# Multidimensional Assessment of Lake Water Ecosystem Services Using Remote Sensing
## 3 Results
### Spatio-Temporal Development of Water Provisioning
#### 3.1.2 Spatial Analysis Results  
We selected 1998, 2003, 2008, 2013, and 2018 as the representative years to explore the spatial characteristics of water provisioning ecosystem services at the county level. The water provisioning ecosystem services provided by each lake belong to the county where the lake contour geometric center is located. From the perspective of water provisioning total output (i.e., P-score), water provisioning output has a stable spatial distribution. The above-average areas are mainly located in the North Central and Northeast. St. Louis, Cass, and Mille Lacs (Figure 10) have the highest water provisioning output where P-scores were three times the standard deviation, higher than the average. In contrast, the below-average areas dispersed in West Center, Central, Southwest, South Central, and Southeast. Moreover, there is no P-score less than \(-1\), which means no county where the P-score is one standard deviation less than the average. In other words, water provisioning ecosystem services have been abundant in the study area. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(Z_{c}\) & \(\alpha\) & **Var(S)** & \(Z\)(\(1-\alpha/2\)) & \(p\)**-Value** & \(\beta\) \\ \hline \(-\)0.8757 & 0.05 & 1096.67 & 1.9600 & 0.3812 & \(-\)0.7027 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mann–Kendall test and Sen’s slope estimator. Figure 9: The temporal trend of total lake water storage and lake surface area in Minnesota (1998–2018). According to the hotspot analysis results (Figure 10), water provisioning services have a stable spatial clustering pattern without any cold spot for 21 years. The high P-score values are concentrated in North Central, East Central, and Northeast. It reveals that the zones with lower water provisioning services exhibited a random distribution while the higher service output zones clustered with high spatial autocorrelation. Q-scores reflect the efficiency of water provisioning services and have a stable spatial distribution similar to P-scores. North Central, East Central, and Northeast are where the above-average Q-scores concentrate, while the below-average Q-scores dominate other zones. Hubbard and Mille Lacs (Figure 11) have the highest Q-scores from 1998-2013, with twice the standard deviation above the average. It shows that Hubbard and Mille Lacs counties have the best water provisioning service efficiency. Comparing the Q-scores spatial distribution at these 5 years, we found that the water provisioning service efficiency deteriorates. The areas with above-average Q-scores shrink year by year, while areas with below-average Q-scores expand. The area with one standard deviation above the average Q-scores dropped from 34.43% of the total area to 28.82% during 1998-2018. The Q-scores area, one standard deviation below the average, grew from 2003 and expanded to 15.69% of the total area in 2018. The Q-score hotspot analysis results identified hot spots and colds pots. Hot spots are mainly located in North Central and Northeast, with an apparent eastward shift. Cold spots expanded before 2008 and then contracted. There are two cold spots, and the larger one was concentrated in Southwest, South Central, and Southeast in 1998, and shrank to  
Figure 11: Q-score distribution and spatial clustering. Figure 10: P-score distribution and spatial clustering. Southwest in 2018. The other one appeared in Northwest in 2003, with expansion, reached the enormous areal scale in 2008, and shrank afterwards. The D-scores distribution shows a \"comparable average values dominated, and extreme values dispersed\" pattern (Figure 12). They are mainly between one standard deviation below the average and one standard deviation above the average. In comparison, the water provisioning service trend's stability declines, which is witnessed by the expansion of extreme D-scores and the erosion of comparable average D-scores. Cold spots and hot spots have changed significantly. Hot spots shifted towards the south; they passed East Central from Northeast and moved to South Central.