underwater.bioacoustics.weighting

Regulatory auditory weighting and exposure criteria for marine mammals.

Noise-exposure assessments weight a spectrum by a hearing-group filter before comparing it with a threshold. The filter is the same band-pass form in all current guidance (NMFS 2018 Equation 1, Southall et al. 2019 Equation 2):

$$W(f)=C+10{\log }_{10}\frac{(f/f_1{)}^{2a}}{[1+(f/f_1{)}^2{]}^a[1+(f/f_2{)}^2{]}^b}$$

with f in kilohertz. C is fixed by putting the peak of W at 0 dB, so the companion exposure function $E(f)=K-10{\log }_{10}(\dots )=K+C-W(f)$ has its minimum at the weighted threshold $T_w=K+C$. Only the parameter table changes between guidance versions, so the version is explicit in the API and is carried on every result object:

• "nmfs-2024" — NOAA Fisheries, Updated Technical Guidance, version 3.0 (October 2024), Table 5 and Table ES3. The default: it supersedes the 2018 revision, uses $b=5$ for every group, renames the groups to the Southall scheme (LF/HF/VHF cetaceans, PW/OW in water, PA/OA in air) and replaces “PTS onset” with “auditory injury (AUD INJ) onset”.
• "nmfs-2018" — the 2018 revision, version 2.0, Table 3 and Table ES3. Still cited by assessments already in flight.
• "southall-2019" — Southall et al., Aquatic Mammals 45(2), Tables 5, 6 and 7, the peer-reviewed criteria; adds sirenians (SI) and both in-air carnivore groups. Numerically identical to NMFS 2018 on the five shared groups.

Group names are not portable between versions. NMFS 2018 calls the mid-frequency cetaceans MF and the porpoise-type group HF; NMFS 2024 and Southall call the same two HF and VHF. Each guidance version only accepts its own codes.

The module exposes the weighting itself (auditory_weighting), the published thresholds (exposure_criteria) and the assessment chain (weighted_exposure), which weights a band spectrum, accumulates it over a number of events and reports the exceedance of each applicable criterion.

Implemented clean-room from the three documents; validated against the worked example of NMFS (2018) Appendix D ($W(1\text{kHz})$ for the five groups), against C recomputed as the peak of W for all three parameter sets, and against the published $T_w=K+C$ and injury = TTS + 20 dB identities.

Note

NMFS (2024) Table 5 prints $C=1.37$ dB for otariid pinnipeds in water, and its own footnote states the value should be 1.36 dB (NMFS kept 1.37 for consistency with the U.S. Navy). Recomputing C from the peak of W with that row’s parameters gives 1.3643 dB, confirming 1.36. This module implements 1.36; the printed 1.37 remains available as WeightingParameters.c_db_as_printed. See docs/ERRATA.md.

Auto-generated from the source docstrings by scripts/generate_api_docs.py (make api-docs). Do not edit by hand.

auditory_weighting

auditory_weighting(
    frequency_hz: NDArray[np.float64] | list[float] | float,
    group: str,
    *,
    guidance: str = 'nmfs-2024',
) -> AuditoryWeightingResult

Auditory weighting function W(f) of a marine-mammal hearing group.

Parameters

Name	Description
frequency_hz	Frequency or frequencies, in Hz (strictly positive).
group	Hearing-group code as used by guidance.
guidance	"nmfs-2024" (default, current), "nmfs-2018" or "southall-2019".

Returns: An AuditoryWeightingResult.

Raises

Exception	When
ValueError	If an input is invalid.

AuditoryWeightingResult

AuditoryWeightingResult(
    frequencies: NDArray[np.float64],
    weighting: NDArray[np.float64],
    exposure_function: NDArray[np.float64],
    parameters: WeightingParameters,
    guidance: str,
    group: str,
    weighted_tts_onset: float,
)

Auditory weighting and exposure functions of one hearing group.

Attributes

Name	Description
frequencies	Frequencies, in Hz.
weighting	Weighting-function amplitude W(f), in dB ($\le 0$).
exposure_function	Exposure function $E(f)=K+C-W(f)$, in dB (the frequency-dependent TTS-onset level).
parameters	The WeightingParameters used.
guidance	The guidance version.
group	Hearing-group code.
weighted_tts_onset	$T_w=K+C$, the minimum of the exposure function, in dB.

AuditoryWeightingResult.plot()

AuditoryWeightingResult.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot the weighting function versus frequency.

exposure_criteria

exposure_criteria(
    group: str,
    *,
    guidance: str = 'nmfs-2024',
    impulsive: bool = False,
) -> ExposureCriteria

Published TTS and injury onset criteria of a hearing group.

Parameters

Name	Description
group	Hearing-group code as used by guidance.
guidance	"nmfs-2024" (default), "nmfs-2018" or "southall-2019".
impulsive	Return the impulsive-noise criteria (dual metric: a weighted SEL and an unweighted peak SPL) instead of the non-impulsive ones.

Returns: An ExposureCriteria.

Raises

Exception	When
ValueError	If the version or the group is unknown.

ExposureCriteria

ExposureCriteria(
    group: str,
    guidance: str,
    impulsive: bool,
    tts_sel: float | None,
    injury_sel: float | None,
    tts_peak_spl: float | None,
    injury_peak_spl: float | None,
    injury_label: str,
    sel_reference: str,
    peak_reference: str,
    source: str,
)

Published TTS and injury (PTS / AUD INJ) onset criteria for one group.

Sound exposure levels are weighted; peak sound pressure levels are unweighted (“flat”), as every source states. None means the criterion is not published by that guidance version.

Attributes

Name	Description
group	Hearing-group code.
guidance	The guidance version.
impulsive	Whether these are the impulsive-noise criteria.
tts_sel	Weighted TTS-onset sound exposure level, in dB.
injury_sel	Weighted injury-onset (PTS / AUD INJ) SEL, in dB.
tts_peak_spl	Unweighted TTS-onset peak SPL, in dB.
injury_peak_spl	Unweighted injury-onset peak SPL, in dB.
injury_label	"PTS" or "AUD INJ", as the source names it.
sel_reference	Human-readable SEL reference of the group.
peak_reference	Human-readable peak-SPL reference of the group.
source	Table the numbers come from.

hearing_groups

hearing_groups(guidance: str = 'nmfs-2024') -> tuple[str, ...]

Hearing-group codes defined by a guidance version.

Parameters

Name	Description
guidance	One of WEIGHTING_GUIDANCE.

Returns: The group codes, in the order the source tabulates them.

Raises

Exception	When
ValueError	If the version is unknown.

weighted_exposure

weighted_exposure(
    frequency_hz: NDArray[np.float64] | list[float],
    band_sel: NDArray[np.float64] | list[float],
    group: str,
    *,
    guidance: str = 'nmfs-2024',
    impulsive: bool = True,
    n_events: int = 1,
    peak_spl: float | None = None,
) -> WeightedExposureResult

Weight a band spectrum, accumulate it and compare it with the criteria.

The per-band single-event sound exposure levels are weighted with auditory_weighting, summed on an energy basis and accumulated over n_events identical events ($+10{\log }_{10}N$, the ISO 18406 Formula 9 identity used by cumulative_sel_identical). The result is compared with the group’s TTS and injury onset criteria; the peak sound pressure level, if supplied, is compared unweighted, as the dual-metric rule requires.

Parameters

Name	Description
frequency_hz	Band centre frequencies, in Hz (1-D, positive).
band_sel	Per-band single-event SEL, in dB re 1 µPa²·s (or dB re (20 µPa)²·s for an in-air group); same length. -inf is accepted for a band that carries no energy, which is what strike_sel_spectrum returns for bands narrower than its FFT bin spacing; such a band adds nothing to the energy sum. Both input arrays are copied, so the result never aliases the caller’s data.
group	Hearing-group code as used by guidance.
guidance	"nmfs-2024" (default), "nmfs-2018" or "southall-2019".
impulsive	Compare against the impulsive criteria (the default, the case for pile driving and air guns).
n_events	Number of identical accumulated events, $\ge 1$.
peak_spl	Unweighted zero-to-peak sound pressure level of the loudest single event, in dB; enables the peak-SPL half of the dual metric.

Returns: A WeightedExposureResult.

Raises

Exception	When
ValueError	If an input is invalid.

WeightedExposureResult

WeightedExposureResult(
    frequencies: NDArray[np.float64],
    band_sel: NDArray[np.float64],
    weighting: NDArray[np.float64],
    weighted_band_sel: NDArray[np.float64],
    unweighted_sel: float,
    weighted_sel: float,
    cumulative_sel: float,
    peak_spl: float | None,
    n_events: int,
    criteria: ExposureCriteria,
    sel_margin: float | None,
    tts_margin: float | None,
    peak_margin: float | None,
    tts_peak_margin: float | None,
    exceeds_injury: bool,
    exceeds_tts: bool,
    guidance: str,
    group: str,
)

Weighted exposure of a spectrum against a hearing group’s criteria.

Attributes

Name	Description
frequencies	Band centre frequencies, in Hz.
band_sel	Per-band single-event sound exposure level, in dB.
weighting	Weighting-function amplitude at each band, in dB.
weighted_band_sel	band_sel + W(f) per band, in dB.
unweighted_sel	Energy sum of band_sel, in dB.
weighted_sel	Energy sum of weighted_band_sel, in dB.
cumulative_sel	weighted_sel plus $10{\log }_{10}(N)$ for the n_events accumulated events, in dB.
peak_spl	The unweighted peak sound pressure level supplied, in dB (None when not given).
n_events	Number of accumulated events (e.g. hammer strikes).
criteria	The ExposureCriteria compared against.
sel_margin	cumulative_sel - injury_sel, in dB (None when the criterion is not published); positive means the criterion is exceeded.
tts_margin	cumulative_sel - tts_sel, in dB (or None).
peak_margin	peak_spl - injury_peak_spl, in dB (or None).
tts_peak_margin	peak_spl - tts_peak_spl, in dB (or None) — the peak-SPL half of the dual metric on the TTS side, which can trip exceeds_tts on its own.
exceeds_injury	Whether any injury-onset criterion is reached. The test is margin >= 0, so an exposure landing exactly on the criterion counts as exceeding it; the criteria are onset thresholds and the precautionary reading is the one an assessment wants.
exceeds_tts	Whether any TTS-onset criterion is reached, on the same margin >= 0 convention as exceeds_injury.
guidance	The guidance version.
group	Hearing-group code.

WeightedExposureResult.plot()

WeightedExposureResult.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot the unweighted and weighted band spectra with the criteria.

WEIGHTING_GUIDANCE

Constant (tuple).

WEIGHTING_GUIDANCE = ('nmfs-2024', 'nmfs-2018', 'southall-2019')

weighting_parameters

weighting_parameters(
    group: str,
    *,
    guidance: str = 'nmfs-2024',
) -> WeightingParameters

Weighting/exposure parameters of one hearing group.

Parameters

Name	Description
group	Hearing-group code as used by guidance (case-insensitive).
guidance	One of WEIGHTING_GUIDANCE.

Returns: The WeightingParameters row.

Raises

Exception	When
ValueError	If the version or the group is unknown.

WeightingParameters

WeightingParameters(
    group: str,
    guidance: str,
    description: str,
    a: float,
    b: float,
    f1_khz: float,
    f2_khz: float,
    c_db: float,
    c_db_as_printed: float,
    k_db: float,
    in_air: bool,
    hearing_range_hz: tuple[float, float] | None,
)

Auditory weighting and exposure function parameters for one group.

Attributes

Name	Description
group	Hearing-group code as used by its own guidance version.
guidance	The guidance version the row comes from.
description	Plain-language name of the hearing group.
a	Low-frequency exponent a.
b	High-frequency exponent b.
f1_khz	Low-frequency transition f1, in kHz.
f2_khz	High-frequency transition f2, in kHz.
c_db	Gain C that puts the peak of W at 0 dB, in dB.
c_db_as_printed	C exactly as printed in the source table, in dB (differs from c_db only for the NMFS 2024 otariid row).
k_db	Exposure-function constant K, in dB.
in_air	Whether the group’s reference is 20 µPa (in air).
hearing_range_hz	Generalised hearing range of the group, in Hz, or None. Only the NMFS documents tabulate one (their Table ES1); Southall et al. do not, and the field is None for those rows rather than borrowed from elsewhere.