Geostatistical analyses involve the statistical processing of vast datasets, like measurements of wind speed over time and at various altitudes and locations, to develop a model of how specific parameters behave and are correlated both spatially and temporally in the real world.
KAUST researchers have developed a more accurate method for modeling wind-driven phenomena. They demonstrated their model by applying it to a dataset of air pollution across Saudi Arabia. Image Credit: © 2022 KAUST; Morgan Bennett Smith.
However, the analytical model framework heavily influences how well these models can characterize that behavior and anticipate “what occurs next”. To better model such natural events, a group of KAUST scientists under the direction of Marc Genton have been building more physically sound analytical frameworks.
Many space-time geostatistical models do not necessarily reflect fundamental scientific relationships. There is demand for space–time geostatistical models with a physics basis, as most environmental data obey various fundamental laws of nature.
Mary Salvaña, King Abdullah University of Science and Technology
Mary Salvaña—who worked with Genton and Amanda Lenzi on the research—adds, “In this study, we took a modeling concept in physics called the Lagrangian framework and formulated it in the language of space–time multivariate geostatistics to develop a suite of data-driven space–time models that are more appropriate for datasets involving transport by media, such as wind.”
Incorporating wind into a useful statistical model is a challenging task. It varies by height and is asymmetric in association, flowing from one location to another. To simulate flows in a fashion that is equivalent to the underlying physics, the Lagrangian framework was established by tracking a fluid parcel as it moves through space and time.
The difficulty faced by Salvaa and her colleagues was ensuring that this framework could be effectively applied to a space–time geostatistics model across a variety of variables.
Our results, which confirmed the validity of the model, showed that failing to account for multiple advections or transport phenomena can lead to poor predictions.
Mary Salvaña, King Abdullah University of Science and Technology
By using a bivariate pollutant dataset of particulate matter across Saudi Arabia, the researchers gave a demonstration of their model. The findings demonstrated that models of black carbon distributions that incorporate altitude-dependent wind are substantially more accurate.
Our modeling framework could also be applied to the study of space–time correlation of ocean variables, since water is another transport medium, which could be important for understanding ocean patterns before and after a tropical cyclone.
Mary Salvaña, King Abdullah University of Science and Technology
Journal Reference:
Salvaña, M. L. O., et al. (2022) Spatio-Temporal Cross-Covariance Functions under the Lagrangian Framework with Multiple Advections. Journal of the American Statistical Association. doi.org/10.1080/01621459.2022.2078330.