climpred.metrics._rps¶

climpred.metrics._rps(forecast, verif, dim=None, **metric_kwargs)[source]¶

Ranked Probability Score.

$RPS(p, k) = \sum_{m=1}^{M} [(\sum_{k=1}^{m} p_k) - (\sum_{k=1}^{m} o_k)]^{2}$

Parameters

forecast (xr.object) – Forecasts.
verif (xr.object) – Verification.
dim (list or str) – Dimensions to aggregate.
xs.rps (**metric_kwargs, see) –

Note

If category_edges is xr.Dataset or tuple of xr.Datasets, climpred will broadcast the grouped dimensions season, month, weekofyear, dayfofyear onto the dimensions init for forecast and time for observations. see climpred.utils.broadcast_time_grouped_to_time.

Details:

minimum	0.0
maximum	∞
perfect	0.0
orientation	negative

See also

rps()

Example

>>> category_edges = np.array([-.5, 0., .5, 1.])
>>> HindcastEnsemble.verify(metric='rps', comparison='m2o', dim=['member', 'init'],
...     alignment='same_verifs', category_edges=category_edges)
<xarray.Dataset>
Dimensions:                     (lead: 10)
Coordinates:
  * lead                        (lead) int32 1 2 3 4 5 6 7 8 9 10
    observations_category_edge  <U67 '[-np.inf, -0.5), [-0.5, 0.0), [0.0, 0.5...
    forecasts_category_edge     <U67 '[-np.inf, -0.5), [-0.5, 0.0), [0.0, 0.5...
    skill                       <U11 'initialized'
Data variables:
    SST                         (lead) float64 0.115 0.1123 ... 0.1687 0.1875

Provide category_edges as xr.Dataset for category_edges varying along dimensions.

>>> category_edges = xr.DataArray([9.5, 10., 10.5, 11.], dims='category_edge').assign_coords(category_edge=[9.5, 10., 10.5, 11.]).to_dataset(name='tos')
>>> # category_edges = np.array([9.5, 10., 10.5, 11.]) # identical
>>> PerfectModelEnsemble.verify(metric='rps', comparison='m2c',
...     dim=['member','init'], category_edges=category_edges)
<xarray.Dataset>
Dimensions:                     (lead: 20)
Coordinates:
  * lead                        (lead) int64 1 2 3 4 5 6 7 ... 15 16 17 18 19 20
    observations_category_edge  <U71 '[-np.inf, 9.5), [9.5, 10.0), [10.0, 10....
    forecasts_category_edge     <U71 '[-np.inf, 9.5), [9.5, 10.0), [10.0, 10....
Data variables:
    tos                         (lead) float64 0.08951 0.1615 ... 0.1399 0.2274

Provide category_edges as tuple for different category_edges to categorize forecasts and observations.

>>> q = [1 / 3, 2 / 3]
>>> forecast_edges = HindcastEnsemble.get_initialized().groupby('init.month').quantile(q=q, dim=['init','member']).rename({'quantile':'category_edge'})
>>> obs_edges = HindcastEnsemble.get_observations().groupby('time.month').quantile(q=q, dim='time').rename({'quantile':'category_edge'})
>>> category_edges = (obs_edges, forecast_edges)
>>> HindcastEnsemble.verify(metric='rps', comparison='m2o',
...     dim=['member', 'init'], alignment='same_verifs',
...     category_edges=category_edges)
<xarray.Dataset>
Dimensions:                     (lead: 10)
Coordinates:
  * lead                        (lead) int32 1 2 3 4 5 6 7 8 9 10
    observations_category_edge  <U101 '[-np.inf, 0.3333333333333333), [0.3333...
    forecasts_category_edge     <U101 '[-np.inf, 0.3333333333333333), [0.3333...
    skill                       <U11 'initialized'
Data variables:
    SST                         (lead) float64 0.1248 0.1756 ... 0.3081 0.3413