Most image dehazing deep learning models target synthetic datasets of hazy images, resulting in not considering features in natural hazy images. Leveraging on depth attention with adaptation, we propose a novel dehazing network called depthUNet, that is focused on natural images. Utilizing the correlation between depth information and haze distribution, our network enhances its generalization performance on natural images. Furthermore, our method improves the PSNR for the non-homogeneous realistic haze dataset NH-HAZE from 20.66 (DeHamer's result) to 20.74, using only 1.6% of the parameters. Similarly, for the outdoor scenes realistic haze dataset O-HAZE, our method enhances the PSNR from 24.36 (MSBDN's result) to 25.77, with just 6% of the parameters. On natural road images with haze from dataset RTTS, our method improved the vehicle detection rate by 10% in terms of the R-squared value. In summary, our method outperforms all state-of-the-art methods while utilizing the least number of parameters.