1 4th year Topics in Oceanography Week 5 Nov 10th, 2016 Yves PlancherelThe evolution of climate models 1. mechanics of modeling 2. climate modeling 3. model coupling 4. key challenges 4th year Topics in Oceanography Week 5 Nov 10th, 2016 Yves Plancherel

2 Common thoughts about modelingThe goal of modeling is to reproduce data If a model doesn’t fit the data, the model is useless (…and modeler also) Since modelers don’t measure anything, they don’t know anything about data or care about them Measurement(s) of “X” can be used to better constrain climate models Process “W” is not explicitly implemented in the model, hence the model cannot model the the effect of the “Z-cycle”on climate as “W” as an effect of the “Z-cycle”

3 Some propositions All models are “wrong” and “incomplete”(modeling with the sole goal of fitting data is futile) (state-or-the-art models have many free parameters, uniqueness of the fit/solution is not guaranteed) Models have the merit of being internally consistent and possess fundamental conservation properties (mass, momentum, energy) that harm-wavy arguments do not have Models can be wrong in different ways (figuring out why they are wrong is where learning occurs) (data come in to inform parameterizations and testing simulations) The skill of a “modeler” is less in knowing how to model (i.e math, computer science) and more in how to make useful sense of model results

4 What do we need to make a model?(Any model, not necessarily a climate one)

5 What does a model need? A very simple analytical exampleRequires equations (hypotheses about underlying physics)

6 What does a model need? A very simple analytical exampleRequires equations (hypotheses about underlying physics) Requires boundary conditions

7 What does a model need? A very simple analytical exampleMany equations cannot be solved analytically… What do we have to do to solve them numerically?

8 What does a model need? A very simple numerical example (review)Requires discretization of derivatives and numerical integration to step forward from ti to tf=NDT Forward difference (aka Forward Euler)

9 What does a model need? Discretization needed to implement numericallyBackward difference (aka backward Euler) Requires solving an extra equation (implicit scheme)

10 What does a model need? Disretization needed to implement numericallyCentered difference Requires knowing more things from more points

11 The “dynamical/numerical core” of a model matters … a lot!System of equation (partial differentials in 3D) Discretization and integration scheme These 3 are mathematically all valid but can produce very different answers when implemented… Forward difference (aka Forward Euler) Backward difference (aka backward Euler) Centered difference etc…

12 Exact solution

13 Idealized simulationsTesting the numerical core …when we don’t have an exact solution to compare to Idealized simulations ~ numerical equivalent of calibration in a lab This highlights the problem of numerical diffusion

14 What does a model need? summaryNeed equations Output = function(input) Need a starting point Boundary conditions Must define time and space scales of interest Integration time step Spatial resolution Duration of model run Decisions about time/space scales also translate into “filtering” the equations (parts of the equations can be neglected and the equations simplified)

15 Why model climate? FIGURE 3.2 The landscape of the various types of climate models within a hierarchy of models is complex and overlapping. This is one view of that landscape centered on the three broad types of models and analytic frameworks in climate change research that contribute to the IPCC reports: integrated assessment models, physical climate models, and models and other approaches used to help assess impacts, adaptation, and vulnerability. SOURCE: Moss et al., Reprinted by permission from Macmillan Publishers Ltd., copyright 2010.

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17 What are coupled climate models?FIGURE1.3 Climatemodelsaremathematicalrepresentationsofthephysical,chemical,andbiological processes in the Earth system. SOURCE: Marian Koshland Science Museum.

18 Why coupling the models in the first place?Nonlinear feedbacks

19 The “coupler” is the heart of climate models

20 A few key major coupling mechanisms between the ocean the the atmosphere

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22 Interconnecting reservoirs with their own time-scales105 s=1.5 days 106 s=11 days 107 s=4 months 1010 s= 300 years

23 What is model “coupling”?Exchanges of properties at the interfaces: Heat Water Momentum Energy Modules are run quite independently, but regularly exchange information about each other’s states to calculate exchange fluxes Challenges: Grids of various modules may not match E.g. part of an atmospheric grid box covers ocean+land+sea-ice Properties must be conserved Characteristic time-scales in each module differ affecting the time-step of integration needed

24 Some key challenges FIGURE1.3 Climatemodelsaremathematicalrepresentationsofthephysical,chemical,andbiological processes in the Earth system. SOURCE: Marian Koshland Science Museum.

25 Model complexity : need vs greedFrom Bader et al (2008) The climate system includes a wide range of complex processes, involving spatial and temporal scales that span many orders of magnitude. As our understanding of these processes expands, climate models need to become more complex to reflect this understanding. The balance between increased complexity and increased resolution, subject to computational limitations, represents a fundamental tension in the development of climate models.

26 Model complexity vs resolution Late 1960s: UNIVAC 1108 (0Model complexity vs resolution Late 1960s: UNIVAC 1108 (0.5MB of memory!)

27 The UK’ shared supercomputing facility4920 nodes x 12 cores = CPUs Each node as 64GB memory

28 Model resolution Increasing spatial resolution…also mean increasing temporal resolution to maintain numerical stability (i.e. decrease time step) Huge cost of resolution: 2x increase resolution in all dimensions means 8x more computations 8x more memory 8x more time With decreased time-step >16x slower and more demanding Computation of the solution is carried out on a three-dimensional spatial grid. Increasing model resolution enables better resolution of processes, but this comes at considerable computational cost. For example, increasing horizontal resolution by a factor of 2 (say from 100 to 50 km2) generally requires a factor of 2 decrease in time step for numerical stability. Thus, the overall computational cost is a factor of 8. Furthermore, to avoid distortion of the results, the horizontal resolution cannot be increased without concomitant increases in vertical resolution. Increasing complexity independently adds to the computational cost of a model, so a balance must be sought between resolution and complexity. In practice, the ensemble of these considerations has led to an increase in atmospheric grid resolution from ~500 km to ~100 km in state-of-the-science climate models since the 1970s. There is considerable evidence that refining the horizontal spatial resolution of climate models improves the fidelity of their simulations. At the most fundamental level, increasing resolution should improve the accuracy of the approximate numerical solutions of the governing equations that are at the heart of climate simulation. However, because the climate system is complex and nonlinear, numerical accuracy in solving the dynamical equations is a prerequisite to climate model fidelity, but is not the only consideration. One of the more obvious impacts of improving climate model resolution is the representation of geographic features. Resolving continental topography, particularly mountain ranges and islands, can significantly improve the representation of atmospheric circulation. Examples include the South Asian monsoon region and the vicinities of the Rockies, Andes, Alps, and Caucasus, where the mountains alter the large-scale flow and give rise to small-scale eddies and instabilities. Resolving topography can also improve simulations of land-surface processes such as snowpack and runoff that rely strongly on orographically modulated precipitation and temperature (e.g., Leung and Qian, 2003) and may also have upscaled or downstream effects on atmospheric circulation (e.g., Gent et al., 2010) and clouds (e.g., Richter and Mechoso, 2006). Similarly, weather and climate variability associated with landscape heterogeneity, as well as coastal winds influenced by local topography and coastlines, are better represented in models with refined spatial resolution, which can also lead to improved simulation of tropical variability through improved coastal forcing (Navarra et al., 2008). Finally, there is evidence of feedbacks that are strongly dependent on model resolution and that therefore influence a model’s response to perturbations, for example: •  atmospheric blocking, which is dependent on the feedbacks between the large-scale atmospheric circulation and mesoscale eddies (Jung et al., 2011); •  feedbacks between western boundary currents with sharp temperature gradients in the ocean and the overlying atmospheric circulation (Bryan et al., 2010; Minobe et al., 2008); •  feedbacks between tropical instability waves in the ocean and wind speed in atmospheric eddies (Chelton and Xie, 2010); •  air-sea interactions in presence of a sea-ice cover, which depend on the accuracy of detailed representation of sea-ice states, including ice edge position, thickness distribution, and deformations; and •  ice sheet-ocean interactions, which require representation of local flow under and into the ice, including fjord circulation and exchanges.

29 Benefits of improving resolution?Better numerical accuracy in solving dynamical equations Smaller discretization steps Better representation of topography/bathymetry (mountains, islands, seamounts…) Grid-boxes have vertical walls! Explicit inclusion of subgrid-scale processes Parameterizing vs. resolving Property gradients are larger Affects pressure gradients (i.e. velocity of currents) Model becomes more advective and less diffusive Exchange-processes that depend on gradient become stronger (strong exchange, although on shorter spatial scales, e.g. air-sea heat fluxes) Better agreement with the way data are collected (i.e. what observations mean) Averaging over space/time and variability

30 Atmospheric resolution: 3 casesFIGURE1.4 Annual-meanprecipitationinthewesternUnitedStatessimulatedbyaclimatemodelwith three different resolutions (300, 75, and 50 km) compared with observational data (VEMAP) at 50-km reso- lution. The higher-resolution model (c) shows better agreement with observations (d). SOURCES: Walter, 2002, based on Figure 13 in Duffy et al., 2003.

31 Gulf Stream Labrador Sea

32 Ocean resolution: 2 cases resolving eddies (the ocean’ storms)Figure 6.1. Surface-Current Speed in Two Simulations of the Southern Ocean in Low- and High-Resolution Ocean Models. [From Fig. 6 in R. Hallberg and A. Gnanadesikam 2006:The role of eddies in determining the structure and response of the wind-driven Southern Hemisphere overturning: Results from the modeling eddies in the Southern Ocean (MESO) project. J. Physical Oceanography, 36, 2232–2252. Reproduced by permission of the American Meteorological Society (AMS).] Figure 6.1. Surface-Current Speed in Two Simulations of the Southern Ocean in Low- and High-Resolution Ocean Models. [From Fig. 6 in R. Hallberg and A. Gnanadesikam 2006:The role of eddies in determining the structure and response of the wind-driven Southern Hemisphere overturning: Results from the modeling eddies in the Southern Ocean (MESO) project. J. Physical Oceanography, 36, 2232–2252. Reproduced by permission of the American Meteorological Society (AMS).]

33 The atmosphere matters … a lot! Radiative-convective equilibrium

34 The hydrologic cycle and Relative humidity (h)It is the ratio of partial pressure of water vapor to the equilibrium partial pressure “the salinity of the atmosphere” What happens when relative humidity = 100%? Relative humidity decreases as T increases Warm air can hold more water More water = more clouds? More low clouds = more albedo? More high clouds = more greenhouse? If T increases and air can hold more water, what happens over deserts?

35 The “clouds” challengeClouds can both cool and warm the climate The microphysics responsible for cloud formation is not well understood The grid cells in models are much much bigger than time/space scales relevant for cloud physics

36 Weather and climate – bridging the gap

37 Comparing models with dataWhat is a data point? Are model solutions at a point similar to a data point? Spatially? Temporally? Using data well is not a trivial task. It requires understanding the model well and the data well A trend towards “Observational System Simulation Experiments” (OSSE)

38 The role of observations in modeling

39 1. What are climate models1. What are climate models? What are they made of, what are they used for? Manabe S. and Wetherald, R.T. (1967). Thermal equilibrium of the atmosphere with a given distribution of relative humidity. Journal of Atmospheric sciences, 24(3): Manabe S. and Bryan, K. (1969). Climate calculation with a combined ocean-atmosphere model. Journal of Atmospheric Sciencces, 26, Stouffer R.J., Manabe S. and Bryan K. (1989). Interhemispheric asymmetry in climate response to a gradual increase of atmospheric carbon dioxide. Nature, 342: Manabe S. and Stouffer R.J. (1993). Century-scale effects of increased atmospheric CO2 on the ocean-atmosphere system. Nature, 364: Delworth T.M. et al. (2006). GFDL’s CM2 Global coupled climate models. Part I: formulation and simulation characteristics. Journal of Climate, 19: Roberts J.M. et al. (2016). Impact of ocean resolution on coupled air-sea fluxes and large-scale climate. Geophysical Research Letters, doi: /2016GL

40 2. The role of ocean circulation in climate simulations, freshwater hosing and hysteresisRahmstorf S. (1994). Rapid climate transitions in a coupled ocean-atmosphere model. Nature, 373:82-85. Manabe S. and Stouffer R.J. (1999). The role of the thermohaline circulation in climate. Tellus, 51A-B: Manabe S. and Stouffer R.J. (2000). Study of abrupt climate change by a coupled ocean-atmosphere model. Quaternary Science Review, 19: Stouffer R.J. et al. (2006). Investigating the causes of the response of the thermohaline circulation to past and future climate changes. Journal of Climate, 19: Stouffer R. J. et al. (2007). Climate response to external sources of freshwater: North Atlantic versus the Southern Ocean. Journal of Climate, 20: Hawkins E. et al. (2011). Bistability of the Atlantic overturning circulation in a global climate model and links to ocean freshwater transport. Geophysical research Letters, 38, L10605, doi: /2011GL Jackson L. C. et al. (2016) Ocean and atmosphere feedbacks affecting AMOC hysteresis in a GCM. Climate Dynamics, doi: /s

41 4. The experimental design of model simulations and interpreting model resultsHeld I. et al. (2010). Probing the fast and slow components of global warming by returning abruptly to preindustrial forcing. Journal of Climate, 23: Taylor K.E. et al. (2012). An overview of CMIP5 and the experiment design. Bulleting of the American Meteorological Society (BAMS), April, , doi: /BAMS-D Knutti R. and Sedlacek J. (2013). Robustness and uncertainties in the new CMIP5 climate model projections. Nature Climate Change, 3: , doi: /NCLIMATE1716. Froelicher, T.L. et al. (2014). Continued global warming after CO2 emissions stoppage. Nature Climate Change, 4:40-44, doi: /NCLIMATE2060 Paynter D. and Froelicher T.L. (2015). Sensitivity of radiative forcing, ocean heat uptake and climate feedback to changes in anthropogenic greenhouse gases and aerosols. Journal of Geophysical Research: Atmosphere, doi: /2015JD Delworth, T.L. et al. (2016). The North Atlantic Oscillation as a driver of rapid climate change in the Northern Hemisphere. Nature Geoscience, 9: , doi: /NGEO2738. Froelicher T.L. et al. (2016). Sources of uncertainties in 21st century projections of potential ocean ecosystem stressors. Global Biogeochemical Cycles, 30: , doi: /2015GB

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43 Are models ever “right”?Since models are incomplete by construction, what does “right” even mean? What do we do if one model can represent a variable better but another variable worst? A model can reproduce the mean state well but not the variability. Is it a “good” model?

44 3. Model performance and deciding which is the best model?Gregory J.M. et al. (2005). A model intercomparison of changes in the Atlantic thermohaline circulation in response to increasing atmospheric CO2 concentration. Geophysical Research Letters, 32, L12703, doi: /2005GL Gleckler P.J. et al. (2008). Performance metrics for climate models. Journal of Geophysical Research, 113:D06104, doi: /2007JD Pincus R. et al. (2008). Evaluating the present-day simulation of clouds, precipitation and radiation in climate models. Journal of Geophysical Research, 113:D14209, doi: JD Reichler T. and Kim J. (2008). How well do climate models simulate today’s climate? BAMS (Bulletin of the American Meteorological Society), March, , doi: /BAMS Knutti, R. (2010) The end of model democracy? An editorial comment. Climatic Change 102: , doi: /s Bellenger, H. et al. (2014). ENSO representation in climate models: from CMIP3 TO CMIP5. Climate Dynamics, 42: , doi: /s z. Cesena G. and Waliser D.E. (2016). Characterizing and understanding systematic biases in the vertical structure of clouds in CMIP5/CFMIP2 models. Geophysical Research Letters, doi: /2016GL

45 Metrics: a judgment call?Figure 2.5. Model Metrics for 23 Different Climate Fields. Values less than 0 indicate an error less than the average CMIP3 model, while values greater than 0 are more than the average.The black triangles connected by the black line show a total score obtained by averaging all 23 fields. Each tick mark represents a different model. [Figure adapted from P.J. Gleckler, K.E. Taylor, and C. Doutriaux 2008: Performance metrics for climate models. J. Geophysical Research, 113, D06104, doi: /2007JD Reproduced by permission of the American Geophysical Union (AGU).]

46 Internal variability vs “forced” response?Figure 5.3a. Simulation of 20th Century Globally Averaged Surface Temperature from GFDL CM2.1. “CRU” is the value based on the Climate Research Unit gridded observational dataset,“IPCC Mean” is the average value of all CMIP3 models, and “IPCC Mean Volc” is the average of all CMIP3 models that included volcanic forcing. Individual realizations of the CMIP3 20th Century experiment are denoted by the dotted curves labeled “run(1–3),” and the ensemble mean is marked “Mean.”

47 What model for what process?

48 Processes operate on various time/space scalesCan one model do it all? Processes operate on various time/space scales The climate modeling primer

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