Linear Theory of Orographic Precipitation
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
- numpy
Optional dependencies (required for fastscape extension):
orographic_precipitation can be installed using pip
:
$ pip install orographic_precipitation
Alternatively, you can install orographic_precipitation from conda-forge:
$ conda install orographic_precipitation -c conda-forge
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.
lapse_rate = -5.8
lapse_rate_m = -6.5
ref_density = 7.4e-3
param = {
'latitude': 40,
'precip_base': 7, # uniform precipitation rate
'wind_speed': 10,
'wind_dir': 270, # wind direction (270: west)
'conv_time': 1000, # conversion time
'fall_time': 1000, # fallout time
'nm': 0.005, # moist stability frequency
'hw': 5000, # water vapor scale height
'cw': ref_density * lapse_rate_m / lapse_rate # 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.