MBC (version 0.10-6)

MBC-package: 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: because empirical quantiles and their changes are used by QDM, sample sizes of the observed, model calibration, and model projection datasets should be approximately equal.

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

if (FALSE) {
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')
}