# Scalability of Water Property Measurements in Space and Time on a Brackish Archipelago Coast
## 3 Results  
### General Vertical and Seasonal Patterns in Water Properties  
Based on the BIC, the best models for all four response variables had similar base structures (Table 3). All models included \"week\" and \"depth\" as predictors, the interaction term between \"week\" and \"depth\" and up to seventh-order polynomials for \"week\" (Table 3). Only the chlorophyll-a model included a higher-order (second-order) term for \"depth\". The selection of terms included in the models remained identical throughout the modelling steps, i.e., in the observation-level, random intercept, and random slope models. In addition, the estimated coefficients of the predictor terms remained almost identical throughout the modelling process (Table 3). These results indicated that the estimated fixed effects were robust: the identified relationships were not sensitive to the selection of the modelling method.  
The estimated model coefficients showed considerable variation between response variables (Table 3). Thus, the fitted models indicated that the four response variables had  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{Estimates (Variation between Model-Fitting Steps)} \\
**Term** & **Temperature** & **Salinity** & **pH** & **Chlorophyll-a** \\ \hline Intercept & 0.72 (0) & 0.38 (0.01) & \(-\)0.23 (0.07) & 0.64 (0) \\ Week & \(-\)0.46 (0) & 0.24 (0.02) & \(-\)2.27 (0.02) & \(-\)0.91 (0.01) \\ Depth & \(-\)0.13 (0) & 0.06 (0) & \(-\)0.15 (0.01) & \(-\)0.11 (0) \\ Week:Depth & 0.10 (0) & \(-\)0.05 (0) & 0.05 (0) & \(-\)0.18 (0) \\ Week\({}^{2}\) & 0.35 (0) & \(-\)0.75 (0.05) & & \(-\)0.99 (0.04) \\ Depth\({}^{2}\) & & & & \(-\)0.14 (0) \\ Week\({}^{3}\) & 5.32 (0) & 0.61 (0.05) & 8.42 (0.02) & 5.07 (0.06) \\ Depth\({}^{3}\) & & & & \\ Week\({}^{4}\) & \(-\)1.40 (0) & 0.21 (0.02) & 0.25 (0.07) & 0.26 (0.02) \\ Depth\({}^{4}\) & & & & \\ Week\({}^{5}\) & \(-\)5.64 (0) & & \(-\)8.55 (0.03) & \(-\)4.54 (0.11) \\ Depth\({}^{5}\) & & & & \\ Week\({}^{6}\) & 0.37 (0) & & \(-\)0.07 (0.02) & \\ Depth\({}^{6}\) & & & & \\ Week\({}^{7}\) & 1.49 (0) & \(-\)0.08 (0.01) & 2.21 (0.01) & 1.09 (0.03) \\ Depth\({}^{7}\) & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Observation-level terms included in the best-performing observation-level and multilevel models, and their estimates based on the multilevel random slope models. In addition, the variation of the estimates between model-fitting steps are reported in the brackets. This is the difference between largest and smallest estimates at the predictor variable’s scale, considering the best observation-level, intercept-only and random slope models. Note that the model selection was repeated at each step of the modelling process, but the term selection was identical at each step. Common terms across all four models are highlighted with grey background.  
different relationships with time and depth. Temperature showed a unimodal relationship with time, peaking during week 34 in late August (Figure 3A). The linear drop of temperature with depth decreased and finally disappeared with time (Figure 3A). Salinity increased during the study period, and the slight layering (least saline water at the top) decreased and disappeared with time (Figure 3B). pH generally decreased with time, with the largest changes at the beginning of the period (Figure 3C). The layering in pH decreased slightly with time (Figure 3C).  
The temporal changes in the chlorophyll-a concentration were most complex. Chlorophyll-a reached its minimum during week 23 (early June) and peak during weeks 31-34 (August; Figure 3D). The vertical pattern in chlorophyll-a turned over during the period: the topmost layer had the lowest concentration in early spring but the largest concentration in late autumn (Figure 3D). Based on the model, the layering was strongest at the end of the period (Figure 3D).