rd {hydroGOF}R Documentation

Relative Index of Agreement


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.


rd(sim, obs, ...)

## Default S3 method:
rd(sim, obs, na.rm=TRUE, ...)

## S3 method for class 'data.frame'
rd(sim, obs, na.rm=TRUE, ...)

## S3 method for class 'matrix'
rd(sim, obs, na.rm=TRUE, ...)

## S3 method for class 'zoo'
rd(sim, obs, na.rm=TRUE, ...)



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


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


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.


rd = 1 - [ sum( ( (obs - sim) / obs )^2 ] / sum( ( (abs(sim - mean(obs) ) + abs(obs - mean(obs) ) ) / mean(obs) )^2 )

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


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.


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.

If some of the observed values are equal to zero (at least one of them), this index can not be computed.


Mauricio Zambrano Bigiarini <mzb.devel@gmail.com>


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


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
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)

[Package hydroGOF version 0.3-10 Index]