The approach to calculation of model physics using accurate and fast neural network (NN) emulations, has been previously proposed, developed and thoroughly tested by the authors for National Centers for Environmental Prediction (NCEP) oceanic models [Krasnopolsky et al. 2002] and for the National Center for Atmospheric Research (NCAR) Community Atmospheric Model (CAM) [Krasnopolsky et al. 2005, Krasnopolsky and Fox-Rabinovitz 2006a,b]. In this study the NN approach has been implemented for the NCEP climate forecast system (CFS) model. NN emulations of model physics are based on the fact that any parameterization of physics can be considered as a continuous or almost continuous mapping (input vector vs. output vector dependence), and NNs are a generic tool for approximation of such mappings [Funahashi 1989]. NN is an analytical approximation that uses a family of functions like a combination of hyperbolic tangents (for more details see Krasnopolsky [2007]). NN emulations approximate the functional dependence between inputs and outputs of a parameterization. They learn this functional dependence during the NN training utilizing a training data set which was simulated using the original parameterization.

The model radiation is the most time consuming component of model physics in CFS. This study is the first step in developing the NN emulations of the full CFS model radiation. Namely, the NN emulations have been developed and tested for the original long-wave radiation (LWR) parameterization for the CFS model [Mlawer et al. 1997].

A number of NNs has been trained using a training set composed of two years of data simulated using the CFS model with the original LWR parameterization. The developed NN emulations use from 60 to 100 neurons. Then bulk validation statistics for the accuracy of approximation and computational performance for the developed NNs emulations were estimated. The accuracy of NN emulations has been estimated against the original CFS LWR. For these NN emulations, bias is negligible (about 10-3 K/day) and RMSE is limited (about 0.3 K/day). Obtaining very small NN emulation biases is important for providing non-accumulating errors in the course of model integrations using NN emulations. The developed highly accurate NN emulations for LWR, in terms of code-by-code comparison at each model time step when LWR is calculated, are about two orders of magnitude faster than the original/control NCEP CFS LWR.

The next step is validation of LWR NN emulation in the CFS model integrations. The LWR emulation NN75 was selected for such an initial validation in the CSF model runs because it seems to be acceptable in terms of both its accuracy and minimal complexity. The results of the 2-year (2005-2006) CFS model integration performed with NN75 emulation have been validated against the parallel control NCEP CFS model integration using the original LWR. The comparison of instantaneous model prognostic and diagnostic fields produced for the first week of model integrations shows that the differences are comparable with observational errors or uncertainties of data analysis. The comparison of time averaged (for the first four seasons and for two years) model prognostic and diagnostic fields shows a close similarity for the parallel runs. For example, the 2-year mean upward LWR flux at the top of the atmosphere shows similar distributions for the parallel runs, with small differences or bias (presented in Fig. 1). Bias for the extratropics is close to 0 and does not exceed 5 W/m² within just a few spots. Bias in the tropics is limited to the 0 – 5 W/m² range and does not exceed 10 – 20 W/m².

The further steps will include refinement of NN emulations for the CFS model, implementation of the concept of a compound parameterization including a quality control procedure [Krasnopolsky et al. 2007], and the NN ensemble approach [Fox-Rabinovitz et al. 2006]. The developed methodology will be applied to short wave radiation to obtain NN emulations for the entire radiation block of the CFS model.

ACKNOWLEDGMENTS. The authors would like to thank 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.

Fig. 1 Bias or the difference of 2-year mean upward LWR fluxes at the top of the atmosphere (TOA), in W/m², for the CFS model integrations with the original LWR and the LWR NN75 emulation. The contour interval is 10 W/m².

REFERENCES

Fox-Rabinovitz M. S., 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

Funahashi, K., 1989: “On the Approximate Realization of Continuous Mappings by Neural Networks. Neural Networks”, 2, 183-192.

Krasnopolsky V. M., D. V. Chalikov, and H. L. Tolman, 2002: "A Neural Network Technique to Improve Computational Efficiency of Numerical Oceanic Models", Ocean Modelling, v.4, 363-383.

Krasnopolsky, V.M., M.S. Fox-Rabinovitz, and D.V. Chalikov, 2005: “Fast and Accurate Neural Network Approximation of Long Wave Radiation in a Climate Model”, Monthly Weather Review, vol. 133, No. 5, pp. 1370-1383.

Krasnopolsky, V.M., and M.S. Fox-Rabinovitz, 2006a: “A New Synergetic Paradigm in Environmental Numerical Modeling: Hybrid Models Combining Deterministic and Machine Learning Components”, Ecological Modelling, 191, pp. 5–18.

Krasnopolsky, V.M., and M.S. Fox-Rabinovitz, 2006b: “Complex hybrid models combining deterministic and machine learning components for numerical climate modeling and weather prediction”, Neural Networks, 19, 122–134.

Krasnopolsky, V.M., 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

Krasnopolsky, V.M., M.S. Fox-Rabinovitz, H.L. Tolman, and A. A. Belochitski, 2007: “Neural Network Approach for Robust and Fast Calculation of Physical Processes in Numerical Environmental Models: Compound Parameterization with a Quality Control of Larger Errors”, Neural Networks, submitted.

Mlawer, E.J., S.J. Taubman, P.D. Brown, M.J. Iacono, and S.A. Clough, 1997: “Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave, J. Geophys. Res., 102, D14, 16,663-16,682