A) Bayesian Spatially Varying Coefficient (SVC) Model for LST
B) Bayesian SVC Model for SUHI
where
- \( y_i(s) \) = LST at day \( i \) and pixel \( s \)
- \( z_i(s) \) = SUHI at day \( i \) and pixel \( s \)
- \( \mathbf{X}_i(s)\boldsymbol{\beta} \) = linear predictor for day \( i \) and pixel \( s \)
- \( u(s) \) = spatially varying intercept (residual spatial effect)
- \( t_i \cdot v(s) \) = spatially varying linear effect of time (long-term
summer linear trend)
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Spatially varying intercept and
spatially varying linear effect of time
modelled as latent Gaussian random fields using the SPDE
(Stochastic Partial Differential Equation) approach
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Posterior excursion sets at 95% probability for
\( t_i \cdot v(s) > 0 \) and
\( t_i \cdot v(s) < 0 \) to identify warming and cooling regions
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Inference performed with INLA
summer linear trend)
(Stochastic Partial Differential Equation) approach
\( t_i \cdot v(s) < 0 \) to identify warming and cooling regions