shows calculations for organic matter as mass/mass or volume/volume using a 1 square meter section to a 2 cm depth as an example

om_mass_volume.R

## OM246 on a volume basis
## starting thought: what is 5% OM by mass on a volume basis?

library(ggplot2)
library(cowplot)

## assign bulk densities; these don't vary, nor does compressibility
bd_sand <- 1.56
bd_om <- 0.22

## calculates bulk density of a mixed material
## given the measured OM value on a mass basis
bulk_density <- function(om) {
    bd <- 100 / ((om / bd_om) + ((100 - om) / bd_sand))
    return(bd)
}

## simulate data with OM to 2 cm depth from 0 to 100%
d <- data.frame(om2 = seq(0, 100, 1))

d$bd2 <- bulk_density(d$om2)

### I calculate this on a square meter basis
### This is the mass of a soil layer to 2 cm depth
### and 100 by 100 cm
d$mass2 <- d$bd2 * 2 * 100 * 100

## This is the OM on a mass basis
d$om2mass <- d$om2 / 100 * d$mass2

## The volume of that mass of OM
d$vol <- d$om2mass / bd_om

## OM mass as a percent of soil mass
d$mass_percent <- d$om2mass / d$mass2 * 100

## OM volume as a percent of soil volume
d$vol_percent <- d$vol / (2 * 100 * 100) * 100

## make a chart
p <- ggplot(data = d,
            aes(x = mass_percent,
                y = vol_percent))
yo <- p + theme_cowplot(font_family = "Roboto Condensed") +
  background_grid() +
  geom_line(colour = "#002b36") +
    scale_y_continuous(breaks = seq(0, 100, 10),
                       expand = expansion(mult = c(0, 0.05))) +
    scale_x_continuous(breaks = seq(0, 100, 2),
                       limits = c(0, 20),
                       expand = expansion(mult = c(0, 0.05))) +
    labs(x = "Organic material by mass %",
         y = "Organic material by volume %",
         caption = expression(paste("Calculated for a bulk density of 1.56 g/",
                                    cm^{3},
                                    " for sand and 0.22 g/",
                                    cm^{3},
                                    " for organic material.")),
         title = "Calculated conversions between soil organic material by mass & by volume") +
    theme(plot.caption = element_text(size = 8)) +
    annotate("segment",
             x = 5,
             xend = 5,
             y = 0,
             yend = 26.5,
             colour = "#cb4b16",
             size = 0.5,
             arrow=arrow(type = 'closed',
                         length = unit(0.3, 'cm'))) +
    annotate("label",
             colour = "#cb4b16",
             fill = "#eee8d5",
             x = 5.25,
             y = 13,
             hjust = 0,
             family = "Roboto Condensed",
             label = "When the OM by mass is 5%,\nthe OM by volume is 27%.") +
     annotate("label",
             colour = "#cb4b16",
             fill = "#eee8d5",
             x = 2,
             y = 55,
             hjust = 0,
             family = "Roboto Condensed",
             label = "The standard reporting units for soil\norganic material on soil tests is mass.\nThat is, the mass of organic material\nper mass of soil. Here's what it works out\nto in volume.") +
     annotate("segment",
             x = 12.5,
             xend = 12.5,
             y = 0,
             yend = 50,
             colour = "#859900",
             size = 0.5,
             arrow=arrow(type = 'closed',
                         length = unit(0.3, 'cm'))) +
     annotate("label",
             colour = "#859900",
             fill = "#eee8d5",
             x = 13,
             y = 45,
             hjust = 0,
             family = "Roboto Condensed",
             label = "When the OM by mass is 12.5%,\nOM by volume is 50%.")

yo