TS-Length Inversion

TS-Length Inversion#

echopop.inversion.ts_length_regression(length: ndarray | float, slope: float, intercept: float) → ndarray#

Convert length values into acoustic target strength (TS, dB re. 1 \(\text{m}^{-2}\)).

Parameters:
lengthUnion[np.ndarray, float]

Length value(s) typically represented in ‘cm’ that will be converted into acoustic target strength (TS, dB re. 1 \(\\text{m}^{-2}\)).

slopefloat

TS-length regression slope coefficient

interceptfloat

TS-length regression intercept coefficient

Returns:
np.ndarray

Target strength values in dB re. 1 \(\\text{m}^{-2}\)

Notes

The TS-length relationship follows the standard log-linear form:

\[\begin{split}\\text{TS} = \\beta_1 \\times \\log_{10}(L) + \\beta_0\end{split}\]

where \(L\) is the length, \(\\beta_1\) is the slope, and \(\\beta_0\) is the \(y\)-intercept. This is commonly used in fisheries acoustics where the relationship between fish length and acoustic backscatter follows this logarithmic pattern.

Examples

Single length

>>> ts = ts_length_regression(20.0, slope=20.0, intercept=-68.0)
>>> print(f"TS for 20cm fish: {ts:.2f} dB")
TS for 20cm fish: -42.00 dB

Multiple lengths

>>> # Multiple length values
>>> lengths = np.array([10, 15, 20, 25, 30])
>>> ts_values = ts_length_regression(lengths, slope=20.0, intercept=-68.0)
>>> print("Lengths:", lengths)
>>> print("TS values:", ts_values)
Lengths: [10 15 20 25 30]
TS values: [-48.   -44.77 -42.   -39.82 -38.   ]
class echopop.inversion.InversionLengthTS(model_parameters: dict[str, Any])#

Perform acoustic inversion using a log-linear length–TS relationship.

This class implements acoustic inversion by relating fish length to acoustic backscatter through empirical TS-length relationships. It calculates stratified mean backscattering cross-sections and converts \(S_\\text{A}\) (vertically integrated backscatter) to estimates of number density.

Parameters:
model_parametersDict[str, Any]

Dictionary containing model configuration. Required keys:

  • 'ts_length_regression': Dictionary with 'slope' and 'intercept' for the TS-length regression equation.

  • 'stratify_by': str or List[str] - stratification columns (e.g., 'stratum_number')

Optional keys:

  • 'expected_strata': An array of specific strata to expect in the data

  • 'impute_missing_strata': A boolean argument that elects whether or not to impute missing strata values

  • 'haul_replicates': A boolean argument that elects whether or not to use haul numbers/ids as replicates instead of individuals to account for pseudoreplication.

Attributes:
sigma_bs_haulpandas.DataFrame or None

Haul-level backscattering cross-sections

sigma_bs_stratapandas.DataFrame or None

Stratum-level backscattering cross-sections

Methods

get_stratified_sigma_bs(length_data[, ...])

Calculate stratified mean backscattering cross-sections (sigma_bs) by stratum.

invert(nasc_data, length_data)

Invert NASC data to number density using the TS-length regression.

set_haul_sigma_bs(length_data)

Compute the mean linear scattering coefficient (sigma_bs) for each haul.

Notes

The inversion process follows these steps:

  1. Quantize length data and compute TS using the regression equation

  2. Convert TS to linear backscattering cross-section (\(\\sigma_\\text{bs}\))

  3. Calculate stratified mean sigma_bs values

  4. Impute missing strata if specified

  5. Convert vertically integrated backscatter to number density where:

\[\begin{split}\\rho_\\text{v} = \\frac{S_\\text{A}}{4\\pi \\times \\sigma_\\text{bs}}\end{split}\]

where \(\\rho_\\text{v}\) is number density (animals \(\\text{nmi}^{-2}\)) and \(S_\\text{A}\) is the vertically integrated backscatter over an area (\(\\text{m}^2\\, \\text{nmi}^{-2}\)) that is commonly called the nautical area scattering coefficient (NASC).

Examples

>>> # Define model parameters
>>> params = {
...     "ts_length_regression": {"slope": 20.0, "intercept": -68.0},
...     "stratify_by": "stratum_ks",
...     "strata": [1, 2, 3, 4, 5],
...     "impute_missing_strata": True
... }
>>>
>>> # Initialize inverter
>>> inverter = InversionLengthTS(params)
>>>
>>> # Set haul-level sigma_bs from biological data
>>> inverter.set_haul_sigma_bs([specimen_df, length_df])
>>>
>>> # Perform inversion on NASC data
>>> result = inverter.invert(nasc_df)
>>> print(result['number_density'].sum())
1234567.89