Additional Experiments - Contrained Dynamics or "Nudging"

At our March meeting there was some interest in QBOi coordination of “nudging” or “constrained dynamics” (CD) experiments.  It was agreed that the initial QBOi focus would be on (i) long-term “control” runs together with “global climate perturbation” runs and (ii) seasonal hindcast experiments.  These would use some versions of the “full” GCMs with constraints imposed only on the initial conditions and perhaps lower boundary conditions.  In contrast, the CD experiments would (by definition) involve some additional constraints on the model dynamics acting continuously as the integration proceeds.

At the meeting we arrived at a suggested time line where at least the first group of integrations for the (i) and (ii) experiments would take up to about 18 months (to be ready for the fall 2016 QBOi workshop).  So there may be no urgency for QBOi to plan for CD experiments now, but this blog posting of some general ideas of mine may start an online discussion of such experiments for interested participants. 

I will consider here only CD experiments that constrain dynamical fields (horizontal winds and possibly also temperatures) by means of a linear relaxation.  The potential experiments can then be classed by what scales are constrained (here notably either relaxation of the full 3D fields or relaxation of only the zonal-mean fields), what height regions are constrained (stratosphere only, toposphere only, both), what geographical regions are constrained (tropics, extratropics, global), and what “target” the fields are relaxed towards (climatology, actual times series of data, idealized profiles…). 

Continuously relaxing the tropical stratosphere zonal-mean flow

The simplest experiments to think about are those that involve just adding an extra zonally-symmetric momentum source so that tropical stratospheric zonal-mean winds are forced to

(a) undergo a prescribed (idealized) QBO cycle, or

(b) undergo a QBO based on another model simulation, or

(c) follow the actual observed winds for some period, or

(d) remain nearly constant. i.e. held to some specified profile.

There are several such experiments already reported in the literature (for example Kodera et al., 1991; Hamilton, 1995, 1998; Balachandran and Rind, 1995; Giorgetta & Bengtsson, 1999; Bruhwiler & Hamilton, 1999;  Hamilton et al., 1984; Stenchikov et al., 1984; Thomas et al., 2008; Mathes et al, 2010; Garfinkel & Hartman, 2011).  We can imagine that the extra forcing of the mean zonal momentum accounts for missing (or misrepresented) eddy fluxes, and so conceptually these experiments are somewhat similar to model simulations with QBOs generated by highly tuned nonstationary gravity wave parameterizations.  However by using relaxation to a prescribed “target” wind field, these experiments could provide a suite of simulations performed with different models, but with nearly identical mean flow profiles in the tropical stratosphere through which waves will propagate.  By choosing an appropriate “target” to relax towards we can also ensure that the stratospheric mean winds in the models will be quite realistic. 

Nudging the troposphere

A set of possibly interesting experiments could result from nudging the tropospheric fields towards observations.  This might be most plausibly done with some kind of prescribed relaxation of the full 3D wind and temperature field towards some global reanalysis product.  This could, in principle, let one compare the stratospheric simulation among e.g. different versions of one model with different vertical resolutions,  or different models all with the resolved (or at least sufficiently large scale) wave fluxes expected to be realistic.  I believe something like this approach has been tried (e.g. by a Canadian group some years ago?), but I can’t easily locate relevant references. Of course there are problematic aspects as well, notably how the convection parameterization in each model will react with an effectively “imposed” horizontal divergence. 

Nudging to produce initial conditions for free running integrations

As was discussed in Victoria, a focus of the initial stage of QBOi will be on seasonal hindcasts from realistic initial conditions.  Some centers are no doubt set up to easily start their models from a realistic initial state.  Another option that some groups could conceivably adopt is producing an initial state by running their model for some time with 3D relaxation to global reanalyses, and then at t=0 turning off the relaxation and beginning the hindcast.  So one application of this approach might be for some groups to participate in the QBOi  “realistic” hindcast experiments, but one could also imagine this machinery being used for other experiments.  For example one could compare two hindcasts made with the same model: (i) with the full 3D fields “initialized” this way, and (ii) with just the tropical stratosphere (or even just the tropical stratospheric zonal-mean flow) initialized.  This would allow one to see how dependent the evolution of the zonal-mean equatorial stratospheric flow is on the details of the day to day weather situation in the troposphere.   



Balachandran, N. K., and D. Rind, 1995: Modeling the effects of solar variability and the QBO on the troposphere/stratosphere system. Part I: The middle atmosphere. J. Climate, 8, 2058–2079.

Bruhwiler, L.P., and K. Hamilton, 1999: A numerical simulation of the stratospheric ozone quasi-biennial oscillation using a comprehensive general circulation model.  J. Geophys. Res., 104, 30,525–30,557.

Garfinkel, C.I., and D.L. Hartmann, 2011: The influence of the Quasi-Biennial Oscillation on the troposphere in winter in a hierarchy of models. Part II: Perpetual winter WACCM runs.  J. Atmos. Sci., 68, 2026-2041.

Giorgetta, M., and L. Bengtsson, 1999: The potential role of the quasi-biennial oscillation in the stratosphere-troposphere exchange as found in water vapour in general circulation model experiments.  J. Geophys. Res., 104, 6003–6019.

Hamilton,K., 1995: Interannual variability in the Northern Hemisphere winter middle atmosphere in control and perturbed experiments with the SKYHI general circulation model. J. Atmos. Sci., 52, 44–66

Hamilton, K., 1998: Effects of an imposed Quasi-Biennial Oscillation in a comprehensive troposphere–stratosphere–mesosphere General Circulation Model.  J. Atmos. Sci., 55, 2393–2418.

Hamilton, K., A. Hertzog, F. Vial, and G. Stenchikov, 2004: Longitudinal variation of the stratospheric Quasi-Biennial Oscillation.  J. Atmos. Sci., 61, 383–402

Kodera, K., Chiba, M., & Shibata, K., 1991: A general circulation model study of the solar and QBO modulation of the stratospheric circulation during the Northern Hemisphere winter. Geophys. Res. Lett., 18, 1209-1212.

Matthes, K., D.R. Marsh, R.R. Garcia, D.E. Kinnison, F. Sassi, and S. Walters, 2010: Role of the QBO in modulating the influence of the 11-year solar cycle on the atmosphere using constant forcings. J. Geophys. Res., 115, D18110, doi:10.1029/2009JD013020.

Stenchikov, G., K. Hamilton, A. Robock, V. Ramaswamy, and M.D. Schwarzkopf, 2004: Arctic oscillation response to the 1991 Pinatubo eruption in the SKYHI general circulation model with a realistic quasi-biennial oscillation, J. Geophys. Res., 109, D03112, doi:10.1029/2003JD003699.

Thomas, M.A., M.A. Giorgetta, C. Timmreck, H.F. Graf & G. Stenchikov, 2008: Simulation of the climate impact of Mt. Pinatubo eruption using ECHAM5: Part 2: Sensitivity to the phase of the QBO.  Atmos. Chem. Phys. Discussions, 8, 9239-9261.

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