nrmse {hydroGOF} R Documentation

## 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, ...)

## 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 <mzb.devel@gmail.com>

### 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)

[Package hydroGOF version 0.3-10 Index]