Multivariate quantile mapping bias correction: an N-dimensional probability density function transform for climate model simulations of multiple variables

Abstract

Index (FWI) System, a complicated set of multivariate indices that characterizes the risk of wildfire, are then calculated and verified against observed values. Third, MBCn is used to correct biases in the spatial dependence structure of CanRCM4 precipitation fields. Results are compared against a univariate quantile mapping algorithm, which neglects the dependence between variables, and two multivariate bias correction algorithms, each of which corrects a different form of inter-variable correlation structure. MBCn outperforms these alternatives, often by a large margin, particularly for annual maxima of the FWI distribution and spatiotemporal autocorrelation of precipitation fields.

Contributions of different bias‐correction methods and reference meteorological forcing data sets to uncertainty in projected temperature and precipitation extremes

“…To make a stronger statement in this regard, the inclusion of other bias-correction methods [e.g., Ines et al, 2011;Grillakis et al, 2013;Cannon et al, 2015] and various settings in the bias correction, including baseline periods to consider the nonstationarity [Chen et al, 2011[Chen et al, , 2015 may be necessary. Related to this point, a comparison between univariate bias-correction methods (e.g., CDFDM) and multivariate ones [e.g., Cannon, 2017] would be useful to examine how those methods are different in terms of the intervariable physical consistency in bias-corrected data. Lastly, we only analyzed the temperature and precipitation indices, despite the criticism from Alexander [2016].…”

Multivariate bias adjustment of high-dimensional climate simulations: the Rank Resampling for Distributions and Dependences (R<sup>2</sup>D<sup>2</sup>) bias correction

“…It is therefore crucial to adjust not only the marginal distributions of the climate simulations but also their multivariate dependence structures, which is the goal of the present study. A few multivariate methodologies have been proposed over the last few years (e.g., Bardossy and Pegram, 2012;Piani and Haerter, 2012;Mao et al, 2015;Vrac and Friederichs, 2015;Cannon, 2017;Dekens et al, 2017;Li et al, 2017). Most of these methods can be categorized into one of the two following approaches: the "marginal/dependence" correction approach and the "successive conditional" correction approach.…”

“…Most of these methods can be categorized into one of the two following approaches: the "marginal/dependence" correction approach and the "successive conditional" correction approach. The "marginal/dependence" BC methods (e.g., "matrix recorrelation" approach in Bardossy and Pegram, 2012;Vrac and Friederichs, 2015;Cannon, 2017;Li et al, 2017) separately correct the 1d-marginal distributions (e.g., one variable at one given location) and the dependence structure, usually under the form of the underlying copula function linking the different marginal distributions. Once those two components of the joint distribution have been corrected, they are reassembled to obtain adjusted data that respect both the univariate and multivariate dependencies.…”

Attributing extreme fire risk in Western Canada to human emissions

“…Other studies have employed simple downscaling models Wang et al 2015) to increase resolution or statistical models to relate model outputs to the number or area of fires (Wotton et al 2010;Balshi et al 2009). Here, the large ensemble output was downscaled to the resolution of the GFWED data and then bias corrected following the methodology of Cannon (2017), which bias corrects the marginal distributions and maintains the multivariate dependence structure between the four variables (tair, RH, wspd, prcp). If debiased separately, the relationship between weather variables could be altered, which would have implications for the calculation of the CFFDRS indices (Cannon 2017).…”

“…Here, the large ensemble output was downscaled to the resolution of the GFWED data and then bias corrected following the methodology of Cannon (2017), which bias corrects the marginal distributions and maintains the multivariate dependence structure between the four variables (tair, RH, wspd, prcp). If debiased separately, the relationship between weather variables could be altered, which would have implications for the calculation of the CFFDRS indices (Cannon 2017). The downscaling/bias correction considers internal variability between realizations and maintains the separation between the ALL and NAT responses; the procedure is described in more detail in the supplementary material.…”