hydroGOF (version 0.4-0)

nrmse: Normalized Root Mean Square Error

Description

Normalized root mean square error (NRMSE) between sim and obs, with treatment of missing values.

Usage

nrmse(sim, obs, ...)
# S3 method for default
nrmse(sim, obs, na.rm=TRUE, norm="sd", ...)
# S3 method for data.frame
nrmse(sim, obs, na.rm=TRUE, norm="sd", ...)
# S3 method for matrix
nrmse(sim, obs, na.rm=TRUE, norm="sd", ...)
# S3 method for zoo
nrmse(sim, obs, na.rm=TRUE, norm="sd", ...)

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.

norm

character, indicating the value to be used for normalising the root mean square error (RMSE). Valid values are: -) sd : standard deviation of observations (default). -) maxmin: difference between the maximum and minimum observed values

…

further arguments passed to or from other methods.

Value

Normalized root mean square error (nrmse) between sim and obs. The result is given in percentage (%)

If sim and obs are matrixes, the returned value is a vector, with the normalized root mean square error between each column of sim and obs.

Details

$$ nrmse = 100 \frac {\sqrt{ \frac{1}{N} \sum_{i=1}^N { \left( S_i - O_i \right)^2 } } } {nval} $$ $$nval= \left\{ \begin{array}{cl} sd(O_i) & , \: \textrm{norm="sd"} \\ O_{max} - O_{min} & , \: \textrm{norm="maxmin"} \end{array} \right.$$

See Also

rmse, ssq, gof, ggof

Examples

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

obs <- 1:10
sim <- 2:11
nrmse(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 normalized root mean squared error for the "best" (unattainable) case
nrmse(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 normalized root mean squared error
nrmse(sim=sim, obs=obs)
# }