A Convolution Process for Spatial Statistical Models on Directed Linear Networks

This work addresses the problem of geo-statistical analysis on a linear network by introducing an innovative process based on a moving average construction. The proposed random process generates a valid covariance model, explicitly accounting for the directional dependencies in the domain given by a velocity field. We apply this methodology to real-world data, modeling water temperatures in the Mediterranean Sea under projected climate change scenarios. To preserve the directionality of water currents, we approximate the continuous domain by a linear network. We then construct prediction intervals for temperature projections, providing insights into potential climate impacts on the region.