Embed Size (px)
Citation preview
Supplement of Earth Syst. Dynam., 11, 537–562, 2020https://doi.org/10.5194/esd-11-537-2020-supplement© Author(s) 2020. This work is distributed underthe Creative Commons Attribution 4.0 License.
Supplement of
Multivariate bias corrections of climate simulations:which benefits for which losses?Bastien François et al.
Correspondence to: Bastien François ([email protected])
The copyright of individual parts of the supplement might differ from the CC BY 4.0 License.
Mod
el
CD
F−t
R2D
2
2d−d
OTC
Spat
ial−
dOTC
Full−
dOTC
MBC
n
2d−M
Rec
Spat
ial−
MR
ec
Full−
MR
ec
0.0
0.5
1.0
1.5
2.0
2.5
Mea
n d
iffer
ence
(T2)
(a)
Mod
el
CD
F−t
R2D
2
2d−d
OTC
Spat
ial−
dOTC
Full−
dOTC
MBC
n
2d−M
Rec
Spat
ial−
MR
ec
Full−
MR
ec
0.0
0.2
0.4
0.6
0.8
Mea
n re
lativ
e di
ffere
nce
(PR
)
(b)
Mod
el
CD
F−t
R2D
2
2d−d
OTC
Spat
ial−
dOTC
Full−
dOTC
MBC
n
2d−M
Rec
Spat
ial−
MR
ec
Full−
MR
ec
−0.4
−0.3
−0.2
−0.1
0.0
Stan
dard
dev
. rel
ativ
e di
ffere
nce
(T2)
(c)
Mod
el
CD
F−t
R2D
2
2d−d
OTC
Spat
ial−
dOTC
Full−
dOTC
MBC
n
2d−M
Rec
Spat
ial−
MR
ec
Full−
MR
ec
−0.2
0.0
0.2
0.4St
anda
rd d
ev. r
elat
ive
diffe
renc
e (P
R)
(d)
Figure S1. Boxplots of mean (a and b) and standard deviation (c and d) differences for Temperature (T2, a and c) and Precipitation (PR,
b and d) during winter over the 1979-2016 period for the Brittany region (SAFRAN reference). Results are shown for: plain IPSL; CDF-t;
R2D2; dOTC (2d-, Spatial- and Full-versions); MBC-n and MRec (2d-, Spatial- and Full-versions) outputs. Red asterisks indicate values
lying outside the plotted range.
2
42
46
50
−0.25−0.05 0.15 0.35 0.55
La
titu
de
(a1) Reference (b1) Model (c1) CDF−t
42
46
50
(d1) 2d−R2D2
La
titu
de
(e1) Spatial−R2D2 (f1) Full−R2D2
42
46
50
(g1) 2d−dOTC
La
titu
de
(h1) Spatial−dOTC (i1) Full−dOTC
42
46
50
(j1) 2d−MBCn
La
titu
de
(k1) Spatial−MBCn (l1) Full−MBCn
−5 0 5 10
42
46
50
(m1) 2d−MRec
La
titu
de
Longitude−5 0 5 10
(n1) Spatial−MRec
Longitude−5 0 5 10
(o1) Full−MRec
Longitude
47
.54
8.5
0.160.240.330.410.50
La
titu
de
(a2) Reference (b2) Model (c2) CDF−t
47
.54
8.5
(d2) 2d−R2D2
La
titu
de
(e2) Spatial−R2D2 (f2) Full−R2D2
47
.54
8.5
(g2) 2d−dOTCL
atitu
de
(h2) Spatial−dOTC (i2) Full−dOTC4
7.5
48
.5
(j2) 2d−MBCn
La
titu
de
(k2) Spatial−MBCn (l2) Full−MBCn
−5.0 −4.0 −3.0
47
.54
8.5
(m2) 2d−MRec
La
titu
de
Longitude−5.0 −4.0 −3.0
(n2) Spatial−MRec
Longitude−5.0 −4.0 −3.0
(o2) Full−MRec
Longitude
Figure S2. Maps of temperature vs. precipitation Spearman correlation maps computed at each grid cell using WFDEI reference (a1-o1) and
SAFRAN reference (a2-o2) during winter over the 1979-2016 period. Results are shown for: Reference; plain IPSL; CDF-t; R2D2; dOTC;
MBC-n and MRec outputs for respectively 2d-, Spatial- and Full- versions. Note that the color scales between (a1-o1) and (a2-o2) are not
the same to better emphasize intensities of values of the two regions.
3
●
●
●
●
●
●
●
●
●
●
●
●● ● ●
●●
● ●●
●
●
●
●
●
●
−0
.50
.00
.51
.0
Distance (km)
T2
Sp
ea
rma
n s
pa
tial c
orr
ela
tion
0 300 600 900 1200
● ReferenceModelCDF−t
(a1)
●
●
●
●
●
●
●
●
●
●
●
●● ● ●
●●
● ●●
●
●
●
●
●
●−
0.5
0.0
0.5
1.0
Distance (km)
T2
Sp
ea
rma
n s
pa
tial c
orr
ela
tion
0 300 600 900 1200
● ReferenceModel2d−R2D2Spatial−R2D2Full−R2D2
(b1)
●
●
●
●
●
●
●
●
●
●
●
●● ● ●
●●
● ●●
●
●
●
●
●
●
−0
.50
.00
.51
.0
Distance (km)
T2
Sp
ea
rma
n s
pa
tial c
orr
ela
tion
0 300 600 900 1200
● ReferenceModel2d−dOTCSpatial−dOTCFull−dOTC
(c1)
●
●
●
●
●
●
●
●
●
●
●
●● ● ●
●●
● ●●
●
●
●
●
●
●
−0
.50
.00
.51
.0
Distance (km)
T2
Sp
ea
rma
n s
pa
tial c
orr
ela
tion
0 300 600 900 1200
● ReferenceModel2d−MBCnSpatial−MBCnFull−MBCn
(d1)
●
●
●
●
●
●
●
●
●
●
●
●● ● ●
●●
● ●●
●
●
●
●
●
●
−0
.50
.00
.51
.0
Distance (km)
T2
Sp
ea
rma
n s
pa
tial c
orr
ela
tion
0 300 600 900 1200
● ReferenceModel2d−MRecSpatial−MRecFull−MRec
(e1)
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●●
● ● ● ●●
●
● ●●
0 50 100 150 200
−0
.50
.00
.51
.0
Distance (km)
T2
Sp
ea
rma
n s
pa
tial c
orr
ela
tion
● ReferenceModelCDF−t
(a2)
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●●
● ● ● ●●
●
● ●●
0 50 100 150 200
−0
.50
.00
.51
.0
Distance (km)
T2
Sp
ea
rma
n s
pa
tial c
orr
ela
tion
● ReferenceModel2d−R2D2Spatial−R2D2Full−R2D2
(b2)
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●●
● ● ● ●●
●
● ●●
0 50 100 150 200
−0
.50
.00
.51
.0
Distance (km)
T2
Sp
ea
rma
n s
pa
tial c
orr
ela
tion
● ReferenceModel2d−dOTCSpatial−dOTCFull−dOTC
(c2)
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●●
● ● ● ●●
●
● ●●
0 50 100 150 200
−0
.50
.00
.51
.0
Distance (km)
T2
Sp
ea
rma
n s
pa
tial c
orr
ela
tion
● ReferenceModel2d−MBCnSpatial−MBCnFull−MBCn
(d2)
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●●
● ● ● ●●
●
● ●●
0 50 100 150 200
−0
.50
.00
.51
.0
Distance (km)
T2
Sp
ea
rma
n s
pa
tial c
orr
ela
tion
● ReferenceModel2d−MRecSpatial−MRecFull−MRec
(e2)
Figure S3. Correlograms for temperature using WFDEI reference (a1-e1) and SAFRAN reference (a2-e2) during winter over the 1979-2016
period. Results are shown for Reference (circles) and plain IPSL (black line). Results are displayed for: CDF-t; R2D2; dOTC; MBC-n and
MRec outputs for respectively 2d- (dotted), Spatial- (dashed) and Full-versions (solid lines).
4
42
46
50
−0.03 0.10 0.23 0.36 0.50
La
titu
de
(a1) Reference−0.40−0.20 0.00 0.20 0.40
(b1) Model (c1) CDF−t
42
46
50
(d1) 2d−R2D2
La
titu
de
(e1) Spatial−R2D2 (f1) Full−R2D2
42
46
50
(g1) 2d−dOTC
La
titu
de
(h1) Spatial−dOTC (i1) Full−dOTC
42
46
50
(j1) 2d−MBCn
La
titu
de
(k1) Spatial−MBCn (l1) Full−MBCn
−5 0 5 10
42
46
50
(m1) 2d−MRec
La
titu
de
Longitude−5 0 5 10
(n1) Spatial−MRec
Longitude−5 0 5 10
(o1) Full−MRec
Longitude
47
.54
8.5
0.110.190.270.340.42
La
titu
de
(a2) Reference−0.23−0.11 0.00 0.11 0.23
(b2) Model (c2) CDF−t
47
.54
8.5
(d2) 2d−R2D2
La
titu
de
(e2) Spatial−R2D2 (f2) Full−R2D2
47
.54
8.5
(g2) 2d−dOTC
La
titu
de
(h2) Spatial−dOTC (i2) Full−dOTC
47
.54
8.5
(j2) 2d−MBCn
La
titu
de
(k2) Spatial−MBCn (l2) Full−MBCn
−5.0 −4.0 −3.0
47
.54
8.5
(m2) 2d−MRec
La
titu
de
Longitude−5.0 −4.0 −3.0
(n2) Spatial−MRec
Longitude−5.0 −4.0 −3.0
(o2) Full−MRec
Longitude
Figure S4. Differences of order 1 autocorrelation for precipitation using WFDEI reference (a1-o1) and SAFRAN reference (a2-o2) during
winter over the 1979-2016 period. Results are shown for: Reference; plain IPSL; CDF-t; R2D2; dOTC; MBC-n and MRec outputs for
respectively 2d-, Spatial- and Full- versions. Note that the color scales between (a1-o1) and (a2-o2) are not the same to better emphasize
intensities of values of the two regions.
5
CD
F−
t
2d−
R2D
2
Spa
tial−
R2D
2
Ful
l−R
2D2
2d−
dOT
C
Spa
tial−
dOT
C
Ful
l−dO
TC
2d−
MB
Cn
Spa
tial−
MB
Cn
Ful
l−M
BC
n
2d−
MR
ec
Spa
tial−
MR
ec
Ful
l−M
Rec
0.0
0.2
0.4
0.6
0.8
1.0
Spe
arm
an c
orr.
T2
(a)C
DF
−t
2d−
R2D
2
Spa
tial−
R2D
2
Ful
l−R
2D2
2d−
dOT
C
Spa
tial−
dOT
C
Ful
l−dO
TC
2d−
MB
Cn
Spa
tial−
MB
Cn
Ful
l−M
BC
n
2d−
MR
ec
Spa
tial−
MR
ec
Ful
l−M
Rec
0.0
0.2
0.4
0.6
0.8
1.0S
pear
man
cor
r. P
R
(a)C
DF
−t
2d−
R2D
2
Spa
tial−
R2D
2
Ful
l−R
2D2
2d−
dOT
C
Spa
tial−
dOT
C
Ful
l−dO
TC
2d−
MB
Cn
Spa
tial−
MB
Cn
Ful
l−M
BC
n
2d−
MR
ec
Spa
tial−
MR
ec
Ful
l−M
Rec
0.0
0.2
0.4
0.6
0.8
1.0
Spe
arm
an c
orr.
T2
(b)
CD
F−
t
2d−
R2D
2
Spa
tial−
R2D
2
Ful
l−R
2D2
2d−
dOT
C
Spa
tial−
dOT
C
Ful
l−dO
TC
2d−
MB
Cn
Spa
tial−
MB
Cn
Ful
l−M
BC
n
2d−
MR
ec
Spa
tial−
MR
ec
Ful
l−M
Rec
0.0
0.2
0.4
0.6
0.8
1.0
Spe
arm
an c
orr.
PR
(b)
Figure S5. Boxplots of rank correlation computed at each grid cell between the bias corrected and the raw climate model time series for
precipitation using WFDEI for France (a) and SAFRAN for Brittany (b) region during winter over the 1979-2016 period. For both boxplots,
results are shown for: CDF-t; R2D2; dOTC; MBC-n and MRec outputs for 2d-, Spatial- and Full-versions.
6
42
46
50
−0.19−0.10 0.00 0.10 0.19
La
titu
de
(a1) Reference (b1) Model (c1) CDF−t
42
46
50
(d1) 2d−R2D2
La
titu
de
(e1) Spatial−R2D2 (f1) Full−R2D2
42
46
50
(g1) 2d−dOTC
La
titu
de
(h1) Spatial−dOTC (i1) Full−dOTC
42
46
50
(j1) 2d−MBCn
La
titu
de
(k1) Spatial−MBCn (l1) Full−MBCn
−5 0 5 10
42
46
50
(m1) 2d−MRec
La
titu
de
Longitude−5 0 5 10
(n1) Spatial−MRec
Longitude−5 0 5 10
(o1) Full−MRec
Longitude
47
.54
8.5
−0.12−0.06 0.00 0.06 0.12
La
titu
de
(a2) Reference (b2) Model (c2) CDF−t
47
.54
8.5
(d2) 2d−R2D2
La
titu
de
(e2) Spatial−R2D2 (f2) Full−R2D2
47
.54
8.5
(g2) 2d−dOTC
La
titu
de
(h2) Spatial−dOTC (i2) Full−dOTC
47
.54
8.5
(j2) 2d−MBCn
La
titu
de
(k2) Spatial−MBCn (l2) Full−MBCn
−5.0 −4.0 −3.0
47
.54
8.5
(m2) 2d−MRec
La
titu
de
Longitude−5.0 −4.0 −3.0
(n2) Spatial−MRec
Longitude−5.0 −4.0 −3.0
(o2) Full−MRec
Longitude
Figure S6. Differences of temperature vs. precipitation Spearman correlation computed at each grid cell between the 1979-1997 and 1998-
2016 periods during summer. WFDEI (a1-o1) and SAFRAN (a2-o2) data are used for the bias correction. Note that the color scales between
(a1-o1) and (a2-o2) are not the same to better emphasize intensities of values of the two regions.
7
●
●
●
●
● ●
●● ●
●
●●
●
●
(a) *
0
50
100
Ref
.
CD
F−t
2d−R
2D2−
T2
2d−R
2D2−
PR
Spa
tial−
R2D
2
Full−
R2D
2
2d−d
OTC
Spa
tial−
dOTC
Full−
dOTC
2d−M
BC
n
Spa
tial−
MB
Cn
Full−
MB
Cn
2d−M
Rec
Spa
tial−
MR
ec
Full−
MR
ec
Was
sers
tein
dis
tanc
e●
Wd on Spatial T2Wd on Spatial PRWd on Spatial T2/PR
●●
●
● ● ● ●● ●
●
●
●
●●
●
(b)
0
50
100
Ref
.
CD
F−t
2d−R
2D2−
T2
2d−R
2D2−
PR
Spa
tial−
R2D
2
Full−
R2D
2
2d−d
OTC
Spa
tial−
dOTC
Full−
dOTC
2d−M
BC
n
Spa
tial−
MB
Cn
Full−
MB
Cn
2d−M
Rec
Spa
tial−
MR
ec
Full−
MR
ec
Was
sers
tein
dis
tanc
e
●Wd on Spatial T2Wd on Spatial PRWd on Spatial T2/PR
Figure S7. Values of the three Wasserstein distances between 1979-1997 and 1998-2016 periods during winter for temperature (square),
precipitation (circle) and both temperature and precipitation (triangle) for the region of France (a) and Brittany (b). Results are presented
for: Reference; plain IPSL (lines); CDF-t and the different multivariate BC outputs. 2d-R2D2-T2 (resp. 2d-R2D2-PR) indicates results for
2d-R2D2 with temperature (resp. precipitation) used as reference dimension. Black asterisks indicate values lying outside the plotted range.
8
Mod
el
2d−M
Rec
Spat
ial−
MR
ec
Full−
MR
ec
−1.0
−0.5
0.0
0.5
1.0
1.5
2.0M
ean
diff
eren
ce (T
2)(a)
Mod
el
2d−M
Rec
Spat
ial−
MR
ec
Full−
MR
ec
−0.5
0.0
0.5
1.0
Mea
n re
lativ
e di
ffere
nce
(PR
)
(b)
Mod
el
2d−M
Rec
Spat
ial−
MR
ec
Full−
MR
ec−0.2
−0.1
0.0
0.1
Stan
dard
dev
. rel
ativ
e di
ffere
nce
(T2)
(c)
Mod
el
2d−M
Rec
Spat
ial−
MR
ec
Full−
MR
ec
−0.6
−0.4
−0.2
0.0
0.2
0.4
Stan
dard
dev
. rel
ativ
e di
ffere
nce
(PR
)
(d)
Figure S8. Boxplots of mean (a and b) and standard deviation (c and d) differences for Temperature (T2, a and c) and Precipitation (PR,
b and d) during winter over the 1979-2016 period for the France region (WFDEI reference) with seasonal BC. Results are shown for: plain
IPSL and MRec (2d-, Spatial- and Full-versions) outputs. Red asterisks indicate values lying outside the plotted range.
9
−5 0 5 10
42
44
46
48
50
52
−0.25−0.05 0.15 0.35 0.55
La
titu
de
Longitude
(a1) 2d−MRec
−5 0 5 10
(b1) Spatial−MRec
Longitude−5 0 5 10
(c1) Full−MRec
Longitude
Figure S9. Temperature vs. precipitation Spearman correlation maps computed at each grid cell using WFDEI reference (a1-c1) during
winter over the 1979-2016 period with seasonal BC. Results are shown for MRec (a1-c1) outputs for respectively 2d-, Spatial- and Full-
versions.
10
●●
●
●
●
●
●
●
●
●
●●
● ● ● ●●
● ● ●
●
●
●
●●
●
−0
.50
.00
.51
.0
Distance (km)
T2
Sp
ea
rma
n s
pa
tia
l co
rre
latio
n
0 300 600 900 1200
● ReferenceModel2d−MRecSpatial−MRecFull−MRec
(a)
●
●
●
●
●
●
●
●
●●
●●
● ● ● ● ● ● ● ●● ● ● ●
●
●
−0
.20
.20
.40
.60
.81
.0
Distance (km)
PR
Sp
ea
rma
n s
pa
tia
l co
rre
latio
n
0 300 600 900 1200
● ReferenceModel2d−MRecSpatial−MRecFull−MRec
(b)
Figure S10. Correlograms for temperature (a) and precipitation (b) using WFDEI reference for France during winter over the 1979-2016
period with seasonal BC. Results are shown for: Reference (circles), plain IPSL (black line) and MRec outputs for respectively 2d- (dotted),
Spatial- (dashed) and Full-versions (solid lines).
11
−5 0 5 10
42
44
46
48
50
52
−0.02 0.20 0.42 0.64 0.86
La
titu
de
Longitude
(a1) 2d−MRec
−5 0 5 10
(b1) Spatial−MRec
Longitude−5 0 5 10
(c1) Full−MRec
Longitude
Figure S11. Order 1 Pearson autocorrelation for temperature using WFDEI reference during winter over the 1979-2016 period for the
seasonal BC. Results are shown for MRec outputs for 2d-, Spatial- and Full-versions.
12
−5 0 5 10
42
44
46
48
50
52
−0.02 0.11 0.24 0.37 0.50
La
titu
de
Longitude
(a1) 2d−MRec
−5 0 5 10
(b1) Spatial−MRec
Longitude−5 0 5 10
(c1) Full−MRec
Longitude
Figure S12. Order 1 Pearson autocorrelation for precipitation using WFDEI reference during winter over the 1979-2016 period for the
seasonal BC. Results are shown for MRec outputs for 2d-, Spatial- and Full-versions.
13
![Abstract arXiv:1609.08669v1 [cs.CV] 27 Sep 2016 · September 2016 Abstract Transport based distances, such as the Wasserstein distance and earth mover’s distance, have been shown](https://img.pdfslide.us/doc/110x75/5f067ad67e708231d4183355/abstract-arxiv160908669v1-cscv-27-sep-2016-september-2016-abstract-transport.jpg)
