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

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 correlations (%) with CPC GSOD 1980–2003 coupleduncoupled obs daily rainfall frequency

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 Dynamics / Physics ConvectionAdvectionMixingPBLRadiationClouds ∂A/∂t = –  UA + M + P – LA { ∂A/∂t = Dynamical CorePhysics } } +

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 semi- implicit 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 N2ON2O NOy OBSERVATIONS Enormous amount of information Mixing physics Mixing time scales Chemical production and loss

Spectral method and correlations N2ON2O NOy Spectral Method (widens over time) Sources of pathology Inability to fit local features Inconsistency between tracer and fluid continuity equation Dispersion errors Filtering

Van Leer method and correlations N2ON2O NOy Van Leer Method Why does this work? Consideration of volumes and mixing these volumes consistently.

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