Differences in KRM implementations

[gavinmacaulay]

The Clay & Horne (1994) paper, in the line immediately after equation 13, says

and $k_b \approx k$ at low contrast.

Setting $k_b$ to $k$ gives TS results that differ by around 1 dB compared to not setting $k_b$ to be $k$ for some example datasets. It is not clear why this approximation is necessary (it doesn't simplify the calculations at all) and it perhaps leads to less accurate TS results. Some other implementations of the KRM that echoSMs has been compared against set $k_b$ to $k$, so echoSMs currently does the same.

To allow for testing and comparison of other KRM implementations, the fish shapes from the online KRM TS calculator (https://www.fisheries.noaa.gov/data-tools/krm-model) have been included in echoSMs in a toml-formatted file (or use the KRMorganism Python class for easy access).

The TS for the sardine shape from there can be calculated and compared to the online results with:

from echosms import KRMModel, KRMdata
import matplotlib.pyplot as plt
import numpy as np

mod = KRMModel()

fish = KRMdata().model('Sardine')

p = {'medium_c': 1490, 'medium_rho': 1030, 'organism': fish, 'theta': 90,
     'f': np.arange(12, 121, 1)*1e3}

krm_ts = mod.calculate_ts(p)

noaa_ts = KRMdata.ts('Sardine')

d = np.mean(np.abs(np.array(krm_ts) - np.array(noaa_ts[' TS (dB).1'])))
print(f'Mean difference in results is {d:.2f} dB')

plt.plot(fish.body.x, fish.body.z_U, fish.body.x, fish.body.z_L, c='black')
for s in fish.inclusions:
    plt.plot(s.x, s.z_U, s.x, s.z_L, c='C0' if s.boundary == 'fluid' else 'C1')
plt.gca().set_aspect('equal')
plt.show()