Green Gross Domestic Product (GDP) is an important indicator to reflect the trade-off between the ecosystem and economic system. Substantial research has mapped historical green GDP spatially. But few studies have concerned future variations of green GDP. In this study, we have calculated and mapped the spatial distribution of the green GDP by summing the ecosystem service value (ESV) and GDP for China from 1990 to 2015. The pattern of land use change simulated by a CA-Markov model was used in the process of ESV prediction (with an average accuracy of 86%). On the other hand, based on the increasing trend of GDP during the period of 1990 to 2015, a regression model was built up to present time-series increases in GDP at prefecture-level cities, having an average value of R square (R²) of approximately 0.85 and significance level less than 0.05. The results indicated that (1) from 1990 to 2015, green GDP was increased, with a huge growth rate of 78%. Specifically, the ESV value was decreased slightly, while the GDP value was increased substantially. (2) Forecasted green GDP would increase by 194,978.29 billion yuan in 2050. Specifically, the future ESV will decline, while the rapidly increased GDP leads to the final increase in future green GDP. (3) According to our results, the spatial differences in green GDP for regions became more significant from 1990 to 2050.

Urban green space (UGS) is important in urban systems, as it benefits economic development, ecological conservation, and living conditions. Many studies have evaluated the economic, ecological, and social value of UGS worldwide, and spatial optimization for UGS has been carried out to maximize its value. However, few studies have simultaneously examined these three values of UGS in one optimization system. To fill this gap, this study evaluated the economic value of UGS in terms of promoting housing prices, its ecological value through the relief of high land surface temperature (LST), and its social value through the provision of recreation spaces for residents within a 255 m distance. Subsequently, these three values were set as objectives in a genetic algorithm (GA)-based multi-objective optimization (MOP) system. Shenzhen was taken as the case study area. The results showed that the influencing distance of UGS in Shenzhen for house prices was 345 m, and the influencing distance of UGS for LST was 135 m. Using MOP, the Pareto solutions for increasing UGS were identified and presented. The results indicate that MOP can simultaneously optimize UGS’s economic, ecological, and social value.

The spatial learned index constructs a spatial index by learning the spatial distribution, which performs a lower cost of storage and query than the spatial indices. The current update strategies of spatial learned indices can only solve limited updates at the cost of query performance. We propose a novel spatial learned index structure based on a Block Range Index (SLBRIN for short). Its core idea is to cooperate history range and current range to satisfy a fast spatial query and efficient index update simultaneously. SLBRIN deconstructs the update transaction into three parallel operations and optimizes them based on the temporal proximity of spatial distribution. SLBRIN also provides the spatial query strategy with the spatial learned index and spatial location code, including point query, range query and kNN query. Experiments on synthetic and real datasets demonstrate that SLBRIN clearly outperforms traditional spatial indices and state-of-the-art spatial learned indices in the cost of storage and query. Moreover, in the simulated real-time update scenario, SLBRIN has the faster and more stable query performance while satisfying efficient updates.

Understanding the spatiotemporal dynamics of atmospheric PM_2.5 concentration is highly challenging due to its evolution processes have complex and nonlinear patterns. Traditional mode decomposition methods struggle to accurately capture the mode features of PM_2.5 concentrations. In this study, we utilized the global linearization capabilities of the Koopman method to analyze the hourly and daily spatiotemporal processes of PM_2.5 concentration in the Beijing–Tianjin–Hebei (BTH) region from 2019 to 2021. This approach decomposes the data into the superposition of different spatial modes, revealing their hierarchical spatiotemporal structure and reconstructing the dynamic processes. The results show that PM_2.5 concentrations exhibit high-frequency cycles of 12 and 24 h, as well as low-frequency cycles of 124 and 353 days, while also revealing spatiotemporal modes of growth, recession, and oscillation. The superposition of these modes enables the reconstruction of spatiotemporal dynamics with a mean absolute percentage error (MAPE) of only 0.6%. Unlike empirical mode decomposition (EMD), Koopman mode decomposition (KMD) method avoids mode aliasing and provides a clearer identification of global and key modes compared to wavelet analysis. These findings underscore the effectiveness of KMD method in analyzing and reconstructing the spatiotemporal dynamics of PM_2.5 concentration, offering new insights into the understanding and reconstruction of other complex spatiotemporal phenomena.