## Materials and Methods
### Distorted wave-Born Approximation (DWBA) Model  
Zooplankton tends to aggregate in schools at some layer. Consequently, special consideration for understanding the characteristics of acoustic backscatter must be given to specifying the single object detected from the ADCP instrument. In addition, the orientation angle of zooplankton to incidence acoustic sources from upward and downward looking method affected the TS variation. The scattering model was used to describe the echo returned by the single object to predict the theoretical target strength from dominant species of zooplankton compared to the angle of orientation, since we found various species of zooplankton in this research. On the other hand, each zooplankton species has a specific shape which affected the TS value from a different orientation of the body.  
In this study, the distorted wave-Born approximation (DWBA) model was used. This model uses theoretical backscatter by considering the overall shape and length (body length, \(L\)) of the detected zooplankton body from the net samples. It was assumed that the zooplankton body shape was a deformed cylinder and was categorized as a weak scatterer. The DWBA model was used because it was related to the detection of zooplankton in the water column by different frequency and acquisition method of ADCP used in this research. This model is valid for all acoustic frequencies, the angle of orientation, and arbitrary shapes of zooplankton [33; 34; 35]. General mathematical equations for scattering amplitude can be written as follows [36]:  
\[f_{bs}=\frac{k_{1}^{2}}{4\pi}\int\int\int_{V}\left(\gamma_{\kappa}-\gamma_{\rho} \right)\exp{i2(\overrightarrow{k}_{i})_{2}\cdot\overrightarrow{r}_{pos}}\; \mathrm{d}\
u, \tag{6}\]  
where \(f_{bs}\) is the complex backscattering amplitude, \(k_{1}\) is the acoustic wave number in the surrounding medium that is related to the equation \(k=2\pi/\lambda\) with \(\lambda\) is acoustic wavelength, \(r_{0}\) is position vector, \(\overrightarrow{r}_{pos}\) value is the position in a particular line of the body axis. The material properties of zooplankton body, \(\gamma_{\rho}\) and \(\gamma_{\kappa}\) were expressed as:  
\[\gamma_{\rho}\equiv\ \frac{\rho_{2}-\rho_{1}}{\rho_{2}}=\ \frac{g-1}{g}, \tag{7}\]  
\[\gamma_{\kappa}\equiv\ \frac{\kappa_{2}-\kappa_{1}}{\kappa_{2}}=\frac{1-gh^{2} }{gh^{2}}, \tag{8}\]  
where \(g\) is density contrast, \(h\) is sound speed contrast, and \(\kappa\) is compressibility and can be written as:  
\[\kappa=\left(\rho c^{2}\right)^{-1}, \tag{9}\]  
where \(\rho\)is mass density, and \(c\) is sound speed. The simplified form of the DWBA model for the deformed cylinder was used [34]. Since the zooplankton species found in this study mainly consisted of very small (\(<\)1 mm) copepods with high diversity, the \(g\) and \(h\) measurement were relatively difficult and did not need to be measured directly [5]. The approximate solution was considered using \(g\) and \(h\) from other research based on the acoustic properties of the weakly scattering sphere of fluid-like bodies which is true for copepods [37; 38]. Density (\(\rho\)) and sound speed (\(c\)) in the zooplankton body were 1028 kg m\({}^{-3}\) and 1480.3 m s\({}^{-1}\), respectively, against the surrounding medium 1026.9 kg m\({}^{-3}\) and 1477.4 m s\({}^{-1}\).