# Spatio-temporal interpolation in R or ArcGIS?

I'm trying to calculate average rainfall value from a number of points using Inverse Weighted Distance tool in ArcGIS 9.3.

My problem is that: each point has it own time series, therefore the interpolation process should be able to carry out for all years (kind of iteration so to speak).

Following is a sample attribute table:

``````ID X Y Name Rain1990 Rain1991 Rain1992 Rain1993 .... Rain2010

1 xx1 yy1 AA 1210 1189 1863 1269 ......
2 xx2 yy2 BB 1492 1502 2187 1923 ......
......
``````

Could anybody show me how to do that?

Edit 1: I finally did this by using C++ code which required ArcGIS mask grid, data files & locations of all the points.

Edit 2: I recently used R to do this interpolation task. You can use either `hydroTSM`, `gstat` or `spacetime` packages. Few example links below:

http://www.geostat-course.org/Topic_Bivand_2012

• Will this help? Time series Nov 22 '10 at 18:03
• It could be done in R, but I imagine there is a simple way to do it directly in ArcMap. All the OP wants is to iterate through the separate variables (years) and calculate the interpolated raster for each separate variable. The fact that the values in this example are sequential years makes no difference. Nov 22 '10 at 19:17
• Thx for your reply. Actually there's a batch option when right click on IDW tool but still it's a quite tedious job if you have an hourly or daily data. KR
– Tung
Nov 23 '10 at 6:37
• @thecatalyst - If the batch IDW tool does the job then you should post it as an answer. Although it may be tedious, if it is infrequent (as yearly rainfall estimates are infrequent) then there is little reason to search for other solutions. Nov 23 '10 at 14:00
• @Andy: The batch tool would help if you have a limited number but I have hundreds of data which make the idea of using it a little bit unrealistic. I'm still searching for the solution of this problem. KR
– Tung
Nov 26 '10 at 22:25

I solved this by inserting a "Feature Selection" iterator into a model. (In the ModelBuilder Window, under Insert->Iterators menu.)

Use your time field as your "group by" variable. By doing this, the model will iterate once for each time in your feature class.

Then attach your preferred interpolation tool (spline, IDW, whatever) to the feature output from the iterator. Run the model, go on vacation for a few weeks, and when you come back, you will have as many grids as you have time points in the feature class.

Note that this solution assumes you have discrete time sampling points with a date or numeric field that indicates a single time point for each record in your feature set. If you are using the "begin time" and "end time" format, it might not be so straight forward.

• Also, don't forget to use the "%n%" variable in your output file name (or some other way of generating a unique file name), or else you may overwrite you raster every iteration. For more info, see help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//… or just google "Examples of in-line variable substitution with ModelBuilder system variables"
– user2445
Mar 24 '11 at 5:34
• TY. Good to know there's a different way to do it. Cheers!
– Tung
May 5 '14 at 21:46

It seems that this thread is answered by the IDW tool, but if you were to request and input of the start year and then iterate through the year fields using an inline variable in model builder then this would be a more elegant way to handle the modelling.

PS: I agree with @AndyW that if you solved it using the IDW, post as an answer yourself and then "mark with the tick"

Add my own solution using `R` & random precipitation data

``````library(tidyverse)
library(sp) # for coordinates, CRS, proj4string, etc
library(gstat)
library(maptools)

# Coordinates of gridded precipitation cells
precGridPts <- ("ID lat long
1 46.78125 -121.46875
2 46.84375 -121.53125
3 46.84375 -121.46875
4 46.84375 -121.40625
5 46.84375 -121.34375
6 46.90625 -121.53125
7 46.90625 -121.46875
8 46.90625 -121.40625
9 46.90625 -121.34375
10 46.90625 -121.28125
11 46.96875 -121.46875
12 46.96875 -121.40625
13 46.96875 -121.34375
14 46.96875 -121.28125
15 46.96875 -121.21875
16 46.96875 -121.15625
")

``````

Convert to a sp object

``````sp::coordinates(precGridPtsdf) <- ~long + lat # longitude first
``````

Add a spatial reference system (SRS) or coordinate reference system (CRS).

``````# CRS database: http://spatialreference.org/ref/epsg/
sp::proj4string(precGridPtsdf) <- sp::CRS("+proj=longlat +ellps=WGS84 +datum=WGS84")
str(precGridPtsdf)
#> Formal class 'SpatialPointsDataFrame' [package "sp"] with 5 slots
#>   ..@ data       :'data.frame':  16 obs. of  1 variable:
#>   .. ..\$ ID: int [1:16] 1 2 3 4 5 6 7 8 9 10 ...
#>   ..@ coords.nrs : int [1:2] 3 2
#>   ..@ coords     : num [1:16, 1:2] -121 -122 -121 -121 -121 ...
#>   .. ..- attr(*, "dimnames")=List of 2
#>   .. .. ..\$ : chr [1:16] "1" "2" "3" "4" ...
#>   .. .. ..\$ : chr [1:2] "long" "lat"
#>   ..@ bbox       : num [1:2, 1:2] -121.5 46.8 -121.2 47
#>   .. ..- attr(*, "dimnames")=List of 2
#>   .. .. ..\$ : chr [1:2] "long" "lat"
#>   .. .. ..\$ : chr [1:2] "min" "max"
#>   ..@ proj4string:Formal class 'CRS' [package "sp"] with 1 slot
#>   .. .. ..@ projargs: chr "+proj=longlat +ellps=WGS84 +datum=WGS84 +towgs84=0,0,0"
``````

Convert to UTM 10N

``````utm10n <- "+proj=utm +zone=10 ellps=WGS84"
precGridPtsdf_UTM <- spTransform(precGridPtsdf, CRS(utm10n))
``````

Hypothetical annual precipitation data generated using Poisson distribution.

``````precDataTxt <- ("ID PRCP2016 PRCP2017 PRCP2018
1 2125 2099 2203
2 2075 2160 2119
3 2170 2153 2180
4 2130 2118 2153
5 2170 2083 2179
6 2109 2008 2107
7 2109 2189 2093
8 2058 2170 2067
9 2154 2119 2139
10 2056 2184 2120
11 2080 2123 2107
12 2110 2150 2175
13 2176 2105 2126
14 2088 2057 2199
15 2032 2029 2100
16 2133 2108 2006"
)

precData <- read_table2(precDataTxt, col_types = cols(ID = "i"))
``````

Merge Prec data frame with Prec shapefile

``````precGridPtsdf <- merge(precGridPtsdf, precData, by.x = "ID", by.y = "ID")
precdf <- data.frame(precGridPtsdf)
``````

Merge Precipitation data frame with Precipitation shapefile (UTM)

``````precGridPtsdf_UTM <- merge(precGridPtsdf_UTM, precData, by.x = "ID", by.y = "ID")

# sample extent
region_extent <- structure(c(612566.169007975, 5185395.70942594, 639349.654465079,
5205871.0782451), .Dim = c(2L, 2L), .Dimnames = list(c("x", "y"
), c("min", "max")))
``````

Define the extent for spatial interpolation. Make it 4km larger on each direction

``````x.range <- c(region_extent[1] - 4000, region_extent[3] + 4000)
y.range <- c(region_extent[2] - 4000, region_extent[4] + 4000)
``````

Create desired grid at 1km resolution

``````grd <- expand.grid(x = seq(from = x.range[1], to = x.range[2], by = 1000),
y = seq(from = y.range[1], to = y.range[2], by = 1000))

# Convert grid to spatial object
coordinates(grd) <- ~x + y
# Use the same projection as boundary_UTM
proj4string(grd) <- "+proj=utm +zone=10 ellps=WGS84 +ellps=WGS84"
gridded(grd) <- TRUE
``````

Interpolate using Inverse Distance Weighted (IDW)

``````idw <- idw(formula = PRCP2016 ~ 1, locations = precGridPtsdf_UTM, newdata = grd)
#> [inverse distance weighted interpolation]

# Clean up
idw.output = as.data.frame(idw)
names(idw.output)[1:3] <- c("Longitude", "Latitude", "Precipitation")

precdf_UTM <- data.frame(precGridPtsdf_UTM)
``````

Plot interpolation results

``````idwPlt1 <- ggplot() +
geom_tile(data = idw.output, aes(x = Longitude, y = Latitude, fill = Precipitation)) +
geom_point(data = precdf_UTM, aes(x = long, y = lat, size = PRCP2016), shape = 21, colour = "red") +
viridis::scale_fill_viridis() +
scale_size_continuous(name = "") +
theme_bw() +
scale_x_continuous(expand = c(0, 0)) +
scale_y_continuous(expand = c(0, 0)) +
theme(axis.text.y = element_text(angle = 90)) +
theme(axis.title.y = element_text(margin = margin(t = 0, r = 10, b = 0, l = 0)))
idwPlt1
``````

``````### Now looping through every year
list.idw <- colnames(precData)[-1] %>%
set_names() %>%
map(., ~ idw(as.formula(paste(.x, "~ 1")),
locations = precGridPtsdf_UTM, newdata = grd))

#> [inverse distance weighted interpolation]
#> [inverse distance weighted interpolation]
#> [inverse distance weighted interpolation]

idw.output.df = as.data.frame(list.idw) %>% as.tibble()
idw.output.df

#> # A tibble: 1,015 x 12
#>    PRCP2016.x PRCP2016.y PRCP2016.var1.pred PRCP2016.var1.var PRCP2017.x
#>  *      <dbl>      <dbl>              <dbl>             <dbl>      <dbl>
#>  1    608566.   5181396.              2114.                NA    608566.
#>  2    609566.   5181396.              2115.                NA    609566.
#>  3    610566.   5181396.              2116.                NA    610566.
#>  4    611566.   5181396.              2117.                NA    611566.
#>  5    612566.   5181396.              2119.                NA    612566.
#>  6    613566.   5181396.              2121.                NA    613566.
#>  7    614566.   5181396.              2123.                NA    614566.
#>  8    615566.   5181396.              2124.                NA    615566.
#>  9    616566.   5181396.              2125.                NA    616566.
#> 10    617566.   5181396.              2125.                NA    617566.
#> # ... with 1,005 more rows, and 7 more variables: PRCP2017.y <dbl>,
#> #   PRCP2017.var1.pred <dbl>, PRCP2017.var1.var <dbl>, PRCP2018.x <dbl>,
#> #   PRCP2018.y <dbl>, PRCP2018.var1.pred <dbl>, PRCP2018.var1.var <dbl>
``````