### Chlorophyll-a inversion model

The selection of a chlorophyll-a inversion formula is important for accurate measurement of chlorophyll-a concentration. The commonly used chlorophyll-a inversion models include linear model, logarithmic model, and polynomial model [13]. Due to different natural environments, different sea areas need the corresponding inversion model. In this study, we need to find a suitable chlorophyll-a inversion model through experimental discussions. The models we established and discussed are as follows:

$$ ChLa=a\times B+k $$

(1)

where *ChLa* is the concentration of chlorophyll-a, *B* is the waveband we selected, and *a* and *k* are the coefficients.

$$ ChLa=a\times \mathit{\ln}(B)+k $$

(2)

where *ChLa* is the concentration of chlorophyll-a, *B* is the waveband we selected with natural log from Eq. (1), and *a* and *k* are the coefficients.

$$ ChLa=a\times {B}^2+b\times B+k $$

(3)

where \( C\mathit{\mathsf{h}} La \) is the concentration of chlorophyll-a, *B* is the waveband we selected, and a, *b*, and *k* are the coefficients.

### Model for typhoon regression

Many complex factors like atmospheric density, fictitious force, and wind speed impact the correlation between a typhoon and chlorophyll-a. It is more effective to set up the optimal combination with multiple independent variables to predict and estimate dependent variables than to use one independent variable.

The regression model is constructed with the chlorophyll-a concentration change rate, typhoon intensity, and typhoon speed, which come from the experiment with the data from the South China Sea by Shao [12].

$$ \mathrm{Rate}={\beta}_0+{\beta}_1{S}_1+{\beta}_2{S}_2+\varepsilon $$

(4)

where Rate is the change rate of chlorophyll-a concentration between normal and typhoon weather; *S*_{1} is the intensity of typhoon; *S*_{2} is the speed of typhoon; *β*_{0}, *β*_{1}, and *β*_{2} are the regression coefficients and estimated by data; and *ε* is the random error.

### Fujitais empirical formula

Many experiments have confirmed that the longitudinal distribution of typhoon’s atmospheric pressure above sea surface can meet the requirements of Fujitais empirical formula [14]. Fujitais empirical formula is as follows:

$$ {p}_{(r)}={p}_E-\Delta p{\left[1+{\left(\frac{r}{R}\right)}^2\right]}^{-0.5} $$

(5)

*p*_{(r)} is the atmospheric pressure of typhoon above sea surface; *p*_{E} is the standard atmospheric pressure (generally 1000hpa); *∆p* is the intensity factor of typhoon, which also is the pressure difference between the environment and the center of typhoon; *R* is the scale factor of typhoon; and \( {\left[1+{\left(\frac{r}{R}\right)}^2\right]}^{-0.5} \) is used to standardize typhoon.

### The balance model of four forces of typhoon

A typhoon is well-structured and strong because it is a complete weather system. It is a type of large storm system having a circular or spiral system of violent winds, typically hundreds of kilometers or miles in diameter; the structure of typhoon is clear and has a specific pathway and landing location. There are many factors that affect the movement of a typhoon such as pressure gradient, centrifugal force, Coriolis force, and friction force. The four forces balance to make ideal conditions, as follows:

$$ {F}_p+{F}_c+{F}_{Co}+{F}_f=0 $$

(6)

*F*_{p} is due to the difference in horizontal pressure, and it pushes air particles from a high-pressure area to a low-pressure area, as follows:

$$ {F}_p=\frac{\partial p}{\partial r} $$

(7)

Р is the atmospheric pressure of the observed place; and г is the distance from the observed place to a typhoon.

Since the circular motion in a typhoon-specific region is due to the inertia of an object, there is always a tendency for the object to fly along the tangential direction of the circle. This tendency is described as follows:

$$ {F}_c=\rho \frac{v^2}{r} $$

(8)

*ρ* is the measure of atmospheric density in the region of a typhoon, and ν is the wind speed of the circumferential tangential direction.

The Coriolis force is a fictitious force used to explain a deflection in the path of a body moving in latitude relative to the earth when observed from earth. This force is described as follows:

$$ {F}_{Co}=\left\{\begin{array}{c}-\rho fu,\left(\mathrm{tangential}\ \mathrm{Coriolis}\ \mathrm{force}\right)\\ {}\ \rho fv,\left(\mathrm{meridional}\ \mathrm{Coriolis}\ \mathrm{force}\right)\end{array}\right. $$

(9)

*f* is a constant determined by the selected region: *f* = 2*ω* ∗ sin *φ*; *ω* is the angular velocity of the earth’s rotation; and *φ* is the dimension value of the selected area, which is positive in northern latitudes and negative in southern latitudes.

Rubbing action on the surface may result from the friction force of earth’s surface, as follows:

$$ {F}_f=\left\{\begin{array}{c}\rho k{h}_uu,\left(\mathrm{meridional}\ \mathrm{friction}\ \mathrm{force}\right)\\ {}\rho k{h}_vv,\left(\mathrm{tangential}\ \mathrm{friction}\ \mathrm{force}\right)\end{array}\right. $$

(10)

*k* is the friction coefficient, 푢 and 푣 are the wind speeds, and *h*_{u} and *h*_{v} are the wind shear factors.

### Chlorophyll-a Typhoon Model

Usually, the coefficient of friction *k* is estimated by the undermined parameters. We make *h*_{u}*h*_{v} = 1. Then, Eq. (4) can be changed as follows:

$$ \frac{v^2}{r}+ fv-\frac{1}{\rho}\frac{\partial p}{\partial r}+\frac{1}{f}{k}^2v=0 $$

(11)

We make integration and induction operation between Eq. (3) and Eq. (11), as follows:

$$ frv+{v}^2+{frv}^3{\left(\frac{k^{{\prime\prime} }}{f}\right)}^2=\frac{\Delta p}{\rho}\frac{a^2-1}{a^3},\kern0.5em a=\sqrt{1+{\left(\frac{r}{R}\right)}^2} $$

(12)

By using the measured data and data fitting method, we can find the parameters of the typhoon region. The scale factor of the typhoon and the friction factor are obtained in this way: the scale factor *R* = 21.9 and the friction factor *k* = 3.7 × 10^{−6}. The parameters are taken into Eq. (12), and then, we get the typhoon wind speed equation as follows:

$$ v=\frac{1}{2}\left(- fr+\sqrt{(fr)^2+4\frac{\Delta p}{\rho}\frac{a^2-1}{a^3}}\right) $$

(13)

Equation (12) is modified and integrated with the Eq. (13) to obtain the wind power disaster model in the different regions of typhoon area based on the change rate of chlorophyll-a concentration. The Chlorophyll-a Typhoon Model (CTM) is described as follows:

$$ {S}_1=\frac{\mathrm{Rate}-{\beta}_0-\frac{1}{2}{\beta}_2\left(- fr+\sqrt{(fr)^2+4\frac{\Delta p}{\rho }\ \frac{a^2-1}{a^3}}\right)-\varepsilon }{\beta_1} $$

(14)