq.4) then
n4 = floattointeger( 0.61*npts )
dum9(n-1) = gsn_add_polyline(wks,taylor,xx(0:n4),yy(0:n4),respl)
end if
end do
delete(ang)
delete(xx)
delete(yy)
taylor@$unique_string("dum")$ = dum9
end if
; ---------------------------------------------------------------
; Part 4:
; generic resources that will be applied to all users data points
; of course, these can be changed
; http://www.ncl.ucar.edu/Document/Graphics/Resources/gs.shtml
; ---------------------------------------------------------------
if (rOpts .and. isatt(rOpts,"Markers")) then
Markers = rOpts@Markers
else
Markers = (/ 4, 6, 8, 0, 9, 12, 7, 2, 11, 16/) ; Marker Indices
end if
if (rOpts .and. isatt(rOpts,"Colors")) then
Colors = rOpts@Colors
else
Colors = (/ "red", "blue", "green", "cyan", "orange" \
, "turquoise", "brown", "yellow", "purple", "black"/)
end if
if (rOpts .and. isatt(rOpts,"gsMarkerThicknessF")) then
gsMarkerThicknessF = rOpts@gsMarkerThicknessF
else
gsMarkerThicknessF = 1.0
end if
if (rOpts .and. isatt(rOpts,"gsMarkerSizeF")) then
gsMarkerSizeF = rOpts@gsMarkerSizeF
else
gsMarkerSizeF = 0.0085 ; Default: 0.007
end if
gsRes = True
gsRes@gsMarkerThicknessF = gsMarkerThicknessF ; default=1.0
gsRes@gsMarkerSizeF = gsMarkerSizeF ; Default: 0.007
ptRes = True ; text options for points
ptRes@txJust = "BottomCenter"; Default="CenterCenter".
ptRes@txFontThicknessF = 1.2 ; default=1.00
ptRes@txFontHeightF = 0.0125 ; default=0.05
if (rOpts .and. isatt(rOpts,"txFontHeightF")) then
ptRes@txFontHeightF = rOpts@txFontHeightF
end if
markerTxYOffset = 0.0175 ; default
if (rOpts .and. isatt(rOpts,"markerTxYOffset")) then
markerTxYOffset = rOpts@markerTxYOffset ; user defined offset
end if
dum10 = new((nCase*nVar),graphic)
dum11 = dum10
do n=0,nCase-1
gsRes@gsMarkerIndex = Markers(n) ; marker style (+)
gsRes@gsMarkerColor = Colors(n) ; marker color
ptRes@txFontColor = gsRes@gsMarkerColor
do i=0,nVar-1
dum10(n*nVar+i) = gsn_add_polymarker(wks,taylor,X(n,i),Y(n,i),gsRes)
dum11(n*nVar+i) = gsn_add_text(wks,taylor,(i+1),X(n,i),Y(n,i)+markerTxYOffset,ptRes)
end do
end do
; ---------------------------------------------------------------
; Part 5: ; add case legend and variable labels
; ---------------------------------------------------------------
if (rOpts .and. isatt(rOpts,"caseLabels")) then
if (isatt(rOpts,"caseLabelsFontHeightF")) then
caseLabelsFontHeightF = rOpts@caseLabelsFontHeightF
else
caseLabelsFontHeightF = 0.05
end if
lgres = True
lgres@lgMarkerColors = Colors ; colors of markers
lgres@lgMarkerIndexes = Markers ; Markers
lgres@lgMarkerSizeF = gsMarkerSizeF ; Marker size
lgres@lgItemType = "Markers" ; draw markers only
lgres@lgLabelFontHeightF = caseLabelsFontHeightF ; font height of legend case labels
if (isatt(rOpts,"legendWidth")) then
lgres@vpWidthF = rOpts@legendWidth
else
lgres@vpWidthF = 0.15 ; width of legend (NDC)
end if
if (isatt(rOpts,"legendHeight")) then
lgres@vpHeightF = rOpts@legendHeight
else
lgres@vpHeightF = 0.030*nCase ; height of legend (NDC)
end if
lgres@lgPerimOn = False ; turn off perimeter
nModel = dimsizes( rOpts@caseLabels )
lbid = gsn_create_legend(wks,nModel,rOpts@caseLabels,lgres)
amres = True
amres@amParallelPosF = 0.35
amres@amOrthogonalPosF = -0.35
annoid1 = gsn_add_annotation(taylor,lbid,amres) ; add legend to plot
end if
if (rOpts .and. isatt(rOpts,"varLabels")) then
nVar = dimsizes(rOpts@varLabels)
if (isatt(rOpts,"varLabelsFontHeightF")) then
varLabelsFontHeightF = rOpts@varLabelsFontHeightF
else
varLabelsFontHeightF = 0.013
end if
txres = True
txres@txFontHeightF = varLabelsFontHeightF
txres@txJust = "CenterLeft" ; justify to the center left
;delta_y = 0.02
delta_y = 0.06
if (rOpts .and. isatt(rOpts,"varLabelsYloc")) then
ys = rOpts@varLabelsYloc ; user specified
else
ys = max( (/nVar*delta_y , 0.30/) )
end if
do i = 1,nVar
if (i.eq.1) then
dum12 = new(nVar,graphic)
end if
dum12(i-1) = gsn_add_text(wks,taylor,i+" - "+rOpts@varLabels(i-1), .125,ys,txres)
ys = ys- delta_y
end do
taylor@$unique_string("dum")$ = dum12
end if
taylor@$unique_string("dum")$ = dum0 ; x-axis
taylor@$unique_string("dum")$ = dum1 ; y-axis
taylor@$unique_string("dum")$ = dum2 ; 1.0 std curve
taylor@$unique_string("dum")$ = dum5 ; labels [COR]
taylor@$unique_string("dum")$ = dum6 ; major tm [COR]
taylor@$unique_string("dum")$ = dum7 ; minor tm
taylor@$unique_string("dum")$ = dum10 ; markers
taylor@$unique_string("dum")$ = dum11 ; text
if (.not.isatt(rOpts,"taylorDraw") .or. \
(isatt(rOpts,"taylorDraw") .and. rOpts@taylorDraw)) then
draw(taylor)
end if
if (.not.isatt(rOpts,"taylorFrame") .or. \
(isatt(rOpts,"taylorFrame") .and. rOpts@taylorFrame)) then
frame(wks)
end if
return(taylor)
end
