Bias Correction

This section describes two approaches used to post-process and calibrate the direct output of the numerical modeling: Bias correction techniques and Model Output Statistics. As a difference with the Perfect Prog approach, these two methodologies correct directly the target variable from the GCM (or RCM) output, e.g. precipitation, using the corresponding local observations at a desired number of stations (or at a regular grid of interpolated observations).

Other packages for bias correction:

https://github.com/pacificclimate/ClimDown

https://cran.r-project.org/web/packages/qmap

Bias Correction:

Bias Correction (BC) techniques work with the predicted and observed PDFs/CDFs and, thus, do not preserve the original temporal correspondence of the model output. These techniques have became popular in the last decade due to their simplicity and straightforward application; however, several limiting problems have been recently identified for these methods (White and Toumi, 2013; Maraun, 2013). In order to alleviate some of these problems, a number of extensions have been recently published. For instance, to avoid stationarity, BC techniques conditioned on weather types have been recently introduced, showing that they are more sensitive to possible shifts in the large-scale circulation during the projection period (Wetterhall et al., 2012).

In the downscaleR R-package, the user can find the standard bias correction techniques used in the literature (scaling factors and qq-map) as well as other recently published extensions of these techniques (e.g. the multi-variable bias-correction ISI-MIP method, Hempel et al. 2013). In the case of precipitation, an additional parametric qqmap method (Piani) is also available and a frequency adaptation is implemented in all versions of qqmap to alleviate the problem that arise when the dry day frequency in the raw model output is larger than in the observations (Wilcke et al. 2013).

The bias correction methods implemented in downscaleR are included in the functions biasCorrection and isimip. These two functions work with the object obtained loading Observations and/or Simulations with the loadeR or the ECOMS-UDG R-access packages, which provide the data in the format required for the input arguments of the above functions:

• y: A grid or station data containing the observed climate data for the training period
• x: A grid containing the simulated climate by the model for the same variable y for the training period.
• newdata: A grid containing the simulated climate for the variables used in x, but considering the test/projection period.

Function biasCorrection

The bias correction methods implemented can be classified into scaling- and distributional-based methods. The former ones consist of using an additive or multiplicative scaling factors (e.g. delta and scaling) to correct the model simulations. The latter methods are the so-called quantile mapping techniques that adjust empirically (eQM) or parametrically (pQM and gpQM) some features of the probability distribution function.

Among the available options for the different methods, a frequency adaptation is implemented for precipitation to alleviate the problem that arise when the dry day frequency in the raw model output is larger than in the observations, which would lead to a strong positive bias after the correction (Wilcke et al. 2013). More often the model overestimates the light precipitation frequency (drizzling-effect), which is caught by the quantile mapping automatically.

The application of different methods in biasCorrection is controlled by argument method, and available options are:

• Delta (method = "delta")
• Scaling (method = "scaling")
• Empirical Quantile Mapping (eQM) (method = "eqm")
• Parametric Quantile Mapping: gamma distribution (gQM) (method = "pqm")
• Special case of Parametric Quantile Mapping: gamma and Generalized Pareto Distribution (gpQM) (method = "gpqm")
• Variance scaling of temperature (method = "variance")
• Local intensity scaling of precipitation (method = "loci")
• Power transformation of precipitation (method = "ptr)

Each method is documented in detail (including examples of application) in the corresponding help document of the function:

?biasCorrection

For further worked examples of each method go to section 3.1..

In addition to parameters y, x, newdata and method, further arguments in biasCorrection allow multiple configurations:

• precipitation: For considering a special treatment of precipitation data
• cross.val: For applying "loo" or "k-fold" cross-validation.
• folds: For defining the folds in cross-validation mode.
• wet.threshold: For setting the minimum value that is considered as a non-zero precipitation.
• window: For applying a moving calibration time-window.
• scaling.type: For choosing the "additive" or "multiplicative" type when the "scaling" method is applied.
• fitdistr.args: For choosing the theoretical distribution when applying the "pqm" method.
• n.quantiles: For setting the number of quantiles to correct when applying the "eqm" method.
• extrapolation: For setting the extrapolation method to be applied to correct values in newdata that are out of the range of x, when applying method "eqm".
• theta: For setting the threshold value when applying the "gpqm" method.
• join.members: For choosing the strategy to correct datasets containing multiple members (e.g. Seasonal Forecasting).

Function isimip

This function applies * The multi-variable ISI-MIP method. Recently, Hempel et al.2013 proposed a new bias correction methodology within the ISI-MIP Project, the first Inter-Sectoral Impact Model Intercomparison Project, funded by the German Federal Ministry of Education and Research (BMBF). This method has been developed to preserve the change signal (trend, climate change signal, etc.) and can be applied to several variables (precipitation, mean, maximum and minimum temperature, windspeed and eastward/northward components, radiation, pressure and humidity). The main difference with the rest of bias correction methods shown previously is that the ISI-MIP method includes dependencies between some variables. That is, to correct some of the variables (maximum/minimum temperatures and eastward/northward wind components) others are needed (mean temperature and windspeed). Then, this method can not be included in the biasCorrection function and we should use the isimip function.

?isimip

References

1. R.A.I. Wilcke, T. Mendlik and A. Gobiet (2013) Multi-variable error correction of regional climate models. Climatic Change, 120, 871–887, doi:10.1007/s10584-013-0845-x
2. 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: http://dx.doi.org/10.1175/JCLI-D-10-05024.1
3. 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
4. S. Hempel, K. Frieler, L. Warszawski, J. Schewe, and F. Piontek (2013) A trend-preserving bias correction – the ISI-MIP approach. Earth Syst. Dynam., 4, 219–236, doi:10.5194/esd-4-219-2013
5. White, R. H. and Toumi, R. (2013) The limitations of bias correcting regional climate model inputs, Geophysical Research Letters, 40, 29072912, doi:10.1002/grl.50612, http://onlinelibrary.wiley.com/doi/10.1002/grl.50612/abstract.
6. Maraun, D. (2013) Bias Correction, Quantile Mapping, and Downscaling: Revisiting the Inflation Issue, Journal of Climate, 26, 2137–2143, doi:10.1175/JCLI-D-12-00821.1, http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-12-00821.1.
7. 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, http://www.nonlin-processes-geophys.net/19/623/2012/.

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