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.


Version 1.0  Drafted by John Scinocca, Tim Stockdale & Francois Lott

This is a draft protocol for a set of five QBO experiments, and is based on the outcome of discussions at the QBO Modeling and Reanalyses Workshop, Victoria, March 2015. The motivations and goals of the experiments are described below, followed by the technical specification of the experiments and information on data and diagnostics. The experiments themselves are designed to be simple and accessible to a wide range of groups.

It is expected that each group will submit a set of results from all the experiments, made with a single “best shot” model version. Use of the same model version for the different experiments is crucial for learning the most from this study. 

Experiment List & Goals

Version 1.0  Drafted by John Scinocca, Tim Stockdale & Francois Lott

a) Present-Day Climate: Identify and distinguish the properties of and mechanisms underlying the different model simulations of the QBO in present-day conditions:

EXPERIMENT 1: AMIP – specified interannually varying SSTs, sea ice, and external forcings

EXPERIMENT 2: 1xCO2 - identical simulation to the AMIP above except employing repeated annual cycle SSTs, sea ice, and external forcings

These experiments will allow an evaluation of the realism of modelled QBOs under present-day climate conditions, employing diagnostics and metrics discussed in Section 5. The impact of interannual forcing on the model QBO can also be assessed, and Experiment 2 is a control for the climate projection experiments. 

b) Climate Projections: Subject each modelled QBO contribution to an external forcing that is similar to that typically applied for climate projections:

EXPERIMENT 3: 2xCO2 - identical to Experiment 2, but with a change in CO2 concentration and specified SSTs and sea ice appropriate for a 2xCO2 world

EXPERIMENT 4: 4xCO2 - identical to Experiment 2 but with a change in CO2 concentration and specified SSTs and sea ice appropriate for a 4xCO2 world

The response of the QBO, its forcing mechanisms, and its impact/influence will be evaluated by the same set of diagnostics used for diagnosing Experiments 1 and 2, but representing the response 2xCO2 - 1xCO2 and 4xCO2 - 1xCO2.  Obvious questions that will arise:

  • What is the spread/uncertainty of the forced model response?
  • Do different model contributions cluster in any particular way?
  • Can a connection/correlation be made between QBOs with similar metrics/diagnostics in present day climate and their response to CO2 forcing?

The hope is that this sort of sensitivity experiment might indicate what aspects of modelled QBOs determine the spread, or uncertainty, of the QBO response to CO2 forcing.  These aspects are the ones which should receive the most attention by QBOi in order to reduce uncertainty in future projections. Such experiments also will inform the community as to what the general uncertainty might be for state-of-the-art QBOs in CMIP6 projection experiments.

c) QBO Predictions and process study: Evaluate and compare the predictive skill of modelled QBOs in a seasonal prediction hindcast context, and study the model processes driving the evolution of the QBO.

EXPERIMENT 5: A set of initialized QBO hindcasts, with 9-12 month range.  Observed SSTs and forcings specified as in Experiment 1 (these are diagnostic experiments), with reanalysis data for the atmosphere inserted at a set of given start dates.

These are not strictly prediction experiments in the seasonal forecast sense (they use prescribed observed SST), but still represent a challenge as to how well the models can predict the evolution of the QBO from specified initial conditions. Obvious questions that will arise:

  • How much does model prediction skill vary between models, and to what extent are models able to predict the QBO evolution correctly at different vertical levels and different phases of the QBO?
  • How does the forecast skill relate to the behaviour of the QBO in Experiment 1? Does a realistic QBO in a long model run guarantee good predictions, or vice versa, or neither?
  • Do the models that cluster and/or do well in the prediction experiments cluster in the CO2 forcing experiments?

The hope is that this sort of prediction experiment might indicate what aspects of modelled QBOs determine the quality of QBO prediction, so that these aspects can receive attention in order to improve prediction.  Alternatively, the prediction framework may be helpful for directly assessing model changes, to help drive improvements in free-running models. Can prediction experiments help narrow the range of plausible models for climate change experiments?

Process Studies: Experiment 5 has a dual purpose: it not only provides information on the predictive capabilities of the models, it offers a unique opportunity to investigate and evaluate differences in wave dissipation and momentum deposition, so as to understand the processes driving the QBO in each model.  The initialization of the seasonal forecasts will necessarily present each QBO contribution with the same basic state. The evolution of that state immediately after the start of the forecast offers an opportunity to compare and contrast the properties of wave dissipation and momentum deposition between different models given an identical basic state. Specifying the same observed SST in all models (rather than allowing each model to predict its own SST evolution) helps focus attention on the model mechanisms that drive the QBO, and the extent to which they are correctly represented.

It is likely that a special, high-frequency, data request for an early period of each forecast should be defined which focuses on dissipation processes for this study.

Experiment Details

Version 1.0  Drafted by John Scinocca, Tim Stockdale & Francois Lott

Five sets of simulations/experiments have been defined above:

    - EXPERIMENT 1 - AMIP,  interannually varying SSTs, sea ice, and external forcing
    - EXPERIMENT 2 - 1xCO2, repeated annual cycle  SSTs, sea ice, and external forcings
    - EXPERIMENT 3 - 2xCO2, as EXPT 2 with perturbed SSTs and sea ice and     2xCO2
    - EXPERIMENT 4 - 4xCO2, as EXPT 2 with perturbed SSTs and sea ice and 4xCO2
    - EXPERIMENT 5 - QBO hindcasts, with reanalysis initial conditions on specified     start dates.

For all experiments it is requested that all modelling groups use the same set of SST and sea ice boundary conditions, as specified below. External forcings should be followed to the extent possible, although it is recognized that models may vary in how they specify aerosols, volcanic forcing etc. For the purposes of these experiments (sensitivity studies of the QBO), what matters is that the external forcing remains constant when it is supposed to be constant, and varies as realistically as the model allows when it is supposed to vary. In all cases, the experiments are intended to be made using only reasonable efforts. Any changes in experimental details should be documented.

Ensemble sizes are given as a range, from minimum to preferred size. Each group should assess what is reasonable, given costs, resources and expected results (e.g. some models may have a highly regular or phase-locked QBO).

EXPERIMENT 1 - AMIP Cost: 30-90y

This is based on the CMIP5: Expt 3.3

Period:  30y (1979-2008)

Ensemble size: 1-3

Boundary Conditions: CMIP5 interannually varying sea ice and SSTs obtained from:

External Forcings: CMIP5 external forcings for radiative trace gas concentrations, aerosols, solar, explosive volcanoes etc. obtained from:

EXPERIMENT 2 - 1xCO2 Cost: 30-90y

Repeated annual cycle simulation.

Period:  30y, after a suitable spinup (5y?).

Ensemble size: 1-3

Boundary Conditions: CMIP5 "SST Climatology 1988-2007" and "SEA ICE Climatology 1988-2007" obtained from:

External Forcings: repeated annual cycle forcings. Ideally this would be some sort of climatological forcing averaged over the 30 year period used in EXPT1, but that doesn't really exist.  The suggestion is to use year 2002 of the CMIP5 external forcings:

The year 2002 has neutral ENSO, neutral PDO, and is well-away from any historical explosive volcanoes.  Since this experiment will be the base for the 2xCO2/4xCO2 experiments, a constant value of CO2 corresponding to the average over the year 2002 should be used. Note that although these choices are not ideal (the 30 year comparison period, the 20 year SST climatology and the 2002 fixed forcing are all inconsistent with each other), the observed dependence of the QBO on changing climate through this period appears to be negligible. Thus for QBO purposes (and in particular for comparing model responses) the protocol is believed adequate, if all models use the same approach.

EXPERIMENTS 3 and 4 - 2xCO2 / 4xCO2 Cost: 60-180y

Period:  30y, after suitable spinup

Ensemble size: 1-3

Boundary Conditions: repeated annual cycle of SSTs and sea ice will be provided to modelling centres on a 1x1 degree grid as in Experiments 1 and 2. The proposal is to use an ensemble average over the CMIP5 models average over the decade centred on the time of CO2 doubling/quadrupling in the RCP8.5 scenario. [In practice we may use the decades 2050-60 and 2090-2100 from RCP8.5 runs, since 4xCO2 occurs a little later than 2100. But this dataset will be prepared centrally, to ensure we all use the same values].

External Forcings: the forcings in these two experiments should be exactly the same as used in EXPT 2 except for the CO2 concentration, which should be doubled and quadrupled. Only CO2 forcings should be changed, not other greenhouse gases. These are sensitivity experiments, not attempts to predict specific periods in the future.

EXPERIMENT 5 - QBO hindcasts Cost: 68-150y

These are atmosphere-only experiments, initialized from re-analysis data, providing multiple short integrations from a relatively large set of start dates sampling different phases of the QBO.

Start dates: 1 May and 1 November in each of the years 1993-2007 (15 years, 30 start dates)

Hindcast length: 9-12 months

Ensemble size: 3-5 members

The boundary conditions and forcings for this experiment closely follows the prescription of the AMIP experiment (EXPT 1).

Boundary Conditions: CMIP5 interannually varying sea ice and SSTs obtained from:

External Forcings: CMIP5 external forcings for radiative trace gas concentrations, aerosols, solar, explosive volcanoes etc. obtained from:

Initial data for these dates should be taken from the ERA-interim reanalysis.  ERA-interim data is available for download from (registration is required; if downloading lots of start dates from this site, it may be easier to use the “batch access” method described on the site, although interactive download of each date is also possible. Data are available on either standard pressure levels or original model levels, and in either grib or netCDF. Try to download only the data you need, e.g. at 0 z on the 1st of the month).

The ensemble is expected to be generated by perturbing each ensemble member by a small anomaly, which needs do no more than change the bit pattern of the simulation.

Additional Experiments

Version 1.0  Drafted by John Scinocca, Tim Stockdale & Francois Lott

Some groups may want to conduct additional experiments, to provide further information on the sensitivity of the results to various factors.

EXPERIMENT 5A: As EXPT5, but using a coupled ocean-atmosphere model and predicting the SST, instead of specifying observed values. External forcings could also be fixed so as not to use future information. This is then a true forecast experiment for the QBO, and can be compared with the results of EXPT5.

Further, groups may want to run some or all of the experiments with multiple model versions, to explore the sensitivity of some of the results e.g. to vertical resolution or physics package. Although ideally all experiments would be re-run, this may not be practical. Model versions for which complete experiment sets are available are likely to be considered the “primary” results when analysis takes place.

Requested Diagnostics

Version 1.0  Drafted by John Scinocca, Tim Stockdale & Francois Lott

Input to this and a discussion of the rationale has been provided by Francois Lott: see  The text is reproduced below for convenience. This will need to be turned into a specific list of variables and pressure levels to be saved, for both “standard” and “high frequency” diagnostics, and agreement on which parts of EXPTS 1-5 should have high-frequency output archived. This document will be updated with a specific proposal in due course.

Storage is available at BADC, and it is proposed that groups upload their data in a common format (CF compliant netCDF) to BADC. This will involve registering to obtain an account, and preparing datasets to the specified common format. Please contact Scott Osprey for further details.

It will facilitate comparisons if the data are on a common lat-long grid, as well as being on standard pressure levels. SNAP specified a 1.5 deg grid, which is probably adequate for this project, too. (ERAI uses a 0.75 deg standard lat-long grid).

Are there any fields which should be supplied on the original model grid as well as a standard lat-long grid?

Text from Francois Lott:

Here is a table of diagnostics, which include the diagnostics requested by the ISSI group initiated by Joan Alexander a couple of years ago, and from which I started. What I remember from our discussions during the QBOi workshop, is that each group makes a simulation with its best QBO (not necessarily a version suited to CMIP6), and over 30 years (more maybe for histograms and spread?) store at pressure levels as near as they can be from the model levels and between 0.01 and 1000hPa, monthly-mean zonal mean data of:

u,  du/dt, T, v*, w*, F_phi, F_z, divF, G_ogw, G_ngw

Here the time derivative of the mean velocity (dynamical tendency) is to try to make the difference between the advective terms we can deduce from the TEM equations, and the advective plus forcing terms due to explicit/numerical diffusions which are sometimes difficult to extract from models. Also, we nead the EPF divergence (EPFD), and the tendencies due to the orographic and non-orographic gravity waves G_ogw, G_ngw

Also, it is useful to have the eastward and westward component of the non-orographic GWs momentum fluxes, rho_0*\bar{u'w'}_egw, rho_0*\bar{u'w'}_wgw

We could repeat this in 2XCO2+2K SST and 4XCO2+4K SST to see how our QBOs respond to climate change: there seems to be large spread amoing models.

Now, from the QBOi workshop I remember that we need to no know if our models simulate the QBO for the right (or the same reasons) and in particular the fraction of the resolved waves in each models. For this, the EPFD may not be sufficient, and the EPF themselves can include large opposing balance so we have to calculate time-wavenumber spectra of EPF, and this request storage of instantaneous values of u, w, v, and T at pressure levels, every three hours (to be discussed, 1hr?) and during at least one QBO period (for instance over three years). In my opinion, this needs to be done over a good number of levels in the QBO regions, above and below, for instance (to be discussed):

Why many levels: 1) to make better than the spectra in Horinoushi et al.~(2003) on top of the fact that we now all have a QBO (which was not the case in the 2003, paper); 2) A big question is to know how fast the equatorial waves dissipate in the vertical in the QBO region, 3) understand the behaviour around the TTL and in the SAO region. Differences between vertical levels may also help reduce the contribution of the tidal signals in the time-lon spectra, something that can be problematic at sub-diurnal periods (true?).

My rough estimate for one model is almost 500GB if we stay on netcdf format. But this opens the debate (3years of u,v,w,T at 12 vertical levels, 160x90 horizontal levels, every 3hrs).

Also, we would need a good deal of 2D fields, like precipitation, convective prec, OLR, etc. Information on the vertical structure of the tropical heating would be useful also, but I have no especially precise idea right now of about this should be done.

All diagnostics are done according to the TEM formalism as described in, Middle atmosphere dynamics. By D. G. Andrews, J. R. Holton and C. B. Leovy. Academic Press, San Diego, 1987 

Horinouchi, T., S. Pawson, K. Shibata, E. Manzini, M.A. Giorgetta, F. Sassi, R. J. Wilson, K.

Hamilton, J. DeGrandpe and A.A. Scaife, 2003: Tropical cumulus convection and upward propagating waves in middle-atmospheric GCMs, J. Atmos. Sci. , 60, 2765—2782.

Some spectra/composites from CMIP5 models are in:

Lott, F. S. Denvil , N. Butchart, C. Cagnazzo , M. Giorgetta, S. Hardiman, E. Manzini, T. T. Krishmer , J.-P. Duvel, P. Maury, J. Scinocca, S. Watanabe, S. Yukimoto, 2014: Kelvin and Rossby gravity wave packets in the lower stratosphere of some high-top CMIP5 models, J. Geophys. Res., 119, 5, 2156-2173, DOI: 10.1002/2013JD020797

Additional Experiment - Dynamical Cores

These experiments investigate the sensitivity of QBO-like variability in GCM dynamical cores to changes/representations of numerics and resolution.

A first draft for this experiment  is being prepared by Christiane Jablonowski and will appear here shortly. At this time wider discussion will be encouraged to best facilitate wider participation within the group.

Additional Experiment - Nudging to Specifiy Dynamics

The following experiments are suggested for interested groups. These investigate the role of feedbacks in maintaining the QBO. The general idea would be to alter model physics or numerics while maintaining the zonal mean state. This technique will isolate the resolved wave response without feedbacks from the changing zonal men state. Possible experiments might include:

  • nudging zonal-mean conditions in the tropical stratosphere
  • nudging aspects of the tropical troposphere
A first draft for this experiment  is being prepared by Kevin Hamilton and will appear here shortly. At this time wider discussion will be encouraged to best facilitate wider participation within the group.