This is Section 4.7 of the Arctic Climate Impact Assessment. Lead Authors: Vladimir M. Kattsov, Erland Källén; Contributing Authors: Howard Cattle, Jens Christensen, Helge Drange, Inger Hanssen-Bauer,Tómas Jóhannesen, Igor Karol, Jouni Räisänen, Gunilla Svensson, Stanislav Vavulin; Consulting Authors: Deliang Chen, Igor Polyakov, Annette Rinke
To provide more reliable climate change scenarios for the Arctic, several aspects of numerical climate models need further development. The most challenging aspects of model development are the physical parameterization schemes: much of the uncertainty in arctic climate change projections can be attributed to an insufficient knowledge of many of the physical processes active in the arctic domain.There is also substantial natural variability in the arctic climate system and this part of the uncertainty cannot be eliminated simply by model development and a refinement of the descriptions of physical processes.The large-scale flow is dominated by variability patterns such as the AO and the NAO see section 2.2.2. In climate change simulations, both the frequency and nature of these flow patterns may be altered. To assess changes in the flow patterns, there must be a greater focus on the climate predictability problem to probe the inevitable natural uncertainty through a systematic search in probability space.To do this, ensemble projections are required where both initial states and uncertain model parameters are varied within a realistic range associated with a probability distribution.The development of more sophisticated physical parameterization schemes and the introduction of ensemble climate- change scenarios will both require considerable computing resources. Historically, physical parameterization schemes have primarily been based on process descriptions and measurements from mid- and low latitudes (e.g., Randall et al., 1998). Assuming that the same physical processes are relevant to the Arctic, the developments have “propagated” from lower to higher latitudes in global models, and from AOGCMs to RCMs. In recent years, the Arctic has received particular attention from the climate modeling community, motivated by the strong arctic response to an increased GHG forcing in climate models.This has been demonstrated in the northern high latitudes along with a tremendous inter-model scatter, both in sensitivity to the forcing and in simulating the observed climate in this region. In particular, the amplification of global-model systematic errors in regional arctic models presents a serious challenge to future regional model developments. In this section, research and model development priorities are summarized, aimed at an improvement of AOGCM performance in the Arctic and, particularly, at an increase in the credibility of AOGCM-based projections of future climate.
The Arctic part of the climate system – a key focus in developing AOGCMs (4.7.1)
Surface air temperature and precipitation are variables of central interest from the viewpoint of AOGCM based climate change scenarios.The level of confidence that can be placed on the projected changes depends on the accuracy and adequacy of the representations of many physical processes, particularly boundary-layer fluxes of heat, moisture, and momentum; clouds; and radiative fluxes. Sea ice plays a dominant role in determining the intensity of these fluxes in the Arctic and to a large extent determines the climate sensitivity of the Arctic, in particular to GHG forcing. Description of sea ice is thus of central importance in the arctic climate system, and there is a considerable scope for improvement of the sea ice components of current AOGCMs. More sophisticated treatments of sea-ice dynamics and thermodynamics can be included – up to the level of stand-alone regional Arctic Ocean/sea-ice models. However, even in the most comprehensive present-day sea-ice models, some important processes are not properly represented, including heat distribution between concurrent lateral and vertical melt or growth of the ice and convective processes inherent in sea ice (melt-pond and brine convection). Improvements in the performance of AOGCM sea-ice components are hampered by errors in the forcing fields that determine sea-ice distribution. For example, the systematic bias in the arctic surface atmospheric pressure and the associated bias in the wind forcing of sea-ice as simulated by atmospheric components of AOGCMs (and stand-alone AGCMs) prevents even sea-ice models with advanced dynamics from properly simulating spatial distributions of sea ice. The causes of the atmospheric pressure biases are not clear. Possible linkages include topographic (resolution) effects on atmospheric dynamics, lower boundary fluxes, as well as atmospheric chemistry and dynamics of the upper atmosphere.
The atmospheric boundary layer in the Arctic is poorly represented in current AOGCMs. It is unlikely that the representation can be improved just by increasing model vertical resolution. Insufficient understanding of the physics of the atmospheric boundary layer in the Arctic and the inappropriate parameterizations used in the current generation of AOGCMs call for further research in this field.To a certain extent, the same can be said about radiative transfer parameterizations, which should account for specific features of the arctic atmosphere and the underlying surface, including both the vertical and the horizontal heterogeneity of this complex system.
From a global perspective, clouds have been identified as the most serious source of uncertainty in present-day climate models.This is also true for the Arctic. In particular, the multilayer arctic clouds with their specific complexities associated with mixed phases and low temperatures need to be represented better. Other uncertain aspects of clouds involve the radiative properties of ice crystals and the concentration of various types of crystals, which have very different properties with respect to their interaction with electromagnetic radiation.
Present climate-change modeling efforts largely focus upon effects in the atmosphere, including effects on air temperatures and precipitation. Modeling potential climate change in the marine Arctic has received less attention, although changes in the thermohaline circulation have been extensively studied, primarily with low resolution, uncoupled models. Due to the lack of coordination among modeling studies, few definitive projections can be made about changes to such variables as Arctic Ocean temperatures and salinities, stratification, and circulation (including the thermohaline circulation). In light of this, future modeling efforts should attempt to more fully address changes in the ocean.This will require better resolution in the ocean models and improved coupling between the dynamic atmosphere and dynamic ocean components, particularly in the presence of sea ice.
The freshwater budget of the Arctic Ocean (and its possible link to the intermittency of North Atlantic deepwater formation) is affected by the hydrological cycle not only in the region, but also far beyond it, including the vast terrestrial watersheds of the Arctic Ocean. For satisfactory simulations, river discharge into the Arctic Ocean needs to be properly represented in order to maintain the observed stratification and sea-ice distribution and transport. It is not clear whether the simple river discharge schemes used in current AOGCMs are sufficient, although it appears that incorporating more comprehensive river routing schemes will help ensure proper seasonality of the discharge and result in an improvement in the representation of Arctic Ocean general circulation. Accounting for the freshwater influx into the ocean from glaciers and the Greenland Ice Sheet will require more advanced parameterizations than those employed today and, ideally, require introducing dynamics into the ice-sheet components.
Processes and feedbacks associated with vegetation may also play an important role in the terrestrial Arctic, affecting heat, water, and momentum fluxes. The effects of vegetation on terrestrial Snow cover in the Arcticsnow cover and surface albedo, evapotranspiration processes, and the possible expansion of boreal forests into regions currently occupied by tundra are among many processes that may potentially be crucial in the context of climate change. Developing comprehensive interactive dynamic vegetation components of AOGCMs should eventually increase confidence in AOGCM-based projections of future climate.
Climatic changes of special concern for indigenous communities include weather variability and predictability; the extent, thickness, and quality of sea ice; the extent, duration, and hardness of snow cover; freeze-thaw cycles (particularly in autumn, when a layer of ice on the ground may be produced and last all winter, blocking access to forage for grazing animals); sudden changes in wind direction; and changes in the strength and frequency of winds and storms Chapter 3. While most of these quantities are either directly available, or easily derivable from standard model outputs, representation of a few of these variables will require additional efforts from the modeling community in the future.
Improved resolution of arctic processes (4.7.2)
To model climatically important processes in the Arctic, models with a high spatial resolution are required. To achieve this with present-day computing resources, regional models are required. In the future, global models may also have adequate resolution, but for the foreseeable future regional models will be required to complement the global simulations, because their results are closer to actual local climatic conditions and can more easily be translated into impacts than global model results.
When nested within a GCM, the large-scale circulation is imposed by the lateral boundaries of the RCM. Regional models are not able to, nor intended to, correct large-scale errors made by the global model from which conditions are drawn.The role of the regional model is to add regional detail and fine spatial and temporal scales to the simulation, not to improve the largescale simulation. An alternative to regional models is presented by the evolving global variable-resolution stretched-grid approach that provides additional spatial detail over a region of interest (e.g., Giorgi et al., 2001). This technique allows for a feedback to the global scale from the region with high resolution. While this may seem appealing at first, it raises the question of whether this feedback is preferable when similar feedbacks from other regions are represented at a lower resolution.
The need for high resolution is not restricted to the atmospheric model component. To simulate the coupled atmosphere–ice–ocean system in the Arctic, a high resolution ocean component is also required. In particular, the coupling processes occur on small horizontal and vertical scales, thus a high-resolution regional coupled atmosphere–ocean model is needed. Some early versions of such coupled models already exist, but much additional development work is required.
A further increase in atmospheric resolution (to <10 km horizontally) will require the use of non-hydrostatic model equations. New parameterizations of physical processes such as cloud formation and turbulence are also necessary at these scales. With a very high resolution (<1 km), non-hydrostatic models start to resolve individual clouds, thus necessitating further changes in cloud parameterizations. A special emphasis needs to be put on cloud microphysics, including the ice crystals and aerosols that provide nuclei for the condensation process. The arctic climate depends on the unique high-latitude characteristics of processes such as ice dynamics and persistent low-level clouds. Simulation deficiencies are partly due to coarse model resolution and partly due to inadequate model process descriptions. As mentioned previously, most model formulations are based on lowlatitude observations that do not cover the extreme conditions occurring in the Arctic.To validate coupled high-resolution models in the Arctic, improved and extended observational datasets are required. In situ observations exist for a few locations and restricted time periods, but more such datasets are needed. To obtain better coverage in space and time, remote sensing instruments are necessary. Several satellite missions are planned that hopefully will provide observational datasets with a much better coverage.
Better representation of the stratosphere in AGCMs (4.7.3)
Most current AGCMs are aimed at simulating tropospheric processes, and the stratosphere is only included with a limited resolution. On the other hand, many of the middle atmosphere three-dimensional circulation models describe only the stratosphere and the mesosphere, having a lower boundary at the tropopause 2001. Such models are primarily intended to simulate processes that are internal to the stratosphere, and it is assumed that the interaction with the troposphere can be neglected.
To model current arctic climate and stratospheric and tropospheric ozone concentrations, as well as to project their future changes, AGCMs must describe the troposphere and the stratosphere in comparable detail. Most models assume that all ozone-related processes are located in the stratosphere: ozone and ozone-related species, as well as their photochemical sources and sinks and air transport in the ozone layer (20–30 km average height). However, some of the stratospheric transport features have a tropospheric origin. Two important processes in this regard are planetary wave propagation in the northern mid-latitudes and gravitational wave destruction in the middle and upper stratosphere. While the planetary waves are well-resolved by climate models, gravity-wave drag occurs at small scales and is therefore difficult to simulate with the coarse grids of most current AGCMs. In many AGCMs, these dynamic factors are roughly parameterized by Rayleigh friction at upper model levels.This parameterization also serves the purpose of preventing spurious reflection of vertically propagating gravity waves at the upper boundary. This feature is necessary in a climate model, but in order to resolve vertically propagating waves realistically, more resolution is needed in the middle and upper stratosphere. Austin et al. (1997) demonstrated that the shift from 19 to 49 levels in an AGCM with coupled chemistry considerably improved the ozone and temperature simulation in the winter stratosphere. The AO is another important feature affecting the stratosphere.The AO is a naturally occurring phenomenon but difficult to project with current GCMs. A gradual increase in the AO positive phase persistence has been observed in recent years.  While the change may be a natural fluctuation in the AO, it may also be a result of increased atmospheric GHG concentrations. A better resolution of the stratosphere in models is required to determine whether this is the case, and, if it is, whether further increases in GHG concentrations are likely to exert a greater influence on the AO. A change in the AO would also influence the ozone distribution in the arctic stratosphere, giving rise to additional climate-relevant feedbacks in the Arctic. One example could be a change in the latitudinal heating gradient in the stratosphere caused by a change in the ozone distribution. An altered heating gradient would result in a changed temperature gradient, which in turn would change the zonal wind distribution.The zonal wind distribution determines the vertical planetary wave propagation characteristics that
Coupling chemical components to GCMs (4.7.4)
Ozone is an important GHG and moderates fluxes of ultraviolet radiation at ground level. In addition to an adequate description of dynamic processes, GCMs must incorporate detailed photochemical components for better simulation of ozone formation and destruction in the atmosphere. Due to the complicated character of ozone photochemistry in the arctic stratosphere, which has significant input from heterogeneous reactions on polar stratospheric cloud (PSC) particle surfaces, the inclusion of the microphysics of particle formation and destruction must be considered.This is omitted in the photochemical components of most present-day GCMs.
Instead, the observed spectra of PSC particles is assumed to appear immediately when the air temperature drops below a certain threshold temperature and to disappear at once when the temperature rises above the threshold. The actual delay in the observed PSC effects compared to those modeled indicates the importance of considering PSC microphysics in models, especially in the simulation of arctic ozone “mini-holes” and their rapid evolution in space and time. The denitrification of cold polar air in winter is another process in the microphysics of PSC formation and the chemistry that activates ozone-depleting chlorine radicals and repartitioning of bromine species. Polar stratospheric cloud particles that contain liquid nitric acid are supercooled ternary solutions of nitric acid, sulfuric acid, and water. They grow in the stratosphere to nitric acid dihydrate (NAD) and nitric acid trihydrate (NAT) large particles, which remove nitric acid from the stratosphere by gravitational sedimentation and contribute to the denoxification (removal of nitric acid) of the arctic stratosphere. Both NAD and NAT particles are formed intensively at temperatures of 190 to 192 K – the “nucleation window”. These “window temperature” belts are persistent at the periphery of winter polar vortices in the Antarctic for several months, and in the Arctic for about a month, and produce significant denitrified stratospheric layers.
This phenomenon as well as the PSC microphysics and chemistry have spatial and temporal scales finer than current GCM and CTM grids can resolve. A suitable parameterization of these effects is needed in addition to an elaboration of the whole photochemical computation scheme.Together with the necessary refinement of the simulation of dynamic processes, these requirements make the problem of arctic ozone modeling computationally demanding and scientifically challenging. Another atmospheric chemistry aspect of the Arctic is the production of cloud condensation nuclei near the surface and the possible involvement of naturally occurring dimethyl sulfide (DMS) in this process. Dimethyl sulfide particles originate from arctic seawater, and the flux to the atmosphere is thus strongly coupled to the existence of sea ice. It may be that the local arctic production of DMS is a determining factor for droplet size distributions in low clouds and thus may have a significant effect on low-cloud radiative properties. If this is the case, cloud properties would be sensitive to the occurrence of sea ice and a dramatic change in sea-ice distribution would affect the arctic radiative balance. This type of effect, as well as arctic haze effects, whose radiative forcing has been estimated from observations (e.g., Herber et al., 2002; Quinn et al., 2002),  need to be included in AGCMs.
Ensemble simulations (4.7.5)
A more ambitious strategy for ensemble climate simulations is needed in order to better understand natural climate variability in the Arctic and how it may be affected by global climate change. In discussing the impacts of climate change, changes in the distribution of climatic events are as interesting as changes in the mean. The ACIA used the results of five climate models to study future changes in arctic climate. In order to increase the accuracy of the different error estimates, a larger scenario sample is needed. In numerical weather prediction, experience has shown that a sample involving 50 to 100 simulations with identical models but different initial states gives a reasonable estimate of forecast uncertainties. For arctic climate change, error estimates based on a sample of this size could be adequate. In addition, it would be advantageous to increase model resolution to better capture physical processes and to better describe sharp spatial gradients (fronts), which are often the regions where extreme events occur. Both types of improvement require large additional computing resources. Further research is needed to find a reason able balance between ensemble size, model resolution, and the complexity of physical process descriptions. For climate simulation ensembles, it is also necessary to perturb model parameters and external forcings.The uncertainty aspects to be addressed thus include natural variability, uncertainties in model sensitivity to prescribed forcings, and uncertainties in the forcings. Estimates of extreme events and their frequency of occurrence also require ensemble simulations. For precipitation in particular, extreme events are often more interesting than changes in the mean. To obtain reliable estimates of changes in the frequency of extreme events, ensemble simulations are necessary. This is thus an added benefit of climate-change projection ensembles and is required to make projections of changes in storm frequencies or other extreme events. It has recently been shown that an increased GHG forcing could contribute to an increase in intense storm events in particular areas of the North Atlantic Ocean and Western Europe. At the same time, a decrease in storm frequencies is projected for other regions of the North Atlantic.To arrive at this result, a very large ensemble was used, and in order to achieve that, a simplified atmospheric model (quasi-geostrophic, three vertical levels, and a coarse horizontal resolution) had to be utilized.The drawback of using such a simplified model is that storm dynamics are not described in full detail and storm characteristics have to be derived from empirically based, statistical methods similar to the downscaling technique discussed in section 4.6. Other studies using more advanced model tools but smaller ensembles have not been able to simulate significant increases in storm frequencies.   
The general increase in computing resources that have become available for climate system modeling in recent years favors progress in developing new generations of AOGCMs – mostly by adding new components, increasing resolution, and extending ensembles of simulations. Conversely, the Arctic is one of the regions of the world with limited availability of observational data necessary for model validation and evaluation (e.g., Walsh, in press). Nevertheless, it has been shown that model performance can be improved with systematic model improvements and better resolution. For the Arctic, it is necessary to perform climate change simulations involving the entire globe; however, spatial resolution in the Arctic could be improved with the use of regional models driven by global simulations. The ultimate goal is to use as high a resolution as possible over the entire globe. In simulating arctic climate change, sea-ice processes are of primary importance. Boundarylayer fluxes and clouds are closely linked with sea-ice processes. All components require improvements to increase confidence in climate change projections. Expectations for model improvement are increasing because of increasing international activity in the field of model intercomparison exercises (e.g., Puri, 2002; Box 4.2), allowing the identification of model errors, their causes, and how they may be reduced.
Some scientists doubt that AOGCMs can provide realistic scenarios of future climate change. However, even if present day models have major shortcomings and need to be improved, they still provide useful information about possible changes in the future climate.The models are based on a physical understanding of the climate system and, as such, provide a physically coherent picture of likely climate change.There are very few other methods, if any, which can be used to provide such credible climate change estimates. Statistical methods, other than simple extrapolation of present trends, require a physical model in the background to provide a basis to generate statistically representative estimates of variables that cannot be deduced directly from the physical model.The authors of this chapter are thus confident that future model improvements will provide better estimates of the arctic climate change that may occur as a result of increasing atmospheric GHG concentrations.
There will always be uncertainties in the estimates and some of these uncertainties cannot be reduced below a certain level.These include, for example, uncertainties associated with the lack of observations to provide an accurate initial state for a model simulation, model parameter uncertainties, and the inherent limited predictability of any atmospheric/oceanic simulation. While the level of uncertainty can be lowered, it will never be certain that all physical processes relevant to climate change have been included in a model simulation.There could still be surprises to come in the understanding of climate change. Solar variability, the effects of cosmic rays, and volcanic eruptions may all contribute more to arctic climate change than is presently thought, but this remains to be seen. As climate change science progresses there will always be new results that could significantly change understanding of how the arctic climate system works; however, the present estimates are based on the best knowledge available today about climate change.
4.2. Global coupled atmosphere-ocean general circulation models
4.3. Simulation of observed arctic climate with the ACIA designated models
4.4. Arctic climate change scenarios for the 21st century projected by the ACIA-designated models
4.5. Regional modeling of the Arctic
4.6. Statistical downscaling approach and downscaling of AOGCM climate change projections
4.7. Outlook for improving climate change projections for the Arctic
- ^ Randall, D., J. Curry, D. Battisti, G. Flato, R. Grumbine, S. Hakkinen, D. Martinson, R. Preller, J.Walsh and J.Weatherly, 1998. Status of and outlook for large-scale modeling of atmosphere-ice-ocean interactions in the Arctic. Bulletin of the American Meteorological Society, 79:197–219.
- ^Bitz, C., G. Flato and J. Fyfe, 2002. Sea ice response to wind forcing from AMIP models. Journal of Climate, 15:523–535.
- ^ Walsh, J.E., in press. Summary of a workshop on modeling the Arctic atmosphere, Madison,Wisconsin, 20–22 May 2002. Bulletin of the American Meteorological Society.
- ^Randall, D., J. Curry, D. Battisti, G. Flato, R. Grumbine, S. Hakkinen, D. Martinson, R. Preller, J.Walsh and J.Weatherly, 1998. Status of and outlook for large-scale modeling of atmosphere-ice-ocean interactions in the Arctic. Bulletin of the American Meteorological Society, 79:197–219.
- ^ McAvaney, B.J., C. Covey, S. Joussaume,V. Kattsov, A. Kitoh, W. Ogana, A.J. Pitman, A.J.Weaver, R.A.Wood and Z.-C. Zhao, 2001. Model evaluation. In: J.T. Houghton,Y. Ding, D.J. Griggs, M. Noguer, P.J. van der Linden, X. Dai, K. Maskell and C.A. Johnson (eds.). pp. 471–524. Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press.
- ^ Giorgi, F., B. Hewitson, J. Christensen, M. Hulme, H. von Storch, P.Whetton, R. Jones, L. Mearns and C. Fu, 2001. Regional climate information – evaluation and projections. In: J.T. Houghton, Y. Ding, D.J. Griggs, M. Noguer, P.J. van der Linden, X. Dai, K. Maskell and C.A. Johnson (eds.). pp. 583–638. Climate Change 2001:The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press.
- ^ Austin, J., N. Butchart and R. Swinbank, 1997. Sensitivity of ozone and temperature to vertical resolution in a GCM with coupled stratospheric chemistry. Quarterly Journal of the Royal Meteorological Society, 123:1405–1431.
- ^ Wallace, J.M., 2000. North Atlantic Oscillation/annular mode: Two paradigms – one phenomenon. Quarterly Journal of the Royal Meteorological Society, 126:729–805.
- ^ Hoerling, M.P., J.W. Hurrell and T. Xu, 2001.Tropical origin for recent North Atlantic climate change. Science, 292:90–92.
- ^ Shindell, D.T., G.A. Schmidt, R.L. Miller and D. Rind, 2001. Northern Hemisphere winter climate response to greenhouse gas, ozone, solar, and volcanic forcing. Journal of Geophysical Research, 106:7193–7210.
- ^ Austin, J., D. Shindell, S.R. Beagley, C. Bruhl, M. Damers, E. Manzini, T. Nagashima, P. Newman, S. Pawson, G. Pitari, E. Rozanov, C. Schnadt and T.A. Shepherd, 2003. Uncertainties and assessments of chemistry-climate models of the stratosphere. Atmospheric Chemistry and Physics, 3:1–27.
- ^ Tabazadeh, A., E.J. Jensen, O.B.Toon, K. Drdla and M.R. Schoeberl, 2001. Role of the stratospheric polar freezing belt in denitrification. Science, 291:2591–2594.
- ^ ibid
- ^ Herber, A., L.Thomason, H. Gernandt, U. Leiterer, D. Nagel, K.-H. Schulz, J. Kaptur,T. Albrecht and J. Notholt, 2002. Continuous day and night aerosol optical depth observations in the Arctic between 1991 and 1999. Journal of Geophysical Research, 107(D10):4097, doi: 10.1029/2001JD000536.
^ Quinn, P.K.,T.L. Miller,T.S. Bates, J.A. Ogren, E. Andrews and G.E. Shaw, 2002. A 3-year record of simultaneously measured aerosol chemical and optical properties at Barrow, Alaska. Journal of Geophysical Research, 107(D11):4130,
- ^ Palmer,T.N. and J. Räisänen, 2002. Quantifying the risk of extreme seasonal precipitation events in a changing climate. Nature, 415:512–514.
- ^ Van den Brink, H.W., G.P. Konnen and J.D. Opsteegh, 2003.The reliability of extreme surge levels, estimated from observational records of order of hundred years. Journal of Coastal Research, 19:376–388.
- ^ Carnell, R.E. and C.A. Senior, 1998. Changes in mid-latitude variability due to increasing greenhouse gases and sulphate aerosols. Climate Dynamics, 14:369–383.
- ^ Knippetz, P., U. Ulbrich and P. Speth, 2000. Changing cyclones and surface wind speeds over the North Atlantic and Europe in a transient GHG experiment. Climate Research, 15:109–122.
- ^ Lunkeit, F., M. Ponater, R. Sausen, M. Sogalla, U. Ulbrich and M.Windelband, 1996. Cyclonic activity in a warmer climate. Beitrage zur Physik der Atmosphare, 69:393–407.
- ^ Ulbrich, U. and M. Christoph, 1999. A shift of the NAO and increasing storm track activity over Europe due to anthropogenic greenhouse gas forcing. Climate Dynamics, 15:551–559.
- ^ Walsh, J.E., in press. Summary of a workshop on modeling the Arctic atmosphere, Madison,Wisconsin, 20–22 May 2002. Bulletin of the American Meteorological Society.
- ^ Puri, K., 2002. Activities of the CAS/JSC Working Group on Numerical Experimentation (WGNE). In: H. Ritchie (ed.). Research Activities in Atmospheric and Oceanic Modelling. Report No. 32,WMO/TD-No. 1105.
- ^ Lorenz, E.N., 1963.The predictability of hydrodynamic flow. Transactions of the New York Academy of Sciences, Series II, 25:409–432.