## 3 Results
### Transfer Function from TN to A. anophagefferens  
_A. anophagefferens_ is a tiny, spherical and nonmotile picoplankton (cell size 2-3 \(\upmu\)m) pelagophyte with no flagella [18,45]. _A. anophagefferens_ cells were abundant during the brown tide period in Qinhaungdao coastal waters, which can be seen as an indicator of brown tide. [PERSON] et al. [32] reported that _A. anophagefferens_ abundance was strongly positively correlated with nitrite and temperature. DON is commonly thought of as the main nitrite resource, and it is vital for improving _A. anophagefferens_-induced brown tide [46,47]. Since nitrogen is routinely monitored as a chemical element discharged from rivers to sea along the coastline in Qinhaungdao, we seek the relationship between _A. anophagefferens_ density and TN concentration through their correlations with DON. We analyzed the measured data from June 2013 to August 2014, which included two large-scale brown tide events (May 2013 and August 2014) in the sea area. The observation data indicates strong correlation between _A. anophagefferens_ cell density and DON and temperature (T). Figure 7 shows the relationship between the _A. anophagefferens_ density (use the cells concentration to represent) and DON in 2013 and 2014 during the brown tide event periods. Commonly, a concentration of 5 \(\times\) 10\({}^{7}\) cells/L is thought of as the warning indication value to represent brown tide, and we use red circles to mark these values in this figure. As shown in Figure 7a, the density of _A. anophagefferens_ cells increases when the concentration of DON is in the range of 0.00\(\sim\)40.00 \(\upmu\)mol/L and the value reaches a relatively high grade. Therefore, we narrow the range of DON concentration to 10.00\(\sim\)30.00 \(\upmu\)mol/L and find that the density of _A. anophagefferens_ distributes in every value, which implies that the DON concentration is not the only main factor that influences the _A. anophagefferens_ cell density in this range. When the range continuously narrows to 30.00\(\sim\)40.00 \(\upmu\)mol/L, the measured data reduce but the density of _A. anophagefferens_ cells significantly increases, showing that the DON concentration varies in this range and it becomes the main factor of _A. anophagefferens_ cell growth. In Figure 7b, the data in 2014 are similar to the data collected in 2013, showing that the _A. anophagefferens_ cells rapidly grow in the range of 30.00\(\sim\)40.00 \(\upmu\)mol/L, and the concentration is higher than the indicated value. As can be seen in the range of 50.00\(\sim\)60.00 \(\upmu\)mol/L, there is also a point above the warning indication concentration, which means the brown tide can still bloom. However, if the DON concentration is lower than 20.00 \(\upmu\)mol/L, the possibility of bloom becomes lower, indicating that a low concentration can inhibit the propagation of _A. anophagefferens_. Combined with Figure 6a, although the data for DON are finite, the  
Figure 6: (**a**) The distribution of TN concentration during the brown tide period in May 2014. (**b**) The satellite-observed brown tide area in May 2014.  
range of DON concentration from approximately 20.00 to 60.00 \(\mathrm{\SIUnitSymbolMicro mol/L}\) can be seen as the sensitive range for inducing brown tide. With the DON concentration increase, a higher _A. anophageferens_ cell density can cause the brown tide event with more certainty. Separately drawing the fitting relationship in Figure 7a,b, we can see that, in Figure 7b, the data are substantial and the time covers four months, providing greater accuracy than in Figure 7a. So, we preliminarily choose the fitting equation of the data in 2014 to establish the relationship of _A. anophageferens_ cell density and DON concentration as an exponential function:  
\[\rho=5000\mathrm{e}^{0.24 DON} \tag{6}\]  
where \(\rho\) is the _A. anophageferens_ cell density.