Ensuring the safety of dams is critical to maintaining national economic development and social stability, requiring the implementation of accurate displacement prediction methods for early detection of structural anomalies and effective risk mitigation. However, existing statistical models primarily focus on point predictions, failing to quantify the uncertainty in displacement variations, and often neglect the critical environmental factor of solar radiation. To address these limitations, this study proposes a novel interpretable interval prediction framework that integrates solar radiation factors into an advanced hydrostatic-temperature-time (AHTT) model. A variational autoencoder (VAE) is employed to extract robust latent features from a large volume of measured temperature data, effectively reducing temperature-related noise. Subsequently, an improved temporal fusion transformer method is introduced to probabilistic dam displacement prediction. This method uses an enhanced quantile loss function based on the Huber loss to generate both point and interval predictions that dynamically reflect the prediction uncertainty. In addition, an interpretable multi-head attention module is incorporated to quantify the contribution of each environmental factor. Hyperparameter tuning of the improved temporal fusion transformer is further optimized using Bayesian optimization based on the tree-structured Parzen estimator (TPE), which improves prediction accuracy. Engineering case studies validate that the proposed model not only achieves the highest point prediction accuracy, but also provides narrower prediction intervals with the best coverage width criterion. Ablation experiments and interpretability analyses further confirm the significant impact of solar radiation on dam displacement, providing valuable insights for the development of dam displacement prediction models and risk-informed decision making.