Linear Theory of Orographic Precipitation
Project description
A Python framework that implements the Linear Theory of Orographic Precipitation following Smith & Barstad (2004).
The model includes airflow dynamics, condensed water advection, and downslope evaporation. It consists of two vertically-integrated steady-state advection equations describing: (i) the cloud water density and (ii) the hydrometeor density. Solving these equations using Fourier transform techniques, derives a single formula relating terrain and precipitation.
Please refer to the original manuscript of Smith and Barstad (2004) to understand the model physics and limitations.
Installation
Required dependencies:
Python 3.6 or later
orographic precipitation can be installed using pip:
$ pip install orographic_precipitation
Usage
Import relevant functions to compute orographic precipitation, set up a topography and plot the resulting precipitation matrix.
import matplotlib.pyplot as plt
from orographic_precipitation import compute_orographic_precip
2. Create example topography, for instance, an isolated circular Gaussian hill (see original publication, Fig. 4 a-c).
def gauss_topography(dx, dy):
"""Returns synthetic topography for testing.
Analogous to Fig 4 in Smith and Barstedt, 2004.
"""
h_max = 500.
x0 = -25e3
y0 = 0
sigma_x = sigma_y = 15e3
x, y = np.arange(-100e3, 200e3, dx), np.arange(-150e3, 150e3, dy)
X, Y = np.meshgrid(x, y)
h = (h_max *
np.exp(-(((X - x0)**2 / (2 * sigma_x**2)) +
((Y - y0)**2 / (2 * sigma_y**2)))))
return X, Y, h
def plot2d(X, Y, field):
"""Function that plots precipitation matrices"""
fig, ax = plt.subplots(figsize=(6, 6))
pc = ax.pcolormesh(X, Y, field)
ax.set_aspect(1)
fig.colorbar(pc)
dx = 750.
dy = 750.
X, Y, elevation = gauss_topography(dx, dy)
plot2d(X, Y, elevation)
Initialize dictionary with relevant parameters, compute and plot orographic precipitation.
gamma = -5.8 #-6.49
Gamma_m = -6.5 #-5
rhosref = 7.4e-3
param = {
'latitude': 40,
'p0': 7, # uniform precipitation rate
'windspeed': 10,
'winddir': 270, # wind direction (270: west)
'tau_c': 1000, # conversion time
'tau_f': 1000, # fallout time
'nm': 0.005, # moist stability frequency
'hw': 5000, # water vapor scale height
'cw': rhosref * Gamma_m / gamma # uplift sensitivity
}
P = compute_orographic_precip(elevation, dx, dy, **param)
plot2d(X, Y, P)
Acknowledgement
This project is supported by the Earth Surface Process Modelling group at the German Geoscience Research Institute in Potsdam, Germany.
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