A Mathematical Model for Wind Velocity Field Reconstruction and Visualization Taking into Account the Topography...

Area of Science:

• Geosciences
• Applied Mathematics
• Computational Physics

Background:

• Accurate modeling of vector fields, such as wind velocity and marine currents, is crucial for various scientific and engineering applications.
• Existing vector field approximation methods often lack comprehensive consideration of real-world complexities like topography.

Purpose of the Study:

• To develop a global modeling approach for vector field approximation from discrete vector data.
• To enhance the accuracy of vector field approximation by incorporating data fidelity and smoothing terms.
• To account for topographic effects in wind velocity field modeling and propose a visualization method.

Main Methods:

• Global modeling using energy functional minimization in a Hilbert space.
• Incorporation of a fidelity criterion to the data and a smoothing term within the energy functional.
• Discretization of the continuous problem via the finite elements method.
• Inclusion of topographic effects and visualization using a free library.

Main Results:

• A novel global modeling framework for vector field approximation was established.
• The proposed method effectively balances data fidelity with field smoothing.
• Topographic effects were successfully integrated into the wind velocity field approximation.
• A visualization component was developed using a free library, enhancing model utility.

Conclusions:

• The developed model provides a robust and accurate method for vector field approximation.
• The inclusion of topographic effects and visualization offers significant advantages over existing models.
• This approach has potential applications in meteorology, oceanography, and other fields requiring vector field analysis.