Analyte normalisation: bioavailability adjustments in hydroSense • hydroSense

Overview

The ANZG freshwater toxicant guideline values are derived at a specific index water-chemistry condition. When ambient water chemistry differs from that condition, the guideline — and therefore the effective toxicity — changes. hydroSense adjusts measured concentrations to index-condition equivalents before computing PAF values so that all samples are compared on the same basis.

The adjustment is:

$C_\text{norm} = C_\text{field} \times \frac{\text{EC10}_\text{index}}{\text{EC10}_\text{field}}$

This normalised concentration is what enters the SSD lookup. A value of $C_\text{norm} > C_\text{field}$ means the measured concentration is more toxic at site conditions than the same concentration would be at index conditions; $C_\text{norm} < C_\text{field}$ means it is less toxic.

Normalisation formulas are stored in the bundled analyte metadata CSV (inst/extdata/anzecc_analyte_metadata.csv). You can inspect or override them by supplying your own CSV via the analyte_metadata argument to prepare_reference() and add_mspaf().

Implemented normalisations

Ammonia-N (NH₃-N)

Source: ANZG (2021) ammonia freshwater DGV technical brief. Index condition: pH 7.0, temperature 20 °C. Required co-analytes: pH, temperature (°C).

NH₃-N toxicity is driven by the un-ionised fraction, which increases sharply with pH and temperature. The normalisation converts field total ammonia-N to the equivalent concentration at the index condition using the ionisation equilibrium:

$f_\text{un}(\text{pH}, T) = \frac{1}{1 + 10^{\,pK_a(T) - \text{pH}}}$

where $pK_a(T) = 0.09018 + 2729.92 / (T + 273.15)$ .

Water temperature must be supplied as analyte = "temperature" rows in your chemistry data frame. Use estimate_water_temp() if only air temperature records are available.

Cadmium (Cd)

Source: ANZECC & ARMCANZ (2000) Table 3.4.1 hardness correction. Index condition: hardness 30 mg/L CaCO₃. Required co-analyte: hardness (mg/L CaCO₃).

$C_\text{norm} = C \times \left(\frac{30}{\text{hardness}}\right)^{0.8}$

Lead (Pb)

Source: ANZECC & ARMCANZ (2000) Table 3.4.1 hardness correction. Index condition: hardness 30 mg/L CaCO₃. Required co-analyte: hardness (mg/L CaCO₃).

$C_\text{norm} = C \times \left(\frac{30}{\text{hardness}}\right)^{1.0}$

Copper (Cu)

Source: ANZG (2024) copper freshwater DGV draft technical brief, Figure 3. Index condition: DOC 0.5 mg/L. Required co-analyte: DOC (mg/L).

$C_\text{norm} = C \times \left(\frac{0.5}{\text{DOC}}\right)^{0.977}$

DOC is clamped to [0.5, 30] mg/L before applying the formula:

Upper cap (30 mg/L): the formula is not validated above 30 mg/L DOC; use the DGV at 30 mg/L in those cases and consider site-specific assessment.
Lower cap (0.5 mg/L): below the index condition DOC, the formula extrapolates into an unvalidated range; the cap prevents an unbounded upward correction.

Nickel (Ni)

Source: ANZG (2024) nickel freshwater DGV draft technical brief; invertebrate-trophic-level MLR from Peters et al. (2021). Index condition: pH 7.5, Ca 6 mg/L, Mg 4 mg/L, DOC 0.5 mg/L. Required co-analytes: pH, DOC, Ca, Mg (all in mg/L for Ca and Mg). Valid range: pH 6.0–8.5, Ca 2–70 mg/L, Mg 1.6–54 mg/L, DOC 0.5–20 mg/L.

The Peters et al. (2021) MLR for invertebrates:

$\log_e(\text{EC10}) = S + 2.09\log_e[\text{DOC}] + 0.19\log_e[\text{Ca}] + 0.40\log_e[\text{Mg}] - 0.40\,\text{pH} - 0.24\log_e[\text{DOC}]\cdot\text{pH}$

The sensitivity coefficient $S$ cancels in the field-to-index ratio, so:

$C_\text{norm} = C \times \exp\!\Big(\text{MLR}(\text{index}) - \text{MLR}(\text{field})\Big)$

Important limitation: The ANZG Ni DGVs were derived using trophic-level-specific MLRs for algae, aquatic plants, invertebrates and fish applied to all species in the SSD. The invertebrate MLR used here is the most appropriate single model for macroinvertebrate-focused assessment, but it will not exactly reproduce the published lookup-table DGVs, which are based on a full multi-trophic SSD re-derivation at each water chemistry combination. Users whose assessments span a full range of trophic levels may wish to supply a geometric-mean correction across all four MLRs via a custom analyte metadata CSV.

Zinc (Zn)

Source: ANZG (2024) zinc freshwater DGV draft technical brief; Daphnia magna (Arthropoda / crustacean) MLR from Gadd et al. (in prep.). Index condition: pH 7.5, hardness 30 mg/L CaCO₃, DOC 0.5 mg/L. Required co-analytes: pH, hardness (mg/L CaCO₃), DOC (mg/L). Valid range: pH 6.2–8.3, hardness 20–440 mg/L CaCO₃, DOC 0.5–15 mg/L.

The D. magna MLR:

$\log_e(\text{EC10}) = S - 0.52\,\text{pH} + 0.31\log_e[\text{hardness}] - 1.4\log_e[\text{DOC}] + 0.24\log_e[\text{DOC}]\cdot\text{pH}$

Note that lower pH → higher Zn DGV (Zn is less bioavailable at low pH because H⁺ competes with Zn²⁺ at biotic ligands). pH and DOC are clamped to the published valid range before applying the formula.

Limitation — accuracy degrades above pH 8: The published Zn DGVs were derived by applying all four trophic-level MLRs to 31 species and re-fitting the SSD at each water chemistry combination. The D. magna model alone gives a reasonable approximation at low to neutral pH (within ~15% of the lookup-table DGV), but diverges substantially at high pH. At pH 8.3, the Daphnia-model-derived DGV is approximately 2.4 µg/L versus the published 1.0 µg/L, because the highly sensitive Chlorella sp. (PNG isolate, EC10 = 0.91 µg/L at index) and Raphidocelis subcapitata have stronger negative pH coefficients and dominate the lower tail of the SSD at alkaline pH. The practical consequence: for high-pH receiving waters (> 8.0), this formula will underestimate Zn toxicity and should be treated with caution. Users assessing alkaline sites should consider supplying a geometric-mean correction across all four trophic-level MLRs via a custom analyte metadata CSV.

Analytes not yet normalised

The following metals have chemistry-dependent toxicity but normalisation formulas have not yet been added to the bundled metadata:

Analyte	Reason
Al	pH-dependent; ANZECC 2000 equation requires total and dissolved fractions
Cr(III)	Hardness correction exists but species data are limited

Summary table

Analyte	Model	Co-analytes	Valid range
NH₃-N	ANZG (2021) ionisation equilibrium	pH, temperature (°C)	—
Cd	ANZECC 2000 hardness	hardness	—
Pb	ANZECC 2000 hardness	hardness	—
Cu	ANZG (2024) DOC power law	DOC	DOC 0.5–30 mg/L
Ni	Peters et al. (2021) invertebrate MLR	pH, DOC, Ca, Mg	pH 6.0–8.5; Ca 2–70; Mg 1.6–54; DOC 0.5–20 mg/L
Zn	Gadd et al. (in prep.) D. magna MLR	pH, hardness, DOC	pH 6.2–8.3; H 20–440 mg/L CaCO₃; DOC 0.5–15 mg/L

Providing custom normalisation formulas

To override any formula — or add normalisation for analytes not listed above — supply your own metadata CSV via the analyte_metadata argument:

add_mspaf(
  chemistry_df,
  reference      = prep_ref,
  analyte_metadata = "path/to/my_metadata.csv"
)

The CSV must contain at least the columns name.analyte, normalisation_formula, and coanalytes_required. Rows absent from your CSV fall back to the bundled metadata. The normalisation_formula column holds a plain R expression with C as the measured concentration and co-analyte names as free variables. For example:

normalisation_formula = "C * (0.5 / pmin(pmax(DOC, 0.5), 30))^0.977"
coanalytes_required   = "DOC"