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
See terminology for clarification on the differences between
these two experimental setups.
All high-level functions like
PerfectModelEnsemble.bootstrap() take a
comparison keyword to select the
comparison style. See below for a detailed description on the differences between these
HindcastEnsemble, 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. [Boer et al., 2016]
keyword: "e2o", "e2r"
Compare the ensemble mean forecast to the verification data.
keyword: "m2o", "m2r"
Compare each ensemble member individually to the verification data.
Perfect Model Ensembles#
PerfectModelEnsemble, there are many more ways of
verifying forecasts. Séférian et al.  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 Griffies and Bryan .
Compare all members to ensemble mean while leaving out the verif in ensemble mean.
Compare all other member forecasts to a single member verification.
Compare all members to all others in turn while leaving out verification member.
Compare ensemble mean forecast to single member verification.
The goal of a normalized distance metric is to get a constant or comparable value of
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 [Séférian et al., 2018] to accomodate
different comparison styles. For example,
metric="nrmse" gets smaller in
"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
"m2o". It is 1 for
Interpretation of Results#
HindcastEnsemble skill is computed over all
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
[Bushuk et al., 2018], but also returns a mean forecast skill over all initializations.
Compute over dimension#
dim defines over which dimension a metric is computed. We can
apply a metric over all dimensions from the
initialized dataset expect
The resulting skill is then
reduced by this
dim. Therefore, applying a metric over
dim= 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.
dim argument is different from the
comparison argument which
just specifies how
observations are defined.
However, this above logic applies to deterministic metrics. Probabilistic metrics need
to be applied to the
member dimension and
["m2c", "m2m"] in
dim should not contain
member when the comparison already computes ensemble
means as in
You can also construct your own comparisons via the
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 probabilistic
member dimension and
observations without. For deterministic metrics, return
observations with identical dimensions but without an identical comparison:
from climpred.comparisons import Comparison, M2M_MEMBER_DIM def _my_m2median_comparison(initialized, metric=None): """Identical to m2e but median.""" observations_list =  forecast_list =  supervector_dim = "member" for m in initialized.member.values: forecast = initialized.drop_sel(member=m).median("member") observations = initialized.sel(member=m).squeeze() forecast_list.append(forecast) observations_list.append(observations) observations = xr.concat(observations_list, M2M_MEMBER_DIM) forecast = xr.concat(forecast_list, M2M_MEMBER_DIM) forecast[M2M_MEMBER_DIM] = np.arange(forecast[M2M_MEMBER_DIM].size) observations[M2M_MEMBER_DIM] = np.arange(observations[M2M_MEMBER_DIM].size) return forecast, observations
Then initialize this comparison function with
__my_m2median_comparison = Comparison( name="m2me", function=_my_m2median_comparison, probabilistic=False, hindcast=False)
Finally, compute skill based on your own comparison:
PerfectModelEnsemble.verify( metric="rmse", comparison=__my_m2median_comparison, dim=, )
Once you come up with an useful comparison for your problem, consider contributing this
climpred, so all users can benefit from your comparison, see
G. J. Boer, D. M. Smith, C. Cassou, F. Doblas-Reyes, G. Danabasoglu, B. Kirtman, Y. Kushnir, M. Kimoto, G. A. Meehl, R. Msadek, W. A. Mueller, K. E. Taylor, F. Zwiers, M. Rixen, Y. Ruprich-Robert, and R. Eade. The Decadal Climate Prediction Project (DCPP) contribution to CMIP6. Geosci. Model Dev., 9(10):3751–3777, October 2016. doi:10/f89qdf.
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. doi:10/gd7hfq.
S. M. Griffies and K. Bryan. A predictability study of simulated North Atlantic multidecadal variability. Climate Dynamics, 13(7-8):459–487, August 1997. doi:10/ch4kc4.