Attribution of Land-Use/Land-Cover Change Induced Surface Temperature Anomaly: How Accurate Is the First-Order Taylor Series Expansion?

Land surface temperature (LST) responds to land-use/land-cover change (LULCC), which modifies surface properties that control the surface energy balance (SEB). Quantifying changes in LST due to individual perturbations caused by LULCC is an attribution problem. Most attribution methods are based on the first-order Taylor series expansion (FOTSE) of a linearized SEB equation. The accuracy of these methods is affected by the use of FOTSE at two places. The first is to linearize the SEB equation and to obtain an analytical solution for LST (the LST model), and the second is to obtain LST changes as the linear sum of concurrent changes in multiple factors (the attribution model). In this study, we systematically assess the importance of non-linear effects lost in these linearization processes using the second-order Taylor series expansion (SOTSE). Results show that while the SOTSE LST model outperforms the FOTSE LST model, the order of Taylor series expansion in the LST model does not significantly influence the attribution of LST changes. However, the SOTSE attribution model is considerably more accurate than the FOTSE attribution model, especially when the magnitude of perturbations is large. Results suggest that contributions from higher-order and cross-order terms in the attribution model can be as large as 50%. Sensitivity analysis further shows that non-linear effects associated with changing surface resistance for LULCC scenarios with large perturbations (e.g., deforestation and urbanization) are particularly strong. In conclusion, we recommend using the FOTSE LST model and the SOTSE attribution model.