pyi2em

Python bindings for the I2EM rough-surface scattering and emissivity model.

Reference: Ulaby, F.T. and Long, D.G. (2014). Microwave Radar and Radiometric Remote Sensing. University of Michigan Press.

Install

pip install pyi2em

Notes on wheels vs source builds

• PyPI wheels bundle required native libraries, including GSL and embedded cubature routines. End users do not need system packages.
• Source builds require GSL available via pkg-config. The cubature integration code is compiled into the extension automatically.

From source

• Ubuntu: sudo apt-get install -y cmake build-essential libgsl-dev
• macOS: brew install cmake gsl

Then

pip install .

Note: The cubature library (hcubature/pcubature) is fetched automatically during build; you do not need to install a system package for it. GSL remains a system dependency for source builds.

Test

pytest -q

Usage

The high-level Python API exposes three functions. Units are GHz, meters, and degrees throughout.

1. Emissivity

from pyi2em import emissivity

eh, ev = emissivity(
    freq_ghz=5.3,
    rms_height_m=0.0025,
    corr_length_m=0.10,
    theta_deg=30.0,
    er_complex=complex(11.3, 1.5),
    correl="gaussian",         # 'exponential' | 'gaussian' | 'x_power' | 'x_exponential'
)
print(eh, ev)  # linear emissivities

2. Monostatic backscatter (scalar or array incidence)

import numpy as np
from pyi2em import sigma0_backscatter

thetas = np.array([20.0, 30.0, 40.0])
sig = sigma0_backscatter(
    freq_ghz=5.0,
    rms_height_m=0.01,
    corr_length_m=0.05,
    theta_deg=thetas,                 # scalar or array
    er_complex=complex(15.0, 3.0),
    correl="gaussian",
    include_hv=True,
    return_db=True,                   # return dB (default)
)
print(sig["hh"], sig["vv"], sig["hv"])  # arrays in dB

3. Bistatic backscatter

from pyi2em import sigma0_bistatic

sig = sigma0_bistatic(
    freq_ghz=5.0,
    rms_height_m=0.01,
    corr_length_m=0.05,
    thi_deg=40.0,
    ths_deg=40.0,
    phs_deg=180.0,
    er_complex=complex(15.0, 3.0),
    correl="gaussian",
    xcoeff=1.0,
    return_db=True,
)
print(sig["hh"], sig["vv"])  # dB

Correlation options: 'exponential' | 'gaussian' | 'x_power' | 'x_exponential'.

Notes

• sigma0_* return dB by default; set return_db=False for linear values.
• sigma0_backscatter(theta_deg=...) accepts a scalar or a NumPy array.
• emissivity returns linear values in [0, 1].

License and Notices

• Wrapper: MIT (see LICENSE)
• GSL: GPL-licensed dependency; the NOTICE and COPYING.GPL files are included.