hsbadr / hiclimr

Hierarchical Climate Regionalization

HiClimR

HiClimR: Hierarchical Climate Regionalization

Table of Contents

• HiClimR
  • Introduction
  • Features
  • Implementation
  • Installation
    • From CRAN
    • From GitHub
  • Source
  • License
  • Citation
  • History
  • Examples
    • Single-Variate Clustering
    • Multivariate Clustering
    • Miscellaneous Examples

Introduction

HiClimR is a tool for Hierarchical Climate Regionalization 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 a cluster validation function 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.

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Features

HiClimR adds several features and a new clustering method (called, regional linkage) to hierarchical clustering in R (hclust function in stats library) including:

• data regridding
• coarsening spatial resolution
• geographic masking
  • by continents
  • by regions
  • by countries
• contiguity-constrained clustering
• data filtering by thresholds
  • mean threshold
  • variance threshold
• data preprocessing
  • detrending
  • standardization
  • PCA
• faster correlation function
  • splitting big data matrix
  • computing upper-triangular matrix
  • using optimized BLAS library on 64-Bit machines
    • ATLAS
    • OpenBLAS
    • Intel MKL
• different clustering methods
  • regional linkage or minimum inter-regional correlation
  • ward's minimum variance or error sum of squares method
  • single linkage or nearest neighbor method
  • complete linkage or diameter
  • average linkage, group average, or UPGMA method
  • mcquitty's or WPGMA method
  • median, Gower's or WPGMC method
  • centroid or UPGMC method
• hybrid hierarchical clustering
  • the upper part of the tree is reconstructed above a cut
  • the lower part of the tree uses user-selected method
  • the upper part of the tree uses regional linkage method
• multivariate clustering (MVC)
  • filtering all variables before preprocessing
  • detrending and standardization of each variable
  • applying weight for the preprocessed variables
• cluster validation
  • summary statistics based on raw data or the data reconstructed by PCA
  • objective tree cut using minimum significant correlation between region means
• visualization of regionalization results
• exporting region map and mean timeseries into NetCDF-4

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.

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Implementation

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. The figure below shows a detailed flowchart for the package. Cyan blocks represent helper functions, green is input data or parameters, yellow indicates agglomeration Fortran code, and purple shows graphics options. For multivariate clustering (MVC), the input data is a list of matrices (one matrix for each variable with the same number of rows to be clustered; the number of columns may vary per variable). The blue dashed boxes involve a loop for all variables to apply mean and/or variance thresholds, detrending, and/or standardization per variable before weighing the preprocessed variables and binding them by columns in one matrix for clustering. x is the input N x M data matrix, xc is the coarsened N0 x M data matrix where N0 ≤ N (N0 = N only if lonStep = 1 and latStep = 1), xm is the masked and filtered N1 x M1 data matrix where N1 ≤ N0 (N1 = N0 only if the number of masked stations/points is zero) and M1 ≤ M (M1 = M only if no columns are removed due to missing values), and x1 is the reconstructed N1 x M1 data matrix if PCA is performed.

HiClimR is applicable to any correlation-based clustering.

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Installation

There are many ways to install an R package from precompiled binaries or source code. For more details, you may search for how to install an R package, but here are the most convenient ways to install HiClimR:

From CRAN

This is the easiest way to install an R package on Windows, Mac, or Linux. You just fire up an R shell and type:

install.packages("HiClimR")

In theory the package should just install, however, you may be asked to select your local mirror (i.e. which server should you use to download the package). If you are using R-GUI or R-Studio, you can find a menu for package installation where you can just search for HiClimR and install it.

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From GitHub

This is intended for developers and requires a development environment (compilers, libraries, ... etc) to install the latest development release of HiClimR. On Linux and Mac, you can download the source code and use R CMD INSTALL to install it. In a convenient way, you may use pak as follows:

• Install pak from CRAN:

install.packages("pak")

• Make sure you have a working development environment:

  • Windows: Install Rtools.
  • Mac: Install Xcode from the Mac App Store.
  • Linux: Install a compiler and various development libraries (details vary across different flavors of Linux).

• Install HiClimR from GitHub source:

pak::pkg_install("hsbadr/HiClimR")

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Source

The source code repository can be found on GitHub at hsbadr/HiClimR.

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License

HiClimR is licensed under GPL v3. The code is modified by Hamada S. Badr from src/library/stats/R/hclust.R part of R package Copyright © 1995-2021 The R Core Team.

• This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

• This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

A copy of the GNU General Public License is available at https://www.r-project.org/Licenses.

Copyright © 2013-2021 Earth and Planetary Sciences (EPS), Johns Hopkins University (JHU).

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Citation

To cite HiClimR in publications, please use:

citation("HiClimR")

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

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

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History

Version	Date	Comment	Author	Email
	May 1992	Original	F. Murtagh
	Dec 1996	Modified	Ross Ihaka
	Apr 1998	Modified	F. Leisch
	Jun 2000	Modified	F. Leisch
1.0.0	03/07/14	HiClimR	Hamada S. Badr	[email protected]
1.0.1	03/08/14	Updated	Hamada S. Badr	[email protected]
1.0.2	03/09/14	Updated	Hamada S. Badr	[email protected]
1.0.3	03/12/14	Updated	Hamada S. Badr	[email protected]
1.0.4	03/14/14	Updated	Hamada S. Badr	[email protected]
1.0.5	03/18/14	Updated	Hamada S. Badr	[email protected]
1.0.6	03/25/14	Updated	Hamada S. Badr	[email protected]
1.0.7	03/30/14	Hybrid	Hamada S. Badr	[email protected]
1.0.8	05/06/14	Updated	Hamada S. Badr	[email protected]
1.0.9	05/07/14	CRAN	Hamada S. Badr	[email protected]
1.1.0	05/15/14	Updated	Hamada S. Badr	[email protected]
1.1.1	07/14/14	Updated	Hamada S. Badr	[email protected]
1.1.2	07/26/14	Updated	Hamada S. Badr	[email protected]
1.1.3	08/28/14	Updated	Hamada S. Badr	[email protected]
1.1.4	09/01/14	Updated	Hamada S. Badr	[email protected]
1.1.5	11/12/14	Updated	Hamada S. Badr	[email protected]
1.1.6	03/01/15	GitHub	Hamada S. Badr	[email protected]
1.2.0	03/27/15	MVC	Hamada S. Badr	[email protected]
1.2.1	05/24/15	Updated	Hamada S. Badr	[email protected]
1.2.2	07/21/15	Updated	Hamada S. Badr	[email protected]
1.2.3	08/05/15	Updated	Hamada S. Badr	[email protected]
2.0.0	12/22/18	NOTE	Hamada S. Badr	[email protected]
2.1.0	01/01/19	NetCDF	Hamada S. Badr	[email protected]
2.1.1	01/02/19	Updated	Hamada S. Badr	[email protected]
2.1.2	01/04/19	Updated	Hamada S. Badr	[email protected]
2.1.3	01/10/19	Updated	Hamada S. Badr	[email protected]
2.1.4	01/20/19	Updated	Hamada S. Badr	[email protected]
2.1.5	12/10/19	inherits	Hamada S. Badr	[email protected]
2.1.6	02/22/20	Updated	Hamada S. Badr	[email protected]
2.1.7	11/05/20	Updated	Hamada S. Badr	[email protected]
2.1.8	01/04/21	Updated	Hamada S. Badr	[email protected]

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Examples

Single-Variate Clustering

library(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)

#----------------------------------------------------------------------------------#
# 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 = 5, 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

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Multivariate Clustering

#----------------------------------------------------------------------------------#
# 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

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Miscellaneous Examples

#----------------------------------------------------------------------------------#
# 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 constraint
## 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% confidence level
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(y$region, na.rm = TRUE))[y$region], pch = 15, cex = 1)
## Change pch and cex as appropriate!

## Export region map and mean timeseries into NetCDF-4 file
library(ncdf4)
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)

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hiclimr's Issues

Why is n=1 not allowed?

Hi

Thanks for the package! I was checking it as i wanted to do contiguity-constrained clustering, comparing it with R packages constr.hclust and ClustGeo.

I tried to do a univariate analysis, but this does not seem to be allowed? From which step does this constraint come from, as HiClimR has a lot of different steps involved? I just changed the code internally, changing from stop to warning, and was still able to obtain some output, so I guess the constraint is not at the programming level?

Also, have you considered providing a low-level function doing only the contiguity-constrained clustering step? Personally I would only want this step in my analysis, and a lighter version would be very appreciated!

Thanks!

"mm "not found

Hi, I want to create a regionalization on my data ( year precipitation) and I have this error ; "Error in HiClimR(list10$x, lon = longitud, lat = latid, lonStep = 1, latStep = 1, :
object 'mm' not found " mm object is not found ? I have to have a object named mm ? If affirmative, where I must to write it ?

Memory issue : cannot allocate vector of size

Hi,

I got the following error, I was wondering if you can help me regarding this issue? Is there any way to deal with memory issues and big data?

Best regards,
Mohammad

library(HiClimR)
library(ncdf4)
nc_data <- nc_open('/raid-manaslu/maref/InSAR/S1/QdtFilterSenAT76/geo_timeseries_ramp_demErr_multiply-1_msk.nc')
nc <- ncvar_get(nc_data, "timeseries")
lon <- ncvar_get(nc_data, "longitude")
lat <- ncvar_get(nc_data, "latitude", verbose = F)
t <- ncvar_get(nc_data, "time")
xGrid <- grid2D(lon = unique(lon), lat = unique(lat))
lonn <- c(xGrid$lon)
latt <- c(xGrid$lat)
n <- aperm(nc, c(3,2,1))
x <- t(matrix(n, nrow=dim(n)[1], byrow=FALSE))
y <- HiClimR(x, lon = lonn, lat = latt, lonStep = 1, latStep = 1, geogMask = FALSE, meanThresh = FALSE, varThresh = 0, detrend = FALSE,standardize = TRUE, nPC = NULL, method = "single", hybrid = FALSE, kH = NULL,members=NULL,nSplit = 4,upperTri = TRUE, verbose = TRUE,validClimR = TRUE, k = 12, minSize = 1, alpha = 0.01,plot = TRUE, colPalette = NULL, hang = -1,labels = FALSE)
  

The error

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...
---> 60485454 rows found, mean ≤  FALSE
---> Computing variance for each row...
---> Checking rows with near-zero-variance...
---> 41238667 rows found, variance ≤  0
Data preprocessing...
---> Applying mask...
---> Checking columns with missing values...
---> Standardizing data...
Agglomerative Hierarchical Clustering...
---> Computing correlation/dissimilarity matrix...
Error: cannot allocate vector of size 479897.8 Gb

HiClimR other error

I am still testing HiClimR and after the matrix creation, I used xGrid2D to create lon and lat column appended to x as follow:

lon <- c(xGrid$lon)
lat <- c(xGrid$lat)
x2<-cbind(lon,lat,x1)
print(x2)
lon lat 1961 1962 1963 1964 1965 1966
[1,] -30.25 -5.25 NA NA NA NA NA NA
[2,] -30.25 -4.75 NA NA NA NA NA NA
[3,] -30.25 -4.25 NA NA NA NA NA NA
[4,] -30.25 -3.75 NA NA NA NA NA NA

It looks the column names should not be there? which way to do it? because when I run an example on simple regionalization following the tutorial I got an error:
Error in x - t(fitted(lm(t(x) ~ as.integer(colnames(x))))) :
non-conformable arrays
In addition: Warning message:
In eval(predvars, data, env) : NAs introduced by coercion