Spatially Weighted Functional Clustering of River Network Data

Abstract

Incorporating spatial covariance into clustering has previously been considered for functional data to identify groups of functions which are similar across space. However, in the majority of situations that have been considered until now the most appropriate metric has been Euclidean distance. Directed networks present additional challenges in terms of estimating spatial covariance due to their complex structure. Although suitable river network covariance models have been proposed for use with stream distance, where distance is computed along the stream network, these models have not been extended for contexts where the data are functional, as is often the case with environmental data. The paper develops a method of calculating spatial covariance between functions from sites along a river network and applies the measure as a weight within functional hierarchical clustering. Levels of nitrate pollution on the River Tweed in Scotland are considered with the aim of identifying groups of monitoring stations which display similar spatiotemporal characteristics.

Spatial functional data analysis for regionalizing precipitation seasonality and intensity in a sparsely monitored region: Unveiling the spatio‐temporal dependencies of precipitation in Ecuador

“…It was previously applied to temperature with the aim of grouping stations with similar behaviour (Giraldo et al, 2012a;Romano et al, 2013), but not to spatially delineate homogeneous regions. It was also used to nitrate pollution on river network stations (Haggarty et al, 2015) and salinity curves measured on a lagoonal-estuarine system (Romano et al, 2015). Regarding precipitation, some works have been undertaken (Hamdan et al, 2015;Suhaila and Yusop, 2017), without considering the spatial dependencies, however.…”

Connected Sensors, Innovative Sensor Deployment, and Intelligent Data Analysis for Online Water Quality Monitoring

“…Further developments in the modelling of environmental time series has come from the application of functional data analysis (FDA) methods [176]. In this context, the "data point" becomes the time series curve [177,178] this approach often is computationally efficient since it offers substantial data dimension reduction. Another important area of analytics frequently used in WQM concerns extreme value modelling (often using peak over threshold (POT) models).…”

Optimally weighted L2 distances for spatially dependent functional data

“…Frequently in many applied contexts, data are curves available at points in space, and in those cases a challenge is to develop useful multivariate approaches that allow us to pool together information from curves at all locations. Let's think, for example, to the problem of monitoring similarities in temporal patterns of water quality parameters by considering the spatial correlation across networks, this can provide information to feed into future monitoring strategies [9] or to the case in which the aim is to investigate similarities in water profiles like salinity by considering the spatial component [24]. The notion of proximity is one of the most important definitions to provide in such a context.…”

“…The emerging characteristics for recently developed methods are mainly related to modelling correlated functional data using spatial structures (geostatistical data, point patterns and areal data) that can be combined with functional data [17]. For this reason, and based on the specific characteristics of the spatial component related to the functional data, the scientific community has focused on developing methods based on suitable measures of distance, or similarity, related to clustering ( [7], [8], [9], [24], [28]), to the definition of depth [1] and to kriging prediction problems [2].…”