Skip to content

Mountains

gaussian_mountain(lon_array, lat_array, central_lat, central_lon, radius_degrees, std_dev, height)

Returns the height of the land at each latitude, longitude coordinate for a single gaussian mountain.

Parameters:

Name Type Description Default
lon_array ndarray

float [n_lat x n_lon].
Array indicating the longitude at each (latitude, longitude) coordinate in the grid used for the experiment.

 required
lat_array ndarray

float [n_lat x n_lon].
Array indicating the latitude at each (latitude, longitude) coordinate in the grid used for the experiment.

 required
central_lat float

Latitude coordinate of mountain in degrees.

 required
central_lon float

Longitude coordinate of mountain in degrees.

 required
radius_degrees float

Radius of mountain in degrees. Altitude at a distance from the center greater than this will be set to 0, so set to very high number to ignore this functionality. Typical: 20.

 required
std_dev float

Standard deviation indicating how steep the mountain is. The smaller the value, the steeper the mountain. Units are degrees and typical value would be 10.

 required
height float

Height of mountain peak in meters.

 required

Returns:

Type Description
ndarray

h_arr: float [n_lat x n_lon]
h_arr[lat, lon] is the height of the land at the coordinate (lat, lon) in meters. Most coordinates will be 0.
Source code in isca_tools/land/mountains.py 
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
def gaussian_mountain(lon_array: np.ndarray, lat_array: np.ndarray, central_lat: float, central_lon: float,
                      radius_degrees: float, std_dev: float, height: float) -> np.ndarray:
    """
    Returns the height of the land at each latitude, longitude coordinate for a single gaussian mountain.

    Args:
        lon_array: `float [n_lat x n_lon]`.</br>
            Array indicating the longitude at each (latitude, longitude) coordinate in the grid used for the experiment.
        lat_array: `float [n_lat x n_lon]`.</br>
            Array indicating the latitude at each (latitude, longitude) coordinate in the grid used for the experiment.
        central_lat: Latitude coordinate of mountain in degrees.
        central_lon: Longitude coordinate of mountain in degrees.
        radius_degrees: Radius of mountain in degrees. Altitude at a distance from the center greater than this will
            be set to 0, so set to very high number to ignore this functionality. Typical: 20.
        std_dev: Standard deviation indicating how steep the mountain is. The smaller the value, the steeper the
            mountain. Units are degrees and typical value would be 10.
        height: Height of mountain peak in meters.

    Returns:
        `h_arr`: `float [n_lat x n_lon]`</br>
            `h_arr[lat, lon]` is the height of the land at the coordinate (`lat`, `lon`) in meters.
            Most coordinates will be 0.

    """
    rsqd_array = np.sqrt((lon_array - central_lon) ** 2. + (lat_array - central_lat) ** 2.)
    h_arr = height * np.exp(-(rsqd_array**2.)/(2.*std_dev**2.))
    h_arr[rsqd_array > radius_degrees] = 0  # Make sure height goes to 0 at some point
    return h_arr

mountain_range_height(lon_array, lat_array, mountain='rockys')

Returns the height of the land at each latitude, longitude coordinate for a given mountain range.

Parameters:

Name Type Description Default
lon_array ndarray

float [n_lat x n_lon].
Array indicating the longitude at each (latitude, longitude) coordinate in the grid used for the experiment.

 required
lat_array ndarray

float [n_lat x n_lon].
Array indicating the latitude at each (latitude, longitude) coordinate in the grid used for the experiment.

 required
mountain str

There are 2 options indicating different mountain ranges:

  • rockys
  • tibet
 'rockys'

Returns:

Type Description
ndarray

h_arr: float [n_lat x n_lon]
h_arr[lat, lon] is the height of the land at the coordinate (lat, lon) in meters. Most coordinates will be 0.
Source code in isca_tools/land/mountains.py 
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
def mountain_range_height(lon_array: np.ndarray, lat_array: np.ndarray, mountain: str = 'rockys') -> np.ndarray:
    """
    Returns the height of the land at each latitude, longitude coordinate for a given mountain range.

    Args:
        lon_array: `float [n_lat x n_lon]`.</br>
            Array indicating the longitude at each (latitude, longitude) coordinate in the grid used for the experiment.
        lat_array: `float [n_lat x n_lon]`.</br>
            Array indicating the latitude at each (latitude, longitude) coordinate in the grid used for the experiment.
        mountain: There are 2 options indicating different mountain ranges:

            * `rockys`
            * `tibet`

    Returns:
        `h_arr`: `float [n_lat x n_lon]`</br>
            `h_arr[lat, lon]` is the height of the land at the coordinate (`lat`, `lon`) in meters.
            Most coordinates will be 0.

    """
    if mountain.lower() == 'rockys':
        # Rockys from Sauliere 2012
        h_0 = 2670
        central_lon = 247.5
        central_lat = 40
        L_1 = 7.5
        L_2 = 20
        gamma_1 = 42
        gamma_2 = 42
        delta_1 = ((lon_array - central_lon) * np.cos(np.radians(gamma_1)) + (lat_array - central_lat) *
                   np.sin(np.radians(gamma_1))) / L_1
        delta_2 = (-(lon_array - central_lon) * np.sin(np.radians(gamma_2)) + (lat_array - central_lat) *
                   np.cos(np.radians(gamma_2))) / L_2
        h_arr = h_0 * np.exp(-(delta_1 ** 2. + delta_2 ** 2.))
    elif mountain.lower() == 'tibet':
        # Tibet from Sauliere 2012
        h_0 = 5700.
        central_lon = 82.5
        central_lat = 28
        L_1 = 12.5
        L_2 = 12.5
        gamma_1 = -49.5
        gamma_2 = -18
        delta_1 = ((lon_array - central_lon) * np.cos(np.radians(gamma_1)) + (lat_array - central_lat) *
                   np.sin(np.radians(gamma_1))) / L_1
        delta_2 = (-(lon_array - central_lon) * np.sin(np.radians(gamma_2)) + (lat_array - central_lat) *
                   np.cos(np.radians(gamma_2))) / L_2
        h_arr_tibet_no_amp = np.exp(-(delta_1 ** 2)) * (1 / delta_2) * np.exp(-0.5 * (np.log(delta_2)) ** 2)
        # For some reason my maximum value of h_arr_tibet_no_amp > 1. Renormalise so h_0 sets amplitude.
        maxval = np.nanmax(h_arr_tibet_no_amp)
        h_arr = (h_arr_tibet_no_amp / maxval) * h_0
    else:
        raise ValueError(f"mountain was given as {mountain} but it must be 'rockys' or 'tibet'")
    # make sure exponentials are cut at some point - use the value from p70 of Brayshaw's thesis.
    set_to_zero_height_ind = (h_arr / h_0 <= 0.05)
    h_arr[set_to_zero_height_ind] = 0
    return h_arr