Add Oh backscatter model

sigma0/oh_model.py

@@ -0,0 +1,126 @@
+# Copyright (c) 2018, TU Wien, Department of Geodesy and Geoinformation (GEO).
+# All rights reserved.
+
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+# SOFTWARE.
+
+import cmath
+import numpy as np
+
+
+def gammah(eps, theta):
+    """
+    Incoherent reflectivity for H-pol.
+
+    Parameters
+    ----------
+    eps : complex number
+        Complex dielectric constant.
+    theta : float
+        Angle in degrees.
+
+    Returns
+    -------
+    gammah : float
+        Incoherent reflectivity for H-pol.
+    """
+
+    theta_rad = theta / 180.0 * cmath.pi
+    costheta = np.cos(theta_rad)
+    neliojuuri = np.sqrt(eps - np.sin(theta_rad) ** 2)
+    gammah = np.abs((costheta - neliojuuri) / (costheta + neliojuuri)) ** 2
+
+    return gammah
+
+
+def gammav(eps, theta):
+    """
+    Incoherent reflectivity for V-pol.
+
+    Parameters
+    ----------
+    eps : complex number
+        Complex dielectric constant.
+    theta : float
+        Angle in degrees.
+
+    Returns
+    -------
+    gammav : float
+        Incoherent reflectivity for V-pol.
+    """
+    theta_rad = theta / 180.0 * cmath.pi
+    costheta = np.cos(theta_rad)
+    neliojuuri = np.sqrt(eps - np.sin(theta_rad) ** 2)
+    gammav = np.abs((eps * costheta - neliojuuri) /
+                    (eps * costheta + neliojuuri)) ** 2
+
+    return gammav
+
+
+def sigma0_bare(theta, eps_low, f_rms, f, eps_top=1):
+    """
+    Oh et.al. (1992) surface backscatter calculations
+
+    This functions calculations surface backscatter using the
+    Oh et al. (1992) surface model.
+
+    References
+    Oh et al., 1992, An empirical model and an inversion technique for
+    rader scattering from bare soil surfaces. IEEE Trans. Geos. Rem.,
+    30, pp. 370-380
+
+    Parameters
+    ----------
+    theta : float
+        incidence angle in degrees
+    eps_low : complex number
+        complex permittivity of lower medium
+    f : float
+        frequency in hertz
+    f_rms: float
+        fractional rms height. rms_height in meters divided by wavelength
+    eps_top : complex number, optional
+        complex permittivity of upper(incoming) medium
+
+    Returns
+    -------
+    sigma0 : float
+        Surface backscatter.
+    """
+    k_rms = (2. * cmath.pi) * f_rms
+
+    eps_eff = eps_low / eps_top
+
+    gam0 = gammah(eps_eff, 0)
+    gamh = gammah(eps_eff, theta)
+    gamv = gammav(eps_eff, theta)
+    theta = theta / 180.0 * cmath.pi
+
+    # precalulcate cosines of angles
+    ct = np.cos(theta)
+
+    # Oh model equations
+    g = 0.7 * (1. - np.exp(-0.65 * k_rms ** 1.8))
+    root_p = 1. - ((2. * theta / cmath.pi) **
+                   (1. / (3. * gam0))) * np.exp(-k_rms)
+
+    # p = (1 - (2 * theta / cmath.pi) ** (1 / (3 * gam0)) * np.exp(-1 * k_rms)) ** 2
+
+    q = 0.23 * np.sqrt(gam0) * (1. - np.exp(-k_rms))
+
+    sigma0 = {}
+
+    sigma0['vv'] = g * (ct * (ct * ct)) * (gamv + gamh) / root_p
+
+    # sig0vv = ((g*(cos(theta))^3)/sqrt(p))*(gamv+gamh);
+
+    sigma0['vh'] = q * sigma0['vv']
+    sigma0['hh'] = root_p * root_p * sigma0['vv']
+
+    return sigma0