# Reference
(Command)=
## Recommended processing steps (tested variables)


(var-pr)=
### pr

 - Standardization

   - `long name`: Precipitation
   - `units`: kg m-2 s-1

 - Wet-day adjustment `--ssr`
 - [Empirical quantile mapping](QAM) and [Linear smooth spline fitting](sf) `-t pr`

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


(var-tas)=
### tas
- Standardization

    - `long name`: Near-Surface Air Temperature
    - `units`: K

- [Empirical quantile mapping](QAM), [Linear smooth spline fitting](sf) and [additive time-scale separation](addTS) `-t tas`

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


(var-hurs)=
### hurs
- Standardization

     - `long name`: Near-Surface Relative Humidity
     - `units`: %

 - [Empirical quantile mapping](QAM) and [Linear smooth spline fitting](sf) `-t hurs`

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


(var-hurs_inv)=
### hurs_inv

- Standardization

     - `long name`: Near-Surface Relative Humidity
     - `units`: %

 - [Pre-process](hursinv) (hurs -> hurs_inv)
 - [Empirical quantile mapping](QAM) and [Linear smooth spline fitting](sf) (hurs_inv, `-t hurs_inv`)
 - [Post-process](hursinv) (hurs_inv -> hurs)

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

(var-sfcWind)=
### sfcWind
- Standardization

  - `long name`: Near-Surface Wind Speed
  - `units`: m s-1

- [Empirical quantile mapping](QAM) and [Linear smooth spline fitting](sf) `-t sfcWind`

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


(var-tasmax)=
### tasmax

- Standardization

  - `long name`: Near-Surface Maximum Air Temperature
  - `units`: K

- [Pre-process](tasmax_tasmin) (tas,tasmax and tasmin -> tasrange and tasskew)
- [Empirical quantile mapping](QAM) and [Linear smooth spline fitting](sf) (tasrange and tasskew, `-t tasrange`, `-t tasskew`)
- [Empirical quantile mapping](QAM), [Linear smooth spline fitting](sf) and [additive time-scale separation](addTS) (tas, `-t tasmax`)
- [Post-process](tasmax_tasmin) (tas, tasrange, tasskew -> tasmax)

To bias-adjust tasrange and tasskew:
```bash
midas -t tasrange -p reference_period -r reference_input -m model_input -o output
```
```bash
midas -t tasskew -p reference_period -r reference_input -m model_input -o output
```
To bias-adjust tasmax:
```bash
midas -t tasmax -p reference_period -r reference_input -m model_input -o output
```


(var-tasmin)=
### tasmin

- Standardization

  - `long name`: Near-Surface Minimum Air Temperature
  - `units`: K

- [Pre-process](tasmax_tasmin) (tas, tasmax, tasmin -> tasrange and tasskew)
- [Empirical quantile mapping](QAM) and [Linear smooth spline fitting](sf) (tasrange and tasskew, `-t tasrange`, `-t tasskew`)
- [Empirical quantile mapping](QAM), [Linear smooth spline fitting](sf) and [additive time-scale separation](addTS) (tas, `-t tasmin`)
- [Post-process](tasmax_tasmin) (tasrange, tasskew, tas -> tasmin)

To bias-adjust tasrange and tasskew:
```bash
midas -t tasrange -p reference_period -r reference_input -m model_input -o output
```
```bash
midas -t tasskew -p reference_period -r reference_input -m model_input -o output
```
To bias-adjust tasmin:
```bash
midas -t tasmin -p reference_period -r reference_input -m model_input -o output
```


(var-rsds)=
### rsds
- Standardization

  - `long name`: Surface Downwelling Shortwave Radiation
  - `units`: W m−2

- [Empirical quantile mapping](QAM) and [Linear smooth spline fitting](sf) `-t rsds`
```bash
midas -t rsds -p reference_period -r reference_input -m model_input -o output
```

(var-rlds)=
### rlds
- Standardization

   - `long name`: Surface Downwelling Longwave Radiation
   - `units`: W m−2

- [Empirical quantile mapping](QAM) and [Linear smooth spline fitting](sf) `-t rlds`

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


(REF)=
## Literature reference
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         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.