# Scalability of Water Property Measurements in Space and Time on a Brackish Archipelago Coast
## 2 Materials and Methods
### Statistical Analyses  
We performed multivariate regression modelling to partition variation in the four response variables, water temperature, salinity, pH and chlorophyll-a concentration (Table 2), into temporal and vertical dimensions. In practice, we examined the statistical relationship between the response variables and two predictor variables, week and depth (Table 1). Multilevel modelling was applied to examine the site- and sub-site-level variability in water properties. First, we partitioned variation in the four water property variables into temporal and vertical dimensions, by identifying the significance of \"week\" and \"depth\" terms in the multivariate regression model. We accounted for the general vertical and seasonal patterns of water properties of the SW Finnish archipelago by looking for the best linear regression model structure. We fitted multivariate linear regression models to the water property data, using a combination of backward and forward stepwise regression to identify the best model variant for each water property variable. These models are hereafter called \"observation-level models\" for comparison to multilevel models. We considered linear and higher-order (up to 10 th order) terms of \"week\" and \"depth\" and the first-order interaction term (\"Week:Depth\") in the models (Equation (1)). Considering high-order models allowed us to find well-fitting multivariate models that account for complex seasonal cycles in water properties. This ensured that all unexplained variance is due to factors other than time and depth, and thus facilitated the examination of site- and sub-site-specific patterns in the following modelling steps. The predictors were standardised, i.e., centred and scaled, before analysis to reduce convergence and collinearity issues [32; 33]. \[\text{Response }\sim\text{Week }+\text{Depth }+\text{Week}^{2}+\text{Depth}^{2} \ldots\ +\text{Week}^{10}+\text{Depth}^{10}+\text{Week:Depth} \tag{1}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dimension** & **Levels** & **n (min)** & **n (max)** & **Levels with Non-Equal Obs.** \\ \hline Temporal: Week & 8 & 342 & 360 & 2 \\ Vertical: Depth & 6 & 476 & 477 & 1 \\ Spatial: Site & 20 & 126 & 144 & 2 \\ Spatial: Sub-site & 60 (3/Site) & 42 & 48 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dimensions of the in situ data. Levels = number of unique observations, n = total number of repeated observations on each dimension. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Variable** & **Dimension** & **n** & **Min** & **Average** & **Median** & **Max** & **St. Dev.** \\ \hline Temperature & \({}^{\circ}\)C & 2861 & 5.9 & 14.6 & 15.4 & 20.4 & 3.5 \\ Salinity (sp. conductance) & mS/m & 2861 & 906 & 1018 & 1023 & 1145 & 40 \\ pH & & 2861 & 7.0 & 8.1 & 8.0 & 8.7 & 0.2 \\ Chlorophyll-a & RFU & 2861 & \(-\)0.1 & 3.5 & 3.3 & 10.0 & 1.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Descriptive statistics for the four water property variables. Individual terms were sequentially dropped in the order of their t-statistic, and the performance of model variants was examined based on the Bayesian information criterion (BIC). Second, we examined the general variation of the four water property variables along temporal and vertical gradients. After the identification of the best observation-level model variant, the interactive effects of \"week\" and \"depth\" on each water property variable were examined [34] by plotting the back-transformed effect of \"week\" on the water property variable at different depths. Third, we partitioned the variation in the four water property variables into horizontal scales (local and regional). We examined water property variation at the site and sub-site levels by fitting simple linear multilevel models, or intercept-only models, to the water property data.