Abstract
We build a Bayesian spatio-temporal model for rainfall in South Carolina based on a three-stage hierarchical structure with data, process, and parameters. In our Gaussian process model, we model the true underlying process in the first level and the spatio-temporal random effect in the second level of the hierarchy. The prior distribution of the parameters and hyperparameters is specified in the third stage. We also extend the Gaussian process model to an autoregressive model by adding a temporal correlation parameter ρ.
A first-order harmonic regression is used to remove seasonality. Accounting for seasonality is essential to our Gaussian process model since a homogeneous structure across all monthly observations is assumed. In addition, the covariates elevation and temperature are also included in the Gaussian process model. In particular, we incorporate a variable related to sea surface temperature (SST) to reflect the effect of El Niño-Southern Oscillation (ENSO) activity. Kernel smoothing is used to derive this feature. Preliminary model fitting results suggest that SST has a negative effect on the rainfall amount. Another finding is that mean precipitation in South Carolina is significantly higher in 2015, when the area suffered from substantial floods.
We also compare the Gaussian process model with another common framework to handle spatio-temporal data, the dynamic linear model (DLM), which while not predicting out-of-sample rainfall as well as the Gaussian process model allows a more detailed monthly study of the effect of covariates. For example, the SST-based variable affects the rainfall amount more significantly during the first few months of the year.
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Liu, H., Hitchcock, D.B., Samadi, S. (2019). Spatial and Spatio-Temporal Analysis of Precipitation Data from South Carolina. In: Diawara, N. (eds) Modern Statistical Methods for Spatial and Multivariate Data. STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health. Springer, Cham. https://doi.org/10.1007/978-3-030-11431-2_2
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