hydroGOF (version 0.2-2)

rmse: Root Mean Square Error

Description

Root Mean Square Error (RMSE) between sim and obs, in the same units of sim and obs, with treatment of missing values. RMSE gives the standard deviation of the model prediction error. A smaller value indicates better model performance.

Usage

rmse(sim, obs, ...)
## S3 method for class 'default':
rmse(sim, obs, na.rm=TRUE, ...)
## S3 method for class 'data.frame':
rmse(sim, obs, na.rm=TRUE, ...)
## S3 method for class 'matrix':
rmse(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 ar

...

further arguments passed to or from other methods.

Value

• Root mean square error (rmse) between sim and obs. If sim and obs are matrixes, the returned value is a vector, with the RMSE between each column of sim and obs.

Details

$$rmse = \sqrt{ \frac{1}{N} \sum_{i=1}^N { \left( S_i - O_i \right)^2 } }$$

References

http://en.wikipedia.org/wiki/Root_mean_square_deviation

See Also

nrmse, ssq

Examples

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

obs <- 1:10
sim <- 2:11
rmse(sim, obs)

##################
# Loading daily streamflows of the Ega River (Spain), from 1961 to 1970
require(zoo)
data(EgaEnEstellaQts)
obs <- EgaEnEstellaQts

# Generating a simulated daily time series, initially equal to the observed series
sim <- obs 

# Computing the root mean squared error for the "best" (unattainable) case
rmse(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 root mean squared error
rmse(sim=sim, obs=obs)