Abstract: Currently, the demand for higher video quality has grown significantly. However, satellite video has low resolution, complex motion, and weak textures. Haze interference further exacerbates the loss of motion information and texture details, hindering effective spatiotemporal feature fusion and fine-grained feature mining. This presents significant challenges for subsequent super-resolution (SR) reconstruction, especially at continuous scales. To address these problems, this paper models the double-degradation process of hazy low-quality satellite videos and proposes a novel network to learn the optimal joint degradation pattern (ODPNet) for continuous-scale SR of hazy satellite videos. First, we design a prior-based feature soft dehazing module to eliminate haze interference at the feature level. Second, we develop a spatiotemporal self-attention (SSA) to capture long-range feature dependencies, thereby achieving effective spatiotemporal feature fusion. Third, we devise a tri-branch cross-aggregation block (TCB) to enhance feature representations of weak textures in satellite videos by effectively aggregating contextual information. Finally, we propose a cross-scale feature Top-$k$ selection Transformer (CFTST), which aims to adaptively select and aggregate cross-scale latent codes to learn feature representations of satellite videos at arbitrary resolutions, thus enabling continuous-scale SR. Experiments show that ODPNet outperforms existing methods and achieves a better balance between model parameters and performance.