Calculates the sample variogram from spatio-temporal data.
variogramST(formula, locations, data, ..., tlags = 0:15, cutoff, width = cutoff/15, boundaries = seq(0, cutoff, width), progress = interactive(), pseudo = TRUE, assumeRegular = FALSE, na.omit = FALSE, cores = 1)
The spatio-temporal sample variogram contains besides the fields
gamma the spatio-temporal fields,
avgDist, the first of which indicates the time lag
used, the second and third different spatial lags.
spacelag is the midpoint in the spatial
lag intervals as passed by the parameter
avgDist is the average
distance between the point pairs found in a distance interval over all temporal lags (i.e. the
averages of the values
dist per temporal lag.) To compute variograms for space lag $h$ and
time lag $t$, the pseudo cross variogram $(Z_i(s)-Z_i+t(s+h))^2$ is averaged over all time
lagged observation sets $Z_i$ and $Z_i+t$ available (weighted by the number of pairs involved).
formula, specifying the dependent variable.
A STFDF or STSDF containing the variable; kept for
compatibility reasons with variogram, either
must be provided.
STIDF containing the variable.
any other arguments that will be passed to the underlying
variogram function. In case of using data of type
STIDF, the argument
tunit is recommended (and only used in the case of STIDF) to set the temporal unit of the
twindow can be passed to control the temporal window used for temporal distance calculations. This builds on the property of xts being ordered and only the next
twindow instances are considered. This avoids the need of huge temporal distance matrices. The default uses twice the number as the average difference goes into the temporal cutoff.
integer; time lags to consider or in case
data is of class
STIDF the actual temporal boundaries with time unit given by
tunit otherwise the same unit as
diff on the index of the time slot will generate is assumed.
spatial separation distance up to which point pairs are included in semivariance estimates; as a default, the length of the diagonal of the box spanning the data is divided by three.
the width of subsequent distance intervals into which
data point pairs are grouped for semivariance estimates, by default the
cutoff is divided into 15 equal lags.
numerical vector with distance interval upper boundaries; values should be strictly increasing
logical; if TRUE, show text progress bar
integer; use pseudo cross variogram for computing time-lagged spatial variograms? -1: find out from coordinates -- if they are equal then yes, else no; 0: no; 1: yes.
logical; whether the time series should be assumed regular. The first time step is assumed to be representative for the whole series. Note, that temporal lags are considered by index, and no check is made whether pairs actually have the desired separating distance.
NA values in the spatio-temporal variogram be dropped? In case where complete rows or columns in the variogram consists of
plot might produce a distorted picture.
number of cores to use in parallel
Edzer Pebesma, Benedikt Graeler
Cressie, N.A.C., 1993, Statistics for Spatial Data, Wiley.
Cressie, N., C. Wikle, 2011, Statistics for Spatio-temporal Data, Wiley.
Pebesma, E.J., 2004. Multivariable geostatistics in S: the gstat package. Computers and Geosciences, 30: 683-691.
for variogram models:
to fit a spatio-temporal variogram model to a spatio-temporal sample variogram:
# The following spatio-temporal variogram has been calcualted through # vv = variogram(PM10~1, r5to10, width=20, cutoff = 200, tlags=0:5) # in the vignette "st". data(vv) str(vv) plot(vv)
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