[R-sig-Geo] Universal Block Kriging covariate definition for krige in gstat

[Tom Gottfried]

Hi all,

Am 13.01.2016 um 15:31 schrieb Edzer Pebesma:
> I think so, when the operations (computing the drift, and block
> averaging) are both linear, it does not matter in which order they are
> carried out: f(g(x)) = g(f(x)).

... which seems to be one of the messages of this paper:

@article{title = {Spatial aggregation and soil process modelling},
volume = {89},
issn = {0016-7061},
number = {1-2},
journal = {Geoderma},
author = {Heuvelink, G B M and Pebesma, E J},
month = apr,
year = {1999},
pages = {47--65}}


>>     On 13/01/16 14:16, Antonio Manuel Moreno Ródenas wrote:
>>     > As far as I know, what block kriging does is to predict point values inside
>>     > the region (which I could specified with the argument sps.args
>>     > discretization), and later average them.

Not really. In case of the prediction of a block, there are no points to
predict at within that block (there could be data points within the
block, but predicting at these is of no point because kriging is exact
in the sense that the prediction at a data point does not deviate from
the actual datum). The calculation of the kriging weights really differs
between point and block kriging. See e.g. the following publication:

@article{title = {Optimal interpolation and isarithmic mapping of soil
properties. {II} {Block} kriging},
	volume = {31},
	issn = {0022-4588},
	number = {2},
	journal = {Journal of Soil Science},
	author = {Burgess, T M and Webster, R},
	year = {1980},
	pages = {333--341},
}

Adding 'debug.level=32' to both calls of `krige' in Edzer's example
illustrates that there is only one occurrence of kriging weights after
the second call, corresponding to only one prediction location (here the
area) in contrast to many prediction locations (on the grid) in the
first call. The grid is even unknown within the second call and thus the
corresponding point predictions are impossible.

Tom

-- 
Tom Gottfried