## 2 Materials and Methods
### Methodology
#### 2.3.2 Markov Dynamic Evaluation  
As an important method to study the state of an event and the law of transition between states, the Markov process can analyze the changing trend of the state at the time of \(t_{0}+\Delta t\) by the initial \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Season** & **Type of Data** & \multicolumn{2}{c}{**Image Date**} & **Track Number** \\ \hline  & & 9 July 2014 & 30 July 2016 & \\  & & 11 September 2014 & 16 September 2016 & \\  & & 27 September 2014 & 14 May 2017 & \\ Flood & & 13 October 2014 & 30 May 2017 & Path: 124 \\ period & Landsat8 OLI & 12 July 2015 & 18 August 2017 & Row: 45 \\  & & 14 September 2015 & 3 September 2017 & \\  & & 30 September 2015 & 18 June 2018 & \\  & & 16 October 2015 & 6 September 2018 & \\  & & 11 May 2016 & 8 October 2018 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._probability of the different states of the event at the time of \(t_{0}\) and the probability transfer relationship between states, and can intuitively reflect the dynamic process of an event during this period [45]. It has no after-effects, that is, the state transition probability is only related to the transition start state, the number of transfer steps and the post-transition state. It is independent of the initial moment of the transition [46]. Therefore, the combination of large-scale remote sensing evaluation at a single time and the Markov process method with multi-period stochastic dynamic analysis not only breaks through the limitations of static analysis of traditional remote sensing evaluation but also reflects the trend of dynamic changes in multiple periods. The new research method was provided for the change trend evaluation of TSS concentrations in the Hedi Reservoir area. To reflect the trend of dynamic changes in the concentration of TSS in the reservoir area in 2014-2018, grids (k) of \(30\times 30\) m size (equal to the pixel size of Landsat OLI images) are distributed in the reservoir area. Each grid represents a site where every site has a value about the TSS concentration, and each site has a total monitoring of n times in a year. Each site performs multiple monitorings per year based on clear satellite data for the last 5 years. According to Formula (2) in Section 2.2.2, the water quality of the reservoir was classified into 4 levels: levels I, II, III and IV. We set \(E\) as the above 4 levels, and the corresponding state space can be expressed as \(E=\{1,2,3,4\}\) in turn. The Markov process is a time series model, and the construction process is described below [23; 35; 47]:  
Step 1: Establishing the probability transition matrix \(P\)  
The possibility transition in which the water quality changed from \(i\) level to \(j\) level can be simulated using an equation as follows:  
\[p_{ij}=\frac{n_{ij}}{M_{i}-m_{i}},0\leq p_{i,j}\leq 1;\sum_{i}p_{ij}=1 \tag{5}\]  
where \(p_{ij}\) is the transition probability of level \(i\) transferred from level \(j\), \(n_{ij}\) is the number of original data of level \(i\) transferred from level \(j\) for \(n\) times in the same site of the reservoir, \(M_{i}\) is the number of original data sites at level \(i\) during the \(y_{n}\)th monitoring and \(m_{i}\) is the number of original data sites at level \(i\) in the monitoring of \(n\) times. Then, the matrix \(P=\left(p_{ij}\right)_{n\times n}\) can be found, and this is the possible transition matrix of the reservoir. Step 2: Build the progress matrix \(S\)  
The progress matrix is used to show how to distinguish the water quality deteriorated or improved from \(i\) level to \(j\) level in the time of monitoring and it can be calculated using an equation as follows:  
\[s_{ij}=(i-j)\big{|}i-j\big{|}p_{ij},(i,j\in E) \tag{6}\]  
where \(s_{ij}\) is the weight which can figure out the extent the water quality deteriorated or improved, and \(i\) and \(j\) are the levels of water quality that follows as \(E=\{1,2,3,4\}\).