# Scalability of Water Property Measurements in Space and Time on a Brackish Archipelago Coast
## 4 Discussion  
We present a detailed examination of the variation of key water properties in horizontal, vertical and temporal dimensions on a brackish archipelago coast, based on a unique high-density dataset. Our results demonstrate that the four water properties, temperature, salinity, pH and chlorophyll-a concentration, vary significantly at temporal and vertical scales. This alone confirms that the spatio-temporal variation of water properties in a com \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variable** & **Temporal** & **Vertical** & **Regional (104 m)** & **Local (102 m)** \\ \hline Temperature & x & x & - & - \\ Salinity & x & x & x & - \\ pH & x & x & x & - \\ Chlorophyll-a & x & x & x & - \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Relevant scales (x) of water property variables, based on ordinary and multilevel regression modelling. Figure 6: Chlorophyll-a random coefficients and the partial effect of “week” in the random slope model: (**A**) site-specific intercepts, (**B**) site-specific slopes for the first-order term, (**C**) the main effects of “week” on chlorophyll-a at four very different sites and (**D**) coefficients on a map. The four different sites highlighted in the figure are “TURM220” and “KUS44” with highest and lowest intercepts, respectively, and “PALA115” and “TSA385” with most and least inclined slopes for “week”, respectively. Note that all coefficients and effects are at the scale of scaled and centred variables. plex coastal archipelago cannot be captured by temporally and vertically sparse sampling, as also suggested by previous studies (e.g., [9,10]). Further, the impact of time on water properties varies notably and somewhat predictably along the vertical gradient. Chlorophyll-a exhibits the most complex temporal and vertical patterns, including a vertical shift of the chlorophyll-a concentration (Figures 3D and 6C). In the spring, the lowest values are measured close to the surface, and highest values at the 10 m depth, while the situation is reversed in the autumn (Figure 3D). This indicates that there are different vertical distributions of the life cycles between the phytoplankton species occurring in the spring and in the later summer (e.g., [43,44]). The model captures the spring and later summer peaks in algal growth [45], as well as a continuous increase in salinity throughout the study period. A notable part of the variation in salinity, pH and chlorophyll-a occurs at the site level (12-34%), i.e., between locations that are several kilometres apart. Thus, salinity, pH and chlorophyll-a vary notably at the regional scale (10\({}^{4}\) m). Temperature varies more homogeneously at the regional scale, but finer details of the temporal-vertical patterns are site-dependant. No notable variance remains at the sub-site level. In other words, there is no local-scale (10\({}^{2}\) m) variation in water properties (Table 5). These findings statistically confirm the indicative results by [PERSON] et al. [9]. Instead of trying to explain why the variation among the water properties occurs, the aim of this study is to portray how the variation occurs spatio-temporally, and how it is divided into the horizontal, vertical and temporal dimensions. There are many underlying phenomena and measurable variables, such as nutrient concentrations, which regulate the chlorophyll concentration and the seasonal distribution of solar radiation, which regulates, among other things, the water temperature [46]. Instead of coupling the drivers with outcomes, this study confirms the significance of the water property variation in all dimensions. Multilevel modelling proves to be an appropriate statistical approach to partitioning variation in water property variables into temporal, vertical and horizontal dimensions and examining their temporal and vertical gradients in different areas. As they are designed for accounting for the spatially nested structure of observations, they would be suitable for testing hypotheses on the drivers of water properties based on such spatial data.