# Multidimensional Assessment of Lake Water Ecosystem Services Using Remote Sensing
## 2 Materials and Methods
### Exploratory Spatial Data Analysis  
Much of the groundwork in spatial statistics is concerned with the description and exploration of spatial datasets [76]. The generic term for such methods in the context of spatial analysis is exploratory spatial data analysis (ESDA). In practical applications, ESDA emphasizes the natural distribution of spatial data, focusing on the correlation of events, inheriting the quantitative geographic analysis methods, and exploring the spatial patterns of data [77]. Spatial clustering is the grouping of spatial datasets, with maximized intra-group similarities and the differences among groups, which is an efficacious method for spatial \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Index** & **Formula** & **Introduction** \\ \hline P & \(P_{ij}=\frac{P_{ij}-\overline{P_{i}}}{\sigma_{ij}}\) & \begin{tabular}{c} \(P_{ij}\) is the P-score of the county \(i\) in the year \(j\), \(P_{ij}^{\prime}\) is the lake water storage of the county \(i\) in the year \(j\), \(P_{ij}^{\prime}\) is the average lake water storage of the state in year \(j\), \(\sigma_{P_{j}}\) is the standard deviation of all counties in year \(j\). \\ Q & \(Q_{ij}=\frac{Q_{ij}^{\prime}-Q_{ij}}{\sigma_{Q_{ij}^{\prime}}}\) & \begin{tabular}{c} \(P_{ij}\) is the Q-score of ecosystem service efficiency of the county \(i\) in the year \(j\), \(Q_{ij}^{\prime}\) is the water storage of unit lake area in the county \(i\) in the year \(j\), is the average water storage of unit lake area in the state in year \(\sigma_{Q_{ij}^{\prime}}\) is the standard deviation of all counties in year \(j\). \\ D & \(D_{ij}=\frac{\Delta D_{ij}-\Delta D_{j}^{\prime}}{\sigma_{\Delta D_{j}^{\prime}}}\) & \
\begin{tabular}{c} \(D_{ij}\) is the D-score of the county \(i\) in the year \(j\), \(\Delta D^{\prime}\) is the annual efficiency change in the county \(i\) in year \(j\), \(\Delta D^{\prime}\); is the average of annual efficiency change in the entire state in year \(j\), \(\sigma_{\Delta D^{\prime}}\) is the annual efficiency change standard deviation of all counties in year \(j\). \\ \end{tabular} \\ D & \(\Delta D_{ij}=Q_{ij}-\Delta D_{i(j-1)}\) &
\begin{tabular}{c} \(P_{ij}\) is the D-score of the county \(i\) in the year \(j\), \(\Delta D^{\prime}\); is the annual efficiency change in the county \(i\) in year \(j\), \(\Delta D^{\prime}\); is the average of annual efficiency change in the entire state in year \(j\), \(\sigma_{\Delta D^{\prime}}\); is the annual efficiency change standard deviation of all counties in year \(j\). \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Formulas of assessment indices. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Space** & **P** & **Q** & **D** & **Properties** & **Description** \\ \hline
1 & + & + & + & The total output, efficiency, and trend index are above average. & Progression \\
2 & + & + & \(-\) & The total output and efficiency are above average, but the trend index is below average. & Degradation \\
3 & + & \(-\) & + & Although the efficiency is below average, it has been raised. The & Progression \\  & + & \(-\) & \(-\) & The efficiency is below average, and it has degraded. The above-average & Degradation \\  & + & \(-\) & \(-\) & output depends on the ecosystem scales. & Degradation \\
5 & \(-\) & + & + & The output is below average, indicating that the ecosystem scale should be expanded. & Progression \\
6 & \(-\) & + & \(-\) & Both the output and the trend index are below average, but it has high efficiency. & Degradation \\
7 & \(-\) & \(-\) & + & The output and efficiency are below average, but it has an above-average & Progression \\  & & & trend index. & & \\
8 & \(-\) & \(-\) & \(-\) & All three indices are below average. It has a lower output and efficiency. & Degradation \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Multidimensional assessment spaces and their properties. distribution identification and outlier detection.