Overview of Bias-Correct Methods Used in Statistical Adjustment of GCM/RCM/SDSM Outputs

Bias Correction (BC) methods are post-processing tools for numerical modeling which aim to improve the model agreement with the observations. Although the spatial resolutions and skills of GCMs/RCMs have obviously increased in recent years, it is still not enough for their direct application in impact studies at local or site scales. Even for the outputs from statistical downscaling models (SDSM), they could be biased due to the model biases from up-stream GCMs/RCMs. Under such a case, Bias-Correction methods provide a solution, which combine information from the local observations and simulations leading to smaller biases and higher resolution predictions/projections.

According to their features, Bias Correction (BC) methods can be categorized into three groups: Simple methods, Equal distance-based Methods and Replacement-based Methods. The latter two both depend on Cumulative Distribution Functions (CDFs).

1. Simple Methods

Delta

This is the simplest bias correction method which only adds the mean changes (described as Delta) to the observations (A) just like

A' = A + Delta.

The Delta are calculated as the differences between future projections and baseline period from GCM/RCM/SDSM simulations. This method is applicable to any kind of variable, especially for unbounded variables (such as temperature). However, it is preferable not to apply it to bounded variables (e.g. precipitation and wind speed, etc.) because values out of range could be obtained. For example, a minus Delta may cause A' <0, which is not a meaningful value for precipitation.

Scaling

This method is proposed mainly for bounded variables (e.g. precipitation, wind speed, etc.). The mean change projected by GCM/RCM/SDSM simulations is presented as a ratio or a quotient (Scaling) of future projections to baseline period simulations. Then the ratio or quotient is applied to scale observations (A) through a multiplicative operator just like

A' = Scaling *A.

2. Equal Distance-based CDF Quantile Mapping Methods  

eQM - Empirical Quantile Mapping

This is the most widely-used bias correction method which consists on calibrating the simulated Cumulative Distribution Function (CDF) by adding to the observed quantiles both the mean delta change and the individual delta changes in the corresponding quantiles.

aQM - adjusted Quantile Mapping

The method is a variant of empirical quantile mapping (eQM),which added two extra parameters of 'f' and 'g'. 'g' is a factor that modulates the variation in the mean delta change, while 'f' calibrates the change in variability and shape expressed by the individual delta changes in the quantiles. This method is applicable to any kind of variable.

gQM - Parametric Quantile Mapping: Gamma Distribution

This method is an improved version of empirical quantile mapping (eQM), which fits both observed and simulated intensity distributions into gamma distributions and then carried out quantile mapping. The only difference between gQM and eQM is the former uses the theoretical instead of the empirical distribution. It is only applicable to precipitation.

gpQM - Parametric Quantile Mapping: Gamma and Generalized Pareto Distribution

This method is also an improved and parametric version of eQM and is only applicable to precipitation. It uses the Gamma distribution to adjust the non-extreme part which uses the Generalized Pareto Distribution (GPD) for the extreme part of the observed and the predicted wet-day distribution (e.g., above 95th percentile) , respectively.

3. Replacement-based CDF Mapping Methods

The method uses a search-replace procedure to adjust the target variable. To bias correct modeled values for a future period, the method needs firstly to find the corresponding percentile values for these future (modeled) values on the CDF of the modeled values during the baseline period and then search for the observed values on the CDF of the observations at the same found percentile locations.

Certainly, the modeled and observed values can be fitted into empirical or different theoretical distributions ((e.g., gamma distribution for precipitation or normal distribution for temperature). Thus they can get names like eRM, aRM, gRM, gpRM, etc.

Summary and Discussions

The Bias-Correction Methods always depend on three groups of data: observations (A), modeled data for baseline (B) and future periods (C). Therefore, the technical solution is obvious: Use two of them to adjust the third just like:

A + (C-B) or A*(C/B) or A*[1.0 + (C-B)/B].

• Bias-Correction is a kind of quick and efficient post-processing tool for statistical adjustment of GCM/RCM/SDSM outputs to local/site scales. The outputs can be used directly in down-steam studies such as cropping or hydrology simulations.
• Bias-Correction has its own limitations. For example, it is a statistically instead of physically based method. It is only operated on a single variable. Some Bias-Correction methods presume that biases are stationary (transfer function) in the future.
• For sub-daily or daily precipitation, it is necessary to adjust precipitation frequency (i.e., wet days) through cleaning the overmuch drizzles. At the same time, the resultant change of total precipitation amount should be taken into consideration.
• Equal distance-based methods seems more straightforward to keep the climate change signals than replacement-based methods, and possibly more suitable for extreme value analysis. However, this needs more studies.
• Since CDF-based methods work upon CDFs, the idea behind them is also applicable for adjusting extreme precipitation distributions such as the Intensity-Duraton-Frequency (IDF) curves.

References

A. Amengual, V. Homar, R. Romero, S. Alonso, and C. Ramis (2012) A Statistical Adjustment of Regional Climate Model Outputs to Local Scales: Application to Platja de Palma, Spain. J. Climate, 25, 939–957. doi: https://dx.doi.org/10.1175/JCLI-D-10-05024.1

C. Piani, J. O. Haerter and E. Coppola (2009) Statistical bias correction for daily precipitation in regional climate models over Europe, Theoretical and Applied Climatology, 99 (1-2), 187-192, doi: 10.1007/s00704-009-0134-9

Wetterhall, F., Pappenberger, F., He, Y., Freer, J. and Cloke, H.L. (2012) Conditioning model output statistics of regional climate model precipitation on circulation patterns, Nonlin. Processes Geophys., 19, 623–633, doi:10.5194/npg-19-623-2012, https://www.nonlin-processes-geophys.net/19/623/2012/.

Wood, A.W., L.R Leung, V. Sridhar, and D.P. Lettenmaier, 2004: Hydrologic implications of dynamical and statistical approaches to downscaling climate model outputs(link is external). Climatic Change, 62, 189–216, doi:10.1023/B:CLIM.0000013685.99609.9e.

Yin, C. (2011). Applications of Self-Organizing Maps to Statistical Downscaling of Major Regional Climate Variables (Doctoral dissertation, University of Waikato).