wradlib.atten.correct_attenuation_constrained(gateset, a_max=0.000167, a_min=2.33e-05, n_a=4, b_max=0.7, b_min=0.65, n_b=6, gate_length=1.0, constraints=None, constraint_args=None, sector_thr=10)

Gate-by-Gate attenuation correction based on the iterative approach of and with a generalized and scalable number of constraints.

Differing from the original approach, the method for addressing small sectors which conflict with the constraints is based on a bisection forward calculating method, and not on backwards attenuation calculation.

Parameters
• gateset (numpy.ndarray) – Multidimensional array, where the range gates (over which iteration has to be performed) are supposed to vary along the last array-dimension and the azimuths are supposed to vary along the next to last array-dimension.

Data has to be provided in decibel representation of reflectivity [dBZ].

• a_max (float) – Initial value for linear coefficient of the k-Z relation ( $$k=a \cdot Z^{b}$$ ).

Per default set to 1.67e-4.

• a_min (float) – Minimal allowed linear coefficient of the k-Z relation ( $$k=a \cdot Z^{b}$$ ) in the downwards iteration of ‘a’ in case of breaching one of thresholds constr_args of the optional conditions constraints.

Per default set to 2.33e-5.

• n_a (int) – Number of iterations from a_max to a_min.

Per default set to 4.

• b_max (float) – Initial value for exponential coefficient of the k-Z relation ( $$k=a \cdot Z^{b}$$ ).

Per default set to 0.7.

• b_min (float) – Minimal allowed exponential coefficient of the k-Z relation ( $$k=a \cdot Z^{b}$$ ) in the downwards iteration of ‘b’ in case of breaching one of thresholds constr_args of the optional conditions constraints and the linear coefficient ‘a’ has already reached the lower limit a_min.

Per default set to 0.65.

• n_b (int) – Number of iterations from b_max to b_min.

Per default set to 6.

• gate_length (float) – Radial length of a range gate [km].

Per default set to 1.0.

• constraints (list) – List of constraint functions. The signature of these functions has to be constraint_function(gateset, k, *constr_args). Their return value must be a boolean array of shape gateset.shape[:-1] set to True for beams, which do not fulfill the constraint.

• constraint_args (list) – List of lists, which are to be passed to the individual constraint functions using the *args mechanism (len(constr_args) == len(constraints)).

• sector_thr (int) – Number of adjacent beams, for which in case of breaching the constraints the attenuation with downward iterated a and b - parameters is recalculated. For more narrow sectors the integrated attenuation of the last gate is interpolated and used as reference for the recalculation.

Returns

pia (numpy.ndarray) – Array with the same shape as gateset containing the calculated path integrated attenuation [dB] for each range gate.

Examples

Implementing the original Hitschfeld & Bordan (1954) algorithm with otherwise default parameters:

from wradlib.atten import *
pia = correct_attenuation_constrained(gateset, a_max=8.e-5,
b_max=0.731, n_a=1, n_b=1,
gate_length=1.0)


Implementing the basic Kraemer algorithm:

pia = atten.correct_attenuation_constrained(gateset, a_max=1.67e-4,
a_min=2.33e-5, n_a=100,
b_max=0.7, b_min=0.65,
n_b=6, gate_length=1.,
constraints=
[wrl.atten.constraint_dbz],
constraint_args=[[59.0]])


Implementing the PIA algorithm by Jacobi et al.:

pia = atten.correct_attenuation_constrained(gateset, a_max=1.67e-4,
a_min=2.33e-5, n_a=100,
b_max=0.7, b_min=0.65,
n_b=6, gate_length=1.,
constraints=
[wrl.atten.constraint_dbz,
wrl.atten.constraint_pia],
constraint_args=
[[59.0],[20.0]])