We present a novel reduced-order modeling (ROM) framework that leverages optimal transport (OT) theory to address the challenges of capturing highly nonlinear dynamics in atmospheric flows. Our approach combines displacement interpolation with data augmentation strategies to enhance the representation of complex physical phenomena, particularly in scenarios where observational data is limited. The framework generates physically consistent synthetic snapshots by computing optimal transport plans between consecutive checkpoints and using displacement interpolation to trace geodesic paths in the space of probability distributions. A key innovation of our method is its ability to provide continuous temporal representation through a virtual-to-real time mapping, enabling solution reconstruction at arbitrary time points. We further improve prediction accuracy by incorporating a correction step based on Proper Orthogonal Decomposition with Gaussian Process Regression (POD-GPR), which learns and compensates for systematic biases in the interpolated solutions. We demonstrate the effectiveness of our approach using two challenging atmospheric mesoscale benchmarks: the rising thermal bubble and the density current. These test cases are characterized by highly nonlinear, advection-dominated dynamics that traditionally pose significant challenges for reduced-order modeling. Our results show that the proposed method achieves substantial computational speedup while maintaining accuracy, with errors comparable to the underlying temporal discretization of the training data. The framework proves particularly effective at capturing complex flow features such as the mushroom-shaped thermal plume and the propagating cold front with Kelvin-Helmholtz instabilities. Our method's ability to generate physically consistent synthetic data while preserving important dynamical features makes it particularly valuable for applications requiring real-time predictions or large-scale parametric studies in atmospheric sciences. The framework's modular nature also allows for its extension to other complex fluid dynamics problems where traditional ROM techniques face limitations due to strong nonlinearities or limited observational data.