I'd like to add something to the discussion of soil color description, the Munsell system in general, and how one could simulate a reasonable estimate of color mixtures.
The genius of the Munsell system is that it provides a quantitative (numeric) description of color that is approximately linear in terms of average human perception, and, conveniently isolates the independent qualities of color into hue, value, and chroma. Moving from one chip to the next represents a linear traversal through a continuous, 3D (hue, value, chroma) color space. The presentation (soil color book) and notation (e.g. 10YR 3/3) that we are familiar with is based on a discretization of that space into perceptually-compact units (the color chips) that offers sufficient contrast for field identification without an overwhelming number of possibilities. For example, our ability to perceive contrast in lightness (Munsell value) is roughly 2-4x greater than our ability to perceive contrast in chroma: hence the lack of chips representing /5, /7, /9, etc..
Given that the Munsell system is quantitative and roughly linear in terms of human color perception, it is entirely possible to:
* treat value and chroma as numeric entities
* interpolate between chips (hue, value, or chroma)
* simulate mixtures of two or more colors in Munsell notation
I'd recommend SSSA special publication #31, any book on color science, or this website for an in-depth description of the Munsell system: http://www.applepainter.com/. In fact, our definition of "soil color contrast" is based on the quantitative, linear nature of the Munsell system: https://www.nrcs.usda.gov/wps/portal/nrcs/detail/soils/ref/?cid=nrcs142p2_053569.
An accurate simulation of pigment mixtures ("subtractive" color mixtures) is incredibly complex due to the factors that aren't easily measured or controlled: pigment solubility, pigment particle size distribution, water content, substrate composition, and physical obstruction to name a few. That said, it is possible to simulate reasonable, subtractive color mixtures given a reference spectra library (350-800nm) and some assumptions about pigment qualities and lighting. For the purposes of estimating a mixture of soil colors (these are pigments after all) we can relax these assumptions and assume a standard light source. The only missing piece is the spectral library for all Munsell chips in our color books.
Thankfully, Scott Burns has outlined the entire process in this document (https://arxiv.org/ftp/arxiv/papers/1710/1710.06364.pdf), and Paul Centore has provided a Munsell color chip reflectance spectra library (http://www.munsellcolourscienceforpainters.com/). The estimation of a subtractive mixture of soil colors can proceed as follows:
1. lookup the associated spectra for each color
2. computed the weighted (area proportion) geometric mean of the spectra
3. search for the closest matching spectra in the reference library
4. suggest that Munsell chip as the best candidate for the simulated mixture
Key assumptions include: 1) similar particle size distribution, 2) similar mineralogy (i.e. pigmentation qualities), and 3) similar water content. For the purposes of estimating a mixed soil color within the top 18cm these assumptions are usually valid. Again, these are estimates that are ultimately "snapped" to the nearest chip and not higher precision descriptions of soil color than the original field-observed colors.
This process is fully implemented in the "aqp" package for R, with specific examples listed here: https://ncss-tech.github.io/AQP/aqp/mix-colors.html
See the attached figure for a visual description of the spectral-mixing of 50% 5YR 2/2 and 50% 10YR 4/4.
Dylan E. Beaudette
Soil Scientist
National Soil Survey Center
USDA-NRCS
209.591.5180
