nrmse: Normalized Root Mean Square Error

In hydroGOF: Goodness-of-Fit Functions for Comparison of Simulated and Observed Hydrological Time Series

Description

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

Usage

nrmse(sim, obs, ...)

## Default S3 method:
nrmse(sim, obs, na.rm=TRUE, norm="sd", ...)

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

## S3 method for class 'matrix'
nrmse(sim, obs, na.rm=TRUE, norm="sd", ...)

## S3 method for class '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.

Details

nrmse = 100 \frac {√{ \frac{1}{N} ∑_{i=1}^N { ≤ft( S_i - O_i \right)^2 } } } {nval}

nrmse = 100 * [ rmse(sim, obs) / nval ] ; nval= range(obs, na.rm=TRUE) OR nval=sd(obs), depending on the \code{norm} value

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.

Note

obs and sim have to have the same length/dimension

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

Author(s)

Mauricio Zambrano Bigiarini <[e-mail]>

See Also

rmse, ssq, gof, ggof

Examples

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)

Example output

Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric

[1] 0
[1] 33
[1] 0
[1] 37.1

hydroGOF documentation built on March 14, 2020, 1:07 a.m.