\name{RMS}
\alias{RMS}
\alias{.RMS}
\title{
Computes Root Mean Square Error
}
\description{
Computes the root mean square error for an array of forecasts, var_exp and an array of observations, var_obs, which should have the same dimensions except along the posloop dimension where the lengths can be different, with the number of experiments/models for var_exp (nexp) and the number of obserational datasets for var_obs (nobs).\cr
The RMSE is computed along the posRMS dimension which should correspond to the startdate dimension.\cr
If compROW is given, the RMSE is computed only if rows along the compROW dimension are complete between limits[1] and limits[2], i.e. there are no NAs between limits[1] and limits[2]. This option can be activated if the user wishes   to account only for the forecasts for which observations are available at all leadtimes.\cr
Default: limits[1] = 1 and limits[2] = length(compROW dimension).\cr
The confidence interval relies on a chi2 distribution. \cr

.RMS provides the same functionality but taking a matrix of ensemble members as input (exp).
}
\usage{
RMS(var_exp, var_obs, posloop = 1, posRMS = 2, compROW = NULL, limits = NULL, siglev = 0.95, conf = TRUE)

.RMS(exp, obs, limits = NULL, siglev = 0.95, conf = TRUE)      
}
\arguments{
  \item{var_exp}{
Matrix of experimental data.
  }
  \item{var_obs}{
Matrix of observational data, same dimensions as var_exp except along posloop dimension, where the length can be nobs instead of nexp.
  }
  \item{posloop}{
Dimension nobs and nexp.
  }
  \item{posRMS}{
Dimension along which RMSE are to be computed (the dimension of the start dates).
  }
  \item{compROW}{
Data taken into account only if (compROW)th row is complete.\cr
Default = NULL.
  }
  \item{limits}{
Complete between limits[1] & limits[2]. Default = NULL.
  }
  \item{siglev}{
Confidence level of the computed confidence interval. 0.95 by default.
  }
  \item{conf}{
Whether to compute confidence interval or not. TRUE by default.
  }
  \item{exp}{
N by M matrix of N forecasts from M ensemble members.
  }
  \item{obs}{
Vector of the corresponding observations of length N.
  }
}
\value{
RMS: Array with dimensions:\cr
  c(length(posloop) in var_exp, length(posloop) in var_obs, 1 or 3, all other dimensions of var_exp & var_obs except posRMS).\cr
The 3rd dimension corresponds to the lower limit of the  95\% confidence interval (only present if \code{conf = TRUE}), the RMSE, and the upper limit of the 95\% confidence interval (only present if \code{conf = TRUE}). \cr
.RMS: 
 \item{$rms}{
The root mean square error, 
  }
  \item{$conf_low}{
Corresponding to the lower limit of the \code{siglev}\% confidence interval (only present if \code{conf = TRUE}) for the rms.
  } 
   \item{$conf_high}{
Corresponding to the upper limit of the \code{siglev}\% confidence interval (only present if \code{conf = TRUE}) for the rms.
  } 
}
\examples{
# Load sample data as in Load() example:
example(Load)
clim <- Clim(sampleData$mod, sampleData$obs)
ano_exp <- Ano(sampleData$mod, clim$clim_exp)
ano_obs <- Ano(sampleData$obs, clim$clim_obs)
runmean_months <- 12
dim_to_smooth <- 4  # Smooth along lead-times
smooth_ano_exp <- Smoothing(ano_exp, runmean_months, dim_to_smooth)
smooth_ano_obs <- Smoothing(ano_obs, runmean_months, dim_to_smooth)
dim_to_mean <- 2  # Mean along members
required_complete_row <- 3  # Discard start-dates for which some leadtimes are missing
leadtimes_per_startdate <- 60
rms <- RMS(Mean1Dim(smooth_ano_exp, dim_to_mean), 
           Mean1Dim(smooth_ano_obs, dim_to_mean), 
           compROW = required_complete_row, 
           limits = c(ceiling((runmean_months + 1) / 2), 
                      leadtimes_per_startdate - floor(runmean_months / 2)))
PlotVsLTime(rms, toptitle = "Root Mean Square Error", ytitle = "K", 
            monini = 11, limits = NULL, listexp = c('CMIP5 IC3'), 
            listobs = c('ERSST'), biglab = FALSE, hlines = c(0), 
            fileout = 'tos_rms.eps')
 \dontrun{
  library(easyVerification)  
  dim(smooth_ano_obs) <- dim(smooth_ano_obs)[-2] # see ?veriApply for how to use the 'parallel' option
  rms2 <- veriApply(".RMS", smooth_ano_exp, smooth_ano_obs, tdim = 3, ensdim = 2)
  }
}
\author{
History:\cr
0.1  -  2011-05  (V. Guemas, \email{vguemas at ic3.cat})  -  Original code\cr
1.0  -  2013-09  (N. Manubens, \email{nicolau.manubens at ic3.cat})  -  Formatting to R CRAN\cr
2.0  -  2017-02  (A. Hunter, \email{alasdair.hunter at bsc.es})  -  Adapted to veriApply()
}
\keyword{datagen}
