About MBCn

Method overview

The N-Dimensional Multivariate Bias Correction (MBCn) is a statistical method used to correct biases in climate model simulations. Unlike traditional bias correction methods that focus on correcting biases in individual variables, MBCn considers the relationships between multiple variables across different spatial and temporal dimensions. This approach allows for a more comprehensive correction that preserves the coherence and relationships between variables, resulting in improved outputs for various applications such as adaptation planning. MBCn uses a modified form of quantile delta mapping (QDM), as is used in BCCAQv2, which can work with multiple variables at once and preserves the statistical properties between each variable. 

How the method works

MBCn uses the statistical characteristics of reference multivariate distributions from a target dataset, to adapt the multivariate distributions of climate model variables.¹

First, the method applies a univariate adjustment to each climate variable, using the same QDM method as in BCCAQv2. 

Then, the dependent structure between variables is adjusted using a multi-step, iterative process. This procedure is adapted from image processing, where colour information is transferred from one image to another.

This procedure finishes when the multivariate distributions of the reference observations (i.e., target dataset) and historical climate simulations agree to within a specified tolerance. 

By design, adjusted multivariate distributions match those of QDM.

When to use it

MBCn has been shown² to outperform univariate QDM methods, particularly for the annual maxima of fire weather index distributions and the spatio-temporal autocorrelation of precipitation.

Since the relationship between variables is preserved in the downscaling process, MBCn is appropriate when downscaling climate variables to calculate climate indices based on more than one variable, such as Humidex or SPEI.