# Calculate probabilistic impact yearset¶

This module generates a yearly impact yimp object which contains probabilistic annual impacts for a specified amount of years (sampled_years). The impact values are extracted from a given impact imp object that contains impact values per event. The amount of sampled_years can be specified as an integer or as a list of years to be sampled for. The amount of events per sampled year (events_per_year) are determined with a Poisson distribution centered around n_events per year (lam = sum(event_impacts.frequency). Then, the probabilistic events occuring in each sampled year are sampled uniformaly from the input imp object and summed up per year. Thus, the yimp object contains the sum of sampled (event) impacts for each sampled year. In contrast to the expected annual impact (eai), an yimp object contains an impact for EACH sampled year and this value differs among years. The number of events_per_year and the selected_events are saved in a sampling vector (sampling_vect).

The function impact_yearsets performs all these computational steps, taking an imp and the number of sampled_years (sampled_years) as input. The output of the function is the yimp object and the sampling_vect. Moreover, a sampling_vect (generated in a previous run) can be provided as optional input and the user can define lam and decide whether a correction factor shall be applied (the default is applying the correction factor). Reapplying the same sampling_vect does not only allow to reproduce the generated yimp, but also for a physically consistent way of sampling impacts caused by different hazards. The correction factor that is applied when the optional input correction_fac= True is a scaling of the computed yimp that assures that the eai(yimp) = eai(imp).

To make the process more transparent, this tutorial shows the single computations that are performed when generating an yimp object for a dummy event_impacts object.

:

import numpy as np

# dummy event_impacts object containing 10 event_impacts with the values 10-110
# and the frequency 0.2 (Return period of 5 years)
imp = Impact()
imp.at_event = np.arange(10,110,10)
imp.frequency = np.array(np.ones(10)*0.2)

# the number of years to sample impacts for (length(yimp.at_event) = sampled_years)
sampled_years = 10

# sample number of events per sampled year
lam = np.sum(imp.frequency)
events_per_year = yearsets.sample_from_poisson(sampled_years, lam)
events_per_year

:

array([2, 2, 2, 0, 4, 5, 4, 2, 3, 1])

:

# generate the sampling vector
sampling_vect = yearsets.sample_events(events_per_year, imp.frequency)
sampling_vect

:

[array([8, 3]),
array([7, 0]),
array([4, 6]),
array([], dtype=int32),
array([5, 9, 1, 2]),
array([1, 6, 0, 7, 2]),
array([4, 9, 5, 8]),
array([9, 8]),
array([5, 3, 4]),
array()]

:

# calculate the impact per year
imp_per_year = yearsets.compute_imp_per_year(imp, sampling_vect)
imp_per_year

:

[130, 90, 120, 0, 210, 210, 300, 190, 150, 20]

:

# calculate the correction factor
correction_factor = yearsets.calculate_correction_fac(imp_per_year, imp)
correction_factor

:

0.7746478873239436

:

# compare the resulting yimp with our step-by-step computation without applying the correction factor:
yimp, sampling_vect = yearsets.impact_yearset(imp, sampled_years=list(range(1,11)), correction_fac=False)

print('The yimp.at_event values equal our step-by-step computed imp_per_year:')
print('yimp.at_event = ', yimp.at_event)
print('imp_per_year = ', imp_per_year)

The yimp.at_event values equal our step-by-step computed imp_per_year:
yimp.at_event =  [90, 240, 150, 70, 40, 90, 60, 90, 170, 110]
imp_per_year =  [130, 90, 120, 0, 210, 210, 300, 190, 150, 20]

:

# and here the same comparison with applying the correction factor (default settings):
yimp, sampling_vect = yearsets.impact_yearset(imp, sampled_years=list(range(1,11)))

print('The same can be shown for the case of applying the correction factor.'
'The yimp.at_event values equal our step-by-step computed imp_per year:')
print('yimp.at_event = ', yimp.at_event)
print('imp_per_year = ', imp_per_year/correction_factor)

The same can be shown for the case of applying the correction factor.The yimp.at_event values equal our step-by-step computed imp_per year:
yimp.at_event =  [ 54.54545455  47.72727273  95.45454545 109.09090909   0.
40.90909091  27.27272727   0.         109.09090909  27.27272727]
imp_per_year =  [167.81818182 116.18181818 154.90909091   0.         271.09090909
271.09090909 387.27272727 245.27272727 193.63636364  25.81818182]