Natural Variability Section 2.4

2. Natural Climate Variability
2.1 Introduction
2.2 Decadal Variability
2.3 Interannual Variability
2.4 Climate Prediction
2.5 Variability of High Impact Weather
2.4 Climate Prediction
Prediction and Predictability
2.4 Climate Prediction
Prediction and Predictability
Activity of making forecasts!
2.4 Climate Prediction
Prediction and Predictability
Activity of making forecasts!
Does it make sense to make forecasts?
Predictability
• “If we claim to understand the climate system surely we should
be able to predict it!”
• If we cannot predict the atmosphere is this because our
understanding is inadequate or are there deeper reasons?
•The study of predictability concerns the systematic investigation
of the extent to which it is possible to predict a system
• Active area of research in weather and climate
Basic Concepts
Phase space
The state of any physical system can be uniquely defined by
giving the values of some set of variables e.g. pendulum is
defined uniquely by its angle from the vertical and its angular
velocity


Phase space
1.0

0.0
-1.0
-1.0

0.0
1.0
Undamped Pendulum
Phase space trajectory
1.0

0.0
-1.0
-1.0

0.0
1.0
1.0

0.0
Small error
in initial
condition
-1.0
-1.0

0.0
1.0
1.0

0.0
Small error
in prediction
-1.0
-1.0

0.0
1.0
Basic Concepts
How do errors evolve in time? How rapidly do phase space
trajectories diverge?
If diverge very slowly or not at all – then a small error in initial
conditions implies a small error in the prediction of the future
state – system relatively predictable
If trajectories diverge rapidly – system is unpredictable
Basic Concepts
Pendulum is an example of a predictable system
Two trajectories starting close together tend to stay close
together
Opposite extreme – are chaotic systems – e.g. atmosphere
In these systems errors grow exponentially and thus even in a
perfect model they are hard to predict far in advance
Such systems have a strong sensitivity to initial conditions
Predictability of the Atmosphere
To make weather forecasts we need at least two things:
(a) knowledge of the state of the atmosphere now
(b) a model that will produce a prediction of the future state
Lets assume that the model is perfect (BIG ASSUMPTION!)
•
Analyses have errors (big gaps in observing network)
•
Hence there are many possible initial states consistent with
our observations
Predictability of the Atmosphere
Recognizing that we cannot pick one state has led to the
development of ensemble forecasting
Rather than a single forecast we make many forecasts each from
slightly different initial conditions (and each equally likely)
Spread of forecasts gives us an idea of confidence in forecasts
Predictability of the Second Kind
Previous is predictability of the 1st kind – growth of errors in
initial value problems such as weather forecasting
Initial value problems are not the only sort of prediction in which
we are interested
Response of climate system to changing levels of greenhouse
gases – we do not believe that this will depend on the state of the
atmosphere today or tomorrow
We wish to know the response of a system to externally imposed
forcing - this is predictability of the second kind
Predictability of the Second Kind
Need to use statistics to characterise the system (not useful to
consider wind at Albany on a particular day)
Probability density functions (PDFs) – how will pdf change in
response to external forcing?
Predictaility of the Second Kind
Probability density functions (PDFs) – how will pdf change in
response to external forcing?
shift in mean?
more variance?
greater likelihood of extreme events?
See sketches
Predictability of the coupled atmosphere-ocean system
Weather forecasts – little use after a week or so
1-2 weeks = “predictability horizon” for weather (cf plumes seen
earlier)
Seasonal Forecasts – exploits the fact that atmosphere is
influenced by surface conditions that vary slowly (e.g. SSTs)
Possible because “predictability horizon” for the ocean is much
longer: months, years and even decades
Also possible because the atmosphere strongly responds to SST
anomalies – especially in the tropics (Clausius-Clapeyron)
predictability can arise in association with persistent soil
moisture and snow cover (important for Asian monsoon) too
Predictability of the coupled atmosphere-ocean system
Seasonal prediction – is a prediction problem of the first kind in
that it is an initial value problem
Need a coupled ocean-atmosphere model and an estimate of
initial state of ocean as well as atmosphere
As before we need to use ensemble techniques using slightly
different initial conditions
Predictability of the coupled atmosphere-ocean system
If the system is predictable – it makes sense to make predictions.
BIG ISSUES:
Initialisation of the coupled system (especially ocean)
TAO observations in Pacific have gaps – these are filled in
by models (as for NWP). This results in errors in initial
conditions which must be considered.
Ensembles are therefore essential.
This figure shows vertical
sections along the
equator of the upper
400m of the ocean
(Indian , Pacific and
Atlantic oceans from left
to right). Panel a) shows
anomalies for October
1996, b) for January 1997
and c) for April 1997. The
propagation and
amplification of
temperature anomalies
from west to east is
clearly visible
Plot of SST predictions made at weekly intervals from November 1996. Each forecast is for 6
months . The thick solid curve shows the observed SST anomaly. Although three forecasts are
made each week, only one is plotted in order to avoid clutter. The onset of El Nino in April is well
predicted by the coupled system. The subsequent evolution is also well forecast, although
one can see a tendency to underpredict the amplitude of the event. The vertical axis is the
monthly mean SST anomaly in the NINO 3 region, shown in the inset.
Predictability of the coupled atmosphere-ocean system
Seasonal prediction – is also prediction of the 2nd kind
External forcing of atmosphere due to changing SSTs lead to
changes in PDFs as before
Given the strong atmospheric sensitivity to changes in tropical
SSTs means that seasonal forecasts are more useful for the
tropics
Some Comments
A current research topic relates to how we link seasonal
predictions to applications (e.g. water resources, food security,
health)
Applications require information about statistics rather than the
seasonal mean anomaly for example
How predictable are weather statistics?
Back to considering predictability of PDFs – an understudied
area.
Prediction
(i) Two-Tier Systems
• Forecasting SSTs
- statistical models and dynamical models
• Using SSTs to predict Climate – can force atmospheric model
with given SSTs
(ii) Single Tier Systems
• Coupled atmosphere-ocean models
(iii) Statistical
• Statistical Forecast Models of climate variability
(iv) Consensus
• Use all forecasts (done at IRI)
Prediction
BIG ISSUES
• Initialisation (ocean and land)
• Evaluation of probabilistic forecasts
• Predictability of statistics of weather for applications
• Dynamical model improvements needed
Seasonal Prediction Centres
http://www.metoffice.gov.uk/research/areas/seasonal-to-decadal
http://www.cpc.ncep.noaa.gov/products/predictions/90day/
http://nsipp.gsfc.nasa.gov/
http://www.ecmwf.int/products/forecasts/seasonal/introduction/
http://iri.columbia.edu/