Detecting leachate with the Leachate Mixing Fraction (LMF)

What the LMF answers

add_lmf() asks a single question of each water sample:

What fraction of this sample’s chemistry can be explained as a mixture of local reference water and landfill leachate?

The answer — the leachate mixing fraction (LMF) — is reported as a percentage: 0 means the sample is chemically indistinguishable from local reference water, 100 means it matches the leachate end-member. It is a source-detection index, deliberately separate from toxicity: a sample can carry a clear leachate signature (high LMF) while still being well below guideline values, and vice versa.

LMF is built on the classic two-component end-member mixing model used in catchment hydrochemistry (Christophersen & Hooper, 1992). Leachate-impacted freshwater is treated as a blend of two sources, and the major-ion signature is used to estimate the blend ratio.

The method in brief

For each sample, add_lmf():

Converts to milliequivalents. Concentrations are converted to meq/L with [to_meq()] so that ions combine on a charge-equivalent basis. Transforming species are collapsed to conserved totals — the nitrogen species (NH₃-N, NO₃-N, NO₂-N) to total N, and the carbonate species to total alkalinity — so that redox or speciation shifts between source and sample do not break the mixing assumption.
Builds two end-members. The reference end-member is the mean and standard deviation of each ion in local background water. The leachate end-member is anchored to chloride (a conservative tracer) and expressed as Cl-scaled ratios.
Computes a per-ion mixing fraction for each measured ion i: $f_i = \frac{x_i - R_i}{L_i - R_i}$ where $x_i$ is the sample, $R_i$ the reference, and $L_i$ the leachate end-member.
Combines the ions into one estimate by an inverse-variance weighted mean, so ions measured precisely and with a large leachate–reference gradient count for more. An informativeness screen (the reference scatter relative to the leachate–reference gap) admits a sample only if enough high-information ions are present.
Down-weights disagreeing ions with a robust (Huber) reweighting pass, so a single ion behaving non-conservatively (sulfate reduction, an extra source) does not drag the estimate. A χ² diagnostic flags overall ion disagreement.

A worked example

The package ships a small synthetic dataset, leachate_demo, with three sites: an impacted downstream site, a clean reference site, and the leachate end-member. (It is fictional — generated from a mixing model so the example is reproducible.)

demo <- leachate_demo()
unique(demo$site_id)
#> [1] "downstream" "reference"  "leachate"
head(subset(demo, site_id == "downstream"), 4)
#>   sample_id    site_id   datetime analyte    value detected units.analyte
#> 1     DS-01 downstream 2024-01-15      Na 149.4775     TRUE          mg/L
#> 2     DS-01 downstream 2024-01-15       K  29.9655     TRUE          mg/L
#> 3     DS-01 downstream 2024-01-15      Ca  75.4548     TRUE          mg/L
#> 4     DS-01 downstream 2024-01-15      Mg  25.9333     TRUE          mg/L
#>   valence.analyte atomic_mass.analyte
#> 1               1               22.99
#> 2               1               39.10
#> 3               2               40.08
#> 4               2               24.31

Supplying the leachate and reference chemistry directly uses the caller-provided end-member path (no site-matching infrastructure required):

out <- add_lmf(
  df             = subset(demo, site_id == "downstream"),
  leachate_data  = subset(demo, site_id == "leachate"),
  reference_data = subset(demo, site_id == "reference")
)

lmf <- subset(out, analyte == "LMF",
              c("sample_id", "value", "sigma_lmf", "n_ions_used", "chi2_per_df"))
lmf
#> # A tibble: 6 × 5
#>   sample_id value sigma_lmf n_ions_used chi2_per_df
#>   <chr>     <dbl>     <dbl>       <int>       <dbl>
#> 1 DS-01      14.9     0.472           8       0.163
#> 2 DS-02      14.7     0.467           8       0.208
#> 3 DS-03      14.7     0.465           8       0.155
#> 4 DS-04      15.1     0.476           8       0.129
#> 5 DS-05      14.6     0.463           8       0.201
#> 6 DS-06      14.9     0.471           8       0.268

The downstream samples return an LMF of about 15% — consistent with how the demo data were constructed (a 15% leachate blend). sigma_lmf is the uncertainty on the estimate (percentage points), n_ions_used the number of ions that contributed, and chi2_per_df the ion-agreement diagnostic (values near 1 indicate the ions tell a consistent mixing story).

Interpreting the result

LMF is a continuous index: the raw percentage is the primary output. The following tier breaks are a suggested starting point for interpretation:

Tier	LMF (%)	Suggested interpretation
1	≤ 1	Background — indistinguishable from local reference
2	1–5	Trace impact — detectable signature, monitor trend
3	5–20	Significant impact — clear signature, investigate
4	> 20	Severe impact — urgent investigation

Note: These breaks are starting points, not regulatory thresholds. Classification decisions should be made by the reporting system or analyst, not imposed automatically. The tier 1/2 boundary in particular should be reviewed against the LMF distribution of your own reference samples after deployment — ideally it should sit near the 95th percentile of LMF on known-clean water.

When LMF returns `NA`

A sample is not scored (its lmf_reason explains why) when it lacks enough high-information ions, when the estimate is too imprecise (sigma_lmf above the max_sigma_lsi threshold), or when no ion has a usable leachate–reference gradient. These are honest non-answers: the major-ion panel measured at that sample simply cannot distinguish the two sources.

References