# Scalability of Water Property Measurements in Space and Time on a Brackish Archipelago Coast
## 1 Introduction  
Coastal waters form a globally important environment at the land-sea interface, where the aquatic ecosystems are diverse, and the human influence on the sea is at its highest. Particularly in estuaries and other semi-enclosed coastal areas, the brackish water zone is often a very complex marine environment where the physicochemical processes, water flows and ecological features from dynamic and detailed patterns. However, understanding the patterns and processes of these environments is crucially important when trying to maintain and improve their ecological status, and to prepare for the impacts of global change [1; 2; 3; 4]. A better understanding of the current status and the processes is needed to improve the science-based management of the marine archipelago environments in the future [5; 6; 7; 8]. Coastal waters are typically complex and gradually shifting zones between the mainland shoreline and the pelagic realm. Within this zone, high local variability and temporal inconsistency in water properties often occur [9; 10; 11; 12; 13; 14; 15], and the variation is usually different among the parameters. When monitoring the status of the coastal marine environment and the impacts of nature conservation measures, the sampling must be carefully fitted to the spatial and temporal scales of the phenomena [9; 16], since the results of a monitoring campaign are highly sensitive to the timing and location of the sampling [17; 18; 19; 20]. Archipelago coasts, in particular, are characterised by a notable spatial and temporal variation in water properties [9; 10; 21]. Our study area, the SW Finnish archipelago coast in the Baltic Sea, is a good example, where small and large islands, deep basins, shallows and sills create a very complex bathymetry [9]. The varying bathymetry causes restrictions in water exchange [22]. In addition, the location of many archipelagos at the land-sea-interface causes local and temporal variation in marine and terrestrial influences [23]. For example, a large component of the variability in water properties in the SW Finnish archipelago is persistent and depends on the location along the land-sea transition: [PERSON] et al. [9] reported clear spatial trends in the water properties along the mainland-open sea axis. Seasonality causes an important component of variability in water properties in higher latitudes. This includes a high annual temperature and stratification cyclicity, winter ice cover, and high variability in runoff due to snow accumulation and melting. Thus, in addition to the spatial complexity, the temporal complexity is distinct. These complexities together make brackish coastal archipelagos, such as the SW Finnish coast, very dynamic and challenging to monitor. The environmental conditions vary due to the presence of islands and shallow topography, causing the seasonal developments (i.e., timing and magnitude) of, e.g., algal growth, to differ within small areas--numerous previous studies, which have utilised in situ and remotely sensed data and spatial modelling, highlight these features in the SW Finnish archipelago in terms of spatial [11; 24; 25], temporal [9; 12; 26], and spatio-temporal variability [10; 27]. Many studies conclude that the variation is difficult to capture, and it is advisable to use combined methods to complement in situ sampling (e.g., [9; 10; 11; 26]). However, to our knowledge, the four-dimensional (temporal, vertical and horizontal) patterns of water quality have not yet been statistically quantified. This study aimed at statistically examining the scalability of water properties in space and time in a heterogeneous archipelago (Figure 1). More specifically, we examined how the variation in archipelago water properties is divided into the temporal, vertical and horizontal dimensions (Figure 1). We pursued this by statistically reanalysing a unique, pre-existing dataset from the SW Finnish archipelago (described in [PERSON] et al. [9]).