Nonlinear Averaging of Global NCEP Wave Ensemble Using NNs

In our early work [1], we demonstrated that a neural network (NN) technique could be successfully used for averaging multi-model ensemble for precipitation over the Continental US. We showed that neural network (NN) provides significantly better results than conservative ensemble. In fact, NN results are comparable with those obtained by a human meteorologist-analyst. In [2] we developed NN models for averaging the Global Wave Ensemble Forecast System [3] at single points using two NDBC buoys in the Atlantic and Pacific Oceans. In [4] performed a larger experiment, using NNs for nonlinear ensemble averaging in the Gulf of Mexico. Here we present nonlinear ensemble averaging expanded to the whole globe using satellite data. The main goal remains the same, which is to improve the skills of long-range forecasts of the Global Wave Ensemble Forecast System [3] forced by surface winds from the atmospheric Global Ensemble Forecast System.

GWES was implemented in 2005 [3] and initially validated by [5]. After upgrades reported in [6], it is now run with four cycles per day, using a spatial grid with 0.5^o resolution, with forecast range to 10 days. A total of 20 perturbed members plus a control member compose the GWES, which consists of an implementation of the WAVEWATCH III model [7], forced by winds from NCEP’s Global Ensemble Forecast System. A recent assessment and comparison of deterministic and ensemble products using altimeter data is provided in [3]. Their results show that although the general bias of the ensemble system does not show significant improvement over the deterministic global wave, after the fifth forecast day, root mean square errors from the GWES become smaller than the deterministic run. Furthermore, the GWES continuous ranked probability scores (CRPS) systematically outperforms the corresponding deterministic model’s mean absolute error (MAE) in all forecast times.

In the current study, we propose an improvement of the quality of output products from the GWES on a global scale, using NN to compute nonlinear averages. Currently a conservative ensemble approach is used to calculate the ensemble mean (EM) in the GWES as an average of ensemble members. The ensemble mean for variable p is calculated as a simple arithmetic mean. Which

assumes a linear relationship between EM and the ensemble members; however, in reality, this relationship may be significantly nonlinear, and we can use a nonlinear statistical tool like NN to derive a relationship between ensemble members and nonlinear EM (NEM) can be calculated.

In our previous works we showed that NEM produces significantly more accurate ensemble mean than LREM. In this work, the quality-controlled satellite data from Jason2, Jason3, and Cryosat-2 were allocated to the 0.5°X0.5° grid of GWES for 2017, including a ten-day forecast range, were used for NN training. The experiment is restricted to deep water areas and large ocean basins, with minor influence of wave-bottom interactions and refraction. There is a strong spatial dependence of GWES errors. At mid and high latitudes both U10 and Hs tend to be overestimated by GWES, especially in the Southern Hemisphere, while tropical areas have underestimation, apart from the Inter Tropical Convergence Zone (ITCZ) that show some overestimation in the Pacific Ocean. The systematic errors vary from -10% to +10% at most locations. The EM has higher absolute errors than the control run, which is more evident for Hs, indicating that the ensemble approach is adding bias to the control run. The nonlinear ensemble average, using NN, reduces the bias to values below the control run. This benefit is especially important at extra-tropical locations where the NBias can reach 12% for Hs.

As the next steps of the project, we consider the extension of forecast horizon beyond week 2 and using ensemble of NNs greater sophistication in the construction of ANN ensembles is a promising research direction.

References

[1] Krasnopolsky V., and Y. Lin, 2012: "A Neural Network Nonlinear Multimodel Ensemble to Improve Precipitation Forecasts over Continental US", Advances in Meteorology, Volume 2012, Article ID 649450, 11 pages, doi:10.1155/2012/649450

[2] Krasnopolsky V., R. Campos, J.H. Alves, S. Penny 2017: “Using NN for Nonlinear Averaging of NCEP Wave Model Ensemble”, Research activities in Atmospheric and Oceanic Modelling, Edited by E.Astakhova, July 2017,WCRP Report No.12/2017; http://wmc.meteoinfo.ru/bluebook/uploads/2017/docs/08_Krasnopolsky_Vladimir_data_assimilation_for_waves.pdf

[3] Chen, H. S., 2006: Ensemble prediction of ocean waves at NCEP. Proc. 28^th Ocean Engineering Conf., Taipei, Taiwan, NSYSU, 25–37.

[4] Campos, R.M., Krasnopolsky, V., Alves, J.H.G.M., Penny, S.G., 2019. Nonlinear Wave Ensemble Averaging in the Gulf of Mexico using Neural Networks. Journal of Atmospheric and Oceanic Technology, 36, pp. 113-127. DOI: 10.1175/JTECH-D-18-0099.1

[5] Cao, D., H. S. Chen, and H. L. Tolman, 2007: Verification of ocean wave ensemble forecasts at NCEP. Proc. 10^th Int. Workshop on Wave Hindcasting and Forecasting and First Coastal Hazards Symp., Oahu, Hawaii, G1.

[6] Alves, J.H.G.M., Wittman, P., Sestak, M., Schauer,J., Stripling, S., Bernier, N.B., McLean, J., Chao, Y., Chawla, A., Tolman, H., Nelson, G., Klots, S., 2013. The NCEP–FNMOC combined wave ensemble product. Expanding Benefits of Interagency Probabilistic Forecasts to the Oceanic Environment. Bull. American Met. Society, BAMS, December 2013.

[7] WAVEWATCH III® Development Group, 2016: User manual and system documentation of WAVEWATCH III® version 5.16. Tech. Note 329, NOAA/NWS/NCEP/MMAB, College Park, MD, USA, 326 pp. + Appendices.