hydroGOF (version 0.4-0)

br2: br2

Description

Coefficient of determination (r2) multiplied by the slope of the regression line between sim and obs, with treatment of missing values.

Usage

br2(sim, obs, ...)
# S3 method for default
br2(sim, obs, na.rm=TRUE, use.abs=FALSE, ...)
# S3 method for data.frame
br2(sim, obs, na.rm=TRUE, use.abs=FALSE, ...)
# S3 method for matrix
br2(sim, obs, na.rm=TRUE, use.abs=FALSE, ...)
# S3 method for zoo
br2(sim, obs, na.rm=TRUE, use.abs=FALSE, ...)

Arguments

sim

numeric, zoo, matrix or data.frame with simulated values

obs

numeric, zoo, matrix or data.frame with observed values

na.rm

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.

use.abs

logical value indicating whether the condition to select the formula used to compute br2 should be 'b<=1' or 'abs(b) <=1'. Krausse et al. (2005) uses 'b<=1' as condition, but strictly speaking this condition should be 'abs(b)<=1'. However, if your model simulations are somewhat "close" to the observations, this condition should not have much impact on the computation of 'br2'. This argument was introduced in hydroGOF 0.4-0, following a comment by E. White. Its default value is FALSE to ensure compatibility with previous versions of hydroGOF.

…

further arguments passed to or from other methods.

Value

br2 between sim and obs.

If sim and obs are matrixes, the returned value is a vector, with the br2 between each column of sim and obs.

Details

$$ br2 = |b| R2 , b <= 1 ; br2 = \frac{R2}{|b|}, b > 1 $$

A model that systematically over or under-predicts all the time will still result in "good" r2 (close to 1), even if all predictions were wrong (Krause et al., 2005). The br2 coefficient allows accounting for the discrepancy in the magnitude of two signals (depicted by 'b') as well as their dynamics (depicted by r2)

References

Krause, P., Boyle, D. P., and Base, F.: Comparison of different efficiency criteria for hydrological model assessment, Adv. Geosci., 5, 89-97, 2005

See Also

cor, lm, gof, ggof

Examples

# NOT RUN {
# Looking at the difference between r2 and br2 for a case with systematic 
# over-prediction of observed values
obs <- 1:10
sim1 <- 2*obs + 5
sim2 <- 2*obs + 25

# The coefficient of determination is equal to 1 even if there is no one single 
# simulated value equal to its corresponding observed counterpart
r2 <- (cor(sim1, obs, method="pearson"))^2 # r2=1

# 'br2' effectively penalises the systematic over-estimation
br2(sim1, obs) # br2 = 0.3684211
br2(sim2, obs) # br2 = 0.1794872

ggof(sim1, obs)
ggof(sim2, obs)

# Computing 'br2' without forcing the intercept be equal to zero
br2.2 <- r2/2 # br2 = 0.5

##################
# 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 'br2' for the "best" (unattainable) case
br2(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  'br2'
br2(sim=sim, obs=obs)

# }