Climate model data often show deviations from reference data, e.g. gridded observational or reanalysis data when assessed over a longer period of time, typically 30 years. For climate impact indicators that are sensitive to a threshold or for impact models calibrated on certain reference data, it is therefore important to bias adjust the climate model data. A commonly used family of bias adjustment methods is called quantile mapping that aim to adjust the quantile distribution of climate model data in a way that it becomes very similar to the quantile distribution of the reference data. In other words, they do not only adjust the mean of the climate model data but the full distribution and are therefore assumed to be better applicable for analysis of, e.g., extreme events.

The MultI-scale bias AdjuStment tool (MIdAS, Berg et al. 2022) is a semi-parametric quantile-mapping method. In contrast to the fully parametric methods, it does not pre-assume a certain statistical distribution for the data but uses an empirical spline-fit to describe the distribution of the data.

MIdAS works as follows:

  1. For every day of the year throughout the annual cycle, a quantile-quantile relation is estimated between model and reference data that falls between the day of the year plus/minus 15 days throughout the reference period. For e.g., for day of year 16, all January 1 to January 31 throughout the reference period are used to construct the quantile-quantile relation.
  2. The quantile-quantile relation is smoothed by a linear spline-fit. This is meant to reduce the impact of variability in the data, especially on the tails of the data.
  3. The quantile-quantile relation is applied to all data of the same day of the year throughout the whole climate projection time series.
Processing steps 1) to 3) are the basic elements used for every variable. For different variable, MIdAS adds a few special processing steps which are described in detail in the following.


For the case of precipitation, the adjustment of wet-day frequency is done by the method singularity stochastic removal (Vrac et al., 2016). This method is able to adjust the wet-day frequency in both cases of too few or too many wet days in the climate model data compared to the reference data.

Daily mean temperature

For the case of daily mean temperature, the steps 1) to 3) are made in a cascade-like succession first on the monthly time scale represented by applying a 31-day moving average to the time series, and next on the daily anomalies around the moving average. In that way, systematic biases at different time scales can be handled separately and do not interfere. Like this, one avoids introducing bias at one temporal resolution by bias-adjusting the data at the other resolution.

Daily minimum and maximum temperature

Daily minimum and maximum temperature are bias-adjusted following the concept presented by Lange (2019). We derive first diurnal temperature range and skewness from the data for daily mean, minimum and maximum temperature, run bias-adjustment according to steps 1) to 3) on those derived variables, and reconstruct bias-adjusted minimum and maximum temperature from the bias-adjusted data for daily mean temperature, diurnal temperature range and temperature skewness. The method makes sure that bias-adjusted daily mean, minimum and maximum temperature are physically consistent (i.e. mean temperature is between minimum and maximum temperature).


Berg, P., Bosshard, T., Yang, W., & Zimmermann, K. (2022). MIdASv0.2.1 – MultI-scale bias AdjuStment. Geoscientific Model Development, 15(15), 6165–6180.

Lange, S.: Trend-preserving bias adjustment and statistical downscaling with ISIMIP3BASD (v1.0), Geoscientific Model Development, 12, 3055–3070,, 2019

Vrac, M., Noël, T., & Vautard, R. (2016). Bias correction of precipitation through singularity stochastic removal: Because occurrences matter. Journal of Geophysical Research, 121(10), 5237–5258.