Predicting ENSO
1. WEATHER FORECASTS vs. CLIMATE FORECASTS
For practical purposes climate prediction is different from weather prediction in
important ways. First, the adjustment time of the atmosphere to a thermal or dynamical
perturbation is very fast (days to a few months) compared to that of the ocean, land
surface or land ice (seasons to millennia). Hence, in making weather forecasts you can
fix the water temperature and ice extent to be that observed. The accuracy of the weather
forecast depends on how good your numerical model is and (mostly) the quality of the
model initialization; i.e., how closely you are to reality at the time you start the forecast.
The limit for skillful weather prediction is a few days to a week.
Climate forecasts take advantage of the fact that there are media (ocean/land/cryosphere)
that have larger thermal and dynamical interia than the overlying atmosphere, and that the
atmosphere responds in a statistical sense to these slower changes in lower boundary
conditions. Of course, climate is the aggregate statistics of weather. Hence, by definition
a climate forecast is a forecast of the coupled atmosphere/ocean/land/cryosphere system.
These are most commonly made by coupling an Atmosphere General Circulation Model
(AGCM) to a numerical model of the slower media (typically a land surface plus ocean
model). It appears that the limit of predictability of a climate forecast is a few seasons to
a year, and this limit is mainly determined by the efficacy of the slow component of the
coupled model and the AGCM, and by how accurately the slow component is initialized
to the real world at the time of the forecast is started; the climate forecast is insensitive to
the state of the atmosphere at initialization time.
2. ENSO FORECASTS
El Nino/Southern Oscillation (ENSO) is a climate phenomenon that is due to coupling
between the atmosphere and ocean in the tropical Pacific. Important for the evolution of
the atmosphere is the distribution of the Sea Surface Temperature (SST) that creates near
surface pressure gradients in the atmosphere (via atmosphere-ocean heat exchange,
hydrostatic balance, and the ideal gas law) and hence drives the winds. Important for the
ocean is the surface wind stress, which drives ocean currents and upwelling (especially
along the equator) and hence affects strongly the SST.
The time scale of ENSO (interannual) results from a competition of processes with
comparable time scales (6-10 months): the dynamical adjustment time of the upper ocean
in the tropics to a change in the wind stress; the time for the upper ocean and atmosphere
to come to a thermodynamic equilibrium. The result is a interannual climate
phenomenon that occurs every 2-7 years, with an average time between peak events (eg.,
El Nino) of about four years. ENSO creates global scale climate changes via atmospheric
teleconnections.
A forecast of the state of ENSO over the next year is an example of a climate forecast.
The forecast accuracy will depend on the quality of the AGCM, the ocean model (often
an ocean GCM), the representation of the energy and moisture transfer between the two
media, and the quality of the initialization of the ocean. (the state of the ocean at
initialization time is a result of the integrated effects of the wind forcing over the past
few years). This is very different set of criteria from the criteria for a good weather
forecast (cf, section 1).
3. A DIADACTIC MODEL OF ENSO
A simple diadactic model of ENSO can be used to illustrate the basic methodology used
to make a climate forecast, and the type of products that result from a climate forecast.
The essence of this toy model of ENSO is as follows. ENSO is usually described as the
departure (anomaly) of the coupled atmosphere/ocean system from the average
climatological annual cycle. For our puposes, the state of ENSO is defined using two
quantities: the SST anomalies averaged near the equator in the eastern half of the tropical
Pacific (Nino3.4, T) and the thermocline depth anomaly, h, in the eastern equatorial
Pacific (the latter tells us something about the dynamical state of the ocean and is
important for the evolution of ENSO). In this model, we will assume that the SST
changes slowly compared to the time scale of the synoptic waves (weather) in the
atmosphere, so that a portion of the atmospheric variability is affected by the changing
SST (observations indicate about half the variance in the surface wind in the tropics is
directly related to variance in SST). Hence, the slow changes in the atmosphere (e.g., the
Southern Oscillation) are implicit in T. The evolution of the toy model of ENSO can thus
be written as:
dZ/dt = R Z,
where Z = {T, h}, and t is time. The matrix R contains the ocean dynamics and the part of
the atmospheric variability that is affected by the changing SST. Of course, the
atmosphere will still have weather events (with time and space scales of days and
<2000km, respectively) that are largely independent of the (small) changes in SST. These
weather features provide a stochastic forcing on the ocean that will have some affect on
the SST, and hence they will affect the evolution of ENSO. Since this weather is
unpredictable and largely independent of small changes in SST, we add it as a stochastic
forcing to the ocean. Since observations suggest the ENSO phenomenon is nearly linear,
the simple model is actually solved in discrete time steps:
Z(t+tau) = M Z(t) + N(t),
where N is the stochastic forcing.
4. ILLUSTRATION OF ENSO FORECASTING USING THE TOY MODEL
4a) Running the model
The MATLAB script “enso.m” contains a toy model of ENSO.
1) Run the model by typing “enso” in MATLAB. You will be asked how long
you want to integrate the model; try 50 years. If we define an El Nino event as
a positive SST anomaly that is 1.0 standard deviations above the mean (the
red horizontal line in the plot) that lasts for 6 months, estimate the average
time between ENSO events.
4b) Estimating the forecast skill of the coupled system
Forecast skill depends on how good your model is (we will assume it is perfect), the
forecast lead time, and how well you have initialized the model. Lets examine each of
these separately. First, lets make lots of forecasts and calculate some typical measures of
skill.
2) Create a time series of the Truth by running the model for again, this time for
300 years.
3) First, assume we have perfect initial conditions for every forecast (chose
perfect=1), and lets make forecasts for 40 months. The code will run and
create a 40-month forecast, starting every 10 days for 300 years. [That is
300*(360/10)=10,800 forecasts!] Each forecast will start with the exact
observed initial conditions. The n-month forecast skill is measured by creating
a time series of all the n-month forecast Nino3.4 index an comparing that time
series to the Truth using linear correlation (Figure 2, top) and root mean
square error (Figure 2, bottom). Lets define the limit of forecast skill to be
the lead time for which the forecast is correlated with the observed conditions
at 0.6 (has an rms error with the observed record that is equal to 2/3 of the
standard deviation of Nino3.4 in the control integration). These levels are
indicated by the red lines in Figure 2. What is the limit of skill for ENSO
forecasts? Can you extend the limit of forecast skill above this value? Explain.
4) Now lets assume there are errors in the initial conditions. Run the model again
(for 300 years) and choose option “perfect = 0” for initial conditions. How do
errors in the initial conditions affect the forecast skill at 1-month? How do
they affect the limit of forecast skill? Explain.
Finally, lets explore how long the instrumental record needs to be for us to get a reliable
estimate of the limit of forecast skill for ENSO.
5) Re-run the model for 20, 30, 40, 50, 75, 100 and 1000 years. In each case,
assume errors in the initial conditions (perfect = 0) and make forecasts for 12
months, and note the correlation at 9 months lead time and 12 months lead
time, and the limit of forecast skill (i.e., where correation = 0.6). How many
years of data are required to determine the true limit of forecast skill? If this
model is representative of the real world, do we have enough data (30-50
years) to determine the true limit of predictability of ENSO? Do we have
enough data to determine the true skill level of a forecast with a 9 month lead
time? A 12 month lead time?
4c) Forecasts for a particular start time: individual forecasts
Now lets look at a single forecast using the MATLAB script “ensob.m”. This routine will
create many forecasts from a single start time, using either perfect initial conditions or
initial conditions that are slightly different from Truth. It explores the value of using an
ensemble of forecasts. When you run the model, the output is as a function of forecast
lead time and is displayed in Figure 3. In each panel, the observed Nino3.4 is shown in
black. In the top panel, the observed Nino3.4 (Truth) is plotted against a single forecast,
while the middle panel shows the observed Nino3.4 and has a red line for each of the
Nino3.4 forecasts in the ensemble. The bottom panel shows the observed Nino3.4, the
mean of the ensemble of forecasts (red solid line), and the 1-sigma error in the forecasts
(red dashed lines).
6) You may have to re-run the model (type “enso”) to set up the dynamical
matrix. Then type “ensob” to create 12 forecasts from the same initial
conditions. You will be asked to chose the lead time and whether you want to
start from perfect initial conditions or not: try fcast=6 months and perfect=0,
respectively. In each plot, the black line is the same (Truth), and the red line is
an individual forecast. Study these twelve plots. What do you conclude? Run
the model a few more times (use the same values for fcast and perfect). What
do you conclude? How predictable is ENSO?
4d) Forecasts for a particular start time: skill vs. ensemble size
Now lets look at an ensemble of forecast using the MATLAB script “ensoc.m”. This
routine will create many forecasts from a single start time, using either perfect initial
conditions or initial conditions that are slightly different from Truth. It explores the value
of using an ensemble of forecasts. When you run the model, the output is as a function of
forecast lead time and is displayed in Figure 4.
7) You may have to re-run the model (type “enso”) to set up the dynamical
matrix. Then type “ensoc” to create many forecasts from the same initial
conditions. You will be asked to chose the number of forecast to make, the
lead time and whether you want to start from perfect initial conditions or not:
try perfect=0, fcast=24 months and ncast=25, respectively. In each panel, the
observed Nino3.4 is shown in black. In the top panel, the observed Nino3.4
(Truth) is plotted along with a red line for each of the Nino3.4 forecasts in the
ensemble. The bottom panel shows the observed Nino3.4, the mean of the
ensemble of forecasts (red solid line), and the 1-sigma error in the forecasts
(red dashed lines). Study these two plots. Try a couple of more forecasts,
using the same values of perfect, fcast, and ncast (each set of forecasts will be
for a unique Truth). What do you conclude? Try smaller ensembles (change
ncast to be 5 and 10). In light of these results and those in (6), what do you
conclude? How predictable is ENSO?