VariogramFunction

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`VariogramFunction`

[Experimental]

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VariogramFunction

is an option to SpatialEstimate that specifies the local variation model to use.

Details

VariogramFunction together with SpatialNoiseLevel is used to make local predictions of spatial values. Combining local predictions with a global trend gives the full spatial prediction function.

The local variation is described using a variogram , where is a spatial field of values. When the spatial field is weakly stationary and isotropic, $gamma(p_1,p_2)=gamma(TemplateBox[{{{p, _, 1}, -, {p, _, 2}}}, Norm])$ . A typical isotropic variogram can be described in terms of its sill, range and noise variance.

For full details, see the EstimatedVariogramModel page.
The following settings can be used:

	Automatic	automatically compute a variogram
	"model"	fit "model" variogram
	{"model",pars}	use "model" with given parameters pars
	VariogramModel[…]	use fully specified variogram model

The possible "model" values are given in VariogramModel.

Examples

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Basic Examples (1)Summary of the most common use cases

Use SpatialEstimate with specified variogram function:

In[1]:=1

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https://wolfram.com/xid/0cpt7ywxvs3kwi-lg8fg6

The data consists of rainfall observations in Switzerland:

In[2]:=2

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https://wolfram.com/xid/0cpt7ywxvs3kwi-lkly80

Out[2]=2

Create spatial predictor function with exponential variogram model:

In[3]:=3

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https://wolfram.com/xid/0cpt7ywxvs3kwi-fq7obh

In[5]:=5

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https://wolfram.com/xid/0cpt7ywxvs3kwi-eg5usm

Out[5]=5

Visualize the estimator values over the observation region:

In[10]:=10

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https://wolfram.com/xid/0cpt7ywxvs3kwi-xw431z

In[16]:=16

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https://wolfram.com/xid/0cpt7ywxvs3kwi-j8183n

Out[16]=16

Scope (1)Survey of the scope of standard use cases

Use SpatialEstimate with fitted variogram function:

In[1]:=1

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https://wolfram.com/xid/0cpt7ywxvs3kwi-4mek18

The data consists of rainfall observations in Switzerland:

In[2]:=2

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https://wolfram.com/xid/0cpt7ywxvs3kwi-iizqrs

Out[2]=2

Fit a cubic variogram model and use it for spatial prediction:

In[3]:=3

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https://wolfram.com/xid/0cpt7ywxvs3kwi-kjzgtw

In[5]:=5

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https://wolfram.com/xid/0cpt7ywxvs3kwi-cope7a

Out[5]=5

In[6]:=6

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https://wolfram.com/xid/0cpt7ywxvs3kwi-fi8ayn

Out[6]=6

Compute the prediction functions with the fitted cubic variogram model:

In[7]:=7

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https://wolfram.com/xid/0cpt7ywxvs3kwi-foxvg

Out[7]=7

In[10]:=10

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https://wolfram.com/xid/0cpt7ywxvs3kwi-f9pp3x

Out[10]=10

Applications (1)Sample problems that can be solved with this function

Specifying VariogramFunction in SpatialEstimate allows you to obtain a gallery of models:

In[1]:=1

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https://wolfram.com/xid/0cpt7ywxvs3kwi-6u8zor

Out[1]=1

Visualize data:

In[2]:=2

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https://wolfram.com/xid/0cpt7ywxvs3kwi-tw74ri

Out[2]=2

Compute estimates using specific models:

In[3]:=3

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https://wolfram.com/xid/0cpt7ywxvs3kwi-6xlag2

In[4]:=4

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https://wolfram.com/xid/0cpt7ywxvs3kwi-t2mtbn

Create a set of random points and compute the estimated values at these locations:

In[5]:=5

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https://wolfram.com/xid/0cpt7ywxvs3kwi-55lkd

Visualize rainfall values over the whole region:

In[7]:=7

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https://wolfram.com/xid/0cpt7ywxvs3kwi-7lp199

Out[7]=7

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