cp: Coefficient of persistence

Description

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

Usage

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

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.

Details

$c p = 1 - \frac{\sum_{i = 2}^{N} {(S_{i} - O_{i})}^{2}}{\sum_{i = 1}^{N - 1} {(O_{i + 1} - O_{i})}^{2}}$

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.

References

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

Examples

Run this code

# NOT RUN {
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
data(EgaEnEstellaQts)
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)
# }

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