# Scalability of Water Property Measurements in Space and Time on a Brackish Archipelago Coast
## 3 Results
### Variability of Temporal and Vertical Patterns at Regional and Local Scales  
Sequential fitting of the random slope models and examination of the BIC indicated that the best multilevel models for all four water property variables included random slopes for the first- and second-order \"week\" terms (Table 5). In addition, all models included a random slope for \"depth\" (Table 5). Thus, the best-performing multilevel models allowed the intercept and slope coefficients for both \"week\" and \"depth\" to vary between sites. In practice, the random intercept allowed the overall level of the response variable to vary between sites, thus reflecting real-life differences in the level of a water property variable. The random slope coefficient for \"week\" meant that the value of each water property variable changed more rapidly with time in specific sites than in others. Similarly, the random slope coefficients for \"depth\" indicated that the strength of the vertical water property gradients varied between sites. The best multilevel models succeeded in explaining 95%, 92%, 79% and 60% of variance in temperature, salinity, pH and chlorophyll-a, respectively (Table 6). The improvement of model performance, compared to the corresponding observation-level model, was notable for salinity (Figure 4), pH and chlorophyll-a, since the models were able to accommodate site-specific relationships between water properties, time and depth. For example, compared to linear regression models, the best multilevel model for salinity decreased residual variance from 0.46 to 0.08 (Table 6; Figure 4). Overall, the chlorophyll-a models performed worst, but the improvement in performance compared to observation-level models was notable (decrease in residual variance from 0.72 to 0.40; Table 6). For temperature, the performance of the best observation-level model was so high that there was little room for improvement in multilevel models (Table 6). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Response Variable** & **ICC (Site)** & **ICC (Site:Sub-Site)** \\ \hline Temperature & 0.01 & 0.00 \\ Salinity (conductivity) & 0.34 & 0.00 \\ pH & 0.12 & 0.00 \\ Chlorophyll-a & 0.17 & 0.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Intraclass correlations (ICC) in the intercept-only models. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Random Slopes**} \\ \multirow{2}{*}{**Variable**} & **Random** & \multirow{2}{*}{**(Week1 Site)**} & \multirow{2}{*}{**(Week21 Site)**} & \multirow{2}{*}{**(Depth | Site)**} & \multirow{2}{*}{**(Depth21 Site)**} \\  & **Intercept** & & & \\  & **(1 1 Site)** & & & \\ \hline Temperature & x & x & x & - \\ Salinity & x & x & x & - \\ pH & x & x & x & - \\ Chlorophyll-a & x & x & x & - \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Site-level random terms included (x) and excluded (-) in best-performing random slope models. The random slope models for salinity (Figure 5) and chlorophyll-a (Figure 6) indicated the most distinct random effects, i.e., the largest site-specific variation in the overall levels and in the temporal and vertical patterns. For example, salinity was generally highest (highest intercept) in the southern sites in the outer archipelago and lowest in the inner archipelago (e.g., KORP110 and TSA385, respectively; Figure 5). The slope of the first-order \"week\" term was generally steepest in the north-western part of the study area, meaning that the increase in salinity during the summer season was most distinct (Figure 5). In some other sites, such as \"PAR01\", salinity did not exhibit a clear increasing trend (Figure 5). The overall level (intercept) of chlorophyll-a was highest in the central inner archipelago, as well as in the southern sites (Figure 6). The random effects indicated very different and even opposite temporal changes in chlorophyll-a concentration in the archipelago (Figure 6). For example, the model predicted the chlorophyll-a concentration to remain relatively low throughout the summer season in \"KUS44\" (Figure 6).