Title: The Boundary Layer Dispersion and Footprint Model: A fast numerical solver of the Eulerian steady-state advection-diffusion equation Show Chinese title

Title: 边界层分散和足迹模型：欧拉稳态对流扩散方程的快速数值求解器

Abstract: Understanding how greenhouse gases and pollutants move through the atmosphere is essential for predicting and mitigating their effects. We present a novel atmospheric dispersion and footprint model: the Boundary Layer Dispersion and Footprint Model (BLDFM), which solves the three-dimensional steady-state advection-diffusion equation in Eulerian form using a numerical approach based on the Fourier method, the linear shooting method and the exponential integrator method. The model is designed to be flexible and can be used for a wide range of applications, including climate impact studies, industrial emissions monitoring, agricultural planning and spatial flux attribution. We validate the model using an analytical test case. The numerical results show excellent agreement with the analytical solution. We also compare the model with the Kormann and Meixner (Boundary-Layer Meteorology, 2001) footprint model (FKM), and the results show overall good agreement but some differences in the fetch of the footprints, which are attributed to the neglect of streamwise turbulent mixing in the FKM model. Our results demonstrate the potential of the BLDFM model as a useful tool for atmospheric scientists, biogeochemists, ecologists, and engineers. Show Chinese abstract

Abstract: 理解温室气体和污染物如何在大气中传播对于预测和减轻它们的影响至关重要。 我们提出了一种新的大气扩散和足迹模型：边界层扩散与足迹模型（BLDFM），该模型使用基于傅里叶方法、线性射击法和指数积分法的数值方法，以欧拉形式求解三维稳态平流-扩散方程。 该模型设计灵活，可用于广泛的领域，包括气候影响研究、工业排放监测、农业规划以及空间通量归因。 我们使用一个解析测试用例验证了该模型。 数值结果与解析解高度吻合。 我们还将该模型与Kormann和Meixner（《边界层气象学》，2001年）提出的足迹模型（FKM）进行了比较，结果显示总体上一致性良好，但在足迹的范围上存在一些差异，这些差异归因于FKM模型忽略了沿流向的湍流混合。 我们的结果表明，BLDFM模型作为大气科学家、生物地球化学家、生态学家和工程师的有用工具具有潜力。