Reference

Recommended processing steps (tested variables)

pr

• Standardization

  • long name: Precipitation

  • units: kg m-2 s-1

• Wet-day adjustment --ssr

• Empirical quantile mapping and Linear smooth spline fitting -t pr

midas -t pr -p reference_period --ssr -r reference_input -m model_input -o output

tas

• Standardization

  • long name: Near-Surface Air Temperature

  • units: K

• Empirical quantile mapping, Linear smooth spline fitting and additive time-scale separation -t tas

midas -t tas -p reference_period -r reference_input -m model_input -o output

hurs

• Standardization

  • long name: Near-Surface Relative Humidity

  • units: %

• Empirical quantile mapping and Linear smooth spline fitting -t hurs

midas -t hurs -p reference_period -r reference_input -m model_input -o output

hurs_inv

• Standardization

  • long name: Near-Surface Relative Humidity

  • units: %

• Pre-process (hurs -> hurs_inv)

• Empirical quantile mapping and Linear smooth spline fitting (hurs_inv, -t hurs_inv)

• Post-process (hurs_inv -> hurs)

midas -t hurs_inv -p reference_period -r reference_input -m model_input -o output

sfcWind

• Standardization

  • long name: Near-Surface Wind Speed

  • units: m s-1

• Empirical quantile mapping and Linear smooth spline fitting -t sfcWind

midas -t sfcWind -p reference_period -r reference_input -m model_input -o output

tasmax

• Standardization

  • long name: Near-Surface Maximum Air Temperature

  • units: K

• Pre-process (tas,tasmax and tasmin -> tasrange and tasskew)

• Empirical quantile mapping and Linear smooth spline fitting (tasrange and tasskew, -t tasrange, -t tasskew)

• Empirical quantile mapping, Linear smooth spline fitting and additive time-scale separation (tas, -t tasmax)

• Post-process (tas, tasrange, tasskew -> tasmax)

To bias-adjust tasrange and tasskew:

midas -t tasrange -p reference_period -r reference_input -m model_input -o output

midas -t tasskew -p reference_period -r reference_input -m model_input -o output

To bias-adjust tasmax:

midas -t tasmax -p reference_period -r reference_input -m model_input -o output

tasmin

• Standardization

  • long name: Near-Surface Minimum Air Temperature

  • units: K

• Pre-process (tas, tasmax, tasmin -> tasrange and tasskew)

• Empirical quantile mapping and Linear smooth spline fitting (tasrange and tasskew, -t tasrange, -t tasskew)

• Empirical quantile mapping, Linear smooth spline fitting and additive time-scale separation (tas, -t tasmin)

• Post-process (tasrange, tasskew, tas -> tasmin)

To bias-adjust tasrange and tasskew:

midas -t tasrange -p reference_period -r reference_input -m model_input -o output

midas -t tasskew -p reference_period -r reference_input -m model_input -o output

To bias-adjust tasmin:

midas -t tasmin -p reference_period -r reference_input -m model_input -o output

rsds

• Standardization

  • long name: Surface Downwelling Shortwave Radiation

  • units: W m−2

• Empirical quantile mapping and Linear smooth spline fitting -t rsds

midas -t rsds -p reference_period -r reference_input -m model_input -o output

rlds

• Standardization

  • long name: Surface Downwelling Longwave Radiation

  • units: W m−2

• Empirical quantile mapping and Linear smooth spline fitting -t rlds

midas -t rlds -p reference_period -r reference_input -m model_input -o output

Literature reference

Berg, P., Bosshard, T., Yang, W., and Zimmermann, K.: MIdASv0.2.1 – MultI-scale bias AdjuStment, Geosci. Model Dev., Vol.15, Issue 15, p. 6165–6180, https://doi.org/10.5194/gmd-15-6165-2022, 2022.

Berg, P., Bosshard, T., Bozhinova, D., Bärring, L., Löw, J., Nilsson, C., Strandberg, G., Södling, J., Thuresson, J., Wilcke, R., and Yang, W.: Robust handling of extremes in quantile mapping – “Murder your darlings”, Geosci. Model Dev., 17, 8173–8179, https://doi.org/10.5194/gmd-17-8173-2024, 2024

Gudmundsson, L., Bremnes, J. B., Haugen, J. E., and Engen-Skaugen, T.: Technical Note: Downscaling RCM precipitation to the station scale using statistical transformations – a comparison of methods, Hydrol. Earth Syst. Sci., 16, 3383–3390, https://doi.org/10.5194/hess-16-3383-2012, 2012

Gudmundsson L.: Statistical Transformations for Post-Processing Climate Model Output, Version 1.0-4, 2016

Lange, S.: Trend-preserving bias adjustment and statistical downscaling with ISIMIP3BASD (v1.0), Geosci. Model Dev., 12, 3055–3070, https://doi.org/10.5194/gmd-12-3055-2019, 2019.

Dierckx, P.: An algorithm for smoothing, differentiation and integration of experimental data using spline functions, J.Comp.Appl.Maths 1, 165-184, 1975

Dierckx, P.: A fast algorithm for smoothing data on a rectangular grid while using spline functions, SIAM J.Numer.Anal. 19, 1286-1304, 1982

Dierckx, P.: An improved algorithm for curve fitting with spline functions, report tw54, Dept. Computer Science,K.U. Leuven, 1981.

Dierckx, P.: Curve and surface fitting with splines, Monographs on Numerical Analysis, Oxford University Press, 1993.

Sen, P. K.: Estimates of the regression coefficient based on Kendall’s tau, Am. Stat. Assoc. Bull., 63, 1379–1389, 1968.

Theil, H.: A rank-invariant method of linear and polynomial regression analysis, Indag. Math., 12, 173, 1950

Virtanen, P., Gommers, R., Oliphant, T.E. et al.: SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat Methods 17, 261–272, https://doi.org/10.1038/s41592-019-0686-2, 2020.

Vrac, M., Noël, T., and Vautard, R.: Bias correction of precipitation through Singularity Stochastic Removal: Because occurrences matter, J. Geophys. Res.-Atmos., 121, 5237–5258, https://doi.org/10.1002/2015jd024511, 2016.