Toward Probabilistic Seasonal
Prediction
Nir Krakauer,
Hannah Aizenman, Michael Grossberg, Irina Gladkova
Department of Civil Engineering
and CUNY Remote Sensing of the Earth Institute,
The City College of New York.
nkrakauer@ccny.cuny.edu
In this talk
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Seasonal and probabilistic prediction
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Quantifying probabilistic forecast skill
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An application and future prospects
Weather forecasts degrade
rapidly with lead time
Effect of atmosphere initial conditions dissipates
NRC, 2010
But there is hope for some skill at
month-season lead times
Persistent initial conditions (SST, soil, snow, strat, …)
Between synoptic and climate-change timescales
Deterministic vs. probabilistic prediction

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Deterministic (point) forecasts

"Partly cloudy, high of …"

How much confidence should we have in this? The
forecast doesn't tell us; we must rely on our
intuition/experience.
Partly probabilistic forecasts

"40% chance of precipitation"

How much? When?
Fully probabilistic forecasts

Distribution functions or an ensemble of possible
outcomes

If well calibrated, can be used directly in scenario
modeling and optimization
Information in a probability distribution

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How much more would we need to be told
to know the outcome?
Information theory (Shannon 1948):

Suppose one of n outcomes must
happen, for which we assign probability
pi

If we learn that this outcome did happen,
we've learned log(pi) bits

Summed over possible outcomes,n our
expected missing information is ∑ pi log (pi )
i=1
How useful is a forecast?
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Suppose that we learn that outcome i took
place
Under our baseline ignorance (e.g.
climatology), the probability of i was pi
Suppose a forecaster had given the
outcome a probability qi instead. Intuitively,
the forecast proved useful if qi > pi.
The information gain from the forecast is
log(qi / pi)
A forecaster's track record

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Across multiple forecast verifications, the average
information content of forecasts is given by the
average log(qi / pi)
Best case is to assign probability 1 to something
that does happen: log(1 / pi) bits gained
Assigning zero probability to something that does
happen ruins a forecaster's track record [log(0)]
Information (in bits) can be converted to a
forecast skill score (1 for a perfect forecast)
Generalization to continuous variables

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If x is the outcome and q, p are probability
densities, the information gain is
log(q(x)/p(x))
If the forecast was Gaussian with mean m
and SD σ, and the climatology had mean
m0 and SD σ0, the information gain is
(z2 – z02)/2 - log(σ/σ0), where z = (x – m)/σ
Probabilistic seasonal forecasting


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Based on known
sources of
persistence,
particularly ENSO
E.g., probabilistic
USA forecasts for T
and P tercile issued
by NOAA CPC since
1990s
Potentially valuable
for agricultural, water
management, etc.
Diagnosing probabilistic forecast bias

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Confidence is how much
skill a forecast claims to
have (relative to climatology)
If the forecast is wellcalibrated, this should be
similar to the information
gain estimated by comparing
forecasts to outcomes
It turns out CPC temperature
forecasts are overconfident
(claim 0.014 bits, actual
0.024 bits info gain), but with
geographic variability
Improving on existing forecasts
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It turns out that CPC's
forecasts underestimate the
impact of warming and
precipitation change
Naive Bayesian combination
of CPC's probabilities with a
trend estimate based on an
exponentially weighted
moving average resulted in
much higher skill and more
consistency across regions
Other model combination
techniques being tested
Next steps
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Better / more relevant observation targets
–

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Seasonal outlooks of extreme event
(drought, flood, …) risk?
Convert GCM ensemble outputs (NMME,
ECMWF …) to probabilistic forecasts –
need robust bias and trend adjustment
methods, information-based skill metrics
Better approaches may be needed for
presenting probabilistic forecasts
Summary


Probabilistic forecasts
provide explicit measures of
uncertainty, necessary for
management applications
More work needed to make
use of existing forecast
systems in a probabilistic
framework
"A person with a
clock always knows
what time it is; a
person with two
clocks is never sure."
Questions?
Krakauer, N. Y.; Grossberg, M. D.; Gladkova, I. & Aizenman, H. ( 2013 )
Information Content of Seasonal Forecasts in a Changing Climate,
Advances in Meteorology, 2013: 480210
Krakauer, N. Y. & Fekete, B. M. ( 2014 ) Are climate model simulations
useful for forecasting precipitation trends? Hindcast and synthetic-data
experiments, Environmental Research Letters, 9: 024009
Krakauer, N. Y. ( 2014 ) Stakeholder-driven research for climate
adaptation in New York City, in Drake, J.; Kontar, Y. & Rife, G. (ed.), New
Trends in Earth Science Outreach and Engagement: The Nature of
Communication, 195-207
nkrakauer@ccny.cuny.edu