Introduction to Dynamical Models and Theory Behind
Seasonal Forecasting
David G. DeWitt
Thanks to Amit Apte, Ravi Nanjundaiah , and Sulochana Gadgil for
inviting me to come speak and sponsoring my trip.
Thanks to L. Goddard,R. Koster, A. Weigel, for letting me borrow slides.
Outline
1. Relationship of this talk to data assimilation.
2. Dominant mechanisms of seasonal variability
a. ENSO
i. Delayed Oscillator
ii. Global teleconnections
b. Soil moisture
c. Stratosphere-troposphere connections
3. Two-tiered (uncoupled) versus one-tiered (coupled) forecast systems
4. Dynamical cores:
a. Current (spectral) versus future (finite volume)
b . Equations for spectral method
5.
Relationship between these talks and data assimilation:
Seasonal forecasts of the climate state need data assimilation in at
least 2 ways:
1. Dynamical seasonal forecasting with general circulation models
requires specification of the initial state of the ocean and
atmosphere (ice, land, etc). This is frequently done using data
assimilation products.
2. Given the sparseness of observed data in the ocean
(atmosphere), data assimilation products also act as an estimate of
the observed state for verification procedures. This is not without
problems especially the fact that different assimilation products can
produce different estimates of the observed state.
Hypothesis:
In order to construct assimilation systems it is desirable to know
about the physical system and the models that represent it. These
talks will try to give some insight on these aspects for the seasonal
climate forecasting problem.
Physical Phenomena Associated with Seasonal Climate Variations
1. El-Nino Southern Oscillation (ENSO)
a.SST variability in central and eastern equatorial Pacific
b. Global teleconnections forced by changes in convective heating
(rainfall) associated with SST variability in central and eastern
Pacific
2. Soil moisture anomalies
3. Straosphere-troposphere interactions
4. SST variability in other parts of the ocean (Indian Ocean Dipole)
5. Sea-ice variability
ENSO is the dominant factor in seasonal climate variations. It has an
irregular period of 3 to 5 years.
Fortunately, it is also the phenomena we can model “most” skillfully but
there is still room for improving these forecasts.
How does ENSO work?
First order model for ENSO is known as the Delayed Oscillator.
This model relies on the properties of equatorial ocean waves and
fast response of the tropical atmosphere to SST anomalies.
Variants of this theory such as the Recharge Oscillator which differs
in how mass gets transported back to Equator from Rossby Waves
Main aspect of theory is how to get period plus why oscillation in SST exists.
Key oceanic equatorial wave properties:
1. First vertical mode Eq. Kelvin waves travel eastward at about 2.8m/s.
2. First vertical model Eq. Rossby waves travel westward at 1/3 Eq. Kelvin
wave speed.
3. Eq. Rossby waves reflect at western boundaries as Eq. Kelvin waves.
4. Eq. Kelvin waves reflect at eastern boundaries as Eq. Rossby waves and
coastal Kelvin waves.
5. A westward wind stress anomaly will produce downwelling Kelvin waves and
upwelling Rossby waves.
Rectifying the ENSO Period
Simple wave dynamics gives a 2 year oscillation for ENSO but the
observed period is slower: Why?
-The equatorial atmosphere quickly responds to SST anomalies.
the wind stress response to SST anomalies forces the ocean in a way
that reinforces the SST anomalies.
-Warm SST anomalies lead to westerly wind anomalies which lead to
downwelling Kelvin waves which leads to maintaining or intensifying
the warm SST anomalies.
-In order to change phase of SST need for opposite signed Kelvin
waves to be generated in the central and western Pacific and cancel
original anomaly plus whatever growth occurred due to coupling.
-Oscillation is irregular with warm events usually followed closely by
cold events but not vice versa.
-Lower order mode Rossby waves with wider meridional structure are
important. These have much slower phase velocities
Response to Anomalous Convection Associated with El Nino
Anomalous convective heating along the equator drives global
atmospheric circulation anomalies:
1.
Warm zonal anomaly near the equator associated with Kelvin
waves propagating eastward. Leads to positive height anomalies
near the equator.
2.
Quasi-stationary Rossby waves that propagate meridionally away
from the equator and eastward. This leads to some well known
patterns of variability in the NH, in particular the PNA.
3.
These dynamic and thermodynamic anomalies interact with the
local flow to alter precipitation patterns including Indian monsoon.
4.
Modifications to the Hadley circulation.
5.
Response to El-Nino and La-Nina although generally of opposite
sign has important asymmetries.
6.
Effects of El-Nino are felt globally: Summary studies by
Ropelewski and Halpert, Goddard and Mason.
A. Weigel
Probabilistic
composites of
above normal
precipitation
keyed to …
El Nino
La Nina
Seasonal
climate
forecasting
works because
ENSO has a
strong
influence
globally and
ENSO
variability is
predictable
Soil Moisture Anomalies Effect on Seasonal Climate
After (Tropical) SST anomalies, soil moisture anomalies are considered
to be important for driving seasonal climate anomalies.
Realizing the predictive skill associated with soil moisture anomalies is
problematic because there are very few observations of soil moisture
On large spatial and long temporal (decades) scale. Most soil moisture
Older systems drive land surface models offline with observed
precipitation and radiation to get soil moisture anomalies.
More formal data assimilation approach to assimilating the sparse
observations into land surface models is now an area of active
research.
Comparison experiment on impacts of “correctly” initializing soil
moisture on seasonal forecast skill: GLACE(2)
R. Koster
R. Koster
R. Koster
R. Koster
Different Approaches to Dynamical Seasonal Forecasts
In order to do dynamical seasonal climate forecasting a minimum
system needs an AGCM and a method for forecasting SST. There
are 2 common approaches:
1. One-tier (coupled) models: Include an oceanic model such as an
OGCM.
2. Two-tiered (uncoupled) models: Use an offline model (statistical or
dynamical) to predict SST and prescribe for AGCM.
Large part of the community believes that one-tier models are needed
because of air-sea interaction in places like Indian ocean. Smaller
part of the community (DeWitt, Gadgil and collaborators, Kumar)
believes that two-tier approach still has value. Ultimately, with a
marginal skill problem you should take skill where you can get it
(multi-model ensemble). Finally, the real argument here isn’t
whether coupling is important but when, i.e. timescale. Weather
services generally don’t use coupled models.
Positive Attributes of Different Approaches to
Seasonal Forecasting
2-Tiered Forecast Systems:
-Relatively inexpensive computationally
-Potentially more accurate SST data due
to input from multiple sources
-No drift of SST annual cycle on which
anomalies are superimposed
1-Tiered Forecast Systems:
-Potentially more accurate representation
of physical interaction between ocean
and atmosphere: Transient (waves) and
time mean
Effect of Coupling on Simulated Indian
Summer Monsoon
obs daily rainfall frequency
coupled
uncoupled
correlations (%) with CPC GSOD 1980–2003
Simple Test for Importance of Coupling
1. Run set of coupled model forecasts.
2. Take SST from coupled model forecasts and prescribe in AGCM
component model with less frequency than every time step.
3. Compare uncoupled and coupled model fields such as
Precipitation, near-surface air temperature, oceanic surface fluxes.
For long free-running coupled runs differences are large and
important.
For seasonal forecasting results are very similar. One place they
are different is southeastern Asia. But is one solution better than
another?
Precipitation-SST (SST Tend) JJA Forecast (May IC)
Precipitation Forecast Skill JJA Forecast (May IC)
T2m Forecast Skill JJA Forecast (May IC)
Organizing models
Clouds
PBL
Convection
Radiation
Mixing
Advection
Dynamics / Physics
{
∂A/∂t = – UA + M + P – LA
}
}
∂A/∂t =
Dynamical Core
+
Physics
Spectral Core Essential Elements
Spherical harmonic representation of dynamics
Exact calculation of horizontal derivatives
Physical parameterizations and non-linear dynamical
products calculated on an associated Gaussian grid
Gibbs phenomena associated with sharp gradients
Need to include artificial horizontal diffusion to keep
model stable, i.e. spectral blocking
Time step constraint due to CFL instability
Still used by many forecast centers for seasonal
forecasting (ECMWF, JMA, NCEP,CMA)
Finite Volume Dynamical Core Elements
Employs finite volume as opposed to finite difference
No Gibbs phenomena
Diffusion occurs due to choice of curve fit
No stability constraint for time step
Has become dominant dynamical core in US large
scale modeling that cares about tracer transport
(upper level moisture, chemical species, aerosols):
GSFC, GFDL, NCAR (CAM)
How do Simulations with FV and Spectral Compare?
Finite volume much more accurate for tracer transport (flux
conservative)
Finite volume tends to produce smaller scale precipitation
features
Finite volume has less wavy artificial features
Finite volume schemes generally use fully implicit time integration
schemes allowing timestep to be set by accuracy not stability
(CFL) constraints. Spectral methods generally employ semiimplicit methods and so are still CFL constrained.
Compare FV versus Finite Difference
Conventional finite difference
Lin-Rood built with Piecewise
Parabolic Method
Consider the measurements of
atmospheric constituents
OBSERVATIONS
NOy
Enormous amount of information
• Mixing physics
• Mixing time scales
• Chemical production and loss
N2O
Spectral method and correlations
Spectral Method
(widens over time)
NOy
Sources of pathology
• Inability to fit local features
• Inconsistency between tracer and
fluid continuity equation
• Dispersion errors
• Filtering
N2O
Van Leer method and correlations
Van Leer Method
NOy
Why does this work?
• Consideration of volumes and
mixing these volumes consistently.
N2O
What does Spectral Filtering Due to Orography?
Smooth out maxim
Create negative values even for positive definite fields
such as orography
More recent techniques of smoothing orography help
to minimize these effects but it still exists.
DKRZ, ECHAM3
DKRZ, ECHAM3
DKRZ, ECHAM3
DKRZ, ECHAM3
DKRZ, ECHAM3