isofit.inversion.inverse_simple

Functions

heuristic_atmosphere(fm, x_surface, x_RT, ...[, ...])

From a given radiance, estimate atmospheric state with band ratios.

invert_algebraic(surface, RT, instrument, x_surface, ...)

Inverts radiance algebraically using Lambertian assumptions to get a

invert_analytical(fm, winidx, meas, geom, x0, sub_state)

Perform an analytical estimate of the conditional MAP estimate for

invert_simple(forward, meas, geom)

Find an initial guess at the state vector. This currently uses

invert_liquid_water(rfl_meas, wl[, l_shoulder, ...])

Given a reflectance estimate, fit a state vector including liquid water path length

beer_lambert_model(x, y, wl, alpha_lw)

Function, which computes the vector of residuals between measured and modeled surface reflectance optimizing

Module Contents

heuristic_atmosphere(fm: ForwardModel, x_surface: numpy.array, x_RT: numpy.array, x_instrument: numpy.array, meas: numpy.array, geom: Geometry, wl_lo: int = 865, wl_center: int = 945, wl_hi: int = 1040)[source]

From a given radiance, estimate atmospheric state with band ratios. Used to initialize gradient descent inversions.

Parameters:

  • fm – isofit forward model

  • x_surface – surface portion of the state vector

  • x_RT – radiative transfer portion of the state vector

  • x_instrument – instrument portion of the state vector

  • meas – a one-D numpy vector of radiance in uW/nm/sr/cm2

  • geom – geometry object corresponding to given measurement

  • wl_lo – Low wavelength to use for the continuum removal H2O fit

  • wl_center – Center wavelength to use for the continuum removal H2O fit

  • wl_hi – High wavelength to use for the continuum removal H2O fit

Returns:

updated estimate of x_RT

Return type:

x_new

invert_algebraic(surface: Surface, RT: RadiativeTransfer, instrument: Instrument, x_surface: numpy.array, x_RT: numpy.array, x_instrument: numpy.array, meas: numpy.array, geom: Geometry)[source]

Inverts radiance algebraically using Lambertian assumptions to get a reflectance. If the appropriate transmittance terms are available, surface slope will enter for the initial guess. Otherwise, the surface will be treated as if flat.

Parameters:

  • surface – surface model

  • RT – radiative transfer model to use

  • instrument – instrument model

  • x_surface – surface portion of the state vector

  • x_RT – radiative transfer portion of the state vector

  • x_instrument – instrument portion of the state vector

  • meas – a one-D numpy vector of radiance in uW/nm/sr/cm2

  • geom – geometry object corresponding to given measurement

Returns:

estimate of the surface reflectance based on the given surface model and specified atmospheric state coeffs: atmospheric parameters used for the inversion, returned for convenience

Return type:

rfl_est

invert_analytical(fm: ForwardModel, winidx: numpy.array, meas: numpy.array, geom: Geometry, x0: numpy.array, sub_state, num_iter: int = 1, hash_table: OrderedDict = None, hash_size: int = None, diag_uncert: bool = True, outside_ret_const: float = -0.01, fill_value: float = -9999.0)[source]

Perform an analytical estimate of the conditional MAP estimate for a fixed atmosphere. Based on the “Inner loop” from Susiluoto, 2022.

Parameters:

  • fm – isofit forward model

  • winidx – indices of surface components of state vector (to be solved)

  • meas – a one-D numpy vector of radiance in uW/nm/sr/cm2

  • geom – geometry object corresponding to given measurement

  • x0 – the initialization state including surface from the superpixel and the atm from the smoothed atmosphere.

  • num_iter – number of interations to run through

  • hash_table – a hash table to use locally

  • hash_size – max size of given hash table

  • diag_uncert – flag indicating whether to diagonalize the uncertainty

Returns:

MAP estimate of the mean S: diagonal conditional posterior covariance estimate

Return type:

x

invert_simple(forward: ForwardModel, meas: numpy.array, geom: Geometry)[source]

Find an initial guess at the state vector. This currently uses traditional (non-iterative, heuristic) atmospheric correction.

Parameters:

  • forward – isofit forward model

  • meas – a one-D numpy vector of radiance in uW/nm/sr/cm2

  • geom – geometry object corresponding to given measurement

Returns:

estimate of the full statevector based on initial conditions, geometry, and a heuristic guess

Return type:

x

invert_liquid_water(rfl_meas: numpy.array, wl: numpy.array, l_shoulder: float = 850, r_shoulder: float = 1100, lw_init: tuple = (0.02, 0.3, 0.0002), lw_bounds: tuple = ([0, 0.5], [0, 1.0], [-0.0004, 0.0004]), ewt_detection_limit: float = 0.5, return_abs_co: bool = False)[source]

Given a reflectance estimate, fit a state vector including liquid water path length based on a simple Beer-Lambert surface model.

Parameters:

  • rfl_meas – surface reflectance spectrum

  • wl – instrument wavelengths, must be same size as rfl_meas and in units of nm

  • l_shoulder – wavelength of left absorption feature shoulder

  • r_shoulder – wavelength of right absorption feature shoulder

  • lw_init – initial guess for liquid water path length, intercept, and slope

  • lw_bounds – lower and upper bounds for liquid water path length, intercept, and slope

  • ewt_detection_limit – upper detection limit for ewt

  • return_abs_co – if True, returns absorption coefficients of liquid water

Returns:

estimated liquid water path length, intercept, and slope based on a given surface reflectance

Return type:

solution

beer_lambert_model(x, y, wl, alpha_lw)[source]

Function, which computes the vector of residuals between measured and modeled surface reflectance optimizing for path length of surface liquid water based on the Beer-Lambert attenuation law.

Parameters:

  • x – state vector (liquid water path length, intercept, slope)

  • y – measurement (surface reflectance spectrum)

  • wl – instrument wavelengths

  • alpha_lw – wavelength dependent absorption coefficients of liquid water

Returns:

residual between modeled and measured surface reflectance

Return type:

resid