Level Set Based Data Assimilation Method And Its Application In Oil Spill Dispersion Prediction

In the field of geophysics, the motion of fluids is generally described by differential equations. On one hand, observations for the initial value, boundary value of differential equation are usually inaccurate due to the error of observer and weather conditions. On the other hand, coefficients of the differential equation are unknown because of the material with different physical properties. Prediction for a long time with inaccurate initial boundary value and coefficients can cause large error. Therefore, it is necessary to inverse and correct boundary value, the initial field and parameters timely by using the existing observations. Four dimensional variational data assimilation method(4D-Var), a research method of inverse problem, is widely used in numerical weather forecast. This method can achieve the purpose of the inversion when lack of observations or variables cannot be observed by assimilating observations.In this paper, we propose an novel level set based 4D-Var method(LS-4D-Var), which makes full use of image edge structure information to inverse the initial field and diffusion coefficients of level set equation. Variables of level set equation are related, by a new image operator, to the edge structure information of images. Furthermore, we will apply this method to oil spill dispersion prediction. Level set method has been a popular and versatile technique for interface tracking, and has a certain advantage of characterizing the dynamics information between observation images of oil spill. As a new type of image assimilation technology, the LS-4D-Var method can predict the diffusion range of oil and pollutants by using a small amount of observation information compared with the previous4D-Var method based on concentration, temperature, color and salinity.For LS-4D-Var method, firstly, wavelet maximum module method should be used for edge feature extraction of observations; Then image operator will be constructed for variational model; Finally, we will utilize the adjoint method of 4D-Var technology to inverse the initial field and diffusion coefficients of level set equation. Experiment results show that the proposed LS-4D-Var algorithm can restore the edge of initial interface and diffusion coefficients exactly by assimilating the edge information of observations.