The effects of spatial reference systems on interpolations and accuracy are 
minimal, and lat and long can be used. Please see the following studies for 
details.

Jiang, W., Li, J., 2013. Are Spatial Modelling Methods Sensitive to Spatial 
Reference Systems for Predicting Marine Environmental Variables, 20th 
International Congress on Modelling and Simulation: Adelaide, Australia, pp. 
387-393.
Jiang, W., Li, J., 2014. The effects of spatial reference systems on the 
predictive accuracy of spatial interpolation methods. Record 2014/01. 
Geoscience Australia: Canberra, pp 33. 
http://dx.doi.org/10.11636/Record.2014.001.
Turner, A.J., Li, J., Jiang, W., 2017. Effects of Spatial Reference Systems on 
the Accuracy of Spatial Predictive Modelling along a Latitudinal Gradient, 22nd 
International Congress on Modelling and Simulation: Hobart, Tasmania, 
Australia, pp. 106-112.


-----Original Message-----
From: R-sig-Geo [mailto:r-sig-geo-boun...@r-project.org] On Behalf Of Dominik 
Schneider
Sent: Wednesday, 14 February 2018 3:21 AM
To: Stefano Sofia
Cc: r-sig-geo@r-project.org
Subject: [DKIM] 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> 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$ExtractedElevationValues,
> rain_data,  :
>   Either input_data or new_data is in LongLat, please reproject.
>    input_data:  +init=epsg:4326 +proj=longlat +datum=WGS84 +no_defs
> +ellps=WGS84 +towgs84=0,0,0
>    new_data:    +init=epsg:4326 +proj=longlat +datum=WGS84 +no_defs
> +ellps=WGS84 +towgs84=0,0,0
>
> but I did pay attention to have the same reference system in 
> rain_data, drg and the Digital Elevation Model.
>
> Moreover, if I impose the class of the DEM to SpatialGridDataFrame 
> when I extraxt the elevation points from the DEM I get the following error:
> Error in (function (classes, fdef, mtable)  :
>   unable to find an inherited method for function ‘extract’ for 
> signature ‘"SpatialGridDataFrame", "SpatialPoints"’
> Calls: extract -> <Anonymous>
>
>
> Would you please somebody help to show me where is my mistake?
>
> Thank you for all your attention
> Stefano
>
>          (oo)
> --oOO--( )--OOo----------------
> Stefano Sofia PhD
> Area Meteorologica e  Area nivologica - Centro Funzionale Servizio 
> Protezione Civile - Regione Marche Via del Colle Ameno 5
> 60126 Torrette di Ancona, Ancona
> Uff: 071 806 7743
> E-mail: stefano.so...@regione.marche.it
> ---Oo---------oO----------------
> ________________________________________
> Da: R-sig-Geo [r-sig-geo-boun...@r-project.org] per conto di Daniel 
> Knitter [knit...@geographie.uni-kiel.de]
> Inviato: lunedì 12 febbraio 2018 9.16
> A: r-sig-geo@r-project.org
> Oggetto: Re: [R-sig-Geo]  Interpolating snowfall values on a Digital 
> Elevation Model
>
> ...sorry, I missed one step: you need to extract the elevation values 
> to your points via extract function from the raster package:
>
> YourPoints$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> 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
> > ---Oo---------oO----------------
> >
> > ________________________________
> >
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> --
>
> Dr. Daniel Knitter
> CRC1266 -- Scales of Transformation
> Project A2 "Integrative Modeling of Socio-Environmental Dynamics"
>
> Christian-Albrechts-Universität zu Kiel Department of Geography 
> Physical Geography -- Landscape Ecology and Geoinformation 
> Ludewig-Meyn-Str. 14, room 109 D - 24118 Kiel, Germany
>
> Phone: +49 431 880 2941
> Email: knit...@geographie.uni-kiel.de
>
> ________________________________
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> visionata da persone estranee al destinatario.
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