We describe a new way to apply a spatial filter to gridded data from models or observations, focusing on low-pass filters. The new method is analogous to smoothing via diffusion, and its implementation requires only a discrete Laplacian operator appropriate to the data. The new method can approximate arbitrary filter shapes, including Gaussian filters, and can be extended to spatially varying and anisotropic filters. The new diffusion-based smoother's properties are illustrated with examples from ocean model data and ocean observational products. An open-source Python package implementing this algorithm, called gcm-filters, is currently under development.

中文翻译：

---

用于网格地球物理数据空间滤波的基于扩散的平滑器

我们描述了一种将空间滤波器应用于来自模型或观测的网格数据的新方法，重点是低通滤波器。新方法类似于通过扩散进行平滑，其实现只需要一个适合数据的离散拉普拉斯算子。新方法可以近似任意滤波器形状，包括高斯滤波器，并且可以扩展到空间变化和各向异性滤波器。新的基于扩散的平滑器的属性通过来自海洋模型数据和海洋观测产品的示例进行了说明。一个实现该算法的开源 Python 包，称为 gcm-filters，目前正在开发中。