Note: This addon document is for an older version of GRASS GIS that will be discontinued soon. You should upgrade your GRASS GIS installation, and read the current addon manual page.
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
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
> 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_fr1.5and 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"
Available at: r.series.decompose source code (history)
Latest change: Mon Jun 28 07:54:09 2021 in commit: 1cfc0af029a35a5d6c7dae5ca7204d0eb85dbc55
Note: This addon document is for an older version of GRASS GIS that will be discontinued soon. You should upgrade your GRASS GIS installation, and read the current addon manual page.
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© 2003-2023 GRASS Development Team, GRASS GIS 7.8.8dev Reference Manual