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Development of Neural Network Emulations of Model Radiation for Improving the Computational Performance of the NCEP Climate Simulations and Seasonal Forecasts.

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Presentation on theme: "Development of Neural Network Emulations of Model Radiation for Improving the Computational Performance of the NCEP Climate Simulations and Seasonal Forecasts."— Presentation transcript:

1 Development of Neural Network Emulations of Model Radiation for Improving the Computational Performance of the NCEP Climate Simulations and Seasonal Forecasts Vladimir Krasnopolsky NOAA/NCEP/SAIC University of Maryland/ESSIC In collaboration with: M. Fox-Rabinovitz, Y-T. Hou, S. Lord, and A. Belochitski Acknowledgements: H. Pan, S. Saha, S. Moorthi, M. Iredell CTB Seminar Series

2 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 2 Outline Background –CFS; Motivation for Development of NN Radiation –Neural Networks NN Radiation: –Accurate and Fast NN Emulations of LWR and SWR Parameterizations –Validation Approximation Accuracy Parallel Runs –17 year climate simulation –Seasonal predictions Conclusions

3 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 3 CFS Background and Motivations for Development of NN Radiation

4 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 4 NCEP Climate Forecast System (CFS) (1) The set of conservation laws (mass, energy, momentum, water vapor, ozone, etc.) Deterministic First Principles Models, 3-D Partial Differential Equations on the Sphere: –  - a 3-D prognostic/dependent variable, e.g., temperature –x - a 3-D independent variable: x, y, z & t –D - dynamics (spectral) –P - physics or parameterization of physical processes (1-D vertical r.h.s. forcing) Continuity Equation Thermodynamic Equation Momentum Equations

5 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 5 NCEP CFS (2) Physics – P, currently represented by 1-D (vertical) parameterizations Major components of P = {R, W, C, T, S, CH}: –R - radiation (long & short wave processes): AER Inc. rrtm, ncep0, and ncep1 –W – convection, and large scale precipitation processes –C - clouds –T – turbulence –S – land (noah), ocean (MOM3/4), ice – air interaction –CH – chemistry (aerosols) Components of P are 1-D parameterization of complicated set of multi-scale theoretical and empirical physical process models simplified for computational reasons P is the most time consuming part of climate/weather models!

6 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 6 Distribution of NCEP CFS Calculation Time NCEP CFS T126L64 ~60% ~20%

7 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 7 Motivations Calculation of model radiation takes usually a very significant part (> 50%) of the total model computations. Calculation of model radiation is always a trade-off between the accuracy and computational efficiency: –NCEP and UKMO reduce the frequency of calculations –ECMWF: reduces horizontal resolution of radiation calculations in climate and NWP models uses neural network long wave radiation in DAS – Canadian Meteorological Service reduces vertical resolution of radiation calculations

8 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 8 Developed Accurate and Fast NN Radiation: Allows sufficiently frequent calculations of radiation Allows radiation calculations at each grid point of high resolution 3D grid NN developed for both long and short wave radiations

9 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 9 NN Background

10 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 10 Mapping and NNs MAPPING (continuous or almost continuous) is a relationship between two vectors: a vector of input parameters, X, and a vector of output parameters, Z, NN is a generic approximation for any continuous or almost continuous mapping given by a set of its input/output records: SET = {X i, Z i } i = 1, …,N

11 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 11 NN - Continuous Input to Output Mapping Multilayer Perceptron: Feed Forward, Fully Connected Input Layer Output Layer Hidden Layer Y = F NN (X) Jacobian ! Neuron tjtj

12 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 12 NN as a Universal Tool for Approximation of Continuous & Almost Continuous Mappings Some Basic Theorems: Any function or mapping Z = F (X), continuous on a compact subset, can be approximately represented by a p (p  3) layer NN in the sense of uniform convergence (e.g., Chen & Chen, 1995; Blum and Li, 1991, Hornik, 1991; Funahashi, 1989, etc.) The error bounds for the uniform approximation on compact sets (Attali & Pagès, 1997): ||Z -Y|| = ||F (X) - F NN (X)|| ~ O(1/k) k -number of neurons in the hidden layer

13 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 13 NN Training One Training Iteration WW E ≤ 

14 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 14 Major Advantages of NNs: NNs are generic, very accurate and convenient mathematical (statistical) models which are able to emulate 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 NO FREE LUNCH! Training is complicated and time consuming nonlinear optimization task; however, training should be done only once for a particular application! NNs are well-suited for parallel and vector processing

15 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 15 Basis for Accurate and Fast NN Emulations of Model Physics Any parameterization of model physics is a continuous or almost continuous mapping NN is a generic tool for emulating such mappings

16 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 16 NN Emulations of Model Physics Parameterizations Learning from Data GCM X Y Original Parameterization F X Y NN Emulation F NN Training Set …, {X i, Y i }, …  X i  D phys NN Emulation F NN

17 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 17 NN for Radiation Long Wave Radiation Long Wave Radiative Transfer: Absorptivity & Emissivity (optical properties):

18 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 18 NN Emulation of Input/Output Dependency: Input/Output Dependency: The Magic of NN Performance XiXi Original Parameterization YiYi Y = F(X) XiXi NN Emulation YiYi Y NN = F NN (X) Mathematical Representation of Physical Processes Numerical Scheme for Solving Equations Input/Output Dependency: {X i,Y i } I = 1,..N

19 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 19 NCEP LW Radiation and NN Characteristics 612 Inputs: –10 Profiles: temperature, humidity, ozone, pressure, cloudiness, CO 2, etc –Relevant surface and scalar characteristics 69 Outputs: –Profile of heating rates (64) –5 LW radiation fluxes Hidden Layer: One layer with 50 to 300 neurons Training: nonlinear optimization in the space with dimensionality of 15,000 to 100,000 –Training Data Set: Subset of about 200,000 instantaneous profiles simulated by CFS for 17 years –Training time: about 1 to several days –Training iterations: 1,500 to 8,000 Validation on Independent Data: –Validation Data Set (independent data): about 200,000 instantaneous profiles simulated by CFS

20 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 20 NCEP SW Radiation and NN Characteristics 650 Inputs: –10 Profiles: pressure, temperature, water vapor, ozone concentration, cloudiness, CO 2, etc –Relevant surface and scalar characteristics 73 Outputs: –Profile of heating rates (64) –9 LW radiation fluxes Hidden Layer: One layer with 50 to 200 neurons Training: nonlinear optimization in the space with dimensionality of 25,000 to 130,000 –Training Data Set: Subset of about 200,000 instantaneous profiles simulated by CFS for 17 year –Training time: about 1 to several days –Training iterations: 1,500 to 8,000 Validation on Independent Data: –Validation Data Set (independent data): about 200,000 instantaneous profiles simulated by CFS

21 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 21 NN Approximation Accuracy and Performance vs. Original Parameterization ( on independent data set ) ParameterModelBiasRMSERMSE t RMSE b Performance LWR (  K/day) NCEP CFS AER rrtm 2. 10 -3 0.400.090.64  12 times faster NCAR CAM W.D. Collins 3. 10 -4 0.280.060.86  150 times faster SWR (  K/day) NCEP CFS AER rrtm 5. 10 -3 0.200.210.22 ~45 times faster NCAR CAM W.D. Collins -4. 10 -3 0.190.170.43  20 times faster

22 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 22 Error Vertical Variability Profiles LWR – solid line; SWR – dashed line RMSE profiles in K/day

23 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 23 Individual Profiles (NCEP CFS)

24 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 24 Validation of Full NN Radiation in CFS The Control CFS run with the original LWR and SWR parameterizations is run for 17 years. The NN Full Radiation run: CFS with LWR and SWR NN emulations is run for 17 years. Another Control CFS Run after updates of FORTRAN compiler and libraries Validation of the NN Full Radiation run is done against the Control run. The differences/biases are less than/within observation errors and uncertainties of reanalysis The differences between two controls (“butterfly”/”round off” differences) have been also calculated and shown for comparison.

25 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 25 Climate Simulation 17 years: 1990 – 2006

26 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 26 Zonal and time mean Top of Atmosphere Upward Fluxes (Winter) The solid line – the difference (the full radiation NN run – the control (CTL)), the dash line – the background differences (the differences between two control runs). All in W/m 2. LWR SWR

27 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 27 Zonal and time annual mean Downward and Upward Surface Long Wave Fluxes The solid line – the difference (the full radiation NN run – the control (CTL)), the dash line – the background differences (the differences between two control runs). All in W/m 2. Downward Upward

28 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 28 The time mean (1990-2006) SST statistics for summer & winter Control Run NN Full Radiation Run NN - Control Control1 – Control2 The contour intervals for the SST fields are 5º K and for the SST differences are 0.5º K. Fields Differences

29 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 29 CTL NN FR NN - CTL CTL_O – CTL_N SST CTL1 – CTL2

30 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 30 CTL NN FR NN - CTL CTL1 – CTL2 SST

31 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 31 The time mean (1990-2006) total precipitation rate (PRATE) statistics for summer & winter Control Run NN Full Radiation Run NN - Control Control1 – Control2 The contour intervals for the PRATE fields are 1 mm/day for the 0 – 6 mm/day range and 2 mm/day for the 6 mm/day and higher; for the PRATE differences the contour intervals are 1 mm/day Fields Differences

32 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 32 CTL NN FR NN - CTL PRATE CTL1 – CTL2

33 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 33 CTL NN FR NN - CTL CTL1 – CTL2 PRATE

34 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 34 The time mean (1990-2006) total) total clouds statistics for summer & winter Control Run NN Full Radiation Run NN - Control Control1 – Control2 The contour intervals for the total clouds fields the cloud fields are 10% and for the differences – 5%. Fields Differences

35 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 35 JJA CTL NN FR NN - CTL CTL1 – CTL2

36 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 36 DJF CTL NN FR NN - CTL CTL1 – CTL2

37 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 37 The time mean (1990-2006) convective precipitation clouds statistics for summer & winter Control Run NN Full Radiation Run NN - Control Control1 – Control2 The contour intervals for the ) total clouds fields the cloud fields are 10% and for the differences – 5%. Fields Differences

38 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 38 JJA CTL NN FR NN - CTL CTL1 – CTL2

39 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 39 DJF CTL NN FR NN - CTL CTL1 – CTL2

40 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 40 The time mean (1990-2006) boundary layer clouds statistics for summer & winter Control Run NN Full Radiation Run NN - Control Control1 – Control2 The contour intervals for the boundary clouds fields the cloud fields are 10% and for the differences – 5%. Fields Differences

41 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 41 JJA CTL NN FR NN - CTL CTL1 – CTL2

42 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 42 DJF CTL NN FR NN - CTL CTL1 – CTL2

43 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 43 Some Time Series

44 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 44

45 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 45 Temperature at 850 hPa, K Solid – NN run Dashed – Control Runs

46 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 46 Seasonal Predictions

47 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 47 SST seasonal differences for winter Control Run NN Full Radiation Run NN - Control Control1 – Control2 The contour intervals for the SST fields are 5º K and for the SST differences are 0.5º K. Fields Differences

48 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 48

49 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 49 Total precipitation rate (PRATE) seasonal differences for summer Control Run NN Full Radiation Run NN - Control Control1 – Control2 The contour intervals for the PRATE fields are 1 mm/day for the 0 – 6 mm/day range and 2 mm/day for the 6 mm/day and higher; for the PRATE differences the contour intervals are 1 mm/day Fields Differences

50 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 50

51 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 51 Total clouds differences for winter Control Run NN Full Radiation Run NN - Control Control1 – Control2 The contour intervals for the ) total clouds fields the cloud fields are 10% and for the differences – 5%. Fields Differences

52 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 52

53 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 53 Convective precipitation clouds seasonal differences for summer Control Run NN Full Radiation Run NN - Control Control1 – Control2 The contour intervals for the ) total clouds fields the cloud fields are 10% and for the differences – 5%. Fields Differences

54 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 54

55 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 55 NN Emulations of Model Radiation Conclusions – 1 NN is a powerful tool for speeding up calculations of model radiation through developing NN emulations –Accurate and fast NNs emulations have been successfully developed for: NCEP LWR & SWR parameterizations NCAR CAM LWR & SWR parameterizations NASA LWR parameterization –The simulated diagnostic and prognostic fields are very close for the parallel climate and seasonal prediction runs performed with NN emulations and the original parameterizations –NN emulations approach works well for high vertical resolutions L > 60. It provides simultaneously high accuracy and satisfactory speedup.

56 NCEP-CTB: 5/27/2009V. Krasnopolsky, Neural Network Emulations of Model Radiation 56 Conclusions – 2 Upcoming Developments Developments and improvements for facilitating transition to operational use –Investigation of robustness of NN emulations with respect to: Increasing CFS horizontal resolution Increasing the frequency of radiation calculations in CFS Changes in the model (e.g., change of other parameterizations in CFS) Transition of the NN radiation into GFS Developments allowing to reduce probability of larger errors and outliers: –Quality control and compound parameterization –NN ensembles Development of dynamically adjustable NN emulations (to climate changes, etc.) Using NN emulations for generating ensembles with perturbed physics NN emulations can be introduced in DAS (fast calculations + fast adjoint)

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