hydroGOF (version 0.4-0)

d: Index of Agreement

Description

This function computes the Index of Agreement between sim and obs, with treatment of missing values.

If x is a matrix or a data frame, a vector of the Index of Agreement of the columns is returned.

Usage

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

Index of agreement between sim and obs.

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

Details

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

The Index of Agreement (d) developed by Willmott (1981) as a standardized measure of the degree of model prediction error and varies between 0 and 1. A value of 1 indicates a perfect match, and 0 indicates no agreement at all (Willmott, 1981).

The index of agreement can detect additive and proportional differences in the observed and simulated means and variances; however, it is overly sensitive to extreme values due to the squared differences (Legates and McCabe, 1999).

References

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

md, rd, gof, ggof

Examples

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

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