What is Multivariate Bias Correction (MBC)?
Assessment of the potential climate change impacts relies on global climate model (GCM) simulations. In recent years, great progress has been made in improving GCMs developed by climate centers around the world, and current GCMs are capable of producing higher resolution and relatively more precise simulations. However, systematic bias still remains in GCM outputs, due partially to temporal and spatial discretization and inadequate representation of basic physical processes.
All GCMs are unable to accurately simulate climate variables at local and site-specific scales, and deviations between observations and climate model simulations exist in various aspects of model outputs, like variable means, standard deviations, and distributions. Thus,it is uncommon to directly input climate model outputs to environmental models for local and site-specific climate change impact studies. In a foreseeable future, the biases of climate model outputs may remain. Therefore, several bias correction approaches have been developed to solve this problem.
Bias correction as a post-processing approach for climate model outputs and its main principle is to establish statistical relationships between observed climate variables and their corresponding climate model simulations in a historical period. The established relationships are then used to correct the bias of climate simulations for a future period. Owing to its simple theoretical basis and ease of implementation, bias correction has become a practical tool to link climate models and impacts models for climate change impact studies. Most commonly used bias correction methods operate on a single variable, which ignores dependency among multiple variables. The misrepresentation of multivariable dependence may result in biased assessment of climate change impacts. To solve this problem, multivariate bias correction methods have been developed and successfully implemented in recent years.
Multivariate Bias Correction (MBC) Methodologies
Most bias correction algorithms used in climatology, for example quantile mapping, are applied to univariate time series. They neglect the dependence between different variables. Concerning the necessity of considering inter-variable correlations of climate model outputs, bias correction methods taking into account inter-variable correlations began to appear in the climate science literature in recent years. To overcome the shortcomings of univariate methods, multiple multivariate bias correction algorithms have been introduced, including the joint bias correction (JBC) method, the empirical copula-bias correction (EC-BC) method, and MBCp, MBCr, and MBCn for correcting climate model outputs. MBCp and MBCr are two similar methods, which respectively correct Pearson and Spearman correlation coefficients by combining univariate bias correction and a multivariate linear bias correction algorithm. MBCn can transfer all components of an observed multivariate distribution to the corresponding multivariate distribution of the climate model-simulated variable.
Use Cases and Industries That Use MBC
The use of simulations from climate or meteorological models at large or regional scales is now common in many impact studies, such as hydrological, environmental, infrastructure resilence/risk assessment studies, or economic impact studies among others. In these studies, MBC can help agencies and industries to get more realistic and accurate assessment of the potential climate change impacts relies on global climate model (GCM) simulations. Typical use cases of MBC may include and not limit to:
Hydrological modelling and studies: flood and drought projections, river basin simulation, or glacier studies (projected snow cover characteristics, snowmeltdriven streamflow components, and expected glacier disappearance dates)
Country-Wide/Regional Economy Impact Studies of Climate Change
Infrastruture (3Waters, Transport, Energy and Buildings) Resilience or Risk Assessement Studies for the Impacts of Climate Change
Procedure for Use of MBC in Climate Change Impact Studies
Below are a flowchart for a typical MBC process and an example outputs of a study with a MBC component.
MBC Analysis with R - Sample Codes and Visual Outputs
MBC Analysis with R
In R open-source programming software, 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.
Both multivariate bias correction approaches, namely, Multivariate Recursive Nested Bias Correction (MRNBC) and the Multivariate Recursive Quantile-matching Nested Bias Correction (MRQNBC) are included in the MBC packag andand allows applying MRNBC and MRQNBC bias correction approaches in a fairly simple manner. The package requires all essential information to be provided in the ‘basic.dat’ file. In addition, four data files are to be prepared and included before running the package. These include observed and raw data files for calibration as well as verification period.
Upon successful completion of the program, 6 output files are generated, two files containing bias corrected time series for calibration and verification periods and four statistics results files, containing important statistics of 1) Observed and Raw data for calibration; 2) observed and raw data for verification; 3) observed and bias corrected data for calibration; and 4) observed and bias corrected data for verification time periods. Some of the important statistics calculated include means, standard deviations, skewness, LAG1 and LAG2 auto correlations, and distribution plots at daily, monthly, seasonal and annual time scales. In case of multiple variables, auto and LAG1 cross correlations are also computed. The package allows the users to look at a few raw and bias corrected statistics either in the form of a table or as plots at multiple time scales of interest. Package also provides plots of empirical distribution of raw and bias corrected time series.
Sample Codes and Visual Outputs
The following example demonstrates the MBC process with a dataset includes four files of equal lengths with daily records of 7 atmospheric variables averaged over Sydney, Australia, obtained from NCEP-reanalysis and CSIRO data bases. A subset of 30 years of records from 1950 to 1979 is considered for model calibration while remaining 30 years from 1980 to 2009 is used for the model verification.
The bias correction model selected is a multivariate recursive nested bias correction (MRNBC) model with the option of bias correction in mean, standard deviation, LAG1 auto and LAG0 cross correlations at daily, monthly and annual time scales. Four seasons in a year are considered. Daily GCM data is considered to have fixed 28 days in each February and thus activating the option of fixed days in a month format for GCM calibration and verification datasets. Observed (reanalysis) data sets for calibration and verification periods still follow standard leap year format.
Upon successful completion of the bias correction process, four result files containing a few important statistics of the raw and bias corrected data are created. Raw data exhibits some biases in these statistics. Bias correction model provides near perfect fit for the calibration period and a reasonably good fit for the verification period. Similarly, scatter plots of scaled means, standard deviations, LAG1 autocorrelation, LAG0 cross correlations and LAG1 cross correlations of raw and bias corrected time series for these two periods show a good match all points should lie close to diagonal. Model does a good job in reproducing these statistics during verification period albeit some scatter for some variables. Empirical distribution plots of daily, monthly, seasonal and annual time series of reanalysis and raw and bias corrected GCM data for calibration and verification time periods for a selected variable-Temperature depression at 700hPa indicate the model performs well at all time scales during calibration, however, exhibits some biases at higher time scales during verification.
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