gDist | R Documentation |

Calculate geostatistical distances (Ghosh-distances) between areas

```
## S3 method for class 'rtop'
gDist(object, params = list(), ...)
## S3 method for class 'SpatialPolygonsDataFrame'
gDist(object, object2 = NULL, ...)
## S3 method for class 'SpatialPolygons'
gDist(object, object2 = NULL, ...)
## S3 method for class 'list'
gDist(object, object2 = NULL, diag = FALSE, debug.level = 0, ...)
```

`object` |
object of class |

`params` |
a set of parameters, used to modify the default parameters for
the |

`object2` |
an object of same type as |

`diag` |
logical; if TRUE only calculate the geostatistical distances between each element and itself, only when the objects are lists of discretized areas and object2 = object or object2 = NULL |

`debug.level` |
debug.level = 0 will suppress output from the call to varMat, done for calculation of the geostatistical distances |

`...` |
other parameters, for |

If called with one list of discretized elements, a matrix with the geostatistical distances
between the elements within the list. If called with two lists of discretized elements,
a matrix with the geostatistical distances between the elements in the two lists.
If called with `diag = TRUE`

, the function returns an array of the geostatistical
distance within each of the elements in the list.

If called with one `SpatialPolygons`

or `SpatialPolygonsDataFrame`

or the function returns a list with one matrix with geostatistical distances between
the elements of the object. If called with two objects, the list will also containt
a matrix of the geostatistical distances between the elements of the two objects, and an array
of the geostatistical distances within the elements of the second object.

If called with an rtop-object, the function will return the object, amended with the list above.

The geostatistical distance can be seen as the average distance between points in two elements, or the average distance within points in a single element. The distance measure is also sometimes referred to as Ghosh-distance, from Ghosh (1951) who found analytical expressions for these distances between blocks with regular geometry.

The use of geostatistical distances within `rtop`

is based on an idea
from Gottschalk (1993), who suggested
to replace the traditional regularization of variograms within block-kriging
(as done in the original top-kriging application of Skoien et al (2006))
with covariances of the geostatistical distance. The covariance between two
areas can then be found as `C(a1,a2) = cov(gd)`

where `gd`

is the geostatistical
distance between the two areas `a1`

and `a2`

, instead of an integration
of the covariance function between the two areas.

`rtop`

is based on semivariograms
instead of covariances, and the semivariogram value between the two areas
can be found as `gamma(a1,a2) = g(gd) - 0.5 (g(gd1) + g(gd2))`

where
`g`

is a semivariogram valid for point support, `gd1)`

and `gd2`

are the geostatistical distances within each of the two areas.

Jon Olav Skoien

Ghosh, B. 1951. Random distances within a rectangle and between two rectangles. Bull. Calcutta Math. Soc., 43, 17-24.

Gottschalk, L. 1993. Correlation and covariance of runoff. Stochastic Hydrology and Hydraulics, 7, 85-101.

Skoien, J. O., R. Merz, and G. Bloschl. 2006. Top-kriging - geostatistics on stream networks. Hydrology and Earth System Sciences, 10, 277-287.

Skoien, J. O., Bloschl, G., Laaha, G., Pebesma, E., Parajka, J., Viglione, A., 2014. Rtop: An R package for interpolation of data with a variable spatial support, with an example from river networks. Computers & Geosciences, 67.

```
rpath = system.file("extdata",package="rtop")
library(sf)
observations = st_read(rpath, "observations")
gDist = gDist(observations)
```

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