Joint Spatial Modeling of Nutrients and Their Ratio in the Sediments of Lake Balaton (Hungary): A Multivariate Geostatistical Approach

Eutrophication, water quality, and environmental status of lakes is a global issue that depends not only on external loadings from industrial, agricultural, and municipal sources but often also on internal loadings from lake sediments. In the latter case, in addition to the quality and quantity of nutrients stored in sediments, their relative content may be an important factor. In the example of Lake Balaton, we jointly modeled the spatial distribution of the nutrients nitrogen (N) and phosphorus (P) and their ratio (i.e., N:P) in the sediments of the lake and then provided spatial predictions at different scales (i.e., point, basin, and entire lake) with the associated uncertainty. Our aim was to illustrate the merits of applying multivariate geostatistics when spatial modeling of more than one variable is targeted at various scales in water ecosystems. Variography confirmed that there is a spatial interdependence between the nutrients. The results revealed that multivariate geostatistics allows this interdependence to be taken into account and exploited to provide coherent and accurate spatial models. Additionally, stochastic realizations, reproducing the joint spatial variability, can be generated that allow providing spatially aggregated predictions with the associated uncertainty at various scales. Our study highlighted that it is worthy of applying multivariate geostatistics in case spatial modeling of two or more variables, which jointly vary in space, is targeted in water ecosystems