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Underwater images bring about substantial information to many tasks regarding marine science or coastal engineering. Meanwhile, enhancement of serious underwater image degradation like wavelength-dependent color distortion or decreased contrast is essential in practical applications. Although deep learning-based underwater image enhancement methods have increasingly been developed, construction of a large-scale underwater image dataset is still a remaining issue. Currently, expensive cost and the difficulty of measurement disturb collection of real data. On the other hand, alternatively employed synthetic underwater images based on simplified physical model or generative adversarial network may deviate from real data. In order to reduce the domain gap between real and synthetic underwater images, we generate underwater images based on physically revised underwater image formation model. By reformulating the model as Monte Carlo integration in statistical physics, we avoid variable multiplication and enable the calculation. The constructed dataset is shown to include diverse degradation and be closer to real images as well. Subsequently, underwater image color correction is tackled via exemplar-based style transfer to cope with diverse color cast. Finally, simply designed image sharpening algorithm combining discrete wavelet transform and Laplacian pyramid is proposed to improve the visibility. The proposed scheme mainly achieves superior or competitive performance compared to other latest methods.