1. Corrective Dynamics for Atmospheric Single Column Models J. Bergman, P. Sardeshmukh, and C. Penland NOAA-CIRES Climate Diagnostics Center With special thanks to: M. Alexander, J. Barsugli, J. Hack, B. Mapes, J. Pedretti, P. Rasch, B. Stevens, J. Truesdale

2. The Pros Single Column Modeling (see Randall et al.; BAMS 1996) SCMs are economical They represent a single vertical column within the atmosphere Yet detailed The typically contain all of the parameterizations of subgrid processes from a full GCM Thus, SCM are potentially useful as: Test beds for GCM parameterizations – allowing investigations of regional sensitivity to parameterization changes Regional-scale diagnostic models – for climate sensitivity experiments and investigations of dynamical interactions among components of the climate system

3. The Cons of Single Column Modeling The single dimensionality that makes single column model economical can also prevent the SCM from being as useful as one would hope. Large scale circulations are prescribed in the traditional SCM This prevents diabatic heating in the column from impacting that circulation – effectively decoupling these two components. This allows the rapid growth of errors in the temperature and humidity profiles (e.g., Hack and Pedretti, J. Climate 2000; Bergman and Sardeshmukh, J. Climate 2004) The specified humidity advection allows the SCM to simulate realistic precipitation rates despite very unrealistic temperature and humidity profiles producing misleading results (Sobel and Bretherton, J.Climate 2000)

4. Overview We are revising the single column framework Use interactive large-scale dynamics: This is from our previous work that effectively stabilized the NCAR SCM using parameterized tropical dynamics that restore coupling to the large-scale flow. Use additional systematic and stochastic forcing to simulate observed and GCM variability – create replicas Use a linear diagnostic model to both create the SCM replicas and perform model diagnosis in a single conceptual framework

5. Diagnostic Strategy: Using Replicas We alter the model dynamics (tendencies) to coerce the SCM to replicate the statistics of the observed state vector evolution The corrections are determined in preliminary calculations. These corrections are then incorporated into the model. Subsequent model integrations have no explicit adjustments to the observed state. (Similar to simplified coupled ocean/atmosphere models) ● The process of constructing the replica is instructive ● We then use the replica to for diagnostic studies ● The GCM replica is used as an economical version of the GCM - a test bed for model development.

6. THE FOUNDATION The Coupled Single Column Model (CSCM) Based on previous work: Bergman and Sardeshmukh (J. Climate 2004) Vertical advection X is calculated from time-history of diabatic heating rates Q Important properties ● Works best for regions of active tropical convection ● Reduces systematic errors and short-term error growth ● Effectively stabilizes the SCM (allows us to add variability) ● Represents only the component of the large-scale flow that is directly linked to diabatic heating in the column (why we need to add variability)

7. Linear Modeling Decompose the state evolution into a ‘systematic’ component and linear ‘random’ deviations Systematic component can be separated from random component (e.g., via filtering) L is a constant stable linear operator and S is stationary Gaussian white noise This formulation has a strong mathematical foundation. Given a well-behaved time series. L and Q can be determined via ‘Linear Inverse Modeling’ (e.g., Penland and Sardeshmukh 1995)

8. Constructing a Replica Let X scm describe the state evolution of the coupled SCM and X obs be the state evolution of the observations The replica X is constructed from the Coupled SCM by adding corrective dynamics dX correction that coerce the SCM to behave like observations A systematic correction  M A correction to the linear dynamics  L and additive white noise  S

9. Constructing a Replica: Method I Begin with coupled SCM of Bergman and Sardeshmukh (J. Climate 2004) Calculate the systematic temperature and humidity correction from single time step calculations – each time resetting T and Q to mean conditions. Calculate corrective linear operator from 6-hour error growth. Use a constructed observational time series based on linear inverse modeling applied to observations. Use noise covariance obtained from observations via LIM.

10. A Comparison of Observations, traditional SCM, and Stochastically forced SCMs Use IOP data from TOGA COARE Compare observed variability to 5 different models: The traditional SCM (just for comparison) A linear model derived from TOGA COARE observations with linear inverse modeling (to understand its limitations) The coupled SCM with a systematic correction and white noise forcing The coupled SCM with a systematic correction and red noise forcing The coupled SCM with a systematic correction, a corrective linear operator and white noise forcing

11. Corrective dynamics reduce SCM bias Traditional SCMSCM with corrective dynamics

12. Systematic Errors and the Systematic Correction have very Different Vertical Structures Temperature Relative Humidity Error Correction Error Nudging with a relaxation term gives the wrong Systematic correction

13. Temperature fluctuations Observations Traditional SCM Linear Model SCM with full corrective dynamics

14. Temperature Standard Deviation ObservationsTraditional SCMLinear model Full corrective dynamicsRed noise forcingWhite noise forcing

15. Temperature Time Scales Lag Correlations Linear model Red noise forcing White noise forcing SCM with full corrective dynamics

16. Relative Humidity Standard Deviation ObservationsTraditional SCMLinear model White noise forcingRed noise forcingFull Corrective Dynamics

17. Precipitation Observations Traditional SCMRed noise forcing Corrective dynamics White noise forcing Relaxation to observations

18. Conclusions Developed a single column model of tropical variability with: Stable statistics (1000 day run) Small temperature and humidity biases Reproduces many realistic aspects of observed variability Enhances the utility of the SCM framework Can run this model from station data We have big plans for this model Climate sensitivity Dynamical interactions GCM development