MBC-package: Multivariate Bias Correction of Climate Model Outputs
In MBC: Multivariate Bias Correction of Climate Model Outputs
MBC-package R Documentation
Multivariate Bias Correction of Climate Model Outputs
Description
Calibrate and apply multivariate bias correction algorithms for climate model
simulations of multiple climate variables. Three iterative methods are
supported: (i) MBC Pearson correlation (MBCp), (ii) MBC rank correlation (MBCr),
and (iii) MBC N-dimensional probability density function transform (MBCn).
The first two, MBCp and MBCr (Cannon, 2016), match marginal distributions
and inter-variable dependence structure. Dependence structure can be measured
either by the Pearson correlation (MBCp) or by the Spearman rank
correlation (MBCr). The energy distance score
(escore) is recommended for model selection.
The third, MBCn (Cannon, 2018), which operates on the full
multivariate distribution, is more flexible and can be considered to be a
multivariate analogue of univariate quantile mapping. All aspects of the
observed distribution are transferred to the climate model simulations.
In each of the three methods, marginal distributions are corrected by the
change-preserving quantile delta mapping (QDM) algorithm
(Cannon et al., 2015). Finally, an implementation of the Rank Resampling for
Distributions and Dependences (R2D2) method introduced by Vrac (2018) is also
included.
An example application of the three MBC methods using the cccma dataset
can be run via:
example(MBC, run.dontrun=TRUE)
Note: these functions apply bias correction to the supplied data without
reference to other conditioning variables (e.g., time of year or season). The
user must partition their data in a way that makes sense for a particular
application. Furthermore, if MBCn is being applied to multiple
spatial locations or grid cells, it is recommended that the same sequence of
random rotations be used for each location. This can be achived by generating
the random rotations first and then passing the sequence using the
rot.seq argument:
rot.seq <- replicate(niterations, list(rot.random(nvars)))
bias_correction <- MBCn(..., rot.seq=rot.seq)
Details
Package: MBC
Type: Package
License: GPL-2
LazyLoad: yes
References
Cannon, A.J., 2018. Multivariate quantile mapping bias correction: An
N-dimensional probability density function transform for climate model
simulations of multiple variables. Climate Dynamics, 50(1-2):31-49.
doi:10.1007/s00382-017-3580-6
Cannon, A.J., 2016. Multivariate bias correction of climate model output:
Matching marginal distributions and inter-variable dependence structure.
Journal of Climate, 29:7045-7064. doi:10.1175/JCLI-D-15-0679.1
Cannon, A.J., S.R. Sobie, and T.Q. Murdock, 2015. Bias correction
of simulated precipitation by quantile mapping: How well do methods
preserve relative changes in quantiles and extremes? Journal of
Climate, 28:6938-6959. doi:10.1175/JCLI-D-14-00754.1
Francois, B., M. Vrac, A.J. Cannon, Y. Robin, and D. Allard, 2020.
Multivariate bias corrections of climate simulations: Which benefits
for which losses? Earth System Dynamics, 11:537-562.
doi:10.5194/esd-11-537-2020
Vrac, M., 2018. Multivariate bias adjustment of high-dimensional
climate simulations: the Rank Resampling for Distributions and
Dependences (R2D2) bias correction. Hydrology and Earth System
Sciences, 22:3175-3196. doi:10.5194/hess-22-3175-2018
See Also
QDM, MBCp, MBCr, MBCn, R2D2, escore, rot.random, cccma
Examples
## Not run:
data(cccma)
set.seed(1)
# Univariate quantile mapping
qdm.c <- cccma$gcm.c*0
qdm.p <- cccma$gcm.p*0
for(i in seq(ncol(cccma$gcm.c))){
fit.qdm <- QDM(o.c=cccma$rcm.c[,i], m.c=cccma$gcm.c[,i],
m.p=cccma$gcm.p[,i], ratio=cccma$ratio.seq[i],
trace=cccma$trace[i])
qdm.c[,i] <- fit.qdm$mhat.c
qdm.p[,i] <- fit.qdm$mhat.p
}
# Multivariate MBCp bias correction
fit.mbcp <- MBCp(o.c=cccma$rcm.c, m.c=cccma$gcm.c,
m.p=cccma$gcm.p, ratio.seq=cccma$ratio.seq,
trace=cccma$trace)
mbcp.c <- fit.mbcp$mhat.c
mbcp.p <- fit.mbcp$mhat.p
# Multivariate MBCr bias correction
fit.mbcr <- MBCr(o.c=cccma$rcm.c, m.c=cccma$gcm.c,
m.p=cccma$gcm.p, ratio.seq=cccma$ratio.seq,
trace=cccma$trace)
mbcr.c <- fit.mbcr$mhat.c
mbcr.p <- fit.mbcr$mhat.p
# Multivariate MBCn bias correction
fit.mbcn <- MBCn(o.c=cccma$rcm.c, m.c=cccma$gcm.c,
m.p=cccma$gcm.p, ratio.seq=cccma$ratio.seq,
trace=cccma$trace)
mbcn.c <- fit.mbcn$mhat.c
mbcn.p <- fit.mbcn$mhat.p
colnames(mbcn.c) <- colnames(mbcn.p) <-
colnames(cccma$rcm.c)
# Correlation matrices (Pearson and Spearman)
# MBCp
dev.new()
par(mfrow=c(2, 2))
plot(c(cor(cccma$rcm.c)), c(cor(qdm.c)), col='black',
pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCp',
main='Pearson correlation\nMBCp calibration')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.c)), c(cor(mbcp.c)), col='red')
plot(c(cor(cccma$rcm.p)), c(cor(qdm.p)),
col='black', pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCp',
main='Pearson correlation\nMBCp evaluation')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.p)), c(cor(mbcp.p)), col='red')
plot(c(cor(cccma$rcm.c, m='s')), c(cor(qdm.c, m='s')),
col='black', pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCp',
main='Spearman correlation\nMBCp calibration')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.c, m='s')), c(cor(mbcp.c, m='s')),
col='red')
plot(c(cor(cccma$rcm.p, m='s')), c(cor(qdm.p, m='s')),
col='black', pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCp',
main='Spearman correlation\nMBCp evaluation')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.p, m='s')), c(cor(mbcp.p, m='s')),
col='red')
# MBCr
dev.new()
par(mfrow=c(2, 2))
plot(c(cor(cccma$rcm.c)), c(cor(qdm.c)), col='black',
pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCr',
main='Pearson correlation\nMBCr calibration')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.c)), c(cor(mbcr.c)), col='blue')
plot(c(cor(cccma$rcm.p)), c(cor(qdm.p)),
col='black', pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCr',
main='Pearson correlation\nMBCr evaluation')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.p)), c(cor(mbcr.p)), col='blue')
plot(c(cor(cccma$rcm.c, m='s')), c(cor(qdm.c, m='s')),
col='black', pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCr',
main='Spearman correlation\nMBCr calibration')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.c, m='s')), c(cor(mbcr.c, m='s')),
col='blue')
plot(c(cor(cccma$rcm.p, m='s')), c(cor(qdm.p, m='s')),
col='black', pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCr',
main='Spearman correlation\nMBCr evaluation')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.p, m='s')), c(cor(mbcr.p, m='s')),
col='blue')
# MBCn
dev.new()
par(mfrow=c(2, 2))
plot(c(cor(cccma$rcm.c)), c(cor(qdm.c)), col='black',
pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCn',
main='Pearson correlation\nMBCn calibration')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.c)), c(cor(mbcn.c)), col='orange')
plot(c(cor(cccma$rcm.p)), c(cor(qdm.p)),
col='black', pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCn',
main='Pearson correlation\nMBCn evaluation')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.p)), c(cor(mbcn.p)), col='orange')
plot(c(cor(cccma$rcm.c, m='s')), c(cor(qdm.c, m='s')),
col='black', pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCn',
main='Spearman correlation\nMBCn calibration')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.c, m='s')), c(cor(mbcn.c, m='s')),
col='orange')
plot(c(cor(cccma$rcm.p, m='s')), c(cor(qdm.p, m='s')),
col='black', pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCn',
main='Spearman correlation\nMBCn evaluation')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.p, m='s')), c(cor(mbcn.p, m='s')),
col='orange')
# Pairwise scatterplots
dev.new()
pairs(cccma$gcm.c, main='CanESM2 calibration', col='#0000001A')
dev.new()
pairs(cccma$rcm.c, main='CanRCM4 calibration', col='#0000001A')
dev.new()
pairs(qdm.c, main='QDM calibration', col='#0000001A')
dev.new()
pairs(mbcp.c, main='MBCp calibration', col='#FF00001A')
dev.new()
pairs(mbcr.c, main='MBCr calibration', col='#0000FF1A')
dev.new()
pairs(mbcn.c, main='MBCn calibration', col='#FFA5001A')
# Energy distance skill score relative to univariate QDM
escore.qdm <- escore(cccma$rcm.p, qdm.p, scale.x=TRUE)
escore.mbcp <- escore(cccma$rcm.p, mbcp.p, scale.x=TRUE)
escore.mbcr <- escore(cccma$rcm.p, mbcr.p, scale.x=TRUE)
escore.mbcn <- escore(cccma$rcm.p, mbcn.p, scale.x=TRUE)
cat('ESS (MBCp):', 1-escore.mbcp/escore.qdm, '\n')
cat('ESS (MBCr):', 1-escore.mbcr/escore.qdm, '\n')
cat('ESS (MBCn):', 1-escore.mbcn/escore.qdm, '\n')
## End(Not run)
MBC documentation built on April 4, 2025, 3:41 a.m.
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| MBC-package | R Documentation |
Multivariate Bias Correction of Climate Model Outputs
Description
Calibrate and apply multivariate bias correction algorithms for climate model simulations of multiple climate variables. Three iterative methods are supported: (i) MBC Pearson correlation (MBCp), (ii) MBC rank correlation (MBCr), and (iii) MBC N-dimensional probability density function transform (MBCn).
The first two, MBCp and MBCr (Cannon, 2016), match marginal distributions
and inter-variable dependence structure. Dependence structure can be measured
either by the Pearson correlation (MBCp) or by the Spearman rank
correlation (MBCr). The energy distance score
(escore) is recommended for model selection.
The third, MBCn (Cannon, 2018), which operates on the full
multivariate distribution, is more flexible and can be considered to be a
multivariate analogue of univariate quantile mapping. All aspects of the
observed distribution are transferred to the climate model simulations.
In each of the three methods, marginal distributions are corrected by the
change-preserving quantile delta mapping (QDM) algorithm
(Cannon et al., 2015). Finally, an implementation of the Rank Resampling for
Distributions and Dependences (R2D2) method introduced by Vrac (2018) is also
included.
An example application of the three MBC methods using the cccma dataset
can be run via:
example(MBC, run.dontrun=TRUE)
Note: these functions apply bias correction to the supplied data without
reference to other conditioning variables (e.g., time of year or season). The
user must partition their data in a way that makes sense for a particular
application. Furthermore, if MBCn is being applied to multiple
spatial locations or grid cells, it is recommended that the same sequence of
random rotations be used for each location. This can be achived by generating
the random rotations first and then passing the sequence using the
rot.seq argument:
rot.seq <- replicate(niterations, list(rot.random(nvars)))
bias_correction <- MBCn(..., rot.seq=rot.seq)
Details
| Package: | MBC |
| Type: | Package |
| License: | GPL-2 |
| LazyLoad: | yes |
References
Cannon, A.J., 2018. Multivariate quantile mapping bias correction: An N-dimensional probability density function transform for climate model simulations of multiple variables. Climate Dynamics, 50(1-2):31-49. doi:10.1007/s00382-017-3580-6
Cannon, A.J., 2016. Multivariate bias correction of climate model output: Matching marginal distributions and inter-variable dependence structure. Journal of Climate, 29:7045-7064. doi:10.1175/JCLI-D-15-0679.1
Cannon, A.J., S.R. Sobie, and T.Q. Murdock, 2015. Bias correction of simulated precipitation by quantile mapping: How well do methods preserve relative changes in quantiles and extremes? Journal of Climate, 28:6938-6959. doi:10.1175/JCLI-D-14-00754.1
Francois, B., M. Vrac, A.J. Cannon, Y. Robin, and D. Allard, 2020. Multivariate bias corrections of climate simulations: Which benefits for which losses? Earth System Dynamics, 11:537-562. doi:10.5194/esd-11-537-2020
Vrac, M., 2018. Multivariate bias adjustment of high-dimensional climate simulations: the Rank Resampling for Distributions and Dependences (R2D2) bias correction. Hydrology and Earth System Sciences, 22:3175-3196. doi:10.5194/hess-22-3175-2018
See Also
QDM, MBCp, MBCr, MBCn, R2D2, escore, rot.random, cccma
Examples
## Not run:
data(cccma)
set.seed(1)
# Univariate quantile mapping
qdm.c <- cccma$gcm.c*0
qdm.p <- cccma$gcm.p*0
for(i in seq(ncol(cccma$gcm.c))){
fit.qdm <- QDM(o.c=cccma$rcm.c[,i], m.c=cccma$gcm.c[,i],
m.p=cccma$gcm.p[,i], ratio=cccma$ratio.seq[i],
trace=cccma$trace[i])
qdm.c[,i] <- fit.qdm$mhat.c
qdm.p[,i] <- fit.qdm$mhat.p
}
# Multivariate MBCp bias correction
fit.mbcp <- MBCp(o.c=cccma$rcm.c, m.c=cccma$gcm.c,
m.p=cccma$gcm.p, ratio.seq=cccma$ratio.seq,
trace=cccma$trace)
mbcp.c <- fit.mbcp$mhat.c
mbcp.p <- fit.mbcp$mhat.p
# Multivariate MBCr bias correction
fit.mbcr <- MBCr(o.c=cccma$rcm.c, m.c=cccma$gcm.c,
m.p=cccma$gcm.p, ratio.seq=cccma$ratio.seq,
trace=cccma$trace)
mbcr.c <- fit.mbcr$mhat.c
mbcr.p <- fit.mbcr$mhat.p
# Multivariate MBCn bias correction
fit.mbcn <- MBCn(o.c=cccma$rcm.c, m.c=cccma$gcm.c,
m.p=cccma$gcm.p, ratio.seq=cccma$ratio.seq,
trace=cccma$trace)
mbcn.c <- fit.mbcn$mhat.c
mbcn.p <- fit.mbcn$mhat.p
colnames(mbcn.c) <- colnames(mbcn.p) <-
colnames(cccma$rcm.c)
# Correlation matrices (Pearson and Spearman)
# MBCp
dev.new()
par(mfrow=c(2, 2))
plot(c(cor(cccma$rcm.c)), c(cor(qdm.c)), col='black',
pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCp',
main='Pearson correlation\nMBCp calibration')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.c)), c(cor(mbcp.c)), col='red')
plot(c(cor(cccma$rcm.p)), c(cor(qdm.p)),
col='black', pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCp',
main='Pearson correlation\nMBCp evaluation')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.p)), c(cor(mbcp.p)), col='red')
plot(c(cor(cccma$rcm.c, m='s')), c(cor(qdm.c, m='s')),
col='black', pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCp',
main='Spearman correlation\nMBCp calibration')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.c, m='s')), c(cor(mbcp.c, m='s')),
col='red')
plot(c(cor(cccma$rcm.p, m='s')), c(cor(qdm.p, m='s')),
col='black', pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCp',
main='Spearman correlation\nMBCp evaluation')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.p, m='s')), c(cor(mbcp.p, m='s')),
col='red')
# MBCr
dev.new()
par(mfrow=c(2, 2))
plot(c(cor(cccma$rcm.c)), c(cor(qdm.c)), col='black',
pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCr',
main='Pearson correlation\nMBCr calibration')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.c)), c(cor(mbcr.c)), col='blue')
plot(c(cor(cccma$rcm.p)), c(cor(qdm.p)),
col='black', pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCr',
main='Pearson correlation\nMBCr evaluation')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.p)), c(cor(mbcr.p)), col='blue')
plot(c(cor(cccma$rcm.c, m='s')), c(cor(qdm.c, m='s')),
col='black', pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCr',
main='Spearman correlation\nMBCr calibration')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.c, m='s')), c(cor(mbcr.c, m='s')),
col='blue')
plot(c(cor(cccma$rcm.p, m='s')), c(cor(qdm.p, m='s')),
col='black', pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCr',
main='Spearman correlation\nMBCr evaluation')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.p, m='s')), c(cor(mbcr.p, m='s')),
col='blue')
# MBCn
dev.new()
par(mfrow=c(2, 2))
plot(c(cor(cccma$rcm.c)), c(cor(qdm.c)), col='black',
pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCn',
main='Pearson correlation\nMBCn calibration')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.c)), c(cor(mbcn.c)), col='orange')
plot(c(cor(cccma$rcm.p)), c(cor(qdm.p)),
col='black', pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCn',
main='Pearson correlation\nMBCn evaluation')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.p)), c(cor(mbcn.p)), col='orange')
plot(c(cor(cccma$rcm.c, m='s')), c(cor(qdm.c, m='s')),
col='black', pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCn',
main='Spearman correlation\nMBCn calibration')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.c, m='s')), c(cor(mbcn.c, m='s')),
col='orange')
plot(c(cor(cccma$rcm.p, m='s')), c(cor(qdm.p, m='s')),
col='black', pch=19, xlim=c(-1, 1), ylim=c(-1, 1),
xlab='CanRCM4', ylab='CanESM2 MBCn',
main='Spearman correlation\nMBCn evaluation')
abline(0, 1)
grid()
points(c(cor(cccma$rcm.p, m='s')), c(cor(mbcn.p, m='s')),
col='orange')
# Pairwise scatterplots
dev.new()
pairs(cccma$gcm.c, main='CanESM2 calibration', col='#0000001A')
dev.new()
pairs(cccma$rcm.c, main='CanRCM4 calibration', col='#0000001A')
dev.new()
pairs(qdm.c, main='QDM calibration', col='#0000001A')
dev.new()
pairs(mbcp.c, main='MBCp calibration', col='#FF00001A')
dev.new()
pairs(mbcr.c, main='MBCr calibration', col='#0000FF1A')
dev.new()
pairs(mbcn.c, main='MBCn calibration', col='#FFA5001A')
# Energy distance skill score relative to univariate QDM
escore.qdm <- escore(cccma$rcm.p, qdm.p, scale.x=TRUE)
escore.mbcp <- escore(cccma$rcm.p, mbcp.p, scale.x=TRUE)
escore.mbcr <- escore(cccma$rcm.p, mbcr.p, scale.x=TRUE)
escore.mbcn <- escore(cccma$rcm.p, mbcn.p, scale.x=TRUE)
cat('ESS (MBCp):', 1-escore.mbcp/escore.qdm, '\n')
cat('ESS (MBCr):', 1-escore.mbcr/escore.qdm, '\n')
cat('ESS (MBCn):', 1-escore.mbcn/escore.qdm, '\n')
## End(Not run)
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