SBCK (Statistical Bias Correction Kit)

Clone

Python and R version are given in git submodules, so use:

git clone --recurse-submodules https://github.com/yrobink/SBCK

Release

The last release is the 0.4.13 version, in the version-0.4.X branch. The developpment version is the 0.5.X version.

Features

• python3 and R version
• c++ independent files for Sparse Histogram
• Implement classic methods of bias correction (see [8,9] for the definition of bias correction)
• Quantile Mapping [5,7,14], parametric and non parametric version
• CDFt methods [6]
• OTC and dOTC methods [9]
• R2D2 method [11]
• MBCn method [4]
• QDM method [3]
• MRec method [1]
• ECBC method [12]
• TSMBC method [15], for autocorrelations.

How to select a bias correction method ?

This summary of ability of each method to perform a bias correction is proposed by François, (2020). Please refer to this article for further interpretation.

Characteristics	CDF-t	R2D2	dOTC	MBCn	MRec
Correction of univariate dist. prop.	✔️	✔️	✔️	✔️	✔️
Modification of correlations of the model	❌	✔️	✔️	✔️	✔️
Capacity to correct inter-var. prop.	❌	✔️	✔️	✔️	✔️
Capacity to correct spatial prop.	❌	✔️	✔️	⚠️	⚠️
Capacity to correct temporal prop.	❌	❌	❌	❌	❌
Preserve the rank structure of the model	✔️	⚠️	⚠️	⚠️	⚠️
Capacity to correct small geographical area	n.a.	✔️	✔️	✔️	✔️
Capacity to correct large geographical area	n.a.	⚠️	⚠️	⚠️	❌
Allow for change of the multi-dim. prop.	✔️	❌	✔️	⚠️	✔️

Python instruction

Requires:

• python3
• Eigen
• numpy
• scipy
• pybind11
• a C++ compiler

For python, just use the command:

python3 setup.py install --user

If the Eigen library is not found, use:

python3 setup.py install --user eigen="path-to-eigen"

Conda

If using conda to manage environments and packages, the module can be installed with:

conda create -n sbck eigen numpy scipy pybind11 cxx-compiler
conda activate sbck
python setup.py install

Make sure that you never try to import the package in an interpreter who's current working directory is the source folder. This would fail with ModuleNotFoundError: No module named 'SBCK.tools.__tools_cpp' since the compiled version of the module is not present in the source folder, but rather in the conda environment itself.

R instruction

SBCK is available in CRAN.

Requires:

• R
• roxygen2 (>= 7.0.0)
• devtools
• Rcpp
• RcppEigen
• methods
• R6
• ROOPSD

Just run:

Rscript build.R -c -v -i

Examples

For bias correction example, X0 and X1 are respectively the random variable to correct in calibration and projection period. Y0 is the reference during calibration period. Z0 and Z1 are the corrections during calibration and projection period.

Univariate bias correction: QM, CDFt and QDM

Bivariate bias correction: dOTC

Bivariate bias correction: MBCn

Bivariate bias correction: MRec

License

Copyright(c) 2021 Yoann Robin

This file is part of SBCK.

SBCK is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

SBCK is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with SBCK. If not, see https://www.gnu.org/licenses/.

References

• [1] Bárdossy, A. and Pegram, G.: Multiscale spatial recorrelation of RCM precipitation to produce unbiased climate change scenarios over large areas and small, Water Resources Research, 48, 9502–, https://doi.org/10.1029/2011WR011524, 2012.
• [2] Bazaraa, M. S., Jarvis, J. J., and Sherali, H. D.: Linear Programming and Network Flows, 4th edn., John Wiley & Sons, 2009.
• [3] Cannon, A. J., Sobie, S. R., and Murdock, T. Q.: Bias correction of simulated precipitation by quantile mapping: how well do methods preserve relative changes in quantiles and extremes?, J. Climate, 28, 6938–6959, https://doi.org/10.1175/JCLI-D-14-00754.1, 2015.
• [4] Cannon, Alex J.: Multivariate quantile mapping bias correction: an N-dimensional probability density function transform for climate model simulations of multiple variables, Climate Dynamics, nb. 1, vol. 50, p. 31-49, 10.1007/s00382-017-3580-6, 2018.
• [5] Déqué, M.: Frequency of precipitation and temperature extremes over France in an anthropogenic scenario: Model results and statistical correction according to observed values, Global Planet. Change, 57, 16–26, https://doi.org/10.1016/j.gloplacha.2006.11.030, 2007.
• [6] Michelangeli, P.-A., Vrac, M., and Loukos, H.: Probabilistic downscaling approaches: Application to wind cumulative distribution functions, Geophys. Res. Lett., 36, L11708, https://doi.org/10.1029/2009GL038401, 2009.
• [7] Panofsky, H. A. and Brier, G. W.: Some applications of statistics to meteorology, Mineral Industries Extension Services, College of Mineral Industries, Pennsylvania State University, 103 pp., 1958.
• [8] Piani, C., Weedon, G., Best, M., Gomes, S., Viterbo, P., Hagemann, S., and Haerter, J.: Statistical bias correction of global simulated daily precipitation and temperature for the application of hydrological models, J. Hydrol., 395, 199–215, https://doi.org/10.1016/j.jhydrol.2010.10.024, 2010.
• [9] Robin, Y., Vrac, M., Naveau, P., Yiou, P.: Multivariate stochastic bias corrections with optimal transport, Hydrol. Earth Syst. Sci., 23, 773–786, 2019, https://doi.org/10.5194/hess-23-773-2019
• [10] Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances. arXiv, https://arxiv.org/abs/1306.0895
• [11] Vrac, M.: Multivariate bias adjustment of high-dimensional climate simulations: the Rank Resampling for Distributions and Dependences (R2 D2 ) bias correction, Hydrol. Earth Syst. Sci., 22, 3175–3196, https://doi.org/10.5194/hess-22-3175-2018, 2018.
• [12] Vrac, M. and P. Friederichs, 2015: Multivariate—Intervariable, Spatial, and Temporal—Bias Correction. J. Climate, 28, 218–237, https://doi.org/10.1175/JCLI-D-14-00059.1
• [13] Wasserstein, L. N. (1969). Markov processes over denumerable products of spaces describing large systems of automata. Problems of Information Transmission, 5(3), 47-52.
• [14] Wood, A. W., Leung, L. R., Sridhar, V., and Lettenmaier, D. P.: Hydrologic Implications of Dynamical and Statistical Approaches to Downscaling Climate Model Outputs, Clim. Change, 62, 189–216, https://doi.org/10.1023/B:CLIM.0000013685.99609.9e, 2004.
• [15] Robin, Y. and Vrac, M.: Is time a variable like the others in multivariate statistical downscaling and bias correction?, Earth Syst. Dynam. Discuss. [preprint], https://doi.org/10.5194/esd-2021-12, in review, 2021.
• François, B., Vrac, M., Cannon, A., Robin, Y., and Allard, D.: Multivariate bias corrections of climate simulations: Which benefits for which losses?, Earth Syst. Dyn., 11, 537–562, https://doi.org/10.5194/esd-11-537-2020, https://esd.copernicus.org/articles/11/537/2020/, 2020.