This paper makes a step towards modeling the modality discrepancy in the cross-spectral re-identification task. Based on the Lambertain model, we observe that the non-linear modality discrepancy mainly comes from diverse linear transformations acting on the surface of different materials. From this view, we unify all data augmentation strategies for cross-spectral re-identification as mimicking such local linear transformations and categorize them into moderate transformation and radical transformation. By extending the observation, we propose a Random Linear Enhancement (RLE) strategy which includes Moderate Random Linear Enhancement (MRLE) and Radical Random Linear Enhancement (RRLE) to push the boundaries of both types of transformation. Moderate Random Linear Enhancement is designed to provide diverse image transformations that satisfy the original linear correlations under constrained conditions, whereas Radical Random Linear Enhancement seeks to generate local linear transformations directly without relying on external information. The experimental results not only demonstrate the superiority and effectiveness of RLE but also confirm its great potential as a general-purpose data augmentation for cross-spectral re-identification.