Systematic
Intercomparison of Cloud feedbacks in Climate Models: A proposal
Despite a decade of intense research on the role of water vapour and clouds in climate change, the Third Assessment Report of the IPCC concluded that “the sign of net cloud feedback is still a matter of uncertainty, and the various models exhibit a large spread” and also that “the balance of evidence favours a positive clear sky water vapour feedback of a magnitude comparable to that found in simulations”. Furthermore the IPCC recommended further work was needed to “understand and characterise more completely the dominant processes and feedbacks (e.g. from clouds and sea ice) in the atmosphere”.
Similarly at a recent WCRP Workshop on Cloud Processes and Cloud feedbacks a conclusion was that “reducing the uncertainty in cloud-climate feedbacks is one of the toughest challenges facing atmospheric scientists”.
The anthropogenic climate change component of the CLIVAR Initial Implementation Plan (WCRP, 1998) called for a specially focussed research project to identify the mechanisms of climate change and understand the reasons for differences in model response. In response the JSC/CLIVAR Working Group on Climate Models is attempting to encourage coordinated research in the area of feedbacks in climate models.
The study of cloud feedbacks raises a number of scientific questions that need to be addressed systematically using both the current generation of climate models and cloud resolving models (CRMs) together with a close connection to observations. Some of the broad questions are:
How well do current climate models simulate the distribution and behaviour of clouds?
What is the relationship between feedbacks on different timescales (seasonal and longer)?
What is the reason for the wide range in climate and hydrologic sensitivity in climate models?
To what extent do the processes producing feedbacks in cloud resolving models resemble those in climate models?
This document contains a strategic plan of action, a set of specific proposals and some more detailed plans for a sub-set of the proposals. Strategic issues will depend on the assessment of scientific colleagues as to how well scientific questions are put for substantial progress to be made. In cases where specific proposals are made but implementation plans are not well advanced, further input from interested scientific parties is sought.
Cloud feedbacks in climate models can be evaluated in climate models through the two basic steps; (a) linking simulated feedbacks to the observational record (especially the cloud archives) or to results from cloud resolving models and (b) relating the spread in results from ocean-atmosphere models to the spread in feedbacks found in a hierarchy of simpler models (eg slab ocean, perturbed SST).
This requires a carefully crafted and interlocking set of intercomparisons that optimises the benefits from existing well designed intercomparisons (AMIP and CMIP), especially through their associated diagnostic sub-projects. Where necessary, additional new simulations are proposed in order to diagnose the components of cloud feedback in a more comprehensive manner and to relate those components to observations. The wider availability of ISCCP cloud observations and the associated ISCCP simulator have now made it possible to compare, in much more detail, the behaviour of clouds in different dynamical regimes in models against observations. The input from, and close association with, the clouds (GCSS) and radiation components (GRP) of GEWEX is obviously crucial. Because of the current highly evolved state of cloud resolving models input from, and collaboration with, the GCSS area is particularly important.
3. Principal Research Areas
Since systematic investigation of cloud feedbacks in climate models remains very much in its infancy only a few specific research areas have emerged. There have been some purely modelling based approaches but, until very recently, attempts to link such studies with observations have been very few. The remainder of this section attempts to outline some key research areas and point out the links between them (and other components of WCRP). Success in any of the areas presented below will depend on the level of commitment of resources from individual diagnostic and modelling groups to fully explore those details of models that are important for cloud feedback.
The cloud information obtained from the International Satellite Climate Climatology Project (ISCCP; Rossow and Schiffer, 1991) is a very valuable source of information that has not, in general, been extensively used as part of standard model evaluation exercises because of problems in relating the clouds diagnosed within a model to those observed by the satellites. Tools now exist that, using model variables, produce clouds that are consistent with the satellite algorithms (Webb et al 2001). The ISCCP cloud simulator is now available from http://gcss-dime.gis.nasa.gov/simulator.html. A more straightforward evaluation of model performance against both ISCCP and ERBE is then practical.
With “ISCCP clouds” available from the model it will be possible to compare the behaviour of various types of model clouds with observations under differing dynamical regimes. Differing dynamical regimes in the current climate may be a suitable proxy for climate change since, as the earth warms, cloud feedbacks may arise through a transition from one dynamically induced cloud regime to another. Confidence in the ability of models to simulate climate change will be increased if models correctly simulate the contrast between cloud regimes for the current climate. Tselioudis and Jakob (2001) have obtained interesting results for two different models using this approach.
There are also a number of statistical relationships between cloud amount and albedo and cloud amount and outgoing long wave radiation that have been found using combined information from ERBE and ISCCP. Since these relationships are likely to affect the sensitivity of the radiation budget to perturbations in cloud amount it is reasonable to assume that climate models that fail to capture these relationships are likely to misrepresent those cloud feedbacks that depend upon cloud amount. (Webb et al 2001). Other statistical relationships between radiative fluxes and sea surface temperature (or SST anomalies) have been found in observations and the assessment of the ability of models to reproduce them has been attempted (Bony et al, 1997).
The ±2K SST perturbation experiments reported by Cess et al (1990, 1996) still represent the only systematic study of the strength of cloud feedback across a range of models used for climate projection. The basic experiment is quite simple to perform and, because it is for a fixed season (July), the computational demands are very modest. Most modelling groups already include the cloud radiative forcing diagnostic and its components as part of their standard model. This experiment is the simplest experiment called for in the CLIVAR Implementation Plan. There is great interest amongst the broad scientific community in discovering whether the spread in model results in the earlier (1990s) experiments has altered in any way. Since the total feedback is the result of a diverse set of compensating effects, in some models, despite the greater complexity in the parametrisation of cloud radiation interactions, the strength of the cloud feedback may be relatively unchanged (eg Yao and Del Genio, 1999). While many variants of the classic ±2K perturbation experiment have been proposed, the overwhelming reason for conducting this experiment is connection with past experiments hence enabling continuation of the monitoring begun in 1990.
Model
Experiments: 2. Equilibrium 1* CO2
and 2* CO2 Slab Ocean Experiments
Slab
ocean experiments are usually performed by all modelling groups as part of
their overall model development strategy.
They represent the simplest climate change experiment with a responsive
ocean. The common IPCC definition
of model ‘climate sensitivity’ as the
change in surface air temperature at the time of equilibrium at with 2* CO2
forcing requires such a calibrating experiment.
There has been little formal agreement on the form of slab ocean
experiments but common practices such as using a 50m deep slab ocean and a
‘q-flux’ technique need to be standardised where necessary. These experiments are amenable to a great
deal of analysis little of which has been conducted systematically under a
common framework.
It is
strongly urged that the modelling community undertake 1*CO2 and 2*CO2 slab
ocean experiments under an agreed framework and that sufficient information be
saved that an analysis of the strength of, at least, the cloud feedback can be
made for each model. It is also strongly
urged that the behaviour of the clouds in the simulated warmer climate be
evaluated against similar cloud regimes in the 1*CO2 case. In order to maximise
the information obtained from such an experiment it is important that the
atmospheric component of the slab ocean experiment be as similar as possible to
that submitted to AMIP and should also be the atmospheric component of coupled
model simulations submitted to CMIP and the new Climate of 20th
Century Project.
Model Experiments: 3. Climate Change Experiments with cloud
resolving models
Cloud
resolving Models have proven to be a very valuable tool in exploring the
complexity of the structure of cloud systems.
Up to now there has been little work in exploring the response of cloud
resolving models within a climate change framework. With the computer capacity now available it
should be possible to investigate the response of Cloud resolving models to
idealised climate change forcing (eg response to ±2K SST perturbation) and to
explore the complexity of the cloud radiation interaction. It is also noted that some experimentation
has begun using 2D cloud resolving models embedded in 3D climate models, while
the computational cost of such a configuration is high, results from an
idealised climate change experiment using such a combination would be of great
scientific interest.
Only a relatively few analysis techniques have been devised thus far to quantify the feedbacks operating in climate models and the analysis has proceeded following the engineering analogy of feedback in an amplifier or a simple first order partial differentiation approach. The full richness of feedbacks in non-linear climate system remains to be explored. Use of satellite derived cloud information in evaluating climate models has been hampered by the differing definitions of clouds n climate models and in satellite derived products, there is a continuing need to ensure that data from climate models is compared with observations from all sources in a more optimal manner (i.e. climate model information is presented in the form that is as close as possible to the original observation).
Feedbacks
The cloud forcing methodology of Cess et al (1990) provides the most straightforward measure of cloud feedback. This method computes a total derivative so that complete separation of cloud feedback from other feedbacks (particularly water vapour and lapse rate) is not possible (Zhang et al., 1996). The cloud forcing approach has bee extended a little further by Watterson et al (1999) and has proved useful in a more regional intercomparison, particularly allowing estimates of snow and ice albedo feedback; investigation of the potential for further separation .
It is also desirable to perform a quantitative analysis of all of the feedback processes acting in a climate change experiment. A suitable methodology has been developed by Wetherald and Manabe (1988) and used with many variants by some modelling groups (e.g. Le Treut et al (1991), Zhang et al (1994), Colman and McAvaney (1995), Watterson and Dix (1996) and Colman (2001)). Although very powerful, using such techniques may not be possible for all of the participating models due to the disparity of model design, particularly in terms of cloud specification for radiative algorithms and the inconsistencies between radiation transfer codes.
Another technique has used simple one dimensional radiative convection models (RCMs) (eg. Hansen et al, 1984) however this technique still requires consistency of radiation and convection codes and suffers from the additional limitation that considerable temporal and spatial averaging is required.
Clouds
It is highly desirable that the model equivalent of ISCCP clouds (Webb et al, 2001) should be determined for the control climate of each participating climate model. At the current time the use of the ISCCP simulator in “off line” mode is strongly encouraged to determine the various ISCCP cloud types from the model. The behaviour of these model clouds under different dynamical regimes and when subject to changes in forcing should also be investigated.
Several more focussed scientific questions are posed around specific numerical experiments in addition to the broader questions above:
What is the current spread in cloud feedbacks as determined by simple idealised (SST perturbation) climate change experiments and what are the main components responsible?
What is the degree of the spread in cloud feedback strength in current slab ocean climate models and what are the main contributing factors to that spread?
To what extent are the changes in clouds seen in 2*CO2 slab ocean models consistent with the change in clouds in different dynamical regimes?
To answering these questions in any detail specific scientific diagnostic projects are required.
During the design of AMIP and CMIP considerable difficulties emerged in specifying cloud diagnostics since the manner in which clouds are diagnosed in models is not necessarily the same as the manner they are diagnosed in programs such as ISCCP. As outlined above tools now exist that, using model variables, produce clouds that are consistent with the satellite algorithms (Webb et al 2001).
Hence it is proposed that, as part of AMIP 2 (and CMIP 2), a “numerical experimentation” sub-group be formed to re-run experiments (AMIP 2 and CMIP 2) as necessary either to produce model “ISCCP clouds” online or to produce sufficient data (3D fields of cloud fraction, cloud optical thickness and cloud emissivity as well as air temperature and water vapour content) to enable model “ISCCP clouds” to be created offline. The model derived “ISCCP clouds” can then be readily compared with available ISCCP and ERBE data following the approach of Webb et al (2001). In addition it is suggested that several diagnostic sub-projects be formed that would use the model “ISCCP cloud” data in different ways.
Mid-latitude clouds can be investigated using existing techniques (Tselioudis et al, 2001; Tselioudis and Jakob, 2001). Optimal methods of investigating tropical and high latitude cloud diagnostics in different dynamical regimes may require further investigation.
The project will require both simulated “ISCCP clouds” and “ISCCP clouds” deduced from re-analysis systems.
The original approach consisted of looking
at SST and large scale circulation influences on the greenhouse effect and on
cloud radiative forcing. A key
diagnostic is the Clear Sky Greenhouse effect:
: where F is LW
radiation which is compared with column integrated water vapour amount and
surface temperature. (Bony et al 1995; 1997).
While Bony et al., (1997) used binning techniques relative to the
absolute SST, Williams et al. (2001) have extended this idea to follow SST
anomalies and also have binned “ISCCP clouds” with very interesting results. A
model intercomparison along the general lines of Williams et al (2001) would be
of great interest.
It is well recognised that it is relatively easy to suggest a model intercomparison exercise; however designing an experiment in a manner that maximises the chances of answering specific questions can be much more difficult. Since the magnitude of cloud feedback in an individual model can depend critically on the precise configuration of that model it is crucial that all model experiments that are designed to intercompare cloud feedbacks are conducted with the consistent experimental protocols and with consistent model versions. Of course even given the considerations presented below an individual investigator may feel too constrained by the experimental protocol involved. For such investigators we would urge that at least one experiment be conducted within the common protocol framework and that individual ideas be handled as pilot projects that may be shared with the broader modelling community at a later date.
In order to maximise overlap with existing successful model intercomparison exercises it is recommended that the Atmospheric Model Intercomparison Project (AMIP) guidelines be adopted wherever possible and moreover it is strongly recommended that the model version used for any of the experiments outlined below be as close as possible to a version submitted for inclusion in the AMIP data base and that the data management protocols of AMIP be followed.
The model experiments considered follow the outlines of the CLIVAR implementation plan and include SST perturbation experiments and slab ocean experiments. In the case of SST perturbation experiments there is a very wide range in choices that could be made from fixed season experiments to experiments with a full seasonal cycle and from SST perturbations that are uniform over the globe or specific regions or where the SST perturbation varies geographically in some prescribed manner either analytically or from some previous experiment. Choices with slab ocean experiments have less possible variation in experimental protocol but nevertheless constraints need to be imposed.
The Basic Experiment: Fixed season ±2K
SST perturbation (Cess et al., 1990).
The basic analysis output of the experiment will be the globally averaged clear and cloudy sky sensitivity (defined as in Cess et al., 1990) separated into long wave and short wave contributions.
The experiment should be conducted with the
perpetual month of July. It is
recommended that the SST data set chosen
be the AMIP 2 SST climatology for July (earlier experiments were conducted with
Alexander and Mobley SST data set – experiments have shown that the
experimental results for the perturbation are not very sensitive the actual SST
used). Both snow and soil moisture to be held fixed (so as to remove a
potential albedo feedback). The SST perturbation of ±2K is applied
uniformly. Although much of the analysis
can be accomplished using data saved from the ± 2K experiments alone it is
recommended at a 0K control experiment also be performed (expressively for the
purpose of obtaining information on the clouds in the control climate). Data should be collected for at least 120
days after the initial spin up (participants to check on spin-up).
Use the AMIP LATS system or netCDF files that are COARDS compliant.
Provide two dimensional latitude, longitude fields, at minimum averaged over the post spin-up phase , but daily data should be stored if possible.
The fields required are:
Clear (Method II) and Cloudy fluxes – SW and LW -Top of Atmosphere (and Surface)
Cloud Amount – at least Low, Middle and High plus Total
Surface Temperature – Skin temperature and surface air temperature.
Components of surface energy budget.
Sensible Heat Flux
Latent Heat Flux
Ground Heat Flux
Net SW at surface
Downward LW at surface
Precipitation
Precipitable Water
(This list is a subset of the standard AMIP 2 diagnostics, participants are encouraged, wherever possible, to provide the standard AMIP 2 diagnostics: tables 1a, 1c(cloud portion) and 5)
Also for use in the ISCCP simulator:
Air Temperature (all levels)
Water Vapour mixing ratio (all levels)
Cloud Fraction (all levels)
Cloud Optical Thickness (all levels)
Cloud Emissivity (all levels)
In addition, participation in sub-projects will require further data as outlined below.
Project Coordinator: Bryant McAvaney (on behalf of WGCM) and Steve Klein
Sub-Project
1: Comparison of “ISCCP clouds” with ISCCP July climatology.
This project will require participating models to use the “ISCCP cloud” algorithm to produce the “ISCCP clouds” corresponding to a fixed season. The general climatology of the simulated cloud distribution is to be compared with the ISCCP climatology. Also some exploration of the simulated cloud regimes in the fixed season case as compared to the full AMIP 2 case would be of interest.
Sub-Project Leaders – ISCCP Simulator: Steve Klein (GFDL) and Mark Webb (Hadley Centre)
Sub-Project
1: Changes in clear sky radiation.
This project should explore the changes in clear sky radiation and its relation with the simulated changes in the temperature and water vapour profiles. Of particular interest may be an exploration of the possible different behaviour of the models in very dry and very moist areas.
Time averaged vertical profiles of air temperature, relative humidity and specific humidity.
Sub-Project
2: Instantaneous CO2 radiative Forcing.
There has been some improvement in the construction of broad band radiation algorithms for use in climate models over the last few years. In the early 1990s Cess et al (1993) found a large scatter (from ~3.2 W m-2 to ~4.8 W m-2) in the CO2 radiative forcing at the tropopause (200hPa) which was attributed to the neglect of certain CO2 absorption bands. Despite the recommendation that CO2 forcing values be kept as a routine diagnostic this has generally failed to be the case and hence we do not have a clear idea whether models have converged. There is considerable merit in repeating the Cess et al (1993) CO2 forcing calculations within the context of the repeat of the basic ±2K SST perturbation experiment.
The basic analysis would consist of the global average CO2 radiative forcing in the models under both clear and cloudy conditions and separation of the forcing into appropriate radiatively interesting spectral bands.
Additional Experimental Conditions.
Each time the radiative transfer code is used in the model call the code a second time with the CO2 amount doubled (but without letting the resultant radiative fluxes interact with the simulations). Save both the 1*CO2 and 2*CO2 radiative fluxes for the bands …
Additional data required
Time averaged net radiative flux profiles for LW and SW plus several LW bands (to be agreed by participants)
Sub-Project
Leader: - Volunteer needed.
Sub-Project
3: Changes in Surface Energy Balance.
The intercomparison paper of Randall et al., 1992 (using additional model output from the Cess et al 1990 experiments) concluded that the major differences in the responses of models in the component of the surface energy budget to a 4K warming were due to:
Differences in the simulated hydrologic cycles
Parametrisation of long wave radiation (especially the water vapour continuum)
Cumulus convection.
In contrast cloud-radiation effects were found to have only a secondary importance.
In both Cess et al 1990 and Randall et al 1992 the conclusions reached are consistent with problems and uncertainties with moist processes.
It was further argued that the wide range of model sensitivities that were found would not be narrowed through simply increasing model resolution but that improvements in the model physics would be needed.
While there have been many improvements to models since 1992, it is not self-evident that the differences in model response at the surface to a 4K SST perturbation have reduced especially since there are many deficiencies in the representation of the hydrologic cycle in climate models.
To be agreed by participants but no doubt water vapour and temperature profiles will be required. Daily data may also be required in order (possibly) to determine the main sources of model differences.
Sub-project Leader: - Volunteer needed.
This type of experiment is the next step up from a fixed season and has been suggested (and performed) by some European modelling groups. It overcomes any problems modellers might have with handling a fixed calendar and a fixed SST and permits some exploration of feedbacks that are associated with seasonal change. However all feedbacks are free to operate and it is less straightforward to separate cloud feedback. Although this experiment is not recommended as part of this proposal some investigators may wish to explore this approach further.
A “time slice” experiment overcomes the computational cost of a full slab ocean experiment while providing a much more realistic climate change perturbation. However problems (mostly associated with potential incompatibilities in the sea ice distribution and land-sea mask between the model providing the SST perturbation and other models. Since this approach has been used quite frequently for many different purposes no doubt some investigators may wish to explore this approach in the context of exploration of cloud feedback. However, in the immediate future, any such experiments will remain outside this proposal.
This type of experiment forms part of the “normal” development path for any model used for climate change research and hence runs should be relatively easy to do. The computational cost is higher than a SST perturbation experiment because of the longer time needed to reach equilibrium.
It is expected that, provided sufficient model data is stored, these experiments will be analysed in many more ways other than those aspects that relate to cloud feedback.
For the purpose of this proposal the basic analysis will consist of; (i) the determination of change in surface air temperature and precipitation and (ii) the change in cloud forcing (shortwave and long wave) components at the top of atmosphere and also the change in the components of the surface energy budget.
Experimental Conditions
The atmospheric model (and associated astronomical and radiative forcing) should conform to all AMIP 2 requirements (except of course for the SST). A “q-flux” correction should be applied to the slab ocean to ensure that SST errors in the control (1*CO2) simulation are less than 0.5K and that errors in the sea-ice area in the control case are less than 5%. It is suggested that the specially constructed sea ice thickness data set available at:
http://www-pcmdi.llnl.gov/amip/RESOURCES/synice.html
be used when constructing the q-flux under ice following the method discussed by McFarlane et al,1992.
Data
required
Data should be provided using the AMIP LATS system or alternatively in COARDS compliant netCDF.
It is requested that participants save the variables of the AMIP 2 standard diagnostics (see Table 1a, 1c (cloud portion only), Table 5 on AMIP web page ( http://www-pcmdi.llnl.gov/amip) for the last 20 years of each of the 1X and 2X CO2 experiments. The land sea mask and topography should also be provided. In addition participants are requested to save the information required (cloud fraction, cloud optical depth and cloud emissivity) for input to the ISCCP cloud simulator.
Project
Coordinators: Bryant McAvaney and Herve LeTreut (on behalf of WGCM)
Sub-Project
1: Changes in
“ISCCP clouds”
If different dynamical regimes in the current climate are be taken for proxies for future climate then it is important to relate the cloud changes seen in a climate change experiment to the shifted dynamical regimes. Thus a careful investigation of the changes in “ISCCP clouds” is needed. The changes in “ISCCP clouds” will need to be related to the changes in the cloud radiative forcing in order to explore more fully which aspects of the cloud distribution contribute most to the cloud feedback. Any consistency found between models would provide valuable information to assist in model evaluation studies in simulations of the current climate.
Sub-Project 2: Changes in Surface Energy Balance
The repartitioning of energy at the surface is an important component of the climate change problem. A systematic re-evaluation of the changes in the surface energy budget would provide valuable information. Of particular interest is the role of the clouds (through the surface cloud forcing) in controlling the energy partitioning.
The total derivative of cloud feedback determined by changes in cloud radiative forcing is a rather blunt instrument. Use of analysis techniques that can separate out water vapour, lapse rate and albedo feedbacks from cloud feedbacks would allow a more consistent intercomparison of models. New analysis techniques may be required.
Sub-Project Leader: Volunteer Needed.
Cloud
Resolving Models
Increases in
computing capacity have meant that it is now feasible to use cloud resolving
models as tools to investigate cloud feedback.
Cloud resolving models are also now beginning to be incorporated (albeit
in a limited experimental basis) as alternatives to cloud parametrisations in
climate models. It would be very interesting if these models were used in modes
similar (where possible) to those for full climate models and a comparison of
the net cloud feedback (and its components) in cloud resolving models be made
with the cloud feedbacks produced by the more highly parametrised processes in
climate models. Active participation of
the GEWEX GCSS community is sought in this endeavour.
New Analysis Methodologies
Although current analysis methods for diagnosing feedbacks in climate change experiments have provided much useful information the techniques are all limited in scope, Particularly frustrating has been the inability to relate the climate on seasonal and interannual time scales to feedback processes. Another area needing further work is a methodology that enables the separation of the non linear interaction between cloud feedback and other feedback factors such as water vapour and lapse rate. Further thought in these areas is clearly called for.
It is
expected that the discussions at Feedback Workshop held in Atlanta, USA
November 2002 will provide some further guidance.
4. Summary
A systematic intercomparison of cloud feedbacks in climate models is proposed as part of a programme to provide continuing documentation of the strength of cloud feedbacks in climate models and an evaluation of the performance of climate models in simulating aspects of clouds that are important in cloud feedback.
The proposal consists of two main parts one with a heavy link between models and observations and the other an intercomparison between models.
The first part of the proposal calls for a more complete investigation of the behaviour of clouds in climate models as compared to ISCCP data. In general this requires the diagnosis, within models, of simulated clouds in a manner that is consistent with the ISCCP cloud algorithms. Systematic investigation of cloud behaviour in different dynamical regimes across a range of climate models as compared to the behaviour of ISCCP clouds in dynamical regimes determined from reanalysis products should aid in categorising the potential for climate models to produce realistic cloud feedbacks. Extensions to existing model intercomparison projects (AMIP and CMIP) are suggested.
The second part of the proposal calls for systematic model experiments of two types, the first type (using perturbation to the SST as a “forcing” to an atmosphere only model) is mainly to provide a link to previous intercomparisons conducted by Cess and collaborators (Cess, 1990 and 1996), the second type (using a slab ocean model interacting with an atmospheric model) is expected to become the “standard” over the next decade. This second type of experiment is also linked to AMIP and CMIP and the behaviour of model clouds in different dynamical regimes in the “control” climate should be compared with observations in the same manner as in the first part of the proposal.
It is also suggested that a range of “cloud feedbacks experiments” be conducted with cloud resolving models, active participation of GEWEX GCSS is sought.
It is hoped that this intercomparison will serve as an important contribution to the IPCC aim to “characterise more completely the dominant processes in cloud feedback” in climate models.
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