A Novel Multiscale Geographically and Temporally Gravity-Weighted Regression Model: Algorithm Principle and an Application in Assessment of Forest Biomass in Karst Region

The spatiotemporal patterns and driving forces of forest aboveground biomass (AGB) in subtropical karst region provide key information for forest carbon sink management and regional ecological environment governance planning. In this article, a novel multiscale geographically and temporally gravity-weighted regression (G-MGTWR) model was proposed to assess the spatiotemporal patterns of AGB in the Guizhou province, China. First, the spatial bandwidths of the G-MGTWR model are optimized. Then, all the AGB data from four periods are put into the model. Finally, the center of gravity of AGB at a county scale is calculated to build the G-MGTWR model. It performed the best with an $R^{2}$ of 0.933, against 0.725, 0.847, 0.856, and 0.913 for the ordinary least squares (OLSs), geographically weighted regression (GWR), multiscale GWR (MGWR), and geographically temporally weighted regression (GTWR), respectively. It also has a corrected Akaike information criterion (AICc) index of 63.924, a Bayesian information criterion (BIC) of 26.272, and a residual sum of squares (RSSs) of 5.518 Mg/ha, and all the metrics of the G-MGTWR are superior to the other models. Compared to a fixed bandwidth used in the GTWR for all factors, the G-MGTWR significantly improves accuracy and makes the better interpretation of each factor more convincing by seeking the optimal bandwidth size for each factor and using the varying biomass centers over different periods instead of a fixed geographic center. The driving forces analysis results show that rocky desertification (RD) and population are the main negative factors causing AGB change while sunshine and precipitation were the main positive factors.