Patch/nasc

[simedroniraluca]

NASC (Nautical Area Scattering Coefficient) Computation Correction

This PR is opened to propose a solution for https://github.com/OSOceanAcoustics/echopype/pull/1136

Changes Made:

1. Conversion Factors: Conversion factors have been incorporated to facilitate the conversion from backscattering cross-section to scattering cross-section and from meters to nautical miles (nmi).

2. Computation Approach:

   • Cells Selection: Cells are chosen based on their depth and distance. The distance calculation is based on latitude and longitude coordinates.
   • NASC Calculation: For each channel and cell, the NASC is computed using the following steps:
     • Multiply the Sv (in linear units) with the height of the samples. The sample height is determined as the difference between consecutive depth values.
     • Compute the mean of the obtained values.
     • Multiply the mean value by the number of samples within the selected cell per the number of pings in the same cell.
     • Further multiply the result by $4 \times \pi \times 1852^2$
     • Finally, divide the obtained result by the percentage of non-NaN samples present in the analysis.

[leewujung]

Hey @simedroniraluca : Thanks very much for pointing out the bug and sending in the above! I did some investigation and comparison and put the results in this gist. In it I compare the echopy implementation with the Echoview one, and an adaption that we'll use in echopype using flox.

For the bug in #1136 and the different implementations, it boils down to:

• for some reason I completely forgot about the scaling to the reference units of nautical miles and the mean "height" of the pixels when trying to implement the Echoview NASC in the first implementation
• echopy handles NaN samples in Sv data by a scaling, which is probably up for debate
• echopy computes ping-by-ping NASC, while Echoview computes NASC in an average sense across the defined cell depth range and distance range

To make compute_NASC more efficient we are moving away from the looping approach (#1127). I'll send in a separate and incomplete PR in a moment that has the barebone stuff using flox, which @lsetiawan will carry forward to finish it.

[leewujung]

For visibility, here I copy-paste some notes from the gist:

Regarding echopy implementation

The implementation in echopy integrated Sv between the range limits r0 and r1.

There are a few specifics to note:

• if method="mean", the function takes the mean of sv*sh and multiply that by the number of vertical samples, and treat this number as the integration output
• if method=""sum, the function just takes the sum of sv*sh to be the integration output
• the resulting integrated output is "corrected" by scaling according to the number of valid samples in each column (distance_nmi). For example, if there are only 2 non-NaN samples out of 3 total samples along depth, then the integrated output NASC_raw is scaled by 3/2: NASC_corrected = NASC_raw / (2/3)
• the code also assumes that the "height" of the samples are conserved across ping, which may not be the case unless the Sv data has been regridded

I am not sure about the final correction of the NASC based on the missing non-NaN values. This would result in inflating the NASC number if there are a lot of NaNs in sv, and would not be accurate if the goal is to obtain NASC from masked Sv dataset.

Regarding echopy vs Echoview differences

• the Echoview implementation computes NASC in a sense of a mean across multiple pings
• the Echopy implementation computes ping-by-ping NASC with some scaling to compensate for potential NaN samples along depth in some pings

[leewujung]

Hey @simedroniraluca: I think we can close this issue and move our discussions to #1167, so that everything is in one place. Thanks again for your contribution!!