hydroGOF (version 0.4-0)

rd: Relative Index of Agreement

Description

This function computes the Relative Index of Agreement (d) between sim and obs, with treatment of missing values. If x is a matrix or a data frame, a vector of the relative index of agreement among the columns is returned.

Usage

rd(sim, obs, ...)
# S3 method for default
rd(sim, obs, na.rm=TRUE, ...)
# S3 method for data.frame
rd(sim, obs, na.rm=TRUE, ...)
# S3 method for matrix
rd(sim, obs, na.rm=TRUE, ...)
# S3 method for zoo
rd(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.

Value

Relative index of agreement between sim and obs.

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

Details

$$rd = 1 - \frac{ \sum_{i=1}^N { \left( \frac{O_i - S_i}{O_i} \right) ^2} } { \sum_{i=1}^N { \left( \frac{ \left| S_i - \bar{O} \right| + \left| O_i - \bar{O} \right|}{\bar{O}} \right)^2 } } $$

It varies between 0 and 1. A value of 1 indicates a perfect match, and 0 indicates no agreement at all.

References

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

Willmott, C. J. 1981. On the validation of models. Physical Geography, 2, 184--194

Willmott, C. J. (1984). On the evaluation of model performance in physical geography. Spatial Statistics and Models, G. L. Gaile and C. J. Willmott, eds., 443-460

Willmott, C. J., S. G. Ackleson, R. E. Davis, J. J. Feddema, K. M. Klink, D. R. Legates, J. O'Donnell, and C. M. Rowe (1985), Statistics for the Evaluation and Comparison of Models, J. Geophys. Res., 90(C5), 8995-9005

Legates, D. R., and G. J. McCabe Jr. (1999), Evaluating the Use of "Goodness-of-Fit" Measures in Hydrologic and Hydroclimatic Model Validation, Water Resour. Res., 35(1), 233--241

See Also

d, md, gof, ggof

Examples

# NOT RUN {
obs <- 1:10
sim <- 1:10
rd(sim, obs)

obs <- 1:10
sim <- 2:11
rd(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 relative index of agreement for the "best" (unattainable) case
rd(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 relative index of agreement
rd(sim=sim, obs=obs)

# }