climpred.classes.HindcastEnsemble.bootstrap

HindcastEnsemble.bootstrap(metric=None, comparison=None, dim=None, alignment=None, reference=None, iterations=None, sig=95, resample_dim='member', pers_sig=None, **metric_kwargs)

Bootstrap with replacement according to Goddard et al. 2013.

Parameters

• metric (str, Metric) – Metric to apply for verification, see metrics.

• comparison (str, Comparison) – How to compare to the observations/verification data, see comparisons.

• dim (str, list of str) – dimension(s) to apply metric over. dim is passed on to xskillscore.{metric} and includes xskillscore’s member_dim. dim should contain member when comparison is probabilistic but should not contain member when comparison='e2o'. Defaults to None meaning that all dimensions other than lead are reduced.

• reference (str, list of str) – Type of reference forecasts with which to verify. One or more of [‘uninitialized’, ‘persistence’, ‘climatology’]. If None or empty, returns no p value.

• alignment (str) –

  which inits or verification times should be aligned?

  • ’maximize’: maximize the degrees of freedom by slicing init and verif to a common time frame at each lead.

  • ’same_inits’: slice to a common init frame prior to computing metric. This philosophy follows the thought that each lead should be based on the same set of initializations.

  • ’same_verif’: slice to a common/consistent verification time frame prior to computing metric. This philosophy follows the thought that each lead should be based on the same set of verification dates.

• iterations (int) – Number of resampling iterations for bootstrapping with replacement. Recommended >= 500.

• sig (int, default 95) – Significance level in percent for deciding whether uninitialized and persistence beat initialized skill.

• resample_dim (str or list) –

  dimension to resample from. default: ‘member’.

  • ’member’: select a different set of members from hind

  • ’init’: select a different set of initializations from hind

• pers_sig (int, default None) – If not None, the separate significance level for persistence.

• **metric_kwargs (optional) – arguments passed to metric.

Returns

with dimensions results (holding skill, p, low_ci and high_ci) and skill (holding initialized, persistence and/or uninitialized):

• results=’verify skill’, skill=’initialized’:

  mean initialized skill

• results=’high_ci’, skill=’initialized’:

  high confidence interval boundary for initialized skill

• results=’p’, skill=’uninitialized’:

  p value of the hypothesis that the difference of skill between the initialized and uninitialized simulations is smaller or equal to zero based on bootstrapping with replacement.

• results=’p’, skill=’persistence’:

  p value of the hypothesis that the difference of skill between the initialized and persistence simulations is smaller or equal to zero based on bootstrapping with replacement.

Return type

xr.Datasets

Example

Calculate the Pearson’s Anomaly Correlation (‘acc’) comparing the ensemble mean forecast to the verification (e2o) over the same verification times (same_verifs) for all leads reducing dimensions init 50 times after resampling member dimension with replacement. Also calculate reference skill for the persistence, climatology and uninitialized forecast and compare whether initialized skill is better than reference skill: Returns verify skill, probability that reference forecast performs better than initialized and the lower and upper bound of the resample.

>>> HindcastEnsemble.bootstrap(metric='acc', comparison='e2o',
...     dim='init', iterations=50, resample_dim='member',
...     alignment='same_verifs',
...     reference=['persistence', 'climatology' ,'uninitialized'])
<xarray.Dataset>
Dimensions:  (skill: 4, results: 4, lead: 10)
Coordinates:
  * lead     (lead) int32 1 2 3 4 5 6 7 8 9 10
  * results  (results) <U12 'verify skill' 'p' 'low_ci' 'high_ci'
  * skill    (skill) <U13 'initialized' 'persistence' ... 'uninitialized'
Data variables:
    SST      (skill, results, lead) float64 0.9313 0.9119 ... 0.8078 0.8078
Attributes:
    prediction_skill:            calculated by climpred https://climpred.read...
    number_of_initializations:   61
    number_of_members:           10
    alignment:                   same_verifs
    metric:                      pearson_r
    comparison:                  e2o
    dim:                         ['init']
    units:                       None
    confidence_interval_levels:  0.975-0.025
    bootstrap_iterations:        50
    p:                           probability that reference performs better t...