Piper diagrams using ggplot2.

ggplot_piper.R

### A piper diagram based on the ternary plot example here: http://srmulcahy.github.io/2012/12/04/ternary-plots-r.html
### This was written quickly, and most likely contains bugs - I advise you to check it first.
### Jason Lessels [email protected]

### This now consists of two functions. transform_piper_data transforms the data to match 
### the coordinates of the piper diagram. ggplot_piper does all of the background.


transform_piper_data <- function(Mg, Ca, Cl,SO4, name=NULL){
  if(is.null(name)){
    name = rep(1:length(Mg),3)
  } else {
    name = rep(name,3)
  }
  y1 <- Mg * 0.86603
  x1 <- 100*(1-(Ca/100) - (Mg/200))
  y2 <- SO4 * 0.86603
  x2 <-120+(100*Cl/100 + 0.5 * 100*SO4/100)
  new_point <- function(x1, x2, y1, y2, grad=1.73206){
    b1 <- y1-(grad*x1)
    b2 <- y2-(-grad*x2)
    M <- matrix(c(grad, -grad, -1,-1), ncol=2)
    intercepts <- as.matrix(c(b1,b2))
    t_mat <- -solve(M) %*% intercepts
    data.frame(x=t_mat[1,1], y=t_mat[2,1])
  }
  np_list <- lapply(1:length(x1), function(i) new_point(x1[i], x2[i], y1[i], y2[i]))
  npoints <- do.call("rbind",np_list)
  data.frame(observation=name,x=c(x1, x2, npoints$x), y=c(y=y1, y2, npoints$y))
}


ggplot_piper <- function() {
  library(ggplot2)
  grid1p1 <<- data.frame(x1 = c(20,40,60,80), x2= c(10,20,30,40),y1 = c(0,0,0,0), y2 = c(17.3206,34.6412,51.9618, 69.2824))
  grid1p2 <<- data.frame(x1 = c(20,40,60,80), x2= c(60,70,80,90),y1 = c(0,0,0,0), y2 = c(69.2824, 51.9618,34.6412,17.3206))
  grid1p3 <<- data.frame(x1 = c(10,20,30,40), x2= c(90,80,70,60),y1 = c(17.3206,34.6412,51.9618, 69.2824), y2 = c(17.3206,34.6412,51.9618, 69.2824))
  grid2p1 <<- grid1p1
  grid2p1$x1 <- grid2p1$x1+120
  grid2p1$x2 <- grid2p1$x2+120
  grid2p2 <<- grid1p2
  grid2p2$x1 <- grid2p2$x1+120
  grid2p2$x2 <- grid2p2$x2+120
  grid2p3 <<- grid1p3
  grid2p3$x1 <- grid2p3$x1+120
  grid2p3$x2 <- grid2p3$x2+120
  grid3p1 <<- data.frame(x1=c(100,90, 80, 70),y1=c(34.6412, 51.9618, 69.2824, 86.603), x2=c(150, 140, 130, 120), y2=c(121.2442,138.5648,155.8854,173.2060))
  grid3p2 <<- data.frame(x1=c(70, 80, 90, 100),y1=c(121.2442,138.5648,155.8854,173.2060), x2=c(120, 130, 140, 150), y2=c(34.6412, 51.9618, 69.2824, 86.603))
  
  p <- ggplot() +
    ## left hand ternary plot
    geom_segment(aes(x=0,y=0, xend=100, yend=0)) +
    geom_segment(aes(x=0,y=0, xend=50, yend=86.603)) +
    geom_segment(aes(x=50,y=86.603, xend=100, yend=0)) +
    ## right hand ternary plot
    geom_segment(aes(x=120,y=0, xend=220, yend=0)) +
    geom_segment(aes(x=120,y=0, xend=170, yend=86.603)) +
    geom_segment(aes(x=170,y=86.603, xend=220, yend=0)) +
    ## Upper diamond
    geom_segment(aes(x=110,y=190.5266, xend=60, yend=103.9236)) +
    geom_segment(aes(x=110,y=190.5266, xend=160, yend=103.9236)) +
    geom_segment(aes(x=110,y=17.3206, xend=160, yend=103.9236)) +
    geom_segment(aes(x=110,y=17.3206, xend=60, yend=103.9236)) +
    ## Add grid lines to the plots
    geom_segment(aes(x=x1, y=y1, yend=y2, xend=x2), data=grid1p1, linetype = "dashed", size = 0.25, colour = "grey50") +
    geom_segment(aes(x=x1, y=y1, yend=y2, xend=x2), data=grid1p2, linetype = "dashed", size = 0.25, colour = "grey50") +
    geom_segment(aes(x=x1, y=y1, yend=y2, xend=x2), data=grid1p3, linetype = "dashed", size = 0.25, colour = "grey50") +
    geom_segment(aes(x=x1, y=y1, yend=y2, xend=x2), data=grid2p1, linetype = "dashed", size = 0.25, colour = "grey50") +
    geom_segment(aes(x=x1, y=y1, yend=y2, xend=x2), data=grid2p2, linetype = "dashed", size = 0.25, colour = "grey50") +
    geom_segment(aes(x=x1, y=y1, yend=y2, xend=x2), data=grid2p3, linetype = "dashed", size = 0.25, colour = "grey50") +
    geom_segment(aes(x=x1, y=y1, yend=y2, xend=x2), data=grid3p1, linetype = "dashed", size = 0.25, colour = "grey50") +
    geom_segment(aes(x=x1, y=y1, yend=y2, xend=x2), data=grid3p2, linetype = "dashed", size = 0.25, colour = "grey50") +
    ### Labels and grid values
    #geom_text(aes(50,-10, label="Ca^2"), parse=T, size=4) + # Commented out, as parse=TRUE can cause issues

    geom_text(aes(c(20,40,60,80),c(-5,-5,-5,-5), label=c(80, 60, 40, 20)), size=3) +
    geom_text(aes(c(35,25,15,5),grid1p2$y2, label=c(80, 60, 40, 20)), size=3) +
    geom_text(aes(c(95,85,75,65),grid1p3$y2, label=c(80, 60, 40, 20)), size=3) +
    # geom_text(aes(17,50, label="Mg^2"), parse=T, angle=60, size=4) +
    coord_equal(ratio=1)+  
    geom_text(aes(17,50, label="Mg^2"), angle=60, size=4, parse=TRUE) +  
    geom_text(aes(82.5,50, label="Na + K"), angle=-60, size=4) +
   geom_text(aes(50,-10, label="Ca^2"), size=4, parse=TRUE) +
    
    
    geom_text(aes(170,-10, label="Cl^-phantom()"), size=4, parse=TRUE) +
    geom_text(aes(205,50, label="SO^4"), angle=-60, size=4, parse=TRUE) +
    geom_text(aes(137.5,50, label="Alkalinity~as~HCO^3"), angle=60, size=4, parse=TRUE) +
    geom_text(aes(72.5,150, label="SO^4~+~Cl^-phantom()"), angle=60, size=4, parse=TRUE) +
    geom_text(aes(147.5,150, label="Ca^2~+~Mg^2"), angle=-60, size=4, parse=TRUE) + 

    geom_text(aes(c(155,145,135,125),grid2p2$y2, label=c(20, 40, 60, 80)), size=3) +
    geom_text(aes(c(215,205,195,185),grid2p3$y2, label=c(20, 40, 60, 80)), size=3) +
    geom_text(aes(c(140,160,180,200),c(-5,-5,-5,-5), label=c(20, 40, 60, 80)), size=3) +
    geom_text(aes(grid3p1$x1-5,grid3p1$y1, label=c(80, 60, 40, 20)), size=3) +
    geom_text(aes(grid3p1$x2+5,grid3p1$y2, label=c(20, 40, 60, 80)), size=3) +
    geom_text(aes(grid3p2$x1-5,grid3p2$y1, label=c(20, 40, 60, 80)), size=3) +
    geom_text(aes(grid3p2$x2+5,grid3p2$y2, label=c(80, 60, 40, 20)), size=3) +
    theme_bw() +
    theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
          panel.border = element_blank(), axis.ticks = element_blank(),
          axis.text.x = element_blank(), axis.text.y = element_blank(),
          axis.title.x = element_blank(), axis.title.y = element_blank())
  return(p)
}
### A plan and simple piper diagram
data=as.data.frame(list("Ca"=c(43,10,73,26,32),"Mg"=c(30,50,3,14,12),Cl=c(24,10,12,30,43),"SO4"=c(24,10,12,30,43),"WaterType"=c(2,2,1,2,3)),row.names=c("A","B","C","D","E"))
#transform the data into piper based coordinates
piper_data <- transform_piper_data(Ca=data$Ca, Mg = data$Mg, Cl=data$Cl, SO4= data$SO4, name=data$WaterType)
# The piper function now just plots the background
ggplot_piper()
# Now points can be added like...
ggplot_piper() + geom_point(aes(x,y), data=piper_data)
# colouring the points can be done using the observation value.
ggplot_piper() + geom_point(aes(x,y, colour=factor(observation)), data=piper_data)
# The size can be changed like..
ggplot_piper() + geom_point(aes(x,y, colour=factor(observation)), size=4, data=piper_data)
## Change colours and shapes and merging the legends together
ggplot_piper() + geom_point(aes(x,y, colour=factor(observation), shape=factor(observation)), size=4, data=piper_data) + 
  scale_colour_manual(name="legend name must be the same", values=c("#999999", "#E69F00", "#56B4E9"), labels=c("Control", "Treatment 1", "Treatment 2")) +
  scale_shape_manual(name="legend name must be the same", values=c(1,2,3), labels=c("Control", "Treatment 1", "Treatment 2"))

Thank you so much for this code. Glad to be able to add this to the list of analyses that can be done in R. One more thing that could improve aesthetics is subscripting the number of elements in the geom_text like this:

label="SO[4]"

This follows the conventional notation of formulas. Also you can add the plus sign if you are so inclined like this:

label="Ca^'2+'~+~Mg^'2+'"

many thanks
z

Thank you so much for writing some code for ggplot to make a Piper diagram, but I'm having a little bit of trouble with the code. There seems to be a problem plotting my data correctly. Here is what I've got so far

data <- data.frame(Ca = c(27.10435, 34.04255, 33.53141, 41.24484), Mg = c(45.17392, 31.91489, 32.68251, 17.49781), Cl = c(27.10435, 34.04255, 33.53141, 41.24484), SO4 = c(0.61737690, 0.00000000, 0.25466893, 0.01249844), WaterType = c(1, 1, 2, 2))
piper_data <- transform_piper_data(Ca=data$Ca, Mg = data$Mg, Cl=data$Cl, SO4= data$SO4, name=data$WaterType)
ggplot_piper() + geom_point(aes(x,y), data=piper_data)

Yet plotting the same data on the 'Hydrogeo' package yields much different results, most notably the way each point is plotted on the "main" tetrahedron.

data$pt.pch <- c(1, 1, 2, 2)
piper <- piper(data)
plot(piper)

Any suggestions as to the discrepancy?

Thanks for the nice script! Some minor improvements on the sub-and superscripts on the axes are necessary though.

@bmbagley: Your discrepancys might come from discrepancies in your units. Note that input data need to be percent of meq/l. The hydrogeo package has a function to convert meq/l to percent (toPercent), but you need to convert to meq/l before by yourself.

Hey Jason, I forked your gist to a regular git-hub repo to be able to provide a README with your example plots:
https://github.com/markolipka/ggplot_Piper

Unfortunately, the fork process did not preserve the relation to your gist. Sorry for that, I'm linking to it in the README file.

Thank you very much for the code, Jason.
If anyone wants to color the plot based on major water type/chemistry, run this to create polygons:

##Upper Diamond##
ids <- factor(c("Sodium Bicarbonate", "Sodium Chloride",
"Calcium Bicarbonate", "Calcium Sulfate"))
values <- data.frame(
id = ids,
value = c(1,2,3,4))
positions <- data.frame(
id=rep(ids, each = 4),
x=c(110,85,110,135,
135,110,135,160,
85,60,85,110,
110,85,110,135),
y=c(17.3206,60.6221, 103.9236,60.6221,
60.6221, 103.9236, 147.2251, 103.9236,
60.6221,103.9236,147.2251,103.9236,
103.9236,147.2251,190.5266,147.2251))
polygons <- merge(values, positions)

##Left Ternary Plot##
ids2 <- factor(c("5", "6", "7", "8"))
values2 <- data.frame(
id = ids,
value = c(5,6,7,8))
positions2 <- data.frame(
id=rep(ids2, each = 3),
x=c(50,0,25,
50,25,75,
100,50,75,
75,25,50),
y=c(0,0,43.3015,
0,43.3015,43.3015,
0,0,43.3015,
43.3015,43.3015,86.603))
polygons2 <- merge(values2, positions2)

##Right Ternary Plot##
ids3 <- factor(c("9", "10", "11", "12"))
values3 <- data.frame(
id = ids,
value = c(9,10,11,12))
positions3 <- data.frame(
id=rep(ids2, each = 3),
x=c(170,120,145,
170,145,195,
220,170,195,
195,145,170),
y=c(0,0,43.3015,
0,43.3015,43.3015,
0,0,43.3015,
43.3015,43.3015,86.603))
polygons3 <- merge(values3, positions3)

Then, add a line for each 'plot' (upper, left, right) within the ggplot_piper function by Jason, for example:

left hand ternary plot:
geom_polygon(data=polygons2, aes(x=x,y=y,fill=id,group=id)) +
geom_segment(aes(x=0,y=0, xend=100, yend=0)) …

Excellent post, after 2 weeks of troubles with the code I could plot my data.
,

how can I change the legend name? instead of "factor(observation)"

thanks