One of the main problems of development and implementation of high-quality high-resolution environmental models is the complexity of physical (chemical and biological) processes involved. For example, for the state-of-the-art climate model, the NCAR (National Center for Atmospheric Research) CAM (Community Atmospheric Model), calculation of a model physics package takes about 70% of the total model computations. For this and other numerical models neural network (NN) techniques have been developed (Krasnopolsky et al., 2002, 2005, Tolman et al. 2005, Krasnopolsky and Fox-Rabinovitz 2006, Krasnopolsky 2007) for speeding up calculations of model physics (i.e., components of atmospheric and oceanic numerical models describing physical processes) up to two to five orders of magnitude. The speed up is achieved through the development of NN emulations of model physics. The development of NN emulations of model physics depends significantly on our ability to generate a representative training set to avoid using NNs for extrapolation beyond the domain covered by the training set. Because of high dimensionality of the input domain (i.e., dimensionality of the NN input vector) which is of the order of several hundreds or more, it is difficult if not impossible to cover the entire domain, especially its “far corners” associated with rare or extreme events, even when we use model simulated data for the NN training. Also, the domain may change with time as in the case of climate change. In such situations the emulating NN may be forced to extrapolate beyond its generalization ability which may lead to larger errors in NN outputs in the numerical models in which they are used.

We have developed NN emulations of major components of climate model physics (Krasnopolsky et al. 2005, Krasnopolsky and Fox-Rabinovitz 2006, Krasnopolsky 2007) for the widely recognized and used NCAR CAM. Specifically, we developed the NN emulations of the NCAR CAM long wave radiation (LWR) and short wave radiation (SWR) parameterizations which are the most time consuming components of model physics. They are highly accurate and much more computationally efficient than the original NCAR CAM LWR and SWR, respectively. The NN emulations using 50 neurons (NN50) for the LWR NN emulation and 55 neurons (NN55) for the SWR NN emulation in the single hidden layer provide, if run separately (code by code comparison) at every model physics time step (1 hour), the speed-up of ~ 150 times for LWR and of ~ 20 times for SWR as compared with the original LWR and SWR, respectively.

In another numerical model, an ocean wind wave model that is used for simulation and forecast of ocean waves, we applied an NN technique to develop a NN emulation of the exact nonlinear interactions that is about five orders of magnitude faster than the exact interactions, and hence comparable in costs to the simple parameterization (Krasnopolsky et al 2002 and Tolman et al. 2005). Unlike the simple parameterization, the NN approximation retains major details of the exact interactions. This NN emulation was further validated through integration for a limited time in the National Centers for Environment Prediction (NCEP) operational wave model (WAVEWATCH III).

NN emulations are very accurate. Larger errors and outliers (a few extreme errors) in NN emulation outputs have a very low probability and are distributed randomly in space and time. However, when decadal climate simulations are performed and NN emulations are used in the model for such a long integration time, the probability for occurrence of larger errors increases. As we learned from our experiments with NCAR CAM, the model was in many but not all cases robust enough to filter out such randomly distributed errors, without their accumulation in time. In the application of a NN approximation to nonlinear interactions in a wave model, the model did not prove sufficiently robust to retain stability for time integrations of even a few hours. Thus, in this model, an internal quality control (QC) method to identify NN errors is essential for successful application of the NN approximation of the model physics (Tolman and Krasnopolsky 2004). Therefore, it is desirable to introduce a QC procedure for larger errors, which can predict and eliminate such errors during the integration of highly nonlinear numerical models, not just relying upon the robustness of the model that can vary significantly for different models. Such a mechanism would make our NN emulation approach more reliable, robust, and generic.

In this paper, we introduce a compound parameterization (CP) which combines NN emulation with a QC technique. We present two different designs of CP both based on the use of NN techniques. We also discuss the possibility of using CP as a tool for introducing a dynamical adjustment of NN emulations to climate change.

Krasnopolsky,V.M, Chalikov, D.V., and Tolman, H.L. (2002). A neural network technique to improve computational efficiency of numerical oceanic models. Ocean Modelling, 4, 363-383

Krasnopolsky, V.M., Fox-Rabinovitz, M.S., and Chalikov, D.V. (2005). New Approach to Calculation of Atmospheric Model Physics: Accurate and Fast Neural Network Emulation of Long Wave Radiation in a Climate Model. Month. Weath. Rev, 133, 1370-1383

Krasnopolsky, V.M. 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 ,

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

Tolman, H.L. and V.M. Krasnopolsky (2004), Nonlinear Interactions in Practical Wind Wave Models, in Proceedings of 8th International Workshop on Wave Hindcasting and Forecasting, Turtle Bay, Hawaii, 2004, E.1, CD-ROM

Tolman, H. L., V. M. Krasnopolsky, and D. Chalikov, (2005). Neural Network Approximations for Nonlinear Interactions in Wind Wave Spectra: Direct Mapping for Wind Seas in Deep Water, Ocean Modelling, 8, 253-278