Diagnosing Potential Predictability¶
This demo demonstrates climpred
’s capabilities to diagnose areas containing potentially predictable variations from a control/verification product alone without requiring multi-member, multi-initialization simulations. This notebook identifies the slow components of internal variability that indicate potential predictability. Here, we showcase a set of methods to show regions indicating probabilities for decadal predictability.
[1]:
# linting
%load_ext nb_black
%load_ext lab_black
[2]:
%matplotlib inline
import climpred
[3]:
# Sea surface temperature
varname = "tos"
control3d = climpred.tutorial.load_dataset("MPI-control-3D")[varname].load()
Diagnostic Potential Predictability (DPP)¶
We can first use the [Resplandy 2015] and [Seferian 2018] method for computing the unbiased DPP by not chunking the time dimension.
[4]:
# calculate DPP with m=10
DPP10 = climpred.stats.dpp(control3d, m=10, chunk=False)
# calculate a threshold by random shuffling (based on bootstrapping with replacement at 95% significance level)
threshold = climpred.bootstrap.dpp_threshold(
control3d, m=10, chunk=False, iterations=10, sig=95
)
# plot grid cells where DPP above threshold
DPP10.where(DPP10 > threshold).plot(
yincrease=False, vmin=-0.1, vmax=0.6, cmap="viridis"
)
[4]:
<matplotlib.collections.QuadMesh at 0x7f83fd1e8c70>
Now, we can turn on chunking (the default for this function) to use the [Boer 2004] method.
[5]:
# chunk = True signals the Boer 2004 method
DPP10 = climpred.stats.dpp(control3d, m=10, chunk=True)
threshold = climpred.bootstrap.dpp_threshold(
control3d, m=10, chunk=True, iterations=10, sig=95
)
DPP10.where(DPP10 > 0).plot(yincrease=False, vmin=-0.1, vmax=0.6, cmap="viridis")
/Users/aaron.spring/anaconda3/envs/climpred-dev/lib/python3.8/site-packages/xarray/core/nputils.py:227: RuntimeWarning: Degrees of freedom <= 0 for slice.
result = getattr(npmodule, name)(values, axis=axis, **kwargs)
/Users/aaron.spring/anaconda3/envs/climpred-dev/lib/python3.8/site-packages/xarray/core/nputils.py:227: RuntimeWarning: Degrees of freedom <= 0 for slice.
result = getattr(npmodule, name)(values, axis=axis, **kwargs)
[5]:
<matplotlib.collections.QuadMesh at 0x7f83ef504970>
Variance-Weighted Mean Period¶
A periodogram is computed based on a control simulation to extract the mean period of variations, which are weighted by the respective variance. Regions with a high mean period value indicate low-frequency variations with are potentially predictable [Branstator2010].
[6]:
vwmp = climpred.stats.varweighted_mean_period(control3d, dim="time")
threshold = climpred.bootstrap.varweighted_mean_period_threshold(
control3d, iterations=10
)
vwmp.where(vwmp > threshold).plot(yincrease=False, robust=True)
[6]:
<matplotlib.collections.QuadMesh at 0x7f84090defa0>
Lag-1 Autocorrelation¶
The lag-1 autocorrelation also indicates where slower modes of variability occur by identifying regions with high temporal correlation [vonStorch1999].
[7]:
from esmtools.stats import autocorr
[8]:
# use climpred.bootstrap._bootstrap_func to wrap any stats function. `esmtools.stats.autocorr` computes the autocorrelation
# coefficient out to N lags. The first lag is at lag 0, so we select `lead=1`).
threshold = climpred.bootstrap._bootstrap_func(
autocorr, control3d, nlags=2, resample_dim="time", iterations=10
).isel(lead=1)
corr_ef = autocorr(control3d, nlags=2, dim="time").isel(lead=1)
corr_ef.where(corr_ef > threshold).plot(yincrease=False, robust=False)
[8]:
<matplotlib.collections.QuadMesh at 0x7f8408c096d0>
Decorrelation time¶
Taking the lagged correlation further over all lags, the decorrelation time shows the time after which the autocorrelation fell beyond its e-folding [vonStorch1999]
[9]:
threshold = climpred.bootstrap._bootstrap_func(
climpred.stats.decorrelation_time, control3d, "time", iterations=10
)
decorr_time = climpred.stats.decorrelation_time(control3d)
decorr_time.where(decorr_time > threshold).plot(yincrease=False, robust=False)
[9]:
<matplotlib.collections.QuadMesh at 0x7f8408a6b970>
Verify diagnostic potential predictability in predictability simulations¶
Do we find predictability in the areas highlighted above also in perfect-model experiments?
[10]:
ds3d = climpred.tutorial.load_dataset("MPI-PM-DP-3D")[varname]
control3d = climpred.tutorial.load_dataset("MPI-control-3D")[varname]
ds3d["lead"].attrs["units"] = "years"
pm = climpred.PerfectModelEnsemble(ds3d).add_control(control3d)
/Users/aaron.spring/Coding/climpred/climpred/utils.py:122: UserWarning: Assuming annual resolution due to numeric inits. Change init to a datetime if it is another resolution.
warnings.warn(
[11]:
bootstrap_skill = pm.bootstrap(
metric="rmse",
comparison="m2e",
dim=["init", "member"],
reference=["uninitialized"],
iterations=10,
)
/Users/aaron.spring/Coding/climpred/climpred/checks.py:229: UserWarning: Consider chunking input `ds` along other dimensions than needed by algorithm, e.g. spatial dimensions, for parallelized performance increase.
warnings.warn(
[12]:
init_skill = bootstrap_skill.sel(results="verify skill", skill="initialized")
# p value: probability that random uninitialized forecasts perform better than initialized
p = bootstrap_skill.sel(results="p", skill="uninitialized")
[13]:
init_skill.where(p <= 0.05)[varname].plot(
col="lead", robust=True, yincrease=False, x="x"
)
[13]:
<xarray.plot.facetgrid.FacetGrid at 0x7f83744f2fd0>
The metric rmse
is negatively oriented, e.g. higher values show large disprepancy between members and hence less skill.
As suggested by DPP, the variance-weighted mean period and autocorrelation, also in slight perturbed initial values ensembles there is predictability in the North Atlantic, North Pacific and Southern Ocean in sea-surface temperatures.
References¶
Boer, Georges J. “Long time-scale potential predictability in an ensemble of coupled climate models.” Climate dynamics 23.1 (2004): 29-44.
Resplandy, Laure, R. Séférian, and L. Bopp. “Natural variability of CO2 and O2 fluxes: What can we learn from centuries‐long climate models simulations?.” Journal of Geophysical Research: Oceans 120.1 (2015): 384-404.
Séférian, Roland, Sarah Berthet, and Matthieu Chevallier. “Assessing the Decadal Predictability of Land and Ocean Carbon Uptake.” Geophysical Research Letters, March 15, 2018. https://doi.org/10/gdb424.
Branstator, Grant, and Haiyan Teng. “Two Limits of Initial-Value Decadal Predictability in a CGCM.” Journal of Climate 23, no. 23 (August 27, 2010): 6292–6311. https://doi.org/10/bwq92h.
Storch, H. v, and Francis W. Zwiers. Statistical Analysis in Climate Research. Cambridge ; New York: Cambridge University Press, 1999.