# Transformation

deterministic-only

It is common practice in hydrology to apply transform functions to the streamflow data prior to the computation of the evaluation metrics on them.

This is typically done because most evaluation metrics are based on the squared residuals, such that errors on high flows contribute more to the metric value than errors on low flows. To reduce the emphasis on high flows, various transform functions can be applied (see e.g. Garcia et al. (2017) for transformations putting more emphasis on low flows).

`evalhyd` offers a variety of transform functions accessible through the transform parameter and whose possible values are summarised in the table below.

transformations

details

`"sqrt"`

The square root function f(Q) = √Q is applied.

`"pow"`

The power function f(Q) = Qⁿ is applied (where the power n can be set through the exponent parameter).

`"inv"`

The reciprocal function f(Q) = 1/Q is applied.

`"log"`

The natural logarithm function f(Q) = ln(Q) is applied.

Note

Since none of the reciprocal function, the natural logarithm, nor the power function with a negative exponent are defined for zero, a small constant ε must be added to both the streamflow observations and predictions prior to the calculation of the evaluation metrics. By default, one hundredth of the mean of the streamflow observations is used as value for ε, as recommended by Pushpalatha et al. (2012). It is customisable through the epsilon parameter.

A few examples of flow transformations are provided below.

```>>> res = evalhyd.evald(obs, prd, ["NSE"], transform="sqrt")
>>> res = evalhyd.evald(obs, prd, ["RMSE"], transform="log")
>>> res = evalhyd.evald(obs, prd, ["KGE"], transform="inv", epsilon=.5)
>>> res = evalhyd.evald(obs, prd, ["NSE"], transform="pow", exponent=.8)
```
```> res <- evalhyd::evald(obs, prd, c("NSE"), transform = "sqrt")
> res <- evalhyd::evald(obs, prd, c("RMSE"), transform = "log")
> res <- evalhyd::evald(obs, prd, c("KGE"), transform = "inv", epsilon = .5)
> res <- evalhyd::evald(obs, prd, c("NSE"), transform = "pow", exponent = .8)
```
```\$ ./evalhyd evald "obs.csv" "prd.csv" "NSE" --to_file --transform "sqrt"
\$ ./evalhyd evald "obs.csv" "prd.csv" "RMSE" --to_file --transform "log"
\$ ./evalhyd evald "obs.csv" "prd.csv" "KGE" --to_file --transform "inv" --epsilon .5
\$ ./evalhyd evald "obs.csv" "prd.csv" "NSE" --to_file --transform "pow" --exponent .8
```