Re: regression-kriging and co-kriging (Edzer Pebesma)

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Re: regression-kriging and co-kriging (Edzer Pebesma)

Emanuele Barca
Dear Edzer,

sorry for bothering you once more but I need to be sure about my R
script.

In summary, i'm comparing the performance of regression-kriging and
collocated co-kriging.

Regression-kriging was based on an unique covariate, the elevation Z.

I use Z as unique ancillary variable in the Co-kriging.

As first attempt, the final raster maps were completely different. It
appeared that it was due

to the fact that the dataset was non-stationary and only
regression-kriging overcomes this issue, while co-kriging not.

But if I pass to universal co-kriging introducing Z as covariate, it
bacomes useless as ancillary variable!

What is my mistake?

emanuele




Il 2019-08-15 12:00 [hidden email] ha scritto:

> Send R-sig-Geo mailing list submissions to
> [hidden email]
>
> To subscribe or unsubscribe via the World Wide Web, visit
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
> or, via email, send a message with subject or body 'help' to
> [hidden email]
>
> You can reach the person managing the list at
> [hidden email]
>
> When replying, please edit your Subject line so it is more specific
> than "Re: Contents of R-sig-Geo digest..."
>
>
> Today's Topics:
>
>    1. Error running codes (Enoch Gyamfi Ampadu)
>    2. Re: regression-kriging and co-kriging (Edzer Pebesma)
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Thu, 15 Aug 2019 06:51:49 +0200
> From: Enoch Gyamfi Ampadu <[hidden email]>
> To: [hidden email]
> Subject: [R-sig-Geo] Error running codes
> Message-ID:
> <[hidden email]>
> Content-Type: text/plain; charset="utf-8"
>
> Dear List,
>
> Please I have been running a certain the codes below to read my image,
> shapeffile to enable me classify for cover with Random forest. I have
> gotten to the point of extracting the raster values and the raster
> information. However I keep getting errors. though I have tried
> different
> combination and other codes like readOGR for importing the training
> polygon. I will be glad if you could be of help as I am new to using R.
>
> #import clip image of study area
>
> TestImg3 <- brick("C:\\Users\\hp\\Desktop\\Data collection\\Nkandla
> Images\\Landsat\\2019\\08052019\\Corrected\\New
> Folder\\Image08052019_Clip.tif")
>
> #Assign name of bands
> names(TestImg3) <- c(paste0("B", 1:7, coll=""), "B9")
> plotRGB(TestImg3, r=4, g=3, b=2, stretch ="lin")
>
> #Import training shapefile
> sample <- shapefile("C:/Users/hp/Desktop/Data collection/Nkandla
> Images/Landsat/2019/08052019/Corrected/Train08052019_2.shp")
>
> responseCol <- "class"
>
> #(I have tried options of changing "class" to "classname" as reflect
> actaul
> name assigned in ArcMap)
>
> # Overlap the sample polygons on the image (combine the class
> information
> with extracted values).
>
> pixels = data.frame(matrix(vector(), nrow = 0, ncol =
> length(names(img)) +
> 1))
> for (i in 1:length(unique(sample[[responseCol]]))){
>   category <- unique(sample[[responseCol]])[i]
>   categorymap <- sample[sample[[responseCol]] == category,]
>   dataSet <- extract(img, categorymap)
>   dataSet <- dataSet[!unlist(lapply(dataSet, is.null))]
>   if(is(sample, "SpatialPointsDataFrame")){
>     dataSet <- cbind(dataSet, class = as.numeric(category))
>     pixeles <- rbind(pixeles, dataSet)
>   }
>   if(is(sample, "SpatialPolygonsDataFrame")){
>     dataSet <- lapply(dataSet, function(x){cbind(x, class =
> as.numeric(rep(category,
>
>  nrow(x))))})
>     df <- do.call("rbind", dataSet)
>     pixels <- rbind(pixeles, df)
>   }
>
> }
>
> THIS IS THE ERROR I GET FROM RUNNING THE ABOVE CODES
>
>> for (i in 1:length(unique(samples[[responseCol]]))){
> +   category <- unique(samples[[responseCol]])[i]
> +   categorymap <- samples[samples[[responseCol]] == category,]
> +   dataSet <- extract(img, categorymap)
> +
> +   if(is(sample, "SpatialPointsDataFrame")){
> +     dataSet <- cbind(dataSet, class = as.numeric(category))
> +     pixeles <- rbind(pixeles, dataSet)
> +   }
> +   if(is(sample, "SpatialPolygonsDataFrame")){
> +     dataSet <- lapply(dataSet, function(x){cbind(x, class =
> as.numeric(rep(category,
> +
>   nrow(x))))})
> +     df <- do.call("rbind", dataSet)
> +     pixels <- rbind(pixeles, df)
> +   }
> +
> + }
> Error in y[i, ] :
>   cannot get a slot ("Polygons") from an object of type "NULL"
>
>
> Please help me out.
> Thank you.
>
> Best regards,
>
> Enoch
>
> --
> *Enoch Gyamfi - Ampadu*
>
> *Geography & Environmental Sciences*
>
> *College of Agriculture, Engineering & Science*
>
> *University of KwaZulu-Natal, Westville Campus*
>
> *Private Bag X54001*
> *Durban, South Africa **– 4000**.*
> *Phone: +27 835 828255*
>
> *email: [hidden email] <[hidden email]>*
>
>
> *skype: enoch.ampadu*
> *The highest evidence of nobility is self-control*.
>
> *A simple act of kindness creates an endless ripple*.
>
> [[alternative HTML version deleted]]
>
>
>
>
> ------------------------------
>
> Message: 2
> Date: Thu, 15 Aug 2019 08:33:59 +0200
> From: Edzer Pebesma <[hidden email]>
> To: [hidden email]
> Subject: Re: [R-sig-Geo] regression-kriging and co-kriging
> Message-ID: <[hidden email]>
> Content-Type: text/plain; charset="utf-8"
>
>
>
> On 8/12/19 8:21 PM, Emanuele Barca wrote:
>> Dear Edzer,
>>
>> maybe I found the solution. I found this in the predict function help:
>> "When a non-stationary (i.e., non-constant) mean is used, both for
>> simulation and prediction purposes the variogram model defined should
>> be
>> that of the residual process, and not that of the raw observations"
>> Since my data were, actually, non-stationary, I applied the universal
>> co-kriging instead usual co-kriging.
>> now the maps of regression-kring and co-kriging are actually similar s
>> expected.
>> did I understand correctly the quoted sentence?
>
> I think so, but hard to be sure given the information you provide.
>
>>
>> regards
>>
>> emanuele barca
>> ------------------------------
>>>
>>> Message: 2
>>> Date: Sat, 10 Aug 2019 10:41:38 +0200
>>> From: Edzer Pebesma <[hidden email]>
>>> To: [hidden email]
>>> Subject: Re: [R-sig-Geo] regression-kriging and co-kriging
>>> Message-ID: <[hidden email]>
>>> Content-Type: text/plain; charset="utf-8"
>>>
>>> Hard to tell from your script. Maybe give a reproducible example?
>>>
>>> On 8/6/19 1:07 PM, Emanuele Barca wrote:
>>>> Dear  r-sig-geo friends,
>>>>
>>>> I produced two maps garnered in the following way:
>>>>
>>>> # for regression-kriging
>>>> Piezo.map <-autoKrige(LivStat ~  Z, input_data = mydata.sp, new_data
>>>> = covariates,  model = "Ste")
>>>>
>>>> Piezork.pred <- Piezo.map$krige_output$var1.pred
>>>> Piezork.coords <- Piezo.map$krige_output@coords
>>>> Piezork.out <- as.data.frame(cbind(Piezork.coords, Piezork.pred))
>>>> colnames(Piezork.out)[1:2] <- c("X", "Y")
>>>> coordinates(Piezork.out) = ~ X + Y
>>>> gridded(Piezork.out) <- TRUE
>>>>
>>>> spplot(Piezork.out, main = list(label = "R-k Hydraulic head", cex =
>>>> 1.5))
>>>>
>>>> #for co-kriging
>>>> g <- gstat(id = "Piezo", formula = LivStat ~ 1, data = mydata.sp,
>>>> set
>>>> = list(nocheck = 1))
>>>> g <- gstat(g, id = "Z", formula = Z ~ 1, data = mydata.sp, set =
>>>> list(nocheck = 1))
>>>>
>>>> v.g <- variogram(g)
>>>>
>>>> #g <- gstat(g, id = "Piezo", model = vgm(150, "Mat", 1350, 0.0,
>>>> kappa
>>>> = 1.9), fill.all = T)#
>>>> g <- gstat(g, id = "Piezo", model = vgm(0.7, "Ste", 1300, 18, kappa
>>>> =
>>>> 1.9), fill.all = T)#
>>>> g.fit <- fit.lmc(v.g, g, fit.lmc = TRUE, correct.diagonal = 1.01) #
>>>> fit multivariable variogram model , fit.lmc = TRUE, correct.diagonal
>>>> = 1.01
>>>> g.fit
>>>> plot(v.g, model = g.fit, main = "Fitted Variogram Models - Raw
>>>> Data")#
>>>> #gridded(covariates) <- TRUE
>>>> g.cok <- predict(g.fit, newdata = covariates)#grid
>>>>
>>>> g.cok.pred <- g.cok@data$Piezo.pred
>>>> aaaa <- na.omit(g.cok.pred)
>>>> g.cok.coords <- g.cok@coords
>>>> g.cok.out <- as.data.frame(cbind(g.cok.coords, g.cok.pred))
>>>> colnames(g.cok.out)[1:2] <- c("X", "Y")
>>>> coordinates(g.cok.out) = ~ X + Y
>>>> gridded(g.cok.out) <- TRUE
>>>> spplot(g.cok.out, main = list(label = "Hydraulic head with
>>>> Co-kriging", cex = 1.5))
>>>>
>>>> ###########################################################################################################################
>>>>
>>>>
>>>> I am unable to understand why the first map appears as a raster and
>>>> the second not, notwithstanding the fact that they are both computed
>>>> on the same "covariates" DEM???
>>>>
>>>> where is the mistake???
>>>>
>>>> regards
>>>>
>>>> emanuele
>>>>
>>>> ________________________________________________________
>>>> Emanuele Barca                               Researcher
>>>> Water Research Institute                       (IRSA-CNR)
>>>> Via De Blasio, 5                       70123 Bari (Italy)
>>>> Phone +39 080 5820535               Fax  +39 080 5313365
>>>> Mobile +39 340 3420689
>>>> _________________________________________________________
>>>>
>>>>
>>>>
>>>> ---
>>>> Questa e-mail è stata controllata per individuare virus con Avast
>>>> antivirus.
>>>> https://www.avast.com/antivirus
>>>>
>>>>     [[alternative HTML version deleted]]
>>>>
>>>> _______________________________________________
>>>> R-sig-Geo mailing list
>>>> [hidden email]
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>>>>
>>>
>>> --
>>> Edzer Pebesma
>>> Institute for Geoinformatics
>>> Heisenbergstrasse 2, 48151 Muenster, Germany
>>> Phone: +49 251 8333081
>>>
>>> -------------- next part --------------
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>>> <https://stat.ethz.ch/pipermail/r-sig-geo/attachments/20190810/b5cb9d77/attachment-0001.bin>
>>>
>>>
>>>
>>> ------------------------------
>>>
>>> Subject: Digest Footer
>>>
>>> _______________________________________________
>>> R-sig-Geo mailing list
>>> [hidden email]
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>>>
>>>
>>> ------------------------------
>>>
>>> End of R-sig-Geo Digest, Vol 192, Issue 7
>>> *****************************************
>>
>> _______________________________________________
>> R-sig-Geo mailing list
>> [hidden email]
>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>
> --
> Edzer Pebesma
> Institute for Geoinformatics
> Heisenbergstrasse 2, 48151 Muenster, Germany
> Phone: +49 251 8333081
>
> -------------- next part --------------
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>
>
> ------------------------------
>
> Subject: Digest Footer
>
> _______________________________________________
> R-sig-Geo mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>
>
> ------------------------------
>
> End of R-sig-Geo Digest, Vol 192, Issue 12
> ******************************************

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Re: regression-kriging and co-kriging (Edzer Pebesma)

edzer


On 8/15/19 12:31 PM, Emanuele Barca wrote:

> Dear Edzer,
>
> sorry for bothering you once more but I need to be sure about my R script.
>
> In summary, i'm comparing the performance of regression-kriging and
> collocated co-kriging.
>
> Regression-kriging was based on an unique covariate, the elevation Z.
>
> I use Z as unique ancillary variable in the Co-kriging.
>
> As first attempt, the final raster maps were completely different. It
> appeared that it was due
>
> to the fact that the dataset was non-stationary and only
> regression-kriging overcomes this issue, while co-kriging not.
>
> But if I pass to universal co-kriging introducing Z as covariate, it
> bacomes useless as ancillary variable!
>
> What is my mistake?
You assume that someone else can be sure about your analysis by looking
at your R script without having access to your data.

And you are starting a personal dialogue on a list, essentially
uninviting everyone else to get involved.

>
> emanuele
>
>
>
>
> Il 2019-08-15 12:00 [hidden email] ha scritto:
>> Send R-sig-Geo mailing list submissions to
>>     [hidden email]
>>
>> To subscribe or unsubscribe via the World Wide Web, visit
>>     https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>> or, via email, send a message with subject or body 'help' to
>>     [hidden email]
>>
>> You can reach the person managing the list at
>>     [hidden email]
>>
>> When replying, please edit your Subject line so it is more specific
>> than "Re: Contents of R-sig-Geo digest..."
>>
>>
>> Today's Topics:
>>
>>    1. Error running codes (Enoch Gyamfi Ampadu)
>>    2. Re: regression-kriging and co-kriging (Edzer Pebesma)
>>
>> ----------------------------------------------------------------------
>>
>> Message: 1
>> Date: Thu, 15 Aug 2019 06:51:49 +0200
>> From: Enoch Gyamfi Ampadu <[hidden email]>
>> To: [hidden email]
>> Subject: [R-sig-Geo] Error running codes
>> Message-ID:
>>     <[hidden email]>
>> Content-Type: text/plain; charset="utf-8"
>>
>> Dear List,
>>
>> Please I have been running a certain the codes below to read my image,
>> shapeffile to enable me classify for cover with Random forest. I have
>> gotten to the point of extracting the raster values and the raster
>> information. However I keep getting errors. though I have tried different
>> combination and other codes like readOGR for importing the training
>> polygon. I will be glad if you could be of help as I am new to using R.
>>
>> #import clip image of study area
>>
>> TestImg3 <- brick("C:\\Users\\hp\\Desktop\\Data collection\\Nkandla
>> Images\\Landsat\\2019\\08052019\\Corrected\\New
>> Folder\\Image08052019_Clip.tif")
>>
>> #Assign name of bands
>> names(TestImg3) <- c(paste0("B", 1:7, coll=""), "B9")
>> plotRGB(TestImg3, r=4, g=3, b=2, stretch ="lin")
>>
>> #Import training shapefile
>> sample <- shapefile("C:/Users/hp/Desktop/Data collection/Nkandla
>> Images/Landsat/2019/08052019/Corrected/Train08052019_2.shp")
>>
>> responseCol <- "class"
>>
>> #(I have tried options of changing "class" to "classname" as reflect
>> actaul
>> name assigned in ArcMap)
>>
>> # Overlap the sample polygons on the image (combine the class information
>> with extracted values).
>>
>> pixels = data.frame(matrix(vector(), nrow = 0, ncol =
>> length(names(img)) +
>> 1))
>> for (i in 1:length(unique(sample[[responseCol]]))){
>>   category <- unique(sample[[responseCol]])[i]
>>   categorymap <- sample[sample[[responseCol]] == category,]
>>   dataSet <- extract(img, categorymap)
>>   dataSet <- dataSet[!unlist(lapply(dataSet, is.null))]
>>   if(is(sample, "SpatialPointsDataFrame")){
>>     dataSet <- cbind(dataSet, class = as.numeric(category))
>>     pixeles <- rbind(pixeles, dataSet)
>>   }
>>   if(is(sample, "SpatialPolygonsDataFrame")){
>>     dataSet <- lapply(dataSet, function(x){cbind(x, class =
>> as.numeric(rep(category,
>>
>>  nrow(x))))})
>>     df <- do.call("rbind", dataSet)
>>     pixels <- rbind(pixeles, df)
>>   }
>>
>> }
>>
>> THIS IS THE ERROR I GET FROM RUNNING THE ABOVE CODES
>>
>>> for (i in 1:length(unique(samples[[responseCol]]))){
>> +   category <- unique(samples[[responseCol]])[i]
>> +   categorymap <- samples[samples[[responseCol]] == category,]
>> +   dataSet <- extract(img, categorymap)
>> +
>> +   if(is(sample, "SpatialPointsDataFrame")){
>> +     dataSet <- cbind(dataSet, class = as.numeric(category))
>> +     pixeles <- rbind(pixeles, dataSet)
>> +   }
>> +   if(is(sample, "SpatialPolygonsDataFrame")){
>> +     dataSet <- lapply(dataSet, function(x){cbind(x, class =
>> as.numeric(rep(category,
>> +
>>   nrow(x))))})
>> +     df <- do.call("rbind", dataSet)
>> +     pixels <- rbind(pixeles, df)
>> +   }
>> +
>> + }
>> Error in y[i, ] :
>>   cannot get a slot ("Polygons") from an object of type "NULL"
>>
>>
>> Please help me out.
>> Thank you.
>>
>> Best regards,
>>
>> Enoch
>>
>> --
>> *Enoch Gyamfi - Ampadu*
>>
>> *Geography & Environmental Sciences*
>>
>> *College of Agriculture, Engineering & Science*
>>
>> *University of KwaZulu-Natal, Westville Campus*
>>
>> *Private Bag X54001*
>> *Durban, South Africa **– 4000**.*
>> *Phone: +27 835 828255*
>>
>> *email: [hidden email] <[hidden email]>*
>>
>>
>> *skype: enoch.ampadu*
>> *The highest evidence of nobility is self-control*.
>>
>> *A simple act of kindness creates an endless ripple*.
>>
>>     [[alternative HTML version deleted]]
>>
>>
>>
>>
>> ------------------------------
>>
>> Message: 2
>> Date: Thu, 15 Aug 2019 08:33:59 +0200
>> From: Edzer Pebesma <[hidden email]>
>> To: [hidden email]
>> Subject: Re: [R-sig-Geo] regression-kriging and co-kriging
>> Message-ID: <[hidden email]>
>> Content-Type: text/plain; charset="utf-8"
>>
>>
>>
>> On 8/12/19 8:21 PM, Emanuele Barca wrote:
>>> Dear Edzer,
>>>
>>> maybe I found the solution. I found this in the predict function help:
>>> "When a non-stationary (i.e., non-constant) mean is used, both for
>>> simulation and prediction purposes the variogram model defined should be
>>> that of the residual process, and not that of the raw observations"
>>> Since my data were, actually, non-stationary, I applied the universal
>>> co-kriging instead usual co-kriging.
>>> now the maps of regression-kring and co-kriging are actually similar s
>>> expected.
>>> did I understand correctly the quoted sentence?
>>
>> I think so, but hard to be sure given the information you provide.
>>
>>>
>>> regards
>>>
>>> emanuele barca
>>> ------------------------------
>>>>
>>>> Message: 2
>>>> Date: Sat, 10 Aug 2019 10:41:38 +0200
>>>> From: Edzer Pebesma <[hidden email]>
>>>> To: [hidden email]
>>>> Subject: Re: [R-sig-Geo] regression-kriging and co-kriging
>>>> Message-ID: <[hidden email]>
>>>> Content-Type: text/plain; charset="utf-8"
>>>>
>>>> Hard to tell from your script. Maybe give a reproducible example?
>>>>
>>>> On 8/6/19 1:07 PM, Emanuele Barca wrote:
>>>>> Dear  r-sig-geo friends,
>>>>>
>>>>> I produced two maps garnered in the following way:
>>>>>
>>>>> # for regression-kriging
>>>>> Piezo.map <-autoKrige(LivStat ~  Z, input_data = mydata.sp, new_data
>>>>> = covariates,  model = "Ste")
>>>>>
>>>>> Piezork.pred <- Piezo.map$krige_output$var1.pred
>>>>> Piezork.coords <- Piezo.map$krige_output@coords
>>>>> Piezork.out <- as.data.frame(cbind(Piezork.coords, Piezork.pred))
>>>>> colnames(Piezork.out)[1:2] <- c("X", "Y")
>>>>> coordinates(Piezork.out) = ~ X + Y
>>>>> gridded(Piezork.out) <- TRUE
>>>>>
>>>>> spplot(Piezork.out, main = list(label = "R-k Hydraulic head", cex =
>>>>> 1.5))
>>>>>
>>>>> #for co-kriging
>>>>> g <- gstat(id = "Piezo", formula = LivStat ~ 1, data = mydata.sp, set
>>>>> = list(nocheck = 1))
>>>>> g <- gstat(g, id = "Z", formula = Z ~ 1, data = mydata.sp, set =
>>>>> list(nocheck = 1))
>>>>>
>>>>> v.g <- variogram(g)
>>>>>
>>>>> #g <- gstat(g, id = "Piezo", model = vgm(150, "Mat", 1350, 0.0, kappa
>>>>> = 1.9), fill.all = T)#
>>>>> g <- gstat(g, id = "Piezo", model = vgm(0.7, "Ste", 1300, 18, kappa =
>>>>> 1.9), fill.all = T)#
>>>>> g.fit <- fit.lmc(v.g, g, fit.lmc = TRUE, correct.diagonal = 1.01) #
>>>>> fit multivariable variogram model , fit.lmc = TRUE, correct.diagonal
>>>>> = 1.01
>>>>> g.fit
>>>>> plot(v.g, model = g.fit, main = "Fitted Variogram Models - Raw Data")#
>>>>> #gridded(covariates) <- TRUE
>>>>> g.cok <- predict(g.fit, newdata = covariates)#grid
>>>>>
>>>>> g.cok.pred <- g.cok@data$Piezo.pred
>>>>> aaaa <- na.omit(g.cok.pred)
>>>>> g.cok.coords <- g.cok@coords
>>>>> g.cok.out <- as.data.frame(cbind(g.cok.coords, g.cok.pred))
>>>>> colnames(g.cok.out)[1:2] <- c("X", "Y")
>>>>> coordinates(g.cok.out) = ~ X + Y
>>>>> gridded(g.cok.out) <- TRUE
>>>>> spplot(g.cok.out, main = list(label = "Hydraulic head with
>>>>> Co-kriging", cex = 1.5))
>>>>>
>>>>> ###########################################################################################################################
>>>>>
>>>>>
>>>>>
>>>>> I am unable to understand why the first map appears as a raster and
>>>>> the second not, notwithstanding the fact that they are both computed
>>>>> on the same "covariates" DEM???
>>>>>
>>>>> where is the mistake???
>>>>>
>>>>> regards
>>>>>
>>>>> emanuele
>>>>>
>>>>> ________________________________________________________
>>>>> Emanuele Barca                               Researcher
>>>>> Water Research Institute                       (IRSA-CNR)
>>>>> Via De Blasio, 5                       70123 Bari (Italy)
>>>>> Phone +39 080 5820535               Fax  +39 080 5313365
>>>>> Mobile +39 340 3420689
>>>>> _________________________________________________________
>>>>>
>>>>>
>>>>>
>>>>> ---
>>>>> Questa e-mail è stata controllata per individuare virus con Avast
>>>>> antivirus.
>>>>> https://www.avast.com/antivirus
>>>>>
>>>>>     [[alternative HTML version deleted]]
>>>>>
>>>>> _______________________________________________
>>>>> R-sig-Geo mailing list
>>>>> [hidden email]
>>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>>>>>
>>>>
>>>> --
>>>> Edzer Pebesma
>>>> Institute for Geoinformatics
>>>> Heisenbergstrasse 2, 48151 Muenster, Germany
>>>> Phone: +49 251 8333081
>>>>
>>>> -------------- next part --------------
>>>> A non-text attachment was scrubbed...
>>>> Name: pEpkey.asc
>>>> Type: application/pgp-keys
>>>> Size: 2472 bytes
>>>> Desc: not available
>>>> URL:
>>>> <https://stat.ethz.ch/pipermail/r-sig-geo/attachments/20190810/b5cb9d77/attachment-0001.bin>
>>>>
>>>>
>>>>
>>>>
>>>> ------------------------------
>>>>
>>>> Subject: Digest Footer
>>>>
>>>> _______________________________________________
>>>> R-sig-Geo mailing list
>>>> [hidden email]
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>>>>
>>>>
>>>> ------------------------------
>>>>
>>>> End of R-sig-Geo Digest, Vol 192, Issue 7
>>>> *****************************************
>>>
>>> _______________________________________________
>>> R-sig-Geo mailing list
>>> [hidden email]
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>> --
>> Edzer Pebesma
>> Institute for Geoinformatics
>> Heisenbergstrasse 2, 48151 Muenster, Germany
>> Phone: +49 251 8333081
>>
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>> End of R-sig-Geo Digest, Vol 192, Issue 12
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--
Edzer Pebesma
Institute for Geoinformatics
Heisenbergstrasse 2, 48151 Muenster, Germany
Phone: +49 251 8333081

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