Regularized inversion method for retrieval of aerosol particle size distribution function in W(1,2) space

Area of Science:

• Atmospheric Science
• Remote Sensing
• Computational Physics

Background:

• Determining aerosol particle size distribution from extinction data involves solving an ill-posed integral equation.
• Existing regularization methods, like Phillips-Twomey, struggle with highly oscillatory aerosol distributions common in Junge-type distributions.
• These limitations stem from the ill-conditioned scale matrix, which cannot effectively filter noise and perturbations.

Purpose of the Study:

• To develop an improved regularization technique for aerosol particle size distribution retrieval.
• To address the limitations of current methods when dealing with complex aerosol profiles.
• To enhance the accuracy of aerosol distribution determination from remote sensing measurements.

Main Methods:

• The problem is reformulated and solved within the W1,2 space, leveraging Sobolev's embedding theorem.
• A novel a posteriori parameter choice method, based on the discrepancy principle, is developed for regularization parameter selection.
• The algorithm's feasibility is validated using real-world remote sensing data.

Main Results:

• The proposed method demonstrates superior performance in simulating true particle size distributions compared to traditional approaches.
• Numerical results indicate enhanced accuracy in retrieving aerosol particle size distributions, even with noisy data.
• The developed technique effectively handles oscillations present in Junge-type distributions.

Conclusions:

• The W1,2 space approach combined with the discrepancy principle offers a robust solution for aerosol particle size distribution retrieval.
• This method provides a significant advancement over existing regularization techniques, particularly for complex atmospheric conditions.
• The findings are validated by practical application to CE318 sunphotometer data, confirming the algorithm's effectiveness.