帮我写一个中性气扩散的高斯烟羽模型代码

中性气扩散的高斯烟羽模型通常用于描述污染物随风向和风速扩散的过程。这个模型基于高斯分布，假设污染物排放点为中心，扩散半径与风速、扩散系数以及时间有关。以下是一个简单的Python版本的代码示例，使用了NumPy库来处理数学计算：

import numpy as np

def gaussian_plume_model(x, y, uwind, vwind, dispersion_coeff, emission_height, t, dt):
    """
    Gaussian Plume Model for neutral atmospheric dispersion.
    
    Parameters:
    x, y (array-like): Cartesian coordinates in the horizontal plane.
    uwind, vwind (floats): Wind speed components (Ux, Vy) in m/s.
    dispersion_coeff (float): Turbulent diffusion coefficient, kappa in m^2/s.
    emission_height (float): Emission height above ground level in meters.
    t, dt (floats): Time in seconds and time step for calculation.

    Returns:
    array-like: Contaminant concentration at given points.
    """
    R = np.sqrt((dispersion_coeff * (t + dt)**2) / (2 * 9.81))  # Effective plume radius
    z0 = 0.7  # Roughness length for momentum flux (assumed)
    wind_dir_rad = np.arctan2(uwind, vwind)  # Wind direction in radians
    
    # Calculate distance from center
    r = np.hypot(np.subtract.outer(x, 0), np.subtract.outer(y, emission_height))

    # Apply Gaussian decay with respect to distance
    exp_term = - ((r**2 + (R*np.cos(wind_dir_rad))^2) / (2*R**2))
    concentration = np.exp(exp_term)

    # Apply stability correction for neutral conditions (no wind shear)
    stability_correction = np.exp(-((z0 / r)**1.5))
    concentration *= stability_correction
    
    return concentration

# Example usage
x_grid = np.linspace(0, 1000, 100)
y_grid = np.linspace(0, 1000, 100)
uwind = 5
vwind = 5
dispersion_coeff = 0.067
emission_height = 30
time_steps = [0, 1, 3]  # Simulate after 0, 1, and 3 minutes

for t in time_steps:
    c_at_t = gaussian_plume_model(x_grid, y_grid, uwind, vwind, dispersion_coeff, emission_height, t, 1)
    print(f"Concentration at {t} minutes: \n{c_at_t}")

请注意，这只是一个基本的模型示例，实际应用中可能需要考虑更多的因素，如气象条件的变化、地形影响等。此外，计算性能可能会受限于大规模网格的大小。