% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/CST_EnsClustering.R
\name{CST_EnsClustering}
\alias{CST_EnsClustering}
\title{Ensemble clustering}
\usage{
CST_EnsClustering(
  exp,
  time_moment = "mean",
  numclus = NULL,
  lon_lim = NULL,
  lat_lim = NULL,
  variance_explained = 80,
  numpcs = NULL,
  time_dim = NULL,
  time_percentile = 90,
  cluster_dim = "member",
  verbose = F
)
}
\arguments{
\item{exp}{An object of the class 's2dv_cube', containing the variables to be 
analysed. Each data object in the list is expected to have an element named 
\code{$data} with at least two spatial dimensions named "lon" and "lat", and 
dimensions "dataset", "member", "ftime", "sdate".}

\item{time_moment}{Decides the moment to be applied to the time dimension. Can 
be either 'mean' (time mean), 'sd' (standard deviation along time) or 'perc' 
(a selected percentile on time). If 'perc' the keyword 'time_percentile' is 
also used.}

\item{numclus}{Number of clusters (scenarios) to be calculated. If set to NULL 
the number of ensemble members divided by 10 is used, with a minimum of 2 
and a maximum of 8.}

\item{lon_lim}{List with the two longitude margins in `c(-180,180)` format.}

\item{lat_lim}{List with the two latitude margins.}

\item{variance_explained}{variance (percentage) to be explained by the set of 
EOFs. Defaults to 80. Not used if numpcs is specified.}

\item{numpcs}{Number of EOFs retained in the analysis (optional).}

\item{time_dim}{String or character array with name(s) of dimension(s) over 
which to compute statistics. If omitted c("ftime", "sdate", "time") are 
searched in this order.}

\item{time_percentile}{Set the percentile in time you want to analyse (used 
for `time_moment = "perc").}

\item{cluster_dim}{Dimension along which to cluster. Typically "member" or 
"sdate". This can also be a list like c("member", "sdate").}

\item{verbose}{Logical for verbose output}
}
\value{
A list with elements \code{$cluster} (cluster assigned for each 
member), \code{$freq} (relative frequency of each cluster), 
\code{$closest_member} (representative member for each cluster), 
\code{$repr_field} (list of fields for each representative member), 
\code{composites} (list of mean fields for each cluster), \code{$lon} 
(selected longitudes of output fields), \code{$lat} (selected longitudes of 
output fields).
}
\description{
This function performs a clustering on members/starting dates
and returns a number of scenarios, with representative members for each of 
them. The clustering is performed in a reduced EOF space.

Motivation:
Ensemble forecasts give a probabilistic insight of average weather conditions
on extended timescales, i.e. from sub-seasonal to seasonal and beyond.
With large ensembles, it is often an advantage to be able to group members
according to similar characteristics and to select the most representative 
member for each cluster. This can be useful to characterize the most probable 
forecast scenarios in a multi-model (or single model) ensemble prediction.  
This approach, applied at a regional level, can also be used to identify the 
subset of ensemble members that best represent the full range of possible 
solutions for downscaling applications. The choice of the ensemble members is 
made flexible in order to meet the requirements of specific (regional) climate 
information products, to be tailored for different regions and user needs. 

Description of the tool:
EnsClustering is a cluster analysis tool, based on the k-means algorithm, for 
ensemble predictions. The aim is to group ensemble members according to 
similar characteristics and to select the most representative member for each 
cluster. The user chooses which feature of the data is used to group the 
ensemble members by clustering: time mean, maximum, a certain percentile 
(e.g., 75% as in the examples below), standard deviation and trend over the 
time period. For each ensemble member this value is computed at each grid 
point, obtaining N lat-lon maps, where N is the number of ensemble members.
The anomaly is computed subtracting the ensemble mean of these maps to each of 
the single maps. The anomaly is therefore computed with respect to the 
ensemble members (and not with respect to the time) and the Empirical 
Orthogonal Function (EOF) analysis is applied to these anomaly maps. Regarding 
the EOF analysis, the user can choose either how many Principal Components 
(PCs) to retain or the percentage of explained variance to keep. After 
reducing dimensionality via EOF analysis, k-means analysis is applied using 
the desired subset of PCs. 

The major final outputs are the classification in clusters, i.e. which member 
belongs to which cluster (in k-means analysis the number k of clusters needs 
to be defined prior to the analysis) and the most representative member for 
each cluster, which is the closest member to the cluster centroid. Other 
outputs refer to the statistics of clustering: in the PC space, the minimum 
and the maximum distance between a member in a cluster and the cluster 
centroid (i.e. the closest and the furthest member), the intra-cluster 
standard deviation for each cluster (i.e. how much the cluster is compact).
}
\examples{
dat_exp <- array(abs(rnorm(1152))*275, dim = c(dataset = 1, member = 4, sdate = 6,
                                              ftime = 3, lat = 4, lon = 4))
lon <- seq(0, 3)
lat <- seq(48, 45)
coords = list(lon = lon, lat = lat)
exp <- list(data = dat_exp, coords = coords)
attr(exp, 'class') <- 's2dv_cube'
res <- CST_EnsClustering(exp = exp, numclus = 3,
                        cluster_dim = c("sdate"))

}
\author{
Federico Fabiano - ISAC-CNR, \email{f.fabiano@isac.cnr.it}

Ignazio Giuntoli - ISAC-CNR, \email{i.giuntoli@isac.cnr.it}

Danila Volpi - ISAC-CNR, \email{d.volpi@isac.cnr.it}

Paolo Davini - ISAC-CNR, \email{p.davini@isac.cnr.it}

Jost von Hardenberg - ISAC-CNR, \email{j.vonhardenberg@isac.cnr.it}
}
