Bias Adjustment and Downscaling Algorithms

The xclim.sdba submodule provides a collection of bias-adjustment methods meant to correct for systematic biases found in climate model simulations relative to observations. Almost all adjustment algorithms conform to the train - adjust scheme, meaning that adjustment factors are first estimated on training data sets, then applied in a distinct step to the data to be adjusted. Given a reference time series (ref), historical simulations (hist) and simulations to be adjusted (sim), any bias-adjustment method would be applied by first estimating the adjustment factors between the historical simulation and the observation series, and then applying these factors to sim, which could be a future simulation:

# Create the adjustment object by training it with reference and model data, plus certain arguments
Adj = Adjustment.train(ref, hist, group="time.month")
# Get a scenario by applying the adjustment to a simulated timeseries.
scen = Adj.adjust(sim, interp="linear")  # adjustment factors.

Most method support both additive and multiplicative correction factors. Also, the group argument allows adjustment factors to be estimated independently for different periods: the full time series, months, seasons or day of the year. For monthly groupings, the interp argument then allows for interpolation between adjustment factors to avoid discontinuities in the bias-adjusted series. See Grouping below.

The same interpolation principle is also used for quantiles. Indeed, for methods extracting adjustment factors by quantile, interpolation is also done between quantiles. This can help reduce discontinuities in the adjusted time series, and possibly reduce the number of quantile bins that needs to be used.

Modular Approach

The module attempts to adopt a modular approach instead of implementing published and named methods directly. A generic bias adjustment process is laid out as follows:

The train-adjust approach allows to inspect the trained adjustment object. The training information is stored in the underlying Adj.ds dataset and usually has a af variable with the adjustment factors. Its layout and the other available variables vary between the different algorithm, refer to Adjustment methods.

Parameters needed by the training and the adjustment are saved to the Adj.ds dataset as a adj_params attribute. Parameters passed to the adjust call are written to the history attribute in the output scenario DataArray.


For basic time period grouping (months, day of year, season), passing a string to the methods needing it is sufficient. Most methods acting on grouped data also accept a window int argument to pad the groups with data from adjacent ones. Units of window are the sampling frequency of the main grouping dimension (usually time). For more complex grouping, one can pass an instance of xclim.sdba.base.Grouper directly. For example, if one wants to compute the factors for each day of the year but across all realizations of an ensemble : group = Grouper("time.dayofyear", add_dims=['realization']). In a conventional empirical quantile mapping (EQM), this will compute the quantiles for each day of year and all realizations together, yielding a single set of adjustment factors for all realizations.


If grouping according to the day of the year is needed, the xclim.core.calendar submodule contains useful tools to manage the different calendars that the input data can have. By default, if 2 different calendars are passed, the adjustment factors will always be interpolated to the largest range of day of the years but this can lead to strange values, so we recommend converting the data beforehand to a common calendar.

Application in multivariate settings

When applying univariate adjustment methods to multiple variables, some strategies are recommended to avoid introducing unrealistic artifacts in adjusted outputs.

Minimum and maximum temperature

When adjusting both minimum and maximum temperature, adjustment factors sometimes yield minimum temperatures larger than the maximum temperature on the same day, which of course, is nonsensical. One way to avoid this is to first adjust maximum temperature using an additive adjustment, then adjust the diurnal temperature range (DTR) using a multiplicative adjustment, and then determine minimum temperature by subtracting DTR from the maximum temperature [Agbazo and Grenier, 2020, Thrasher et al., 2012].

Relative and specific humidity

When adjusting both relative and specific humidity, we want to preserve the relationship between both. To do this, Grenier [2018] suggests to first adjust the relative humidity using a multiplicative factor, ensure values are within 0-100%, then apply an additive adjustment factor to the surface pressure before estimating the specific humidity from thermodynamic relationships.

Radiation and precipitation

In theory, short wave radiation should be capped when precipitation is not zero, but there is as of yet no mechanism proposed to do that, see Hoffmann and Rath [2012].

Usage examples

The usage of this module is documented in two example notebooks: SDBA and SDBA advanced.

Discussion topics

Some issues were also discussed on the Github repository. Most of these are still open questions, feel free to participate to the discussion!

  • Number quantiles to use in quantile mapping methods: GH/1162

  • How to choose the quantiles: GH/1015

  • Bias-adjustment when the trend goes to zero: GH/1145

  • Spatial downscaling: GH/1150

Experimental wrap of SBCK

The SBCK python package implements various bias-adjustment methods, with an emphasis on multivariate methods and with a care for performance. If the package is correctly installed alongside xclim, the methods will be wrapped into xclim.sdba.adjustment.Adjust classes (names beginning with SBCK_) with a minimal overhead so that they can be parallelized with dask and accept xarray objects. For now, these experimental classes can’t use the train-adjust approach, instead they only provide one method, adjust(ref, hist, sim, multi_dim=None, **kwargs) which performs all steps : initialization of the SBCK object, training (fit) and adjusting (predict). All SBCK wrappers accept a multi_dim argument for specifying the name of the “multivariate” dimension. This wrapping is still experimental and some bugs or inconsistencies might exist. To see how one can install that package, see Extra Dependencies.

Notes for Developers

To be scalable and performant, the sdba module makes use of the special decorators :py:func`xclim.sdba.base.map_blocks` and xclim.sdba.base.map_groups(). However, they have the inconvenient that functions wrapped by them are unable to manage xarray attributes (including units) correctly and their signatures are sometime wrong and often unclear. For this reason, the module is often divided in two parts : the (decorated) compute functions in a “private” file (ex: and the user-facing functions or objects in corresponding public file (ex: See the sdba-advanced notebook for more info on the reasons for this move.

Other restrictions : map_blocks will remove any “auxiliary” coordinates before calling the wrapped function and will add them back on exit.

User API

See: SDBA Module

Developer API

See: SDBA Utilities

SDBA Footnotes


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