The Geoengineering Model Intercomparison Project (GeoMIP): a control perspective

ATMOSPHERIC SCIENCE LETTERSAtmos. Sci. Let. (2012)Published online in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/asl.387

The Geoengineering Model Intercomparison Project(GeoMIP): a control perspectiveAndrew Jarvis* and David LeedalLancaster Environment Centre, Lancaster University, Lancaster, LA1 4YQ, UK

*Correspondence to:A. Jarvis, Lancaster EnvironmentCentre, Lancaster University,Lancaster, LA1 4YQ, UK. E-mail:[email protected]

Received: 14 October 2011Revised: 17 April 2012Accepted: 17 April 2012

AbstractThe Geoengineering Model Intercomparison Project (GeoMIP) has been designed as amethod to compare a set of benchmark geoengineering interventions across modelling groupswithin the World Climate Research Program (WCRP) Coupled Model IntercomparisonProject (CMIP). While we agree with the objectives of GeoMIP, this paper describes how thepresent experimental design could be extended by adding a simple control component. Usinga model predictive control framework we show this control provides an automated solutionfor the problem of balancing radiative forcings within a climate model as required by theG1 and G2 GeoMIP scenarios. By automating this process, the control removes the need fortrial-and-error model run iterations as suggested by the present guidelines. In addition, thecontrol allows for some further standardization of the experimental conditions, potentiallymaking inference of the side effects of geoengineering more straightforward. Finally, thecontrol provides an interesting analogue for geoengineering deployment governed by apolicy agent acting under conditions of uncertainty over the effectiveness of the technology.Copyright 2012 Royal Meteorological Society

Keywords: geoengineering; GeoMIP; climate; control; model predictive control

1. Introduction

Concerns over the inability of society to engagewith meaningful global-scale greenhouse gas emis-sions reduction is fuelling interest in direct inter-ventions in the climate system designed to counter-act the radiative effects of greenhouse gases (Raschet al., 2008; Lenton and Vaughan, 2009; Vaughan andLenton, 2011). Investments in research are alreadybeing made to inform decisions on the effectivenessand side effects of these ‘geoengineering’ interven-tions, research that is almost exclusively conductedwithin global climate models (Virgoe, 2009). TheIntergovernmental Panel on Climate Change (IPCC)Fifth Assessment Report will consider geoengineer-ing explicitly (IPCC, 2011) and the GeoengineeringModel Intercomparison Project (GeoMIP) has beenestablished to co-ordinate the modelling efforts in sup-port of this.

A proposal has emerged within GeoMIP for a suiteof four benchmark scenarios to be used by the globalclimate modelling community (Kravitz et al., 2010;Kravitz et al., 2011), hereafter referred to jointly asK2011. Three of the four GeoMIP scenarios (G1,G2, and G3) call for the climate modeller to specifya pattern of solar radiation management (SRM) thatbalances a prescribed pattern of forcing arising froma stylized greenhouse gas emission scenario. Thefourth scenario, G4, simply investigates a constantSO2 injection rate. The four scenarios are shown inFigure 1. These scenarios have largely been proposedto evaluate the side effects of geoengineering such

as weakening of the African and Asian summermonsoon, ozone depletion, and untoward interferencein localized patterns of temperature and precipitation(Robock et al., 2009). However, scenarios G1, G2, andG3 require the modeller to control the net radiativebalance of the model atmosphere, thereby regulatingchanges in the global energy balance. Not surprisinglytherefore, these tests have very strong links to thediscipline of systems and control. In this paper, wereflect on the proposed GeoMIP test cases from thisstandpoint and offer some additional experiments tocomplement those proposed by K2011.

To illustrate the parallels between the GeoMIPexperiments set out by K2011 and control we offera particularly simple control design for regulating thetop of atmosphere (TOA) radiative forcings as couldbe used in the G1 and G2 scenarios (because ofthe significant additional issues raised by handlingthe initial conditions implied by the ‘more realistic’G3, this scenario will be discussed briefly here, butconsidered in more detail in a follow-up paper). Wethen show the performance results for this design usinga simple stochastic climate model. The aim of thefollowing sections is to not only make the controlapproach transparent, but also explicitly set out todesign a scheme that can be added to existing climatemodel code in the expectation of take-up withinGeoMIP. Finally, we reflect on some as yet unexploredcontrol issues associated with SRM geoengineeringthat are flagged by the development of the controldesign, particularly around the handling of uncertainty.

Copyright 2012 Royal Meteorological Society

A. Jarvis and D. Leedal

Figure 1. The proposed GeoMIP standard test scenarios as advocated by Kravitz et al. (2011).

2. Model predictive control of globalradiative balance

To illustrate the parallels between the K2011 GeoMIPscenarios and control we develop a very simplemodel predictive control (MPC) framework designedto achieve the objective of a neutral TOA radiativebalance given a known greenhouse gas forcing distur-bance. MPC is an appropriate approach here because itallows us to exploit a model that is very familiar to theclimate modelling community, thereby aiding commu-nication. However, it must be stressed that there are abroad range of alternative linear and nonlinear controlmethods that could and should be explored for appli-cations such as this. The predictive model we exploitis the following simple TOA radiative balance whereall terms represent annual global mean values,

N (t) = Q(t) − R(t) − f {�T (t)} (1)

and where N (t) (W m−2) is the sum net TOA radia-tive flux; Q(t) (W m−2) is the net TOA radiativeflux attributed to changes in anthropogenic greenhousegas concentrations; R(t) (W m−2) is the net TOAradiative flux attributed to geoengineering actions,and f {�T (t)} (W m−2) the net TOA radiative fluxattributed to disturbances in surface temperature,�T (t) (K). Because �T (t) arises from imbalancesin N (t), f {�T (t)} are, by definition, feedback per-turbations on the TOA radiative balance. The decadaltimescales for the proposed GeoMIP runs and thedesire to ignore seasonal variations in N (t) means wewill assume an annual sample interval, �t , for thesampling of all variables and the specification of thecontrol.

Assuming R(t) is proportional to the level of SRMgeoengineering, U (t), without any lag because of theannual timescales we will consider (Kaufman et al.,2002), i.e. R(t) = εU (t) where ε is the effectivenessof the geoengineering at causing changes in R(t)(Lenton and Vaughan, 2009), then to impose thecondition N (t) = 0 in Equation (1) gives the inverseMPC law,

U (t) = ε−1[Q(t) − f {�T (t)}] (2)

We assume that there are no political, socioeconomic,or engineering constraints on the specification of U (t)in line with the GeoMIP experiments (also see laterdiscussion on this). In addition to assuming N (t) isobserved (e.g. by satellite), albeit with measurementerror, we will assume that Q(t) is predictable sowe can specify the 1 year ahead values Q(t + �t)and hence U (t + �t) as assumed in the GeoMIPexperiments.

Within GeoMIP the carbon cycle and climate sys-tem will invariably be represented by complex climatemodels. The degree of internal variability generatedby these models is such that the observation of theterms required to solve Equation (2) will be uncer-tain (Deser et al., 2012). The magnitude of climatefeedback, f {�T (t)}, is effectively impossible to cal-culate a priori. Likewise, the effectiveness of a givengeoengineering technology, ε, is also subject to sig-nificant uncertainty for similar reasons (Heckendornet al., 2009). For example, the effectiveness of sul-phate aerosol injection would most likely be both non-stationary and nonlinear (Heckendorn et al., 2009).Because of this, any approach to regulate N (t) basedon Equation (2) alone is likely to fail when, for all

Copyright 2012 Royal Meteorological Society Atmos. Sci. Let. (2012)

GeoMIP: a control perspective

cases of practical interest, the terms in Equation (2) areeither not known with sufficient accuracy or the obser-vations used to infer these values are subject to signifi-cant natural variability and/or measurement error. Theeffect this uncertainty has on the deployment of anygeoengineering measure could be an important issuefor GeoMIP to include because this would be oneof the defining features of any proposed real-worlddeployment.

One approach to overcoming these uncertainties isto recognize that the terms in Equation (1) can beestimated from time-series data describing aggregateproperties of climate models (e.g. Gregory et al.,2004). At t = 0 (the initiation of the geoengineering)we have some prior knowledge of what ε shouldbe (e.g. for G1 and G2, ε = (1 − α) where α isthe global albedo of the climate model). Because ofuncertainty over the value of the global albedo westart with an initial estimate ε(0). However, ratherthan using ε(0) to do a trial run followed by a seriesof reruns with supervised iterative updates of ε(0)

as, in effect, advocated by K2011, we propose usingrecursive least squares (RLS) estimation to provideannual updates of ε(t) within Equation (1). We thenuse this recursive update of ε(t) to update U (t + �t)in Equation (2) in a single automated simulation.Providing ε(t) converges on ε within an appropriatetimeframe, then N (t) → 0 as required for G1 and G2.

While N (t) �= 0 the climate system accumulatesheat leading to transients in �T (t) and hence thefeedbacks leading to the perturbation f {�T (t)}. Asa result, if we want to force N (t) → 0 we also needto account for these feedback effects when adjustingU (t). Because we are uncertain over the nature ofthe feedbacks driving f {�T (t)} (Bony et al., 2006)we assume f {�T (t)} ≈ λ(t)�T (t) (Gregory et al.,2004; Forster and Taylor, 2006) and again use RLSto update the estimate of the feedback parameter λ(t)(W m−2 K−1) starting from λ(0).

Building on Equation (1) the regression equationused here is given by

N (t) − Q(t) = ε(t)U (t) − λ(t)�T (t) + ξ(t) (3)

where ξ(t) (W m−2) are the regression model residu-als. Here we use the RLS algorithm given by Young(2011, Ch. 3). RLS estimation will be inefficient ifthe statistical properties of ξ(t) deviate too far fromthe ideal of an independent, white noise series. Inextreme cases this may produce parameter estimateswhich generate an unstable control scheme. For thesimple stochastic climate model used in this paper thisis not an issue and inspection of the properties of ξ(t)for complex climate models such as atmosphere-oceangeneral circulation models (A-OGCMs) suggests thesame is likely to be true for these also (Forster andTaylor, 2006). In the event this was an issue, con-straints could be applied to the parameter estimatesto prevent such instabilities, or more sophisticated

recursive estimation procedures could be exploited(Kalman, 1960; Young, 2011).

From Equation (2) the one step ahead control lawusing the recursive estimates ε(t) and λ(t) is given by

U (t + �t) = ε(t)−1[Q(t + �t) − λ(t)�T (t)] (4)

In Equation (3) the fact that there are non-anthropo-genic components to both N (t) and �T (t) is incidentalgiven the RLS acts as a low pass filter when returningestimates of ε(t), and λ(t). However, in Equation (4)the natural variability in �T (t) could be amplifiedin the specification of U (t + �t), something we maywish to avoid. The ideal solution to this is to havea robust detection/attribution system that is able topartition �T (t) into its natural and anthropogeniccomponents (Mann and Lees, 1996). A simple proxyfor this is to derive recursive estimates of the variationsin �T (t) that filter out the ‘unwanted’ inter-annualvariations, i.e.

�T (t) = �T (t − 1) + β(�T (t) − �T (t − 1)) (5)

where �T (t) is the filtered global mean surfacetemperature perturbations and β defines the cut-offtimescale of the filter, which is taken as 5 years inthis illustration (i.e. β = 1 − e−�t/5).

3. A simple climate model example

Equations (3)–(5), in conjunction with the RLS algo-rithm, form the MPC for the candidate GeoMIP exper-iments. Here we illustrate solving the G1 and G2scenarios in Figure 1 using this MPC design. The sim-ple climate model structure we use for the experimentsis shown in Figure 2. This model has the core global-scale feedback dynamics of A-OGCMs (Jarvis, 2011)and is expressed in such a way that f {�T (t)} can becomputed directly from, but is not a static functionof, �T (t). A 103 member Monte Carlo evaluation ofthe proposed MPC was performed for both the G1 andG2 scenarios where variability was introduced into theensemble as follows:

1. The fast, intermediate, and slow feedbacks in thesimple climate model were varied in strength bysampling the transfer function amplitude parameter(labelled bfast, bint, and bslow in Figure 2) from atrivariate normal distribution with means −2.3, 1.0,and 0.5 W m−2 K−1 and variances 0.080, 0.014,and 0.004 respectively. The trivariate distributionalso included covariance between the feedbackamplitudes to reflect interactions between the feed-back processes they attempt to represent, wherecov(bfast, bint) = 0.0173, cov(bfast, bslow) = 0.0091,and cov(bint, bslow) = 0.0037. This increased the5th and 95th percentiles for the 2 × CO2 equilib-rium range for �T from 2.33–6.64 to 2.18–7.62 K.



Figure 2. Feedback system block diagram of the simple climatemodel used in the MPC evaluation (adapted from Jarvis, 2011).The blocks represent continuous time transfer functions wheres is the differential operator. The multiplier for s is the timeconstant for the feedback response in years. To representuncertainty in the climate model a 103 member ensemble ofclimate models was generated where the fast, intermediate,and slow feedback amplitude parameters (labelled bfast, bint, andbslow) were sample from the distributions shown. Covariancewas added to represent reinforcement between the feedbackcomponents further increasing the dynamic range of the modelensemble (see text).

2. N (t) had two zero mean white noise compo-nents added to reflect both annual stochastic vari-ations and measurement error. The annual stochas-tic variations, which had a standard deviation of0.5 W m−2, were allowed to pass into the climatemodel where they are translated into a signifi-cant red noise component on �T (t) by the cli-mate model dynamics, reminiscent of the effects oflarge-scale stochastic climate phenomena such asEl Nino/La Nina events (Roe, 2009; see Figure 3).The measurement error on N (t) had a standarddeviation of 0.25 W m−2.

3. The albedo of the climate model was assumed tobe 0.3 and hence ε = 0.7. Q2×CO2 was assumedto be 3.7 W m−2 (IPCC, 2001, Ch. 6). For theinitial parameter estimates ε(0) and λ(0) weassumed prior distributions with means of 0.8and 2.0 W m−2 K−1 and standard deviations of0.1 and 0.5 W m−2 K−1 respectively (note thedeliberate mismatches here). A value of λ(0) =2.0 W m−2 K−1 was adopted because only thefaster feedbacks were assumed to be importantbecause of the relatively short timeframe of theGeoMIP experiments.

From Equation (1) the condition N (t) → 0 arisingfrom the ‘correct’ cancellation of Q(t) by R(t) (thestated aim of the G1 and G2 scenarios in K2011)implies f {�T (t)} → 0. Therefore, although not statedexplicitly in K2011, �T (t) → 0 is a co-requisite of

Figure 3. Results from the MPC implementation of the G1scenario. The bands are 95% confidence intervals for the 103

member ensemble (see text for simulation conditions). Singlesolid black lines show one realization. For the net TOA radiativefluxes the colour convention follows Figure 1. Units as definedin text.

N (t) → 0 and any failure to achieve the dual condi-tion N (t) → 0; �T (t) → 0 must imply the incorrectspecification of R(t). While N (t) �= 0, especially fol-lowing the initial application of the disturbance inQ(t), the climate system accumulates heat resultingin a perturbation in �T (t). The transient for this per-turbation will take many years to play out. For exam-ple, the simple climate model illustrated in Figure 2has a reference system time constant of ∼5 yearsand feedback time constants of 0, 50, and 500 years.Given these dynamics will result in perturbations last-ing significantly longer than the GeoMIP experimentruns of 50 years, a prudent step to take would be toimplement an additional set of control feedbacks thatextinguish the perturbation in �T (t) well within the50 year GeoMIP timeframe. Not only would this leadto a much more standardized set of A-OGCM experi-ments free from the confounding factors introduced by�T (t) �= 0, but also through ultimately removing thefeedback effect f {�T (t)} this will ensure the MPCbecomes more robust, ultimately depending only onthe recursive estimation of ε(t). This does not meanthat the patterns of regional changes in temperature asa result of the geoengineering are abolished, they aresimply constrained to occur within the context of nochange to the global average, i.e. they are standardized.



Given the surface ocean mixed layer dominatesthe dynamics of �T (t) on timescales <10 years(Watterson, 2000) the simplest control law for �T (t)that offers full control of these first order mixed layerdynamics is given by

Uc(t + �t) = Uc(t) − g(1)(�T (t) − �T (t − �t))

− g(2)�T (t) (6)

where Uc(t) are the adjustments to U (t) required toextinguish the perturbation in �T (t) and the feed-back control gains (see Jarvis et al., 2009 for fur-ther details), g = [4.9288 0.6906], yield a closed loopresponse that again only responds on timescales of∼5 years, i.e. it will act to abolish any �T (t) pertur-bation well within the GeoMIP 50 year run but willfilter out the inter-annual variability.

4. Results

Figures 3 and 4 summarize the G1 and G2 MPCexperiments. As can be seen, the TOA energy balanceis achieved within the observable limits for all butthe first few years following the introduction ofthe G1-forcing disturbances when the estimate of

Figure 4. Results from the MPC implementation of the G2scenario. The bands are 95% confidence intervals for the 103

member ensemble (see text for simulation conditions). Singlesolid black lines show one realization. For the net TOA radiativefluxes the colour convention follows Figure 1. Units as definedin text.

ε differs significantly from its ‘true’ value and theforcing disturbance is large enough to expose this.Not surprisingly, the imposition of the large changein Q(t) at t = 0 in G1 yields enough information on εfor the RLS to rapidly converge on the ‘true’ valueof 0.7. Note that the corrective actions are alwayslagged 1 year behind unforeseen disturbances because,in a truly sequential setting like this, the unforeseencannot be pre-empted. Here we have amplified theeffects of the RLS learning process by deliberatelychoosing an unrealistically high value of ε(0) in orderto demonstrate the convergence. In choosing valuesof ε(0) closer to its expected value, adherence to thedesign criteria of N (t) < 0.1 W m−2 could be metthroughout the G1 and G2 experiments.

Thereafter, convergence of ε(t) on its true valueis more gradual and associated with increases in theconfidence of the RLS estimates as noise effects arefiltered out and the effects of f {�T (t)} are eliminatedby the control action in Equation (6). For G2, theinformation content of the time-series data is greatlyreduced because of the more gradual disturbancebeing imposed. This makes the estimation of ε moreproblematic, but at the same time the consequences ofany mismatch between the estimated and ‘true’ valueof effectiveness are less significant. As a result, a pointof note for the G2 scenario is that the effectiveness ofgeoengineering is much harder to evaluate but lessimportant for the control of the TOA forcings.

The estimates of λ(t) remain rather uncertainthroughout both simulations due to the very small per-turbation in �T (t) experienced as a result of the con-trol (Figures 3 and 4). However, the perturbations in�T (t) are large enough to initiate a feedback responsef {�T (t)} and it is the weakening of this feedback overtime (mimicking the loss of ocean heat uptake; Jarvis,2011) that is causing the estimates of λ(t) to drift up.Again, the transient in f {�T (t)} is ultimately extin-guished by the control action driving �T (t) back tozero. Not only does this help fulfil the TOA radiativebalance, it also ensures ε(t) converges on its ‘true’value by eventually removing the effects of f {�T (t)}from the RLS.

The success of the MPC is borne out in the secondperturbation in the G1 scenario when Q(t) is reducedback to zero. As can be seen, the RLS estimates ofε(t) and λ(t) are sufficiently good when allied to theMPC design for there to be no net TOA disturbance atthis point. However, as with all simulation exercisesthere is always a tendency to over-represent priorknowledge because of the difficulty of divorcing themodelling from the modeller. Even in the simpleexample presented here the priors for ε(t) and λ(t)were probably unrealistically close to their ‘true’values if we wanted to represent a realistic scenariowhen faced with a complex model. As a result, itwould be valuable to execute such simulations as blindtrials where a GeoMIP-agreed set of priors for ε(t)and λ(t) were applied to all models in the GeoMIPensemble as if there were some initial consensus on



effectiveness and climate sensitivity informing theearly stage deployment of geoengineering.

5. Discussion

The results from the G1 and G2 examples show thatit appears possible to successfully automate the spec-ification of the global level of SRM geoengineer-ing within GeoMIP using a relatively simple MPCapproach. This approach also conveniently estimatesthe effectiveness of SRM within the climate modelin question. The most obvious advantage of the MPCapproach advocated here over the iterative learningadvocated by K2011 is the possible significant timesaving that could be gained. Not only does the MPCreduce the evaluation to a single run, but also removesthe need for repeat interventions by the modeller. Thiscould help increase the size of ensembles consideredwithin the GeoMIP evaluation. Furthermore, throughremoving significant global mean surface temperatureperturbations this should help standardize model out-put making the intercomparison of the side effects ofgeoengineering more transparent.

There are several trade-offs to consider here. Firstly,the control requires the on-line calculation of aggre-gate metrics such as N (t) and �T (t). This is not cur-rently standard practice within A-OGCM code given itis usually performed off-line in higher level scriptingsoftware. However, given all the necessary disaggre-gated states (both past and present) should be availablewithin an A-OGCM run, this simply requires a smallpiece of additional code to perform the on-line spa-tial averaging. Secondly, the RLS structure also needsembedding within the A-OGCM along with the asso-ciated control law(s). Again, this requires very littleadditional code (see Young, 2011, Ch 3). If thesetwo logistic barriers were insurmountable, e.g. if amore sophisticated control architecture was required,an alternative approach would be to design a sim-ple client/server middleware scheme that allowed foran on-line data exchange between the A-OGCM andthe appropriate scripting software, where the annu-ally revised control could be specified, returning thesequentially updated level of SRM back to the A-OGCM. Experience of applying Equation (3) to A-OGCM data (Forster and Taylor, 2006) would indicatethe signal-to-noise ratio in N (t) and �T (t) are suchthat the likelihood is that the RLS should converge,although finding circumstances where this broke downis likely to yield important insights into some of therisks presented by SRM deployment.

Beyond these practical issues, the MPC approachoffers a very different perspective on geoengineeringevaluation. Unlike the model world, any proposed real-world deployment of geoengineering would not havethe benefit of reruns of reality in order to fully identifythe effectiveness and side effects of technologies orportfolios of technologies prior to deployment. Whenthis is allied to the conditions of deep uncertainty

surrounding the climate science and associated models(Allen et al., 2000; Reilly et al., 2001; Stott andKettleborough, 2001) it is clear that research onthe sequential decision making and adaptive learningprocesses for handling this uncertainty is an aspect ofgeoengineering research.

Control approaches such as MPC can contribute sig-nificantly to the way we might address the potentialsequential nature of geoengineering. Learning proto-cols such as RLS can act as useful proxies for dataassimilation and model updating strategies, while thecontrol that these models inform would act as a proxyfor a ‘rational’ decision making process. In this con-text, the design criteria of simply maintaining a neu-tral TOA radiative balance without any constraintsis clearly too narrow. Traditionally, control strategiessuch as MPC would consider a more nuanced approachwhich might include trading off objectives, includ-ing costs relating to the environmental side effects,while handling constraints describing the capacity ofthe human system to monitor and respond to dan-gerous climate change. Similarly, model independentcontrol strategies would act as useful proxies for robustobservation-led policies for geoengineering deploy-ment. Using this, one could explore the controllabilityof climate states using geoengineering. For example,the G2 scenario shown in Figure 4 raises an interestingquestion about SRM deployment where the effective-ness remains undetected despite the control objectivebeing met. Under these circumstances the pressure toabandon SRM would be obvious, particularly if delete-rious side effects were perceived to be being incurred.

Finally, the apparent success of the scenarios shownin Figures 3 and 4 must not be interpreted as ademonstration of the controllability of climate statesusing geoengineering. Such evaluations need to beperformed under much more realistic conditions whereconstraints are applied to the control and the evaluationencompasses more realistic conditions of uncertaintyand observability. The spatially explicit case wherethere are point sources for SRM attempting to regulatelocal anomalies will no doubt prove to be extremelychallenging to control. Whether climate models canact as accurate proxies for the real world in suchan evaluation remains an open question. They could,however, provide useful virtual environments wheredifferent adaptive strategies could be explored andlessons learnt.

Acknowledgement

This work was supported under UK-EPSRC research contract:Integrated Assessment of Geoengineering Proposals – EPSRCEP/I014721/1.

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