Multivariate Quantile Mapping Bias Correction for Climate Model Simulations of Multiple Variables

The MBCn bias correction algorithm is a multivariate generalization of quantile mapping that transfers all aspects of an observed continuous multivariate distribution, i.e., marginal distributions and joint dependence structure, to the corresponding multivariate distribution of variables from a climate model. When applied to climate model projections, changes in all quantiles of each variable between the historical and projection period are also preserved. The MBCn algorithm is demonstrated on two case studies. First, MBCn is used to correct biases in the spatiotemporal dependence structure of Canadian Regional Climate Model (CanRCM4) precipitation fields. Second, the method is used to correct 3-hourly surface temperature, pressure, specific humidity, wind speed, incoming shortwave radiation, incoming longwave radiation, and precipitation outputs from CanRCM4 across a North American domain. Components of the Canadian Forest Fire Weather Index (FWI) System, a complicated set of multivariate indices that characterizes the risk of wildfire, are then calculated and verified against observed values. 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. For instance, in the FWI example univariate quantile mapping does not correct model biases in dependence structure and is therefore unable to reproduce observed annual maxima of the FWI distribution. While the correlation-based multivariate bias correction algorithms lead to some improvements, they are not able to match the ability of MBCn to simulate the entire distribution of FWI values. In the precipitation example, MBCn successfully corrects simulated biases in spatial and temporal autocorrelation.