spatio temporal anisotropy: help with stAni argument

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spatio temporal anisotropy: help with stAni argument

Bruno Sesti
Hi,
I have some problems in understanding the usage of argument 'stAni' of
vgmST and krigeST functions, for.the setting of spatio temporal anisotropy.
How have I to interpret this argument, that is the integer value that I saw
I have to assign to it, what does it means?
How can this argument influence the result of prediction?
Are units of spatial and temporal ranges and lags related to this argument?
How can I study the spatio temporal anisotropy of my data?
Kind regards.

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Re: spatio temporal anisotropy: help with stAni argument

Dr. Benedikt Gräler
Dear Bruno,

stAni relates spatial and temporal distances to each other in the model
for the data set under study. A value of 100 km/day reflects that two
stations 100 km apart have about the same strength of dependence as the
values one day apart at the same location (This is in general only true
for at most one pair of spatial and temporal distances and a 'global'
compromise is sought). The function gstat::estiStAni provides a few
heuristics to estimate the spatio-temporal anisotropy.

When a spatio-temporal vgm including a metric component is fitted, the
stAni parameter is optimized under the objective to find the theoretical
vgm surface that best fits the empirical one.

In krigeST, an additional and approximate stAni parameter can be
provided to ease the (pre-)selection of the most relevant observations
in the space-time cube for the prediction when local kriging is carried
out. Note that the most relevant (i.e. strongest correlated)
observations need not to form a cube, but depend on the actual vgm-model
in use (see also the vignette "Spatio-Temporal Interpolation using
gstat" at [1]).

The unit of stAni depends on the spatial and temporal units of your data
set. Check the units of the empirical variogram to find out which units
R/gstat uses for your data set.

Miss-specifying the stAni parameter will put too large or too small
weights on the observations with a temporal difference resulting in bad
predictions (this also holds vise-versa for spatial distances).

HTH,

  Ben

[1]
https://cran.r-project.org/web/packages/gstat/vignettes/spatio-temporal-kriging.pdf


On 21.05.2018 15:16, Bruno Sesti wrote:

> Hi,
> I have some problems in understanding the usage of argument 'stAni' of
> vgmST and krigeST functions, for.the setting of spatio temporal anisotropy.
> How have I to interpret this argument, that is the integer value that I saw
> I have to assign to it, what does it means?
> How can this argument influence the result of prediction?
> Are units of spatial and temporal ranges and lags related to this argument?
> How can I study the spatio temporal anisotropy of my data?
> Kind regards.
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-Geo mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>

--
Dr. Benedikt Gräler
52°North Initiative for Geospatial Open Source Software GmbH
Martin-Luther-King-Weg 24
48155 Muenster, Germany

E-Mail: [hidden email]
Fon: +49-(0)-251/396371-39
Fax: +49-(0)-251/396371-11

http://52north.org/
Twitter: @FiveTwoN

General Managers: Dr. Albert Remke, Dr. Andreas Wytzisk
Local Court Muenster HRB 10849

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Re: spatio temporal anisotropy: help with stAni argument

Barry Rowlingson
This question has also been posted to gis.stackexchange.com:

https://gis.stackexchange.com/questions/283607/spatio-temporal-anisotropy-in-r-stani-argument-in-vgmst-and-krigest/

and better answers than mine there are welcome...

Barry


On Tue, May 22, 2018 at 8:39 AM, Dr. Benedikt Gräler <[hidden email]>
wrote:

> Dear Bruno,
>
> stAni relates spatial and temporal distances to each other in the model
> for the data set under study. A value of 100 km/day reflects that two
> stations 100 km apart have about the same strength of dependence as the
> values one day apart at the same location (This is in general only true for
> at most one pair of spatial and temporal distances and a 'global'
> compromise is sought). The function gstat::estiStAni provides a few
> heuristics to estimate the spatio-temporal anisotropy.
>
> When a spatio-temporal vgm including a metric component is fitted, the
> stAni parameter is optimized under the objective to find the theoretical
> vgm surface that best fits the empirical one.
>
> In krigeST, an additional and approximate stAni parameter can be provided
> to ease the (pre-)selection of the most relevant observations in the
> space-time cube for the prediction when local kriging is carried out. Note
> that the most relevant (i.e. strongest correlated) observations need not to
> form a cube, but depend on the actual vgm-model in use (see also the
> vignette "Spatio-Temporal Interpolation using gstat" at [1]).
>
> The unit of stAni depends on the spatial and temporal units of your data
> set. Check the units of the empirical variogram to find out which units
> R/gstat uses for your data set.
>
> Miss-specifying the stAni parameter will put too large or too small
> weights on the observations with a temporal difference resulting in bad
> predictions (this also holds vise-versa for spatial distances).
>
> HTH,
>
>  Ben
>
> [1] https://cran.r-project.org/web/packages/gstat/vignettes/spat
> io-temporal-kriging.pdf
>
>
> On 21.05.2018 15:16, Bruno Sesti wrote:
>
>> Hi,
>> I have some problems in understanding the usage of argument 'stAni' of
>> vgmST and krigeST functions, for.the setting of spatio temporal
>> anisotropy.
>> How have I to interpret this argument, that is the integer value that I
>> saw
>> I have to assign to it, what does it means?
>> How can this argument influence the result of prediction?
>> Are units of spatial and temporal ranges and lags related to this
>> argument?
>> How can I study the spatio temporal anisotropy of my data?
>> Kind regards.
>>
>>         [[alternative HTML version deleted]]
>>
>> _______________________________________________
>> R-sig-Geo mailing list
>> [hidden email]
>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>>
>>
> --
> Dr. Benedikt Gräler
> 52°North Initiative for Geospatial Open Source Software GmbH
> Martin-Luther-King-Weg 24
> 48155 Muenster, Germany
>
> E-Mail: [hidden email]
> Fon: +49-(0)-251/396371-39
> Fax: +49-(0)-251/396371-11
>
> http://52north.org/
> Twitter: @FiveTwoN
>
> General Managers: Dr. Albert Remke, Dr. Andreas Wytzisk
> Local Court Muenster HRB 10849
>
> _______________________________________________
> R-sig-Geo mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>

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