1: Question being asked
How do ion and isotope concentrations vary spatially? And what trends in concentrations account for variability between my samples?
For detailed background information, I point you towards my problem statement for this class. In short, I’m hoping to use geochemical and isotope values for wells 32 well I sampled last summer in order to better understand how groundwater flows across faults in the Walla Walla Subbasin in northeastern Oregon. In the analysis for this post, I only used a subset of 18 wells for which I had the largest suite of measured parameters.
2: Approach used
For this exercise, I’m investigating spatial patterns of my ion and isotope concentrations. I could do this by individually examining distributions of all 19 of the parameters that I sampled for… but that would be graphically overwhelming and not terribly useful. It’s too difficult to draw conclusions by comparing 19 different maps of distributions. Instead, I’m using a method called principal component analysis (PCA for short) to statistically evaluate my samples by the groups of parameters that account for large amounts of the variation that differentiates one sample from another.
The nuts and bolts of PCA involve sophisticated analysis that calculates eigenvectors, linear algebra, and n-dimensional properties of a data set, and I will let people more knowledgeable than me explain this if you’re curious about how exactly PCA works.
R spits out two kinds of useful graphic output for PCA based on the concept of a “biplot”. The first is called a loading plot, where two principal components are graphed against each other, for example PC1 and PC2. The value for each parameter in PC1 and PC2 is used to give the point a cartesian coordinate which defines a vector in comparison to the origin. The second kind of output is called a scree plot, which applies the same concept to the sample points (called “individuals” in the code) instead of to the parameters (called “variables” in the code). I used an R package called ggbiplot to combined the scree and loading plots in one figure.
I used R to calculate the principal component vectors for my data and to create charts for them, and then symbolized my data in ArcGIS Pro to see if there was a spatial pattern to the information in the PCA output. The code in R is fairly manageable. I’ve included it below with my comments.
# Preliminary set up stuff – add libraries, set working directory
setwd(“~/_Oregon State University/Thesis/Summer Fieldwork/PCA”)
# Before importing your data, make sure that every entry in its table has a numeric entry in it.
# This process will spit out garbage if you have any blank cells or text.
# The number of rows in the data set needs to exceed the number of columns. I used an argument like [,c(1:11)] to enforce this in my data
#Process 1 of 2: read data set 1 into R, view it, compute PCA, display summaries and biplots
# it’s important to set the row names so we can use them as labels in ggbiplot
PCAdata.ions2 <- read.csv(“ions_allchem20190401_usgsdwnld.csv”, row.names = 1)
Ions2.pca <- prcomp(PCAdata.ions2[,c(1:11)], center = TRUE, scale. = TRUE)
ggbiplot(Ions2.pca, choices=c(1,2), labels=rownames(PCAdata.ions2))
ggbiplot(Ions2.pca, choices=c(1,3), labels=rownames(PCAdata.ions2))
#read data set 2 into R, view it, compute PCA, display summaries and biplots
PCAdata.nonions <-read.csv(“NonIons_allchem20190401_usgsdwnld.csv”, row.names = 1)
NonIons.pca <- prcomp(PCAdata.nonions[,c(1:8)],center = TRUE, scale. = TRUE)
ggbiplot(NonIons.pca, choices=c(1,3), labels=rownames(PCAdata.nonions))
# if you want plots other than PC1 vs PC2 or PC1 vs PC3 just change the argument “choices = (1,2)”
# Process 2 of 2 add tools to get individual coordinates
# only install the package if you haven’t before. You will need to have RTools 3.5 already installed
# now run things, it will spit out tab-delimited data. The “ind” command outputs PC information for the individuals, and the “var” command outputs the PC information for the variables.
ind <- get_pca_ind(Ions2.pca)
ind2 <- get_pca_ind(NonIons.pca)
# copy that info into text files, import them into csv format, join in Arc!
var1 <- get_pca_var(Ions2.pca)
Next, I symbolized my data in ArcGIS Pro. Because I only had 18 samples, it wasn’t too onerous to use selection in the attribute table to export data to another layer to symbolize the groups I saw in the principle component analysis biplot.
To examine how the principle components affected individual points, I used the second process in the above code to generate a tab-delimited chart of the principal component loadings for each sample. I copied this into a .txt file, imported it into Excel to create a CSV, and then joined that CSV to my shapefile of well locations. For the variables’ coordinates, I likewise created .txt files and imported the into Excel, but I symbolized them in Excel.
In this section, I’ll show the graphs and maps that I created for the ion section of my data, and give an explanation of what I learned from this analysis.
For my ion data, the first two out of the 11 principle components explain about 80% of the variation in my data.
The first one, PCI, explains 55% of the variation in my data set and is shown on the X axis of the graph below. It is strongly influenced by concentrations of calcium, magnesium, chloride, alkalinity, sulfate, bromide, and sodium, which all have eigenvalues on the X axis greater than |1|. Comparing the scree plot to the loading plot, wells 56287, 3074, 4179, and 4167 are the primary individual drivers of this PC.
PC2 explains another 25% of the variance in my data, and is shown on the Y axis. Fluoride, silicon, and manganese are the primary variable drivers of variation between the individuals in PC2.
Based on the coordinate information for the variables, the variation explained by PC1 is due to increased levels of calcium, magnesium, potassium, sodium, alkalinity, bromide, chloride, and sulfate at four wells. This combination of ions all being similar could be explained by recent recharge influenced by agricultural chemicals, such as fertilizers. In an undisturbed basalt setting though time, calcium and magnesium tend to decrease as sodium and potassium increase. The fact the these four parameters vary together in PCI indicates that a process other than ion replacement is driving ion concentration. The variation in PC2 is predominantly explained by fluoride, dissolved silica, and manganese. Elevated concentrations of these three variables in comparison to the other variables indicates that the groundwater has spent more time in the basalt.In PC2, calcium and magnesium are inversely related to sodium, indicating that the cation concentrations are driven by the ion replacement process.
While the figure above locates wells based on their grouping on a biplot comparing two principle components, the following figures show the wells color-coded by their loadings in PC1 and in PC2. I’m hypothesizing that wells with smaller PC1 values are influenced by agricultural recharge, and wells with more positive values on PC2 are more influenced by the processes of ion dissolution as water travels through the basalt.
PC1 is heavily driven by four particular wells, which show up here as being in colors of blue and blue-grey.
The distribution of PC2 values shows a pattern that I find really interesting. More negative – bluer – values indicate samples which were less influenced by the ion replacement and dissolution processes of groundwater traveling through the basalt. The values at high elevation are negative, which makes sense because they’re closer to the upland recharge zone, but so do some samples in the lowlands to the north which are downgradient of certain faults. This could indicate that those PC2 negative downgradient wells are cut off from the longer flowpaths of groundwater by faults that act as barriers to groundwater flow. The pinker – more positive – points indicate samples that were more influenced by the along-flowpath ion reactions.
Next, I present the PCA results for the non-ion parameters. Unlike the “ions” set whose title was somewhat self-explanatory, this PCA brought together different types of chemical and physical properties of water. These include pH, temperature, and specific conductivity which were measured in the field, the analyzed values of hydrogen and oxygen isotopes as well as tritium, the elevation of the bottom of the well, and the cation ratio. The cation ratio is a standard calculated parameter for groundwater chemistry which is equal to ([Na] + [K]) / ([Ca] + [Mg]). As water spends more time in contact with the rock, its ion exchange with the rock leads to a smaller cation ratio. The first biplot graphs PC1 (~40% of variation) on the X axis against PC2 (22% of variation) on the Y axis, and the second biplot graphs PC1 on the X axis versus PC3 (~18% of variation) on the Y axis.
The PC1 grouping explains variance among the samples by inversely correlating tritium, deuterium (d2H) and oxygen-18 (d18O) with pH and the cation ratio. More positive PC1 values show that the individual has high d18O and d2H values, and low cation ratio and pH values. All d18O and d2H values are negative; values that are closer to 0 (“larger: for the purposes of this plot) are more enriched in the heavier isotope. PC2 is predominantly driven by an inverse correlation between well bottom elevation and temperature. PC3 inversely correlates tritium, specific conductance, and well bottom elevation with temperature, deuterium, and 18-oxygen.
Yellow/orange points on this map have more positive PC1 loadings. They have higher d18O and d2H values, and lower cation ratio and pH values. The lower cation ratio and pH values indicate that the sample is less chemically evolved based on the expected ion exchange reactions in the basalt. I found it interested that samples on that end of the spectrum were also more enriched in the heavier isotopes of hydrogen and oxygen.
Unfortunately I can’t seem to upload the maps for PC2 and PC3 for non-ions, I’m getting a message that all of my allowance for image uploads has been used up…
I’m pretty happy with what I put together using principal component analysis. In a perfect world I would have learned to do the spatial visualization elegantly in R instead of messing around with exporting data to Arc, and made my variable charts in R instead of exporting them to excel. However for the purposes of this project the less elegant method was quicker for me.