Yes, thank you for all your observations.
I realized that I needed projected coordinates, I changed it and now it works.
I will read the suggested papers as soon as I can.

Thank you
Stefano

         (oo)
--oOO--( )--OOo----------------
Stefano Sofia PhD
Area Meteorologica e  Area nivologica - Centro Funzionale
Servizio Protezione Civile - Regione Marche
Via del Colle Ameno 5
60126 Torrette di Ancona, Ancona
Uff: 071 806 7743
E-mail: stefano.so...@regione.marche.it
---Oo---------oO----------------
________________________________
Da: Dominik Schneider [dosc3...@colorado.edu]
Inviato: marted� 13 febbraio 2018 17.21
A: Stefano Sofia
Cc: Daniel Knitter; r-sig-geo@r-project.org
Oggetto: Re: [R-sig-Geo] Interpolating snowfall values on a Digital Elevation 
Model

You can't use a lat/long coordinate system when kriging because the concept of 
distance is ambiguous. Convert all your data a UTM grid like you had in your 
first post and it should work.

Another note, It looks like you are working at 0.01 deg which is on the order 
of 1km resolution so you may find  other covariates such as aspect, slope, and 
wind sheltering/exposure, terrain roughness for estimating snow on the ground 
useful. see some of the earliest papers by Carroll, Cressie, and Elder.

Carroll, S. S., and N. Cressie (1996), A comparison of geostatistical 
methodologies used to estimate snow water equivalent, JAWRA Journal of the 
American Water Resources Association, 32(2), 267�278, 
doi:10.1111/j.1752-1688.1996.tb03450.x.

Carroll, S. S., and N. Cressie (1997), Spatial modeling of snow water 
equivalent using covariances estimated from spatial and geomorphic attributes, 
Journal of Hydrology, 190(1-2), 42�59.

Balk, B., and K. Elder (2000), Combining binary decision tree and 
geostatistical methods to estimate snow distribution in a mountain watershed, 
Water Resources Research, 36(1), 13�26, doi:10.1029/1999WR900251.

Erxleben, J., K. Elder, and R. Davis (2002), Comparison of spatial 
interpolation methods for estimating snow distribution in the Colorado Rocky 
Mountains, Hydrological Processes, 16(18), 3627�3649, doi:10.1002/hyp.1239.

Erickson, T. A., M. W. Williams, and A. Winstral (2005), Persistence of 
topographic controls on the spatial distribution of snow in rugged mountain 
terrain, Colorado, United States, Water Resour. Res., 41(4), W04014, 
doi:10.1029/2003WR002973.


On Tue, Feb 13, 2018 at 3:45 AM, Stefano Sofia 
<stefano.so...@regione.marche.it<mailto:stefano.so...@regione.marche.it>> wrote:
Dear Daniel and list users,
I tried to follow the instructions but I encountered two kinds of errors.
This is a reproducibile code:

---------------------------------------------------------------------------------------------------------------
library(automap)
library(ggplot2)
library(gstat)
library(raster)
library(rasterVis)
library(rgdal)
library(maptools)

## LOADING DEM
ita_DEM <- getData('alt', country='ITA', mask=TRUE)
crs(ita_DEM) <- "+init=epsg:4326 +proj=longlat +datum=WGS84 +no_defs 
+ellps=WGS84 +towgs84=0,0,0"
#ita_DEM <- as(ita_DEM, "SpatialGridDataFrame")
str(ita_DEM)

## LOADING RAINFALL DATA
rain_data <- data.frame(Cumulata=c(11.8, 9.0, 8.0, 36.6, 9.4), 
Long_Cent=c(12.61874, 12.78690, 12.96756, 13.15599, 13.28157), 
Lat_Cent=c(43.79447, 43.85185, 43.76267, 43.03470, 43.08003), 
Altitude=c(112.20, 42.93, 36.14, 747, 465))

stations <- data.frame(rain_data$Long_Cent, rain_data$Lat_Cent)
rain_data <- SpatialPointsDataFrame(stations, rain_data, 
proj4string=CRS("+init=epsg:4326"))
stations <- SpatialPoints(stations, proj4string=CRS("+init=epsg:4326"))

## EXTRACT THE ELEVATION VALUES TO MY POINTS
rain_data$ExtractedElevationValues <- extract(x=ita_DEM, y=stations)

## CREATE GRID FOR KRIGING OUTPUT
minx <-  rain_data@bbox[1,1]
maxx <- rain_data@bbox[1,2]
miny <- rain_data@bbox[2,1]
maxy <- rain_data@bbox[2,2]
pixel <- 0.01
grd <- expand.grid(x=seq(minx, maxx, by=pixel), y=seq(miny, maxy, by=pixel))
coordinates(grd) <- ~x+y
gridded(grd) <- TRUE
proj4string(grd) <- CRS("+init=epsg:4326")

## KRIGING: autoKrige(YourMeasurements ~ YourExtractedElevationValues, 
YourMeasurementLocations, TargetGrid)
OK_snow <- autoKrige(Cumulata ~ rain_data$ExtractedElevationValues, rain_data, 
grd)
-------------------------------------------------------------------------------------------------------------------------------

The error I get is:
Error in autoKrige(Cumulata ~ rain_data$ExtractedElevationValues, rain_data,  :
  Either input_data or new_data is in LongLat, please reproject.
   input_data:  +init=epsg:4326 +proj=longlat +datum=WGS84 +no_defs 
+ellps=WGS84 +towgs84=0,0,0
   new_data:    +init=epsg:4326 +proj=longlat +datum=WGS84 +no_defs 
+ellps=WGS84 +towgs84=0,0,0

but I did pay attention to have the same reference system in rain_data, drg and 
the Digital Elevation Model.

Moreover, if I impose the class of the DEM to SpatialGridDataFrame when I 
extraxt the elevation points from the DEM I get the following error:
Error in (function (classes, fdef, mtable)  :
  unable to find an inherited method for function �extract� for signature 
�"SpatialGridDataFrame", "SpatialPoints"�
Calls: extract -> <Anonymous>


Would you please somebody help to show me where is my mistake?

Thank you for all your attention
Stefano

         (oo)
--oOO--( )--OOo----------------
Stefano Sofia PhD
Area Meteorologica e  Area nivologica - Centro Funzionale
Servizio Protezione Civile - Regione Marche
Via del Colle Ameno 5
60126 Torrette di Ancona, Ancona
Uff: 071 806 7743
E-mail: stefano.so...@regione.marche.it<mailto:stefano.so...@regione.marche.it>
---Oo---------oO----------------
________________________________________
Da: R-sig-Geo 
[r-sig-geo-boun...@r-project.org<mailto:r-sig-geo-boun...@r-project.org>] per 
conto di Daniel Knitter 
[knit...@geographie.uni-kiel.de<mailto:knit...@geographie.uni-kiel.de>]
Inviato: luned� 12 febbraio 2018 9.16
A: r-sig-geo@r-project.org<mailto:r-sig-geo@r-project.org>
Oggetto: Re: [R-sig-Geo]  Interpolating snowfall values on a Digital Elevation 
Model

...sorry, I missed one step: you need to extract the elevation values to your 
points via extract function from the raster package:

YourPoints$YourExtractedElevationValues <- extract(x = DEM, y = YourPoints)

autoKrige(YourMeasurements ~ YourExtractedElevationValues, 
YourMeasurementLocations, TargetGrid)


Sorry for spamming.

Best,
Daniel

On Mon, 12 Feb 2018 08:03:41 +0000
Stefano Sofia 
<stefano.so...@regione.marche.it<mailto:stefano.so...@regione.marche.it>> wrote:

> Dear list users,
> I have to produce rainfall maps. I know how to create a (bi-dimensional) grid 
> and interpolate rainfall values (from automatic rain gauges) on that grid 
> using Kriging:
>
> myinterpolation <- autoKrige(myrainfall_cumulate ~ 1, rain_data_UTM, mygrid)
>
> In reality I am dealing with snowfall values on mountain regions, and in this 
> case altitude is an important factor, the use of a Digital Elevation Model 
> might make the difference.
> Looking in the web I found some important material about accessing elevation 
> data in R with the "elevatr" package (by J.W.Hollister), I am reading it.
> My concern would then be to interpolate snowfall values on a Digital 
> Elevation Model. Did somebody already use R for these kinds of calculations? 
> Could somebody share with me some useful hints?
>
> Thank you for your attention
> Stefano Sofia
>
>
>          (oo)
> --oOO--( )--OOo----------------
> Stefano Sofia PhD
> Area Meteorologica e  Area nivologica - Centro Funzionale
> Servizio Protezione Civile - Regione Marche
> Via del Colle Ameno 5
> 60126 Torrette di Ancona, Ancona
> Uff: 071 806 7743
> E-mail: 
> stefano.so...@regione.marche.it<mailto:stefano.so...@regione.marche.it>
> ---Oo---------oO----------------
>
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