1. Development of Fast and Accurate Neural Network Emulations of Long Wave Radiation for the NCEP Climate Forecast System Model V. Krasnopolsky, M. Fox-Rabinovitz, S. Lord, Y.-T. Hou, and A. Belochitski, Acknowledgments: Drs. H.-L. Pan, S. Saha, S. Moorthi, and M. Iredell for their useful consultations and discussions. The research is supported by the NOAA CPO CDEP CTB grant NA06OAR4310047. NOAA 32nd Annual Climate Diagnostics and Prediction Workshop, Oct. 22-26, 2007, Tallahassee, FL

2. OUTLINE CTB project: Transferring the developed Neural Network (NN) methodology applied to physics of NCEP CFS Goals: (a) improving computational efficiency of radiation of the CFS model, (b) providing a practical opportunity for using new more sophisticated and time-consuming radiation and other physics components for the CFS model NN applications to the CFS model: Development of NN emulations for LW and SW radiation of the CFS model (SWR – work in progress) Background information on the NN approach Development of NN emulations of LWR (Long-Wave Radiation) for the CFS model and evaluation of their accuracy vs. the original LWR Validation of NN emulations of LWR through the CFS model run using the LWR NN emulations vs. the control run using the original LWR Conclusions and plans

3. Background Any parameterization of model physics is a relationship or MAPPING (continuous or almost continuous) between two vectors: a vector of input parameters, X, and a vector of output parameters, Y, NN is a generic approximation for any continuous or almost continuous mapping given by a set of its input/output records: SET = {X i, Y i } i = 1, …,N

4. Neural Network Y = F NN (X) Continuous Input to Output Mapping Neuron

5. Major Advantages of NNs: NNs are generic, very accurate and convenient mathematical (statistical) models which are able to emulate numerical model components, which are complicated nonlinear input/output relationships (continuous or almost continuous mappings ). NNs are robust with respect to random noise and fault- tolerant. NNs are analytically differentiable (training, error and sensitivity analyses): almost free Jacobian! NNs emulations are accurate and fast but there is NO FREE LUNCH! –Training is a complicated and time consuming nonlinear optimization procedure; however, training should be done only once for a particular application! NNs are well-suited for parallel and vector processing

6. NN Emulations of Model Physics Parameterizations Learning from Data GCM X Y Parameterization F X Y NN Emulation F NN Training Set …, {X i, Y i }, …  X i  D phys NN Emulation F NN

7. CFS Model: LWR NN emulation NN dimensionality and other parameters:  591 inputs: 12 variables (pressure, T, moisture, cloudiness parameters, surface emissivity, gases (ozone, CO2)  69 outputs: 6 variables (heating rates, fluxes)  Number of neurons for NN versions: 50 to 150  Dimensionality of NN training space: 50,000 to 100,000  Training and testing data sets are produced by saving inputs and outputs of LWR during 2-year T126L64 CFS simulations; half of the data is used for training and another half for validation or NN accuracy estimation vs. the original LWR

8. NN Approximation Accuracy (on independent data set) vs. Original Parameterization (all in K/day), Mean HR = -1.88,  HR = 2.28 ParameterizationNNBiasPRMSE LWR (K/day) NN751.5 10 -3 0.37 NN954. 10 -3 0.28 NN2000.3 10 -3 0.21 NN Computational Performance: LWR NN emulations are two orders of magnitude faster than the original LWR Overall CFS model computational performance: ~30% faster when using LWR NN emulations vs. the original LWR

9. Profiles of RMSE for NNs, in K/day

10. Individual HR Profiles

11. Global and time mean Seasonal & Daily T-850 Temperatures and their Differences Max Difference = 0.06 K Max Difference = 0.1 K

12. Top of Atmosphere Upward LWR Flux Differences Season 2: 0-5 W/m², max 10-20 W/m² Season 4: 0-5 W/m², max 10-20 W/m²

13. Differences between the seasonal (1- 4) CFS runs with NN LWR emulation and with the original LWR Field Mean Max Top of Atm. Upward LWR Flux (in W/m²) 0 – 0.5 10 – 20 Surface Downward LWR Flux (in W/m²) 0 – 0.5 10 – 20 Zonal mean T (in K) 0 – 0.51.5 – 2.5 Zonal mean U (in m/s) 0 – 1 2 Zonal mean V (in m/s) 0 – 0.10.2 – 0.4 T-500 (in K) 0 – 1 2 - 3 Relative Humidity (in %) 0 – 2 4 - 6 NOTE-1: For seasons 1-4 the mean and maximum differences are about the same, i.e. the differences are not increasing during seasonal CFS model integrations. NOTE-2: The differences are within the uncertainty of observations or reanalysis

14. Day-2: Differences between CFS runs with NN LWR emulation and with the original LWR Field Mean Max Upward Top of Atmosphere LWR Flux (in W/m**2) 0 - 2 10 - 20 Surface Upward LWR Flux (in W/m**2) 0 - 2 10 - 20 T-850 (in K) 0 – 0.20.5 – 1.5 U-850 (in m/s) 0 - 0.10.5 – 1 Day Seven: T- 850 Differences (in K): 0 – 1, max 2 - 3 Multi-year Mean Upward Top of Atmosphere LWR Flux (in W/m²) Differences: 0-5, max 10-20

15. Recent Journal and Conference Papers Journal Papers: V.M. Krasnopolsky, M.S. Fox-Rabinovitz, and A. Beloshitski, 2007, “Compound Parameterization for a Quality Control of Outliers and Larger Errors in NN Emulations of Model Physics", Neural Networks, submitted. V.M. Krasnopolsky, M.S. Fox-Rabinovitz, and A. Beloshitski, 2007, “Decadal climate simulations using accurate and fast neural network emulation of full, long- and short wave, radiation. Mon. Wea. Rev., accepted. V.M. Krasnopolsky, 2007, “Neural Network Emulations for Complex Multidimensional Geophysical Mappings: Applications of Neural Network Techniques to Atmospheric and Oceanic Satellite Retrievals and Numerical Modeling”, Reviews of Geophysics, in press V.M. Krasnopolsky, 2007: “Reducing Uncertainties in Neural Network Jacobians and Improving Accuracy of Neural Network Emulations with NN Ensemble Approaches”, Neural Networks, Neural Networks, 20, pp. 454-46 V.M. Krasnopolsky and M.S. Fox-Rabinovitz, 2006: "Complex Hybrid Models Combining Deterministic and Machine Learning Components for Numerical Climate Modeling and Weather Prediction", Neural Networks, 19, 122-134 V.M. Krasnopolsky and M.S. Fox-Rabinovitz, 2006: "A New Synergetic Paradigm in Environmental Numerical Modeling: Hybrid Models Combining Deterministic and Machine Learning Components", Ecological Modelling, v. 191, 5-18 Conference Papers; V.M. Krasnopolsky, M. S. Fox-Rabinovitz, Y.-T. Hou, S. J. Lord, and A. A. Belochitski, 2007, “Development of Fast and Accurate Neural Network Emulations of Long Wave Radiation for the NCEP Climate Forecast System Model”, submitted to the NOAA 32nd Annual Climate Diagnostics and Prediction Workshop V.M. Krasnopolsky, M. S. Fox-Rabinovitz, Y.-T. Hou, S. J. Lord, and A. A. Belochitski, 2007, “Accurate and Fast Neural Network Emulations of Long Wave Radiation for the NCEP Climate Forecast System Model”, submitted to 20th Conference on Climate Variability and Change, New Orleans, January 2008 M. S. Fox-Rabinovitz, V. Krasnopolsky, and A. Belochitski, 2006: “Ensemble of Neural Network Emulations for Climate Model Physics: The Impact on Climate Simulations”, Proc., 2006 International Joint Conference on Neural Networks, Vancouver, BC, Canada, July 16- 21, 2006, pp. 9321-9326, CD-ROM

16. Conclusions Developed NN emulations of LWR for the CFS model show high accuracy and computational efficiency. Due to a near zero bias, NN errors are not accumulating in time during model integrations. Validation of NN emulations for LWR through CFS model runs using the NN emulations vs. the CFS model run with the original LWR show a close similarity of the runs, namely the differences are within the uncertainty of observational data and/or reanalysis for seasonal predictions, climate simulations, and short- to medium-range forecasts. Obtaining small and not accumulating in time differences between the NN and control runs is crucially important for the CFS model as a complex nonlinear system Near-term plans: Development of SWR NN emulations is in progress. Using SWR NN emulations will improve the overall CFS model computational performance by ~ 60 - 70% Opportunity for using new more sophisticated and time- consuming radiation and other physics components Future developments: Other model physics components Potential applications of the NN approach to GFS and DAS