# Chapter 9 Bias correction and Downscaling

## 9.1 Terminology

- In the scientific literature both ‘bias correction’ and ‘bias adjustment’ are used, here we use
**bias correction**.

## 9.2 Why are models biased and do we need bias correction?

**Why do we need bias correction?**—> direct output from Climate Data Store could be used, but: for impact studies these outputs are often not useful because of significant biases, for example:**Temperature**can be consistently too high- Rainfall too high or low
- Model does an incorrect simulation of the monsoon, the rains start too early or too late
- Climate models tend to overestimate the number of days with rain and underestimate precipitation extremes.

**Why are the models biased?**- Limited spatial resolution (large grid boxes)
- Simplified physics
- Incomplete knowledge of the earth’s climate system

## 9.3 Examples of model bias

### 9.3.1 Geographical differences

**Precipitation example**: for a result of model precipitation estimates (a), there is a certain bias (*Multi Model Mean Bias*) depending on the location (b). This can also be expressed in *Multi Model Mean of Absolute Error* (c) and *Multi Model Mean of Relative Error* (d). A similar analysis can be made for **temperature**.

### 9.3.2 Differences in amount of bias

When looking at model bias for temperature and precipitation for different regions (x-axis), it can be seen that the predicted change in temperature is equal to the bias in the model. For precipitation the bias is even more important. Lots of models over- or underestimate precipitation (sometimes only 50 % of what is observed on-site/in-situ)

## 9.4 Impact of model bias on climate assessments

- If your main
**interest is relative change**in future climate, bias is**not a big problem**. - Bias is important for:
**Threshold analysis**(crop behavior at certain temperatures, …)**Water availability**analysis: bias in rainfall can have large impact- Estimation of
**extremes**: future changes in flood risk can be calculated wrong

## 9.5 Theory of bias correction and downscaling

For an overview of theory of dynamical and statistical downscaling, see [the dedicated chapter above][Dynamical and statistical downscaling theory]

**Bias correction model**: present climate as simluated by the climate model (**G**) or observed (**O**) : difference is bias **B**. We also have change (**C**) to a future climate as modeled by the model (**G’**) and the future observed climate (**O’**).

**Assumptions**applied when using this model:**Bias of present and future model is equal**- The
**climate model results of the current climate is more or less correct**

**function B**can have different shapes:*Linear*function*Scale transfer*function with**mean**,**variance**and**shape**.

**B**can be**estimated**:- Dynamical (using climate models)
- Statistical, using:
- weather typing/analogues
- weather generator [ (non) stationary ]
- transfer functions: (non) linear or PDF mapping functions (with distribution)

## 9.6 Bias correction example - tutorial

See excel files `Bias correction tutorial COP10 ULS.xlsx`

and `Bias correction tutorial COP10 ULS-solution.xlsx`

. Given data (for Kenya) is the historical rainfall (observations + 4 GCM model results) and 4 GCM predictions.

**calculate average**rainfall for observations + each of the GCM models —> large differences, bias needed**calculate absolute bias**by**substracting observations from global climate model results**.- To
**correct future data**(2070-2099) and calculate**future average rainfall**, we need**relative bias correction factors**: divide the observation output by the GCM output. - To correc the future data, multiply the non-bias corrected GCM output with the relative bias correction factor, and calculate the average for each GCM.