# pbias: Percent Bias In hydroGOF: Goodness-of-Fit Functions for Comparison of Simulated and Observed Hydrological Time Series

## Description

Percent Bias between `sim` and `obs`, with treatment of missing values.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```pbias(sim, obs, ...) ## Default S3 method: pbias(sim, obs, na.rm=TRUE, ...) ## S3 method for class 'data.frame' pbias(sim, obs, na.rm=TRUE, ...) ## S3 method for class 'matrix' pbias(sim, obs, na.rm=TRUE, ...) ## S3 method for class 'zoo' pbias(sim, obs, na.rm=TRUE, ...) ```

## Arguments

 `sim` numeric, zoo, matrix or data.frame with simulated values `obs` numeric, zoo, matrix or data.frame with observed values `na.rm` a logical value indicating whether 'NA' should be stripped before the computation proceeds. When an 'NA' value is found at the i-th position in `obs` OR `sim`, the i-th value of `obs` AND `sim` are removed before the computation. `...` further arguments passed to or from other methods.

## Details

PBIAS = 100 * [ sum( sim - obs ) / sum( obs ) ]

Percent bias (PBIAS) measures the average tendency of the simulated values to be larger or smaller than their observed ones.

The optimal value of PBIAS is 0.0, with low-magnitude values indicating accurate model simulation. Positive values indicate overestimation bias, whereas negative values indicate model underestimation bias

## Value

Percent bias between `sim` and `obs`. The result is given in percentage (%)

If `sim` and `obs` are matrixes, the returned value is a vector, with the percent bias between each column of `sim` and `obs`.

## Note

`obs` and `sim` has to have the same length/dimension

The missing values in `obs` and `sim` are removed before the computation proceeds, and only those positions with non-missing values in `obs` and `sim` are considered in the computation

## Author(s)

Mauricio Zambrano Bigiarini <[email protected]>

## References

Yapo P. O., Gupta H. V., Sorooshian S., 1996. Automatic calibration of conceptual rainfall-runoff models: sensitivity to calibration data. Journal of Hydrology. v181 i1-4. 23-48

Sorooshian, S., Q. Duan, and V. K. Gupta. 1993. Calibration of rainfall-runoff models: Application of global optimization to the Sacramento Soil Moisture Accounting Model, Water Resources Research, 29 (4), 1185-1194, doi:10.1029/92WR02617.

`gof`, `ggof`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25``` ```obs <- 1:10 sim <- 1:10 pbias(sim, obs) obs <- 1:10 sim <- 2:11 pbias(sim, obs) ################## # Loading daily streamflows of the Ega River (Spain), from 1961 to 1970 data(EgaEnEstellaQts) obs <- EgaEnEstellaQts # Generating a simulated daily time series, initially equal to the observed series sim <- obs # Computing the 'pbias' for the "best" case pbias(sim=sim, obs=obs) # Randomly changing the first 2000 elements of 'sim', by using a normal distribution # with mean 10 and standard deviation equal to 1 (default of 'rnorm'). sim[1:2000] <- obs[1:2000] + rnorm(2000, mean=10) # Computing the new 'pbias' pbias(sim=sim, obs=obs) ```