## NAME

r.series.decompose - Calculates decomposition of time series X.

## KEYWORDS

raster, statistics, series, decomposition

## SYNOPSIS

r.series.decompose
r.series.decompose --help
r.series.decompose input=string[,string,...] result_prefix=string coef_prefix=string timevar_prefix=string freq=float[,float,...] [--overwrite] [--help] [--verbose] [--quiet] [--ui]

### Flags:

--overwrite
Allow output files to overwrite existing files
--help
Print usage summary
--verbose
Verbose module output
--quiet
Quiet module output
--ui
Force launching GUI dialog

### Parameters:

input=string[,string,...] [required]
Raster names of equally spaced time series.
result_prefix=string [required]
Prefix for raster names of filterd X(t)
coef_prefix=string [required]
Prefix for names of result raster (rasters of coefficients)
timevar_prefix=string [required]
Prefix for names of result raster (rasters of time variables)
freq=float[,float,...] [required]
List of frequencies for sin and cos functions

## DESCRIPTION

r.series.decompose is a module to calculate decomposintion of signal X.
X(t) = B0 + B1*t + B2*sin(B1*t) + B3 * cos(B1*t) + ... + B{n-1}*sin(Bk*t) + Bn * cos(Bk*t) + e

where X is a raster time series, t is time (t in [0, pi]), sin(Fi*t) and cos(Fi*t) are time variables; Fi are user specifed frequencies; e is a error.

The module used r.mregression.series to find the regression coefficients Bi, then it produces the fitted rasters series X(t) using the coefficients.

So the module makes each output cell value a function of the values assigned to the corresponding cells in the time variable raster map series and the rasters of the coefficients.

input Raster names of equally spaced time series X

result_prefix Prefix for raster names of filterd X(t)

coef_prefix Prefix for names of result raster (rasters of coefficients)

timevar_prefix Prefix for names of result raster (rasters of time variables)

freq List of frequencies for sin and cos functions

## NOTES

X must be equally spaced time serie. If the serie isn't equally spaced, insert NULL raster maps into X.

The list of inputs for each cell (including NULLs) is passed to the regression function. The functin compute the parameters over the non-NULL values, producing a NULL result only if there aren't enough non-NULL values for computing. The regression coefficients Bi are stored in raster maps. They can be used for construct more detail time series via the equation:

X(t) = B0 + B1*t + B2*sin(B1*t) + B3 * cos(B1*t) + ... + B{n-1}*sin(Bk*t) + Bn * cos(Bk*t) + e

To do that the user have to create time variables (t, sin(Fi*t) and cos(Fi*t)) at desired time T0 and then use r.mapcalc to produce the X(T0).

The maximum number of raster maps to be processed is limited by the operating system. For example, both the hard and soft limits are typically 1024. The soft limit can be changed with e.g. ulimit -n 1500 (UNIX-based operating systems) but not higher than the hard limit. If it is too low, you can as superuser add an entry in

/etc/security/limits.conf
# <domain>      <type>  <item>         <value>
your_username  hard    nofile          1500
This would raise the hard limit to 1500 file. Be warned that more files open need more RAM.

## EXAMPLES

Suppose we have time series of MODIS NDVI data (from 01 jan to 27 dec):
> g.mlist rast pattern="mod*", separator=','
mod2003_01_01,mod2003_01_09,...,mod2003_12_27

We use one year data, so we suppose the there is a half of sinusoid signal in the data (NDVI values icrease, then decrease usualy). So 01 jan is t0==0, 27 dec is tn==2*pi, there is a frequence 0.5 in the data (and there are more frequencies, for example 1.0 and 1.5).

Decompose the signal:

> maps = \$(g.list rast pattern="mod*", separator=',')
> r.series.decompose input=\$maps coef_prefix="coef." \
timevar_prefix="dec." result_pref="res." \
freq=0.5,1.0,1.5

The command creates rasters of the coefficiens coef.*:

coef.const
coef.time
coef.sin_fr0.5
coef.cos_fr0.5
coef.sin_fr1.0
coef.cos_fr1.0
coef.cos_fr1.5
coef.sin_fr1.5
and rasters of fitted NDVI res.*:
res.mod2003_01_01
res.mod2003_01_09
...

To compute NDVI for 03 jan we need: (1) find time T for 03 jan (2) create time variables for 02 jan.

The length (in days) of the NDVI time series is 362, 03 jan is the third day of the series, so T = 3 * (2*pi/362) radians. But r.mapcalc uses degrees for sin() and cos() functions. So T = 3 * 360/362 degrees.

Create time variables:

r.mapcalc "T = 3.0 * 360.0/362.0"
r.mapcalc "sin0.5 = sin(0.5*3.0*360.0/362.0)"
r.mapcalc "cos0.5 = cos(0.5*3.0*360.0/362.0)"
r.mapcalc "sin1 = sin(3.0*360.0/362.0)"
r.mapcalc "cos1 = cos(3.0*360.0/362.0)"
r.mapcalc "sin1.5 = sin(1.5*3.0*360.0/362.0)"
r.mapcalc "cos1.5 = cos(1.5*3.0*360.0/362.0)"

Create NDVI for 03 jan:

r.mapcals "ndvi03jan = coef.const + coef.time*T +\
coef.sin_fr0.5*sin0.4 + coef.cos_fr0.5*cos0.5 +\
coef.sin_fr1.0*sin1 + coef.cos_fr1.0*cos1 +\
coef.sin_fr1.5*sin1.5 + coef.cos_fr1.5*cos1.5"

r.regression.series, r.series, r.regression.line, g.list,

## AUTHOR

Dmitry Kolesov

Last changed: \$Date: 2015-11-20 15:36:50 +0100 (Fri, 20 Nov 2015) \$

## SOURCE CODE

Available at: r.series.decompose source code (history)

© 2003-2017 GRASS Development Team, GRASS GIS 7.2.3svn Reference Manual