This paper addresses the challenge of uncertainty quantification in 3D reconstruction of underwater scenes using neural radiance fields (NeRFs). The authors introduce a spatial perturbation field $\mathcal{D}_{\boldsymbol{\omega}}$ and perform Laplace approximation to estimate the uncertainty of the pre-trained SeaThru-NeRF model. The perturbation field is used to perturb the input coordinates, reparameterizing the entire model. The Laplace approximation method estimates the uncertainty at each spatial location by comparing the original and perturbed reconstruction results. The diagonal elements of the covariance matrix $\mathbf{\Sigma}$ correspond to the uncertainty at each spatial location. The authors also employ a thresholding method to remove artifacts from the rendered underwater scenes. The paper highlights the following key contributions: 1. Introducing uncertainty quantification into NeRFs for underwater scenes for the first time, enhancing model reliability and robustness. 2. Avoiding additional training or modifying the training process by introducing an additional perturbation field. 3. Post-processing to remove artifacts from the rendered scenes. The authors demonstrate the effectiveness of their approach through numerical experiments on both synthetic and real-world underwater scenes. They also conduct ablation studies to analyze the impact of parameters such as grid size $M$, regularization parameter $\lambda$, and number of iterations on the uncertainty estimation. The results show that moderate grid sizes and regularization parameters provide optimal performance, while the method remains robust across a wide range of settings.This paper addresses the challenge of uncertainty quantification in 3D reconstruction of underwater scenes using neural radiance fields (NeRFs). The authors introduce a spatial perturbation field $\mathcal{D}_{\boldsymbol{\omega}}$ and perform Laplace approximation to estimate the uncertainty of the pre-trained SeaThru-NeRF model. The perturbation field is used to perturb the input coordinates, reparameterizing the entire model. The Laplace approximation method estimates the uncertainty at each spatial location by comparing the original and perturbed reconstruction results. The diagonal elements of the covariance matrix $\mathbf{\Sigma}$ correspond to the uncertainty at each spatial location. The authors also employ a thresholding method to remove artifacts from the rendered underwater scenes. The paper highlights the following key contributions: 1. Introducing uncertainty quantification into NeRFs for underwater scenes for the first time, enhancing model reliability and robustness. 2. Avoiding additional training or modifying the training process by introducing an additional perturbation field. 3. Post-processing to remove artifacts from the rendered scenes. The authors demonstrate the effectiveness of their approach through numerical experiments on both synthetic and real-world underwater scenes. They also conduct ablation studies to analyze the impact of parameters such as grid size $M$, regularization parameter $\lambda$, and number of iterations on the uncertainty estimation. The results show that moderate grid sizes and regularization parameters provide optimal performance, while the method remains robust across a wide range of settings.