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Kraijenhoff#

class Kraijenhoff(cutoff=0.999, n_terms=10, **kwargs)[source]#

The response function of Van de Leur [1958].

Parameters
  • up (bool or None, optional) – indicates whether a positive stress will cause the head to go up (True, default) or down (False), if None the head can go both ways.

  • gain_scale_factor (float, optional) – the scale factor is used to set the initial value and the bounds of the gain parameter, computed as 1 / gain_scale_factor.

  • cutoff (float, optional) – proportion after which the step function is cut off.

  • n_terms (int, optional) – Number of terms.

Notes

The Kraijenhoff van de Leur function is explained in Van de Leur [1958].

The impulse response function for this class can be viewed on the Documentation website or using latexify by running the following code in a Jupyter notebook environment:

ps.Kraijenhoff.impulse

The function describes the response of a domain between two drainage channels. The function gives the same outcome as equation 133.15 in Bruggeman [1999]. This is the response that is actually calculated with this function.

The response function has three parameters A, a and b:

  • A is the gain (scaled),

  • a is the reservoir coefficient (j in Van de Leur [1958]),

  • b is the location in the domain with the origin in the middle. This means that b=0 is in the middle and b=1/2 is at the drainage channel. At b=1/4 the response function is most similar to the exponential response function.

Methods#

__init__

block

Method to return the block function.

gain

get_init_parameters

Get initial parameters and bounds.

get_t

Internal method to determine the times at which to evaluate the step response, from t=0.

get_tmax

Method to get the response time for a certain cutoff.

impulse

Method to return the impulse response function.

step

Method to return the step function.

to_dict

Method to export the response function to a dictionary.

update_rfunc_settings

Internal method to set the settings of the response function.