**Accurate and Fast Neural Network Emulations of Long and Sort Wave Radiation for the NCEP Global Forecast System Model**

A. A. Belochitski NOAA/NCEP/EMC Camp Springs, MD and University of Maryland, College Park, MD, Y. T. Hou, V. M. Krasnopolsky, S. J. Lord, and F. Yang NOAA/NCEP/EMC Camp Springs, MD

The approach to accurate and fast calculation of model radiation using network (NN) emulations, has been previously proposed, developed and thoroughly tested at National Centers for Environmental Prediction (NCEP) for Climate Forecast System (CFS) [Krasnopolsky et al. 2010] and for the National Center for Atmospheric Research Community Atmospheric Model [Krasnopolsky et al. 2005]. In this study the NN approach has been implemented for the NCEP Global Forecast System (GFS) model. NCEP GFS is a spectral model with the spectral resolution of 574 spectral harmonics and 64 vertical levels (T574L64).

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 GFS. In this study we developed the NN emulations of the full GFS model radiation. Namely, the NN emulations have been developed and tested for the original long-wave radiation (LWR) and short wave radiation (SWR) parameterization for the GFS model [Mlawer et al. 1997].

A number of NNs has been trained using a training set composed of data simulated using the GFS model with the original LWR and SWR parameterizations. The data set was composed of twelve ten day forecasts started on 15^{th} day of each month during one year (2010). The developed NN emulations use from 60 to 150 neurons in one hidden layer and have the same inputs and outputs as the original LWR and SWR parameterizations. 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 GFS radiation parameterizations. For these NN emulations, bias is negligible (about 10^{-3} K/day) and RMSE is limited (about 0.3 – 0.5 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 and SWR, in terms of code-by-code comparison at each model time step when LWR and SWR are calculated, are about 20 and 60 times faster than the original/control NCEP GFS LWR and SWR respectively.

As the next step the developed LWR and SWR NN emulations were validated in GFS model integrations. The LWR and SWR emulations with 100 neurons have been selected for an initial validation because they seem to be acceptable in terms of both their accuracy and minimal complexity. A series of 8-day forecasts has been run using the GSF model. The comparisons of anomaly correlations, biases, and RMS errors have been performed for instantaneous model prognostic and diagnostic fields produced at each day of the 8-day forecasts. The NN radiation and control runs are very close in terms of calculated statistics. For example, Fig. 1 shows the anomaly correlation calculated at 250 mb for the global temperature field. The differences between NN run and control runs increase from day one to day eight remaining small.

Fig. 1 Anomaly correlation at 250 mb for the global temperature field. Black line – control run with the original LWR and SWR; green line – run with NN SWR and the original LWR; and red line – run with NN SWR and NN LWR.

The further steps will include more comprehensive tests in a longer series of 16-day forecasts. Also refinement of NN emulations for the GFS model, implementation of the concept of a compound parameterization including a quality control procedure**,** and the NN ensemble approach [Krasnopolsky et al. 2007] will be introduced.

REFERENCES

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

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., 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,

Krasnopolsky, V. M., M. S. Fox-Rabinovitz, Y. T. Hou, S. J. Lord, and A. A. Belochitski, 2010: "Accurate and Fast Neural Network Emulations of Model Radiation for the NCEP Coupled Climate Forecast System: Climate Simulations and Seasonal Predictions", Monthly Weather Review, v.138, pp. 1822-1842, DOI: 10.1175/2009MWR3149.1

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

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