cp {hydroGOF}R Documentation

Coefficient of persistence


Coefficient of persistence between sim and obs, with treatment of missing values.


cp(sim, obs, ...)

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

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

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

## S3 method for class 'zoo'
cp(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.


cp = 1 - [ sum( (obs[2:n] - sim[2:n])^2 ] / sum( ( obs[2:n] - obs[1:(n-1)] )^2 )

Coefficient of persistence (Kitadinis and Bras, 1980; Corradini et al., 1986) is used to compare the model performance against a simple model using the observed value of the previous day as the prediction for the current day.

The coefficient of persistence compare the predictions of the model with the predictions obtained by assuming that the process is a Wiener process (variance increasing linearly with time), in which case, the best estimate for the future is given by the latest measurement (Kitadinis and Bras, 1980).

Persistence model efficiency is a normalized model evaluation statistic that quantifies the relative magnitude of the residual variance (noise) to the variance of the errors obtained by the use of a simple persistence model (Moriasi et al., 2007).

CP ranges from 0 to 1, with CP = 1 being the optimal value and it should be larger than 0.0 to indicate a minimally acceptable model performance.


Coefficient of persistence between sim and obs.

If sim and obs are matrixes, the returned value is a vector, with the coefficient of persistence 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.


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


Kitanidis, P.K., and Bras, R.L. 1980. Real-time forecasting with a conceptual hydrologic model. 2. Applications and results. Water Resources Research, Vol. 16, No. 6, pp. 1034:1044

Moriasi, D. N. et al. (2007). Model Evaluation Guidelines for Systematic Quantification of Accuracy in Watershed Simulations. Transactions of the ASABE, 50:(3), 885-900

See Also



obs <- 1:10
sim <- 1:10
cp(sim, obs)

obs       <- 1:10
sim[2:10] <- obs[1:9]
cp(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 'cp' for the "best" (unattainable) case
cp(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  'cp'
cp(sim=sim, obs=obs)

[Package hydroGOF version 0.3-10 Index]