STA-HRNN-BiGRU: a spatiotemporal sequence multivariate forecasting model integrating spatiotemporal information

Spatiotemporal sequence forecasting is of great significance in environmental monitoring. High-precision multi-step forecasting across multiple sites is a research hotspot and difficulty in this field. Based on the theories of data time-frequency analysis and nonlinear spatiotemporal sequence modeling, the spatiotemporal interaction effects between different locations are considered when eliminating the influence of noise, by combining wavelet analysis and a recurrent neural network variant (HRNN-BiGRU) using Huber loss. Meanwhile, an attention mechanism is introduced, which in this paper can adaptively learn the relative influences among monitoring sites directly from data without predefining spatial graphs or distance assumptions. A multi-value multi-step forecasting model for spatiotemporal sequences is constructed, abbreviated as STA-HRNN-BiGRU. This study evaluates two model configurations—a preliminary WD-HRNN-BiGRU and the full STA-HRNN-BiGRU—on groundwater levels data from Minqin County and air quality data from Beijing. The full model innovatively fuses station geospatial coordinates with observational data as input. Through an adjustable iterative scheme with \(n_1\) input steps and \(n_2\) output steps, the model successfully forecasts 20 future time steps for all 33 monitoring stations. Furthermore, we extend the STA-HRNN-BiGRU architecture into a Multi-Station Multivariate Forecasting (MS-MVF) framework, which can integrate multivariate information across stations. Experimental results demonstrate that MS-MVF outperforms STA-HRNN-BiGRU in multi-station univariate nonlinear spatiotemporal sequence forecasting. Experimental results on the Beijing air-quality dataset demonstrate that the proposed method achieves an \(R^2\) of 0.935 with MAE and RMSE reduced to 0.0289 and 0.0444, respectively, consistently outperforming state-of-the-art models such as Transformer-, ASTGCN-, and attention-based forecasting frameworks. These findings highlight the robustness and forecasting accuracy of STA-HRNN-BiGRU and MS-MVF, with promising potential for large-scale, multi-station, and cross-domain forecasting.