This Python module serves as a collection of different scale- and distribution-based bias correction techniques for climatic research

The documentation is available at: https://python-cmethods.readthedocs.io/en/stable/

⚠️ For the application of bias corrections on lage data sets it is recommended to use the command-line tool BiasAdjustCXX since bias corrections are complex statistical transformation which are very slow in Python compared to the C++ implementation.

1. About
2. Available Methods
3. Installation
4. Usage and Examples
5. Notes
6. References

These programs and data structures are developed with the aim of reducing discrepancies between modeled and observed climate data. Historical data is utilized to calibrate variables from current and future time series to achieve distributional properties that closely resemble the possible actual values.

For instance, modeled data typically indicate values that are colder than the actual values. To address this issue, an adjustment procedure is employed. The figure below illustrates the observed, modeled, and adjusted values, revealing that the delta adjusted time series ($T^{*DM}{sim,p}$) are significantly more similar to the observed data ($T{obs,p}$) than the raw modeled data ($T{sim,p}$).

All methods except the adjust_3d function requires that the input data sets only contain one dimension.

Except for the variance scaling, all methods can be applied on stochastic and non-stochastic climate variables. Variance scaling can only be applied on non-stochastic climate variables.

• Non-stochastic climate variables are those that can be predicted with relative certainty based on factors such as location, elevation, and season. Examples of non-stochastic climate variables include air temperature, air pressure, and solar radiation.

• Stochastic climate variables, on the other hand, are those that exhibit a high degree of variability and unpredictability, making them difficult to forecast accurately. Precipitation is an example of a stochastic climate variable because it can vary greatly in timing, intensity, and location due to complex atmospheric and meteorological processes.

python3 -m pip install python-cmethods

import xarray as xr
from cmethods import CMethods as cm

obsh = xr.open_dataset('input_data/observations.nc')
simh = xr.open_dataset('input_data/control.nc')
simp = xr.open_dataset('input_data/scenario.nc')

ls_result = cm.linear_scaling(
    obs = obsh['tas'][:,0,0],
    simh = simh['tas'][:,0,0],
    simp = simp['tas'][:,0,0],
    kind = '+'
)

qdm_result = cm.adjust_3d( # 3d = 2 spatial and 1 time dimension
    method = 'quantile_delta_mapping',
    obs = obsh['tas'],
    simh = simh['tas'],
    simp = simp['tas'],
    n_quaniles = 1000,
    kind = '+'
)
# to calculate the relative rather than the absolute change,
# '*' can be used instead of '+' (this is preferred when adjusting
# stochastic variables like precipitation)

Notes:

• When using the adjust_3d method you have to specify the method by name.
• For the multiplicative techniques a maximum scaling factor of 10 is defined. This can be changed by the attribute max_scaling_factor.

Notebook with different methods and plots: /examples/examples.ipynb

There is also an example script (/examples/biasadjust.py) that can be used to apply the available bias correction methods on 1- and 3-dimensional data sets (see /examples/input_data/*.nc).

Help:

╰─ python3 biasadjust.py --help

(1.) Example - Quantile Mapping bias correction on the provided example data:

╰─ python3 biasadjust.py              \
    --ref input_data/observations.nc  \
    --contr input_data/control.nc     \
    --scen input_data/scenario.nc     \
    --kind "+"                        \
    --variable "tas"                  \
    --method quantile_mapping

(2.) Example - Linear Scaling bias correction on the provided example data:

╰─ python3 biasadjust.py              \
    --ref input_data/observations.nc  \
    --contr input_data/control.nc     \
    --scen input_data/scenario.nc     \
    --kind "+"                        \
    --variable "tas"                  \
    --group "time.month"              \
    --method linear_scaling

Notes:

• Data sets must have the same spatial resolutions.
• This script is far away from perfect - so please look at it, as a starting point. (:

• Computation in Python takes some time, so this is only for demonstration. When adjusting large datasets, its best to use the command-line tool BiasAdjustCXX.
• Formulas and references can be found in the implementations of the corresponding functions, on the bottom of the README.md and in the documentation.

• Since the scaling methods implemented so far scale by default over the mean values of the respective months, unrealistic long-term mean values may occur at the month transitions. This can be prevented either by selecting group='time.dayofyear'. Alternatively, it is possible not to scale using long-term mean values, but using a 31-day interval, which takes the 31 surrounding values over all years as the basis for calculating the mean values. This is not yet implemented, because even the computation for this takes so much time, that it is not worth implementing it in python - but this is available in BiasAdjustCXX.

• Schwertfeger, Benjamin Thomas and Lohmann, Gerrit and Lipskoch, Henrik (2023) "Introduction of the BiasAdjustCXX command-line tool for the application of fast and efficient bias corrections in climatic research", SoftwareX, Volume 22, 101379, ISSN 2352-7110, (https://doi.org/10.1016/j.softx.2023.101379)
• Schwertfeger, Benjamin Thomas (2022) "The influence of bias corrections on variability, distribution, and correlation of temperatures in comparison to observed and modeled climate data in Europe" (https://epic.awi.de/id/eprint/56689/)
• Linear Scaling and Variance Scaling based on: Teutschbein, Claudia and Seibert, Jan (2012) "Bias correction of regional climate model simulations for hydrological climate-change impact studies: Review and evaluation of different methods" (https://doi.org/10.1016/j.jhydrol.2012.05.052)
• Delta Method based on: Beyer, R. and Krapp, M. and Manica, A.: "An empirical evaluation of bias correction methods for palaeoclimate simulations" (https://doi.org/10.5194/cp-16-1493-2020)
• Quantile and Detrended Quantile Mapping based on: Alex J. Cannon and Stephen R. Sobie and Trevor Q. Murdock "Bias Correction of GCM Precipitation by Quantile Mapping: How Well Do Methods Preserve Changes in Quantiles and Extremes?" (https://doi.org/10.1175/JCLI-D-14-00754.1)
• Quantile Delta Mapping based on: Tong, Y., Gao, X., Han, Z. et al. "Bias correction of temperature and precipitation over China for RCM simulations using the QM and QDM methods". Clim Dyn 57, 1425–1443 (2021). (https://doi.org/10.1007/s00382-020-05447-4)