% 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_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 needed.}

\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_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{
exp <- lonlat_data$exp
# Example 1: Cluster on all start dates, members and models
res <- CST_EnsClustering(exp, numclus = 3,
                         cluster_dim = c("member", "dataset", "sdate"))
iclus = res$cluster[2, 1, 3]
\donttest{
print(paste("Cluster of 2. member, 1. dataset, 3. sdate:", iclus))
print(paste("Frequency (numerosity) of cluster (", iclus, ") :", res$freq[iclus]))
library(s2dverification)
PlotEquiMap(res$repr_field[iclus, , ], exp$lon, exp$lat,
            filled.continents = FALSE,
            toptitle = paste("Representative field of cluster", iclus))
}
# Example 2: Cluster on members retaining 4 EOFs during 
# preliminary dimensional reduction
res <- CST_EnsClustering(exp, numclus = 3, numpcs = 4, cluster_dim = "member")
# Example 3: Cluster on members, retain 80\% of variance during 
# preliminary dimensional reduction
res <- CST_EnsClustering(exp, numclus = 3, variance_explained = 80,
                         cluster_dim = "member")
# Example 4: Compute percentile in time
res <- CST_EnsClustering(exp, numclus = 3,  time_percentile = 90,
                         time_moment = "perc", cluster_dim = "member")
}
\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}
}

