# Hierarchical Climate Regionalization

`HiClimR.Rd`

HiClimR is a tool for **Hi**erarchical **Clim**ate **R**egionalization
applicable to any correlation-based clustering. Climate regionalization is the process
of dividing an area into smaller regions that are homogeneous with respect to a specified
climatic metric. Several features are added to facilitate the applications of climate
regionalization (or spatiotemporal analysis in general) and to implement cluster validation
with an objective tree cutting to find an optimal number of clusters for a user-specified
confidence level. These include options for preprocessing and postprocessing as well as
efficient code execution for large datasets and options for splitting big data and
computing only the upper-triangular half of the correlation/dissimilarity matrix to
overcome memory limitations. Hybrid hierarchical clustering reconstructs the upper part
of the tree above a cut to get the best of the available methods. Multivariate clustering
(MVC) provides options for filtering all variables before preprocessing, detrending and
standardization of each variable, and applying weights for the preprocessed variables.
The correlation distance for MVC represents the (weighted) average of distances between
all variables.

`HiClimR`

is the main function that calls all helper functions. It adds
several features and a new clustering method (called, *regional* linkage) to
hierarchical clustering in R (`hclust`

function in *stats* library):
data regridding (`grid2D`

function), coarsening spatial resolution
(`coarseR`

function), geographic masking (`geogMask`

function),
contiguity-constrained clustering, data filtering by mean and/or variance thresholds,
data preprocessing (detrending, standardization, and PCA), faster correlation function
(`fastCor`

function), hybrid hierarchical clustering, multivariate clustering
(MVC), cluster validation (`validClimR`

and `minSigCor`

functions),
and visualization of regionalization results, and exporting region map and mean timeseries
into NetCDF-4 file.

Badr et al. (2015) describes the regionalization algorithms, features, and data processing tools included in the package and presents a demonstration application in which the package is used to regionalize Africa on the basis of interannual precipitation variability.

*HiClimR is applicable to any correlation-based clustering.*

## Usage

```
HiClimR(
# Input data matrix (N spatial elements x M observations)
x = list(),
# Geographic coordinates
lon = NULL, lat = NULL,
# Coarsening spatial resolution
lonStep = 1, latStep = 1,
# Geographic masking:
geogMask = FALSE, gMask = NULL, continent = NULL, region = NULL, country = NULL,
# Contiguity constraint:
contigConst = 0,
# Data thresholds:
meanThresh = if (inherits(x, "list")) {
vector("list", length(x))
} else {
list(NULL)
},
varThresh = if (inherits(x, "list")) {
as.list(rep(0, length(x)))
} else {
list(0)
},
# Data preprocessing:
detrend = if (inherits(x, "list")) {
as.list(rep(FALSE, length(x)))
} else {
list(FALSE)
},
standardize = if (inherits(x, "list")) {
as.list(rep(FALSE, length(x)))
} else {
list(FALSE)
},
weightMVC = if (inherits(x, "list")) {
as.list(rep(1, length(x)))
} else {
list(1)
},
nPC = NULL,
# Clustering options:
method = "ward", hybrid = FALSE, kH = NULL, members = NULL,
# Big data support:
nSplit = 1, upperTri = TRUE, verbose = TRUE,
# Cluster validation:
validClimR = TRUE, rawStats = TRUE, k = NULL, minSize = 1, alpha = 0.05,
# Graphical options:
plot = TRUE, dendrogram = TRUE, colPalette = NULL,
hang = -1, labels = FALSE, pch = 15, cex = 1
)
```

## Arguments

- x
an (

`N`

rows by`M`

columns) matrix of 'double' values:`N`

objects (spatial points or stations) to be clustered by`M`

observations (temporal points or years). For gridded data, the`N`

objects should be created from the original matrix`x0`

using`as.vector(t(x0))`

, where`x0`

is an (`n`

rows by`m`

columns) matrix,`n = length(unique(lon))`

and`m = length(unique(lat))`

. Zero-variance rows (e.g., stations with zero variability) and/or missing values (e.g., years with missing observations) are allowed. The zero-variance rows and the columns with missing values will be removed. However, it is recommended to take care of both zero-variance rows and missing values before clustering. For Multivariate Clustering (MVC),`x`

can be a list of`nvar`

matrices for the`nvar`

variables (one matrix for each variable). The matrixes in`x`

list should have the same number of rows (objects: spatial points or stations) Data preprocessing is specified by lists of`meanThresh`

,`varThresh`

,`detrend`

, and`standardize`

with the same length of`x`

where`length(x) = nvar`

. Each variable is separately preprocessed to allow for all possible options. However, it is strongly recommended to standardize all variables since their magnitude range could be different. Note that: for gridded data, the rows of input data matrix for each variable is ordered by longitudes (check`TestCase$x`

for more details).- lon
a vector of longitudes with length

`N`

. Longitudes takes values from`-180`

to`180`

(not`0`

to`360`

). For gridded data, the length may have the value (`n`

) provided that`n * m = N`

where`n = length(unique(lon))`

and`m = length(unique(lat))`

.- lat
a vector of latitudes with length

`N`

or`m`

. See`lon`

.- lonStep
an integer greater than or equal to

`1`

for longitude step to coarsen gridded data in the longitudinal direction. If`lonStep = 1`

, gridded data will not be coarsened in the longitudinal direction (the default). If`lonStep = 2`

, every other grid in longitudinal direction will be retained.- latStep
an integer greater than or equal to

`1`

for latitude step to coarsen gridded data in the latitudinal direction. If`latStep = 1`

, gridded data will not be coarsened in the latitudinal direction (the default). If`latStep = 2`

, every other grid in latitudinal direction will be retained.`lonStep`

and`latStep`

are independent so that user can optionally apply different coarsening level to each dimension.- geogMask
a logical: if

`geogMask = TRUE`

,`geogMask`

function will be called. Additional arguments are required. It requires the longitude and latitude vector together with a string (or array of strings) to specify`continent`

,`region`

name(s), or`country`

ISO3 character code(s). If`gMask != NULL`

, the provided`gmask`

vector will be used for geographic masking without calling`geogMask`

.- gMask
A vector of indices for the spatial elements to be masked, as required by

`HiClimR`

. This is typically an output vector from`geogMask`

function. This helps in saving time when the same geographic mask will be used many times.- continent
`NULL`

or a string (or array of strings) to specify`continent`

name(s): only one of`continent`

,`region`

, or`country`

should be specified. Valid list of`continent`

names can be obtained by running`geogMask()`

.- region
`NULL`

or a string (or array of strings) to specify`region`

name(s): only one of`continent`

,`region`

, or`country`

should be specified. Valid list of`region`

names can be obtained by running`geogMask()`

.- country
`NULL`

or a string (or array of strings) to specify`country`

ISO3 character code(s): only one of`continent`

,`region`

, or`country`

should be specified. Valid list of`country`

ISO3 character code(s) can be obtained by running`geogMask()`

.- contigConst
`0`

or a positive value for contiguity constraint: This is used to apply weighted geographic distances on the initial dissimilarity matrix between the variable(s) in the data matrix`x`

. It should be a positive real value (`contigConst > 0`

, recommended between`0`

and`1`

) where`contigConst = 0`

means that clustering is completely based on the data with no constraints for contiguity while`contigConst > 0`

gives priority to merging contiguous points. Geographic coordinates`lon`

and`lat`

are required to compute the geographic distances.`regional`

linkage method does not support contiguity constraints.- meanThresh
`NULL`

or a threshold for the temporal mean: This is used with`varThresh`

to mask zero- and near-zero-variance data, Observations with mean less than or equal to`meanThresh`

will be removed. If`meanThresh = NULL`

, then the`varThresh`

will be used either to mask zero-variance data by default or by increased variance threshold to mask near-zero-variance data. For Multivariate Clustering (MVC),`meanThresh`

is a list of thresholds with the same length of`x`

where`length(x) = nvar`

. Each variable is separately preprocessed to allow for all possible options. However, it is strongly recommended to standardize all variables since their magnitude range could be different.- varThresh
zero or a threshold for the temporal variance: This is used with

`meanThresh`

to mask zero- and near-zero-variance data, Observations with variance less than or equal to`varThresh`

will be removed. If`varThresh = 0`

, then the zero-variance data will masked (default). For Multivariate Clustering (MVC),`varThresh`

is a list of thresholds with the same length of`x`

where`length(x) = nvar`

. Each variable is separately preprocessed to allow for all possible options. However, it is strongly recommended to standardize all variables since their magnitude range could be different.- detrend
a logical: should the data be detrended before clustering? Detrending (removing the linear trend) is important when variations from temporal point to another is of interest (e.g., interannual variability). The columns of the data matrix

`x`

should be temporally ordered (constant step size) or have appropriate names (e.g.,`colnames(x) = years[1:M]`

). For Multivariate Clustering (MVC),`detrend`

is a list of thresholds with the same length of`x`

where`length(x) = nvar`

. Each variable is separately preprocessed to allow for all possible options. However, it is strongly recommended to standardize all variables since their magnitude range could be different.- standardize
a logical: should the data be standardized before clustering? The standardized data makes use of the mean of equally-weighted objects within each cluster (cluster mean = mean of standardized variables within the cluster). Otherwise, the mean of raw data will be used (cluster mean = mean of raw variables within the cluster). The variance of the mean is updated at each agglomeration step. For Multivariate Clustering (MVC),

`standardize`

is a list of thresholds with the same length of`x`

where`length(x) = nvar`

. Each variable is separately preprocessed to allow for all possible options. However, it is strongly recommended to standardize all variables since their magnitude range could be different.- weightMVC
a list of positive wights (

`weightMVC > 0`

) for Multivariate Clustering (MVC) with the same length of`x`

where`length(x) = number of variables`

. The filtered variables are weighted and combined by column (for each object: spatial points or stations) after preprocessing (detrending and standardization) and before PCA (if requested) and computing the correlation/dissimilarity matrix. The default weight is`weightMVC = 1`

for all variables.- nPC
`NULL`

or number of principal components (PCs) to be retained. If`nPC = NULL`

, then the raw data will be used for clustering. Otherwise, the data will be filtered and reconstructed using`nPC`

PCs obtained from SVD-based PCA. The`detrend`

and/or`standardize`

options will be applied, if requested, before PCA.- method
the agglomeration method to be used. This should be (an unambiguous abbreviation of) one of

`"regional"`

,`"ward"`

,`"single"`

,`"complete"`

,`"average"`

,`"mcquitty"`

,`"median"`

or`"centroid"`

. The default is`"ward"`

method.- hybrid
a logical: should the upper part of the tree be reconstructed using

`regional`

linkage clustering method? This adds hybrid hierarchical clustering feature to get the best of the available methods. It utilizes the pros of available methods, especially the better overall homogeneity in*ward*'s method and the separation, contiguity, and objective tree cut of*regional*linkage method. If`hybrid = FALSE`

, only the default clustering using the selected`method`

will be used (i.e., no hybrid clustering).Otherwise, the upper part of the tree will be reconstructed above a cut of`kH`

clusters using`regional`

linkage method. Note:`hybrid`

option is redundant when using`regional`

linkage as the main clustering method.- kH
`NULL`

or an integer for the number of regions/clusters in the upper part of the tree to be reconstructed with`regional`

linkage method, if`hybrid = TRUE`

. If`kH = NULL`

, the tree will be reconstructed for the upper part with the first merging cost larger than the mean merging cost for the entire tree. If hybrid clustering is requested, the updated upper part of the tree will be used for cluster validation, and so`kH`

should be greater than the final number of clusters`k`

, if selected.- members
`NULL`

or a vector with length size of`d`

. See the ‘Details’ section.- nSplit
integer number greater than or equal to one, to split the data matrix into

`nSplit`

splits of the total number of columns`ncol(xt)`

. If`nSplit = 1`

, the default method will be used to compute correlation matrix for the full data matrix (no splits). If`nSplit > 1`

, the correlation matrix (or the upper-triangular part if`upperTri = TRUE`

) will be allocated and filled with the computed correlation sub-matrix for each split. the first`n-1`

splits have equal size while the last split may include any remaining columns. This is used with`upperTri = TRUE`

to compute only the upper-triangular part of the correlation matrix. The maximum number of splits`nSplitMax = floor(N / 2)`

makes splits with 2 columns; if`nSplit > nSplitMax`

,`nSplitMax`

will be used. Very large number of splits`nSplit`

makes computation slower but it could handle big data or if the available memory is not enough to allocate the correlation matrix, which helps in solving the “Error: cannot allocate vector of size...” memory limitation problem. It is recommended to start with a small number of splits. If the data is very large compared to the physical memory, it is highly recommended to use a 64-Bit machine with enough memory resources and/or use coarsening feature for gridded data by setting`lonStep > 1`

and`latStep > 1`

.- upperTri
logical to compute only the upper-triangular half of the correlation matrix if

`upperTri = TRUE`

and`nSplit > 1`

., which includes all required info since the correlation/dissimilarity matrix is symmetric. This almost halves memory use, which can be very important for big data.- verbose
logical to print processing information if

`verbose = TRUE`

.- validClimR
a logical: If

`validClimR = TRUE`

,`validClimR`

will be called to compute validation indices including statistical summary for inter- and intra-cluster correlations. This is computationally expensive. It can also objectively cut the dendrogram tree for`regional`

clustering method, if`k = NULL`

.- rawStats
a logical: should validation indices be computed based on the raw data or PCA-filtered data?

- k
`NULL`

or an integer`k > 1`

for the number of regions/clusters. Only for`regional`

linkage method,`k = NULL`

is supported, where the "optimal" number of regions will be used at a user specified significance level`alpha`

. It is required to specify number of clusters`k`

for the other methods, since they are not based on inter-cluster correlation. If`k = NULL`

for these methods (except`regional`

) linkage, the`validClimR`

with be aborted. One can use`validClimR`

function to compute inter-cluster correlation at different number of clusters to objectively cut the tree for the other methods, which could be computationally expensive to cover the entire merging history for large number of spatial elements.- minSize
minimum cluster size. The

`regional`

linkage method tend to isolate noisy data in small clusters. The`minSize`

can be used to exclude these very small clusters from the`statSum`

statistical summary, because they are most likely noisy data that need to be checked in a quality control step. The analysis may be then repeated.- alpha
confidence level: the default is

`alpha = 0.05`

for 95% confidence level.- plot
logical to call the plotting method if

`plot = TRUE`

.- dendrogram
logical to enable or disable dendrogram plotting.

- colPalette
a color palette or a list of colors such as that generated by

`rainbow`

,`heat.colors`

,`topo.colors`

,`terrain.colors`

or similar functions.- hang
The fraction of the plot height by which labels should hang below the rest of the plot. A negative value will cause the labels to hang down from 0.

- labels
A character vector of labels for the leaves of the tree. By default the row names or row numbers of the original data are used. If

`labels = FALSE`

no labels at all are plotted.- pch
Either an integer specifying a symbol or a single character to be used as the default in plotting points. See

`points`

for possible values.- cex
A numerical value giving the amount by which plotting symbols should be magnified relative to the

`default = 1`

.

## Value

An object of class `HiClimR`

and `hclust`

, which
describes the tree produced by the clustering process.
The object is a list with the following components:

- merge
an \(n-1\) by 2 matrix. Row \(i\) of

`merge`

describes the merging of clusters at step \(i\) of the clustering. If an element \(j\) in the row is negative, then observation \(-j\) was merged at this stage. If \(j\) is positive then the merge was with the cluster formed at the (earlier) stage \(j\) of the algorithm. Thus negative entries in`merge`

indicate agglomerations of singletons, and positive entries indicate agglomerations of non-singletons.- height
a set of \(n-1\) real values (non-decreasing for ultrametric trees). The clustering

*height*: that is, the value of the criterion associated with the clustering`method`

for the particular agglomeration.- order
a vector giving the permutation of the original observations suitable for plotting, in the sense that a cluster plot using this ordering and matrix

`merge`

will not have crossings of the branches.- labels
labels for each of the objects being clustered.

- method
the cluster method that has been used.

- call
the call which produced the result.

- dist.method
the distance that has been used to create

`d`

(only returned if the distance object has a`"method"`

attribute).- skip
a vector of

`lonStep`

and`latStep`

if`coarseR = TRUE`

.- PCA
if

`nPC != NULL`

, the eigenvalues, explained variance, and accumulated variance will be stored here.- coords
an (

`Nc`

rows by`2`

columns) matrix of 'double' values: longitude and latitude coordinates for the preprocessed data used for clustering, where`NC`

is the number of spatial elements to be clustered after coarsening spatial resolution by`lonStep`

and`latStep`

. It will be returned only if`lon`

and`lat`

vectors were defined. It will be similar to the provided`lon`

and`lat`

if`lonStep = 1`

and`latStep = 1`

.- nvars
number of variables used for multivariate clustering (MVC).

- ncols
number of columns for each variable.

- data
the preprocessed data used for clustering will be stored here. If

`rawData = TRUE`

and`nPC != NULL`

, the preprocessed data without filtering (PCA) will be returned here.- mask
a vector of the indices of masked spatial points by both geographic masking and data thresholds.

- treeH
An object of class

`hclust`

, which describes the upper part of the tree reconstructed by the hybrid clustering process if`hybrid = TRUE`

.

If `validClimR = TRUE`

, an object of class `HiClimR`

, which produces
indices for validating the tree produced by the clustering process, will be merged
in the dendrogram tree above. This object is a list with the following components:

- cutLevel
the minimum significant correlation used for objective tree cut together with the corresponding confidence level.

- clustMean
the cluster means which are the region's mean timeseries for all selected regions.

- clustSize
cluster sizes for all selected regions.

- clustFlag
a flag

`0 or 1`

to indicate the cluster used in`statSum`

validation indices (`interCor`

,`intraCor`

,`diffCor`

, and`statSum`

), based on`minSize`

minimum cluster size. If`clustFlag = 0`

, the cluster has been excluded because its size is less than the`minSize`

minimum cluster size. The sum of`clustFlag`

elements represents the selected number clusters.- interCor
inter-cluster correlations for all selected regions. It is the inter-cluster correlations between cluster means. The maximum inter-cluster correlation is a measure for separation or contiguity, and it is used for objective tree cut (to find the "optimal" number of clusters).

- intraCor
intra-cluster correlations for all selected regions. It is the intra-cluster correlations between the mean of each cluster and its members. The average intra-cluster correlation is a weighted average for all clusters, and it is a measure for homogeneity.

- diffCor
difference between intra-cluster correlation and maximum inter-cluster correlation for all selected regions.

- statSum
overall statistical summary for i

`nterCluster`

,`intraCor`

, and`diffCor`

.- region
ordered regions vector of size

`N`

number of spatial elements for the selected number of clusters, after excluding the small clusters defined by`minSize`

argument.- regionID
ordered regions ID vector of length equals the selected number of clusters, after excluding the small clusters defined by

`minSize`

argument. It helps in mapping ordered regions and their actual names before ordering. Only the`region`

component uses ordered ID, while other components use the names used during the clustering process.

There are `print`

, `plot`

and `identify`

(see `identify.hclust`

) methods and

`rect.hclust()`

functions for `hclust`

objects.

## Details

`HiClimR`

function is based on `hclust`

, which now uses an
optimized algorithm to deal with only the upper/lower triangular-half of the symmetric
dissimilarity matrix instead of the old algorithm that uses the full matrix in the
merging steps. It performs a hierarchical cluster analysis using Pearson correlation
distance dissimilarity for the \(N\) objects being clustered. Initially, each object
is assigned to its own cluster and then the algorithm proceeds iteratively, at each
stage joining the two most similar clusters, continuing until there is just a single
cluster. At each stage distances between clusters are recomputed by a dissimilarity
update formula according to the particular clustering method being used.

All clustering methods in `hclust`

are included. The *regional*
linkage method minimizes inter-cluster correlations between cluster means
(see `Badr et al. 2015`

). *Ward's* minimum variance method aims at finding
compact, spherical clusters. The *complete linkage* method finds similar clusters.
The *single linkage* method (which is closely related to the minimal spanning tree)
adopts a ‘friends of friends’ clustering strategy. The other methods can be
regarded as aiming for clusters with characteristics somewhere between the single and
complete link methods. Note however, that methods `"median"`

and `"centroid"`

are *not* leading to a *monotone distance* measure, or equivalently the
resulting dendrograms can have so called *inversions* (which are hard to interpret).

The `regional`

linkage method is explained in the context of a spatiotemporal
problem, in which `N`

spatial elements (e.g., weather stations) are divided
into `k`

regions, given that each element has a time series of length `M`

.
It is based on inter-regional correlation distance between the temporal means of
different regions (or elements at the first merging step). It modifies the update
formulae of `average`

linkage method by incorporating the standard deviation
of the merged region timeseries, which is a function of the correlation between the
individual regions, and their standard deviations before merging. It is equal to the
average of their standard deviations if and only if the correlation between the two
merged regions is `100%`

. In this special case, the `regional`

linkage
method is reduced to the classic `average`

linkage clustering method.

If `members != NULL`

, then `d`

is taken to be a
dissimilarity matrix between clusters instead of dissimilarities
between singletons and `members`

gives the number of observations
per cluster. This way the hierarchical cluster algorithm can be
‘started in the middle of the dendrogram’, e.g., in order to
reconstruct the part of the tree above a cut (see examples).
Dissimilarities between clusters can be efficiently computed (i.e.,
without `hclust`

itself) only for a limited number of
distance/linkage combinations, the simplest one being squared
Euclidean distance and centroid linkage. In this case the
dissimilarities between the clusters are the squared Euclidean
distances between cluster means.

In hierarchical cluster displays, a decision is needed at each merge to
specify which subtree should go on the left and which on the right.
Since, for \(n\) observations there are \(n-1\) merges,
there are \(2^{(n-1)}\) possible orderings for the leaves
in a cluster tree, or dendrogram.
The algorithm used in `hclust`

is to order the subtree so that
the tighter cluster is on the left (the last, i.e., most recent,
merge of the left subtree is at a lower value than the last
merge of the right subtree).
Single observations are the tightest clusters possible,
and merges involving two observations place them in order by their
observation sequence number.

## References

Hamada S. Badr, Zaitchik, B. F. and Dezfuli, A. K. (2015):
A Tool for Hierarchical Climate Regionalization, *Earth Science Informatics*,
**8**(4), 949-958, doi:10.1007/s12145-015-0221-7
.

Hamada S. Badr, Zaitchik, B. F. and Dezfuli, A. K. (2014):
Hierarchical Climate Regionalization,
*Comprehensive R Archive Network (CRAN)*,
https://cran.r-project.org/package=HiClimR.

Wilks, D. S. (2011):
*Statistical methods in the atmospheric sciences*,
Academic press.

Gordon, A. D. (1999):
*Classification*. Second Edition.
London: Chapman and Hall / CRC

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988):
*The New S Language*.
Wadsworth & Brooks/Cole. (S version.)

Murtagh, F. (1985):
“Multidimensional Clustering Algorithms”, in
*COMPSTAT Lectures 4*.
Wuerzburg: Physica-Verlag
(for algorithmic details of algorithms used).

Hartigan, J. A. (1975):
*Clustering Algorithms*.
New York: Wiley.

Everitt, B. (1974):
*Cluster Analysis*.
London: Heinemann Educ. Books.

Anderberg, M. R. (1973):
*Cluster Analysis for Applications*.
Academic Press: New York.

Sneath, P. H. A. and R. R. Sokal (1973):
*Numerical Taxonomy*.
San Francisco: Freeman.

McQuitty, L.L. (1966):
Similarity Analysis by Reciprocal Pairs for Discrete and Continuous Data.
*Educational and Psychological Measurement*, **26**, 825-831.

Source Code: https://github.com/hsbadr/HiClimR

## Author

Hamada S. Badr <badr@jhu.edu>, Benjamin F. Zaitchik <zaitchik@jhu.edu>,
and Amin K. Dezfuli <amin.dezfuli@nasa.gov>. `HiClimR`

is
a modification of `hclust`

function, which is based
on Fortran code contributed to STATLIB by F. Murtagh.

## See also

`HiClimR`

, `HiClimR2nc`

, `validClimR`

, `geogMask`

,
`coarseR`

, `fastCor`

, `grid2D`

,
`minSigCor`

. `identify.hclust`

, `rect.hclust`

,
`cutree`

, `dendrogram`

, and `kmeans`

.

## Examples

```
require(HiClimR)
#----------------------------------------------------------------------------------#
# Typical use of HiClimR for single-variate clustering: #
#----------------------------------------------------------------------------------#
## Load the test data included/loaded in the package (1 degree resolution)
x <- TestCase$x
lon <- TestCase$lon
lat <- TestCase$lat
## Generate/check longitude and latitude mesh vectors for gridded data
xGrid <- grid2D(lon = unique(TestCase$lon), lat = unique(TestCase$lat))
lon <- c(xGrid$lon)
lat <- c(xGrid$lat)
## Single-Variate Hierarchical Climate Regionalization
y <- HiClimR(x, lon = lon, lat = lat, lonStep = 1, latStep = 1, geogMask = FALSE,
continent = "Africa", meanThresh = 10, varThresh = 0, detrend = TRUE,
standardize = TRUE, nPC = NULL, method = "ward", hybrid = FALSE, kH = NULL,
members = NULL, nSplit = 1, upperTri = TRUE, verbose = TRUE,
validClimR = TRUE, k = 12, minSize = 1, alpha = 0.01,
plot = TRUE, colPalette = NULL, hang = -1, labels = FALSE)
#>
#> PROCESSING STARTED
#>
#> Checking Multivariate Clustering (MVC)...
#> ---> x is a matrix
#> ---> single-variate clustering: 1 variable
#> Checking data...
#> ---> Checking dimensions...
#> ---> Checking row names...
#> ---> Checking column names...
#> Data filtering...
#> ---> Computing mean for each row...
#> ---> Checking rows with mean bellow meanThresh...
#> ---> 4678 rows found, mean ≤ 10
#> ---> Computing variance for each row...
#> ---> Checking rows with near-zero-variance...
#> ---> 3951 rows found, variance ≤ 0
#> Data preprocessing...
#> ---> Applying mask...
#> ---> Checking columns with missing values...
#> ---> Removing linear trend...
#> ---> Standardizing data...
#> Agglomerative Hierarchical Clustering...
#> ---> Computing correlation/dissimilarity matrix...
#> ---> Starting clustering process...
#> ---> Constructing dendrogram tree...
#> Calling cluster validation...
#> ---> Computing cluster means...
#> ---> Computing inter-cluster correlations...
#> ---> Computing intra-cluster correlations...
#> ---> Computing summary statistics...
#> Generating region map...
#>
#> PROCESSING COMPLETED
#>
#> Running Time:
#> user system elapsed
#> 0.424 0.028 0.456
#> Time difference of 0.4569378 secs
## For more examples: https://github.com/hsbadr/HiClimR#examples
if (FALSE) {
#----------------------------------------------------------------------------------#
# Additional Examples: #
#----------------------------------------------------------------------------------#
## Use Ward's method
y <- HiClimR(x, lon = lon, lat = lat, lonStep = 1, latStep = 1, geogMask = FALSE,
continent = "Africa", meanThresh = 10, varThresh = 0, detrend = TRUE,
standardize = TRUE, nPC = NULL, method = "ward", hybrid = FALSE, kH = NULL,
members = NULL, nSplit = 1, upperTri = TRUE, verbose = TRUE,
validClimR = TRUE, k = 12, minSize = 1, alpha = 0.01,
plot = TRUE, colPalette = NULL, hang = -1, labels = FALSE)
## Use data splitting for big data
y <- HiClimR(x, lon = lon, lat = lat, lonStep = 1, latStep = 1, geogMask = FALSE,
continent = "Africa", meanThresh = 10, varThresh = 0, detrend = TRUE,
standardize = TRUE, nPC = NULL, method = "ward", hybrid = TRUE, kH = NULL,
members = NULL, nSplit = 10, upperTri = TRUE, verbose = TRUE,
validClimR = TRUE, k = 12, minSize = 1, alpha = 0.01,
plot = TRUE, colPalette = NULL, hang = -1, labels = FALSE)
## Use hybrid Ward-Regional method
y <- HiClimR(x, lon = lon, lat = lat, lonStep = 1, latStep = 1, geogMask = FALSE,
continent = "Africa", meanThresh = 10, varThresh = 0, detrend = TRUE,
standardize = TRUE, nPC = NULL, method = "ward", hybrid = TRUE, kH = NULL,
members = NULL, nSplit = 1, upperTri = TRUE, verbose = TRUE,
validClimR = TRUE, k = 12, minSize = 1, alpha = 0.01,
plot = TRUE, colPalette = NULL, hang = -1, labels = FALSE)
## Check senitivity to kH for the hybrid method above
#----------------------------------------------------------------------------------#
# Typical use of HiClimR for multivariate clustering: #
#----------------------------------------------------------------------------------#
## Load the test data included/loaded in the package (1 degree resolution)
x1 <- TestCase$x
lon <- TestCase$lon
lat <- TestCase$lat
## Generate/check longitude and latitude mesh vectors for gridded data
xGrid <- grid2D(lon = unique(TestCase$lon), lat = unique(TestCase$lat))
lon <- c(xGrid$lon)
lat <- c(xGrid$lat)
## Test if we can replicate single-variate region map with repeated variable
y <- HiClimR(x=list(x1, x1), lon = lon, lat = lat, lonStep = 1, latStep = 1,
geogMask = FALSE, continent = "Africa", meanThresh = list(10, 10),
varThresh = list(0, 0), detrend = list(TRUE, TRUE), standardize = list(TRUE, TRUE),
nPC = NULL, method = "ward", hybrid = FALSE, kH = NULL,
members = NULL, nSplit = 1, upperTri = TRUE, verbose = TRUE,
validClimR = TRUE, k = 12, minSize = 1, alpha = 0.01,
plot = TRUE, colPalette = NULL, hang = -1, labels = FALSE)
## Generate a random matrix with the same number of rows
x2 <- matrix(rnorm(nrow(x1) * 100, mean=0, sd=1), nrow(x1), 100)
## Multivariate Hierarchical Climate Regionalization
y <- HiClimR(x=list(x1, x2), lon = lon, lat = lat, lonStep = 1, latStep = 1,
geogMask = FALSE, continent = "Africa", meanThresh = list(10, NULL),
varThresh = list(0, 0), detrend = list(TRUE, FALSE), standardize = list(TRUE, TRUE),
weightMVC = list(1, 1), nPC = NULL, method = "ward", hybrid = FALSE, kH = NULL,
members = NULL, nSplit = 1, upperTri = TRUE, verbose = TRUE,
validClimR = TRUE, k = 12, minSize = 1, alpha = 0.01,
plot = TRUE, colPalette = NULL, hang = -1, labels = FALSE)
## You can apply all clustering methods and options
#----------------------------------------------------------------------------------#
# Miscellaneous examples to provide more information about functionality and usage #
# of the helper functions that can be used separately or for other applications. #
#----------------------------------------------------------------------------------#
## Load test case data
x <- TestCase$x
## Generate longitude and latitude mesh vectors
xGrid <- grid2D(lon = unique(TestCase$lon), lat = unique(TestCase$lat))
lon <- c(xGrid$lon)
lat <- c(xGrid$lat)
## Coarsening spatial resolution
xc <- coarseR(x = x, lon = lon, lat = lat, lonStep = 2, latStep = 2)
lon <- xc$lon
lat <- xc$lat
x <- xc$x
## Use fastCor function to compute the correlation matrix
t0 <- proc.time(); xcor <- fastCor(t(x)); proc.time() - t0
## compare with cor function
t0 <- proc.time(); xcor0 <- cor(t(x)); proc.time() - t0
## Check the valid options for geographic masking
geogMask()
## geographic mask for Africa
gMask <- geogMask(continent = "Africa", lon = lon, lat = lat, plot = TRUE,
colPalette = NULL)
## Hierarchical Climate Regionalization Without geographic masking
y <- HiClimR(x, lon = lon, lat = lat, lonStep = 1, latStep = 1, geogMask = FALSE,
continent = "Africa", meanThresh = 10, varThresh = 0, detrend = TRUE,
standardize = TRUE, nPC = NULL, method = "ward", hybrid = FALSE, kH = NULL,
members = NULL, nSplit = 1, upperTri = TRUE, verbose = TRUE,
validClimR = TRUE, k = 12, minSize = 1, alpha = 0.01,
plot = TRUE, colPalette = NULL, hang = -1, labels = FALSE)
## With geographic masking (you may specify the mask produced above to save time)
y <- HiClimR(x, lon = lon, lat = lat, lonStep = 1, latStep = 1, geogMask = TRUE,
continent = "Africa", meanThresh = 10, varThresh = 0, detrend = TRUE,
standardize = TRUE, nPC = NULL, method = "ward", hybrid = FALSE, kH = NULL,
members = NULL, nSplit = 1, upperTri = TRUE, verbose = TRUE,
validClimR = TRUE, k = 12, minSize = 1, alpha = 0.01,
plot = TRUE, colPalette = NULL, hang = -1, labels = FALSE)
## With geographic masking and contiguity contraint
## Change contigConst as appropriate
y <- HiClimR(x, lon = lon, lat = lat, lonStep = 1, latStep = 1, geogMask = TRUE,
continent = "Africa", contigConst = 1, meanThresh = 10, varThresh = 0, detrend = TRUE,
standardize = TRUE, nPC = NULL, method = "ward", hybrid = FALSE, kH = NULL,
members = NULL, nSplit = 1, upperTri = TRUE, verbose = TRUE,
validClimR = TRUE, k = 12, minSize = 1, alpha = 0.01,
plot = TRUE, colPalette = NULL, hang = -1, labels = FALSE)
## Find minimum significant correlation at 95
rMin <- minSigCor(n = nrow(x), alpha = 0.05, r = seq(0, 1, by = 1e-06))
## Validtion of Hierarchical Climate Regionalization
z <- validClimR(y, k = 12, minSize = 1, alpha = 0.01,
plot = TRUE, colPalette = NULL)
## Apply minimum cluster size (minSize = 25)
z <- validClimR(y, k = 12, minSize = 25, alpha = 0.01,
plot = TRUE, colPalette = NULL)
## The optimal number of clusters, including small clusters
k <- length(z$clustFlag)
## The selected number of clusters, after excluding small clusters (if minSize > 1)
ks <- sum(z$clustFlag)
## Dendrogram plot
plot(y, hang = -1, labels = FALSE)
## Tree cut
cutTree <- cutree(y, k = k)
table(cutTree)
## Visualization for gridded data
RegionsMap <- matrix(y$region, nrow = length(unique(y$coords[, 1])), byrow = TRUE)
colPalette <- colorRampPalette(c("#00007F", "blue", "#007FFF", "cyan",
"#7FFF7F", "yellow", "#FF7F00", "red", "#7F0000"))
image(unique(y$coords[, 1]), unique(y$coords[, 2]), RegionsMap, col = colPalette(ks))
## Visualization for gridded or ungridded data
plot(y$coords[, 1], y$coords[, 2], col = colPalette(max(Regions, na.rm = TRUE))[y$region],
pch = 15, cex = 1)
## Export region map and mean timeseries into NetCDF-4 file
y.nc <- HiClimR2nc(y=y, ncfile="HiClimR.nc", timeunit="years", dataunit="mm")
## The NetCDF-4 file is still open to add other variables or close it
nc_close(y.nc)
}
```