Comparisons¶
Forecasts have to be verified against some product to evaluate their performance. However, when verifying against a product, there are many different ways one can compare the ensemble of forecasts. Here we cover the comparison options for both hindcast and perfect model ensembles. See terminology for clarification on the differences between these two experimental setups.
All high-level functions like verify()
and bootstrap()
(for both HindcastEnsemble
and PerfectModelEnsemble
objects) take a
comparison=''
keyword to select the comparison style. See below for a detailed
description on the differences between these comparisons.
Hindcast Ensembles¶
In hindcast ensembles, the ensemble mean forecast (comparison='e2o'
) is expected to
perform better than individual ensemble members (comparison='m2o'
) as the chaotic
component of forecasts is expected to be suppressed by this averaging, while the memory
of the system sustains. [Boer2016]
keyword: 'e2o', 'e2r'
|
Compare the ensemble mean forecast to the verification data for a |
keyword: 'm2o', 'm2r'
|
Compares each ensemble member individually to the verification data for a |
Perfect Model Ensembles¶
In perfect-model frameworks, there are many more ways of verifying forecasts.
[Seferian2018] uses a comparison of all ensemble members against the
control run (comparison='m2c'
) and all ensemble members against all other ensemble
members (comparison='m2m'
). Furthermore, the ensemble mean forecast can be verified
against one control member (comparison='e2c'
) or all members (comparison='m2e'
)
as done in [Griffies1997].
keyword: 'm2e'
|
Compare all members to ensemble mean while leaving out the reference in |
keyword: 'm2c'
|
Compare all other member forecasts to a single member verification, which is the first member. |
keyword: 'm2m'
|
Compare all members to all others in turn while leaving out the verification |
keyword: 'e2c'
|
Compare ensemble mean forecast to single member verification. |
Normalization¶
The goal of a normalized distance metric is to get a constant or comparable value of typically 1 (or 0 for metrics defined as 1 - metric) when the metric saturates and the predictability horizon is reached (see metrics).
A factor is added in the normalized metric formula (see [Seferian2018]) to accomodate
different comparison styles. For example, nrmse
gets smalled in comparison m2e
than m2m
by design, since the ensembe mean is always closer to individual members
than the ensemble members to each other. In turn, the normalization factor is 2
for
comparisons m2c
, m2m
, and m2o
. It is 1 for m2e
, e2c
, and e2o
.
Interpretation of Results¶
When HindcastEnsemble
skill is computed over all initializations dim='init'
of the
hindcast, the resulting skill is a mean forecast skill over all initializations.
PerfectModelEnsemble
skill is computed over a supervector comprised of all
initializations and members, which allows the computation of the ACC-based skill
[Bushuk2018], but also returns a mean forecast skill over all initializations.
The supervector approach shown in [Bushuk2018] and just calculating a distance-based
metric like rmse
over the member dimension as in [Griffies1997] yield very similar
results.
Compute over dimension¶
The argument dim
defines over which dimension a metric is computed. We can
apply a metric over all dimensions from the initialized dataset expect lead
.
The resulting skill is then
reduced by this dim
. Therefore, applying a metric over dim='member'
creates a
skill for all initializations individually. This can show the initial conditions
dependence of skill. Likewise when computing skill over 'init'
, we get skill for
each member. This dim
argument is different from the comparison
argument which
just specifies how forecast
and observations
are defined.
However, this above logic applies to deterministic metrics. Probabilistic metrics need
to be applied to the member
dimension and comparison
from ['m2c'
, 'm2m'
]
in PerfectModelEnsemble
verify()
and 'm2o'
comparison in HindcastEnsemble
verify()
.
dim
should not contain
member
when the comparison already computes ensemble means as in
['e2o'
, 'e2c'
].
User-defined comparisons¶
You can also construct your own comparisons via the
Comparison
class.
|
Master class for all comparisons. |
First, write your own comparison function, similar to the existing ones. If a
comparison should also be used for probabilistic metrics, make sure that
metric.probabilistic
returns forecast
with member
dimension and
observations
without. For deterministic metrics, return forecast
and
observations
with identical dimensions but without an identical comparison:
from climpred.comparisons import Comparison, _drop_members
def _my_m2median_comparison(ds, metric=None):
"""Identical to m2e but median."""
observations_list = []
forecast_list = []
supervector_dim = 'member'
for m in ds.member.values:
forecast = _drop_members(ds, rmd_member=[m]).median('member')
observations = ds.sel(member=m).squeeze()
forecast_list.append(forecast)
observations_list.append(observations)
observations = xr.concat(observations_list, supervector_dim)
forecast = xr.concat(forecast_list, supervector_dim)
forecast[supervector_dim] = np.arange(forecast[supervector_dim].size)
observations[supervector_dim] = np.arange(observations[supervector_dim].size)
return forecast, observations
Then initialize this comparison function with
Comparison
:
__my_m2median_comparison = Comparison(
name='m2me',
function=_my_m2median_comparison,
probabilistic=False,
hindcast=False)
Finally, compute skill based on your own comparison:
skill = compute_perfect_model(ds, control,
metric='rmse',
comparison=__my_m2median_comparison)
Once you come up with an useful comparison for your problem, consider contributing this
comparison to climpred
, so all users can benefit from your comparison, see
contributing.
References¶
- Boer2016
Boer, G. J., D. M. Smith, C. Cassou, F. Doblas-Reyes, G. Danabasoglu, B. Kirtman, Y. Kushnir, et al. “The Decadal Climate Prediction Project (DCPP) Contribution to CMIP6.” Geosci. Model Dev. 9, no. 10 (October 25, 2016): 3751–77. https://doi.org/10/f89qdf.
- Bushuk2018(1,2)
Mitchell Bushuk, Rym Msadek, Michael Winton, Gabriel Vecchi, Xiaosong Yang, Anthony Rosati, and Rich Gudgel. Regional Arctic sea–ice prediction: potential versus operational seasonal forecast skill. Climate Dynamics, June 2018. https://doi.org/10/gd7hfq.
- Griffies1997(1,2)
Griffies and K. Bryan. A predictability study of simulated North Atlantic multidecadal variability. Climate Dynamics, 13(7-8):459–487, August 1997. https://doi.org/10/ch4kc4.
- Seferian2018(1,2)
Roland Séférian, Sarah Berthet, and Matthieu Chevallier. Assessing the Decadal Predictability of Land and Ocean Carbon Uptake. Geophysical Research Letters, March 2018. https://doi.org/10/gdb424.