The Multivariate Bias Correction (MBC) package is a complete package designed to deal with the distribution and, auto and cross dependence biases in a multivariate time series at multiple time steps. It provides the flexibility of applying a simple single time scale univariate bias correction to a comprehensive multivariate multi-time scale bias correction, depending upon the requirement of a particular task. Thus, the package allows the user to frame the structure of their own bias correction model by choosing the type of bias correction, number of time nesting and type of cross nesting required. MBC is a comprehensive package that offers users a wide variety of options by including several variants of standard quantile matching and other routinely used bias correction approaches in a time and cross dependence nesting.

In MBC, distribution behavior of a time series is represented either as a function of both mean and variance or by its empirical distribution. Auto dependence is represented by LAG1 autocorrelation function while cross-dependence is assumed to be a function of LAG0 and LAG1 correlations. The package allows time nesting at daily, monthly, seasonal, annual and tri-annual time scales.

The package allows the user to pick the bias correction for mean only, mean and variance or for distribution only at selected predefined time scales. Similarly, there is flexibility to pick the dependence correction in combinations of LAG1 auto, LAG0 cross and LAG1 cross distributions. User can pick time nesting starting from single to all time scales. 


Mehrotra, R., & Sharma, A. (2016) A Multivariate Quantile-Matching Bias Correction Approach with Auto- and Cross-Dependence across Multiple Time Scales: Implications for Downscaling, J. Climate, 2016 29:10, 3519-3539, doi:

Mehrotra, R., & Sharma, A. (2015). Correcting for systematic biases in multiple raw GCM variables across a range of timescales. Journal of Hydrology, 520, 214-223. doi:10.1016/j.jhydrol.2014.11.037