Cultural & Geographic Distance
Modelling Spheres of Intercation
Oliver Nakoinz, Daniel Knitter
MOSAIC Summer School 2016
Cultural & Geographic Distance
Cultural Distance
- Theory
- Practice
- Distance diagramms
Geographic Distance
- Geographic Space
- Calculating Distance
Cultural Distances
- Introduction
- Cultural distances: Theory
- Cultural distances: Practice
- Distance diagramms: Theory
- Distance diagramms: Practice
Cultural distances
Cultural distances
Imports vs cultural distances
- connectinga site to a provenience region
- individual interactions can be traced
Cultural distance
- interactions are producing cultural similarities
- difference in material culture
- statistical level of interaction between sites or regions
Cultural distances
traditional „Culture“ in Archaeology
Archaeological culture = spatial and temporal limited entity of material culture
Cultures can correspond with:
- language
- people
- race
- collective identity
- more...
Cultural distances | Components of cultural theory
- What is culture?
- Hansen, Tylor
- Why using culture?
- B. Malinowski, A. Schweitzer
- How does culture work?
- T. Parsons, A. Kroeber, R.Dawkins
- How are cultures connected?
- F. Steger
- How do cultures evolve?
- O. Spengler, R. Redfield, R. Linton u. M. Herskovits
- Which components have cultures?
- J. Huxley
What is wrong with the traditional approaches?
Cultural distances | Culture
Culture covers standardisations which
are valid in collectives.
(Hansen 2003, 39)
- Formal and abstract definition which covers most other
- Spatial archaeological cultures as special case
- Applicable in archaeology
Cultural distances
| Structures | Traditional arch. culture | Current arch. culture |
|---|---|---|
| Actors | historical actor | cultures can not act |
| Dimensions | disjunct and exclusive | overlapping, multiple mem. |
| Hierarchy | mono-hierarchic | poly-hierarchic |
| Markers | based on cultural markers | broad basis of material culture |
| ... | * ECNR-System | * No cultural equation |
| ... | * Ethnic Groups = historical identification | * Ethnic Groups are the results of social interaction |
| ... | * Cultures = empirical foundation | * Cultures are the adaptation, caused by interaction |
| ... | * Nations = significance for people | * Nations are the result of political interaction |
| ... | *Races = modern science based on laws of nature | * ’Races’, or rather biological units are the result of biological interaction |
| Entaglement | ethnic group = seed of nation = race = culture | ethnic group ̸= seed of nation ̸= race ̸= culture |
Cultural distances
Cultural distances
'Typenspektren'
- All data are used for the calculation of cultural distances
- No diagnostic types or cultural markers
- ’Typenspektren’ include the relative amount of objects of certain types.
Cultural distances | 'Typenspektren'
Cultural fingerprint
- 'Typenspektren' are a kind of cultural fingerprints.
- 'Typenspektren' don’t assume spatial archaeological cultures.
- 'Typenspektren' consider quantities and not only presence/absence.
- for every type of 'Typenspektren' a group of types, representing a certain part of society can be defines.
- 'Typenspektren' provide much more information and are much more robust than so called 'cultural markers'.
Cultural distances | 'Typenspektren'
'Typenspektren' - using all available information
- 2; ”Beil”; xxx
- 22; ”Beil, Tüllenbeil”; xxx
- 221; ”Beil, T, Schlichte vierkantige T”; xxx
- 2211; ”Beil, T, Schlichte vierkantige T, Norddeutsche T, Var. Hesepe”; xxx
- 4; ”Nadel”; xxx
- 41; ”Nadel, Rippenkopfnadeln”; xxx
- 411; ”Nadel, Rippenkopfnadeln, Var. Nutteln”; xxx
- 412; ”Nadel, Rippenkopfnadeln, Var. Badenstedt”; xxx
Which information can be used in 'Typenspektren'?
Cultural distances
Map of cultural distances
- the cultural distances to one reference point are mapped on a grid
- topography of cultural similarities
- structure of interaction space
Cultural distances
Interaction spaces
- groups of similar material culture indicate interaction spaces
- hierarchical Cluster analysis of regional Typensprektren
- cultural distance as Euclidean distance of two normalised Typensprektren
Cultural distances | Methodology for cultural areas
Interaction areas
Cultural distances
Hunsrück-Eifel-Kultur
- same extent of different groups of material culture
- crisp border
Baden-Württemberg
- fuzzy borders
- overlapping cultural areas
Cultural distances | Methodology for cultural areas
distance diagrams
But how?!
Preparation | Working Directory & Load Data
wd <- ".//home/fon/daten/analyse/mosaic"
setwd(wd)
df.weapons <- read.csv("2data/shkr-weapons.csv", header=TRUE, sep=";")
t <- as.character(df.weapons[,13])
df.weapons <- data.frame(id= df.weapons[,4],
x=df.weapons[,1], y=df.weapons[,2],
t, stringsAsFactors = FALSE)
Exploring Data | Structure & Content
str(df.weapons)
## 'data.frame': 1165 obs. of 4 variables:
## $ id: int 10261 10432 9439 9439 18567 18567 13415 13415 17039 17039 ...
## $ x : num 3510314 3513254 3499751 3499751 3506691 ...
## $ y : num 5433893 5417700 5417080 5417080 5345116 ...
## $ t : chr "B42213" "B4221" "B413" "B4211" ...
df.weapons[1:4,]
## id x y t
## 1 10261 3510314 5433893 B42213
## 2 10432 3513254 5417700 B4221
## 3 9439 3499751 5417080 B413
## 4 9439 3499751 5417080 B4211
Global 'Typenspektrum'
- counting finds per type
- considering type hierarchy
tab.weapons <- table(df.weapons[,4])
tw <- tab.weapons
for (i in seq_along(tab.weapons)) {
a <- dimnames(tab.weapons)[[1]][i]
b <- dimnames(tab.weapons)[[1]][]
tw[i] <- sum(tab.weapons[grepl(a, b)])
}
barplot(tw)
Spatial Data
- packages
- projection data
- conversion
library(sp) # spatial objects
library(proj4) # projection
library(spatstat) # spatial statistics
library(maptools) # spatial tools
crs1 <- "+proj=tmerc +lat_0=0 +lon_0=9
+k=1 +x_0=3500000 +y_0=0
+ellps=WGS84 +units=m +no_defs"
coordinates(df.weapons)=~x+y
proj4string(df.weapons) <-
CRS(as.character(crs1))
What is inside? | Structure of Spatial Objects
str(df.weapons)
## Formal class 'SpatialPointsDataFrame' [package "sp"] with 5 slots
## ..@ data :'data.frame': 1165 obs. of 2 variables:
## .. ..$ id: int [1:1165] 10261 10432 9439 9439 18567 18567 13415 13415 17039 17039 ...
## .. ..$ t : chr [1:1165] "B42213" "B4221" "B413" "B4211" ...
## ..@ coords.nrs : int [1:2] 2 3
## ..@ coords : num [1:1165, 1:2] 3510314 3513254 3499751 3499751 3506691 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : chr [1:1165] "1" "2" "3" "4" ...
## .. .. ..$ : chr [1:2] "x" "y"
## ..@ bbox : num [1:2, 1:2] 3391750 5268797 3606087 5516434
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : chr [1:2] "x" "y"
## .. .. ..$ : chr [1:2] "min" "max"
## ..@ proj4string:Formal class 'CRS' [package "sp"] with 1 slot
## .. .. ..@ projargs: chr "+proj=tmerc +lat_0=0 +lon_0=9 +k=1 +x_0=3500000 +y_0=0 +ellps=WGS84 +units=m +no_defs"
Prep. local 'Typenspektren'
- list of types
- variables
- owin object (
spatstat) - regular sample points
type.list <- unlist(dimnames(tab.weapons))
type.n <- length(type.list)
sdev <- 5000
bb <- bbox(df.weapons)
win <- owin(xrange=c(bb[1,1],bb[1,2]),
yrange= c(bb[2,1],bb[2,2]),
unitname="m")
s.points <- spsample(df.weapons, 100,
type="regular")
samp <- list()
i=0
Loop local 'Typenspektren'
- loop through all types
- producing a point pattern object
- calculating density
- sampling density
- Typenspektren as list of vectors
for (t in type.list) {
i <- i+1
finds <- df.weapons[which(df.weapons
@data$t==t),]
ppp_w <- ppp(finds@coords[,1],
finds@coords[,2], window=win)
dens <- density(ppp_w, kernel="gaussian",
sigma=sdev, dimyx=c(36,56), w=win,
edge=TRUE, at="pixels")
sgdf_w_dens <- as.SpatialGridDataFrame.im(
dens)
proj4string(sgdf_w_dens) <- CRS(
as.character(crs1))
meg_dens_samp <- over(s.points,
sgdf_w_dens)
samp[[i]] <- meg_dens_samp
}
Exploring the result | Structure & Content
str(samp)
## List of 49
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## $ :'data.frame': 99 obs. of 1 variable:
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## $ :'data.frame': 99 obs. of 1 variable:
## ..$ v: num [1:99] -1.00e-28 -1.07e-26 -1.71e-27 1.57e-23 6.76e-16 ...
## $ :'data.frame': 99 obs. of 1 variable:
## ..$ v: num [1:99] 7.89e-25 -1.71e-24 6.25e-16 6.25e-16 -5.83e-25 ...
## $ :'data.frame': 99 obs. of 1 variable:
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## ..$ v: num [1:99] -8.29e-26 6.56e-25 9.37e-16 9.37e-16 7.20e-25 ...
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## $ :'data.frame': 99 obs. of 1 variable:
## ..$ v: num [1:99] 5.88e-26 -8.50e-27 7.65e-27 -2.46e-26 3.50e-26 ...
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## $ :'data.frame': 99 obs. of 1 variable:
## ..$ v: num [1:99] 1.57e-26 4.96e-26 3.50e-27 8.10e-27 1.17e-26 ...
## $ :'data.frame': 99 obs. of 1 variable:
## ..$ v: num [1:99] 2.86e-24 4.21e-12 4.76e-09 1.27e-13 1.53e-10 ...
## $ :'data.frame': 99 obs. of 1 variable:
## ..$ v: num [1:99] 1.54e-25 -1.36e-25 3.39e-25 1.56e-16 5.06e-15 ...
## $ :'data.frame': 99 obs. of 1 variable:
## ..$ v: num [1:99] -3.32e-27 -2.66e-26 -2.63e-26 -2.03e-26 4.81e-27 ...
## $ :'data.frame': 99 obs. of 1 variable:
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## $ :'data.frame': 99 obs. of 1 variable:
## ..$ v: num [1:99] 5.56e-12 6.13e-09 4.79e-15 9.19e-27 3.81e-25 ...
## $ :'data.frame': 99 obs. of 1 variable:
## ..$ v: num [1:99] 2.14e-25 4.38e-25 -4.78e-25 2.43e-22 3.53e-13 ...
Exploring the result | Structure & Content
samp
## [[1]]
## v
## 1 -1.468375e-25
## 2 -4.690261e-25
## 3 2.875436e-22
## 4 3.255933e-19
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##
## [[2]]
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Conversion to Data Frame
- points in rows
- types in columns
- rename columns
ts <- data.frame(matrix(unlist(samp),
nrow=49, byrow=T))
colnames(ts) <- type.list
ts[1:4,1:3]
## B4 B41 B411
## 1 -1.468375e-25 -4.690261e-25 2.875436e-22
## 2 1.991534e-25 5.871202e-26 1.209554e-25
## 3 7.761498e-11 2.546326e-09 5.906874e-17
## 4 7.735967e-26 4.086838e-27 -2.659562e-26
Distance diagram (dd)
- different view-points
- different focus-points
- cultural distance as an inverse interaction proxy
| Viewpoint | fixed vocus | selected focus | all foucused |
|---|---|---|---|
| fixed viewpoint | dd1 fixed profile dd, similarity profiles | dd2 fixed sector dd | dd3 fixed multi-focal dd, fall-off curve |
| selected viewpoints | dd4 selected profile dd | dd5 selected secotr dd | dd6 selected multi-focal dd |
| all viewpointsdd7 aggregated profile dd | dd8 aggregated sector dd | dd9 aggregated multi-focal dd, variogram |
Cultural Distances
Do you have other ideas for interpretation?
Space
Disciplinary spaces
A metrical space is spanned by a metric, which defines distances.
- A social space is constructed by social distances.
- An economic space is constructed by economic distances.
- A cultural space is constructed by cultural distances.
- A geographic space is constructed by geodetic distances.
Interaction model
- fixed starting point
- fixed profile
- ceramics
- interaction friction at Black Forrest?
Interaction model
- fixed starting point
- along the main axes
- ceramics
- rivers as interactive areas?
Interaction model
- from all points
- to all points
- fibulae and adornment
- interaction threshold at 200 km?
Theoretical Models
Interaction decreases with distance. Distance decay functions can quantify the decrease.
Tobler’s first law of geography
Everything is related to everything else, but near things are more related
than distant things.
Gravity models
- involve properties of the interaction partners
- based on an analogy from physics
- population, settlement size, …
- can be used to produce distance decay functions/fall off curves, which consider population
Distance diagram (dd)
- different viewpoints
- different focus-points
- cultural distance as an inverse interaction proxy
| Viewpoint | fixed vocus | selected focus | all foucused |
|---|---|---|---|
| fixed viewpoint | dd1 fixed profile dd, similarity profiles | dd2 fixed sector dd | dd3 fixed multi-focal dd, fall-off curve |
| selected viewpoints | dd4 selected profile dd | dd5 selected secotr dd | dd6 selected multi-focal dd |
| all viewpointsdd7 aggregated profile dd | dd8 aggregated sector dd | dd9 aggregated multi-focal dd, variogram |
Mapping profiles
p.index <- (s.points@coords[,1] > 3475200 & s.points@coords[,1] < 3511200)
p.points <- s.points[p.index,]
p.ts <- ts[p.index,]
plot(s.points)
points(df.weapons, col='grey')
points(p.points, pch=16, col="dark red")
dd1
- distance function
- data for specific distance diagram
- distance calculation
- plot
edist <- function(a,b){sqrt(sum((a-b)^2))}
n <-length(p.points@coords[,1])
x <-1:n
df.d <- data.frame(p1=rep(1,n),p2=x,
d1=x,d2=x)
for (i in seq_along(p.ts[,1])) {
df.d[i,3] <- edist(p.points@coords[1,],
p.points@coords[i,])
}
for (i in seq_along(p.ts[,1])) {
df.d[i,4] <- edist(p.ts[1,],p.ts[i,])
}
plot(df.d[,3:4], pch=16, xlab="spatial
distance (km)", ylab= "density
distance", main="dd1")
lines(df.d[,3:4])
dd3
- similar to dd1
- sampling cultural distances in spatial distance ranges
p.points <- s.points; p.ts <- ts
n <-length(p.points@coords[,1]); x <-1:n
df.d<-data.frame(p1=rep(1,n),p2=x,d1=x,d2=x)
for (i in seq_along(p.ts[,1])) {
df.d[i,3] <- edist(p.points@coords[50,],
p.points@coords[i,])}
for (i in seq_along(p.ts[,1])) {
df.d[i,4] <- edist(p.ts[50,],p.ts[i,])}
df.dd <- data.frame(id=seq(0,250000,20000)
/20000+1,d1=seq(0,250000,20000),
d2=seq(0,250000,20000))
for (i in df.dd[,1]) {
df.dd[i,3] <- mean(df.d[(df.d[,3] >
df.dd[i,2] & df.d[,3] < df.dd[i+1,2]),4])}
plot(df.dd[,2:3], pch=16, xlab="spatial distance (m)",
ylab= "density distance", main="dd3")
lines(df.dd[,2:3])
dd9
- similar to dd1
- sampling cultural distances in spatial distance ranges
p.points <- s.points; p.ts <- ts
n <-length(p.points@coords[,1]); x <-1:n
df.d <- data.frame(p1=rep(1,n),p2=x,d1=x,d2=x)
for (i in 2:n) {
df.d <- rbind(df.d,data.frame(p1=rep
(i,n),p2=x,d1=x,d2=x))}
for (i in seq_along(df.d[,1])) {
df.d[i,3] <- edist(p.points@coords[
df.d[i,1],],p.points@coords[df.d[i,2],])}
for (i in seq_along(df.d[,1])) {
df.d[i,4] <- edist(p.ts[df.d[i,1],],
p.ts[df.d[i,2],])}
df.dd <- data.frame(id=seq(0,250000,20000)
/20000+1,d1=seq(0,250000,20000),
d2=seq(0,250000,20000))
for (i in df.dd[,1]) {
df.dd[i,3] <- mean(df.d[(df.d[,3] >
df.dd[i,2] & df.d[,3] < df.dd[i+1,2]),4])}
dd9
- similar to dd1
- sampling cultural distances in spatial distance ranges
plot(df.dd[,2:3], pch=16, xlab="spatial distance
(m)", ylab= "density distance", main="dd9")
lines(df.dd[,2:3])
How can we interpret the distance diagrams?
Which pitfalls for interpretation can you find?
How can we improve the distance diagrams and develop other versions?
Apply distance diagrams in the workshop this afternoon!
Cultural & Geographic Distance
Distance analyses in geographic space
- abstract concept: can be measured in meters, time, money, strangeness, ...
- influence interactions
Distance analyses in geographic space
- straight/ direct
- Euclidean distance
- "As the crow flies"
- "In a beeline"
- geodesic distance
- great-circle distance
- not direct/ random
- random walk
- "Drunkard's Walk"
Distance analyses in geographic space
Two concepts with different premises
- straight/ direct
- Euclidean distance
- "As the crow flies"
- "In a beeline"
- geodesic distance
- great-circle distance
- least-cost distance
- not direct/ random
- random walk
- "Drunkard's Walk"
Distance analyses in geographic space
A reminder about spatial data.
What is the meaning of the coordinates?
dem@bbox
## min max
## x 3550736 3579036
## y 6022467 6040567
What is the Spatial Reference System (SRS)?
[= Coordinate Reference System (CRS)]
By Peter Mercator - Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=9910926
Distance analyses in geographic space
A reminder about spatial data.
What is the meaning of the coordinates?
dem@bbox
## min max
## x 3550736 3579036
## y 6022467 6040567
What is the Spatial Reference System (SRS)?
[= Coordinate Reference System (CRS)]
Von BerndH - selbst erstellt mit Generic Mapping Tools (psbasemap, psxy), Python, GIMP, CC BY-SA 3.0, https://de.wikipedia.org/w/index.php?curid=4186798
Distance analyses in geographic space
dem@proj4string
## CRS arguments: NA
dem@proj4string <- CRS("+init=epsg:5677")
## dem@proj4string
is.projected(dem)
## [1] TRUE
Distance analyses in geographic space
From a list of points to a spatial object [a reminder]
download.file(
url = "https://raw.githubusercontent.com/dakni/mhbil/master/data/meg_dw.csv",
destfile = "2data/meg_dw.csv")
meg_dw <- read.table(file = "2data/meg_dw.csv",
header = TRUE,
sep = ";")
head(meg_dw)
## id x y
## 1 1 3553751 6028609
## 2 2 3553442 6027416
## 3 3 3552502 6025080
## 4 4 3552518 6024799
## 5 5 3553799 6025130
## 6 6 3551621 6025247
Distance analyses in geographic space
Create SpatialPointsDataFrame (spdf)
library(sp)
coordinates(meg_dw) <- ~x+y
str(meg_dw)
## Formal class 'SpatialPointsDataFrame' [package "sp"] with 5 slots
## ..@ data :'data.frame': 267 obs. of 1 variable:
## .. ..$ id: int [1:267] 1 2 3 4 5 6 7 8 9 10 ...
## ..@ coords.nrs : int [1:2] 2 3
## ..@ coords : num [1:267, 1:2] 3553751 3553442 3552502 3552518 3553799 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : chr [1:267] "1" "2" "3" "4" ...
## .. .. ..$ : chr [1:2] "x" "y"
## ..@ bbox : num [1:2, 1:2] 3551621 6022761 3576305 6040236
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : chr [1:2] "x" "y"
## .. .. ..$ : chr [1:2] "min" "max"
## ..@ proj4string:Formal class 'CRS' [package "sp"] with 1 slot
## .. .. ..@ projargs: chr NA
Distance analyses in geographic space
Project spdf and plot
is.projected(meg_dw)
## [1] NA
proj4string(meg_dw) <- CRS("+init=epsg:5677")
is.projected(meg_dw)
## [1] TRUE
plot(raster(dem)); points(meg_dw)
Distance analyses in geographic space
\[d(i,j) = \sqrt{(x_i-x_j)^2 + (y_i-y_j)^2}\]
Distance analyses in geographic space
Distance between points using Euclidean distance using package rgeos
library(rgeos)
ed <- gDistance(spgeom1 = meg_dw,
byid = TRUE)
## class(ed)
## str(ed)
library(fields)
## Loading required package: spam
## Loading required package: grid
## Spam version 1.3-0 (2015-10-24) is loaded.
## Type 'help( Spam)' or 'demo( spam)' for a short introduction
## and overview of this package.
## Help for individual functions is also obtained by adding the
## suffix '.spam' to the function name, e.g. 'help( chol.spam)'.
##
## Attaching package: 'spam'
## The following objects are masked from 'package:base':
##
## backsolve, forwardsolve
## Loading required package: maps
##
## Attaching package: 'maps'
## The following object is masked from 'package:plyr':
##
## ozone
image.plot(ed)
Distance analyses in geographic space
min(ed)
## [1] 0
round(data.frame(min = min(ed[ed>0]),
max = max(ed[ed>0]),
mean = mean(ed[ed>0]),
median = median(ed[ed>0])
),
2)
## min max mean median
## 1 18.44 27561.77 9565.89 8619.07
Distance analyses in geographic space
hist(ed)
abline(v = mean(ed[ed>0]), col = "red")
abline(v = median(ed[ed>0]), col = "blue")
Distance analyses in geographic space
Some further questions that might be interesting
mp <- apply(X = ed,
MARGIN = 2,
FUN = mean)
tmp <- ed
tmp[tmp==0] <- 9999
cp <- apply(X = tmp,
MARGIN = 2,
FUN = min)
meg_dw$mp <- mp
meg_dw@data$cp <- cp
What is the mean euclidean distance from a point to its surrounding points (mp)?
What is the closest euclidean distance from a point to its surrounding points (cp)?
Question: Why changing 0 to 9999?
Distance analyses in geographic space
Examples how to use spplot: http://rspatial.r-forge.r-project.org/gallery/
spplot(meg_dw, "cp")
spplot(meg_dw, "mp")
Distance analyses in geographic space
Leaflet in R: https://rstudio.github.io/leaflet/
library(leaflet)
tmp <- spTransform(meg_dw, CRSobj = CRS("+init=epsg:4326"))
leaflet(data=tmp$cp) %>%
addTiles() %>%
addCircleMarkers(lng = tmp@coords[,1],
lat = tmp@coords[,2],
radius = tmp$mp/1000,
)
Distance analyses in geographic space
Mapview [as alternative to leaflet]: http://environmentalinformatics-marburg.github.io/mapview/introduction.html
library(mapview)
mapview(meg_dw, zcol = "mp", legend = TRUE)
Distance analyses in geographic space
Least-cost distances
- Cost is --- like distance --- an abstract concept; hence, YOU decide what your costs are (time, energy, ugliness, ...)
- Least-cost distance analyses allow to integrate prior knowledge and more complexity into your model.
Distance analyses in geographic space
Least-cost distances
- Cost is --- like distance --- an abstract concept; hence, YOU decide what your costs are (time, energy, ugliness, ...)
- Least-cost distance analyses allow to integrate prior knowledge and more complexity into your model.
There was a discourse at the LAC about least-cost paths (LCP):
- Opinion 1: LCP follow a capitalistic ideology since their aim is the best optimization. They are blind for post-processual ideas
- Opinion 2: LCP do optimize a certain path. But the rules, how they do it, is defined by parameters chosen for the model. Hence, they are able to grasp post-processual ideas
Distance analyses in geographic space
Basic work about least-cost distances and path analyses (usefulness, applicability, problems,...) was/is conducted quite excessively by Irmela Herzog (https://bodendenkmalpflege-lvr.academia.edu/IrmelaHerzog)
Distance analyses in geographic space
What does it mean?
## km/h
tobler1993a <- function(s){
6 * exp(-3.5 * abs(s + 0.05))
}
## m/min
tobler1993b <- function(s){
0.36 * exp(-3.5 * abs(s + 0.05))
}
Distance analyses in geographic space
Technically speaking, there are two different ways how least-cost paths are created
- create a cost raster
- accumulate the costs from one of your points of interest
- "walk" from a target point along the accumulated raster to your starting point (like water flows into a sink)
In GrassGIS:
- cost raster
r.cost/r.walkr.drain
Distance analyses in geographic space
Technically speaking, there are two different ways how least-cost paths are created
- create a cost raster
- accumulate the costs from one of your points of interest
- "walk" from a target point along the accumulated raster to your starting point (like water flows into a sink)
In GrassGIS:
- cost raster
r.cost/r.walkr.drain
- create cost raster
- create matrix of cell connections
- find "cheapest" path between points along cell connections
gdistance in R a package by Jacob van Etten (https://cran.r-project.org/web/packages/gdistance)
Distance analyses in geographic space
What are the necessary steps?
- Create cost surface
https://cran.r-project.org/web/packages/gdistance/vignettes/gdistance1.pdf
Distance analyses in geographic space
What are the necessary steps?
- Create cost surface
- Create transition matrix, i.e. matrix recording connections between cells
https://cran.r-project.org/web/packages/gdistance/vignettes/gdistance1.pdf
Distance analyses in geographic space
What are the necessary steps?
- Create cost surface
- Create transition matrix, i.e. matrix recording connections between cells
- Transition matrix is filled with conductance, rather than resistance values; hence unconnected cells have value 0 (= no conductance); memory efficient
Distance analyses in geographic space
What are the necessary steps?
- Create cost surface
- Create transition matrix, i.e. matrix recording connections between cells
- Transition matrix is filled with conductance, rather than resistance values; hence unconnected cells have value 0 (= no conductance); memory efficient
- Geocorrection of values
Distance analyses in geographic space
What are the necessary steps?
- Create cost surface
- Create transition matrix, i.e. matrix recording connections between cells
- Transition matrix is filled with conductance, rather than resistance values; hence unconnected cells have value 0 (= no conductance); memory efficient
- Geocorrection of values
- Identify adjacent cells
Distance analyses in geographic space
What are the necessary steps?
- Create cost surface
- Create transition matrix, i.e. matrix recording connections between cells
- Transition matrix is filled with conductance, rather than resistance values; hence unconnected cells have value 0 (= no conductance); memory efficient
- Geocorrection of values
- Identify adjacent cells
- Calculate walking speed for adjacent cells
Distance analyses in geographic space
What are the necessary steps?
- Create cost surface
- Create transition matrix, i.e. matrix recording connections between cells
- Transition matrix is filled with conductance, rather than resistance values; hence unconnected cells have value 0 (= no conductance); memory efficient
- Geocorrection of values
- Identify adjacent cells
- Calculate walking speed for adjacent cells
- Geocorrect speed values
Distance analyses in geographic space
What are the necessary steps?
- Create cost surface
- Create transition matrix, i.e. matrix recording connections between cells
- Transition matrix is filled with conductance, rather than resistance values; hence unconnected cells have value 0 (= no conductance); memory efficient
- Geocorrection of values
- Identify adjacent cells
- Calculate walking speed for adjacent cells
- Geocorrect speed values
- Find path using least-cost ("as the wolf runs") or random walk ("drunkard's walk") algorithm
Distance analyses in geographic space
First we calculate the slope, as this is used as cost
library(raster)
dem <- raster(dem)
slope <- terrain(x = dem,
opt = "slope",
neighbors = 8,
unit = "degrees")
##drawExtent()
crop.extent <- extent(
c(3551000,3578650,6022770,6045000))
slope <- crop(x = slope, y = crop.extent)
Distance analyses in geographic space
We need to get rid of the ocean areas since it is not crossable (by foot)
- get land areas
- reproject them
- mask the slope
- reproject and factorize
- create uncrossable transition area
ab <- getData('GADM', country = 'DEU', level = 1)
ab <- spTransform(ab, CRSobj = CRS("+init=epsg:5677"))
slope <- mask(slope, mask = ab, updatevalue = 9999)
Distance analyses in geographic space
Afterwards we create the transition object and geocorrect it
library(gdistance)
slope.tran <- transition(x = slope,
transitionFunction = mean,
directions = 8,
symm = TRUE)
slope.geo <- geoCorrection(x = slope.tran, scl = TRUE)
To see how the results look like we create a raster stack for easy plotting
slopes <- stack(slope,
raster(slope.tran),
raster(slope.geo))
names(slopes) <- c("Slope","Transition","Geocorrection")
plot(slopes, nr = 1)
Distance analyses in geographic space
Now, the final step. Calculate Tobler's hiking speed, geocorrect again and calculate a shortest path
adj <- adjacent(x = slope,
cells=1:ncell(slope),
pairs=TRUE,
directions=8)
speed <- slope.geo
speed[adj] <- 6 * exp(-3.5 * abs(slope.geo[adj] + 0.05))
speed.geo <- geoCorrection(x = speed, scl=TRUE)
sp1 <- shortestPath(x = speed.geo,
origin = meg_dw@coords[4,],
goal = meg_dw@coords[231,],
output = "SpatialLines")
plot(raster(speed.geo))
lines(sp1)
Distance analyses in geographic space
What about the "drunkard's walk"? theta is the level of drunkenness, i.e. the degree from which
the path randomly deviates from the shortest path
p1 <- passage(x = speed.geo,
origin = meg_dw@coords[4,],
goal = meg_dw@coords[231,],
theta = .005)
p2 <- passage(x = speed.geo,
origin = meg_dw@coords[4,],
goal = meg_dw@coords[231,],
theta = .05)
hs <- hillShade(slope = terrain(x = dem*10, opt = "slope"),
aspect = terrain(x = dem, opt = "aspect"),
angle = 40, direction = 270)
plot(hs, col=grey(0:100/100), legend=FALSE)
plot(p1, alpha = .5, add=TRUE); lines(sp1)
Distance analyses in geographic space
theta = .005
theta = .05
Distance analyses in geographic space
What about the idea of a prehistoric autobahn? Run the code and get some coffee... a lot of coffee
xy <- data.frame(X = meg_dw@coords[,1],
Y = meg_dw@coords[,2])
rows.xy <- row.names(xy)
sa.rows.xy <- sample(row.names(xy), length(xy$X)/2)
starts <- subset(xy, rows.xy %in% sa.rows.xy)
goals <- subset(xy, !(rows.xy %in% sa.rows.xy))
sg.passages <- brick(slope)
for(i in 1:length(starts$X)) {
s <- c(starts$X[i],starts$Y[i])
z <- c(goals$X[i],goals$Y[i])
sg.passages[[i]] <- passage(x = speed.geo, origin = s, goal = z, theta = .05)
cat("iteration ", i, " of ", length(starts$X),"\n")
}
sg.passages.sum <- sum(sg.passages)
Distance analyses in geographic space
Distance analyses in geographic space
Presentations
Monday, 5th of September
Tuesday, 6th of September
Wednesday, 7th of September
- Modelling Interaction: Cultural & Geographic Distance
- Workshop: Geographical and Economic Distances
- Workshop: Cultural Distances
Thursday, 8th of September
- Modelling Interaction: Network Approaches
- Workshop: Pointpattern Analysis
- Workshop: Network Analysis