You signed in with another tab or window. Reload to refresh your session.You signed out in another tab or window. Reload to refresh your session.You switched accounts on another tab or window. Reload to refresh your session.Dismiss alert
Copy file name to clipboardExpand all lines: vignettes/spatio-temporal-kriging.Rnw
+1-1Lines changed: 1 addition & 1 deletion
Original file line number
Diff line number
Diff line change
@@ -74,7 +74,7 @@ We present new spatio-temporal geostatistical modelling and interpolation capabi
74
74
The collection and processing of spatio-temporal data is rapidly increasing due to technological advances and the societal need for analysis of variables that vary in space and time, such as weather and air quality variables, and crop yields. Analysis of spatial and temporal correlations is useful in itself to get insight into the character and causes of variability, but they are also important to predict values at points from neighbouring observations. Spatio-temporal interpolation can potentially provide more accurate predictions than spatial interpolation because observations taken at other times can be included. In addition, spatio-temporal interpolation allows predictions to be made at single locations or entire fields in between and beyond observation times. However, adding the temporal domain implies that variability in space and time must be modelled, which is more complicated than modelling purely spatial or purely temporal variability. The spatial, temporal and spatio-temporal dependence structures, for instance represented as variograms, do not necessarily coincide with each other in terms of their parameters nor in terms of their family. In the simplest case, a spatio-temporal anisotropy parameter might be enough to deal with the different dependence structures, but this poses strong assumptions on the process.
75
75
76
76
Interpolation of spatial random fields is a common task in geostatistics. Simple approaches like inverse distance weighted predictions or the well known kriging procedures have routinely been applied for many years. Nowadays, modern sensors allow to monitor different variables at an increasing temporal resolution producing rich spatio-temporal data sets.
77
-
This calls as well for theory and methods to deal with these data sets to gain a better understanding of the observed spatio-temporal processes. While the theoretical aspects of spatio-temporal geostatistics show good progress \citep{Cressie2011}, implementations lack behind. This hinders a wide application of spatio-temporal modelling, as typically extensive scripting and thorough understanding is necessary to build spatio-temporal models. Handling of spatio-temporal data in R is provided by the \CRANpkg{spacetime} package \citep{Pebesma2012}. In this paper, we present an extension of the \CRANpkg{gstat} package \citep{Pebesma2004} (version 1.1-3) that reuses the \pkg{spacetime} classes for the estimation of spatio-temporal covariance/variogram models and to perform spatio-temporal interpolation. Our implementation handles various types of spatio-temporal covariance structures and facilitates spatio-temporal interpolation. The notation of functions in \pkg{gstat} are extended in a way closely following the purely spatial design. This allows a researcher acquainted with \pkg{gstat} to readily use spatio-temporal tools. The use of the newly implemented functions is presented and illustrated by mapping spatio-temporal air-quality data. Another package that offers extensive spatio-temporal geostatistical functionality is \CRANpkg{RandomFields} \citep{Schlather2014}; further packages are mentioned in the SpatioTemporal CRAN task view\footnote{\url{https://cran.r-project.org/web/views/SpatioTemporal.html}}.
77
+
This calls as well for theory and methods to deal with these data sets to gain a better understanding of the observed spatio-temporal processes. While the theoretical aspects of spatio-temporal geostatistics show good progress \citep{Cressie2011}, implementations lack behind. This hinders a wide application of spatio-temporal modelling, as typically extensive scripting and thorough understanding is necessary to build spatio-temporal models. Handling of spatio-temporal data in R is provided by the \CRANpkg{spacetime} package \citep{Pebesma2012}. In this paper, we present an extension of the \CRANpkg{gstat} package \citep{Pebesma2004} (version 1.1-3) that reuses the \pkg{spacetime} classes for the estimation of spatio-temporal covariance/variogram models and to perform spatio-temporal interpolation. Our implementation handles various types of spatio-temporal covariance structures and facilitates spatio-temporal interpolation. The notation of functions in \pkg{gstat} are extended in a way closely following the purely spatial design. This allows a researcher acquainted with \pkg{gstat} to readily use spatio-temporal tools. The use of the newly implemented functions is presented and illustrated by mapping spatio-temporal air-quality data. Another package that offers extensive spatio-temporal geostatistical functionality is \CRANpkg{RandomFields} \citep{Schlather2014}; further packages are mentioned in the SpatioTemporal CRAN task view.
78
78
79
79
The paper is organised as follows. The next section introduces the general interpolation routine and describes the different spatio-temporal covariance models, followed by a section introducing the German rural background data set for 2005 and performing the parameter estimation (i.e.\ covariance model fitting). Cross-validation results are presented and discussed in the section thereafter. Conclusions are drawn in the closing section. R scripts reproducing this study are available from within the \pkg{gstat} package as demos. \code{stkrige} re-estimates the variogram models, \code{stkrige-prediction} re-executes the prediction for a time series and a couple of stations, and \code{stkrige-crossvalidation} re-runs the entire leave-one-out cross-validation (note that the latter takes a few hours).
0 commit comments