Nonlinear Diffusion Filtering

Goal

The nonlinear diffusion filter applies an edge-preserving Perona-Malik style diffusion to the radial magnetic field. It reduces small-scale noise while limiting smoothing across strong active-region gradients.

Module

coconut_tools.magnetogram.NLD_implicit_method

High-Level API

Use process_config for normal runs:

from coconut_tools.magnetogram.NLD_implicit_method import process_config

results = process_config(config)

This high-level pipeline shares the same date handling, downloading, GONG/ADAPT interpolation, net-flux correction, COCONUT .dat writing, and diagnostic plotting logic as the SPH pipeline.

Single-Date Example

To process one magnetogram, provide date and omit total_hours:

from coconut_tools.magnetogram.NLD_implicit_method import process_config

config = {
    "date": "2020-12-07T15:00:00",
    "map_type": "HMI_small",
    "lmax": 20,
    "tau": 5,
    "iterations": 7,
    "apply_gaussian": True,
    "gaussian_sigma": 1.0,
    "flux_correct": False,
    "write_map": True,
    "show_map": True,
    "output_dir": "./boundary/",
    "output_path_fig": "./figures/hmi_nld.png",
}

results = process_config(config)

Multi-Date GONG Example

The same time-series options used by SPH are available here. This example processes three days at a 3-hour cadence and interpolates each target date from four neighboring GONG maps.

from coconut_tools.magnetogram.NLD_implicit_method import process_config

config = {
    "date": "2025-10-09T18:00:00",
    "map_type": "GONG",
    "cadence_hours": 3,
    "total_hours": 72,
    "interpolation": True,
    "interpolation_order": 2,
    "flux_correct": True,
    "lmax": 20,
    "tau": 5,
    "iterations": 7,
    "apply_gaussian": True,
    "gaussian_sigma": 1.0,
    "write_map": True,
    "show_map": True,
    "output_dir": "./boundary/",
    "download_dir": "./raw/",
    "output_path_fig": "./figures/gong_nld.png",
}

results = process_config(config)

For each target date, the output file is named like:

map_gong_lmax20_NLD_YYYYMMDDHHMMSS.dat

Filter Parameters

• tau: diffusion time step.

• iterations: number of nonlinear diffusion iterations.

• apply_gaussian: apply Gaussian pre-smoothing before nonlinear diffusion, default True.

• gaussian_sigma: Gaussian kernel width.

• dx_override and dy_override: optional grid-spacing overrides used by the implicit solver, both default to 1.0.

Start with tau=5 and around 6 to 7 iterations, then tune according to the remaining small-scale structure and the stability of the COCONUT run.

Advanced API

The low-level filter is still available for custom workflows:

from coconut_tools.magnetogram.NLD_implicit_method import filter_radial_field
from coconut_tools.magnetogram.sph_filtering import write_bc_file, plot_maps

Br_filtered, timestep = filter_radial_field(
    Br,
    Phi[0, :],
    Theta[:, 0],
    iterations=7,
    tau=5,
    apply_gaussian=True,
    gaussian_sigma=1.0,
)

write_bc_file("map_gong_lmax20_NLD_20251009180000.dat", Br_filtered, Theta[:, 0], Phi[0, :])
plot_maps(
    Br,
    Br_filtered,
    Theta[:, 0],
    Phi[0, :],
    "GONG",
    output_path="./figures/gong_nld.png",
    date="2025-10-09T18:00:00",
)