Bias Correction

Bias Correction and Model Output Statistics (MOS)

This section describes two approaches used to post-processing the direct output of the numerical modeling: Bias corection techniques and Model Output Statistics. As a difference with the Perfect Prog approach, these two methodologies use the same variable from the GCM (or RCM) and the local observations (e.g. 2-meters air temperature or precipitation amount).

Bias Correction:

In the downscaleR R-package, the user can find the main bias correction techniques used in the literature (delta method, qq-mapping, etc...) and other recently published (ISI-MIP). For a more detailed description, the user is referred to the main publications describing these techniques which are included at the end of this page.

All the bias correction methods implemented in downscaleR are included in the functions biasCorrection and isimip. These two functions work directly with the object obtained loading Observations and/or Simulations. Then, in our example we will use the observations and simulations obtained in the Practice 1B

# Example 2: Regional-Continental domain selections
pred <- loadECOMS(dataset = "CFSv2_seasonal_16", var = "tas", members = 1:2, lonLim = c(-15,35), latLim = c(32, 75), season = c(12,1,2), years = 2001:2010, leadMonth = 3, time = "DD")
Example.obs <- loadECOMS(dataset = "WFDEI", var = "tas", lonLim = c(floor(min(pred$xyCoords$x, na.rm = TRUE)),ceiling(max(pred$xyCoords$x, na.rm = TRUE))), latLim = c(floor(min(pred$xyCoords$y, na.rm = TRUE)),ceiling(max(pred$xyCoords$y, na.rm = TRUE))), season = c(12,1,2), years = 2001:2010)
# We should interpolate the observations to the grid of model: we use the method "nearest"
obs <- interpGridData(Example.obs, new.grid = pred$xyCoords, method = "nearest")
# We estimate the unbiased simulation
sim <- biasCorrection (obs, pred, pred, method = "unbiasing")

Dealing with precipitation, a frequency adaptation is implemented 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 when using q-q map (Wilcke et al. 2013). More often the model overestimates the light precipitation frequency (drizzling-effect), which is caught by the q-q map automatically.

The methods available are qqmap, delta, unbiasing, scaling and Piani.

• Delta This is the simplest bias correction method, which consist on adding to the observations the mean change signal (delta method). According to Amengual et al. 2012 this would be the case g=1 and f=0. This method is applicable to any kind of variable but it is preferable to not apply it to bounded variables (e.g. precipitation, wind speed, etc.) because could be obtained values out of range.

• Unbiasing This method is very similar to the delta method but, in this case, the correction consist on adding to the simulation the mean diference between the observations and the simulation in the train period. This method is preferably applicable to unbounded variables (e.g. temperature).

• Scaling This method consists on scaling the simulation by the quotient of the mean observed and simulated in the train period. This method is preferably applicable to variables with a lower bound, such as precipitation, because it preserves the frequency also.

• qqmap This is a very extended 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. This is equivalent to f=g=1 in Amengual et al. 2012. This method is applicable to any kind of variable.

• Piani This method is based on the initial assumption that both observed and simulated intensity distributions are well approximated by the gamma distribution, therefore is a parametric q-q map that uses the theorical instead of the empirical distribution. It is described in Piani et al. 2010. It is only applicable to precipitation.

• ISI-MIP

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.