## 2 Materials and Methods
### Methods
#### 2.4.2 Developing a Modified CT Model  
The feature values from remotely sensed data can vary for different aquatic vegetation types as a growing season progresses, but it remains true that the between-class differences are far greater than within-class differences. Therefore, the hierarchic, structure and spectral features of a classification tree should be the same across different image dates, but with fluctuating value of spectral features [15,19].  
CT model thresholds developed for one image might be inappropriate for an image acquired at a different time due to intrinsic and extrinsic factors. We developed a traditional classification CT model for each image date with the respective ground-based training samples corresponding to that date. We then developed modified CT modes based on two hypotheses:  
**Hypothesis I:** The effects of intrinsic and extrinsic factors were the same for every pixel or changed in a linear fashion over time. With this hypothesis we assumed there was a good linear relationship between SFs from the two image dates and could develop a modified CT model for one image based on a linear adjustment of thresholds from a traditional CT model developed for the other date image [30]. We defined modified model as:  
\[a\lambda CT_{n\to m}^{m}\text{-}S\!F_{i}=k\times TCT_{n}\text{-}S\!F_{i}+h \tag{1}\]  
where \(\alpha MCT_{n\to m}^{m}\text{-}S\!F_{i}\) is the threshold of spectral feature \(i\) in the modified CT model based on hypothesis I for date \(m\), calculated using the linearly adjusted traditional CT model for date \(n\); SF\({}_{i}\) is  
Figure 2: Band reflectance from HJ- CCD imagery of emergent, floating-leaved, submerged vegetation and water.  
\begin{table}
\begin{tabular}{c c} \hline \multicolumn{2}{c}{**Spectral Features (SFs)**} & \multicolumn{1}{c}{**Description**} \\ \hline SF\({}_{1}\): (B4 – \(\sum\limits_{j=1}^{3}\)_j_)/(B4 – \(\sum\limits_{j=1}^{3}\)_j_) & B1–4 are the four reflectance bands (_j_ = 1, 2,..., 4). \\ \hline SF\({}_{2}\): PC2 & PC2 is the second principal component of the principal component transform. \\ \hline SF\({}_{3}\): TC1–TC2 & TC1 and TC2 are the greenness index and brightness index of the \\  & tasseled-cap transform. \\ \hline \end{tabular}
\end{table}
Table 3: Spectral features (SFs) in this study.  
spectral feature \(i\) (\(i\) = 1, 2, or 3) (see Table 3); \(k\) is the slope of a linearly fitted line between the SFs of a given aquatic cover type on images for dates \(m\) and \(n\); \(TCT_{n}\)-\(SF_{i}\) is the threshold of spectral feature \(i\) from the traditional CT developed for image date \(n\); and \(h\) is the intercept of a linearly fitted line between the values of SFs for a given aquatic cover type on images for dates \(m\) and \(n\).  
**Hypothesis II:** the ranked value for spectral feature \(i\) in one date image would be linearly related to the ranked values for that feature in a different date image [31]. With this hypothesis we assumed we could developed modified CT thresholds based on a linear model developed from the ranked SF values for the two image dates. We define this modified model as:  
\[bMCT_{n\to m}^{m}\text{-}SF_{i}=p\times TCT_{n}\text{-}SF_{i}+q \tag{2}\]  
where \(bMCT_{n\to m}^{m}\text{-}SF_{i}\) is the threshold of spectral feature \(i\) in the modified CT model based on hypothesis II for date \(m\), calculated using the linearly adjusted traditional model for date \(n\); \(p\) is the slope of a linearly fitted line between the SFs of a given aquatic cover type on images for dates \(m\) and \(n\); \(TCT_{n}\)-\(SF_{i}\) is the threshold of spectral feature \(i\) from the traditional CT model developed for image date \(n\); \(q\) is the intercept of a linearly fitted line between the values of SFs for a given aquatic cover type on images for dates \(m\) and \(n\).  
To develop the methods for modifying the models under hypotheses I and II, we created three regions of interest as representative sample regions for different aquatic vegetation types (Table 4).