1. Scientists from RAND Corporation have created this model to illustrate how a “home computer” could look like in the year 2004. Topics for the day What is a climate model? How is a climate model different from a weather model? How are models developed? (in three simple steps!) Implementing on a computer: trade- offs to get the best answer (resolution, physics, ensembles) Focus on Regional Climate Models Are models getting it right?

2. What is a climate model? Let’s look at a climate model that uses energy balance to predict the temperature of Earth.

3. Our first simple climate model We did this calculation in my class. This climate model predicts that the temperature of the planet would be about 0°F. Earth’s temperature is actually much warmer than this – about 59°F (or 15°C). This climate model gets it wrong (mostly) because it leaves out GHGs. We know that E in = E out, and so our climate model for Earth’s temperature is one simple equation: where: (F) Earth =.25*(1-α)(F) sun α = albedo (F) sun = 1366 W/m 2 σ = 5.67 * 10 -8 (a constant)

4. A little more complicated… 2-layer model of the atmosphere (we’re up to 4 equations now!): For every layer: Energy In = Energy Out Top of the Atmosphere: Layer 1: Layer 2: Surface

5. Another “very simple” climate model Knowns/constants –model inputs: p = altitude λ = longitude θ = latitude t = time f = Coriolis parameter a = radius of Earth R d = gas constant κ = constant S u,B, S v,B, Q R, Q C, Q B = “physics” (parameterizations) Unknowns – model outputs: u = north-south winds v = east-west winds ω = vertical winds Φ = pressure fluctuations T = Temperature The equations of fluid motion on a sphere (in the atmosphere): 5 Equations, 5 unknowns. We can solve this series of equations (with a computer). The model predicts (u, v, ω, Φ, T).

6. Why would I torture you with this? I enjoy torturing you I want to make the point that you already know what a model is!

7. Run this “very simple” model, what do we get? Run for 365 days “cold start” – the atmosphere is at rest and temperature is zonally symmetric (constant across all longitudes). Earth starts spinning and the sun starts shining at t = 0 days. http://www.gfdl.noaa.gov/blog/isaac- held/2012/05/25/28-the-fruit-fly-of-climate- models/#more-4780 http://www.gfdl.noaa.gov/blog/isaac- held/2012/05/25/28-the-fruit-fly-of-climate- models/#more-4780

8. Results using this “very simple” model We reproduced: – Hot equator/cold poles. – jet streams and weather systems in mid-latitudes. – Equatorial easterlies and trade winds. – etc., etc.

9. First Global Warming Forecast from a climate model Manabe and Wetherald (1975): Polar amplification These model simulations also made a prediction that gets a lot of press: Wet areas get wetter & subtropical drying

10. How is a climate model different from a weather model?

11. Weather Forecasting v. Climate Forecasting Weather models and climate models are similar in a lot of ways – Use very similar mathematical equations. But weather forecasting and climate forecasting have different goals – Weather forecasts: Temperature, cloud cover, and precipitation on Monday. – Climate forecasts: Temperature, cloudiness, and precipitation in an average September. Weather forecasting is limited by chaos Chaos: when small changes in observations used to “initialize” the model make a big & unpredictable difference

12. Today in impossible movies that are loosely based on a scientific principle:

13. Can a butterfly flapping its wings in China change the weather in New York? Not really. But this principle, based on chaos, is sound. Small errors in model’s initial state can lead to very big differences in the forecast

14. Ensemble forecasting In order to quantify chaos, weather forecasts are run many times, all with slightly different initial conditions. Each line: run a weather model with different slightly initial conditions. Where the lines are all close together, we know our forecast is good. Where the lines are spread apart, we know that the forecast is uncertain. Green lines are climatology. These lines are not influenced by chaos, and this is what a climate model needs to correctly predict. FYI: This weekend’s nice weather forecast is also a reliable one.

15. Climate models have weather variability, they just aren’t designed to make day-to-day forecasts One year of simulations

16. Now that we know what a model is, let’s talk about IPCC models. IPCC = Intergovernmental Panel on Climate Change. Report synthesizing state of understanding of all things climate every 7 years. – AR4: 2007 – AR5: 2014 CMIP = Coupled Model Intercomparison Project. Every modeling group in the world runs their model(s) through the exact same suite of emissions scenarios, and scientists all analyze the output to determine future climate. – CMIP3: goes with AR4 – CMIP5: goes with AR5

17. Climate model development in three steps: 1.Mathematical equations that govern physical laws. a)ex: “very simple” climate model. 2.Parameterize process that can’t be explicitly calculated. they’re too complex to write an equation for (ex: water storage in soil). they occur on spatial and temporal scales that are too small (ex: cloud droplet formation). 3.Implement everything on a computer.

18. Climate model development in three steps: 1.Mathematical equations that govern physical laws. ex: “very simple” climate model. 2.Parameterize process that can’t be explicitly calculated. they’re too complex to write an equation for (ex: water storage in soil). they occur on spatial and temporal scales that are too small (ex: cloud droplet formation). 3.Implement everything on a computer.

19. Within each grid cell, there are things that are not explicitly modeled (e.g., clouds) that must be approximated or “parameterized” (e.g, the fraction of clouds may be specified given temperature and humidity) Size of cloud droplets: 10 -6 meters Size of typical climate model gridbox: ~100km Cloud processes must be parameterized

20. Cloud parameterization is based on real physics. Ex: cloud forms when RH = 100% in the box.

21. What’s in a parameterization? Let’s develop a parameterization for evaporation of water from the ocean: This depends on: – Relative Humidity of air – Wind speed – Texture of water surface – Temperature

22. What’s in a parameterization? Let’s develop a parameterization for evaporation of water from the ocean: Evap into atmos = K * U * T / RH U = wind speed. More evap for stronger winds. RH = Rel. humid. More evap for drier air. T = Temperature. More evap for warmer air. K = a roughness parameter/constant. More textured ocean surface = more evap. Can use this to tune the parameterization to match observations.

23. Climate model development in three steps: 1.Mathematical equations that govern physical laws. a)ex: “very simple” climate model. 2.Parameterize process that can’t be explicitly calculated. they’re too complex to write an equation for (ex: water storage in soil). they occur on spatial and temporal scales that are too small (ex: cloud droplet formation). 3.Implement everything on a computer.

24. Climate models chop the Earth into grid boxes:

25. GCMs solve every equation in EACH grid box at each time step. Climate models chop the Earth into grid boxes:

26. A close up of Europe The current horizontal size of an atmosphere, land, ocean or sea ice grid cell is between 100-200 km. The vertical extent of a box is typically: Atmosphere/Ocean: 80-500m Sea Ice: 50cm Land: 10cm

27. Model Resolution Evolution Changes in resolution over time (better computers!): (1990) (1995) (2001) (2007) For AR5, we have not improved model resolution much (but AR5 has improvements in other areas).

28. Topography at different Model Resolutions

29. Figure 1.2 Over time, we also include more processes and feedbacks in the climate system. AR5: even more processes are explicitly modeled (e.g., first time with a fully integrated carbon cycle) This is the “very simple” model we discussed earlier.

30. Modeling trade-offs from computing costs 1.Model resolution – Higher resolution = mathematically more accurate, but more expensive to build the computer. – Lower resolution = more parameterizations. 2.Inclusion/exclusion of processes. – Ex: Most models prescribe CO 2 concentrations (they don’t calculate them from emissions). – Ex: Even though we know radiation exactly, most climate models parameterize it to save computational expense. 3.Ensemble forecasting – Need many slightly different integrations to sample natural variability. – Ideally, do initial condition ensembles and parameter ensembles.

31. Modeling trade-offs from computing costs 1.Model resolution – Higher resolution = mathematically more accurate, but more expensive to build the computer. – Lower resolution = more parameterizations. 2.Inclusion/exclusion of processes. – Ex: Most models prescribe CO 2 concentrations (they don’t calculate them from emissions). – Ex: Even though we know radiation exactly, most climate models parameterize it to save computational expense. 3.Ensemble forecasting – Need many slightly different integrations to sample natural variability. – Ideally, do initial condition ensembles and parameter ensembles.

32. Too many choices! Not enough computers! Not enough energy to analyze the output! Too much stuff I don’t understand! What’s a climate modeler to do? … different kinds of models for different kinds of projects.

33. Types of climate models Energy balance models (EBM) – the 1-layer atmosphere is an EBM Atmosphere-only General Circulation Models (AGCM) – The EdGCM is one of these. Atmosphere-Ocean General Circulation Models (AOGCM) – This is the majority of IPCC models. Earth System Models (ESM) – These are new in AR5, so are still in their infancy. These guys do everything (including a dynamic carbon cycle). – $$$$$ to run. Earth System Models of Intermediate Complexity (EMIC) – “Cheaper” ESMs. They have a dynamic carbon cycle, but everything else is simplified (ex: Earth is longitudinally symmetric) – Paper we will read uses these. Regional Climate Model (RCM) – Can be run at very high resolution, but not globally.

34. Modeling trade-offs from computing costs 1.Model resolution – Higher resolution = mathematically more accurate, but more expensive to build the computer. – Lower resolution = more parameterizations. 2.Inclusion/exclusion of processes. – Ex: Most models prescribe CO 2 concentrations (they don’t calculate them from emissions). – Ex: Even though we know radiation exactly, most climate models parameterize it to save computational expense. 3.Ensemble forecasting – Need many slightly different integrations to sample natural variability. – Ideally, do initial condition ensembles and parameter ensembles.

35. Modeling trade-offs from computing costs 1.Model resolution – Higher resolution = mathematically more accurate, but more expensive to build the computer. – Lower resolution = more parameterizations. 2.Inclusion/exclusion of processes. – Ex: Most models prescribe CO 2 concentrations (they don’t calculate them from emissions). – Ex: Even though we know radiation exactly, most climate models parameterize it to save computational expense. 3.Ensemble forecasting – Need many slightly different integrations to sample natural variability. – Ideally, do initial condition ensembles and parameter ensembles.

36. “Prediction is very difficult, especially about the future” Niels Bohr Niels Bohr with Albert Einstein

37. Ensemble forecasting in a climate model There are some things about the future that climate models can’t know about: El Nino/La Nina cycles every 3-7 years makes for warm/cold years. Volcanic eruptions cool climate for 1-2 years. Lots of oscillations in climate that are more or less random: NAO, PDO, ENSO, MJO, acronym soup! Many of these take decades to complete a “cycle.” Climate modelers take these into account by running a bunch of different “ensembles,” and hope that they have sampled the range of possible natural outcomes.

38. Ensemble forecasting in a climate model Ensemble members (orange) Ensemble mean (red) Observations (black)

39. Ensemble forecasting in a climate model The is an initial condition ensemble. Within a single model, the weather on “day 0” is changed to introduce some chaos. The difference between the observations and the model mean is due to two things: 1. natural variability 2. model error This is 99% of what you see in the IPCC report.

40. Ensemble forecasting in a climate model Start a new set of ensembles in 1998 (green), what happens? In a couple of years, green and black lines don’t co-vary anymore. Individual simulations all have their own natural variability! On average, they compare well with observations, but individual warm/cold years don’t usually match up.

41. Using ensembles to compare model uncertainty with emissions uncertainty In the year 2100, uncertainty in global mean temperature is : 1. Due to different emissions scenarios: ~3C 2. Due to model uncertainty: ~1.5C-2C spread amongst model ensemble members for the four emissions scenarios

42. Using ensembles to attribute 20 th Century Warming to Humans Black line: Observed Temperatures Pink: GCM prediction of warming over the 20 th Century (spread of all ensembles) Blue: GCM prediction of warming if GHGs did not increase over 20 th Century (spread of all ensembles). Anthropogenic warming is likely discernible on all inhabited continents

43. Moving into the future: Regional Climate Models (RCMs) We have focused on global-scale output from GCMs, but we do not live in the global mean! The details of the terrain and land- water contrasts can be very important in shaping the climate. These effects are not resolved very well by GCMs Size of a typical GCM gridbox.

44. San Juan Sawatch Sangre de Cristo Breckenridge 4 KM Resolution 12 KM Resolution36 KM Resolution San Juan Sawatch Sangre de Cristo Breckenridge Topography Approximate size of GCM Grid Cell (“flat high place”) Regional Climate Models (RCMs)

45. Our computers aren’t fast enough to run a GCM with a grid size of 4km like we do with NWP models. Instead, use an RCM to look in detail at a region of interest. Using RCMs to downscale GCMs: Regional Effects of Global Warming Source: Eric Salathe, UW Climate Impacts Group

46. An example: RCM simulations over the entire USA  Lots and lots of results  Output files are quite large (40 GB per output file * 24 files/modeled day * 21 days or more of simulation = 20 TB for 21 days!)  Simulations take awhile  12 hours simulated in a 8 hour real time period  768 processors used for the 900x1200x50 grid point simulation  10,000s to 100,000s processors are now becoming available In AR5, many modeling groups are using GCMs and RCMs together

47. How do we know if climate models are right?

48. Annual Average Surface Temperature Observed Model Averag e ºC IPCC 2007

49. Annual Average Surface Temperature Error in a typical model IPCC 2007

50. “Annual Cycle*” in Temperature Observed Model Averag e * Multiply by ~3 to get approximately the difference in July and January temperature IPCC 2007

51. Annual Average Precipitation Observed (cm/year) Average of the models IPCC 2007

52. Other Ways to Validate Climate Models How much cooling after a volcano? Can we reproduce the last Ice Age conditions given CO 2, solar, etc. conditions? Can the climate of the 20 th century be reproduced given greenhouse gas, solar, volcanoes, and aerosols?

53. Other Successful Predictions of Climate Models More warming at night than day Most warming in Arctic than anywhere else (especially during winter) Least warming just south of Greenland Wet regions get wetter, subtropical ocean regions dry Tropopause (at the top of the weather layer of the atmosphere) moves upward Large scale tropical circulations weaken

54. End.

55. Types of Ensembles The previous slide was an initial condition ensemble. Within a single model, the weather on “day 0” is changed to introduce some chaos. The difference between the observations and the model mean is due to natural variability. This is 99% of what the IPCC models are using for their ensembles. Parameter ensembles also exist. Vary the value of a parameter a little bit – Ex: our “roughness parameter” for evaporation.

56. Summertime convection associated with fronts may occur over a long distance (Louisiana to South Carolina is ~1300 km) but the processes are occurring on a smaller scale The location of the heavy rain is occurring over regions of 35 km or less. To represent this in a model, one needs 4-5 grid points for those regions. That means ~5 km grid resolution. 32 km wide Moving into the future: Regional Climate Models (RCMs)

57. NWP Numerical Weather Prediction Model Climate model (GCM, General Circulation Model) GoalPredict weatherPredict climate Time Rangedaysdecades to centuries Spatial Resolution 5-20 km100+km Relevance of initial conditions highlow (only the ocean and sea ice matter much) Relevance of GHG concentration lowhigh Relevance of ocean dynamics lowhigh Relevance of energy balance lowhigh

58. Many physical process are at scales smaller than the grid spacing Need to represent the cumulative effect of sub-gridscale processes on the grid in terms of gridscale parameters. e.g. evaporation depends on humidity, temperature, winds, water roughness. Atmosphere clouds precipitation & radiation evaporation and condensation Surface energy fluxes Evapotranspiration Ocean Mixing by eddies Vertical mixing in mixed layer deep water formation Based on theory and observations “tuned” (usually globally) to get reasonable climate – an important kluge that is present in every climate model. Final accounting of parameterizations