Standardise an indicator against a non-degraded reference soil

Scores an indicator relative to the same indicator measured in an undisturbed reference soil, which takes the value 1 while degraded samples fall toward 0. This is the only documented escape from the comparability problem that makes published soil quality indices impossible to set beside one another.

Usage

standardize_to_reference(
  x,
  reference,
  direction = c("higher", "lower", "optimum"),
  tolerance = NULL,
  clamp = TRUE
)

Arguments

x: Numeric vector of indicator values.
reference: Single numeric value: the same indicator measured in the reference soil. For direction = "optimum" this is the optimal value rather than a measured reference.
direction: One of "higher" (the default), "lower" or "optimum".
tolerance: Required for direction = "optimum": the distance from the optimum at which the score reaches 0.
clamp: If TRUE (the default), scores are confined to [0,1] and a warning reports any sample that exceeded the reference.

Value

Numeric vector of scores, 1 at the reference and falling toward 0 with degradation.

Details

The problem it solves. Every other scoring function in this package – score_higher_better and its relatives – normalises against the sample's own extremes. That guarantees the best site in your data scores about 1 by construction, whether that site is pristine or merely the least ruined of a bad set. Two studies can report an SQI of 0.8 and mean entirely different soils. Standardising against a fixed external reference replaces "best in this data set" with "relative to undisturbed", which is a quantity that means the same thing in both studies.

The price, stated plainly. You need a defensible non-degraded reference soil: same soil type, same parent material, same climate, undisturbed. Kuzyakov et al. (2020) call this the approach's key disadvantage, and it is a real one – a fully converted agricultural landscape often has no such site left within reach. A badly chosen reference does not merely add noise, it silently rescales every index built on it. If you cannot defend the reference, the sample-relative functions are the more honest choice, and you say so in the methods.

The three directions.

"higher": More is better – organic matter, nutrients. The reference holds the maximum, and the score is x / reference.
"lower": Less is better – bulk density, compaction. The minimum belongs to the undisturbed soil, so the score inverts to reference / x.
"optimum": Neither extreme is good – pH, water and air permeability, hydrophobicity. Kuzyakov is explicit that these need the difference from the optimum, not a monotone scale, so the score is 1 - abs(x - reference) / tolerance with reference taken as the optimal value.

Scores above 1. A sample can beat the reference. That is not an error, and it is worth knowing about: it usually means the chosen reference is not actually the least disturbed soil available. With clamp = TRUE the score is capped at 1 and a warning names how many samples exceeded it. With clamp = FALSE the raw ratio is returned.

References

Kuzyakov, Y. et al. (2020). Frontiers of Agricultural Science and Engineering 7(3):282-288. doi:10.15302/J-FASE-2020338

Examples

# Organic matter against an undisturbed reference of 4.2%
standardize_to_reference(c(2.1, 3.0, 4.2), reference = 4.2)
#> [1] 0.5000000 0.7142857 1.0000000

# Bulk density: the reference holds the minimum, so the score inverts
standardize_to_reference(c(1.2, 1.4, 1.6), reference = 1.2,
                         direction = "lower")
#> [1] 1.0000000 0.8571429 0.7500000

# pH: distance from the optimum, not a monotone scale
standardize_to_reference(c(5.0, 6.5, 8.0), reference = 6.5,
                         direction = "optimum", tolerance = 1.5)
#> [1] 0 1 0