Current machine learning methods for simulating sea level change often neglect the intrinsic geometric constraints and physical relationships between multidimensional vector field components, resulting in the loss of spatio-temporal coupling information. To address this problem, this study proposes a geometric algebra (GA)-based method for simulating and reconstructing the rate of sea level variability. Salinity, potential temperature, eastward and northward seawater velocities are uniformly represented as multidimensional geometric objects. Compared with traditional methods, the framework utilizes the unified mathematical structure of geometric algebra to represent scalars and vectors in a holistic manner, avoiding the segmented treatment of temperature, salinity and velocity fields and fully preserving their intrinsic geometric and physical relationships. This effectively captures the complex spatial and temporal dynamics of sea level variability. First, TSGAConvGRU organizes ocean stereodynamic data (such as potential temperature, salinity, and zonal and meridional velocities) into multivector inputs. It then employs GAConvGRU to capture spatial and temporal features while accounting for the geometric relationships among components like potential temperature, salinity, and seawater velocities. Second, Series Embedding is introduced to incorporate time markers into temporal features, enhancing the model’s awareness of temporal context. A Dual Path approach with different receptive fields adapts to local and global dynamic features of sea level variability, using three GRU layers to capture long- and short-term dependencies in time series, further modeling the periodicity and trends of sea level variability. A final linear layer maps to the target. Experimental results demonstrate that the proposed method significantly outperforms existing models in simulating and reconstructing sea level variability in the Northeast Pacific, exhibiting higher accuracy and robustness. Furthermore, by establishing a unified GA-based framework, this approach provides a novel scientific perspective for future studies to explore the physical mechanisms underlying variable interactions, thereby enhancing the understanding of the driving factors of sea level changes.