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- 1. Improving Physical Parametrizations in Climate Models using Machine Learning Noah Brenowitz October 3, 2018 George Mason University
- 2. Acknowledgments Nathan Kutz (Applied Math) Chris Bretherton (Applied Math and Atmos. Sciences)
- 3. What is a weather model? If it is true, as any scientist believes, that subsequent states of the atmosphere develop from preceding ones according to physical laws, one will agree that the necessary and sufficient conditions for a rational solution of the problem of meteorological prediction are the following: 1. One has to know with sufficient accuracy the state of the atmosphere at a given time. 2. One has to know with sufficient accuracy the laws according to which one state of the atmosphere develops from another. - Bjerknes (1904) Vilhelm Bjerknes
- 4. High resolution models produce realistic clouds Giga-LES (Khairoutdinov et al. 2009) 100x100 km with 100 m grid
- 5. Can only solve at coarse resolution Image from NOAA
- 6. Coarse resolution equations Apparent heating (K/day) Apparent moistening (g/kg/day) SW+ LW radiation, latent heating, etc
- 7. How we usually build parametrizations High resolution simulation or observations
- 8. Climate models have biases in mean state CMIP5 (models) GPCP (observations) Hwang and Frierson (2013)
- 9. …and in variability (e.g. MJO) Observations Models Jiang, X. et al. (2015)
- 10. Parametrization is a function approximation problem Machine Learning Q1 Q2Q, T, U, V, … Q3
- 11. Machine learning builds black boxes • Many 1000s of parameters • Need a lot of data • Designed to be trained not interpreted • Examples: Decision trees, neural networks, support vector machines Easy to tune/train Easy to interpret Many parameters Few parameters
- 12. Optimum Parametrization Physical-based parametrizations might “orbit” reality
- 13. Training models with data
- 14. Training black boxes from data • Step 1: Training data • Step 2: Flexible model • Step 3: Supervision (what is error?) • Step 4: Train (minimize error) • Step 5: Test on new data
- 15. Emulation of existing parametrizations Original model Neural network Radiation parametrizations
- 16. Limited area cloud resolving models from Muller and Held (2012)
- 17. Neural networks can diagnose cloud fields from: Krasnopalsky, et al. (2013)
- 18. Global Cloud Resolving Models DYAMOND project • Inter-comparison of 8 GCRMs • 40 day simulations • 1 – 5 km resolution • 3 - 6 hourly outputs for 3D fields No plans to output tendency information!
- 19. But no previous prognostic tests with CRM data
- 20. Single Column Model Prognostic tests of CRM-trained neural network parametrization
- 21. Near-global aqua-planet (NG-Aqua) simulation generated by the System for Atmospheric Modeling (Δ𝑥 = 4km)
- 22. Coarse-grain data to 160 km boxes Training regionTesting region Coarse-graining A B C
- 23. Machine learning inputs 𝜙𝑖 𝑛 Preprocessing: concatenate center/scale(𝑥𝑖, 𝑦𝑖)
- 24. Training Approach 1 1. Use finite differences to compute residual tendencies 2. Train neural network: q, s, SHF, LHF, TOA Q1, Q2 Neural Network
- 25. The diagnostic performance is good! Neural Network Q1 (finite diff.) 𝑅2 ≈ .50
- 26. What about prognostic performance? Single column dynamics
- 27. Uh oh…temperature = 1035 K after 1 day Time (d) p (hPa) Is this why most past studies only show diagnostic results?
- 28. Is fitting the tendencies the right approach? • Assumes that model dynamics are continuous in time • But they are not (Donahue and Caldwell, 2018) • Assumes moist physics tendencies are available and accurate • Not true for DYAMOND outputs • Not true for observations • Does not ensure good predictions over many time steps
- 29. Fitting the approximate Q1 and Q2 is equivalent to minimizing one-step error
- 30. …but that does not ensure longer term performance
- 31. The scheme is now stable Simulated time series at x=1000 km, y=5198 km
- 32. Matches NG-Aqua better than CAM Community Atmosphere Model Version 5 (CAM5) Single Column Mode (default physics, no chemistry) Humidity Anomaly (from true zonal mean ) (g/kg)
- 33. Temperature Anomaly (K)
- 34. Implementation in a GCM Weather forecasting tests
- 35. Coarse Resolution Atmospheric Model Coarse resolution model (cSAM) • System for Atmospheric Modeling (SAM) • 160 km resolution • ”Dry” anelastic dynamics • Advection of water vapor • Virtual temperature effect on buoyancy • Damping + diffusion • Meridionally varying Coriolis force • Double precision important for mass conservation! Neural network • 3 layers of 256 neurons each • Trained with full global NGAqua data
- 36. Estimating large scale forcing for training • SAM has advection and diffusion • To compute known forcing using SAM: 1. Initialize SAM with data at time t: x(t) 2. Evolve forward for 10 minutes 3. Sam Forcing = (x(t+10 min) – x(t))/10 min • Could also account for radiation and other model physics
- 37. 10 Day simulation with NN + SAM at 160 km
- 38. NN improves the forecast accuracy
- 39. ITCZ narrows in the simulation
- 40. Zonal mean of vertical velocity narrow
- 41. Potential Cause: Little vertical momentum mixing in tropics Zonal Momentum
- 42. Solution: parametrize momentum source?
- 43. Another Problem: Loss of stochasticity Net Precipitation at 1 day
- 44. One solution: Stochastic Parametrization
- 45. Another possible solution: Data Assimilation • Filter the unresolvable scales in the training data using Digital Filter Initialization (Lynch 1997) • Defines model error (Kaas, et. al. 1998; Rodwell and Palmer, 2007) From: Rodwell and Palmer (2007)
- 46. Potential algorithm: Assimilate Data Train neural network Trained neural network + coarse resolution model Analyzed initial conditions + large-scale tendencies
- 47. Conclusions and Future Directions • Achievements • Neural network parametrization for unresolved physics • Numerically stable in single column and spatially extended mode • Only trained from coarse resolution snapshots of a GCRM • To do list • Predict momentum source (Q3) • More realistic training data (DYAMOND will be great resource) • Stochastic parametrization • Data Assimilation
- 48. References • Brenowitz, N. D. & Bretherton, C. S. Prognostic Validation of a Neural Network Unified Physics Parameterization. Geophys. Res. Lett. 17, 2493 (2018). • S. Rasp, M. S. Pritchard, P. Gentine, Deep learning to represent subgrid processes in climate models. Proc. Natl. Acad. Sci. U. S. A. 115, 9684–9689 (2018). Noah Brenowitz (nbren12@uw.edu) Contact me!
- 49. Neural networks are a popular machine learning model
- 50. Sometimes negative
- 51. Vertically integrated error is small
- 52. Lower bias in time-mean fields
- 53. Super-parametrized models graphic: Krueger and Bogenschutz
- 54. Mass conserving initial conditions • 4km SAM and 160km cSAM are on a staggered grid • Zonal velocity and meridional velocity are averages along the interfaces (40 grid points) • All other variables: averaged over full 160 km box (40^2 grid points)
- 55. Parametrized source on the equator Moistening Heating
- 56. Super-parametrized CAM (SPCAM) Inputs: u, v, w, q, T, SHF, LHF Outputs: Q1, Q2, TOA Radiative flux, Precip Used neural network. The diagnosed tendencies and precipitation match SPCAM, but they show no prognostic tests. …they do show nice prognostic results in a very recent manuscript.
- 57. Sensitivity to Hyper parameters
- 58. Split-in-time time stepping
- 59. The primitive equations Total Derivative Momentum conservation (zonal) Momentum conservation (meridional) Hydrostatic Balance: Vertical velocity Mass conservation
- 60. Increasing training window size decreases 64- step error
- 61. Precipitation matches patterns match truth
- 62. We want the scheme to make good predi
- 63. Is using more layers another way to break the stability deadlock? arXiv (2018)
- 64. This really nice work, but there are some issues • Still uses true tendencies as inputs • Not clear it will work with GCRM outputs • Takes 8 hours to train (vs 5-20 minutes for our approach)
- 65. Example: Decision Trees Moist boundary layer? no Yes Stable temperature profile? Yes No Strong convection Not much convection Not much convection
- 66. …but can be hard to interpret Very similar to a lookup table…non-continuous outputs