**The Empirical Models to Correct Water Column Effects for Optically Shallow Water**

Chaoyu Yang

[34] Houminer Z, Soicher H: Improved short-term predictions of foF2 using GPS time delay

[35] Stankov SM, Warnant R: Ionospheric slab thickness—analysis, modelling and moni‐

[36] Maltseva OA, Mozhaeva NS, Poltavsky OS, Zhbankov GA: Use of TEC global maps and the IRI model to study ionospheric response to geomagnetic disturbances; Adv.

[37] Kouris SS, Polimeris KV, Cander LjR: Specifications of TEC variability; Adv. Space Res.

[38] Jayachandran B, Krishnankutty TN, Gulyaeva TL: Climatology of ionospheric slab

[39] Maltseva OA, Mozhaeva NS: Obtaining Ionospheric conditions according to data of navigation satellites; Int. J. Antennas Propag. Article 804791. 2015:1–16. doi:

[40] Vryonides P, Tomouzos C, Pelopida G, Haralambous H: Investigation of Ionospheric slab thickness and plasmaspheric TEC using satellite measurements. PIERS Proceed‐

[41] Zakharenkova IE, Krankowski A, Bilitza D, Cherniak YuV, Shagimuratov II, Sieradzki R: Comparative study of foF2 measurements with IRI-2007 model predictions during extended solar minimum; Adv. Space Res. 2011; 51:620–629. doi:10.1016/j.asr.

[42] Gerzen N, Jakowski N, Wilken V, Hoque MM: Reconstruction of F2 layer peak electron density based on operational vertical total electron content maps; Ann. Geophys. 2013;

[43] Sardar N, Singh AK, Nagar A, Mishra SD, Vijay SK: Study of latitudinal variation of Ionospheric parameters—a detailed report; J. Ind. Geophys. Union. 2012; 16(3):113–133.

[44] Muslim B, Haralambous H, Oikonomou C, Anggarani S: Evaluation of a global model of ionospheric slab thickness for foF2 estimation during geomagnetic storm; Ann.

[45] Hernandez-Pajares M, Juan JM, Orus R, Garcia-Rigo A, Feltens J, Komjathy A, Schaer SC, Krankowski A: The IGS VTEC maps: a reliable source of ionospheric information

since 1998; J. Geod. 2009; 83:263–275. doi:10.1007/s00190-008-0266-1

thickness; Ann. Geophys. 2004; 22:25–33. doi:10.5194/angeo-22-25-2004

measurements; Radio Sci. 1996; 31(5):1099–1108. doi:10.1029/96RS01965

toring; Adv. Space Res. 2009; 44:1295–1303. doi:10.1016/j.asr.2009.07.010

Space Res. 2012; 49:1076–1087. doi:10.1016/j.asr.2012.01.005

2006; 37:983–1004. doi:10.1016/j.asr.2005.01.102

ings. Moscow. Russia. August 19–23, 2012:1172–1175.

31:1241–1249. doi:10.5194/angeo-31-1241-2013

Geophys. 2015; 58(5). A0551. doi:10.4401/ag-6721

10.1155/2015/804791

28 Empirical Modeling and Its Applications

2011.11.015

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/63149

#### **Abstract**

Seagrass as one of the blue carbon sinks plays an important role in environment, and it can be tracked remotely in the optically shallow water. Usually the signals of seagrass are weak which can be confused with the water column. The chapter will offer a model to simulate the propagation of light. The model can be used to improve the accuracy of seagrass mapping. Based on the in situ data, we found that the appropriate wave‐ bands for seagrass mapping generally lie between 500–630 nm and 680–710 nm as well. In addition, a strong relationship between the reflectance value at 715 nm and LAI was found with a correlation coefficient of 0.99. The chapter provided an improved algorithm to retrieve bottom reflectance and map the bottom types. That would be meaningful for management and preservation of coastal marine resources.

**Keywords:** seagrass, optical correction model, Sanya Bay, remote sensing technique, optically shallow water

#### **1. Introduction**

Given the rapid change affecting coastal environments, it is a substantial challenge to manage and preserve the coastal marine resources. It is urgent to find an effective and quantitative tool to detect such change in the optically shallow water. The spatial resolution and preci‐ sion of the traditional *in situ* surveys are not enough to detect subtle changes before they become catastrophic [1, 2]. Remote sensing technique developed rapidly and can provide high spatial and temporal resolution of the benthos. Optical properties in the optically shallow waters are relatively more complex than those in the optically deep water, so the application of remote sensing technique in optically shallow waters is still in its infant stage.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

An important problem with remote sensing technique in the aquatic environment is the water column effect [3, 4]. In shallow water, radiance can be affected by phytoplankton, suspended organic and inorganic matter and dissolved organic substances [5, 6].

There are several methods to correct the water column effects. The single/quasi-single scattering theory is one of them to estimate the water column contribution. Morel and Gentili [7] defined the reflectance of the optically shallow waters by removing determinations of the albedo of the substrate covering the floor. The contribution of a finite substrate to the increase in reflectance was interpreted in terms of depth if the optical properties of the optically shallow water and the reflectance at null depth of the deep ocean near the object were known. The quasi-single scattering theory [8] suggests that bottom upwelling signals can be estimated as a sum of contributions from the water column and from the bottom. A semianalytical (SA) model for mapping bottom by using the remote sensing reflectance of shallow waters was developed and most commonly cited [9, 10]. Another algorithm to compensate for water column effects is that of Lyzenga [11–13]. This model was developed from two-flow irradiance transfer. Lyzenga exploited an intrinsic correlation between two color bands. This theory was utilized to generate a pseudodepth and pseudocolor band. The pseudodepth channel can theoretically be retrieved with appropriate ground truth information to estimate absolute depth. The total remote sensing reflectance values with respect to depth were linearized by removing an optically deep water value and taking the natural logarithm of the result. Removing a deep-water reflectance value from each pixel [14, 15] or applying the water optical properties [16] which are calculated from deep waters, were used to eliminate water column influence. However, there are several issues in these methods. Because these models utilized the hypothesis that energy traveling through a water column is not related to the substrate type and water depth. In fact the intensity of light in optically shallow water decreases exponentially with increasing depth, and changes from electromagnetic radiation. The error due to the process has reduced the accuracy of seagrass mapping and bottom classification. Based on these reasons, it is necessary to consider the water depth and the diffuse attenuation coefficient when removing the water column effects.

In this chapter, we will introduce an improved optical model of incoming solar radiation transfer. This model consumed the optically shallow water as multilayer water. This effective and improved method can be applied to research the relationship between reflectance and the LAI of seagrass.

#### **2. The improved optically shallow water model**

In this algorithm the optically shallow water is considered as a plane-parallel water body and segmented into an enormous number of homogenous layers to describe the optical properties of the optically water column. In this model, it is supposed an infinitely thin layer *S* of thickness Δ*zi* at depth *z* existed and can be measured downward from the sensor. The *i*th interval covers depths from *zi* to *zi*+1, with Δ*zi* = *zi* + 1 − *zi* . Figure 1 shows that the light is incident onto the surface and scattered in all directions above the reflecting surface *S*. In order to calculate conveniently, we assume the reflecting surface *S* lies in the *xy* plane of a Cartesian coordinate system. In this model, *z* axis is vertical to the surface, *S*, which is described in Figure 1. The light which is incident onto the surface is defined as the incident irradiance *Ed* (*z*, *λ*). The subscript *d* represents incident and *λ* is the wavelength. The field of view (FOV) of the sensor and the angle of reflection are the key factors to determine if the photons scattered by the optically shallow water can be recorded by the detector (Figure 2). It is notable that attention should paid to those scattered photons which have the ability to get the sensor. We noted the unique reflected path as CO which is used to represent how the scattered photos get the sensor O. We suppose that the layer can be segmented into enormous infinitesimals. Figure 2 shows that a beam of light Φ*di* illuminates the *j*th volume *Δv<sup>j</sup>* of thickness Δ*zi* . In this situation, a fraction of the collimated incident beam is scattered by *S* and get into a solid angle Δ*Ω<sup>j</sup>* . The spectral volume scattering function (VSF) is described as [17, 18]:

An important problem with remote sensing technique in the aquatic environment is the water column effect [3, 4]. In shallow water, radiance can be affected by phytoplankton, suspended

There are several methods to correct the water column effects. The single/quasi-single scattering theory is one of them to estimate the water column contribution. Morel and Gentili [7] defined the reflectance of the optically shallow waters by removing determinations of the albedo of the substrate covering the floor. The contribution of a finite substrate to the increase in reflectance was interpreted in terms of depth if the optical properties of the optically shallow water and the reflectance at null depth of the deep ocean near the object were known. The quasi-single scattering theory [8] suggests that bottom upwelling signals can be estimated as a sum of contributions from the water column and from the bottom. A semianalytical (SA) model for mapping bottom by using the remote sensing reflectance of shallow waters was developed and most commonly cited [9, 10]. Another algorithm to compensate for water column effects is that of Lyzenga [11–13]. This model was developed from two-flow irradiance transfer. Lyzenga exploited an intrinsic correlation between two color bands. This theory was utilized to generate a pseudodepth and pseudocolor band. The pseudodepth channel can theoretically be retrieved with appropriate ground truth information to estimate absolute depth. The total remote sensing reflectance values with respect to depth were linearized by removing an optically deep water value and taking the natural logarithm of the result. Removing a deep-water reflectance value from each pixel [14, 15] or applying the water optical properties [16] which are calculated from deep waters, were used to eliminate water column influence. However, there are several issues in these methods. Because these models utilized the hypothesis that energy traveling through a water column is not related to the substrate type and water depth. In fact the intensity of light in optically shallow water decreases exponentially with increasing depth, and changes from electromagnetic radiation. The error due to the process has reduced the accuracy of seagrass mapping and bottom classification. Based on these reasons, it is necessary to consider the water depth and the diffuse attenuation

In this chapter, we will introduce an improved optical model of incoming solar radiation transfer. This model consumed the optically shallow water as multilayer water. This effective and improved method can be applied to research the relationship between reflectance and the

In this algorithm the optically shallow water is considered as a plane-parallel water body and segmented into an enormous number of homogenous layers to describe the optical properties of the optically water column. In this model, it is supposed an infinitely thin layer *S* of thickness

at depth *z* existed and can be measured downward from the sensor. The *i*th interval covers

and scattered in all directions above the reflecting surface *S*. In order to calculate conveniently,

. Figure 1 shows that the light is incident onto the surface

organic and inorganic matter and dissolved organic substances [5, 6].

30 Empirical Modeling and Its Applications

coefficient when removing the water column effects.

**2. The improved optically shallow water model**

= *zi* + 1 − *zi*

to *zi*+1, with Δ*zi*

LAI of seagrass.

Δ*zi*

depths from *zi*

$$\beta\left(\boldsymbol{\upmu},\boldsymbol{\uplambda}\right) = \lim\_{\boldsymbol{\upmu}\_{\boldsymbol{\upalpha}\_{\boldsymbol{\upbeta}}}} \lim\_{\boldsymbol{\upalpha}\_{\boldsymbol{\upbeta}}} \left| \frac{\boldsymbol{\upPhi}\_{\boldsymbol{\upalpha}}}{\boldsymbol{\upPhi}\_{\boldsymbol{\upalpha}} \boldsymbol{\upmu}\_{\boldsymbol{\upalpha}} \boldsymbol{\upalpha} \boldsymbol{\upalpha}\_{\boldsymbol{\upbeta}}} \right| \tag{1}$$

Where Φ*di* is the incident flux; Φ*si* is the scattered fraction of incident light; *ψ* is the scattering angle between the forward direction of the light and the line between the scattering point C and the detector O. The part of the optically water column related to the upwelling radiant flux, Φ*<sup>u</sup> water*, is given by [19, 20]:

$$\mathcal{O}\_u^{\;\;water} = \sum\_j \sum\_i \beta(\psi\_\prime \; \; \lambda) \cdot \lim\_{\;\;Az\_i \; -0 \; \Lambda \; \Omega\_j \; -0} \left[ \mathcal{O}\_{di} \cdot \Lambda \; \Omega\_j \cdot \Delta z\_i \right] \tag{2}$$

The contribution of downwelling radiant flux, Φ*di*, is defined as:

$$
\Phi\_{di} = \vec{E}\_d \left( z, \lambda \right) \bullet d\vec{s}\_j \tag{3}
$$

Where *E* → *<sup>d</sup>* (*z*, *λ*) is the downwelling irradiance at depth *z*; Φ*<sup>u</sup> water* is the part of upwelling radiant flux and is described as:

$$\Phi\_{\boldsymbol{u}}^{\text{uanar}} = \vec{E}\_{\boldsymbol{u}}^{\text{uanar}} \left( \boldsymbol{z} \mathcal{A} \right) \bullet \vec{s} \tag{4}$$

Where *E* → *u water*(*z*, *λ*) is the fraction of the optically water column to the upwelling irradiance. The scattering part of the upwelling irradiance is:

$$dE^{\text{uur}}\_{\
u} \left( z \mathcal{A} \right) = E\_d \left( z \mathcal{A} \right) \cdot \mathcal{B} \left( \Psi \mathcal{A} \right) d\Omega dz \tag{5}$$

Kirk [21] defined *ku*(*λ*) as vertical diffuse attenuation coefficient for upward flux. Then Philpot introduced the parameter in [22]. *d Eu water*(*z* →*z* <sup>−</sup> *surf*, *λ*) is the part of the upwelling irradiance from the considered layer to the subsurface:

$$\mathrm{d}E\_{\mathrm{u}}^{\mathrm{sator}}\left(\boldsymbol{z}\rightarrow\boldsymbol{z}^{-}\_{\;\mathrm{u}\boldsymbol{w}\prime},\lambda\right) = E\_{\mathrm{d}}\left(\boldsymbol{z},\lambda\right)\cdot\mathcal{J}\left(\boldsymbol{\psi},\lambda\right)\cdot\exp\left(-k\_{\mathrm{u}}\left(\lambda\right)\left(\boldsymbol{z}-\boldsymbol{z}^{-}\_{\;\mathrm{u}\boldsymbol{w}\prime}\right)\right)d\Omega d\boldsymbol{z}\tag{6}$$

*Ed* (*z*, *λ*) can be calculated as [23]:

$$E\_d\left(z,\lambda\right) = E\_d\left(z \xrightarrow{-} z^{-}\_{\text{surf}}, \lambda\right) \exp\left(-k\_{\text{ad}}\left(\lambda\right)\left(z - z^{-}\_{\text{surf}}\right)\right) \tag{7}$$

Where *kd* is the vertical diffuse attenuation coefficient for downwelling irradiance. *d Eu water*(*z* →*z* <sup>−</sup> *surf*, *λ*) can be obtained by:

$$\begin{split} \, \mathrm{d}E\_{\mathrm{u}}^{\mathrm{vator}} \left( \boldsymbol{z} \rightarrow \boldsymbol{z}^{-} \, \_{\mathrm{sav}\_{f}^{\star}}, \lambda \right) &= E\_{d} \left( \boldsymbol{z} \rightarrow \boldsymbol{z}^{-} \, \_{\mathrm{sav}\_{f}^{\star}}, \lambda \right) \cdot \beta \left( \boldsymbol{\nu}, \lambda \right) \\ \cdot \exp \Big[ - \left( k\_{\scriptscriptstyle{u}} \left( \lambda \right) + k\_{d} \left( \lambda \right) \right) \cdot \left( \boldsymbol{z} - \boldsymbol{z}\_{\mathrm{sav}\_{f}^{\star}} \right) \Big] d\Omega dz \end{split} \tag{8}$$

Equation (8) can be further simplified as:

$$\begin{split} \, \mathrm{d}E\_{\mathrm{u}}^{\mathrm{vapor}} \left( z \to z^{-} \_{\mathrm{surf}}, \mathcal{A} \right) &= E\_{\mathrm{d}} \left( z \to z^{-} \_{\mathrm{surf}}, \mathcal{A} \right) \\ \, \cdot \exp \left( -2k \left( \mathcal{A} \right) \left( z - z\_{\mathrm{surf}} \right) \right) \cdot \mathcal{B} \left( \left( \nu \, \mathcal{A} \right) d\Omega dz \end{split} \tag{9}$$

The total VSF *β*(*ψ*, *λ*) can be described as [24]:

$$\mathcal{B}\left(\boldsymbol{\psi}, \boldsymbol{\mathcal{X}}\right) = \mathcal{B}\_{\boldsymbol{w}}\left(\boldsymbol{\psi}, \boldsymbol{\mathcal{X}}\right) + \mathcal{B}\_{\boldsymbol{p}}\left(\boldsymbol{\psi}, \boldsymbol{\mathcal{X}}\right) \tag{10}$$

Where *w* and *p* represent pure sea water and particles, respectively. The VSF can be estimated as [25]:

$$\mathcal{B}\_{\nu} \left( \boldsymbol{\nu}, \lambda \right) = \mathcal{B}\_{\nu} \left( 90^{\circ}, \lambda\_{0} \right) \cdot \left( \frac{\lambda\_{0}}{\lambda} \right)^{4.32} \cdot \left( 1 + 0.835 \cos^{2} \boldsymbol{\nu} \right) \tag{11}$$

The particle VSF is estimated as [26]. Thus,

Where *E* → *u*

32 Empirical Modeling and Its Applications

*d Eu*

as [25]:

*water*(*z* →*z* <sup>−</sup>

The scattering part of the upwelling irradiance is:

introduced the parameter in [22]. *d Eu*

*Ed* (*z*, *λ*) can be calculated as [23]:

from the considered layer to the subsurface:

l

l

*surf*, *λ*) can be obtained by:

Equation (8) can be further simplified as:

The total VSF *β*(*ψ*, *λ*) can be described as [24]:

*water*(*z*, *λ*) is the fraction of the optically water column to the upwelling irradiance.

 l

 l® = × ×- - W - - (6)

*<sup>d</sup>* ( *surf* , ) ( *<sup>d</sup>* ( )( ) *surf* ) - - =® - - (7)

l byl

> l

×- - × W (9)

*,,,* = + (10)

= ×Y W (5)

*surf*, *λ*) is the part of the upwelling irradiance

(8)

( ) ( )( ) *water u d dE z, E z, , d dz*

 lb

*water*(*z* →*z* <sup>−</sup>

( , ) ( ) ( ) () ( ( )) *water <sup>u</sup> surf <sup>d</sup> <sup>u</sup> surf dE z z E z, , exp k z z d dz*

*E z, E z z exp k z z <sup>d</sup>* ( )

( () ()) ( )

 l

× - + ×- W é ù ë û

l

2

byl

l

*water*

*exp k k z z d dz*

, , *water u surf d surf u d surf*

l

*dE z z E z z ,*

® =® × - -

ll

Where *kd* is the vertical diffuse attenuation coefficient for downwelling irradiance.

( ) ( ) ( )

( ) ( )

® =® - -

() () () *w p*

 b yl  byl

> b yl

Where *w* and *p* represent pure sea water and particles, respectively. The VSF can be estimated

, ,

( ( )( )) ( )

*exp k z z , d dz*

*dE z z E z z*

*u surf d surf surf*

l

 l byl

Kirk [21] defined *ku*(*λ*) as vertical diffuse attenuation coefficient for upward flux. Then Philpot

l

$$
\partial\_{\rho} \left( \boldsymbol{\psi}, \mathcal{X} \right) = \boldsymbol{b}\_{\rho} \left( \mathcal{X} \right) \cdot \bar{\boldsymbol{\beta}}\_{\rho} \left( \boldsymbol{\psi}, \mathcal{X} \right) \tag{12}
$$

Where *bp* is the particle scattering coefficient and *β*˜ *<sup>p</sup>* is the particle phase function [27–29]. Here, the Henyey-Greenstein phase function [30] is selected:

$$\tilde{\beta}\_{HG} \left( \boldsymbol{\nu} \right) = \frac{1}{4\pi} \cdot \frac{1 - \operatorname{g}^2}{\left( 1 + \operatorname{g}^2 - 2\operatorname{g} \cos \boldsymbol{\nu} \right)^{3/2}} \tag{13}$$

Here *g* is used to adjust the relative amounts of forward and backward scattering in *βHG*:

$$2\pi \int\_{-1}^{1} \tilde{\boldsymbol{\beta}}\_{HG}(\boldsymbol{\psi}) \cos \boldsymbol{\psi} \, d \cos \boldsymbol{\psi} = \mathbf{g} \tag{14}$$

In which case *dΩ*=*sinψdωdψ*, the contribution from the water column, can be further deduced. By substituting equations (11)–(13) into (9), the flux by the water can be estimated as (see Figure 2):

$$\begin{split}dE\_{u}^{\text{wave}}\left(\boldsymbol{z}\rightarrow\boldsymbol{z}^{-}\_{\;\;\text{surf}},\lambda\right)&=E\_{d}\left(\boldsymbol{z}\rightarrow\boldsymbol{z}^{-}\_{\;\;\text{surf}},\lambda\right)\cdot\exp\left(-2k\left(\lambda\right)\left(\boldsymbol{z}-\boldsymbol{z}\_{\;\;\text{surf}}\right)\right)\\ \cdot\left(\mathcal{J}\_{u}\left(90^{\circ},\lambda\_{0}\right)\cdot\left(\frac{\lambda\_{0}}{\lambda}\right)^{4.32}\cdot\left(1+\cos^{2}\psi\right)+\frac{b\_{\rho}}{4\pi}\cdot\frac{1-\operatorname{g}^{2}}{\left(1+\operatorname{g}^{2}-2\operatorname{g}\cos\psi\right)^{3/2}}\right)\\ \cdot\sin\eta\,d\mu\,d\alpha d\bar{z}\end{split}\tag{15}$$

The irradiance of the water can be calculated:

$$E\_{\boldsymbol{u}}^{\text{vapor}}\left(\boldsymbol{z}\rightarrow\boldsymbol{z}^{-}\_{\text{surf}},\lambda\right)=\int\_{z\_{\text{surf}}}^{H+z\_{\text{surf}}}\int\_{Y}\prod\_{0}^{}E\_{d}\left(\boldsymbol{z}\rightarrow\boldsymbol{z}^{-}\_{\text{surf}},\lambda\right)\cdot\exp\left(-2k\left(\lambda\right)\left(\boldsymbol{z}-\boldsymbol{z}\_{\text{surf}}\right)\right)$$

$$\times\left(\mathcal{J}\_{\boldsymbol{v}}\left(90^{\circ},\lambda\_{0}\right)\cdot\left(\frac{\lambda\_{0}}{\lambda}\right)^{432}\cdot\left(1+\cos^{2}\boldsymbol{\nu}\right)+\frac{b\_{\rho}}{4\pi}\cdot\frac{1-\mathbf{g}^{2}}{\left(1+\mathbf{g}^{2}-2\operatorname{g}\cos\boldsymbol{\nu}\right)^{3/2}}\right)\tag{16}$$
 $\boldsymbol{z}\rightarrow\text{sigmoid}\,\boldsymbol{d}\,\boldsymbol{d}$ 

*sin d d dz* y w y ×

Where *ψ*1, and *ψ*2 can be estimated as:

$$\Psi\_1 = -\left(\alpha\_0 + \theta\_0 + \frac{FOV}{2}\right) + \pi \tag{17}$$

$$\mathcal{W}\_2 = -\left(\alpha\_0 + \theta\_0 - \frac{FOV}{2}\right) + \pi \tag{18}$$

Here, *FOV* is the field of view of the sensor, *α*0 is the solar attitude and *θ*0 is the view angle measured from the *z* axis. Integration of equation (16), *Eu water*(*z* →*z* <sup>−</sup> *surf*, *λ*) can be expressed as:

$$\begin{split} &E\_{u}^{\text{wave}}\left(z \to z^{-}\_{\text{surf}}, \lambda\right) = E\_{d}\left(z \to z^{-}\_{\text{surf}}, \lambda\right) \cdot \left(\frac{\exp\left(-2k\left(\lambda\right)\left(z - z\_{\text{surf}}\right)\right) - 1}{-2k}\right) \\ &\cdot \left[-2\pi\theta\_{\text{w}}\left(90^{\circ}, \lambda\_{0}\right)\left(\frac{\lambda\_{0}}{\lambda}\right)^{4.32} \cdot \left(\cos\Psi + \frac{0.835}{3}\cos^{3}\Psi\right)\right. \\ &-\frac{b\_{p}}{2g} \cdot \frac{1 - \text{g}^{2}}{\left(1 + \text{g}^{2} - 2g\cos\Psi\right)^{1/2}}\bigg|\_{\mathbf{v}\_{1}}^{\text{v}\_{2}} \Bigg] \end{split} \tag{19}$$

The subsurface irradiance reflectance can be estimated [31]. *Rwater*(0<sup>−</sup> , *λ*) can be further expressed as:

$$\begin{split} R^{\text{max}}\left(0^{-},\lambda\right) &= \frac{E\_{\boldsymbol{\mu}}^{\text{max}}\left(\boldsymbol{z}\to\boldsymbol{z}^{-}\_{\text{surf}},\lambda\right)}{E\_{d}\left(\boldsymbol{z}\to\boldsymbol{z}^{-}\_{\text{surf}},\lambda\right)} = \left(\frac{\exp\left(-2k\left(\lambda\right)\left(\boldsymbol{z}-\boldsymbol{z}\_{\text{surf}}\right)\right)-1}{-2k}\right) \\ &\cdot \left[-2\pi\mathcal{B}\_{\boldsymbol{w}}\left(90^{\circ},\lambda\_{0}\right)\cdot\left(\frac{\lambda\_{0}}{\lambda}\right)^{4.32}\cdot\left(\cos\Psi+\frac{0.835}{3}\cos^{\circ}\Psi\right)\right. \\ &\left.-\frac{b\_{p}}{2g}\cdot\frac{1-\mathbf{g}^{2}}{\left(1+\mathbf{g}^{2}-2g\cos\Psi\right)^{1/2}}\right\|\_{\boldsymbol{w}\_{1}}^{\boldsymbol{w}\_{2}} \end{split} \tag{20}$$

The subsurface remote-sensing reflectance just beneath the sea surface [32, 33], *Rrs*(0<sup>−</sup> ,*λ*), can be calculated as:

The Empirical Models to Correct Water Column Effects for Optically Shallow Water http://dx.doi.org/10.5772/63149 35

$$R\_{rs}\left(0^{-},\mathcal{A}\right) = \frac{R\left(0^{-},\mathcal{A}\right)}{\mathcal{Q}}\tag{21}$$

*Q* is the radio of the subsurface upward irradiance to radiance conversion factor [34]. Remotesensing reflectance of the water column just beneath the sea surface *Rrs water*(0<sup>−</sup> , *λ*) can be estimated as:

$$\begin{aligned} R\_{rs}^{\text{uwar}}\left(0^{-},\lambda\right) &= Q \cdot \frac{E\_{u}^{\text{vapor}}\left(z \to z^{-}\_{\text{surf}},\lambda\right)}{E\_{d}\left(z \to z^{-}\_{\text{surf}},\lambda\right)} = Q \cdot \left(\frac{\exp\left(-2k\left(\lambda\right)\left(z - z\_{\text{surf}}\right)\right) - 1}{-2k}\right) \\ \cdot \left[-2\pi\beta\_{\text{v}}\left(90^{\circ},\lambda\_{0}\right)\cdot\left(\frac{\lambda\_{0}}{\lambda}\right)^{4.2} \cdot \left(\cos\Psi + \frac{0.835}{3}\cos^{3}\Psi\right)\right. \\ &- \left.\frac{b\_{p}}{2g} \cdot \frac{1 - g^{2}}{\left(1 + g^{2} - 2g\cos\Psi\right)^{\vee 2}}\right]\bigg|\_{\varphi\_{1}}^{\varphi\_{2}} \end{aligned} \tag{22}$$

Finally, the bottom reflectance can be obtained by *Rrs b* :

$$R\_{rs}^{b} = R\_{rs} \left( 0^{-}, \mathcal{X} \right) - R\_{rs}^{uunv} \left( 0^{-}, \mathcal{X} \right) \tag{23}$$

#### **3. Materials and methods**

Where *ψ*1, and *ψ*2 can be estimated as:

34 Empirical Modeling and Its Applications

1 00 2

2 00 2

æ ö =- + + + ç ÷

æ ö =- + - + ç ÷

( ) ( ) ( ( )( ))

 l

æ ö - -- ® =® ×ç ÷

*surf water*

exp 2 <sup>1</sup> , , <sup>2</sup>

3

0 3

2

y

4.32


0.835 2 90 , cos cos

The subsurface irradiance reflectance can be estimated [31]. *Rwater*(0<sup>−</sup>

( ) ( )

l

l

*water*

( )


<sup>0</sup> , <sup>2</sup>


*u surf surf water*

l

l

4.32

*d surf*

0.835 2 90 , cos cos

<sup>é</sup> æö æ <sup>ö</sup> × - ° × × Y+ Y <sup>ê</sup> ç÷ ç <sup>÷</sup> <sup>ê</sup> èø è <sup>ø</sup> <sup>ë</sup>

2

y

0 3

*E zz k zz*

*Ez z k*

3

® æ ö - -- = = ç ÷

1

The subsurface remote-sensing reflectance just beneath the sea surface [32, 33], *Rrs*(0<sup>−</sup>

y

<sup>é</sup> æö æ <sup>ö</sup> × - ° × × Y+ Y <sup>ê</sup> ç÷ ç <sup>÷</sup> <sup>ê</sup> èø è <sup>ø</sup> <sup>ë</sup>

1

y

 aq

 aq

y

y

measured from the *z* axis. Integration of equation (16), *Eu*

*u surf d surf*

l

*E z z Ez z*

( )

 l

*b g g g g*

*w*

pb

*p*

as:

0

( )

1 2 1 2 cos

( )

 l

*b g g g g*

l


*w*

pb

*R ,*

*p*

be calculated as:

0

( )

1 2 1 2 cos

<sup>ù</sup> - - × <sup>ú</sup>

2 1/ 2 <sup>2</sup>

<sup>ú</sup> +- Y <sup>û</sup>

<sup>ù</sup> - - × <sup>ú</sup>

2 1/ 2 <sup>2</sup>

<sup>ú</sup> +- Y <sup>û</sup>

l

l

*FOV*

*FOV*

Here, *FOV* is the field of view of the sensor, *α*0 is the solar attitude and *θ*0 is the view angle

 p

 p

è ø (17)

è ø (18)

*surf*, *λ*) can be expressed as:

, *λ*) can be further expressed

(19)

(20)

,*λ*), can

*water*(*z* →*z* <sup>−</sup>

*k zz*


( ( )( ))

, exp 2 1

® - è ø

l

l

*k*

In situ survey was carried out in the Sanya Bay (109°25′–109°29′ E, 18°12′–18°13′ N) in the South China Sea on 15–20, April 2008(see **Figure 3**). *Thalassia* seagrass dominates in this area. Sanya Bay [35], which is a typical tropical bay, includes a broad range of habitats. Spectral irradiance was measured by using a spectrometer (S2000, Ocean Optics, Inc.) [36]. The instrument has a spectral resolution with 0.3 nm and bandwidths are from 200 to 1100 nm. Besides, a self-designed remote cosine receptor was used to measure signals proportional to the sky radiance, sea surface radiance and the radiance reflected from a horizontal reference panel by connecting to the S2000 with an optical fiber (P400-2-UV/VIS) with a FOV of 10°. The viewing angle was 40°.

Following the method in Mobley [37], the relative azimuth was set as 135°. The spectral downwelling radiance was measured from a reflectance panel *Lg*(*λ*) (Spectralon). The reflec‐ tance of Spectralon is known, and the relationship between the measured radiance and the incident irradiance *Ed*(*λ*) is given by:

$$E\_d\left(\mathcal{A}\right) = q\left(\mathcal{A}\right) \cdot \frac{1}{\rho} \cdot L\_s\left(\mathcal{A}\right) \tag{24}$$

*q*(*λ*) is an angular and wavelength-dependent factor, and *ρg* is the irradiance reflectance of Spectralon. Clear sky conditions are necessary to in situ survey. 100 shoots of seagrass were selected to count leaf number *jj*, and also to calculate the percentage of shoots with *jj* leaves *Xjj*. Ten shoots with the same leaf number were selected. The leaves were centered on a box (25 cm×40 cm), and then took a photo to record the situation. Based on the pixels of seagrass in the photos, *Mjj*, the average leaf area of seagrass with the different numbers of leaves can be recorded. The leaf area index *M* can be estimated as:

$$M = P \times \sum \left( \mathbf{i} \times M\_{\parallel} \times X\_{\parallel} \right) \tag{25}$$

Here *P* represents the seagrass density of each processing (shoots/m2 ).

#### **4. Results**

The algorithm was employed to obtain the bottom reflectance. Based on the results the seagrass information which was retrieved from the modeled *Rrs b* is reasonable to. In Figure 4, between 550 nm and 750 nm the predicted value *Rrs b* agreed very well with the *in situ* measured bottom reflectance *Rrs b* . Between 600 and 800 nm, *Rrs <sup>b</sup>* was found to be lower than subsurface remotesensing reflectance *Rrs*(0<sup>−</sup> ). This error could be related to the absorption and scattering prop‐ erties of the optically shallow water which mainly affect the spectral reflectance at this band.

It is noted that the subsurface reflectance cannot be used directly to classify the bottom type or substitute the bottom reflectance. We provided a comparison between the subsurface remote sensing reflectance and the remote sensing reflectance of the bottom. The results also illustrate the conclusion in Figure 5(a). It was found that there does indeed exist a considerable difference between the subsurface remote sensing reflectance *Rrs*(0<sup>−</sup> ) and the remote sensing reflectance of the bottom *Rrs b* . Compared to the subsurface reflectance, the retrieved bottom reflectance is more related to in situ measured ones in Figure 5(b). It was found that there is a significant relationship between *in situ* measured *Rrs b* values and modeled ones. Therefore, it is safe to conclude that *Rrs*(0<sup>−</sup> ) cannot be used directly to represent the hyperspectral recognition of seagrass in optically shallow waters is unfitted.

The seagrass reflectance with different LAI (Leaf Area Index) was surveyed to evaluate the relationship between the spectral characteristics of seagrass and also validate the sensitivity bands to LAI. The retrieved bottom reflectance can represent the typical optical properties of seagrass very well than the subsurface remote-sensing reflectance (see Figures 6(a) and (b)). Based on Figure 6(b), it is found that the typical optical characteristics of the seagrass are obvious. In addition, a spectral peak shift from the red edge to the red with leaf areas is increasing. It was found that 555, 650, 675 and 700 nm are relatively good bands to extract LAI information in Figure 6(b). In these regions, an excellent separation among the different LAI index can be done. These bands correspond to the absorption troughs and reflectance peaks, which were also related to the photosynthetic and accessory pigments. Large variations in chlorophyll contents in seagrass leaves could determine a relatively small part of leaf absorp‐ tance. Figure 6(b) shows the properties between 680 and 720 nm in the leaves' spectrum at the different sites. The evident phenomenon is related to the package effect. It was found that the pigment self-shading among thylakoid layers could affect the light absorption and the harvesting efficiency, and thereby the chlorophyll concentration is not linear with the light harvesting efficiency [38]. Cummings and Zimmerman [27], and Enriquez [28] also observed the strong package effect in seagrass, and they concluded that it attributed to the restriction of chloroplasts to the leaf epidermis. Figures 6(c) and (d) show that there is not an obvious relationship between subsurface remote sensing reflectance at 715 nm and LAI. On the contrary, there is a relatively significant relationship between the retrieved bottom reflectance at 715 nm and LAI. This phenomenon also proves that this algorithm is effective to map seagrass distribution and bottom classification.

In Figure 6(b), it was found that the reflectance of Thalassia increased from 518 to 532 nm. This phenomenon was related to the changes in xanthophyll-cycle pigmentation. In addition, the leaves of Thalassia were found to display an olive-drab color in the South China Sea, and that properties was related the peak of the retrieved bottom reflectance curve near 550 nm (see Figure 6(b)). A spectral region of maximum reflectance was found between 800 and 840 nm. It is the typical spectral reflectance of aquatic plants. Based on the spectrum analysis, the modeled bottom reflectance retrieved by the improved algorithm can be used to represent the typical optical properties of seagrass.

#### **5. Conclusions**

() () ( ) <sup>1</sup> *Eq L d g* ll

recorded. The leaf area index *M* can be estimated as:

information which was retrieved from the modeled *Rrs*

. Between 600 and 800 nm, *Rrs*

between the subsurface remote sensing reflectance *Rrs*(0<sup>−</sup>

550 nm and 750 nm the predicted value *Rrs*

*b*

36 Empirical Modeling and Its Applications

*b*

relationship between *in situ* measured *Rrs*

seagrass in optically shallow waters is unfitted.

sensing reflectance *Rrs*(0<sup>−</sup>

**4. Results**

reflectance *Rrs*

of the bottom *Rrs*

conclude that *Rrs*(0<sup>−</sup>

Here *P* represents the seagrass density of each processing (shoots/m2

r

*q*(*λ*) is an angular and wavelength-dependent factor, and *ρg* is the irradiance reflectance of Spectralon. Clear sky conditions are necessary to in situ survey. 100 shoots of seagrass were selected to count leaf number *jj*, and also to calculate the percentage of shoots with *jj* leaves *Xjj*. Ten shoots with the same leaf number were selected. The leaves were centered on a box (25 cm×40 cm), and then took a photo to record the situation. Based on the pixels of seagrass in the photos, *Mjj*, the average leaf area of seagrass with the different numbers of leaves can be

The algorithm was employed to obtain the bottom reflectance. Based on the results the seagrass

erties of the optically shallow water which mainly affect the spectral reflectance at this band.

It is noted that the subsurface reflectance cannot be used directly to classify the bottom type or substitute the bottom reflectance. We provided a comparison between the subsurface remote sensing reflectance and the remote sensing reflectance of the bottom. The results also illustrate the conclusion in Figure 5(a). It was found that there does indeed exist a considerable difference

more related to in situ measured ones in Figure 5(b). It was found that there is a significant

The seagrass reflectance with different LAI (Leaf Area Index) was surveyed to evaluate the relationship between the spectral characteristics of seagrass and also validate the sensitivity bands to LAI. The retrieved bottom reflectance can represent the typical optical properties of seagrass very well than the subsurface remote-sensing reflectance (see Figures 6(a) and (b)). Based on Figure 6(b), it is found that the typical optical characteristics of the seagrass are obvious. In addition, a spectral peak shift from the red edge to the red with leaf areas is

*b*

*b*

*b*

. Compared to the subsurface reflectance, the retrieved bottom reflectance is

) cannot be used directly to represent the hyperspectral recognition of

). This error could be related to the absorption and scattering prop‐

 l

= ×× (24)

*M P iM X* =´ ´ ´ å( *jj jj*) (25)

).

agreed very well with the *in situ* measured bottom

values and modeled ones. Therefore, it is safe to

*<sup>b</sup>* was found to be lower than subsurface remote-

is reasonable to. In Figure 4, between

) and the remote sensing reflectance

An improved optically shallow water algorithm was provided to model the radiation transfer. In the model, the water body was considered as a multilayer, heterogenous, nonhomogenous, natural media. The algorithm could adjust the input parameter to the equation with the different optical properties in water column for retrieving bottom reflectance. The equations which were used to retrieve bottom reflectance or to quantify the benthos can keep the same form. The method could model a wide range of the optical characteristics for radiation fields in these layers. These properties are useful to simulate any contribution of each region and learn the mechanisms of the formation of the radiation characteristics inside and outside the layers. The algorithm can appropriately minimize the effects of the optically shallow water on the remotely sensed signal to obtain an estimate of the reflectance of seagrass.

Based on the results and analysis, the method was proved to be valid for improving the accuracy of bottom mapping. The water column correction algorithm is necessary to retrieve the empirical relationships between satellite data and the interesting features in the optically shallow water. Through the implementation of the algorithm and results analysis between 500–630 nm and 680–710 nm were found to be more effective to discriminate and map seagrass meadows of the Sanya Bay. Therefore, an appropriate spectral band for seagrass mapping should include the narrow bands centered 555, 650, 675 and 700 nm (maximum bandwidth 5– 10 nm). A strong correlation coefficient of 0.99 existed between the bottom reflectance at 715 nm retrieved by the water column correction algorithm and LAI. The input parameters for the algorithm in the study are the remote sensing reflectance from the subsurface. In order to apply the algorithm to the satellite images, the atmosphere correction should be taken into account. The atmosphere influence has a great contribution to affect the blue band. In order to improve the accuracy of the surface reflectance, it could be acquired through further development of the theory and models for the atmospheric correction. Therefore, the reflectance at 715 nm could be used to estimate LAI of seagrass.

#### **Author details**

#### Chaoyu Yang

Address all correspondence to: ycy@scsio.ac.cn

South China Sea Prediction Center, State Oceanic Administration, Guangzhou, China

#### **References**


[8] Smith, R. and Baker, K: Optical properties of the clearest natural waters (200–800 nm). Applied Optics 1981;20:177–184.

meadows of the Sanya Bay. Therefore, an appropriate spectral band for seagrass mapping should include the narrow bands centered 555, 650, 675 and 700 nm (maximum bandwidth 5– 10 nm). A strong correlation coefficient of 0.99 existed between the bottom reflectance at 715 nm retrieved by the water column correction algorithm and LAI. The input parameters for the algorithm in the study are the remote sensing reflectance from the subsurface. In order to apply the algorithm to the satellite images, the atmosphere correction should be taken into account. The atmosphere influence has a great contribution to affect the blue band. In order to improve the accuracy of the surface reflectance, it could be acquired through further development of the theory and models for the atmospheric correction. Therefore, the reflectance at 715 nm

South China Sea Prediction Center, State Oceanic Administration, Guangzhou, China

aquatic vegetation. Science Magazine. 1983;222:51–53.

Applied Optics. 1993;32(33):6864–6879.

[1] Orth, R.J. and Moore, K.A: Chesapeake bay: an unprecedented decline in submerged

[2] Peterson, B.J. and Fourqurean, J.W: Large-scale patterns in seagrass (Thalassia testu‐ dinum) demographics in south Florida. Limnology and Oceanography 2001;46:1077–

[3] Gordon, H.R. and Morel, A: Remote assessment of ocean color for interpretation of satellite visible imagery, a review. Lecture Notes on Coastal and Estuarine Studies.

[4] Yang, D. and Yang, C: Detection of seagrass distribution changes from 1991 to 2006 in Xincun Bay, Hainan, with satellite remote sensing. Sensors 2009;9:830–844.

[5] Dekker, A.G., Malthus, T.J., Wijnen, M.M. and Seyhan, E: Remote sensing as a tool for assessing water quality in Loosdrecht lakes. Hydrobiologia 1992;233:137–159.

[6] Wang, C.K. and Philpot, W.D: Using airborne bathymetric lidar to detect bottom type variation in shallow waters. Remote Sensing of Environment 2007;106:123–125.

[7] Morel, A. and Gentili, B: Diffuse reflectance of oceanic waters: II Bidirectional aspects.

could be used to estimate LAI of seagrass.

Address all correspondence to: ycy@scsio.ac.cn

**Author details**

38 Empirical Modeling and Its Applications

Chaoyu Yang

**References**

1090.

1983;4:114–114.


[35] Huang, L., Tan, Y., Song, X., Huang, X., Wang, H., Zhang, S., Dong, J., Chen, R: The status of the ecological environment and a proposed protection strategy in Sanya Bay, Hainan Island, China. Marine Pollution Bulletin 2003;47:180–186.

[21] Philpot, W.D: Radiative transfer in stratified waters: a single-scattering approximation

[22] Kirk, J.T.O: Light and Photosynthesis in Aquatic Ecosystems, 1994 (Cambridge

[23] Gons, H.J: Optical teledetection of chlorophyll a in turbid inland waters. Environmental

[24] Conger, C.L., Hochberg, E.J., Fletcher, C.H. and Atkison, M.J: Decorrelating remote sensing color bands from bathymetry in optically shallow waters. IEEE Transactions

[25] Becker, B.L., David, P.L. and Qi, J.G: Identifying optimal spectral bands from in situ measurements of Great Lakes coastal wetlands using second-derivative analysis.

[26] Chami, M., Mckee, D., Leymarie, E. and Khomenko, G: Influence of the angular shape of the volume-scattering function and multiple scattering on remote sensing reflec‐

[27] Cummings, M.E. and Zimmerman, R.C: Light harvesting and the package effect in the seagrasses Thalassia testudinum Banks ex Konig and Zostera marina L: optical

[28] Enriquez, S: Light absorption efficiency and the package effect in the leaves of the seagrass Thalassia testudinum. Marine Ecology Progress Series 2005;289:141–150.

[29] Froidefond, J.M. and Ouillon, S: Introducing a mini-catamaran to perform reflectance measurements above and below the water surface. Optics Express. 2005;13(3):926–936.

[30] Henyey, L.C. and Greenstein, J.L: Diffuse radiation in the galaxy. The Astrophysical

[31] Fyfe, S.K. and Dekker, A.G: Seagrass species: are they spectrally distinct? In: Proceed‐ ings of the International Geoscience and Remote Sensing, Sydney, Australia, Reising,

[32] Maffione, R.A. and Dana, D.R: Instruments and methods for measuring the backwardscattering coefficient of ocean waters. Applied Optics. 1997;36(24):6057–6067.

[33] Jennifer, P.C. and Kendall, L.C: Estimating chlorophyll a concentrations from remotesensing reflectance in optically shallow waters. Remote Sensing of Environment.

[34] Louchard, E.M., Reid, R.P. and Stephens, E.C: Optical remote sensing of benthic habitats and bathymetry in coastal environments at Lee Stocking Island, Bahamas: a comparative spectral classification approach. Limnology and Oceanography.

constraints on photoacclimation. Aquatic Botany. 2003;75:261–274.

for irradiance. Applied Optics 1987;26:4123–4132.

University Press, Cambridge, UK).

40 Empirical Modeling and Its Applications

Science and Technology 1999;33:1127–1132.

on Geoscience and Remote Sensing. 2006;44(6):1655–1660.

Remote Sensing of Environment. 2005;97(2):238–248.

tance. Applied Optics. 2006;45(36):9210–9220.

Journal 1941;93:70–83.

2006;101(1):13–24.

2003;48(1, part 2):511–521.

S.V. (Ed.), 2001;6:2740–2742.

